Engineering 
Library 


•;* 


The  Publishers  and  the  Author  will  be  grateful  to 
any  of  the  readers  of  this  volume  who  will  kindly  call 
their  attention  to  any  errors  of  omission  or  of  commis- 
sion that  they  may  find  therein.  It  is  intended  to  make 
our  publications  standard  works  of  study  and  reference, 
and,  to  that  end,  the  greatest  accuracy  is  sought.  It 
rarely  happens  that  the  early  editions  of  works  of  any 
size  are  free  from  errors  ;  but  it  is  the  endeavor  of  the 
Publishers  to  see  them  removed  immediately  upon  being 
discovered,  and  it  is  therefore  desired  that  the  Author 
may  be  aided  in  his  task  of  revision,  from  time  to  time, 
by  the  kindly  criticism  of  his  readers. 

JOHN  WILEY  &  SONS. 
53  EAST  TENTH  STKEET. 


THE 


MECHANICAL  ENGINEER'S 
POCKET-BOOK, 


A  REFERENCE-BOOK  OF  RULES,    TABLES,   DATA, 

AND  FORMULA,   FOR  THE   USE  OF 

ENGINEERS,   MECHANICS, 

AND  STUDENTS. 


v; 


BY 

WILLIAM  KENT,  A.M.,  M.E., 

Consulting  Engineer, 
Member  Amer.  Soc'y  Mechl.  Engrs.  and  Amer   Inst.  Mining  Engrs. 


THIRD  EDITION,  REVISED. 
FIRST    THOUSAND. 

>  or 


JOHN    WILEY   &    SONS. 

LONDON:   CHAPMAN    &    HALL,    LIMITED. 

1897. 


i 


Library 


COPYRIGHT,  1895, 

BY 
WILLIAM  KENT. 


ROBERT  DRUMMOND,   KLECTROTYPER  AND   PRINTER,   NEW  YORK. 


Of  TJ5DH 

I 

PREFACE.Y<^ 


MORE  than  twenty  years  ago  the  author  began  to  follow 
the  advice  given  by  Nystrom  :  "  Every  engineeer  should 
make  his  own  pocket-book,  as  he  proceeds  in  study  and 
practice,  to  suit  his  particular  business."  The  manuscript 
pocket-book  thus  begun,  however,  soon  gave  place  to  more 
modern  means  for  disposing  of  the  accumulation  of  engi- 
neering facts  and  figures,  viz.,  the  index  rerum,  the  scrap- 
book,  the  collection  of  indexed  envelopes,  portfolios  and 
boxes,  the  card  catalogue,  etc.  Four  years  ago,  at  the  re- 
quest of  the  publishers,  the  labor  was  begun  of  selecting 
from  this  accumulated  mass  such  matter  as  pertained  to 
mechanical  engineering,  and  of  condensing,  digesting,  and 
arranging  it  in  form  for  publication.  In  addition  to  this,  a 
careful  examination  was  made  of  the  transactions  of  engi- 
neering societies,  and  of  the  most  important  recent  works 
on  mechanical  engineering,  in  order  to  fill  gaps  that  might 
be  left  in  the  original  collection,  and  insure  that  no  impor- 
tant facts  had  been  overlooked. 

Some  ideas  have  been  kept  in  mind  during  the  prepara- 
tion of  the  Pocket-book  that  will,  it  is  believed,  cause  it  to 
differ  from  other  works  of  its  class.  In  the  first  place  it 
was  considered  that  the  field  of  mechanical  engineering  was 
so  great,  and  the  literature  of  the  subject  so  vast,  that  as 
little  space  as  possible  should  be  given  to  subjects  which 
especially  belong  to  civil  engineering.  While  the  mechan- 
ical engineer  must  continually  deal  with  problems  which 
belong  properly  to  civil  engineering,  this  latter  branch  is 
so  well  covered  by  Trautwine's  "  Civil  Engineer's  Pocket- 
book"  that  any  attempt  to  treat  it  exhaustively  would  not 
only  fill  no  "  long-felt  want,"  but  would  occupy  space 
which  should  be  given  to  mechanical  engineering. 

Another  idea  prominently  kept  in  view  by  the  author  has 
been  that  he  would  not  assume  the  position  of  an  "  au- 
thority "  in  giving  rules  and  formulae  for  designing,  but 
only  that  of  compiler,  giving  not  only  the  name  of  the 
originator  of  the  rule,  where  it  was  known,  but  also  the 
volume  and  page  from  which  it  was  taken,  so  that  its 

iii 


IV  ^        PREFACE, 

derivation  may  be  traced  when  desired.  When  different 
formulae  for  the  same  problem  have  been  found  they  have 
been  given  in  contrast,  and  in  many  cases  examples  have 
been  calculated  by  each  to  show  the  difference  between 
them.  In  some  cases  these  differences  are  quite  remark- 
able, as  will  be  seen  under  Safety-valves  and  Crank  pins. 
Occasionally  the  study  of  these  differences  has  led  to  the 
author's  devising  a  new  formula,  in  which  case  the  deriva- 
tion of  the  formula  is  given. 

Much  attention  has  been  paid  to  the  abstracting  of  data 
of  experiments  from  recent  periodical  literature,  and  numer- 
ous references  to  other  data  are  given.  In  this  respect 
the  present  work  will  be  found  to  differ  from  other  Pocket- 
books. 

The  author  desires  to  express  his  obligation  to  the  many 
persons  who  have  assisted  him  in  the  preparation  of  the 
work,  to  manufacturers  who  have  furnished  their  cata- 
logues and  given  permission  for  the  use  of  their  tables, 
and  to  many  engineers  who  have  contributed  original  data 
and  tables.  The  names  of  these  persons  are  mentioned  in 
their  proper  places  in  the  text,  and  in  all  cases  it  has  been 
endeavored  to  give  credit  to  whom  credit  is  due.  The 
thanks  of  the  author  are  also  due  to  the  following  gentle- 
men who  have  given  assistance  in  revising  manuscript  or 
proofs  of  the  sections  named  :  Prof.  De  Volson  Wood, 
mechanics  and  turbines  ;  Mr.  Frank  Richards,  compressed 
air  ;  Mr.  Alfred  R.  Wolff,  windmills  ;  Mr.  Alex.  C. 
Humphreys,  illuminating  gas  ;  Mr.  Albert  E.  Mitchell, 
locomotives  ;  Prof.  James  E.  Denton,  refrigerating-ma- 
chinery  ;  Messrs.  Joseph  Wetzler  and  Thomas  W.  Varley, 
electrical  engineering  ;  and  Mr.  Walter  S.  Dix,  for  valu- 
able contributions  on  several  subjects,  and  suggestions  as 
to  their  treatment.  WM.  KENT. 

PASSAIC,  N.  J.,  April,  1895. 

THIRD    EDITION,    APRIL,    1897. 

All  the  typographical  and  other  errors  discovered  in  the 
first  and  second  editions  have  been  corrected,  a  few  altera- 
tions have  been  made  in  the  text,  and  the  index  has  been 
revised  and  enlarged.  W.  K. 


CONTENTS. 


(For  Alphabetical  Index  see  page  1075.) 


MATHEMATICS. 

Arithmetic. 

PAGE 

Arithmetical  and  Algebraical  Signs  .......................................  \ 

Greatest  Common  Divisor  ..................  ..............................  2 

Least  Common  Multiple  ...................  .......  .  .......................  2 

Fractions  ................................................................  2 

Decimals  .......................................  .  .........................  3 

Table.    Decimal  Equivalents  of  Fractions  of  One  Inch    ...............  3 

Table.     Products    of    Fractions  expressed  in  Decimals  .................  4 

Compound  or  Denominate  Numbers  .....................................  5 

Reduction  Descending  and  Ascending  .................  .....,,  .............  5 

Ratio  and  Proportion  ......................................  '  ..........  ..  5 

Involution,  or  Powers  of  Numbers  .....  .  ................................  6 

Table.    First  Nine  Powers  of  the  First  Nine  Numbers  ....................  7 

Table.    First  Forty  Powers  of  2  ...........................................  7 

Evolution.      Square  Root  .......................  ....................  ...  7 

Cube  Root  ____  ............  .......  ,  ......................................  8 

Alligation  .....  ................  „  .....................   ....................  10 

Permutation  .......................................  .  ......................  10 

Coin  bination  ................................................................  10 

Arithmetical  Progression  .....   .  .........  .  ............  .....................  11 

Geometrical  Progression  ....  ..............................................  11 

Interest  ...................................................................  13 

Discount  ...........................   ..................     ...............  13 

Compound  Interest  .....................................................  14 

Compound  In  terest  Table,  3,  4,  5,  and  6  per  cent  ........................  14 

Equation  of  Payments  ................  ____     ............................  14 

Partial  Payments  .......................................................  ...  15 

Annuities  ..........................................   ..  ...................  16 

Tables  of  Amount,  Present  Values,  etc.,  of  Annuities  ..................  16 

Weights  and  Measures. 

Long  Measure  ........................................................  ....  17 

Old  Land  Measure  .........................  ................   ..........  17 

Nautical  Measure    ..................................   ....................  17 

Square  Measure  ..........................................................  18 

Solid  or  Cubic  Measure  ...................................................  18 

Liquid  Measure  ........................................................  18 

The  Miners'  Inch  ..........................  ...............................  18 

Apothecaries'  Fluid  Measure  .......  .....................................  18 

Dry  Measure  .........................................................  ...  18 

Shipping  Measure  ............................  ............................  19 

Avoirdupois  Weight  ............................................  .  ........  19 

Troy  Weight  ...............................................................  19 

Apothecaries'  Weight  .......   ..........  .................................  19 

To  Weigh  Correctly  on  an  Incorrect  Balance  ..........  ,  ..................  19 

Circular  Measure  ...............  ..............................  .  ...........  20 

Measure  of  time  .............................  .............................  20 

V 


vi 


COHTENTS. 


PAGE 

Board  and  Timber  Measure 20 

Table.    Contents  in  Feet  of  Joists,  Scantlings,  and  Timber 20 

French  or  Metric  Measures 21 

British  and  French  Equivalents 21 

Metric  Conversion  Tables 23 

Compound  Units. 

of  Pressure  and  Weight 27 

of  Water,  Weight,  and  Bulk 27 

of  Work,  Power,  and  Duty  , 27 

of  Velocity 27 

of  Pressure  per  unit  area 27 

Wire  and  Sheet  Metal  Gauges 28 

Twist-drill  and  Steel-wire  Gauges. 28 

Music-wire  Gauge 29 

Circular- mil  Wire  Gauge - 30 

New  U.  S.  Standard  Wire  and  Sheet  Gauge,  1893 30 

Algebra. 

Addition,  Multiplication,  etc 33 

Powers  ,of  Num  bers 33 

Parentheses,  Division ...  34 

Simple  liquations  and  Problems . 34 

Equations  containing  two  or  more  Unknown  Quantities 35 

Elimination .    ..  35 

Quadratic  Equations  35 

Theory  of  Exponents 36 

Binomial  Theorem 36 

Geometrical  Problems  of  Construction 37 

of  Straight  Lfnes 37 

of  Angles 38 

of  Circles 39 

of  Triangles 41 

of  Squares  and  Polygons 42 

of  the  Ellipse 45 

of  the  Parabola 48 

of  the  Hyperbola. 49 

of  the  Cycloid 49 

of  the  Tractrix  or  Schiele  Anti-friction  Curve 50 

of  the  Spiral 50 

of  the  Catenary .  , 51 

of  the  In  volute 52 

Geometrical  Propositions 53 

Mensuration,  Plane  Surfaces. 

Quadrilateral,  Parallelogram,  etc 54 

Trapezium  and  Trapezoid 54 

Triangles -.- 54 

Polygons.    Table  of  Polygons. , , 55 

Irregular  Figures , 55 

Properties  of  the  Circle 57 

Values  of  TT  and  its  Multiples,  etc 57 

Relations  of  arc,  chord,  etc ...   58 

Relations  of  circle  to  inscribed  square,  etc 58 

Sectors  and  Segments 59 

Circular  Ring 59 

The  Ellipse  59 

The  Helix 60 

The  Spiral 60 

Mensuration,  Solid  Uodies. 

Prism  60 

Pyramid 60 

Wedge , 61 

The  Prismoidal  Formula ..   ( 

Rectangular  Prismoid 61 

Cylinder 61 

Cone 61 


CONTENTS.  vii 

PAGE 

Sphere 61 

Spherical  Triangle 61 

Spherical  Polygon 61 

Spherical  Zone  62 

Spherical  Segment 62 

Spheroid  or  Ellipsoid 63 

Pol.yedron 62 

Cylindrical  Ring 62 

Solids  of  Revolution 62 

Spindles 63 

Frustrum  of  a  Spheroid 63 

Parabolic  Conoid 64 

Volume  of  a  Cask 64 

Irregular  Solids 64 

Plane  Trigonometry. 

Solution  of  Plane  Triangles 65 

Sine,  Tangent,  Secant,  etc 65 

Signs  of  the  Trigonometric  Functions 66 

Trigonometrical  Formulae 66 

Solution  of  Plane  Right-angled  Triangles 68 

Solution  of  Oblique-angled  Triangles 68 

Analytical    Geometry. 

Ordinates  and  Abscissas 69 

Equations  of  a  Straight  Line,  Intersections,  etc 69 

Equations  of  the  Circle ...... , 70 

Equations  of  the  Ellipse  .  70 

Equations  of  the  Parabola  70 

Equations  of  the  Hyperbola 70 

Logarithmic  Curves 71 

Differential  Calculus. 

Definitions 72 

Differentials  of  Algebraic  Functions 72 

Formulae  for  Differentiating 73 

Partial  Differentials 73 

Integrals 73 

Formulae  for  Integration 74 

Integration  between  Limits 74 

Quadrature  of  a  Plane  Surface 74 

8uadrature  of  Surfaces  of  Revolution 75 

ubature  of  Volumes  of  Revolution 75 

Second,  Third,  etc. ,  Differentials , 75 

Maclaurin's  and  Taylor's  Theorems 76 

Maxima  and  Minima 76 

Differential  of  an  Exponential  Function 77 

Logarithms 77 

Differential  Forms  which  have  Known  Integrals 78 

Exponential  Functions 78 

Circular  Functions 78 

The  Cycloid 79 

Integral  Calculus 79 

Mathematical    Tables. 

Reciprocals  of  Numbers  1  to  2000 80 

Squares,  Cubes,  Square  Roots,  and  Cube  Roots  from  0.1  to  1600 86 

Squares  and  Cubes  of  Decimals 101 

Fifth  Roots  and  Fifth  Powers 102 

Circumferences  and  Areas  of  Circles,  Diameters  1  to  1000 103 

Circumferences  and  Areas  of  Circles,  Advancing  by  Eighths  from  SV  to 

100 108 

Decimals  of  a  Foot  Equivalent  to  Inches  and  Fractions  of  an  Inch 112 

Circumferences  of  Circles  in  Feet  and  Inches,  from  1  inch  to  32  feet  11 

inches  in  diameter 113 

Lengths  of  Circular  Arcs,  Degrees  Given 114 

Lengths  of  Circular  A  res.  Height  of  Arc  Given  115 

Areas  of  the  Segments  of  a  Circle 116 


viii  CONTENTS. 

PAGE 

Spheres 118 

Contents  of  Pipes  and  Cylinders,  Cubic  Feet  and  Gallons 120 

Cylindrical  Vessels,  Tanks,  Cisterns,  etc 121 

Gallons  in  a  Number  of  Cubic  Feet 122 

Cubic  Feet  in  a  Number  of  Gallons 122 

Square  Feet  in  Plates  3  to  32  feet  long  and  1  inch  wide 123 

Capacities  of  Rectangular  Tanks  in  Gallons 125 

Number  of  Barrels  in  Cylindrical  Cisterns  and  Tanks 126 

Logarithms 127 

Table  of  Logarithms 129 

Hyperbolic  Logarithms 156 

Natural  Trigonometrical  Functions 159 

Logarithmic  Trigonometrical  Functions 162 

MATERIALS. 

Chemical  Elements 16& 

Specific  Gravity  and  Weight  of  Materials 163 

Metals,  Properties  of 164 

The  Hydrometer 165 

Aluminum 166 

Antimony 166 

Bismuth 166 

Cadmium  167 

Copper .    — 167 

Gold 167 

Iridium 167 

Iron 167 

Lead 167 

Magnesium 168 

Manganese 168 

Mercury 168 

Nickel 168 

Platinum 168 

Silver 168 

Tin ,   168 

Zinc 168 

Miscellaneous  Materials. 

Order  of  Malleability,  etc.,  of  Metals 169 

Formulae  and  Table' for  Calculating  Weight  of  Rods,  Plates,  etc 169 

Measures  and  Weights  of  Various  Materials 169 

Commercial  Sizes  of  Iron  Bars 170 

Weights  of  Iron  Bars 171 

of  Flat  Rolled  Iron 172 

of  Iron  and  Steel  Sheets 174 

of  Plate  Iron 175 

of  Steel  Blooms , 176 

of  Structural  Shapes  — 177 

Sizes  and  Weights  of  Carnegie  Deck  Beams 177 

'  "        Steel  Channels 178 

ZBars 178 

Pencoyd  Steel  Angles 179 

"       Tees 180 

"        Channels ISO 

Roofing  Materials 181 

Terra-cotta 181 

Tiles  181 

Tin  Plates 181 

Slates 183 

Pine  Shingles 183 

Sky-light  Glass ...  1 84 

Weights  of  Various  Roof-coverings 184 

Cast-iron  Pipes  or  Columns. ...   185 

"      "          "      12ft.  lengths -...186 

"  ''      "     Pipe-fittings 187 

"      "     Warer  and  Gas-pipe 188 

"    and  thickness  of  Cast-iron  Pipes 189 

Safe  Pressures  on  Cast  Iron  Pipe  — 189 


CONTENTS.  IX 

PAGE 

Sheet-iron  Hydraulic  Pipe 191 

Standard  Pipe  Flanges 192 

Pipe  Flanges  and  Cast-iron  Pipe 193 

Standard  Sizes  of  Wrought-iron  Pipe 194 

Wrought-iron  Welded  Tubes ...  196 

Riveted  Iron  Pipes  197 

Weight  of  Iron  for  Riveted  Pipe 197 

Spiral  Riveted  Pipe 198 

Seamless  Brass  Tubing 198,  199 

Coiled  Pipes 199 

Brass,  Copper,  and  Zinc  Tubing , 200 

Lead  and  Tin-lined  Lead  Pipe , 201 

Weight  of  Copper  and  Brass  Wire  and  Plates 202 

"       Round  Bolt  Copper 203 

"       Sheet  and  Bar  Brass 203 

Composition  of  Rolled  Brass 203 

Sizes  of  Shot  204 

Screw-thread,  U.  S.  Standard 204 

Limit-gauges  for  Screw-threads 205 

Size  of  Iron  for  Standard  Bolts .,, 206 

Sizes  of  Screw-threads  for  Bolts  and  Taps 207 

Set  Screws  and  Tap  Screws 208 

Standard  Machine  Screws 209 

Sizes  and  Weights  of  Nuts 209 

Weight  of  Bolts  with  Heads 210 

Track  Bolts  210 

Weights  of  Nuts  and  Bolt-heads 211 

Rivets 211 

Sizes  of  Turnbuckles , ...  211 

Washers 212 

Track  Spikes 212 

Railway  Spikes 212 

Boat  Spikes 212 

Wrought  Spikes 213 

Wire  Spikes ...  213 

Cut  Nails  213 

Wire  Nails 214,  215 

Iron  Wire,  Size,  Strength,  etc  216 

Galvanized  Iron  Telegraph  Wire 217 

Tests  of  Telegraph  Wire 217 

Copper  Wire  Table,  B.  W.  Gauge 218 

"      Edison  or  Circular  Mil  Gauge... 219 

"      B.&S.Gauge 220 

Insulated  Wire 221 

Copper  Telegraph  Wire ...  221 

Electric  Cables % 221,  222 

Galvanized  Steel-wire  Strand , 223 

Steel-wire  Cables  for  Vessels 223 

Specifications  for  Galvanized  Iron  Wire 224 

Strength  of  Piano  Wire , 224 

Plough-steel  Wire 224 

Wires  of  different  metals , 225 

Specifications  for  Copper  Wire , 225 

Cable-traction  Ropes 226 

Wire  Ropes 226,  227 

Plough-steel  Ropes 227,  228 

Galvanized  Iron  Wire  Rope 228 

Steel  Hawsers 223,  229 

Flat  Wire  Ropes 2','9 

Galvanized  Steel  Cables 230 

Strength  of  Chains  and  Ropes 280 

Notes  on  use  of  Wire  Rope 231 

Locked  Wire  Rope 231 

Crane  Chains I 232 

Weights  of  Logs,  Lumber,  etc 232 

Sizes  of  Fire  Brick 233 

Fire  Clay,  Analysis , 234 

Magnesia  Bricks 235 

Asbestos , ,..., 235 


X  CONTENTS. 

Strength  of  Materials. 

PAGE 

Stress  and  Strain 236 

Elastic  Limit 236 

Yield  Point 237 

Modulus  of  Elasticity 237 

Resilience 238 

Elastic  Limit  and  Ultimate  Stress 238 

Repeated  Stresses 238 

Repeated  Shocks ,   ....  240 

Stresses  due  to  Sudden  Shocks 241 

Increasing  Tensile  Strength  of  Bars  by  Twisting 241 

Tensile  Strength 242 

Measurement  of  Elongation 243 

Shapes  of  Test  Specimens 243 

Compressive  Strength 244 

Columns,  Pillars,  or  Struts  246 

Hod gkinson's  Formula 246 

Gordon's  Formula 247 

Moment  of  Inertia 247 

Radius  of  Gyration 247 

Elements  of  Usual  Sections 248 

Solid  Cast-iron  Columns 250 

Hollow  Cast-iron  Columns 250 

Wrought-iron  Columns 251 

Safe  load  of  Cast-iron  Columns 253 

Eccentric  loading  of  Columns 255 

Built  Columns 256 

Phoenix  Columns  257 

Working  Formulae  for  Struts 259 

Merriman "s  Formula  for  Columns 260 

Working  Strains  in  Bridge  Members 263 

Working  Stresses  for  Steel 263 

Resistance  of  Hollow  Cylinders  to  Collapse 264 

Collapsing  Pressure  of  Tubes  or  Flues 265 

Formula  for  Corrugated  Furnaces 266 

Transverse  Strength 266 

Formulae  for  Flexure  of  Beams 267 

Safe  Loads  on  Steel  Beams 269 

Elastic  Resilience 270 

Beams  of  Uniform  Strength 271 

Properties  of  Rolled  Structural  Shapes 272 

Spacing  of  I  Beams     273 

Properties  of  Steel  I  Beams  274 

44    Channels 275 

44        "    ZBars 276 

Iron  Beams  and  Channels 277 

Trenton  Angle  Bars 279 

44        Tee  Bars ...  280 

Size  of  Beams  for  Floors 280 

Flooring  Material 281 

Tie  Rods  for  Brick  Arches 281 

Torsional  Strength 281 

Elastic  Resistance  to  Torsion 282 

Combined  Stresses 282 

Stress  due  to  Temperature 283 

Strength  of  Flat  Plates 283 

Strength  of  Unstayed  Flat  Surfaces  284 

Unbraced  Heads  of  Boilers 285 

Thickness  of  Flat  Cast-iron  Plates 286 

Strength  of  Stayed  Surfaces  286 

Spherical  Shells  and  Domed  Heads 286 

Stresses  in  Steel  Plating  under  Water  Pressure 287 

Thick  Hollow  Cylinders  under  Tension •  ...  287 

Thin  Cylinders  under  Tension 289 

Hollow  Copper  Balls  289 

Holding  Power  of  Nails,  Spikes,  Bolts,  and  Screws  289 

Cut  versus  Wire  Nails 290 

Strength  of  Wrought-iron  Bolts 292 


CONTENTS.  XI 

PAGE 

Initial  Strain  on  Bolts 292 

Stand  Pipes  and  their  Design 292 

Riveted  Steel  Water-pipes „ 295 

Mannesinann  Tubes 296 

Kirkaldy 's  Tests  of  Materials 296 

Cast  iron 296 

Iron  Castings 297 

Iron  Bars,  Forgings,  etc 297 

Steel  Rails  and  Tires 298 

Steel  Axles,  Shafts,  Spring  Steel 299 

Riveted  Joints 299 

Welds 300 

Copper,  Brass,  Bronze,  etc 300 

Wire,  WTire-rope 301 

Ropes,  Hemp,  and  Cotton 301 

Belting,  Canvas 302 

Stones,  Brick,  Cement  302 

Tensile  Strength  of  Wire , 303 

Watertown  Testing-machine  Tests 303 

Riveted  Joints 303 

Wrought-iron  Bars,  Compression  Tests 304 

Steel  Eye-bars 304 

Wrought-iron  Columns 305 

Cold  Drawn  Steel 305 

A  merican  Woods 306 

Shearing  Strength  of  Iron  and  Steel 306 

Holding  Power  of  Boiler-tubes 307 

Chains,  Weight,  Proof  Test,  etc 307 

Wrought-iron  Chain  Cables 308 

Strength  of  Glass , , ,...308 

Copper  at  High  Temperatures 309 

Strength  of  Timber 309 

Expansion  of  Timber , 311 

Shearing  Strength  of  Woods 312 

Strength  of  Brick,  Stone,  etc 312 

"    Flagging  313 

"         "    Lime  and  Cement  Mortar 313 

Moduli  of  Elasticity  of  Various  Materials 314 

Factors  of  Safety 314 

Properties  of  Cork 316 

Vulcanized  India-rubber 316 

Xylolith  or  Woodstone , 316 

Aluminum,  Properties  and  Uses 317 

Alloys. 

Alloys  of  Copper  and  Tin,  Bronze 319 

Copper  and  Zinc,  Brass 321 

Variation  in  Strength  of  Bronze 321 

Copper-tin-zinc  Alloys. ..     .. 322 

Liquation  or  Separation  of  Metals 3S>3 

Alloys  used  in  Brass  Foundries 325 

Copper-nickel  Alloys 326 

Copper- zinc-iron  Alloys  326 

Tobin  Bronze , 327 

Phosphor  Bronze 327 

Aluminum  Bronze 328 

Aluminum  Brass 329 

Caution  as  to  Strength  of  Alloys 329 

Aluminum  hardened 330 

Alloys  of  Aluminum,  Silicon,  and  Iron 330 

Tungsten-aluminum  Alloys 331 

Aluminum-tin  Alloys 331 

Manganese  Alloys 331 

Manganese  Bronze  331 

German  Silver ,  332 

Ailoys  of  Bismuth 332 

Fusible  Alloys 333 

Bearing  Metal  Alloys ....,., , ..,.,.,,,.,, 333 


Xll  CONTENTS. 

PAGE 

Alloys  containing  Antimony 336 

White-metal  Alloys 336 

Type-metal * 336 

Babbitt  metals , 336 

Solders 338 

Hopes  and  Chains. 

Strength  of  Hemp,  Iron,  and  Steel  Ropes 33$ 

Flat  Ropes , 339 

Working  Load  of  Ropes  and  Chains 339 

Strength  of  Ropes  and  Chain  Cables 340 

Rope  for  Hoisting  or  Transmission 340 

Cordage,  Technical  terms  of 341 

Splicing  of  Ropes 341 

Coal  Hoisting       ,... 343 

Manila  Cordage,  Weight,  etc 344 

Knots,  how  to  make. , 344 

Splicing  Wire  Ropes 346 

Springs. 

Laminated  Steel  Springs , 347 

Helical  Steel  Springs 347 

Carrying  Capacity  of  Springs 349 

Elliptical  Springs  , 352 

Phosphor-bronze  Springs , 35-3 

Springs  to  Resist  Torsional  Force 352 

Helical  Springs  for  Cars,  etc . . . , 353 

Riveted  Joints. 

Fairbairn's  Experiments. 354 

Loss  of  Strength  by  Punching  .  „ 354 

Strength  of  Perforated  Plates  - 354 

Hand  vs.  Hydraulic  Riveting . .  355 

Formulae  for  Pitch  of  Rivets 357 

Proportions  of  Joints 358 

Efficiencies  of  Joints  359 

Diameter  of  Rivets  360 

Strength  of  Riveted  Joints 361 

Riveting  Pressures 362 

Shearing  Resistance  of  Rivet  Iron 363 

Iron  and  Steel. 

Classification  of  Iron  and  Steel .".-»' 364 

Grading  of  Pig  Iron 365 

Influence  of  Silicon  Sulphur,  Phos.  and  Mn  on  Cast  Iron 365 

Tests  of  Cast  Iron 369 

Chemistry  of  Foundry  Iron 370 

Analyses  of  Castings '. 373 

Strength  of  Cast  Iron 374 

Specifications  for  Cast  Iron , 374 

Mixture  of  Cast  Iron  with  Steel 375 

Bessemerized  Cast  Iron 375 

Bad  Cast  Iron 375 

Malleable  Cast  Iron 375 

Wrought  Iron 377 

Chemistry  of  Wrought  Iron 377 

Influence  of  Rolling  on  Wrought  Iron    . . , . .   377 

Specifications  for  Wrought  Iron 378 

Stay-bolt  Iron 379 

Formulae  for  Unit  Strains  in  Structures 379 

Permissible  Stresses  in  Structures 381 

Proportioning  Materials  in  Memphis  Bridge  382 

Tenacity  of  Iron  at  High  Temperatures 382 

Effect  of  Cold  on  Strength  of  Iron 38? 

Expansion  of  Iron  by  Heat 385 

Durability  of  Cast  Iron .   . .   .-.. 385 

Corrosion  of  Iron  and  Steel 386 

Manganese  Plating  of  Iron  ..,....., 387 


CONTENTS.  Xlll 

PAGE 

Non-oxidizing  Process  of  Annealing 387 

Painting  Wood  and  Iron  Structures 388 

Qualities  of  Paints 389 

Steel. 

Eelation  between  Chem.  and  Phys.  Properties 389 

Variation  in  Strength 391 

Open-hearth 392 

Bessemer 392 

Hardening  Soft  Steel 393 

Effect  of  Cold  Rolling 393 

Comparison  of  Full-sized  and  Small  Pieces 393 

Treatment  of  Structural  Steel . .  394 

Influence  of  Annealing  upon  Magnetic  Capacity 396 

Specifications  for  Steel 397 

Boiler,  Ship  and  Tank  Plates 399 

Steel  for  Springs,  Axles,  etc 400 

May  Carbon  be  Burned  out  of  Steel? 402 

Reealescence  of  Steel 402 

Effectof  Nicking  a  Bar 402 

Electric  Conductivity 403 

Specific  Gravity 403 

Occasional  Failures 403 

Segregation  in  Ingots 404 

Earliest  Uses  for  Structures ..  405 

Steel  Castings 405 

Manganese  Steel 407 

Nickel  Steel  407 

Aluminum  Steel 409 

Chrome  Steel 409 

Tu ngsten  Steel 409 

Compressed  Steel 410 

Crucible  Steel 410 

Effect  of  Heat  on  Grain 412  * 

"      "  Hammering,  etc 412 

Heating  and  Forging 412 

Tempering  Steel 413 

MECHANICS. 

Force.  Unit  of  Force . .  415 

Inertia 415 

Newton's  Laws  of  Motion 415 

Resolution  of  Forces 415 

Parallelogram  of  Forces 416 

Moment  of  a  Force ,.  416 

Statical  Moment,  Stability 417 

Stability  of  a  Dam 417 

Parallel  Forces 417 

Couples 418 

Equilibrium  of  Forces 418 

Centre  of  Gravity 418 

Moment  of  Inertia  419 

Centre  of  Gyration 420 

Radius  of  Gyration , 420 

Centre  of  Oscillation 421 

Centre  of  Percussion 422 

The  Pendulum 422 

Conical  Pendulum  423 

Centrifugal  Force 423 

Acceleration , , 423 

Falling  Bodies 424 

Value  of  g « 424 

Angular  Velocity 425 

Height  due  to  Velocity 425 

Parallelogram  of  Velocities 426 

Mass 427 

Force  of  Acceleration 427 

Motion  on  Inclined  Planes 428 

Momentum  . 428 


XIV  COKTEKTS. 

Vis  Viva 428 

Work,  Foot-pound 428 

Power,  Horse-power 429 

Energy ; 429 

Work  of  Acceleration ,   430 

Force  of  a  Blow ;  t , 430 

Impact  of  Bodies „ 431 

Energy  of  Recoil  of  Guns 431 

Conservation  of  Energy 432 

Perpetual  Motion  432 

Efficiency  of  a  Machine 432 

Animal-power,  Man-power 433 

Work  of  a  Horse 434 

Man-wheel 434 

Horse-gin 434 

Resistance  of  Vehicles 435 

Elements  of  Machines. 

The  Lever 435 

The  Bent  Lever 436 

The  Moving  Strut 436 

The  Toggle-joint 436 

The  Inclined  Plane ,...  437 

The  Wedge 437 

The  Screw 437 

The  Cam 438 

The  Pulley  438 

Differential  Pulley 431> 

Differential  Windlass 439 

Differential  Screw 43£ 

Wheel  and  Axle  ...   439 

Toothed- wheel  Gearing 439 

Endless  Screw , 440 

Stresses  in  Framed  Structures. 

Cranes  and  Derricks 440 

Shear  Poles  and  Guys 442 

King  Post  Truss  or  Bridge 442 

§ueen  Post  Truss 442 
urr  Truss  ... 443 

Pratt  or  Whipple  Truss 443 

Howe  Truss 445 

Warren  Girder 445 

Roof  Truss 448 

HEAT. 

Thermometers  and  Pyrometers  448 

Centigrade  and  Fahrenheit  degrees  compared 449 

Copper-ball  Pyrometer 451 

Thermo-electric  Pyrometer 451 

Temperatures  in  Furnaces 451 

Wiborgh  Air  Pyrometer , 453 

Seeger's  Fire-clay  Pyrometer 453 

Mesur6  and  Nouel's  Pyrometer  453 

Uehling  and  Steinbart's  Pyrometer 453 

Air-thermometer 454 

High  Temperatures  judged  by  Color. 454 

Boiling-points  of  Substances ; 455 

Melting-points 455 

Unit  of  Heat 455 

Mechanical  Equivalent  of  Heat  — 456 

Heat  of  Combustion 456 

Specific  Heat 457 

Latent  Heat  of  Fusion 459,  461 

Expansion  by  Heat 460 

Absolute  Temperature 461 

Absolute  Zero 461 


CONTENTS.  XV 

PAGE 

Latent  Heat 461 

Latent  Heat  of  Evaporation 462 

Total  Heat  of  Evaporation 462 

Evaporation  and  Drying 462 

Evaporation  from  Reservoirs .   .   463 

Evaporation  by  the  Multiple  System , 463 

Resistance  to  Boiling 463 

Manufacture  of  Salt 464 

Solubility  of  Salt  and  Sulphate  of  Lime 464 

Salt  Contents  of  Brines 464 

Concentration  of  Sugar  Solutions 465 

Evaporating  by  Exhaust  Steam 465 

Drying  in  Vacuum 466 

Radiation  of  Heat 467 

Conduction  and  Convection  of  Heat 468 

Steam-pipe  Coverings 470 

Rate  of  External  Conduction  471 

Transmission  through  Plates 473 

in  Condenser  Tubes 473 

Cast-iron  Plates. 474 

from  Air  or  Gases  to  Water 474 

from  Steam  or  Hot  Water  to  Air 475 

through  Walls  of  Buildings 478 

Thermodynamics 478 

PHYSICAL  PROPERTIES  OF  GASES. 

Expansion  of  Gases 479 

Boyle  and  Marriotte's  Law 479 

Law  of  Charles,  Avogadro's  Law 479 

Saturation  Point  of  Vapors 480 

Law  of  Gaseous  Pressure    480 

Flow  of  Gases 480 

Absorption  by  Liquids. . .-, 480 

AIR. 

Properties  of  Air 481 

Air-manometer 481 

Pressure  at  Different  Altitudes 481 

Barometric  Pressures 482 

Levelling  by  the  Barometer  and  by  Boiling  Water 482 

To  find  Difference  in  Altitude 483 

Moisture  in  Atmosphere 483 

Weight  of  Air  and  Mixtures  of  Air  and  Vapor 484 

Specific  Heat  of  Air 484 

Flow  of  Air. 

Flow  of  Air  through  Orifices 484 

Flow  of  Air  in  Pipes 485 

Effect  of  Bends  in  Pipe 488 

Flow  of  Compressed  Air 488 

Tables  of  Flow  of  Air 489 

Anemometer  Measurements 491 

Equalization  of  Pipes 492 

Loss  of  Pressure  in  Pipes 493 

Wind. 

Force  of  the  Wind 493 

Wind  Pressure  in  Storms 495 

Windmills 495 

Capacity  of  Windmills 497 

Economy  of  Windmills  498 

Electric  Power  from  Windmills 499 

Compressed  Air. 

Heating  of  Air  by  Compression 499 

Loss  of  Energy  in  Compressed  Air 499 

Volumes  and  Pressures . . . . ,     500 


£vi  COKTEHTS. 

PAGE 

Loss  due  to  Excess  of  Pressure 501 

Horse-power  Required  for  Compression 501 

.  Table  for  Adiabatic  Compression 5052 

Mean  Effective  Pressures 502 

Mean  and  Terminal  Pressures 503 

Air-compressors ,   503 

Practical  Results 505 

Efficiency  of  Compressed-air  Engines 506 

Requirements  of  Rock-drills 506 

Popp  Compressed-air  System  507 

Small  Compressed-air  Motors . . , 507 

Efficiency  of  Air-heating  Stoves 507 

Efficiency  of  Compressed-air  Transmission 508 

Shops  Operated  by  Compressed  Air  509 

Pneumatic  Postal  Transmission 509 

Mekarski  Compressed-air  Tramways 509 

Compressed  Air  Working  Pumps  in  Mines 511 

Fans  and  Blowers. 

Centrifugal  Fans 511 

Best  Proportions  of  Fans 512 

Pressure  due  to  Velocity , . . . .  513 

Experiments  with  Blowers , 514 

Quantity  of  Air  Delivered 514 

Efficiency  of  Fans  and  Positive  Blowers 516 

Capacity  of  Fans  and  Blowers 517 

Table  of  Centrifugal  Fans  518 

Engines,  Fans,  and  Steam-coils  for  the  Blower  System  of  Heating 519 

Sturtevant  Steel  Pressure-blower , , 519 

Diameter  of  Blast-pipes 519 

Centrifugal  Ventilators  for  Mines 521 

Experiments  on  Mine  Ventilators , 522 

DiskFans , 524 

Air  Removed  by  Exhaust  Wheel 525 

Efficiency  of  Disk  Fans 525 

Positive  Rotary  Blowers 526 

Blowing  Engines .  ...„ 000 526 

Steam-jet  Blowers 00 527 

Steam-jet  for  Ventilation 527 

HEATING  AND  VENTILATION. 

Ventilation 528 

Quantity  of  Air  Discharged  through  a  Ventilating  Duct 530 

Artificial  Cooling  of  Air 531 

Mine-ventilation 531 

Friction  of  Air  in  Underground  Passages 531 

Equivalent  Orifices _ . 533 

Relative  Efficiency  of  Fans  and  Heated  Chimneys 533 

Heating  and  Ventilating  of  Large  Buildings 534 

Rules  for  Computing  Radiating  Surfaces 536 

Overhead  Steam-pipes 537 

Indirect  Heating-surface  ....... 537 

Boiler  Heating-surface  Required 538 

Proportion  of  Grate-surface  to  Radiator-surface 538 

Steam  consumption  in  Car-heating 538 

Diameters  of  Steam  Supply  Mains 539 

Registers  and  Cold-air  Ducts 539 

Physical  Properties  of  Steam  and  Condensed  Water 540 

Size  of  Steam-pipes  for  Heating 540 

Heating  a  Greenhouse  by  Steam 541 

Heating  a  Greenhouse  by  Hot  Water '. . . .  542 

Hot- water  Heating  , 542 

Law  of  Velocity  of  Flow  542 

Proportions  of  Radiating  Surfaces  to  Cubic  Capacities 543 

Diameter  of  Main  and  Branch  Pipes 543 

Rules  for  Hot- water  Heating 544 

Arrangements  of  Mains. 544 


COKTEKTS.  v  XV11 

PAGE 

Blower  System  of  Heating  and  Ventilating 545 

Experiments  with  Radiators 545 

Heating  a  Building  to  70°  F 545 

Heating  by  Electricity 546 

-WATER. 

Expansion  of  Water 547 

Weight  of  Water  at  different  temperatures 547 

Pressure  of  Water  due  to  its  Weight 549 

Head  Corresponding  to  Pressures , 549 

Bu oyancy 550 

Boiling-point 550 

Freezing-point 550 

Sea- water 549,  550 

Ice  and  Snow 550 

Specific  Heat  of  Water 550 

Compressibility  of  Water 551 

Impurities  of  Water 551 

Causes  of  Incrustation 551 

Means  for  Preventing  Incrustation  552 

Analyses  of  Boiler-scale , 552 

Hardness  of  Water 553 

Purifying  Feed-water 554 

Softening  Hard  Water -. 555 

Hydraulics.    Flow  of  Water. 

Fomulae  for  Discharge  through  Orifices 555 

Flow  of  Water  from  Orifices . 555 

Flow  in  Open  and  Closed  Channels 557 

General  Formulae  for  Flow 557 

Table  Fall  of_Feet  per  mile,  etc 558 

Valuesof  4/r  for  Circular  Pipes  559 

Kutter's  Formula 559 

Molesworth's  Formula '., 562 

Bazin's  Formula  ..   563 

I)1  Arcy 's  Formula 563 

Older  Formulae 564 

Velocity  of  Water  in  Open  Channels 564 

Mean,  Surface  and  Bottom  Velocities 564 

Safe  Bottom  and  Mean  Velocities 565 

Resistance  of  Soil  to  Erosion 565 

Abrading  and  Transporting  Power  of  Water 565 

Grade  of  Sewers 566 

Relations  of  Diameter  of  Pipe  to  Quantity  discharged 566 

Flow  of  Water  in  a  20-inch  Pipe 566 

Velocities  in  Smooth  Cast-iron  Water-pipes 567 

Table  of  Flow  of  Water  in  Circular  Pipes 568-573 

Loss  of  Head 573 

Frictional  Heads  at  given  rates  of  discharge 577 

Effect  of  Bend  and  Curves - .  578 

Hydraulic  Grade-line 578 

Flow  of  Water  in  House-service  Pipes 578 

Air-bound  Pipes. 579 

VerticalJets 579 

Water  Delivered  through  Meters 579 

Fire  Streams 579 

Friction  Losses  in  Hose 580 

Head  and  Pressure  Losses  by  Friction 580 

Loss  of  Pressure  in  smooth  2^-inch  Hose 580 

Rated  capacity  of  Steam  Fire-engines 580 

Pressures  required  to  throw  water  through  Nozzles 581 

The  Siphon 581 

Measurement  of  Flowing  Water 582 

Piezometer 582 

Pitot  Tube  Gauge 583 

The  Venturi  Meter...   583 

Measurement  of  Discharge  by  means  of  Nozzles. ...  584 


XV111  COKTEKTS. 


Flow  through  Rectangular  Orifices  ..........  .............  .*..***.»  .......  584 

Measurement  of  an  Open  Stream  ...................  ......................  584 

Miners'  Inch  Measurements  .....  ............  .............  .  ..............  585 

Flow  of  Water  over  Weirs  ..............................................  586 

Francis's  Formula  for  Weirs  ..............................  ...............  586 

Weir  Table  ...............................................................  587 

Bazin^  Experiments  ....................  .................................  587 

Water-power. 
Po  wer  of  a  Fall  of  Water  ..................................................  588 

Horse-power  of  a  Running  Stream    ......................................  589 

Current  Motors.   .   ...................................  .  .................  589 

Horse-power  of  Water  Flowing  in  a  Tube  ..............  .   ................  589 

Maximum  Efficiency  of  a  Long  Conduit  ...............  ....  ..............  589 

Mill-power  .................  .  .............................................  589 

Value  of  Water-power  ......................................  ,  ............  590 

The  Power  of  Ocean  Waves  .................  ,.  ...........................  599 

Utilization  of  Tidal  Power  .............  .  ...........  ......................  600 

Turbine  Wheels. 

Proportions  of  Turbines  ..................................................  591 

Tests  of  Turbines  ...............  .........................  .................  596 

Dimensions  of  Turbines  .........     .......................................  597 

The  Pelton  Water-wheel  ..................................................  597 

Pumps. 
Theoretical  capacity  of  a  pump  .......  .  .................................  601 

Depth  of  Suction  .........  ................................................  602 

Amount  oi  Water  raised  by  a  Single-acting  Lift-pump  ...................  602 

Proportioning  the  Steam  -cylinder  of  a  Direct-acting  Pump  ..............  602 

Speed  of  Water  through  Pipes  and  Pump  -passages  ....................  602 

Sizes  of  Direct-acting  Pumps.  .  .  ...................  .............  .  ......  -----  603 

The  Deane  Pump  ........................................................  603 

Efficiency  of  Small  Pumps  ..............................  .........  .....    603 

The  Worthington  Duplex  Pump  ..........................................  604 

Speed  of  Piston  .................  .........................................  605 

Speed  of  Water  through  Valves.  ............  ----  .  .......................  605 

Boiler-feed  Pumps  ......................................................  605 

Pump  Valves  ...........................................................  606 

Centrifugal  Pumps  .....................................................  606 

Lawrence  Centrifugal  Pumps  ..........................................  607 

Efficiency  of  Centrifugal  and  Reciprocating  Pumps  ......................  608 

Vanes  of  Centrifugal  Pumps  .............................................  609 

The  Centrifugal  Pump  used  as  a  Suction  Dredge  ..................  ......  609 

Duty  Trials  of  Pumping  Engines  ...................................  609 

Leakage  Tests  of  Pumps  ........................  .  ......................  611 

Vacuum  Pnmps  ____   .................................  .  ..................    612 

The  Pulsometer..  .......................................  ................  612 

The  Jet  Pump  ....................  .  ....................  *  ...............  614 

The  Injector  ................................................   ..............  614 

Air-lift  Pump  ..............................................................  6l4 

The  Hydraulic  Ram  ......................................................  614 

Quantity  of  Water  Delivered  by  the  Hydraulic  Ram  ......................  615 

Hydraulic  Pressure  Transmission. 
Energy  of  Water  under  Pressure  ,  .........................  .  ............  616 

Efficiency  of  Apparatus  ..................................................  616 

Hydraulic  Presses  .........................  .  ...........................  617 

Hydraulic  Power  in  London  .............................................  617 

Hyd  raulic  Riveting  Machines  ...........................................  •  618 

Hydrau  lie  Forging  ...................  .  ............  .  .......................  618 

The  Aiken  Intensifier  .........  .  .......................  ...   ................    619 

Hydraulic  Engine  .....................................  .......  .....  •  .......  619 

FUEL.  ,\       ,.,'., 

Theory  of  Combustion  ...............................................  .  .  .  620 

Total  Heat  of  Combustion  ..................  ..„  .......................  621 


COHTENTS.  XiX 

PAGE 

Analyses  of  Gases  of  Combustion , 622 

Temperature  of  the  Fire 622 

Classification  of  Solid  Fuel .. 623 

Classification  of  Coals 624 

Analyses  of  Coals 624 

Western  Lignites  631 

Analyses  of  Foreign  Coals 631 

Nixon's  Navigation  Coal 632 

Sampling  Coal  for  Analyses 632 

Relative  Value  of  Fine  Sizes 632 

Pressed  Fuel 632 

Relative  Value  of  Steam  Coals , 633 

Approximate  Heating  Value  of  Coals 634 

Kind  of  Furnace  Adapted  for  Different  Coals 635 

I )ovvu ward-draught  Furnaces 635 

Calorii Metric  Tests  of  American  Coals....  ! 636 

Evaporative  Power  of  Bituminous  Coals 630 

Weathering  of  Coal , 637 

Coke  637 

Experiments  in  Coking 637 

Coal  Washing 63S 

Recovery  of  By-products  in  Coke  manufacture 638 

Making  Hard  Coke 638 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  from  Coke-ovens.  638 

Products  of  the  Distillation  of  Coal 639 

Wood  as  Fuel 639 

Heating  Value  of  Wood , 639 

Composition  of  Wood 640 

Charcoal . , 640 

Yield  of  Charcoal  from  a  Cord  of  Wood 641 

Consumption  of  Charcoal  in  Blast  Furnaces 641 

Absorption  of  Water  and  of  Gases  by  Charcoal 641 

Composition  of  Charcoals 642 

Miscellaneous  Solid  Fuels 642 

Dust-fuel— Dust  Explosions 642 

Peat  or  Turf 643 

Sawdust  as  Fuel 643 

Horse-manure  as  Fuel 643 

Wet  Tan-bark  as  Fuel 643 

Straw  as  Fuel  643 

Bagasse  as  Fuel  in  Sugar  Manufacture..... 643 

Petroleum. 

Products  of  Distillation 645 

Lima  Petroleum 645 

Value  of  Petroleum  as  Fuel..., 645 

Oil  vs.  Coal  as  Fuel 646 

Fuel  Gas. 

Carbon  Gas 646 

Anthracite  Gas 647 

Bituminous  Gas 647 

Water  Gas 648 

Prod  ucer-gas  from  One  Ton  of  Coal 649 

Natural  Gas  in  Ohio  and  Indiana 649 

Combustion  of  Producer-gas 650 

Use  of  Steam  in  Producers 650 

Gas  Fuel  for  Small  Furnaces 651 

•> 

Illuminating  Gas. 

Coal-gas 651 

Water-gas 652 

Analyses  of  Water-gas  and  Coal  gas 653 

Calorific  Equivalents  of  Constituents 654 

Efficiency  of  a  Water-gas  Plant 654 

Space  Required  for  a  Water-gas  Plant 656 

Fuel-value  ot  Illuminating-gas...' 656 


XX  CONTENTS. 

PAGE 

Flow  of  Gas  in  Pipes 657 

Service  for  Lamps 658 

STEAM. 

Temperature  and  Pressure 659 

Total  Heat  659 

Latent  Heat  of  Steam 659 

Latent  Heat  of  Volume 660 

Specific  Heat  of  Saturated  Steam 660 

Density  and  Volume 660 

Superheated  Steam 661 

Regnault's  Experiments....   661 

Table  of  the  Properties  of  Steam 662 

Flow  of  Steam. 

Napier's  Approximate  Rule 669 

Flow  of  Steam  in  Pipes 669 

Loss  of  Pressure  Due  to  Radiation 671 

Resistance  to  Flow  by  Bends 672 

Sizes  of  Steam-pipes  for  Stationary  Engines , . 67.3 

Sizes  of  Steam -pipes  for  Marine  Engines. 674 

Steam  Pipes. 

Bursting-tests  of  Copper  Steam-pipes 674 

Thickness  of  Copper  Steam-pipes..  ..  675 

Reinforcing  Steam-pipes 675 

Wire- wound  Steam-pipes 675 

Riveted  Steel  Steam-pipes 675 

Valves  in  Steam-pipes 675 

Flanges  for  Steam-pipe . 676 

The  Steam  Loop „ ,  676 

Loss  from  an  Uncovered  Steam-pipe 676 

THE  STEAM  BOILER. 

The  Horse-power  of  a  Steam-boiler ,  677 

Measures  for  Comparing  the  Duty  of  Boilers 678 

Steam-boiler  Proportions 678 

Heating-surface     678 

Horse-power,  Builders1  Rating 679 

Grate-surface 680 

Areas  of  Flues 680 

Air  -passages  Through  Grate-bars  681 

Performance  of  Boilers 681 

Conditions  which  Secure  Economy 682 

Efficiency  of  a  Boiler 683 

Tests  of  Steam-boilers 685 

Boilers  at  the  Centennial  Exhibition 685 

Tests  of  Tubulous  Boilers 686 

High  Rates  of  Evaporation 687 

Economy  Effected  by  Heating  the  Air 687 

Results  of  Tests  with  Different  Coals 688 

Maximum  Boiler  Efficiency  with  Cumberland  Coal 689 

Boilers  Using  Waste  Gases 689 

Boilers  for  Blast  Furnaces 68S 

Rules  for  Conducting  Boiler  Tests .696 

Table  of  Factors  of  Evaporation 695 

Strength  of  Steam-boilers.          „ 

Rules  for  Construction 700 

Shell-plate  Formulae 701 

Rules  for  Flat  Plates 701 

Furnace  Formulae 702 

Material  for  Stays ; 703 

Loads  allowed  on  Stays , 703 

Girders 703 

Rules  for  Construction  of  Boilers  in  Merchant  Vessels  in  U.  S 705 


COKTENTS.  XXI 

PAGE 

U.  S.  Rule  for  Allowable  Pressures '. .  •  • 706 

Safe-working  Pressures  707 

Rules  Governing  Inspection  of  Boilers  in  Philadelphia 708 

Flues  and  Tubes  for  Steam  Boilers 709 

Flat-stayed  Surfaces 709 

Diameter  of  Stay-bolts . . 710 

Strength  of  Stays 710 

Stay-bolts  in  Curved  Surfaces 710 

Boiler  Attachments,  Furnaces,  etc. 

Fusible  Plugs .  710 

Steam  Domes  711 

Height  of  Furnace 711 

Mechanical  Stokers 711 

The  Hawley  Down-draught  Furnace 712 

Under-feed  Stokers 712 

Smoke  Prevention 712 

Gas-fired  Steam-boilers  714 

Forced  Combustion 714 

Fuel  Economizers 715 

Incrustation  and  Scale  716 

Boiler-scale  Compounds 717 

Removal  of  Hard  Scale 718 

Corrosion  in  Marine  Boilers 719 

Use  of  Zinc  720 

Effect  of  Deposit  on  Flues 720 

Dangerous  Boilers 720 

Safety  Valves. 

Rules  for  Area  of  Safety-valves 721 

Spring-loaded  Safety-valves 724 

The  Injector. 

Equation  of  the  Injector 725 

Performance  of  Injectors 726 

Boiler-feeding  Pumps 726 

Feed -water  Heaters. 

Strains  Caused  by  Cold  Feed-water 727 

Steam  Separators. 

Efficiency  of  Steam  Separators 728 

Determination  of  Moisture  in  Steam. 

Coil  Calorimeter 729 

Throttling  Calorimeters 729 

Separating  Calorimeters 730 

Identification  of  Dry  Steam 730 

Usual  Amount  of  Moisture  in  Steam 731 

Chimneys. 

Chimney  Draught  Theory 731 

Force  or  Intensity  of  Draught 73'2 

Rate  of  Combustion  Due  to  Height  of  Chimney 733 

High  Chimneys  not  Necessary 734 

Heights  of  Chimneys  Required  for  Different  Fuels.... ..  734 

Table  of  Size  of  Chimneys 734 

Protection  of  Chimney  from  Lightning 73(5 

Some  Tall  Brick  Chimneys , 737 

Stability  of  Chimneys 738 

Weak  Chimneys 739 

Steel  Chimneys 740 

Sheet-iron  Chimneys 741 

THE   STEAM  ENGINE. 

Expansion  of  Steam 742 

Mean  and  Terminal  Absolute  Pressures , . , .  743 


XXil  CONTENTS. 

PAGE 

Calculation  of  Mean  Effective  Pressure 744 

Work  of  Steam  in  a  Single  Cylinder ".     , 746 

Measures  for  Comparing  the  Duty  of  Engines 748 

Efficiency,  Thermal  Units  per  Minute 749 

Real  Ratio  of  Expansion 750 

Effect  of  Compression 751 

Clearance  in  Low  and  High  Speed  Engines 751 

Cylinder-condensation  752 

Water-consumption  of  Automatic  Cut- off  Engines 753 

Experiments  on  Cylinder-condensation ,.„, 753 

Indicator  Diagrams  754 

Indicated  Horse-power.. 755 

Rules  for  Estimating  Horse-power 755 

Horse-power  Constant , 756 

Errors  of  Indicators 756 

Table  of  Engine  Constants 756 

To  Draw  Clearance  on  Indicator-diagram 759 

To  Draw  Hyperbolic  Curve  on  Indicator-diagram 759 

Theoretical  Water  Consumption  . .   769 

Leakage  of  Steam  761 

Compound  Engines. 

Advantages  of  Compounding 762 

Woolf  and  Receiver  Types  of  Engines 762 

Combined  Diagrams 764 

Proportions  of  Cylinders  inCompound  Engines 765 

Receiver  Space .'.'. 766 

Formula  for  Calculating  Work  9f  Steam , 767 

Calculation  of  Diameters  of  Cylinders 768 

Triple-expansion  Engines 769 

Proportions  of  Cylinders  769 

Annular  Ring  Method 769 

Rule  for  Proportioning  Cylinders 771 

Types  of  Three-stage  Expansion  Engines 771 

Sequence  of  Cranks     772 

Velocity  of  Steam  Through  Passages 772 

Quadruple  Expansion  Engines 772 

Diameters  of  Cylinders  of  Marine  Engines 773 

Progress  in  Steam-engines .773 

A  Double- tandem  Triple-expansion  Engine.... 773 

Principal  Engines,  World's  Columbian  Exhibition,  1893 774 

Steam  Engine  Economy. 

Economic  Performance  of  Steam  Engines 77'5 

Feed-water  Consumption  of  Different  Types 775 

Sizes  and  Calculated  Performances  of  Vertical  High-speed  Engines 777 

Most  Economical  Point  of  Cut-off 777 

Type  of  Engine  Used  when  Exhaust-steam  is  used  for  Heating 780 

Comparison  of  Compound  and  Single-cylinder  Engines ..  780 

Two-cylinder  and  Tnree-cy  linder  Engines 781 

Effect  of  Water  in  Steam  on  Efficiency 781 

Relative    Commercial   Economy   of  Compound  and   Triple-expansion 

Engines  781 

Triple-expansion  Pumping-engines 782 

Test  of  a  Triple-expansion  Engine  with  and  without  Jackets 783 

Relative  Economy  of  Engines  under  Variable  Loads 783 

Efficiency  of  Non-condensing  Compound  Engines 784 

Economy  of  Engines  under  Varying  Loads 784 

Steam  Consumption  of  Various  Si2ies 785 

Steam  Consumption  in  Small  Engines 786 

Steam  Consumption  at  Various  Speeds 786 

Limitation  of  Engine  Speed. 787 

Influence  of  the  Steam  Jacket 787 

Counterbalancing  Engines  788 

Preventing  Vibrations  of  Engines  — 789 

Foundations  Embedded  in  Air , 789 

Cost  of  Coal  for  Steam-power.....  —  ,.     ..,.,,.,,....,,..... 789 


CONTENTS.  XX111 

PAGE 

Storing  Steam  Heat 789 

Cost  of  Steam-power 790 

Rotary  Steam-engines. 

Steam  Turbines 791 

The  Tower  Spherical  Engine 792 

Dimensions  of  Parts  of  Engines. 

Cylinder 792 

Clearance  of  Piston 792 

Thickness  of  Cylinder 792 

Cylinder  Heads , 794 

Cylinder-head  Bolts 795 

The  Piston 795 

Piston  Packing-rings 796 

Fit  of  Piston-rod ,   790 

Diameter  of  Piston-rods 797 

Piston-rod  Guides 798 

The  Connecting-rod - 799 

Connecting-rod  Ends , 800 

Tapered  Connecting-rods 801 

The  Crank-pin 801 

Crosshead-pin  or  Wrist-pin 804 

The  Crank-arm  805 

The  Shaft,  Twisting  Resistance .  806 

Resistance  to  Bending 808 

Equivalent  Twisting  Moment 808 

Fly-wheel  Shafts 809 

Length  of  Shaft-bearings 810 

Crank-shafts  with  Centre-crank  and  Double-crank  Arms  813 

Crank-shaft  with  two  Cranks  Coupled  at  90° 814 

Valve-stem  or  Valve-rod 815 

Size  of  Slot-link 815 

Th.9  Eccentric 816 

Th e  Eccentric-rod 816 

Reversing-gear 816 

Engine-frames  or  Bed-plates 817 

Fly-wheels. 

Weight  of  Fly-wheels 817 

Centrifugal  Force  in  Fly-wheels 820 

Arms  of  Fly-wheels  and  Pulleys 820 

Diameters  for  Various  Speeds 821 

Strains  in  the  Rims 822 

Thickness  of  Rims 823 

A  Wooden  Rim  Fly-wheel  , ....824 

Wire-wound  Fly-wheels  824 

The  Slide-valve. 

Definitions,  Lap,  Lead,  etc 824 

Sweet's  Valve-diagram 826 

The  Zeuner  Valve-diagram  — 827 

Port  Opening  828 

Lead 829 

Inside  Lead 829 

Ratio  of  Lap  and  of  Port-opening  to  Valve-travel 829 

Crank  Angles  for  Connecting-rods  of  Different  Lengths 830 

Relative  Motions  of  Crosshead  and  Crank 831 

Periods  of  Admission  or  Cut-off  for  Various  Laps  and  Travels 831 

Diagram  for  Port-opening,  Cut-off ,  and  Lap 832 

Piston-valves 834 

Setting  the  Valves  of  an  Engine 834 

To  put  an  Engine  on  its  Centre 834 

Link-motion 834 

Governors. 

Pendulum  or  Fly-ball  Governors 836 

To  Change  the  Speed  of  an  Engine , 837 


XXIV  J  ,  CONTEHTS. 

PAGE 

Fly-wheel  or  Shaft-governors 838 

Calculation  of  Springs  for  Shaft-governors 838 

Condensers,  Air-pumps,  Circulating-pumps,  etc. 

The  Jet  Condenser 839 

Ejector  Condensers 840 

The  Surface  Condenser 840 

Condenser  Tubes 840 

Tube-plates 841 

Spacing  of  Tubes '. .....841 

Quantity  of  Cooling  Water 841 

Air-pump 841 

Area  through  Valve-seats 842 

Circulating-pump 843 

Feed-pumps  for  Marine-engines 843 

An  Evaporative  Surface  Condenser 844 

Continuous  Use  of  Condensing  Water $44 

Increase  of  Power  by  Condensers... 846 

Evaporators  and  Distillers 847 

GAS,  PETROLEUM,  AND  HOT-AIR  ENGINES. 

Gas-engines 847 

Efficiency  of  the  Gas-engine 848 

Tests  of  the  Simplex  Gas  Engine ,  848 

A320-H.P.  Gas-engine 848 

Test  of  an  Otto  Gas-engine 849 

Temperatures  and  Pressures  Developed 849 

Test  of  the  Clerk  Gas-engine 849 

Combustion  of  the  Gas  in  the  Otto  Engine ....  849 

Use  of  Carburetted  Air  in  Gas-engines 849 

The  Otto  Gasoline-engine 850 

The  Priestman  Petroleum-engine 850 

Test  of  a  5-H.P.  Priestman  Petroleum-engine 850 

Naptha-engines 851 

Hot-air  or  Caloric-engines 851 

Test  of  a  Hot-air  Engine 851 

LOCOMOTIVES. 

Efficiency  of  Locomotives  and  Resistance  of  Trains 851 

Inertia  and  Resistance  at  Increasing  Speeds 853 

Efficiency  of  the  Mechanism  of  a  Locomotive 854 

Size  of  Locomotive  Cylinders..  854 

Size  of  Locomotive  Boilers 855 

Qualities  Essential  for  a  Free-steaming  Locomotive 855 

Wootten's  Locomotive     855 

Grate-surface,  Smoke-stacks,  and  Exhaust-nozzles  for  Locomotives 855 

Exhaust  Nozzles 856 

Fire-brick  Arches , 856 

Size,  Weight,  Tractive  Power,  etc 856 

Leading  American  Types 858 

Steam  Distribution  for  High  Speed 858 

Speed  of  Railway  Trains 859 

Dimensions  of  Some  American  Locomotives 859-862 

Indicated  Water  Consumption 862 

Locomotive  Testing  Apparatus 863 

Waste  of  Fuel  in  Locomotives 863 

Advantages  of  Compounding'. 863 

Counterbalancing  Locomotives * 864 

Maximum  Safe  Load  on  Steel  Rails ..  865 

Narrow-guage  Railways 865 

Petroleum-burning  Locomotives 865 

Fireless  Locomotives 866 

SHAFTING. 

Diameters  Resist  Torsional  Strain ...  867 

Deflection  of  Shafting. ...    868 

Horse-power  Transmitted  by  Shafting. „ 869 

Table  for  Laying  Out  Shafting ,...,. 871 


CONTENTS  XXV 

PULLEYS. 

PAGE 

Proportions  of  Pulleys 873 

Convexity  of  Pulleys 874 

Cone  or  Step  Pulleys 874 

BELTING. 

Theory  of  Belts  and  Bands 876 

Centrifugal  Tension ,876 

Belting  Practice,  Formulae  for  Belting. 877 

Horse-power  of  a  Belt  one  inch  wide 878 

A.  F.  Nagle's  Formula 878 

Width  of  Belt  for  Given  Horse-power. 879 

Taylor's  Rules  for  Belting 880 

Notes  on  Belting 882 

Lacing  of  Belts 883 

Setting  a  Belt  on  Quarter-twist 883 

To  Find  the  Length  of  Belt 884 

To  Find  the  Angle  of  the  Arc  of  Contact 884 

To  Find  the  Length  of  Belt  when  Closely  Rolled 884 

To  Find  the  Approximate  Weight  of  Belts 884 

Relations  of  the  Size  and  Speeds  of  Driving  and  Driven  Pulleys .  884 

Evils  of  Tight  Belts , 885 

Sag  of  Belts 885 

Arrangements  of  Belts  and  Pulleys 885 

CareofBelts , . 886 

Strength  of  Belting... 886 

Adhesion,  Independent  of  Diameter. 886 

Endless  Belts 886 

Belt  Data 886 

Belt  Dressing 887 

Cement  for  Cloth  or  Leather 88? 

Rubber  Belting , 887 

GEABING. 

Pitch,  Pitch-circle,  etc 887 

Diametral  and  Circular  Pitch , 888 

Chordal  Pitch 889 

Diameter  of  Pitch-line  of  Wheels  from  10  to  100  Teeth , 889 

Proportions  of  Teeth 889 

Proportion  of  Gear-wheels 891 

Width  of  Teeth 891 

Rules  for  Calculating  the  Speed  of  Gears  and  Pulleys 891 

Milling  Cutters  for  Interchangeable  Gears 892 

Forms  of  the  Teeth. 

The  Cycloidal  Tooth 892 

The  Involute  Tooth 894 

Approxim?  tion  by  Circular  Arcs 896 

Stepped  Gears  ....  897 

Twisted  Teeth 897 

Spiral  Gears 89? 

Worm  Gearing 897 

Teeth  of  Bevel-wheels  ...  898 

Annular  and  Differential  Gearing ,.  898 

Efficiency  of  Gearing 899 

Strength  of  Gear  Teeth. 

Various  Formulae  for  Strength 900 

Comparison  ot  Formulae 903 

Maximum  Speed  of  Gearing ,,,.  905 

A  Heavy  Machine-cut  Spur-gear 905 

Frictional  Gearing  905 

Frictional  Grooved  Gearing 906 

HOISTING. 

Weight  and  Strength  of  Cordage 906 

Working  Strength  of  Blocks 906 


CONTENTS. 

PAGfi 

Efficiency  of  Chain-blocks , 907 

Proportions  of  Hooks , 907 

Power  of  Hoisting  Engines 908 

Effect  of  Slack  Rope  on  Strain  in  Hoisting 908 

Limit  of  Depth  for  Hoisting... 908 

Large  Hoisting  Records * 908 

Pneumatic  Hoisting 909 

Counterbalancing  of  Winding-engines 909 

Belt  Conveyors 911 

Bands  for  Carrying  Grain 911 

Cranes. 

Classification  of  Cranes 911 

Position  of  the  Inclined  Brace  in  a  Jib  Crane 912 

A  Large  Travelling-crane .  - 912 

A  150- ton  Pillar  Crane -. 912 

Compressed-air  Travelling  Cranes 912 

Wire-rope  Haulage. 

Self-acting  Inclined  Plane 913 

Simple  Engine  Plane 913 

Tail-rope  System* 913 

Endless  Rope  System 914 

Wire-rope  Tramways 914 

Suspension  Cableways  and  Cable  Hoists 915 

Stress  in  Hoisting-ropes  on  Inclined  Planes 915 

Tension  Required  to  Prevent  Wire  Slipping  on  Drums 916 

Taper  Ropes  of  Uniform  Tensile  Strength 916 

Effect  of  Various  Sized  Drums  on  the  Life  of  Wire  Ropes 917 

WIRE-HOPE  TRANSMISSION. 

The  Driving  Wheels 918 

Horse-power  of  Wire-rope  Transmission 919 

Durability  of  Wire  Ropes 919 

Inclined  Transmissions 919 

The  Wire- rope  Catenary 919 

Diameter  and  Weight  of  Pulleys  for  Wire-rope 921 

Table  of  Transmission  of  Power  by  Wire  Ropes 921 

Long-distance  Transmissions 921 

ROPE  DRIVING. 

Formulae  for  Rope  Driving 92S 

Horse-power  of  Transmission  at  Various  Speeds 924 

Sag  of  the  Rope  Between  Pulleys 925 

Tension  on  the  Slack  Part  of  the  Rope 925 

Miscellaneous  Notes  on  Rope-driving 926 

FRICTION  AND  LUBRICATION. 

Coefficient  of  Friction 928 

Rolling  Friction 928 

Friction  of  Solids 928 

Friction  of  Rest 928 

Laws  of  Unlubricated  Friction 928 

Friction  of  Sliding  Steel  Tires...  928 

Coefficient  of  Rolling  Friction 929 

Laws  of  Fluid  Friction  929 

Angles  of  Repose 929 

Friction  of  Motion 929 

Coefficient  of  Friction  of  Journal 930 

Experiments  on  Friction  of  a  Journal 931 

Coefficients  of  Friction  of  Journal  with  Oil  Bath 932 

Coefficients  of  Friction  of  Motion  and  of  Rest 932 

Value  of  Anti-friction  Metals :.  932 

Cast-iron  for  Bearings 933 

Friction  of  Metal  Under  Steam-pressure 930 

Morin's  Laws  of  Friction , 933 


COKTEHTS.  XXV11 

PAGE 

Laws  of  Friction  of  well-lubricated  Journals 934 

Allowable  Pressures  on  Bearing-surface. .  935 

Oil-pressure  in  a  Bearing 937 

Friction  of  Car-journal  Brasses 937 

Experiments  on  Overheating  of  Bearings 938 

Moment  of  Friction  and  Work  of  Friction  — 938 

Pivot  Bearings 939 

The  Schiele  Curve 939 

Friction  of  a  Flat  Pivot-bearing 939 

Mercury-bath  Pivot 940 

Ball  Bearings 940 

Friction  Rollers 940 

Bearings  for  Very  High  Rotative  Speed 94 

Friction  of  Steam-engines , 941 

Distribution  of  the  Friction  of  Engines 941 

Lubrication. 

Durability  of  Lubricants 942 

Qualifications  of  Lubricants 943 

Amount  of  Oil  to  run  an  Engine 943 

Examination  of  Oils «. 944 

Penna.  R.  R.  Specifications 944 

Solid  Lubricants 945 

Graphite,  Soapstone,  Metaline 945 

THE  FOUNDRY. 

Cupola  Practice..  . .  946 

Charging  a  Cupola  948 

Charges  in  Stove  Foundries 949 

Results  of  Increased  Driving 949 

Pressure  Blowers 950 

Loss  of  Iron  in  Melting 950 

Use  of  Softeners 950 

Shrinkage  of  Castings 951 

Weight  of  Castings  from  Weight  of  Pattern 952 

Moulding  Sand 952 

Foundry  Ladles 952 

THE  MACHINE  SHOP. 

Speed  of  Cutting  Tools 953 

Table  of  Cutting  Speeds 954 

Speed  of  Turret  Lathes 954 

Forms  of  Cutting  Tools , 955 

Rule  for  Gearing  Lathes . 955 

Change-gears  for  Lathes , 956 

Metric  Screw-threads 956 

Setting  the  Taper  in  a  Lathe 956 

Speed  of  Drilling  Holes 956 

Speed  of  Twist-drills 957 

Milli n g  Cutters 957 

Speed  of  Cutters 958 

Results  with  Milling-machines , .. 959 

Milling  with  or  Against  Feed .... 960 

Milling-machine  vs.  Planer 960 

Power  Required  for  Machine  Tools 960 

Heavy  Work  on  a  Planer 960 

Horse-power  to  run  Lathes 961 

Power  used  by  Machine  Tools 963 

Power  Required  to  Drive  Machinery 964 

Power  used  in  Machine-shops 965 

Abrasive  Processes. 

The  Cold  Saw 966 

Reese's  Fusing-disk 966 

Cutting  Stone  with  Wire 966 

The  Sand-blast 966 

Emery-wheels 967-969 

Grindstones 968-970 


XXV111  COHTEKTS. 

Various  Tools  and  Processes. 

PAGE 

Taps  for  Machine-screws 970 

Tap  Drills 971 

Taper  Bolts,  Pins,  Reamers,  etc 972 

Punches,  Dies,  Presses 972 

Clearance  Between  Punch  and  Die 972 

Size  of  Blanks  for  Drawing-press ,....;.... 973 

Pressure  of  Drop-press 973 

Flow  of  Metals 973 

Forcing  and  Shrinking  Fits 973 

Efficiency  of  Screws , 974 

Powell's  Screw-thread 975 

Proportioning  Parts  of  Machine 975 

Keys  for  Gearing,  etc 975 

Holding-power  of  Set-screws 977 

Holding-power  of  Keys 978 

DYNAMOMETERS. 

Traction  Dynamometers 978 

The  Prony  Brake. 978 

The  Alden  Dynamometer , 979 

Capacity  of  Friction-brakes 980 

Transmission  Dynamometers 980 

ICE  MAKING  OR  REFRIGERATING  MACHINES. 

Operations  of  a  Refrigerator-machine 981 

Pressures,  etc.,  of  Available  Liquids 982 

Ice-melting  Effect 983 

Ether-machines 983 

Air-inachines. 983 

Ammonia  Compression-machines , 983 

Ammonia  Absorption-machines 984 

Sulphur-dioxide  Machines.  985 

Performance  of  Ammonia  Compression-machines 986 

Economy  of  Ammonia  Compression-machines 987 

Machines  Using  Vapor  of  Water 988 

Efficiency  of  a  Refrigerating- machine 988 

Test  Trials  of  Refrigerating-rnachines 990 

Temperature  Range 991 

Metering  the  Ammonia  992 

Properties  of  Sulphur  Dioxide  and  Ammonia  Gas 992 

Properties  of  Brine  used  to  absorb  Refrigerating  Effect.  994 

Chloride-of-calciurn  Solution 994 

Actual  Performances  of  Refrigerating  Machines. 

Performance  of  a  75-ton  Ref rigerating-machine 994,  998 

Cylinder-heating 997 

Tests  of  Ammonia  Absorption-machine 997 

Ammonia  Compression-machine,  Results  of  Tests  999 

Means  for  Applying  the  Cold 999 

Artificial  Ice-manufacture. 

Test  of  the  New  York  Hygeia  Ice-making  Plant 1000 

MARINE  ENGINEERING. 

Rules  for  Measuring  Dimensions  and  Obtaining  Tonnage  of  Vessels 1001 

The  Displacement  of  a  Vessel 1001 

Coefficient  of  Fineness 1002 

Coefficient  of  Water-lines 1002 

Resistance  of  Ships 1002 

Coefficient  of  Performance  of  Vessels 1003 

Defects  of  the  Com  mon  Formula  for  Resistance 1003 

Rankings  Formula 1003 

Dr.  Kirk's  Method ". 1004 

To  find  the  I.H.P.  from  the  Wetted  Surface 1005 

E.  R.  Mumford's  Method 1006 

Relative  Horse-power  required  for  different  Speeds  of  Vessels 1006 


CONTENTS.  XXIX 

PAGE 

Resistance  per  Horse-power  for  different  Speeds 1006 

Results  of  Trials  of  Steam-vessels  of  Various  Sizes 1007 

Speed  on  Canals,  1008 

Results  of  Progressive  Speed-trials  in  Typical  Vessels 1008 

Estimated  Displacement,  Horse-power,  etc.,  of  Steam-vessels  of  Various 
Sizes 1009 

The  Screw-propeller. 

Size  of  Screw , 1010 

Propeller  Coefficients 1011 

Efficiency  of  the  Propeller 1012 

Pitch-ratio  and  Slip  for  Screws  of  Standard  Form 1012 

Results  of  Recent  Researches 1013 

The  Paddle-wheel. 

Paddle-wheel  with  Radial  Floats 1013 

Feathering  Paddle-wheels 1013 

Efficiency  of  Paddle-wheels 1014 

Jet-propulsion. 

Reaction  of  a  Jet , . . . . 1015 

Recent  Practice  in  Marine  Engines. 

Forced  Draught 1015 

Boilers.. 1015 

Piston-valves 1016 

Steam-pipes 1016 

Auxiliary  Supply  of  Fresh-water  Evaporators 1016 

Weir's  Feed-water  Heater 1016 

Passenger  Steamers  fitted  with  Twin-screws 1017 

Comparative  Results  of  Working  of  Marine-engine,  1872, 1881,  and  1891..  1017 

Weight  of  Three-stage  Expansion-engines  1017 

Particulars  of  Three-stage  Expansion-engines.  .'. 1018 

CONSTRUCTION  OF   BUILDINGS. 

Walls  of  Warehouses,  Stores,  Factories,  and  Stables. . .  1019 

Strength  of  Floors,  Roofs,  and  Supports 1019 

Columns  and  Posts 1019,1022 

Fireproof  Buildings , ...   1020 

Iron  and  Steel  Columns  ... 1020 

Lintels.  Bearings,  and  Supports 1020 

Strains  on  Girders  and  Rivets 1020 

Maximum  Load  on  Floors 1021 

Strength  of 'Floors 1021 

Safe  Distributed  Loads  on  Southern-pine  Beams 1023 

ELECTRICAL  ENGINEERING. 

Standards  of  Measurement. 

C.  G.  S.  System  of  Physical  Measurement 1024 

Practical  Units  used  in  Electrical  Calculations 1024 

Relations  of  Various  Units 1025 

Equivalent  Electrical  and  Mechanical  Units 1026 

Analogies  between  Flow  of  Water  and  Electricity 1027 

Analogy  between  the  Ampere  and  Miner's  Inch 1027 

Electrical  Resistance. 

Laws  of  Electrical  Resistance , 1028 

Equivalent  Conductors. 1028 

Electrical  Conductivity  of  Different  Metals  and  Alloys    1028 

Relative  Conductivity  of  Different  Metals 1029 

Conductors  and  Insulators  ,  0 1029 

Resistance  Varies  with  Temperature , 1029 

Annealing 1029 

Standard  of  Resistance  of  Copper  Wire 1030 

Electric  Currents. 

Ohm's  Law 1030 

Divided  Circuits 1031 


XXX  CONTENTS. 

PAGE 

Conductors  in  Series 1031 

Internal  Resistance 1031 

Joint  Resistance  of  Two  Branches 1032 

KirchhofTs  Laws 1032 

Power  of  the  Circuit 1032 

Heat  Generated  by  a  Current... , 1032 

Heating  of  Conductors  1033 

Heating  of  Wires  of  Cables : , 1033 

Copper- wire  Table 1034,  1035 

Heating  of  Coils 1036 

Fusion  of  Wires , 1037 

Electric  Transmission. 

Section  of  "Wire  required  for  a  Given  Current 1038 

Constant  Pressure 1038 

Three-wire  Feeder 1039 

Short-circuiti ng 1 039 

Economy  of  Electric  Transmission 1039 

Table  of  Electrical  Horse-powers 1042 

Wiring  Formulae  for  Incandescent  Lighting 1043 

Wire  Table  for  100  and  500  Volt  Circuits 1044 

Cost  of  Copper  for  Long-distance  Transmission 1045 

Graphical  Method  of  Calculating  Leads 1045 

Weight  of  Copper  for  Long-distance  Transmission 104? 

Efficiency  of  Long-distance  Transmission 1047 

Efficiency  of  a  Combined  Engine  and  Dynamo 1048 

Electrical  Efficiency  of  a  Generator  and  Motor 1049 

Efficiency  of  an  Electrical  Pumping  Plant 1049 

Electric  Railways. 

Test  of  a  Street  Railway  Plant 1050 

Proportioning  Boiler,  Engine,  and  Generator  for  Power  Stations 1050 

Electric  Lighting. 

Quantity  of  Energy  Required  to  Produce  Light 1051 

Life  of  Incandescent  Lamps 1051 

Life  and  Efficiency  Tests  of  Lamps - 1051 

Street  Lighting 1051 

Lighting-power  of  Arc-lamps 1052 

Candle-power  of  the  Arc-light 1052 

Electric  Welding 1053 

Electric  Heaters  1054 

Electric  Accumulators  or  Storage-batteries. 

Use  of  Storage-batteries  in  Power  and  Light  Stations 1056 

Working  Current  of  a  Storage-cell 1056 

Electro-chemical  Equivalents 1057 

Electrolysis 1057 

Electro-magnets. 

Units  of  Electro-magnetic  Measurement „ 1058 

Lines  of  Loops  of  Force 1059 

Strength  of  an  Electro-magnet . ....  1059 

Force  in  the  Gap  between  Two  Poles  of  a  Magnet 10(30 

The  Magnetic  Circuit 1060 

Determining  the  Polarity  of  Electro-magnets . .  1060 

Dynamo-Electric  Machines. 

Kinds  of  Dynamo-electric  Machines  as  regards  Manner  of  Winding. . . .  1061 

Current  Generated  by  a  Dynamo-electric  Machine ...  1061 

Torque  of  an  Armature 1062 

Electro-motive  Force  of  the  Armature  Circuit..  .« 1062 

Strength  of  the  Magnetic  Field 1063 

Application  to  Designing  of  Dynamos 1064 

Permeability .'. 1066 

Permissible  Amperage  for  Magnets  with  Cotton-covered  Wire 1066,  1068 

Formulae  of  Efficiency  of  Dynamos 1066 

The  Electric  Motor 1070 


NAMES  AND  ABBREVIATIONS  OF  PERIODICALS 
AND  TEXT-BOOKS  FREQUENTLY  REFERRED  TO 
IN  THIS  WORK. 


Am.  Mach.    American  Machinist. 

App.  Cyl.  Mecli.    Appleton's  Cyclopaedia  of  Mechanics,  Vols.  I  and  II. 

Hull.  I.  &  S.  A.  Bulletin  of  the  American  Iron  and  Steel  Association 
(Philadelphia). 

Burr's  Elasticity  and  Resistance  of  Materials. 

Clark,  R  T.  D.  D.  K.  Clark's  Rules,  Tables,  and  Data  for  Mechanical  En- 
gineers. 

Clark,  S.  E.    D.  K.  Clark's  Treatise  on  the  Steam-engine. 

Engg.     Engineering  (London). 

Eng.  News.    Engineering  News. 


Engr.    The  Engineer  (London). 
Fairbairn's  Useful  Information 


aation  for  Engineers. 

Fly nn's  Irrigation  Canals  and  Flow  of  Water. 

Jour.  A.  C.  I.  W.    Journal  of  American  Charcoal  Iron  Workers'  Association. 

Jour.  F.  I.    Journal  of  the  Franklin  Institute. 

Kapp's  Electric  Transmission  of  Energy. 

Lanza's  Applied  Mechanics. 

Merriman's  Strength  of  Materials. 

Modern  Mechanism.    Supplementary  volume  of  Appleton's  Cyclopaedia  of 
Mechanics. 

Proc.  Inst.  C.  E.    Proceedings  Institution  of  Civil  Engineers  (London). 

Proc.  Inst.  M.  E.    Proceedings  Institution  of  Mechanical  Engineers  (Lon- 
don). 

Peabody's  Thermodynamics, 

Proceedings  Engineers'  Club  of  Philadelphia. 

Rankine,  S.  E.    Rankine'sThe  Steam  Engine  and  other  Prime  Movers. 

Rankiue's  Machinery  and  Millwork. 

Rankine,  R.  T.  D.    Rankine's  Rules,  Tables,  and  Data. 

Reports  of  U.  S.  Test  Board. 

Reports  of  U.  S.  Testing  Machine  at  Watertown,  Massachusetts. 

Rontgen's  Thermodynamics. 

Seaton's  Manual  of  Marine  Engineering. 

Hamilton  Smith,  Jr.'s  Hydraulics. 

The  Stevens  Indicator. 

Thompson's  Dynamo-electric  Machinery. 

Thurston's  Manual  of  the  Steam  Engine. 

Thurston's  Materials  of  Engineering. 

Trans.  A.  I.  E.  E.    Transactions  American  Institute  of  Electrical  Engineers. 

Trans.  A.  I.  M.  E.    Transactions  American  Institute  of  Mining  Engineers. 

Trans.  A.  S.  C.  E.    Transactions  American  Society  of  Civil  Engineers. 

Trans.  A.  S.  M.  E.    Transactions  American  Soc'ty  of  Mechanical  Engineers. 

Trautwine's  Civil  Engineer's  Pocket  Book. 

The  Locomotive  (Hartford,  Connecticut). 

Unwin's  Elements  of  Machine  Design. 

Weisbach's  Mechanics  of  Engineering. 

Wood's  Resistance  of  Materials. 

Wood's  Thermodynamics, 

xxxi 


MATHEMATICS. 


Arithmetical  and  Algebraical  Signs  and  Abbreviations. 


-f  plus  (addition). 
-\-  positive. 

—  minus  (subtraction). 

—  negative. 

±  plus  or  minus. 
T  minus  or  plus. 
=  equals, 
x   multiplied  by. 
ab  or  a.  b  =  a  x  6. 
-4-  divided  by. 
/    divided  by. 

-  or  a-b  =  a/b  =  a  •*-  6. 

2  2 

.2  =-;  -002  =^. 

\f  square  root. 

V  cube  root. 

V  4th  root. 

:    is  to,  ::  so  is,  :  to  (proportion). 

2  :  4  ::  8  :  6,  as  2  is  to  4  so  is  3  to  6. 

:    ratio:  divided  by. 

2   :  4,  ratio  of  2  to  4  =  2/4. 
.'.  therefore. 
>  greater  than. 
<  less  than. 
a  square . 
O  round. 

0  degrees,  arc  or  thermometer. 

'  minutes  or  feet. 

"  seconds  or  inches. 
'  "  '"  accents  to  distinguish  letters,  as 

a',  a",  a'". 

olt  a2,  a3,  a,,  (ic,  read  a  sub  1,  a  sub  6, 
etc. 

(  )  [  1    j   }    vincula,    denoting 

that  the  numbers  enclosed  are 
to  be  taken  together  ;  as, 
(a  +  6)C  =  4  -f  3  x  5  =  35. 

a2,  a3,  a  squared,  a  cubed. 

an,  a  raised  to  thenth  power. 

a$  =    /a. 2  ai  =      «s 


109  =  10  to  the  9th  power  =  1,000  000,- 

000. 

sin.  a  =  the  sine  of  a. 
sin.-Ja^  the  arc  whose  sine  is  a. 

sin.  a-1  = 

sin.  a. 

log.  =  logarithm. 

log.    or  hyp.  log.  =  hyperbolic  loga- 
rithm. 


Z  angle. 

L   right  angle. 

_L  perpendicular  to. 

sin.,  sine. 

cos.,  cosine. 

tang.,  or  tan.,  tangent. 

sec.,  secant. 

versin.,  versed  sine. 

cot.,  cotangent. 

cosec.,  cosecant. 

covers.,  co-versed  sine. 

In  Algebra,  the  first  letters  of  the 
^alphabet,  a,  b,  c,  d,  etc.,  are  gener- 
ally used  to  denote  known  quantities, 
and  the  last  letters,  w,  x,  y,  z,  etc., 
unknown  quantities. 

Abbreviations  and  Symbols   com- 
monly used. 

d,  differential  (in  calculus). 
/,   integral  (in  calculus). 

J  a,  integral  between  limits  a  and  b. 

A,  delta,  difference. 

2.  sigma,  sign  of  summation. 

TT,  pi,  ratio  of  circumference  of  circle 

to  diameter  =  3. 14159. 
g,  acceleration  due  to  gravity  =  32.16 

ft.  per  sec. 

Abbreviations  frequently    used    in 
this  Book. 

L.,  1.,  length  in  feet  and  inches. 

B.,  b.,  breadth  in  feet  and  inches. 

D.,  d.,  depth  or  diameter. 

H.,  h.,  height,  feet  and  inches. 

T.,  t.,  thickness  or  temperature. 

V.,v.,  velocity. 

F.,  force,  or  factor  of  safety. 

f.,  coefficient  of  friction. 

E.,  coefficient  of  elasticity. 

R.,  r.,  radius. 

W.,  w.,  weight. 

P.,  p.,  pressure  or  load. 

H.P.,  horse-power. 

I.H.P.,  indicated  horse-power. 

B.H.P.,  brake  horse-power. 

h.  p.,  high  pressure. 

i.  p.,  intermediate  pressure. 

1.  p.,   low  pressure. 

A.W.  G.,  American  Wire  Gauge 

(Brown  &  Sharpe). 
B.W.G.,  Birmingham  Wire  Gauge, 
r.  p.  m.,  or  revs,  permiu.,  revolutions 
per  minute. 


MATHEMATICS. 


ARITHMETIC. 

The  user  of  this  book  is  supposed  to  have  had  a  training  in  arithmetic  as 
well  as  in  elementary  algebra.  Only  those  rules  are  given  here  which  are 
apt  to  be  easily  forgotten. 

GREATEST   COMMON   MEASURE,  OR  GREATEST 
COMMON   DIVISOR   OF   TWO  NUMBERS. 

Rule,—  Divide  the  greater  number  by  the  less  ;  then  divide  the  divisor 
by  the  remainder,  and  so  on,  dividing  always  the  last  divisor  by  the  last 
remainder,  until  there  is  no  remainder,  and  the  last  divisor  is  the  greatest 
common  measure  required. 

LEAST    COMMON    MULTIPLE    OF    TWO   OR    MORE 
NUMRERS. 

Rule.  —  Divide  the  given  numbers  by  any  number  that  will  divide  the 
greatest:  number  of  them  without  a  remainder,  and  set  the  quotients  with 
the  undivided  numbers  in  a  line  beneath. 

Divide  the  second  line  as  before,  and  so  on,  until  there  are  no  two  numbers 
that  can  be  divided  ;  then  the  continued  product  of  the  divisors  and  last 
quotients  will  give  the  multiple  required. 

FRACTIONS. 

To  reduce  a  common  fraction  to  Its  lowest  terms.—  Divide 
both  terms  by  their  greatest  common  divisor:  ||  =  £. 
To  change  an  improper  fraction  to  a  mixed  number^  — 

Divide  the  numerator  by  the  denominator;  the  quotient  is  the  whole  number, 
and  the  remainder  placed  over  the  denominator  is  the  fraction:  -349  =  (J£. 

To  change  a  mixed  number  to  an  improper  fraction.— 
Multiply  the  whole  number  by  the  denominator  of  the  traction;  to  the  prod- 
uct add  the  numerator;  place  the  sum  over  the  denominator:  ]|  =  -V5. 

To  express  a  whole  number  in  the  form  of  a  fraction 
with  a  given  denominator.  —Multiply  the  whole  number  by  the 
given  denominator,  and  place  the  product,  over  that  denominator:  13  =  j3rj9. 

To  reduce  a  compound  to  a  simple  fraction,  also  to 
multiply  fractions.  —  Multiply  the  numerators  together  for  a  new 
numerator  and  the  denominators  together  for  a  new  denominator: 

2    .4      8    '  248 

5  of  -.-=5,  also     §xs  =  j. 

To  reduce  a  complex  to  a  simple  fraction.  —The  numerator 
and  denominator  must  each  first  be  given  the  form  of  a  simple  fraction; 
then  multiply  the  numerator  of  the  upper  fraction  by  the  denominator  of 
the  lower  for  the  new  numerator,  and  the  denominator  of  the  upper  by  the 
numerator  of  the  lower  for  the  new  denominator: 

I  =  §  =  _6  _  1 
H       I       12"    2' 

To  divide  fractions.—  Reduce  both  to  the  form  of  simple  fractions, 
invert  the  divisor,  and  proceed  as  in  multiplication: 


3  '  3  '  3      34       12* 

Cancellation  of  fractious.  —  In  compound  or  multiplied  fractions, 
divide  any  numerator  and  any  denominator  by  any  number  which  will 
divide  them  both  without  remainder,  striking  out  the  numbers  thus  divided 
and  setting  down  the  quotients  in  their  stead. 

To  reduce  fractions  to  a  common  denominator.—  Reduce 
each  fraction  to  the  form  of  a  simple  fraction;  then  multiply  each  numera- 


DECIMALS.  o 

lor  hv  all  the  denominators  except  its  own  for  the  new  numerators,  and  all 
the  denominators  together  for  the  common  denominator: 


113 

2'    3'    7: 


21      14     18 
42'    42'    42* 


To  add  fractions.— Reduce  them  to  a  common  denominator,  then 
add  the  numerators  and  place  their  sum  over  the  common  denominator: 

11       3  _  21  +  14+18  =  53 
2      ,3       7  ~  42  ~  42  ~ 

To  subtract  fractions.— Reduce  them  to  a  common  denominator, 
subtract  the  numerators  and  place  the  difference  over  the  common  denomi- 
nator: 

1  _  3  _  7-6  _  _1_ 

2  7"    14  -~  14" 


DECIMALS. 

To  add  decimals.— Set  down  the  figures  so  that  the  decimal  points 
are  one  above  the  other,  then  proceed  as  in  simple  addition:  18.75-4-  -012  = 
18.762. 

To  subtract  decimals.— Set  down  the  figures  so  that  the  decimal 
points  are  one  above  the  other,  then  proceed  as  in  simple  subtraction:  18.75 
-  .012  =  18.738. 

To  multiply  decimals. — Multiply  as  in  multiplication  of  whole 
numbers,  then  point  off  as  many  decimal  places  as  there  are  in  multiplier 
and  multiplicand  taken  together:  1.5  X  .02  -  .030  =  .03. 

To  divide  decimals. — Divide  as  in  whole  numbers,  and  point  off  in 
the  quotient  as  many  decimal  places  as  those  in  the  dividend  exceed  those 
in  the  divisor.  Ciphers  must  be  added  to  the  dividend  to  make  its  decimal 
places  at  least  equal  those  in  the  divisor,  and  as  many  more  as  it  is  desired 
to  have  in  the  quotient:  1.5  -=-  .25  =  6.  0.1  -r-  0.3  =  0.10000  -t-  0.3  =  0.3333  + 

Decimal  Equivalents  of  Fractions  of  One  Inch. 


1-64 

.015625 

17-64 

.265625 

33-64 

.515625 

49-64 

.765625 

J-8* 

.03125 

9-32 

.28125 

17-32 

.53125 

25-32 

.78125 

3-64 

.046875 

19-64 

.296875 

35-84 

.546875 

51-64 

.796875 

1-16 

.0625 

5-16 

.3125 

«-16 

.5625 

13-16 

.8125 

5-64 

.078125 

21-64 

.328125 

37-64 

.578125 

53-64 

.828125 

3-32 

.09375 

11-32 

.34375 

|     19-32 

.59375 

1     27-32 

.84375 

7-64 

.109375 

23-64 

.359375 

!     39-64 

.609375 

55-64 

.859375 

1-8 

.125 

3-8 

.375 

5-8 

..625 

7-8 

.875 

9-64 

.140625 

25-64 

.390625 

41-84 

.640625 

57-64 

.890625 

5-32 

.15625 

13-32 

.40625 

21-32 

.65625 

29-32 

.90625 

11-64 

.171&5 

•^7-64 

.421875 

43-64 

.671875 

59-64 

.921875 

3-16 

.1875 

7-16 

.4375 

11-16 

.6875 

15-16 

.9375 

13-64 

.203125 

29-64 

.453125 

45-64 

.703125 

61-64 

.953125 

7-32 

.21875 

15-32 

.46875 

23-32 

.71875 

31-32 

.96875 

15-64 

.234375 

31-04 

.484375 

47-64 

.734375 

63-64 

.984375 

1-4 

.25 

1-2 

.50 

3-4 

.75 

1 

1. 

To  convert  a  common  fraction  into  a  decimal.— Divide  the 
numerator  by  the  denominator,  adding  to  the  numerator  as  many  ciphers 
prefixed  by  a  decimal  point  as  are  necessary  to  give  the  number  of  decimal 
places  desired  in  the  result:  ^  =  1 .0000  -*-8  =  0.3333  -f . 

To  convert  a  decimal  into  a  common  fraction.— Set  down 
the  decimal  as  a  numerator,  and  place  as  the  denominator  1  with  as  many 
ciphers  annexed  as  there  are  decimal  places  in  the  numerator;  erase  the 


£ 
I 

9 

Q 

= 


ttjop 


ARITHMETIC. 


O       O        ~ 


SO        O 

l-«  Tjt 


GO         OO         OS         OS 

GO      t-      eo      »ra 

^  §  s  s§ 


6  A  s. .  JI .  E 

GO         O*         1O         CJ         O* 


CO         lO        GO         O         00         »O 
1-1        <N        CO        O        CO        1-- 

9R     ri     >T     fe:.    Q     52 


I 


s  g 


ac 
2 

I 

fr 
0 


i— I         »O        OS 

S      fc      5 


CO        I-        i-t 


1 


-B 


28    S?    58 


i 


v 
'd 


«o     i>     oo 


i  i 


0     i-     o     to 

t-        TH  5 


s5      co      co 


2?   $   s   £ 

0000 


g   g   g   I 

00         CO         ^         O 


8    §    g    g 


COMPOUND   NUMBERS.  0 

decimal  point  in  the  numerator,  and  reduce  the  fraction  thus  formed  to  its 
lowest  terms: 


To  reduce  a  recurring  decimal  to  a  common  fraction.— 

Subtract  the  decimal  figures  that  do  not  recur  from  the  whole  decimal  in- 
cluding1 one  set  of  recurring  figures;  set  down  the  remainder  as  the  numer- 
ator of  the  fraction,  and  as  many  nines  as  there  are  recurring  figures,  fol- 
lowed by  as  many  ciphers  as  there  are  non-recurring  figures,  in  the  denom- 
inator. Thus: 

.79054054,  the  recurring  figures  being  054. 
Subtract  79 

78975  .  117 

99900  =  (reduced  to  lts  lowest  terms)  —  . 

COMPOUND  OR   DENOMINATE   NUMBERS. 

Reduction  descending.  —  To  reduce  a  compound  number  to  a  lower 
denomination.  Multiply  the  number  by  as  many  units  of  the  lower  denomi- 
nation as  makes  one  of  the  higher. 

3  yards  to  inches:    3  X  36  =  108  inches. 
.04  square  feet  to  square  inches:     .04  X  144  =  5.76  sq.  in. 

If  the  given  number  is  in  more  than  one  denomination  proceed  in  steps 
from  the  highest  denomination  to  the  next  lower,  and  so  on  to  the  lowest, 
adding  in  the  units  of  each  denomination  as  the  operation  proceeds. 

8  yds.  1  ft.  7  in.  to  inches:  3  X  3  =  9,  -f  1  =  10,  10  X  12  =  120,  -f  7  =  127  in. 

Reduction  ascending.  —  To  express  a  number  of  a  lower  denomi- 
nation in  terms  of  a  higher,  divide  the  number  by  the  numb  r  of  units  of 
the  lower  denomination  contained  in  one  of  the  next  higher;  the  quotient  is 
in  the  higher  denomination,  and  the  remainder,  if  any,  in  the  lower. 

I'll  inches  to  higher  denomination. 

127  -s-  12  =  10  feet  -f  7  inches;    10  feet  H-  3  =  3  yards  -f  1  foot. 

Ans.  3  yds.  1  ft.  7  in. 

To  express  the  result  in  decimals  of  the  higher  denomination,  divide  the 
given  number  by  the  number  of  units  of  the  given  denomination  contained 
in  one  of  the  required  denomination,  carrying  the  result  to  as  many  places 
of  decimals  as  may  be  desired. 

127  inches  to  yards:     127  -^-  36  =  3*1  =  3.5277  -f  yards. 
RATIO    AND   PROPORTION. 

Ratio  is  the  relation  of  one  number  to  another,  as  obtained  by  dividing 
one  by  the  other. 

Ratio  of  2  to  4,  or  2  :  4  =  2/4  =  1/2. 
Ratio  of  4  to  2,  or  4  :  2  =  2. 

Proportion  is  the  equality  of  two  ratios.  Ratio  of  2  to  4  equals  ratio 
of  3  to  G,  2/4  =  3/6:  expressed  thus,  2  :  4  :  :  3  :  6;  read,  2  is  to  4  as  3  is  to  6. 

The  first  and  fourth  terms  are  called  the  extremes  or  outer  terms,  the 
second  and  third  the  means  or  inner  terms. 

The  product  of  the  means  equals  the  product  of  the  extremes: 

2  :  4  :  :  3  :  6;    2  x  6  =  12;    3  X  4  =  12. 

Hence,  given  the  first  three  terms  to  find  the  fourth,  multiply  the  second 
and  third  terms  together  and  divide  by  the  first. 

2  :  4  :  :  3  :  what  number  ?    Ans.        *  '  =  6. 


ARITHMETIC. 


Algebraic  expression  of  proportion.— a  :  b  :  :  c  :  d\  --  =  --ad 

o      a' 

be  be    .       ad  ad 

—  be;  from  which  a  =  —  ;  d  =  ~ :  b  =  — :  c  =  — r- . 
d  a  c  b 

Ttlean  proportional  between  two  given  numbers,  1st  and  2d,  is  such 
a  number  that  the  ratio  which  the  first  bears  to  it  equals  the  ratio  which  it 
bears  to  the  second.  Thus,  2  :  4  :  :  4:  8;4isa  mean  proportional  between 
2  and  8.  To  find  the  mean  proportional  between  two  numbers,  extract  the 
square  root  of  their  product. 

Mean  proportional  of  2  and  8  =  ^2  x  8  =  4. 

Single  Rule  of  Three  ;  or,  finding  the  fourth  term  of  a  proportion 
when  three  terms  are  given.— Rule,  as  above,  when  the  terms  are  stated  in 
their  proper  order,  multiply  the  second  by  the  third  and  divide  by  the  first. 
The  difficulty  is  to  state  the  terms  in  their  proper  order.  The  term  which  is 
of  the  same  kind  as  the  required  or  fourth  term  is  made  the  third;  the  first 
and  second  must  be  like  each  other  in  kind  and  denomination.  To  deter- 
mine which  is  to  be  made  second  and  which  first  requires  a  little  reasoning. 
If  an  inspection  of  the  problem  shows  that  the  answer  should  be  greater 
than  the  third  term,  then  the  greater  of  the  other  two  given  terms  should 
be  made  the  second  term— otherwise  the  first.  Thus,  3  men  remove  54  cubic 
feet  of  rock  in  a  day;  how  many  men  will  remove  in  the  same  time  10  cubic 
yards  ?  The  answer  is  to  be  men  -make  men  third  term;  the  answer  is  to 
be  more  than  three  men,  therefore  make  the  greater  quantity,  10  cubic 
yards,  the  second  term ;  but  as  it  is  not  the  same  denomination  as  the  other 
term  it  must  be  reduced,  =  270  cubic  feet.  The  proportion  is  then  stated: 

3  X  270 
54  :  270  :  :  3  :  x  (the  required  number);    x  =  — — —  =  15  men. 

The  problem  is  more  complicated  if  we  increase  the  number  of  given 
terms.  Thus,  in  the  above  question,  substitute  for  the  words  "  in  the  same 
time  "  the  words  "  in  3  days."  First  solve  it  as  above,  as  if  the  work  were 
to  be  done  in  the  same  time;  then  make  another  proportion,  stating  it  thus: 
If  15  men  do  it  in  the  same  time,  it  will  take  fewer  men  to  do  it  in  3  days; 
make  1  day  the  2d  term  and  3  days  the  first  term.  3:1  :  :  15  men  :  5  men. 

Compound  Proportion,  or  Double  Rule  of  Three.— By  this 
rule  are  solved  questions  like  the  one  just:  given,  in  which  two  or  more  stat- 
ings  are  required  by  the  single  rule  of  three.  In  it  as  in  the  single  rule, 
there  is  one  third  term,  which  is  of  the  same  kind  and  dt  nomination  as  the 
fourth  or  required  term,  but  there  may  be  two  or  more  first  and  second 
terms.  Set  down  the  third  term,  take  each  pair  of  terms  of  the  same  kind 
separately,  and  arrange  them  as  first  and  second  by  the  same  reasoning  as 
is  adopted  in  the  single  rule  of  three,  making  the  greater  of  the  pair  the 
second  if  this  pair  considered  alone  should  require  the  answer  to  be 
greater. 

Set  down  all  the  first  terms  one  under  the  other,  and  likewise  all  the 
socond  terms.  Multiply  all  the  first  terms  together  and  all  the  second  terms 
together.  Multiply  the  product  of  all  the  second  terms  by  the  third  term,  and 
divide  this  product  by  the  product  of  all  the  first  terms.  Example:  If  3  men 
remove  4  cubic  yards  in  one  day,  working  12  hours  a  day,  how  many  men 
working  10  hours  a  day  will  remove  20  cubic  yards  in  3  days  ? 
Yards  4  :  20 


Davs 

Hours         10  :    12 


3  men. 


Products  120  :  240  :  :  3  :  6  men.  Ans. 

To  abbreviate  by  cancellation,  any  one  of  the  first  terms  may  cancel 
either  the  third  or  any  of  the  second  terms;  thus.  3  in  first  cancels  3  in  third, 
making  it  1,  10  cancels  into  20  making  the  latter  2.  which  into  4  makes  it  2, 
which  into  12  makes  it  6,  and  the  figures  remaining  are  only  1  :  6  :  :  1  :  6. 

INVOLUTION,  OR   POWERS   OF   NUMBERS. 

Involution  is  the  continued  multiplication  of  a  number  by  itself  a 
given  number  of  times.  The  number  is  called  the  root,  or  first  power,  and 
the  products  are  called  powers.  The  second  power  is  called  the  square  and 


POWERS   OF   NUMBERS. 


the  third  power  the  cube.  The  operation  may  be  indicated  without  being 
performed  by  writing  a  small  figure  called  the  index  or  exponent  to  the 
right  of  and  a  little  above  the  root;  thus,  33  =  cube  of  3,  =  27. 

To  multiply  two  or  more  powers  of  the  same  number,  add  their  exponents; 
thus,  22  X  23'  =  25,  or  4  X  8  =  32  =  25. 

To  divide  two  powers  of  the  same  number,  subtract  their  exponents;  thus, 

03  _,_  32  —  31  —  2;  22  -5-  24  =  2~2  =  —  =  -.  The  exponent  may  thus  be  nega- 
tive. 23  •+•  23  =  2°  =  1,  whence  the  zero  power  of  any  number  =  1.  The 
first  power  of  a  number  is  the  number  itself.  The  exponent  may  be  frac- 
tional as  2*,  2s,  which  means  that  the  root  is  to  be  raised  to  a  power  whose 
exponent  is  the  numerator  of  the  fraction,  and  the  root  whose  sign  is  the 
denominator  is  to  be  extracted  (see  Evolution).  The  exponent  may  be  a 
decimal,  as  2°'5,  21'5;  read,  two  to  the  five-tenths  power,  two  to  the  one  and 
five-tenths  power.  These  powers  are  solved  by  means  of  Logarithms  (which 
see). 

First  Nine  Powers  of  tlie   First  Nine  Numbers. 


1st 

3d 

3d 

4th 

5th 

6th 

7th 

8th 

9th 

Pow'r 

Pow'r 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

Power. 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

4 

8 

16 

32 

64 

128 

256 

512 

3 

9 

27 

81 

243 

729 

2187 

6561 

19683 

4 

16 

64 

256 

1024 

4096 

16384 

65536 

262144 

5 

25 

125 

625 

3125 

15625 

78125 

390625 

1953125 

6 

36 

216 

1296 

7776 

46656 

279936 

1679616 

10077696 

49 

343 

2401 

16807 

117649 

823543 

5764801 

40353607 

8 

64 

512 

4096 

35768 

262144 

2097152 

16777216 

134217728 

9 

81 

729 

6561 

59049 

531441 

4782969 

43046721 

387420489 

The   First  Forty  Powers  of  2. 


9 

3 

S3 
^ 

c5 

1 

s 

cS 
£ 

to 

a 

^ 

o> 
fe 

aJ 

53 

c3 

Q 

13 

g 

"3 

o 

3 

0 

«3 

> 

& 

> 

P- 

> 

PH 

> 

PH 

> 

1 

9 

512 

18 

262144 

27 

134217728 

36 

68719476736 

2 

10 

1024 

19 

524288 

28 

268435456 

37 

137438953472 

4 

11 

2048 

20 

1048576 

29 

536870912 

38 

274877906944 

8 

12 

4096 

21 

2097152 

30 

1073741824 

39 

549755813888 

16 

13 

8192 

22 

4194304 

31 

2147483648 

40 

1099511627776 

32 

14 

16384 

23 

8388608 

32 

4294967296 

64 

15 

32768 

24 

16777216 

33 

8589934592 

128 

16 

65536 

25 

33554432 

34 

17179869184 

256 

17 

131072 

26 

67108864 

35 

34350738368 

EVOLUTION. 

Evolution  is  the  finding  of  the  root  (or  extracting  the  root)  of  any 
number  the  power  of  which  is  given. 

The  sign  \/  indicates  that  the  square  root  is  to  be  extracted :  \  ty  y'i  the 
cube  root,  4th  root,  ?ith  root. 

A  fractional  exponent  with  1  for  the  numerator  of  the  fraction  is  also 
used  to  indicate  that  the  operation  of  extracting  the  root  is  to  be  performed  ; 

thus,  2*,  2^=   472,    Vs. 

When  the  power  of  a  number  is  indicated,  the  involution  not  being  per- 
formed, the  extraction  of  any  root  of  that  power  may  ateo  be  indicated  by 


8  ARITHMETIC. 

dividing  the  index  of  the  power  by  the  index  of  the  root,  indicating  the 
division  by  a  fraction.    Thus,  extract  the  square  root  of  the  6th  power  of  2: 

l/ge  _  gi  _  gf  =  2J  -  8. 
The  6th  power  of  2,  as  in  the  table  above,  is  64  ;  |/64  =  8. 

Difficult  problems  in  evolution  are  performed  by  logarithms,  but  the 
square  root  and  the  cube  root  may  be  extracted  directly  according  to  the 
rules  given  below.  The  4th  root  is  the  square  root  of  the  square  root.  The 
6th  root  is  the  cube  root  of  the  square  root,  or  the  square  root  of  the  cube 
root ;  the  9th  root  is  the  cube  root  of  the  cube  root ;  etc. 

To  Extract  the  Square  Root.— Point  off  the  given  number  into 
periods  of  two  places  each,  beginning  with  units.  If  there  are  decimals, 
point  these  off  likewise,  beginning  at  the  decimal  point,  and  supplying 
as  many  ciphers  as  may  be  needed.  Find  the  greatest  number  whose 
square  is  less  than  the  first  left-hand  period,  and  place  it  as  the  first 
figure  in  the  quotient.  Subtract  its  square  from  the  left-hand  period, 
and  to  the  remainder  annex  the  two  figures  of  the  second  period  for 
a  dividend.  Double  the  first  figure  of  the  quotient  for  a  partial  divisor ; 
find  how  many  times  the  latter  is  contained  in  the  dividend  exclusive 
of  the  right-hand  figure,  and  set  the  figure  representing  that  number  of 
times  as  the  second  figure  in  the  quotient,  and  annex  it  to  the  right  of 
the  partial  divisor,  forming  the  complete  divisor.  Multiply  this  divisor  by 
the  second  figure  in  the  quotient  and  subtract  the  product  from  the  divi- 
dend. To  the  remainder  bring  down  the  next  period  and  proceed  as  before, 
in  each  case  doubling  the  figures  in  the  root  already  found  to  obtain  the 
trial  divisor.  Should  the  product  of  the  second  figure  in  the  root  by  the 
completed  divisor  be  greater  than  the  dividend,  erase  the  second  fig-ure  both 
from  the  quotient  and  from  the  divisor,  and  substitute  the  next  smaller 
figure,  or  one  small  enough  to  make  the  product  of  the  second  figure  by  the 
divisor  less  than  or  equal  to  the  dividend. 

3.141592653611.77245  + 

271214 

1 189 

34712515 
[2429 
3542  8692 
7084 

35444  160865 
1141776 

35448511908936 
j 1772425 

To  extract  the  square  root  of  a  fraction,  extract  the  root  of  numerator 
and  denominator  separately.  A/ -  =  -,  or  first  convert  the  fraction  into  a 


To  Extract  the  Cube  Boot.— Point  off  the  number  into  periods  of 
3  figures  each,  beginning  at  the  right  hand,  or  unifs  place.  Point  off  deci- 
mals in  periods  of  3  figures  from  the  decimal  point.  Find  the  greatest  cube 
that  does  not  exceed  the  left-hand  period;  write  its  root  as  the  first  figure 
in  the  required  root.  Subtract  the  cube  from  the  left-hand  period,  and  to 
the  remainder  bring  down  the  next  period  for  a  dividend. 

Square  the  first  figure  of  the  root;  multiply  by  300,  and  divide  the  product 
into  the  dividend  for  a  trial  divisor  ;  write  the  quotient  after  the  first  figure 
of  the  root  as  a  trial  second  figure. 

Complete  the  divisor  by  adding  to  -SCO  times  the  square  of  the  first  figure, 

30  times  the  product  of  the  first  by  the  second  figure,  and  the  square  of  the 

second  figure.    Multiply  this  divisor  by  the  second  figure ;  subtract  the 

product  from  the  remainder.    (Should  the  product  be  greater  than  the 

*  remainder,  the  last  figure  of  the  root  and  the  complete  divisor  are  too  large  ; 


CUBE    ROOT. 


substitute  for  the  last  figure  the  next  smaller  number,  and  correct  the  trial 
divisor  accordingly.) 

To  the  remainder  bring  down  the  next  period,  and  proceed  as  before  to 
find  the  third  figure  of  the  root— that  is,  square  the  two  figures  of  the  root 
already  found ;  multiply  by  300  for  a  trial  divisor,  etc. 

If  at  any  time  the  trial  divisor  is  less  than  the  dividend,  bring  down  an- 
other period  of  3  figures,  and  place  0  in  the  root  and  proceed. 

The  cube  root  of  a  number  will  contain  as  many  figures  as  there  are 
periods  of  3  in  the  number. 

Shorter  Methods  of  Extracting  the  Cube  Root.— 1.  From 
Went  worth's  Algebra: 

1,881,365,963,625112345 
1 


300  x  1 

t         — 

300 

881 

30x  1 

x  2    = 

60 

22  = 

J364 

728 

64        153365 

300  x  122 
30  x  12  x  3  = 

82  = 


300  x  1232    = 

30  x  123  x  4  = 

42  = 


43200 
1080 

?] 
44289  }•  132867 

1089  J  20498963 
45387001 
14760 I 

_J?1 

4553476  [•  18213904 
14776 j  ~ 


2285059625 


300  x  12342    =  456826800 

30  x  1234  x  5  =   185100 

52=      25 


4570119252285059625 


After  the  first  two  figures  of  the  root  are  found  the  next  trial  divisor  is 
found  by  bringing  down  the  sum  of  the  60  and  4  obtained  in  completing  the 
preceding  divisor ,  then  adding  the  three  lines  connected  by  the  brace,  and 
annexing  two  ciphers.  This  method  shortens  the  work  in  long  examples,  as 
is  seen  in  the  case  of  the  last  two  trial  divisors,  saving  the  labor  of  squaring 
123  and  1234.  A  further  shortening  of  the  work  is  made  by  obtaining  the 
last  two  figures  of  the  root  b}^  division,  the  divisor  employed  being  three 
times  the  square  of  the  part  of  the  root  already  found ;  thus,  after  finding 
the  first  three  figures: 

3  x  1232  =  45387 | 20498963 | 45. 1 -f 
—181548    ~ 
234416 
226935 


74813 

The  error  due  to  the  remainder  is  not  sufficient  to  change  the  fifth  figure  of 
the  root. 

Tof.  H.  A.  Wood  (Stevens  Indicator,  July,  1890): 

,  count- 

the  first 

by  3. 

proceed- 
may  be 
*ied  as 


10  ARITHMETIC. 

EXAMPLE.—  Required  the  cube  root  of  20.    The  nearest  cube  to  20  is  3s, 
32  =  9)20.0 

2.2 
6 

3)0 

2.7  IstT.  R. 
2.  T»=  7.29)20.  000 
1T743 
5.4 
3)8.143 

2.714,  1st  ap.  cube  root. 
2.714*  =  7.365796)20.0000000 
2.7152534 
5.428 

3)8.1432534 
2.7144178  2d  ap.  cube  root. 

REMARK.—  In  the  example  it  will  be  observed  that  the  second  term,  or 
first  two  figures  of  the  root,  were  obtained  by  using  for  trial  root  the  root  of 
the  first  period.  Using,  in  like  manner,  these  two  terms  for  trial  root,  we 
obtained  four  terms  of  the  root  ;  and  these  four  terms  for  trial  root  gave 
seven  figures  of  the  root  correct.  In  that  example  the  last  figure  should  be 
7.  Should  we  take  these  eight  figures  for  trial  root  we  should  obtain  at  least 
fifteen  figures  of  the  root  correct. 

To  Extract  a  Higher  Root  than  the  Cube.—  The  fourth  root  is 
the  square  root  of  the  square  root  ;  the  sixth  root  is  the  cube  root  of  the 
square  root  or  the  square  root  of  the  cube  root.  Other  roots  are  most  con- 
veniently found  by  the  use  of  logarithms. 

ALLIGATION 

shows  the  value  of  a  mixture  of  different  ingredients  when  the  quantity 
and  value  of  each  is  known. 
Let  the  ingredients  be  a,  6,  c,  d,  etc.,  and  their  respective  values  per  unit 


A  =  the  sum  of  the  quantities  =  a-\-b  +  c-+-d,  etc. 
P  —  mean  value  or  price  per  unit  of  A. 
AP  =  aw  -f  bx  -j-  cy  +  dz,  etc. 
aw  +  bx  +  cy  -f-  dz 
—A~~ 

PERMUTATION 

shows  in  how  many  positions  any  number  of  things  may  be  arranged  in  a 
row;  thus,  the  letters  a,  b,  c  may  be  arranged  in  six  positions,  viz.  abc,  acb, 
cab,  cba,  6ac,  bca. 

Rule.—  Multiply  together  all  the  numbers  used  in  counting  the  things;  thus, 
permutations  of  1,  2,  and  3  —  1x2x3  =  6.  In  how  many  positions  can  9 
things  in  a  row  be  placed  ? 

1X2X3X4X5X6X7X8X9^  362880. 
COMBINATION 

shows  how  many  arrangements  of  a  few  things  may  be  made  out  of  a 
greater  number.  Rule  :  Set  down  that  figure  which  indicates  the  greater 
number,  and  after  it  a  series  of  figures  diminishing  by  1,  until  as  many  are 
set  down  as  the  number  of  the  few  things  to  be  taken  in  each  combination, 
Then  beginning  under  the  last  one  set  down  said  number  of  few  things  ; 
then  going  backward  set  down  a  series  diminishing  by  1  until  arriving  under 
the  first  of  the  upper  numbers.  Multiply  together  all  the  upper  numbers  to 
form  one  product,  and  all  the  lower  numbers  to  form  another;  divide  the 
upper  product  by  the  lower  one, 


GEOMETRICAL    PROGRESSION.  11 

How  many  combinations  of  9  things  can  be  made,  taking  3  in  each  com- 
bination ? 

9X8X7  =  ft04  =  84 
1X2X3        6 

ARITHMETICAL  PROGRESSION, 

in  a  series  of  numbers,  is  a  progressive  increase  or  decrease  in  each  succes- 
sive number  by  the  addition  or  subtraction  of  the  same  amount  at  each  step, 
as  1,  2,  3,  4,  5,  etc.,  or  15,  12,  9,  6,  etc.  The  numbers  are  called  terms,  and  the 
equal  increase  or  decrease  the  difference.  Examples  in  arithmetical  pro- 
gression may  be  solved  by  the  following  formulae  : 

Let  a  =  first  term,  I  =  last  term,  d  =  common  difference,  n  —  number  of 
terms,  s  =  sum  of  the  terms: 


2s  s       (n  —  : 

=  »-«'  =»+— 


I  +  a.  ,   J2  -  a3 

^~          ~ 


a  =  i-(n-W,  =!_<i^, 

n  2 


I  — a  _  2(s  -  an) 

1  =  n  — l'  ~   n(n  -  D* 

J2  _  a2  _  %(nl  -  s) 

=  2s  -  I  —  a  ~~  n(n  -  1)' 

I  -  a  _d-2a  ±  \/(2a  -  d)2  +  8ds 
d 
2S  21  +  d  ±  \/(2l  -f-  d)2  -  8ds 


~  I  -f  a  2d 

GEOMETRICAL  PROGRESSION, 

in  a  series  of  numbers,  is  a  progressive  increase  or  decrease  in  each  suc« 
cessive  number  by  the  same  multiplier  or  divisor  at  each  step,  as  1,  2,  4,  8, 
16.  etc.,  or  243,  81,  27,  9,  etc.  The  common  multiplier  is  called  the  ratio. 

Let  a  =  first  term,  I  =  last  term,  r  =  ratio  or  constant  multiplier,  n  = 
number  of  terms,  m  =  any  term,  as  1st,  2d,  etc.,  s  =  sum  of  the  terms: 

=  °  -Ky-3)*  =  (r  -  l)8rtt  ~  1 

r  rw  -  1 

log  Z  =  log  a  +  (w-  —  1)  log  r,  f(s  —  l)n  ~  l  —  «(s  —  a)w  ~  *  =  0. 

m  =  arm  ""  *'  log  m  =  log  a  +  (m  -  1)  log  r. 

n  -  i/—      w  —  i/~~i7 
_  a(rw  —  1)  _  rZ  —  a  /u\n  —        y  a  7rn  —  1 


r-1   '  r-1  ~   n-i-     n  —  i  — 

yz  -      i/a 


ARITHMETIC. 


(r  - 


log  a  -  log  I  ^-  (n  -  1)  log  r. 
_  log  I-  log  a 


*  =  0. 


_  log  I  -  log  a 
n  —  -  ;  —  ~T~  •*» 

logr 

log  I  —  log  a 


rn__r»..i+rL_=a 

'     log  [a  -f  (r  —  l)s]  —  log  a 
log  r 


'  log  (s  -  a)  -  log  (s  —  0 


r-Kl, 


log  r 


Population  of  the  United  States. 

(A  problem  in  geometrical  progression.;* 


Year. 
1860 
1870 
1880 
1890 
1895 
1900 


Population. 
31,443,321 
39,818,449* 
50.155,783 
62,622,250 
Est.  69,733,000 
"    77,652,000 


Increase  in  10     Annual  Increase, 
Years,  per  cent.         per  cent. 


26.63 
25.96 
24.86 


2.39 
2.33 
2.25 

Est.  2.174 
"    2.174 


Est.  24.0 

Estimated  Population  in  Each  Year  from  1860  to  1899. 
(Based  on  the  above  rates  of  increase,  in  even  thousands.) 


I860.... 

31,443 

1870... 

39,818 

1880.... 

50,156 

1890... 

62,622 

1861  .... 

32,195 

1871.... 

40,748 

1881.... 

51,281 

1891.... 

63,984 

1862.... 

32,964 

1872.... 

41,699 

1882  ... 

52,433 

1892... 

65.375 

1863.... 

33,752 

1873.  .. 

42,673 

1883.... 

53.610 

1893.... 

66,797 

1864.... 

34,558 

1874... 

43,670 

1884.... 

54,813 

1894.... 

68,249 

1865... 

35,384 

1875.... 

44,690 

1885... 

56.043 

1895... 

69,733 

18(56.... 

36,229 

1876.... 

45.373 

1886  ... 

57,301 

1896  ... 

71  ,249 

1867.... 

37,095 

1877  .. 

46,800 

1  887  

58.588 

1897.... 

72.799 

1868.... 

37,981 

1878  ... 

47,893 

1888.... 

59.903 

1898  ... 

74,382 

1869.... 

38,889 

1879  .... 

49,011 

1889  ... 

61,247 

1899.... 

75,999 

The  above  table  has  been  calculated  by  logarithms,  as  follows  : 
log  r  =  log  I  -  log  a  H-  (n  —  1),  log  m  =  log  a -\-  (m  —  1)  log  r 

Pop.  1870. . .  39,818449  log  =  7.6000841  =  log  I 

"     1860, . . .  31,443321  log  =  7.49T5288  =  log  a 

diff.  =    .1025553 


n  =  11,  n  -  1  =  10,  diff.  -^-  10  =    .01025553 
a.dd  log  for  1860       7.4975288 


=  log  r, 

=  log  a 


log  for  1861  =  7.50778433  No.  =  32,195  ... 
add  again         .01025553 

log  for  1862      7.51803986  No.  =  32,964  .  .  . 

Compound  interest  is  a  form  of  geometrical  progression;  the  ratio 
being  1  plus  the  percentage. 


*  Corrected  by  addition  of  1,260.078,  estimated  error  of  the  census  of  1870. 
Census  Bulletin  No.  16,  Dec.  12,  1890, 


DISCOUNT.  13 

INTEREST   AND  DISCOUNT. 

Interest  is  money  paid  for  the  use  of  money  for  a  given  time;  the  fac 
tors  are : 

p,  the  sum  loaned,  or  the  principal: 

t,  the  time  iu  years; 

r,  the  rate  of  interest; 

i,  the  amount  of  interest  for  the  given  rate  and  time; 

a  =  p  4-  i  =  the  amount  of  the  principal  with  interest 

at  the  end  of  the  time. 
Formulae  : 

i  =  interest  =  principal  X  time  X  rate  per  cent  —  i  —  ^-rj 
a  =  amount  =  principal  -\-  interest  =  p  -f-  ^n:; 

r  —  rate  =  — ^-\ 
pt 

lOOi  ptr 

tT  100 

lOOi 

t  =  time  = . 

pr 

If  the  rate  is  expressed  decimally  as  a  per  cent,— thus,  6  per  cent  =  .06,— 
the  formulae  become 


1  month  .16§          .25  .33i         .41  §         . 

1  day  =  3£s  year  .0055|      .0083J      .0111$'     .0138|      .016 
1  day  =  3^  year  .005479    .008219    .010959    .013699    .016 


=  =  r  =  =     .  =  __ 

Rules  for  finding  Interest.— Multiply  the  principal  by  the  rate 
per  annum  divided  by  100,  and  by  the  time  in  years  and  fractions  of  a  year. 
If  the  time  is  given  in  days,  interest  =  l^j^X  rate  X  no.  of  days 

ODJ  X  1UU 

In  banks  interest  is  sometimes  calculated  on  the  basis  of  360  days  to  a 
year,  or  12  months  of  30  days  each. 

Short  rules  for  interest  at  6  per  cent,  when  360  days  are  taken  as  1  year: 
Multiply  the  principal  by  number  of  days  and  divide  by  6000. 
Multiply  the  principal  by  number  of  months  and  divide  by  200. 
The  interest  of  1  dollar  for  one  month  is  ^  cent. 

Interest  ol  100  Dollars  for  Different  Times  and  Rates. 

Time.  Z%  3#  \%  5%  6%  8£  10* 

1  year  $2.00       $3.00       $4.00       $5.00       $6.00         $8.00       $10.00 

.83£ 
.02775 
.0273973 

Discount  is  interest  deducted  for  payment  of  money  before  it  is  due. 

True  discount  is  the  difference  between  the  amount  of  a  debt  pay- 
able at  a  future  date  without  interest  and  its  present  worth.  The  present 
worth  is  that  sum  which  put  at  interest  at  the  legal  rate  will  amount  to  the 
debt  when  it  is  due. 

To  find  the  present  worth  of  an  amount  due  at  future  date,  divide  the 
amount  by  the  amount  of  $1  placed  at  interest  for  the  given  time.  The  dis- 
count equals  the  amount  minus  the  present  worth. 

What  discount  should  be  allowed  on  $103  paid  six  months  before  it  is  due, 
interest  being  6  per  cent  per  annum  ? 

=  $100  present  worth,  discount  =  3.00. 

1  +  1  X  .06  X  - 

Bank  discount  is  the  amount  deducted  by  a  bank  as  interest  on 
money  loaned  on  promissory  notes.  It  is  interest  calculated  not  on  the  act- 
ual sum  loaned,  but  on  the  gross  amount  of  the  note,  from  which  the  dis- 
count is  deducted  in  advance.  It  is  also  calculated  on  the  basis  of  360  days 
in  the  year,  and  for  3  (in  some  banks  4)  days  more  than  the  time  specified 'in 
the  note.  These  are  called  days  of  grace,  and  the  note  is  not  payable  till 
the  last  of  these  days.  In  some  States  days  of  grace  have  been  abolished. 


14 


ARITHMETIC. 


What  discount  will  be  deducted  by  a  bank  in  discounting  a  note  for  $103 
payable  6  months  hence  ?    Six  months  =  182  days,  add  3  days  grace  =  185 

,103  X  185 
days-6000—  =  $3'176' 

Compound  Interest.— In  compound  interest  the  interest  is  added  to 
the  principal  at  the  end  of  each  year,  (or  shorter  period  if  agreed  upon). 

Let  p  =  the  principal,  r  =  the  rate  expressed  decimally,  n  =  no  of  years, 
and  a  the  amount : 


a  =  amount  =  p  (1  +  r)n\  r  =  rate  =  A/ I, 

p  =  principal,  =      ^          no  of  years  =  n,  =  • 


log  (1  -f  r) 

Compound  Interest  Table. 

(Value  of  one  dollar  at  compound  interest,  compounded  yearly,  at 
3,  4,  5,  and  6  per  cent,  from  1  to  50  years. ) 


& 

3# 

W 

5# 

6# 

02 

1 

3£ 

4% 

& 

w 

1 

1.03 

1.04 

1.05 

1.06 

16 

1.6047 

1.8730 

2.1829 

2.5403 

2 

.0609 

1.0816 

1.1025 

1.1236 

17 

1.6528 

1.9479 

2.2920 

2.6928 

3 

.0927 

1.1249 

1.1576 

1.1910 

18 

1.7024 

2.0258 

2.4066 

2.8543 

4 

.1255 

1.1699 

1.2155 

1.2625 

19 

1.7535 

2.1068 

25269 

3.0256 

5 

.1593 

1.2166 

1.2763 

1.3382 

20 

1.8061 

2.1911 

2.6533 

3.2071 

6 

.1941 

1.2653 

1.3401 

1.4185 

21 

1.8603 

2.2787 

2.7859 

3.3995 

7 

,2299 

1.3159 

1.4071 

1.5036 

22 

1.9161 

2.3699 

2.9252 

3.6035 

8 

.2668 

1.3686 

1.4774 

1.5938 

23 

1.9736 

2.4647 

3.0715 

3.8197 

9 

.3048 

1  .4233 

1.5513 

1.6895 

24 

2.0328 

2.5633 

3.2251 

4.0487 

10 

1.3439 

1.4802 

1.6289 

1.7908 

25 

2.0937 

2.6658 

3.3864 

4.2919 

11 

1.3842 

1.5394 

1.7103 

1.8983 

30 

2.4272 

3.2434 

4.3219 

5.7435 

12 

1.4258 

1.6010 

1.7958 

2.0122 

35 

2.8138 

3.9460 

5.5166 

7.6861 

13 

1.4685 

1.6651 

1.8856 

2.1329 

40 

3.2620 

4.8009 

7.0100 

10.2858 

14 

1.5126 

1.7317 

1.9799 

2.2609 

45 

3.7815 

5.8410 

8.9850 

13.7646 

15 

1.5580 

1.8009 

2.0789 

2.3965 

50 

4.3838 

7.1064 

11.6792 

18.4190 

At  compound  interest  at  3  per  cent  money  will  double  itself  in  23}^  years, 
at  4  per  cent  in  17%  years,  at  5  per  cent  in  14.2  years,  and  at  6  per  cent  in 
11. 9  years. 

EQUATION    OF    PAYMENTS. 

By  equation  of  payments  we  find  the  equivalent  or  average  time  in  which 
one  payment  should  be  made  to  cancel  a  number  of  obligations  due  at  dif- 
ferent dates ;  also  the  number  of  days  upon  which  to  calculate  interest  or 
discount  upon  a  gross  sum  which  is  composed  of  several  smaller  sums  pay- 
able at  different  dates. 

Rule.— Multiply  each  item  by  the  time  of  its  maturity  in  days  from  a 
fixed  date,  taken  as  a  standard,  and  divide  the  sum  of  the  products  by  the 
sum  of  the  items:  the  result  is  the  average  time  in  days  from  the  standard 
date. 

A  owes  B  $100  due  in  30  days,  $200  due  in  60  days,  and  $300  due  in  90  days. 
In  how  many  days  may  the  whole  be  paid  in  one  sum  of  $600  ? 

100  x  30  -f  200  x  60  -f  300  x  90  =  42,000 ;    42,000  -*-  600  =  70  days,  cms. 

A  owes  B  $100,  $200.  and  $300,  which  amounts  are  overdue  respectively  30, 
60,  and  90  days.  If  he  now  pays  the  whole  amount,  $600,  how  many  days' 
interest  should  he  pay  on  that  sum  v  Ans.  70  days. 


ANNUITIES. 


15 


PARTIAL.    PAYMENTS. 

To  compute  interest  on  notes  and  bonds  when  partial  payments  have  been 
made: 

United  States  Rule. — Find  the  amount  of  the  principal  to  the  time 
of  the  first  payment,  and,  subtracting  the  payment  from  it,  find  the  amount 
of  the  remainder  as  a  new  principal  to  the  time  of  the  next  payment. 

If  the  payment  is  less  than  the  interest,  find  the  amount  of  the  principal 
to  the  time  when  the  sum  of  the  payments  equals  or  exceeds  the  interest 
due,  and  subtract  the  sum  of  the  payments  from  this  amount. 

Proceed  in  this  manner  till  the  time  of  settlement. 

Note.— The  principles  upon  which  the  preceding  rule  is  founded  are: 

1st.  That  payments  must  be  applied  first  to  discharge  accrued  interest, 
and  then  the  remainder,  if  any,  toward  the  discharge  of  the  principal. 

2d.  That  only  unpaid  principal  can  draw  interest. 

Mercantile  Method.— When  partial  payments  are  made  on  short 
notes  or  interest  accounts,  business  men  commonly  employ  the  following 
method : 

Find  the  amount  of  the  whole  debt  to  the  time  of  settlement ;  also  find 
the  amount  of  each  payment  from  the  time  it  was  made  to  the  time  of  set- 
tlement. Subtract  the  amount  of  payments  from  the  amount  of  the  debt; 
the  remainder  will  be  the  balance  due. 

ANNUITIES. 

An  Annuity  is  a  fixed  sum  of  money  paid  yearly,  or  at  other  equal  times 
agreed  upon.  The  values  of  annuities  are  calculated  by  the  principles  of 
compound  interest. 

1.  Let  i  denote  interest  on  $1  for  a  year,  then  at  the  end  of  a  year  the 
amount  will  be  1  +  i.    At  the  end  of  n  years  it  will  be  (1  +  i)n. 

2.  The  sum  which  in  n  years  will  amount  to  1  is or  (l  +  i)~  w,  or  the 

(l  +  i)n 
present  value  of  1  due  in  n  years. 

(1  -4-i)n  —  1 

3.  The  amount  of  an  annuity  of  1  in  any  number  of  years  n  is  —  — . 

4.  The  present  value  of  an  annuity  of  1  for  any  number  of  years  n  is 


5.  The  annuity  which  1  will  purchase  for  any  number  of  years  n  is 

i 

6.  The  annuity  which  would  amount  to  1  in  n  years  is — —  . 

Amounts,    Present    Values,   etc.,    at    5#   Interest. 


Years 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(1  _^  iyn, 

d-f  i)-» 

(l  _}_  i)n  _  1 

l--(l  +  t)~w 

i 

i 

i 

i 

l_(l+i)-n 

a  +*)w-i 

1  

1.05 

.952381 

1. 

.952381 

1.05 

i. 

1.1025 

.907029 

2.05 

1.859410 

.537805 

.487805 

3... 

1.157625 

.  863838 

3.1525 

2.723248 

.367209 

.317209 

4  

1.215506 

.822702 

4.310125 

3.545951 

.282012 

.232012 

5  

1.276282 

.783526 

5.525631 

4.329477 

.230975 

.180975 

G  

1.340096 

.746215 

6.801913 

5.075692 

.1970*7 

.147018 

1.407100 

.710681 

8.142008 

5.786373 

.172820 

.122820 

8... 

1.477455 

.676839 

9.549109 

6.463213 

.  154722 

.104722 

9  

1.55  13-28 

.644609 

11.026564 

7.107822 

.  140690 

.090690 

10  

1.628895 

.613913 

12.577893 

7.721735 

.129505 

.079505 

16 


ARITHMETIC. 


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WEIGHTS   AND   MEASURES. 


1? 


TABLES    FOR    CALCULATING    SINKING-FUNDS    AND 
PRESENT    VALUES. 

Engineers  and  others  connected  with  municipal  work  and  industrial  enter- 
prises often  find  it  necessary  to  calculate  payments  to  sinking-funds  which 
will  provide  a  sum  of  money  sufficient  to  pay  off  a  bond  issue  or  other  debt 
at  the  end  of  a  given  period,  or  to  determine  the  present  value  of  certain 
annual  charges.  The  accompanying  tables  were  computed  by  Mr.  John  W 
Hill,  of  Cincinnati,  Eng'g  News,  Jan.  25,  1894. 

Table  I  (opposite  page)  shows  the  annual  sum  at  various  rates  of  interest 
required  to  net  $1000  in  from  2  to  50  years,  and  Tab!e  II  shows  the  present 
value  at  various  rates  of  interest  of  an  annual  charge  of  $1000  for  from  5  to 
50  years,  at  five-year  intervals  and  for  100  years. 

Table  II.— Capitalization  of  Annuity  or  #1000  for 
from  5  to  10O  Years. 


1 

Rate  of  Interest,  per  cent. 

& 

8 

$ 

4 

^ 

5 

<* 

6 

5 

4,645  88 

4,579.60 

4.514.92 

4,451.68 

4,389.91 

4,329.45 

4,268.09 

4,212.40 

10 

8,752.17 

8,530.13 

8,316.45 

8,110.74 

7,912.67 

7,721.73 

7,537.54 

7,360.19 

15 

12,381.41 

11,937.80 

11,517.23:11,118.06 

10,739.42 

10,379.53 

10,037.48 

9,712.30 

so 

15,589.215 

14,877.27 

14,212.12 

13,590.21 

13,007.88 

12,462.13 

11,950.26 

11,469.96 

25 

18,424.67 

17,413.01 

16,481.28jl5,621.93 

14,828.12 

14,093.86 

13,413.82 

12,783.38 

30 

20,930.59 

19,600.21 

18,391.85 

17,291.86 

16,288.77 

15,372.36 

14,533.63 

13,764.85 

35  123,145.31 

21,487.04 

20,000.43  18,664.37 

17,460.89 

16,374.36 

15,390.48 

14,488.65 

4025,103.53 

23,114.36 

21,354.83 

19,792.65 

18,401.49 

17,159.01 

16,044.92 

15,046.31 

45 

26,833.15 

24,518.49 

22,495.2320,719.89 

19,156.24 

17,773.99 

16,547.65 

15,455.85 

50 

28,362.48 

25,729.58 

23,455.21  21,482.08 

19,761  93 

18,255.86 

16,931.97 

15,761.87 

100 

36,614.21 

31,598.81 

27,655.3624,504.96 

21,949.21 

19,847.90 

18,095.83 

16,612.64 

WEIGHTS  AND  MEASURES. 

Long  Measure.— Measures  of  Length* 

12  inches  =  1  foot. 

3  feet  =1  yard. 

5.}  yards,  or  16£  feet  =  1  rod,  pole,  or  perch. 

40  poles,  or  220  yards  =  1  furlong. 

8  furlongs,  or  1760  yards,  or  5280  feet  =  1  mile. 
3  miles  =  league. 

Additional  measures  of  length  in  occasional  use:  1000  mils  =  1  inch; 
4  inches  =  1  hand  ;  9  inches  =  1  span  ;  2£  feet  =  1  military  pace  ;  2  yards  = 
1  fathom. 

Old  Land  Measure.— 7.92  inches  =  1  link;  100  links,  or  66  feet,  or  4 
poles  =  1  chain;  10  chains  =  1  furlong;  8  furlongs  =  1  mile;  10  square  chains 
=  1  acre. 

Nautical  Measure. 
0080.26  feet,  or  1.1 5156  stat-  |       - 

ute  miles  f  =  l  nautlcal  mile,  or  knot.* 

3  nautical  miles  =  1  league. 

60  "SSSSSSS1  or  69-168  f  = '  a***  <at  the  ei»ato-->- 

360  degrees  =  circumference  of  the  earth  at  the  equator. 

*  The  British  Admiralty  takes  the  round  figure  of  6080  ft.  which  is  the 
length  of  the  "  measured  mile1'  used  in  trials  of  vessels.  The  value  varies 
from  6080.26  to  6088.44  ft.  according  to  different  measures  of  the  earth's  di- 
ameter. There  is  a  difference  of  opinion  among  writers  as  to  the  use  of  the 
word  "  knot"  to  mean  length  or  a  distance— some  holding  that  it  should  be 


IB  ARITHMETIC. 

Square  Measure.— Measures  of  Surface. 

144  square  inches,  or  183.35  circular  | 

inches  f  =  *  square  foot. 
9  square  feet  =  i  square  yard . 

30i  square  yards,  or  272J  square  feet          =  1  square  rod,  pole,  or  percli. 
40  square  poles  —  i  rood. 

4  roods,  or  10  sq.  chains,  or  160  sq.  ) 

poles,  or  4840  sq.  yards,  or  43560  v  =  1  acre, 

sq.  feet,  j 
640  acres  —  1  square  mile. 

An  acre  equals  a  square  whose  side  is  208.71  feet. 

A  circular  inch  is  the  area  of  a  circle  1  inch  in  diameter  =  0.7854  square 
inch. 

1  square  inch  =  1.2732  circular  inches. 

A  circular  mil  is  the  area  of  a  circle  1  mil,  or  .001  inch  in  diameter. 
10002  or  1,000,000  circular  mils  =  1  circular  inch. 

I  square  inch  =  1,273,239  circular  mils. 

The  mil,  and  circular  mil  are  used  in  electrical  calculations  involving 
the  diameter  and  area  of  wires. 

Solid  or  Cubic  Measure.— Measures  of  Volume. 

1728  cubic  inches  =  1  cubic  foot. 
27  cubic  feet      =  1  cubic  yard. 

1  cord  of  wood  =  a  pile,  4x4x8  feet  —  128  cubic  feet. 
1  perch  of  masonry  =  16$  X  H  X  1  foot  =  24|  cubic  feet. 

Liquid  Measure. 

4  gills  =     pint. 

2  pints  =     quart. 

4  oiiarta  -     roll  on  J  U-  S-  231  cubic  inches. 

4  quartg  -     gallon  1  Eng.  277.274  cubic  inches. 


31i  gallons 
42  gallons 

2  barrels,  or  63  gallons         = 
84  gallons,  or  2  tierces 

2  hogsheads,  or  126  gallons  = 


barrel, 
tierce, 
hogshead, 
puncheon, 
pipe  or  butt. 


2  pipes,  or  3  puncheons        =  1  tun. 

The  U.  S.  gallon  contains  231  cubic  iuches;  7.4805  gallons  =  1  cubic  foot. 
A  cylinder  7  in.  diam.  and  6  in.  high  contains  1  gallon,  very  nearly,  or  230.9 
cubic  inches.  The  British  Imperial  gallon  contains  277.274  cubic  inches 
=  1.20032  U.  S.  gallon. 

The  Miner's  Inch.— (Western  U.  S.  for  measuring  flow  of  a  stream 
of  water). 

The  term  Miner's  Inch  is  more  or  less  indefinite,  for  the  reason  that  Cali- 
fornia water  companies  do  not  all  use  the  same  head  above  the  centre  of 
the  aperture,  and  the  inch  varies  from  1.36  to  1.73  cubic  feet  per  minute 
each;  but  the  most  common  measurement  is  through  an  aperture  2  inches 
high  and  whatever  length  is  required,  and  through  a  plank  1*  inches  thick. 
The  lower  edge  of  the  aperture  should  be  2  inches  above  the  bottom  of  the 
measuring-box,  and  the  plank  5  inches  high  above  the  aperture,  thus  mak- 
ing a  6- inch  head  above  the  centre  of  the  stream.  Each  square  inch  of  this 
opening  represents  a  miner's  inch,  which  is  equal  to  a  flow  of  1|  cubic  feet 
per  minute. 

Apothecaries'  Fluid  Measure. 

60  minims  =  1  fluid  drachm. 

8  drachms,  or  4371  grains,  or  1.732  cubic  inches  —  1  fluid  ounce. 

JDry  Measure,  U.  S, 

2  pints     =  1  quart. 
8  quarts  =  1  peck. 
4  pecks   =  1  bushel. 

used  only  to  denote  a  rate  of  speed.  The  length  between  knots  on  the  log 
line  is  T£<j  of  a  nautical  mile  or  50.7  ft.  when  a  half-minute  glass  is  used;  so 
that  a  speed  of  10  knots  is  equal  to  10  nautical  miles  per  hour. 


WEIGHTS   AND   MEASURES.  10 

The  standard  U.  S.  bushel  is  the  Winchester  bushel,  which  is  in  cylinder 
form,  18£  inches  diameter  and  8  inches  deep,  and  contains  2150.42  cubic 
inches. 

A  struck  bushel  contains  2150.42  cubic  inches  =  1.2445  cu.  ft.;  1  cubic  foot 
=  0.80356  struck  bushel.  A  heaped  bushel  is  a  cylinder  18£  inches  diam- 
eter and  8  inches  deep,  with  a  heaped  cone  not  less  than  6  inches  high. 
It  is  equal  to  If  struck  bushels. 

The  British  Imperial  bushel  is  based  on  the  Imperial  gallon,  and  contains 
8  such  gallons,  or  2218.192  cubic  inches  =  1.2837  cubic  feet.  The  English 
quarter  =  8  Imperial  bushels. 

Capacity  of  a  cylinder  in  U.  S.  gallons  =  square  of  diameter,  in  inches  X 
height  in  inches  X  .0034.  (Accurate  within  1  part  in  100,000.) 

Capacity  of  a  cylinder  in  U.  S.  bushels  =  square  of  diameter  in  inches  X 
height  in  inches  X  .0003652. 

Shipping  Measure. 

Register  Ton. — For  register  tonnage  or  for  measurement  of  the  entire 
internal  capacity  of  a  vessel : 

100  cubic  feet  =  1  register  ton. 

This  number  is  arbitrarily  assumed  to  facilitate  computation. 
Shipping  Ton.— For  the  measurement  of  cargo  : 

( 1  U.  S.  shipping  ton. 
40  cubic  feet  =  -<  31.16  Imp.  bushels. 
(  32.143  U.  S.      " 
( 1  British  shipping  ton. 
42  cubic  feet  =  4  32.719  Imp.  bushels. 

(33.75  U.S. 

Carpenter's  Rule. — Weight  a  vessel  will  carry  =  length  of  keel  X  breadth 
at  main  beam  x  depth  of  hold  in  feet  H-  95  (the  cubic  feet  allowed  for  a  ton). 
The  result  will  be  the  tonnage.  For  a  double-decker  instead  of  the  depth 
of  the  hold  take  half  the  breadth  of  the  beam. 

Measures  of  Weight.— Avoirdupois,  or  Commercial 
Weight. 

16  drachms,  or  437.5  grains  =  1  ounce,  oz. 
16  ounces,  or  7000  grains  =  1  pound,  Ib. 
28  pounds  =  1  quarter,  qr. 

4  quarters  =  1  hundredweight,  cwt.  =  112  Ibs.    ' 

20  hundred  weight  =  1  ton  of  2240  pounds,  or  long  ton. 

2000  pounds  =  1  net,  or  short  ton. 

2204.6  pounds  =  1  metric  ton. 

1  stone  =  14  pounds  ;  1  quintal  =  100  pounds. 

Troy  Weight. 

24  grains  —  1  pennyweight,  dwt. 

20  pennyweights   =  1  ounce,  oz.  =  480  grains. 

12  ounces  —  1  pound,  Ib.  =  5760  grains. 

Troy  weight  is  used  for  weighing  gold  and  silver.  The  grain  is  the  same 
in  Avoirdupois,  Troy,  and  Apothecaries'  weights.  A  carat,  used  in  weighing 
diamonds  =  3.168  grains  =  .205  gramme. 

Apothecaries'  Weight. 

20  grains     =  1  scruple,  9 
3  scruples  =  1  drachm,   3—60  grains. 
8  drachms  —  1  ounce,   §       =    480  grains. 

12  ounces    =  1  pound,  Ib.      —  5760  grains. 

To  determine  whether  a  balance  has  unequal  arms.— 

After  weighing  an  article  and  obtaining  equilibrium,  transpose  the  article 
and  the  weights.     If  the  balance  is  true,  it  will  remain  in  equilibrium  ;   if 
untrue,  th*»  pan  suspended  from  the  longer  arm  will  descend. 
To   weigh    correctly  on   an  incorrect  balance.— First,    by 

substitution.     Put  the  article  to  be  weighed  in  one  pan  of  the  balance  and 


20  ARITHMETIC. 

counterpoise  it  by  any  convenient  heavy  articles  placed  on  the  other  pan. 
Remove  the  article  to  be  weighed  and  substitute  for  it  standard  weights 
until  equipoise  is  again  established.  The  amount  of  these  weights  is  the 
weight  of  the  article. 

Second,  by  transposition.  Determine  the  apparent  weight  of  the  article 
as  usual,  then  its  apparent  weight  after  transposing  the  article  and  the 
weights.  If  the  difference  is  small,  add  half  the  difference  to  the  smaller 
of  the  apparent  weights  to  obtain  the  true  weight.  If  the  difference  is  2 
pei-  cent  the  error  of  this  method  is  1  part  in  10,000.  For  larger  differences, 
or  to  obtain  a  perfectly  accurate  result,  multiply  the  two  apparent  weights 
together  and  extract  the  square  root  of  the  product. 

Circular  Measure. 

60  seconds,  "  =  1  minute,  '. 
60  minutes,  '  =  1  degree,  °. 
90  degrees      ==  1  quadrant. 
360       **  =  circumference. 

Time. 

60  seconds  =  1  minute. 
60  minutes  =  1  hour. 
24  hours      =  1  day. 
7  days        =  1  week. 
365  days,  5  hours,  48  minutes,  .48  seconds  =  1  year. 

By  the  Gregorian  Calendar  every  year  whose  number  is  divisible  by  4  is  a 
leap  year,  and  contains  366  days,  the  other  years  containing  365  days,  ex- 
cept that  the  centesimal  years  are  leap  years  only  when  the  number  of  the 
year  is  divisible  by  400. 

The  comparative  values  of  mean  solar  and  sidereal  time  are  shown  by  the 
following  relations  according  to  Bessel : 

365.24222  mean  solar  days  =  366.24222  sidereal  days,  whence 
1  mean  solar  day  =  1.00273791  sidereal  days; 

1  sidereal  day  —  0  99726957  mean  solar  day; 
24  hours  mean  solar  time  =  24h  3m  56s. 555  sidereal  time; 
24  hours  sidereal  time  =  28h  56m  48.091  mean  solar  time, 

whence  1  mean  solar  day  is  3m  558.91  longer  than  a  sidereal  day,  reckoned  in 
mean  solar  time. 

BOARD    AND    TIMBER    MEASURE. 

Board  Measure. 

In  board  measure  boards  are  assumed  to  be  one  inch  in  thickness.  To 
obtain  the  number  of  feet  board  measure  (B.  M.)  of  a  board  or  stick  of 
square  timber,  multiply  together  the  length  in  feet,  the  breadth  in  feet,  and 
the  thickness  in  inches. 

To  compute  tlie  measure  or  surface  in  square  feet.— When 
all  dimensions  are  in  feet,  multiply  the  length  by  the  breadth,  and  the  pro- 
duct will  give  the  surface  required. 

When  either  of  the  dimensions  are  in  inches,  multiply  as  above  and  divide 
the  product  by  12. 

When  all  dimensions  are  in  inches,  multiply  as  before  and  divide  product 
by  141. 

Timber  Measure. 

To  compute  the  volume  of  round  timber.— When  all  dimen- 
sions are  in  feet,  multiply  the  length  by  one  quarter  of  the  product  of  the 
mean  girth  and  diameter,  and  the  product  will  give  the  measurement  in 
cubic  feet.  When  length  is  given  in  feet  and  girth  and  diameter  in  inches, 
divide  the  product  by  144  ;  when  all  the  dimensions  are  in  inches,  divide  by 
1728. 

To  compute  the  volume  of  square  timber.— When  all  dimen- 
sions are  in  feet,  multiply  together  the  length,  breadth,  and  depth;  the 
product  will  be  the  volume  in  cubic  feet.  When  one  dimension  is  given  in 
inches,  divide  by  12;  when  two  dimensions  are  in  inches,  divide  by  144;  when 
all  three  dimensions  are  in  inches,  divide  by  1728. 


WEIGHTS   AKD    MEASURES. 


Contents  in  Feet  of*  Joists,  Scantling,  and  Timber. 

Length   in  Feet. 


Size. 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

Feet  Board  Measure. 


2X4 

8 

9 

11 

12 

13 

15 

16 

17 

19 

20 

2X6 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

2X8 

16 

19 

21 

24 

27 

29 

32 

35 

37 

40 

2  X  10 

20 

23 

27 

30 

33 

37 

40 

43 

47 

50 

2  X  12 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

2X  14 

28 

33 

37 

42 

47 

51 

56 

61 

65 

70 

3X8 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

3  X  10 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

3  X  12 

36 

42 

48 

54 

60 

66 

72 

78 

84 

90 

3  X  14 

42 

49 

56 

63 

70 

77 

84 

91 

98 

105 

4X  4 

16 

19 

21 

24 

27 

29 

32 

35 

37 

40 

4X6 

24 

28 

32 

36 

40 

44 

48 

52 

56 

60 

4X8 

32 

37 

43 

48 

53 

59 

64 

69 

75 

80 

4  X  10 

40 

47 

53 

60 

67 

73 

80 

87 

93 

100 

4  X  12 

48 

56 

64 

72 

80 

88 

96 

104 

112 

120 

4  X  14 

56 

65 

75 

84 

93 

103 

112 

121 

131 

140 

6X6 

36 

42 

48 

54 

60 

66 

72 

78 

84 

90 

6X8 

48 

56 

64 

72 

80 

88 

96 

104 

112 

120 

6  X  10 

60 

70 

80 

90 

100 

110 

120 

130 

140 

150 

6  X  12 

72 

84 

96 

108 

120 

132 

144 

156 

168 

180 

6  X  14 

84 

98 

112 

126 

140 

154 

168 

182 

196 

210 

8X8 

64 

75 

85 

96 

107 

117 

128 

139 

149 

160 

8  X  10 

80 

93 

107 

120 

133 

147 

160 

173 

187 

200 

8  X  12 

96 

112 

128 

144 

160 

176 

192 

208 

224 

240 

8  X  14 

112 

131 

149 

168 

187 

205 

224 

243 

261 

280 

10  X  10 

100 

117 

133 

150 

167 

183 

200 

217 

233 

250 

10  X  12 

120 

140 

160 

180 

200 

220 

240 

260 

280 

300 

10  X  14 

140 

163 

187 

210 

233 

257 

280 

303 

327 

350 

12  X  12 

144 

168 

192 

216 

240 

264 

288 

312 

336 

360 

12  X  14 

168 

196 

224 

252 

280 

308 

336 

364 

392 

420 

14  X  14 

196 

229 

261 

294 

327 

359 

392 

425 

457 

490 

FRENCH  OR   METRIC   MEASURES. 

The  metric  unit  of  length  is  the  metre  =  39.37  inches. 
The  metric  unit  of  weight  is  the  gram  =  15.432  grains. 
The  following  prefixes  are  used  for  subdivisions  and  multiples;  Milli  =  TOVs 
Centi  =  Tfo,  Deci  =  &,  Deca  =  10,  Hecto  =  100,  Kilo  -  1000,  Myria  =  10,000. 

FRENCH   AND  RRITISH  (AND  AMERICAN) 
EQUIVALENT  MEASURES. 

Measures  of  Length. 

FRENCH.  BRITISH  and  U.  S. 

1  metre  —  39.37  inches,  or  3.28083  feet,  or  1.09361  yards. 

.3048  metre  =  1  foot. 

1  centimetre   =  .3937  inch. 
2,54  centimetres  =  1  inch. 

1  milimetre     =  .03937  inch,  or  1/25  inch,  nearly. 
25.4  millimetres  =  1  inch. 

1  kilometre     s=  1093,61  yards,  or  0,62137  mile. 


22  ARITHMETIC. 

Measures  of  Surface. 

FRENCH.  BRITISH. 

1  «nnarp  nipti-P  -   *  10-764  square  feet, 

1  square  uieti  -  }    i.i96  square  yards. 

.836  square  metre  =  1  square  yard. 

.0929  square  metre  =  1  square  foot. 

1  square  centimetre  =  .155  square  inch. 
6.452  square  centimetres  =  1  square  inch. 

1  square  millimetre    =  .00155  square  inch. 
645.2  square  millimetres  =  1  square  inch. 
1  centiare  =  1  sq.  metre  =  10.764  square  feet. 

1  are  =  1  sq.  decametre  =  1076.41      "          " 

1  hectare  =  100  ares  =  107641       "          "  =  2.4711  acres. 

1  sq.  kilometre  =  .386109  sq.  miles    =  247.11      " 

1  sq.  myriametre  =38.6109  "        " 

Of  Volume. 

FRENCH.  BRITISH  and  U.  S. 

1  oiihio  mptrp  -  j  35-314  cubic  feet, 

-  1    1.308  cubic  yards. 
.7645  cubic  metre  —  1  cubic  yard. 

.02832  cubic  metre  =  1  cubic  foot. 

1  piihip  dppimptrp     -  -J  61-°~3    cubic  inches, 

~  1     .0353  cubic  foot. 
28.32  cubic  decimetres    =  1  cubic  foot. 

1  cubic  centimetre  =  .061  cubic  inch. 
16.387  cubic  centimetres  =  1  cubic  inch. 
1  cubic  centimetre  =  1  millilitre  =      .061  cubic  inch. 
1  centilitre  =  =      .610     " 

1  decilitre  =  =    6.102      "" 

1  litre          =  1  cubic  decimetre  =  61.023      "        "       =  1.05671  quarts,  U.  S. 
1  hectolitre  or  decistere  =    3.314  cubic  feet     =    2.8375  bushels,  ** 

1  stere,  kilolitre,  or  cubic  metre  =    1.308  cubic  yards  =     28.37  bushels,  " 

Of  Capacity. 

FRENCH.  BRITISH  and  U.  S. 

f  61.023  cubic  inches, 

1  litre  (=  1  cubic  decimetre)  =  i  %£$£  fl°m'el,Can), 

[2.202  pounds  of  water  at  62°  F. 
28.317  litres  =  1  cubic  foot. 

4.543  litres  =  1  gallon  (British). 

3.785  litres  =  1  gallon  (American). 

Of  Weight. 

FRENCH.  BRITISH  and  U.  S. 

1  gramme  =  15.432  grains. 

.0648  gramme  =  1  grain. 

28.35  gramme  =  1  ounce  avoirdupois. 

1  kilogramme  =  2.2046  pounds. 

.4536  kilogramme  =  1  pound. 

1  tonne  or  metric  ton  =  j  •*%  <™f  ^  P°»nds> 
1000  kilogrammes  =  j  Ke  founds. 

'iolS  kilog^mmes  =  {  ] 

Mr.  O.  H.  Titmann,  in  Bulletin  No.  9  of  the  U.  S.  Coast  and  Geodetic  Sur- 
vey, discusses  the  work  of  various  authorities  who  have  compared  the  yard 
and  the  metre,  and  by  referring  all  the  observations  to  a  common  standard 
has  succeeded  in  reconciling  the  discrepancies  within  very  narrow  limits. 
The  following  are  his  results  for  the  number  of  inches  in  a  metre  according 
to  the  comparisons  of  the  authorities  named: 

1817.  Hassler .  39.36994  inches. 

1818.  Kater 39.36990 

1835.     Baily 39.36973 

1866.    Clarke 39.36970 

1885.    Comstock 39.36984 

The  mean  of  these  is.  ....... 


METRIC    WEIGHTS   AND   MEASURES,  23 

METRIC   CONVERSION  TABLES. 

The  following  tables,  with  the  subjoined  memoranda,  were  published  in 
1890  by  the  United  States  Coast  and  Geodetic  Survey,  office  of  standard 
weights  and  measures,  T.  C.  Mendenhall,  Superintendent. 

Tables  for  Converting  U,  S.  Weigltts  and  Measures— 
Customary  to  Metric* 

LINEAR. 


Inches  to  Milli- 
metres. 

Feet  to  Metres. 

Yards  to  Metres. 

Miles  to  Kilo- 
metres. 

1  _ 

25.4001 

0.304801 

0.914402 

1.60935 

0  _ 

50.8001 

0.609601 

1.828804 

3.21869 

3  = 

76.2002 

0.914402 

2.743205 

4.82804 

4  = 

101.6002 

1.219202 

3.657607 

6.43739 

5  = 

127.0003 

1.524003 

4.572009 

8.04674 

6  = 

152.4003 

1.828804 

5.486411 

9.65608 

177.8004 

2.133604 

6.400813 

11.26543 

8  n= 

203.2004 

2.438405 

7.315215 

12.87478 

9  = 

228.6005 

2.743205 

8.229616 

14.48412 

SQUARE. 


Square  Inches  to 
Square  Centi- 
metres. 

Square  Feet  to 
Square  Deci- 
metres. 

Square  Yards  to 
Square  Metres. 

Acres  to 
Hectares. 

1  = 

6.452 

9.290 

0.836 

0.4047 

12.903 

18.581 

1.672 

0.8094 

3  = 

19.355 

27.871 

2.508 

1.2141 

4  = 

25.807 

37.161 

3.344 

1.6187 

5  = 

32.258 

46.452 

4.181 

2.0234 

6  = 

38.710 

55.742 

5.017 

2.4281 

45.161 

65.032 

5.853 

2.8328 

8  = 

51.613 

74.323 

6.689 

3.2375 

9  = 

58.065 

83.613 

7.525 

3.6422 

CUBIC. 


Cubic  Inches  to 
Cubic  Centi- 
metres. 

Cubic  Feet  to 
Cubic  Metres. 

Cubic  Yards  to 
Cubic  Metres. 

Bushels  to 
Hectolitres. 

1  = 

16.387 

0.02832 

0.765 

0.35242 

32.774 

0.05663 

1.529 

0.70485 

3  = 

49.161 

0.08495 

2.294 

1.05727 

4  = 

65.549 

0.11327 

3.058 

1.40969 

5  = 

81.936 

0.14158 

3.823 

1.76211 

f>  

98.323 

0.16990 

4.587 

2.11454 

•j-  _. 

114.710 

0.19822 

5.352 

2.46696 

8  = 

131.097 

0.22654 

6.116 

2.819:% 

9  = 

147.484 

0.25485 

6.881 

3.17181 

ARITHMETIC. 
CAPACITY. 


Fluid  Drachms 

to  Mill  Hit  res  or 

Fluid  Ounces  to 

Quarts  to  Litres. 

Gallons  to  Litres. 

Cubic  Centi- 

Millilitres. 

metres. 

1  = 

3.70 

29.57 

0.94636 

3.78544 

2  = 

7.39 

59.15 

1.89272 

7  57088 

3  - 

11.09 

88.72 

2.83908 

11.35632 

4  = 

14.79 

118.30 

3.78544 

15.14176 

5  = 

18.48 

147.87 

4.73180 

18.92720 

6  = 

22.18 

177.44 

5.67816 

22.71264 

7  = 

25.88 

207.02 

6.62452 

26.49808 

0     

29.57 

236.59 

7  .  57088 

30.28352 

9  = 

33.28 

266.16 

8.51724 

34.06896 

WEIGHT. 


Grains  to  Milli- 
grammes. 

Avoirdupois 
Ounces  to 
Grammes. 

Avoirdupois 
Pounds  to  Kilo- 
grammes. 

Troy  Ounces  to 
Grammes. 

1  = 

64.7989 

28.3495 

0.45359 

31.10348 

2  = 

129.5978 

56.6991 

0.90719 

62.20696 

3  = 

194.3968 

85.0486 

1.36078 

93.31044 

4  = 

259.1957 

113.3981 

1.81437 

124.41392 

5  = 

323.9946 

141.7476 

2.26796 

155.51740 

6  = 

388.7935 

170.0972 

2.72156 

186.62089 

7  = 

453.5924 

198.4467 

3.17515 

217.72437 

8  — 

518.3914 

226.7962 

3.62874 

248.82785 

9  = 

583.1903 

255.1457 

4.08233 

279.93133 

1  chain               =  20.1169  metres. 

1  square  mile    =  259  hectares. 

1  fathom            =  1.829  metres. 

1  nautical  mile  =  1853.27  metres. 

1  foot                  =  0.304801  metre. 

1  avoir,  pound  =  453.5924277  gram. 

15432.35639  grains    =  1  kilogramme. 


Tables  for  Converting  U.  S.  Weights  and  Measures 
Metric  to  Customary. 

LINEAR. 


II  II  1!  II  II 

T-KNOO  TflO 

Metres  to 
Inches. 

Metres  to 
Feet. 

Metres  to 
Yards. 

Kilometres  to 
Miles. 

39.3700 
78.7400 
118.1100 
157.4800 
196.8500 

3.28083 
6.56167 
9.84250 
13.12333 
16.40417 

1.093611 
2.187222 
3.280833 
4.374444 

5.468056 

0.62137 
1.24274 

1  86411 
2.48548 
3.10685 

6  = 

7  = 

9  = 

236.2200 
275.5900 
314.9600 
354.3300 

19.68500 
22.96583 
26.24667 
29.52750 

6.561667 
7.  (555278 
8.748889 
9.842500 

3.72822 
4.34959 
4.97096 
5.59233 

METRIC   CONVERSION   TABLES.  25 

SQUARE. 


4  = 

5  = 

0.6200 
0.7750 

43.055 
53.819 

4.784 
5.980 

9.884 
12.355 

6  = 

7  = 

Q     

9  = 

0.9300 
1.0850 
1.2400 
1.3950 

64.583 
75.347 
86.111 
96.874 

7.176 
8.37'2 
9.568 
10.764 

14.826 
17.297 
19.768 
22.239 

CUBIC. 

Cubic  Centi- 
metres to  Cubic 
Inches. 

Cubic  Deci- 
metres to  Cubic 
Inches. 

Cubic  Metres  to 
Cubic  Feet. 

Cubic  Metres  to 
Cubic  Yards. 

CT  *.  CO  JC  "-•• 
II  II  II  II  II 

0.0610 
0.1220 
0.1831 
0.2441 
0.3051 

61.023 
122.047 
183.070 
244.093 
305.117 

35.314 
70.629 
105.943 
141.258 
176.572 

1.308 
2.616 
3.924 
5.232 
6.540 

6  = 

8  =r 

9  = 

0.3661 
0.4272 
0.4882 
0.5492 

366,140 
427.163 
488.187 
549.210 

211.887 
247.201 
282.516 
317.830 

7.848 
9.156 
10.464 
11.771 

CAPACITY. 


Millilitres  or 
Cubic  Centi- 
litres to  Fluid 
Drachms. 

Centilitres 
to  Fluid 
Ounces. 

Litres  to 
Quarts. 

Dekalitres 
to 
Gallons. 

Hektolitres 
to 
Bushels. 

1  = 

0.27 

0.338 

1.0567 

2.6417 

2.8375 

2  — 

0.54 

0.676 

2.1134 

5.2834 

5.6750 

3  = 

0.81 

1.014 

3.1700 

7.9251 

8,5125 

4  — 

1.08 

1.352 

4.2267 

10.5668 

11.3500 

5  = 

1.35 

1.691 

5.2834 

13.2085 

14.1875 

6  = 

1.62 

2.029 

6.3401 

15.8502 

17.0250 

7  = 

1.89 

2.368 

7.3968 

18.4919 

19.8625 

8  = 

2.16 

2.706 

8.4534 

21.1336 

22.7000 

9  = 

2.43 

3.043 

9.5101 

23.7753 

25.5375 

ARITHMETIC. 
WEIGHT. 


Milligrammes 
to  Grains. 

Kilogrammes 
to  Grains. 

Hectogrammes 
(100  grammes) 
to  Ounces  Av. 

Kilogrammes 
to  Pounds 
Avoirdupois. 

1  = 

3  = 
4  = 

r>  — 

0.01543 
0.03086 
0.04630 
0.06173 
0.07710 

15432.36 
30864.71 
46297.07 
61729.43 

77161.78 

3,5274 
7.0548 
10.5822 
14.1096 
17.6370 

2.20462 
4.409-24 
6.61386 
8.81849 
Jl.  03811 

0  — 

s  — 

0.09259 
0.10803 
0.12346 
0.13889 

92594.14 
108026.49 
123458.85 
138891.21 

21.1644 
24.6918 
28.2192 
31.7466 

13.22773 
15.43-235 
17.63697 
19.84159 

WEIGHT— (Continued). 


Quintals  to 
Pounds  Av. 

Milliers  or  Tonnes  to 
Pounds  Av. 

Grammes  to  Ounces, 
Troy. 

1  = 

220.46 

2204  6 

0.03215 

2  = 

440.92 

4409.2 

0.06430 

3  = 

661.38 

6613  8 

0.09645 

4  = 

881.84 

8818.4 

0.12860 

5  = 

1102.30 

11023.0 

0.16075 

6  = 

1322.76 

132-27  6 

0.19290 

7  — 

1543.22 

15432.2 

0.22505 

8  — 

1763  68 

17636.8 

0.25721 

9  = 

1984.14 

19841.4 

0.28936 

The  only  authorized  material  standard  of  customary  length  is  the 
Troughton  scale  belonging  to  this  office,  whose  length  at  59°. 62  Fahr.  con- 
forms to  the  British  standard.  The  yard  in  use  in  the  United  States  is  there- 
fore equal  to  the  British  yard. 

The  only  authorized  material  standard  of  customary  weight  is  the  Troy 
pound  of  the  mint.  It  is  of  brass  of  unknown  density,  and  therefore  not 
suitable  for  a  standard  of  mass.  It  was  derived  from  'the  British  standard 
Troy  pound  of  1758  by  direct  comparison.  The  British  Avoirdupois  pound 
was  also  derived  from  the  latter,  and  contains  7000  grains  Troy. 

The  grain  Troy  is  therefore  the  same  as  the  grain  Avoirdupois,  and  the 
pound  Avoirdupois  in  use  in  the  United  States  is  equal  to  the  British  pound 
Avoirdupois. 

The  metric  system  was  legalized  in  the  United  States  in  1866. 

By  the  concurrent  action  of  the  principal  governments  of  the  world  an 
International  Bureau  of  Weights  and  Measures  has  been  established  near 
Paris. 

The  International  Standard  Metre  is  derived  from  the  Metre  des  Archives, 
and  its  length  is  defined  by  the  distance  between  two  lines  at  0°  Centigrade, 
on  a  platinum-iridium  bar  deposited  at  the  International  Bureau. 

The  International  Standard  Kilogramme  is  a  mass  of  platinum-iridium 
deposited  at  the  same  place,  and  its  weight  in  vacua  is  the  same  as  that  of 
i  he  Kilogramme  des  Archives. 

Copies  of  these  international  standards  are  deposited  in  the  office  of 
standard  weights  and  measures  of  the  U.  S.  Coast  and  Geodetic  Survey. 

The  litre  is  equal  to  a  cubic  decimetre  of  water,  and  it  is  measured  by  the 

auantity  of  distilled  water  which,  at  its  maximum  density,  will  counterpoise 
le  standard  kilogramme  in  a  vacuum;  the  volume  of  such  a  quantity  of 
water  being,  as  nearly  as  has  been  ascertained,  equal  to  a  cubic  decimetre. 


WEIGHTS  AKB   MEASURES — COMPOUKD   UNITS.       27 

COMPOUND    UNITS. 

Measures  of  Pressure  and  Weight. 

f  144  Ibs.  per  square  foot. 

2.0355  ins.  of  mercury  at  32°  F. 

1  Ib.  per  square  inch.  = -{       2.0416"      "       "          "  62°  F. 

2.309  ft.  of  water  at  62°  F. 

[     27.71  ins.  "       "      "  62°  F. 

f  2116.3  Ibs.  per  square  foot. 

I     33.947  ft.  of  water  at  62°  F. 
1  atmosphere  (14.7  Ibs.  per  sq.  in.).  -  •{  80  ins.  of  mercury  at  62°  F. 

|      29.922  ins.  of  mercury  at  32°  F. 

1.760  millimetres  of  mercury  at  32°  F. 


(     .0361  Ib.  per  square  inch. 
=s«    5.196  Ibs.    "        "        foot. 
/     .0736  in.  of  mercury  at  62°  F. 


1  inch  of  water  at  62°  F. 

ury  £ 

1  inr-h  of  water  at  ^2°  F  -  •!    5-20§1  }bs-  Per  square  foot. 

-j     .036  125  Ibs.  per   "       inch. 

(  .433  Ib.  per  square  inch. 
1  foot  of  water  at  62°  F.  =•<  62.355  ll>s.  4i  "  foot. 

f     .883  in.  of  mercury  at  62°  F. 

f  .49  Ib.  per  square  inch. 
.  inch  of  mercury  at  6-  F.  =  |  ™;»»»;  of  wa^  «£  p 

I  13  58  ins.    "         •'       tl  62°  F. 

Weight  of  One  C'ubic  Foot  of  Pure  Water. 

At  32°  F.  (freezing-point)  ............................  62.418  Ibs. 

"    39.1°  F.  (maximum  density)  ..........   ............  62.425  " 

"    62°  F.  (standard  temperature)  .....................  62.355   " 

44    212°  F.  (boiling-point,  under  1  atmosphere)  ........  59.76     " 

American  gallon  =  231     cubic  ins,  of  water  at  62°  F.  =  8.3356  Ibs. 

British  =  277.274  k'        "     "      "        "      "        =  10  Ibs. 

Measures  of  Work,    Power,    and   Duty. 

Work.—  The  sustained  exertion  of  pressure  through  space. 

Unit  of  work.—  One  foot-pound,  i.e.,  a  pressure  of  one  pound  exerted 
through  a  space  of  one  foot. 

Horse-power.—  The  rate  of  work.  Unit  of  horse-power  =  33,000ft.- 
Ibs.  per  minute,  or  550  ft.-lbs.  per  second  -  1,980,000  ft.  -Ibs.  per  hour. 

Heat  unit  =  heat  required  to  raise  1  Ib.  of  water  1°  F.  (from  39°  to  40°) 

33000 

Horse-power  expressed  in  heat  units  =  -^5-  =  42.416  heat  units  per  min- 

i  /o 

ute  =  .707  heat  unit  per  second  =  2545  heat  units  per  hour. 
,  U,  of  fuel  per  H.  P.  per  hou,.=  S 


1,000,000  ft.-lbs.  per  Ib.  of  fuel  =  1.98  Ibs.  of  fuel  per  H.  P.  per  hour. 

5280       22 
Velocity.—  Feet  per  second  =  —  ^  =  —  x  miles  per  hour. 

Gross   tons    per    mile  =  g—  =  —  Ibs.  per  yard  (single  rail.) 

French  and  British  Equivalents  of  Weight   and   Press- 
ure per  Unit  of  Area. 

FRENCH.  BRITISH. 

1  gramme  per  square  millimetre  =       1.422  Ibs.  per  square  inch. 

1  kilogramme  per  square  "  =1422.32     "      "        " 

1  "          "       centimetre  =      14.223    "      '*        'k          " 

1.0335  kilogrammes  per  square  centimetre  I          14r,       lt      lt        lc          u 

(1  atmosphere)  l" 

0.070308  kilogramme  per  square  centimetre  =  1  Ib.  per  square  inch. 


ARITHMETIC. 


WIRE    AND    SHEET-METAL,    GAUGES    COMPAREB. 


Number  of 
Gauge. 

Birmingham 
Wire  Gauge. 

American  or 
Brown  and 
Sharpe  Gauge. 

Roebling's  and 
Washburn 
&  Moen's 
Gauge. 

Trenton  Iron 
Co.'s  Wire 
Gauge. 

British  Imperial 
Standard 
Wire  Gauge. 
(Legal  Standard 
in  Great  Britain 
since 
March  1,  1884.) 

U.  S.  Standard 
Gauge  for 
Sheet  and  Plate 
Iron  and  Steel. 
(Legal  Standard 
since  July  1,  1893  ) 

inch. 

inch. 

inch. 

inch. 

inch. 

millim. 

inch. 

0000000 

.49 

.500 

12.7 

.5 

000000 

.46 

.464 

11.78 

.469 

00000 

.43 

.45 

.432 

10.97 

.438 

0000 

.454 

.46 

.393 

.40 

.4 

10.16 

.406 

000 

.425 

.40964 

.362 

.36 

.372 

9.45 

.375 

00 

.38 

.3648 

.331 

.33 

.348 

8.84 

.344 

0 

.34 

.32486 

.307 

.305 

.324 

8.23 

.313 

1 

.3 

.2893 

.283 

.285 

.3 

7.62 

.281 

2 

.284 

.25763 

.263 

.265 

.276 

7.01 

.266 

3 

.259 

.22942 

.244 

.245 

.252 

6.4 

.25 

4 

.238 

.20431 

.225 

.225 

.232 

5.89 

.234 

5 

.22 

.18194 

.207 

.205 

.212 

5.38 

.219 

6 

.203 

.16202 

.192 

.19 

.192 

4.88 

.203 

r- 

.18 

.14428 

.177 

.175 

.176 

4.47 

.188 

8 

.165 

.12849 

.162 

.16 

.16 

4.06 

.172 

9 

.148 

.11443 

.148 

.145 

.144 

3-66 

.156 

10 

.134 

.10189 

.135 

.13 

.128 

3.26 

.141 

11 

.12 

.09074 

.12 

.1175 

.116 

2.95 

.125 

12 

.109 

.08081 

.105 

.105 

.104 

2-64 

.109 

13 

.095 

.07196 

.092 

.0925 

.092 

2-34 

.094 

14 

.083 

.06408 

.08 

.08 

.08 

2-03 

.078 

15 

.072 

.05707 

.072 

.07 

.072 

1.83 

.07 

16 

.065 

.05082 

.063 

.061 

.064 

1.63 

.0625 

17 

.058 

.04526 

.054 

.0525 

.056 

1.42 

.0563 

18 

.049 

.0403 

.047 

.045 

.048 

1.22 

.05 

19 

.042 

.03589 

.041 

.04 

.04 

1.01 

.0438 

20 

.035 

.03196 

.035 

.035 

.036 

.91 

.0375 

21 

.032 

.02846 

.032 

.031 

.032 

.81 

.0344 

22 

.028 

.02535 

.028 

.028 

.028 

.71 

.0313 

23 

.025 

.02257 

.025 

.025 

.024 

.61 

.0281 

24 

.022 

.0201 

.023 

.0225 

.022 

.56 

.025 

25 

.02 

.0179 

.02 

.02 

.02 

.51 

.0219 

26 

.018 

.01594 

.018 

.018 

.018 

.45 

.0188 

27 

.016 

.01419 

.017 

.017 

.0164 

.42 

.0172 

28 

.014 

.01264 

.016 

.016 

.0148 

.38 

.0156 

29 

.013 

.01126 

.015 

.015 

.0136 

.35 

.0141 

30 

.012 

.01002 

.014 

.014 

.0124 

.31 

.0125 

31 

.01 

.00893 

.0135 

.013 

.0116 

29 

.0109 

m 

.009 

.00795 

.013 

.012 

.0108 

!27 

.0101 

33 

.008 

.00708 

.011 

.011 

.01 

.25 

.0094 

34 

.007 

.0063 

.01 

.01 

.0092 

.23 

.0086 

35 

.005 

.00561 

.0095 

.0095 

.0084 

.21 

.0078 

36 

004 

.005 

.009 

.009 

.0076 

.19 

.007 

37 

.00445 

.0085 

.0085 

.0068 

.17 

.0066 

38 

.00396 

.008 

.008 

.006 

.15 

.0063 

39 

.00353 

.0075 

.0075 

.0052 

.13 

40 

.00314 

.007 

.007 

.0048 

.12 

41 

.0044 

.11 

42 

.004 

.10 

43 

.0036 

.09 

44 

.0032 

.08 

45 

.0028 

.07 

46 

.0024 

.06 

47 

.002 

.05 

48 

,0016 

.04 

4f 

.0012 

.03 

50 

.001 

.025 

1 

I 

WIRE    GAUGE   TABLES. 


EDISON,   OR  CIRCULAR   JUIL   GAUGE,    FOR   ELEC- 
TRICAL  WIRES. 


Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter 
in  Mils. 

Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter 
in  Mils. 

Gauge 
Num- 
ber. 

Circular 
Mils. 

Diam- 
eter 
in  Mils. 

3 

3,000 

54.78 

70 

70,000 

264.58 

190 

190,000 

435.89 

5 

5,000 

70.72 

75 

75,000 

273.87 

200 

200,000 

447.22 

8 

8,000 

89.45 

80 

80,000 

282.85 

220 

220,000 

469.05 

1'2 

12,000 

109.55 

85 

85,000 

291.55 

240 

240.000 

489.90 

15 

15,000 

122.48 

90 

90,000 

300.00 

260 

260,000 

509.91 

20 

20,000 

141.43 

95 

95,000 

308.23 

280 

280,000 

529.16 

25 

25,000 

158.12 

100 

100,000 

316.23 

300 

300,000 

547.73 

30 

30,000 

173.21 

110 

110,000 

331.67 

320 

320,000 

565.69 

35 

35,000 

187.09 

120 

120,000 

346.42 

340 

340,000 

583.10 

40 

40,000 

200.00 

130 

130,000 

360.56 

360 

360,000 

600.00 

45 

45,000 

212.14 

140 

140,000 

374.17 

50 

50,000 

223.61 

150 

150,000 

387.30 

55 

55,000 

234.53 

160 

160.000 

400.00 

60 

60,000 

244.95 

170 

170.000 

412.32 

65 

65,000 

254.96 

180 

180,000 

424.27 

TWIST  DRILL   AND  STEEL   WIRE  GAUGE. 

(Morse  Twist  Drill  and  Machine  Co.) 


No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

inch. 

inch. 

inch. 

inch. 

1 

.2280 

16 

.1770 

31 

.1200 

46 

.0810 

2 

.2210 

17 

.1730 

32 

.1160 

47 

.0785 

3 

.2130 

18 

.1695 

33 

.1130 

48 

.0760 

4 

.2090 

19 

.1660 

34 

.1110 

49 

.0730 

5 

.2055 

20 

.1610 

35 

.1100 

50 

.0700 

6 

.2040 

21 

.1590 

36 

.1065 

51 

.0670 

7 

.2010 

22 

.1570 

37 

.1040 

52 

.0635 

8 

.1990 

23 

.1540 

38 

.1015 

53 

.0595 

9 

.1960 

24 

.1520 

39 

.0995 

54 

.0550 

10 

.1935 

25 

.1495 

40 

.0980 

55 

.0520 

11 

.1910 

26 

.1470 

41 

.0960 

56 

.0465 

12 

.1890 

27 

.1440 

42 

.0935 

57 

.0430 

13 

.1850 

28 

.1405 

43 

.0890 

58 

.0420 

14 

.1820 

29 

.1360 

44 

.0860 

59 

.0410  . 

15 

.1800 

30 

.1285 

45 

.0820 

60 

.0400 

STEEL   MUSIC-WIRE   GAUGE. 

(Washburn  &  Moen  Mfg.  Co.) 


No. 

Size. 

No. 

Size. 

No. 

Size. 

No. 

Size. 

inch. 

inch. 

inch. 

inch. 

12 

.0295 

17 

.0378 

21 

.0461 

25 

.0585 

13 

.0311 

18 

.0395 

22 

.0481 

26 

.0626 

14 

.0325 

19 

.0414 

23 

.0506 

27 

.0663 

15 

.0313 

20 

.043 

24 

.0547 

28 

.0719 

16 

.0359 

30  ARITHMETIC. 

Till;   EDISON   OR  CIRCULAR   Mil,   WIRE  GAUGE. 

(For  table  of  copper  wires  by  this^gauge,  giving  weights,  electrical  resist- 
ances, etc.,  see  Copper  Wire.) 

Mr.  C.  J.  Field  (Stevens  Indicator,  July,  1887)  thus  describes  the  origin  of 
the  Edison  gauge: 

The  Edison  company  experienced  inconvenience  and  loss  by  not  having  a 
wide  enough  range  nor  sufficient  number  of  sizes  in  the  existing  gauges. 
This  was  felt  more  particularly  in  the  central-station  work  in  making 
electrical  determinations  for  the  street  system.  They  were  compelled  to 
make  use  of  two  of  the  existing  gauges  at  least,  thereby  introducing  a 
complication  that  was  liable  to  lead  to  mistakes  by  the  contractors  and 
linemen. 

In  the  incandescent  system  an  even  distribution  throughout  the  entire 
system  and  a  uniform  pressure  at  the  point  of  delivery  are  obtained  by  cal- 
culating for  a  given  maximum  percentage  of  loss  from  the  potential  ns 
delivered  from  the  dynamo.  In  carrying  this  out,  on  account  of  lack  of 
regular  sizes,  it  was  often  necessary  to  use  larger  sizes  than  the  occasion 
demanded,  and  even  to  assume  new  sizes  for  large  underground  conductors. 
It  was  also  found  that  nearly  all  manufacturers  based  their  calculation  for 
the  conductivity  of  their  wire  on  a  variety  of  units,  and  that  not  one  used 
the  latest  unit  as  adopted  by  the  British  Association  and  determined  from 
Dr.  Matthiesseu's  experiments  ;  and  as  this  was  the  unit  employed  in  the 
manufacture  of  the  Edison  lamps,  there  was  a  further  reason  for  construct- 
ing a  new  gauge.  The  engineering  department  of  the  Edison  company, 
knowing  the  requirements,  have  designed  a  gauge  that  has  the  widest 
range  obtainable  and  a  large  number  of  sizes  which  increase  in  a  regular 
and  uniform  manner.  The  basis  of  the  graduation  is  the  sectional  area,  and 
the  number  of  the  wire  corresponds.  A  wire  of  100,000  circular  mils  area  is 
No.  100  ;  a  wire  of  one  half  the  size  will  be  No.  50  ;  twice  the  size  No.  200. 

In  the  older  gauges,  as  the  number  increased  the  size  decreased.  With 
this  gauge,  however,  the  number  increases  with  the  wire,  and  the  number 
multiplied  by  1000  will  give  the  circular  mils. 

The  weight  per  mil-foot,  0.00000302705  pounds,  agrees  with  a  specific 
gravity  of  8.889,  which  is  the  latest  figure  given  for  copper.  The  ampere 
capacity  which  is  given  was  deduced  from  experiments  made  in  the  com- 
pany's laboratory,  and  is  based  on  a  rise  of  temperature  of  50°  F.  in  the  wire. 

In  1893  Mr.  Field  writes,  concerning  gauges  in  use  by  electrical  engineers: 

The  B.  and  S.  gauge  seems  to  be  in  general  use  for  the  smaller  sizes,  up 
to  100,000  c.  m..  and  in  some  cases  a  little  larger.  From  between  one  and 
two  hundred  thousand  circular  mils  upwards,  the  Edison  gauge  or  its 
equivalent  is  practically  in  use,  and  there  is  a  general  tendency  to  designate 
all  sizes  above  this  in  circular  mils,  specifying  a  wire  as  200,000,  400,000,  500,- 
000,  or  1,000,000  c.  m. 

In  the  electrical  business  there  is  a  large  use  of  copper  wire  arid  rod  and 
other  materials  of  these  large  sizes,  and  in  ordering  them,  speaking  of  them, 
specifying,  and  in  every  other  use,  the  general  method  is  to  simply  specify 
the  circular  milage.  I  think  it  is  going  to  be  the  only  system  in  the  future 
for  the  designation  of  wires,  and  the  attaining  of  it  means  practically  the 
adoption  of  the  Edison  gauge  or  the  method  and  basis  of  this  gauge  as  the 
correct  one  for  wire  sizes. 

THE  U.   S.   STANDARD  GAUGE   FOR  SHEET  AND 

PLATE  IRON  AND  STEEI,,  1893. 

The  Committee  on  Coinage,  WTeights,  and  Measures  of  the  House  of 
Representatives  in  1893,  in  introducing  the  bill  establishing  the  new  sheet 
and  plate  gauge,  made  a  report  from  which  we  take  the  following  : 

The  purpose  of  this  bill  is  to  establish  an  authoritative  standard  gauge  for 
the  measurement  of  sheet  and  plate  iron. 

There  is  in  this  country  no  uniform  or  standard  gauge,  and  the  same 
numbers  in  different  gauges  represent  different  thicknesses  of  sheets  or 
plates.  This  has  given  rise  to  much  misunderstanding  and  friction  between 
employers  and  workmen  and  mistakes  and  fraud  between  dealers  and  con- 
sumers. 

The  practice  of  describing  the  different  thicknesses  of  sheet  and  plate 
iron  by  gauge  numbers  has  been  so  long  established  and  become  so  uni- 
versal both  here  and  in  Great  Britain  that  it  is  not  deemed  advisable  to 
change  this  mode  of  designation;  but  these  descriptive  gauge  numbers 


GAUUK    FOR   SHEET    AND    PLATE    IRON    AND    STEEL.    31 


U.   S.   STANDARD   GAUGE   FOR   SHEET  AND  PLATE 

IRON   AND   STEEL,    1893. 


o 

If 

I3 

Approximate 
Thickness  in 
Fractions  of 
an  Inch. 

j  Approximate 
Thickness  in 
Decimal 
Parts  of  an 
Inch. 

Approximate 
Thickness 
in 
Millimeters. 

Weight  per 
Square  Foot 
in  Ounces 
Avoirdupois. 

Weight  pei- 
Square  Foot 
in  Pounds 
Avoirdupois. 

%l 

•*  £  § 

Weight  per 
Square  Meter 
in  Kilograms. 

Weight  pei- 
Square  Meter 
in  Pounds 
Avoirdupois,  i 

0000000 

1-2 

0.5 

12  7 

320 

20. 

9.072 

97.65 

215.28 

000000 

15-32 

0.46875 

11.90625 

300 

18.75 

8.505 

91.55 

201.82 

00000 

7-16 

0.4375 

11.1125 

280 

17.50 

7.938 

85  44 

188.37 

0000 

13-32 

0.40625 

10.31875 

260 

16.25 

7.371 

79.33 

174.91 

000 

3-8 

0.375 

9.525 

240 

15. 

6.804 

73.24 

161.46 

00. 

11-32 

0.34375 

8.73125 

220 

13.75 

6.237 

67.13 

148.00 

0 

5-16 

0.3125 

7.9375 

200 

12.50 

5.67 

61.03 

134.55 

1 

9-32 

0.28125 

7.14375 

180 

11.25 

5.103 

54.93 

121.09 

2 

17-64 

0.265625 

6.746875 

170 

10.625 

4.819 

51.88 

114.37 

3 

1-4 

0.25 

6.35 

160 

10. 

4.536 

48.82 

107.64 

4 

15-64 

0.234375 

5.953125 

150 

9.375 

4.252 

45.77 

100.91 

5 

7-32 

0.21875 

5.55625 

140 

8.75 

3.969 

42.72 

94.18 

6 

13-64 

0.203125 

5.159375 

130 

8.125 

3.685 

39.67 

87.45 

7 

3-15 

0.1875 

4.7625 

120 

7.5 

3.402 

36.62 

80.72 

8 

11-64 

0.171875 

4.365625 

110 

6.875 

3.118 

33.57 

74.00 

•  9 

5-32 

0.156-25 

3.98875 

100 

6.25 

2.835 

30.52 

67.27 

10 

9-64 

0.140625 

3.571875 

90 

5.625 

2.552 

27.46 

60.55 

11 

1-8 

0.125 

3.175 

80 

5. 

2.268 

24.41 

53.82 

12 

7-64 

0.109375 

2.778125 

70 

4.375 

1.984 

21.36 

47.09 

13 

3-32 

0.09375 

2.38125 

60 

3.75 

1.701 

18.31 

40.36 

14 

5-64 

0.078125 

1.984375 

50 

3.125 

1.417 

15.26 

33.64 

15 

9-128 

0.0703125 

1.7859375 

45 

2.8125 

1.276 

13.73 

30.27 

16 

1-16 

0.0625 

1.5875 

40 

2.5 

1.134 

12.21 

26.91 

17 

9-160 

0.05625 

1.42875 

36 

2.25 

1.021 

10.99 

24.22 

18 

1-20 

0.05 

1.27 

32 

2 

0.9072 

9.765 

21.53 

19 

7-160 

0.04375 

1.11125 

28 

.75 

0.7938 

8.544 

18.84 

20 

3-80 

0.0375 

0.9525 

24 

.50 

0.6804 

7.324 

16.15 

21 

11-320 

0.034375 

0.873125 

22 

.375 

0.6237 

6.713 

14.80 

22 

1-32 

0.03125 

0.793750 

20 

.25 

0.567 

6.103 

13.46 

23 

8-320 

0.0281-25 

0.714375 

18 

.125 

0.5103 

5.493 

12.11 

24 

1-40 

0.025 

0.635 

16 

1. 

0.4536 

4.882 

10.76 

25 

7-320 

0.021875 

0.555625 

14 

0.875 

0.3969 

4.272 

9.42 

26 

3-160 

0.0187'5 

0.47625 

12 

0.75 

0.3402 

3.662 

8.07 

27 

11-640 

0.0171875 

0.4365625 

11 

0.6875 

0.3119 

3.357 

7.40 

28 

1-64 

0.015625 

0.396875 

10 

0.625 

0.2835 

3.052 

6.73 

29 

9-640 

0.0140625 

0.3571875 

9 

0.5625 

0.2551 

2.746 

6.05 

30 

1-80 

0.0125 

0.3175 

8 

0.5 

0.2268 

2.441 

5  38 

31 

7-640 

0.0109375 

0.2778125 

7 

0.4375 

0.1984 

2.136 

4.71 

32 

13-1280 

0.01015625 

0.25796875 

gi^ 

0.40625 

0.1843 

1.983 

4.37 

33 

3-320 

0.009375 

0.238125 

6 

0.375 

0.1701 

1.831 

4.04 

34 

11-1280 

0.00859375 

0.21828125 

fyS 

0.34375 

0.1559 

1.678 

3  70 

35 

5-640 

0.0078125 

0.1984375 

5  ~ 

0.3125 

0.1417 

1.526 

3  36 

36 

9-1280 

0.00703125 

0.17859375 

41^ 

0.28125 

0.1276 

1.373 

3.03 

37 

17-2560 

0.006640625 

0.168671875 

414 

0.265625 

0.1205 

1.297 

2.87 

38 

1-160 

0.00625 

0.15875 

4 

0.25 

0.1134! 

1.221 

2.69 

32  MATHEMATICS. 

ought  to  have  the  same  meaning  and  significance  at  all  times  and  under  all 
circumstances. 

To  accomplish  this  and  furnish  a  legal  guide  in  the  collection  of  govern- 
ment duties,  the  United  States  should  establish  a  legal  standard  gauge. 
None  of  the  existing  gauge-tables  or  scales  exactly  meet  the  requirements 
of  accuracy  and  convenience,  nor  rest  on  a  systematic  basis;  but  the  one 
submitted  by  your  committee  is  believed  to  fully  meet  these  requirements. 

It  is  based  on  the  fact  that  a  cubic  foot  of  iron  weighs  480  pounds.  This 
is  the  same  basis  on  which  the  Imperial  gauge  of  Great  Britain  rests,  and 
also  the  New  Birmingham  and  Amalgamated  Association  gauges. 

A  sheet  of  iron  1  foot  square  and  1  inch  thick  weighs  40  pounds,  or  640 
ounces,  and  1  ounce  in  weight  should  be  1/640  inch  thick.  The  scale  has  been 
arranged  so  that  each  descriptive  number  represents  a  certain  number  of 
ounces  in  weight,  and  an  equal  number  of  six  hundred  and  fortieths  of  an 
inch  in  thickness,  and  the  weights,  and  hence  the  thicknesses,  have  been 
arranged  in  a  regular  series  of  gradations.  A  micrometer  for  measuring 
the  thickness  of  sheets  and  plates  can  be  constructed  to  indicate  six  hun- 
dred and  fortieths  of  an  inch  as  easily  as  one  thousandths,  and  thus  the 
measurement  of  a  sheet  of  iron  will  give  the  thickness  in  six  hundred  and 
fortieths  of  an  inch  and  in  weight  in  ounces  at  the  same  time. 

It  is  probable  that  the  adoption  of  this  gauge  will  gradually  lead  to  the 
abandonment  of  the  numbers  and  to  the  use  of  the  number  of  ounces  in 
weight  per  square  foot  as  the  descriptive  terms  of  the  different  thicknesses 
of  sheet  and  plate  iron.  It  will  become  as  easy  to  order  a  20-ounce  sheet  as 
a  No.  22,  or  a  10  ounce  as  a  No.  28;  and  this  will  cause  a  more  general  and 
intelligent  comprehension  of  just  what  is  being  contracted  for,  and  the 
opportunity  for  mistake  or  fraud  growing  out  of  an  uncertainty  of  designa- 
tion will  be  removed. 

A  natural  consequence  also  will  be  the  substitution  of  such  weight  desig- 
nation for  the  arbitrary  methods  now  in  vogue  of  describing  tin  and  terne 
plates  as  1C,  IX,  IXX,  DC,  DX,  etc. 

The  law  establishing  the  new  gauge  enacts  as  follows  : 

That  for  the  purpose  of  securing  uniformity,  the  following  is  established 
as  the  only  standard  gauge  for  sheet  and  plate  iron  and  steel  in  the  United 
States  of  America,  namely  : 

And  on  and  after  July 'l,  1893,  the  same  and  no  other  shall  be  used  in 
determining  duties  and  taxes  levied  by  the  United  States  of  America  on 
sheet  and  plate  iron  and  steel. 

SEC.  2.  That  the  Secretary  of  the  Treasury  is  authorized  and  required  to 
prepare  suitable  standards  in  accordance  herewith. 

SEC.  3.  That  in  the  practical  use  and  application  of  the  standard  gauge 
hereby  established  a  variation  of  2^j  per  cent  either  way  may  be  allowed. 


ALGEBRA.  33 


ALGEBRA. 

Addition.— Add  a  and  b.    Ans.  a-\-b.    Add  a,  6,  and —c.   Ans.  a-\-b  —  c. 

Add  2(i-  and  —  3a.     Ans.  —  a.    Add  2a6,  —  3a6,  —  c,  —  3c.    Ans.  —  ab  —  4c. 

Subtraction. — Subtract  a  from  6.  Ans.  6  —  a.  Subtract  —  a  from  —  b. 
Ans.  —  6  -f-  a. 

Subtract  6  +  c  from  a.  Ans.  a  -  b  -  c.  Subtract  3a26-  9c  from  4a26  +  c. 
Ans.  a26  4-  lOc.  RULE:  Change  the  signs  of  the  subtrahend  and  proceed  as 
in  addition. 

Multiplication,— Multiply  a  by  b.  Ans.  ab.  Multiply  ab  bya-\-b. 
Ans.  a26-f  ab2. 

Multiply  a  -f  6  by  a  +  b.    Ans.  (a  +  6)(a  +  6)  =  a2  4-  2a6  +  62. 

Multiply  —  a  by  —  6.  Ans.  ab.  Multiply  -  a  by  b.  Ans.  —  a6.  Like 
signs  give  plus,  unlike  signs  minus. 

Powers  of  numbers.— The  product  of  two  or  more  powers  of  any 
number  is  the  number  with  an  exponent  equal  to  the  sum  of  the  powers: 
a2  x  a3  =  a5 ;  a262  x  ab  =  a363 ;  -  Tab  x  2ac  =  -  14  a26c. 

To  multiply  a  polynomial  by  a  monomial,  multiply  each  term  of  the  poly- 
nomial by  the  monomial  and  add  the  partial  products:  (6a  —  36)  x  3c  =  18ac 
-  36c. 

To  multiply  two  polynomials,  multiply  each  term  of  one  factor  by  each 
term  of  the  other  and  add  the  partial  products:  (5a  —  66)  x  (3a  —  46)  = 
15a2  -  38a6  4-  2462. 

The  square  of  the  sum  of  two  numbers  =  sum  of  their  squares  -\-  twice 
their  product. 

The  square  of  the  difference  of  two  numbers  =  the  sum  of  their  squares 
—  twice  their  product. 

The  product  of  the  sum  and  difference  of  two  numbers  =  the  difference 
of  their  squares: 

(a  4- 6)2  =  a24-2a64-62;     (a  -  6)2  =  a-2a64-62; 
(a 4-6)  x  (a-  6)  =  a2  -  62. 

The  square  of  half  the  sums  of  two  quantities  is  equal  to  their  product  plus 
the  square  of  half  their  difference:  (^  ~t  J  =  ab  4-  (^ — r> —  ) 

The  square  of  the  sum  of  two  quantities  is  equal  to  four  times  their  prod- 
ucts, plus  the  square  of  their  difference:  (a  4  6)2  —  4a6  4-  («  —  &)8 

The  sum  of  the  squares  of  two  quantities  equals  twice  their  product,  plus 
the  square  of  their  difference:  a2  -+-  62  =  2a6  -f-  (a  —  6)2. 

The  square  of  a  trinomial  =  the  square  of  each  term  +  twice  the  product 
of  each  term  by  each  of  the  terms  that  follow  it:  (a  4-6  -fc)2  =  a2  4~&2  + 
c2  -4-  2a&  4-  2ac  4-  26c;  (a  -  b  -  c)2  =  a2  4-  62  4-  c2  -  2ab  -  2ac  +  2bc. 

The  square  of  (any  number  4-  Jg)  =  square  of  the  number  4-  the  number 
-f  14;  =  the  number  X  (the  number  4- 1)  4-  Ml 
(a  +  ^)2  =  a24-a4-M1  =«(a+l)  +  M-    (4}4)2=42 4-44-^=4  X  6  +  14  =  20^. 

The  product  of  any  number  4-  Yz  by  any  other  number  -\-^  =  product  of 
the  numbers -f  half  their  sum  +14.  (a  +  Y2)  X  6  +  ^)  =  «64-  ^(« -f  6)+  J£. 
4i/3  X  61^  =  4  X  6  4-  U(4  +  6)  4-  A4  =  24  4-  5  +  M  =  29^. 

Square,  cube,  4th  power,  etc.,  of  a  binomial  a  4  »• 

(a  4-  6)2  =  a2  -f-  2a6  4-62 ;    (a  4-  6)3  =  a?  -f  3a26  4  3a62  4-  63 ; 
(a  4.  ft)4  =  a4  4. 4as&  4.  6a2{>2  4-  4aft3  ^_  54. 

In  each  case  the  number  of  terms  is  one  greater  than  the  exponent  of 
the  power  to  which  the  binomial  is  raised. 

2.  In  the  first  term  the  exponent  of  a  is  the  same  as  the  exponent  of  the 
power  to  which  the  binomial  is  raised,  and  it  decreases  by  1  in  each  succeed- 
ing term. 

3.  6  appears  in  the  second  term  with  the  exponent  1,  and  its  exponent 
increases  by  1  in  each  succeeding  term. 

4.  The  coefficient  of  the  first  term  is  1. 

5.  The  coefficient  of  the  second  term  is  the  exponent  of  the  power  to 
which  the  binomial  is  raised. 

6.  The  coefficient  of  each  succeeding  term  is  found  from  the  next  pre- 
ceding term  by  multiplying  its  coefficient  by  the  exponent  of  a,  and  divto- 
ing  the  product  by  a  number  greater  by  1  than  the  exponent  of  6.    (See 
Binomial  Theorem,  below,) 


34  ALGEBRA. 

Parentheses.— When  a  parenthesis  is  preceded  by  a  plus  sign  it  rimy  be 
removed  without  changing  the  value  of  the  expression:  a  -f  b  -f  (a  -f  b)  — 
2a  -)-  2b.  When  a  parenthesis  is  preceded  by  a  minus  sign  it  may  be  removed 
if  we  change  the  signs  of  all  the  terms  within  the  parenthesis:  1  -  (a  —  6 
—  c)  =  1  —  a  -f-  b  +  c.  When  a  parenthesis  is  within  a  parenthesis  remove 

the  inner  one  first:  a  —  |6  —  -j  c  —  (d  —  «)  [  ~|  =  a  —  ffc  —  -jc  —  d-fej-1 
=  a  —  [b  —  c  -\-'d  —  e]  =a  —  b  +  c  --  d+e. 

A  multiplication  sign,  X,  has  the  effect  of  a  parenthesis,  in  that  the  oper- 
ation indicated  by  it  must  be  performed  before  the  operations  of  addition 
or  subtraction.  a-\-bXaJrb  =  a-\-ab-\-b;  while  (a  +  b)  X  (a  -f  b)  = 
a2  4-  2a6  -f-  62,  and  (a  -f  6)  X  a  +  6  =  a2  -f  a6  +  b. 

Division.— The  quotient  is  positive  when  the  dividend  and  divisor 
have  like  signs,  and  negative  when  they  have  unlike  signs:  abc  -r-  b  =  etc: 
abc  H b  =  —  ac. 

To  divide  a  monomial  by  a  monomial,  write  the  dividend  over  the  divisor 
with  a  line  between  them.  If  the  expressions  have  common  factors,  remove 
the  common  factors: 

a?bx        ax        a4 
a*bx-s-aby  = — r—   =  — ;      —  =  a; 

aby  y         a3  a         a 

To  divide  a  polynomial  by  a  monomial,  divide  each  term  of  the  polynomial 
by  the  monomial:  (Sab  —  12ac)  -*-  4a  =  2b  —  3c. 

To  divide  a  polynomial  by  a  polynomial,  arrange  both  dividend  and  divi- 
sor in  the  order  of  the  ascending  or  descending  powers  of  some  common 
letter,  and  keep  this  arrangement  throughout  the  operation. 

Divide  the  first  term  of  the  dividend  by  the  first  term  of  the  divisor,  and 
write  the  result  as  the  first  term  of  the  quotient. 

Multiply  all  the  terms  of  the  divisor  by  the  first  term  of  the  quotient  and 
subtract  the  product  from  the  dividend.    If  there  be  a  remainder,  consider 
it  as_a  new  dividend  and  proceed  as  before:    (a2  —  62)  •*•  (a.rj-  b). 
a2  -  ft*  |  a  +  b. 
a?-\-ab  \a "-  b. 
-ab-  &2. 
-  ab  -  b*. 


The  difference  of  two  equal  odd  powers  of  any  two  numbers  is  divisible 
by  their  difference  and  also  by  their  sum: 

(as  _  53)  +  (a  _  6)  _  aa  _j_  a&  _|_  52  .  (as  _  53)  _,_  (a  _|_ 5)  =  ^2  -  ab  -f  b'*. 

The  difference  of  two  equal  even  powers  of  two  numbers  is  divisible  by 
their  difference  and  also  by  their  sum:  (a2  —  62)  H-  (a  —  b)  =  a  -f-  b. 

The  sum  of  two  equal  even  powers  of  two  numbers  is  not  divisible  by 
either  the  difference  or  the  sum  of  the  numbers;  but  when  the  exponent 
of  each  of  the  two  equal  powers  is  composed  of  an  odd  and  an  even  factor, 
the  sum  of  the  given  power  is  divisible  by  the  sum  of  the  powers  expressed 
by  the  even  factor.  Thus  x6  -4-  y6  is  not  divisible  by  x  4-  y  or  by  x  —  y.  but  is 
divisible  by  x*  +  y*. 

Simple  equations. — An  equation  is  a  statement  of  equality  between 
two  expressions;  as,  a  -f-  b  =  c  -f-  d. 

A  simple  equation,  or  equation  of  the  first  degree,  is  one  which  contains 
only  the  first  power  of  the  unknown  quantity.  If  equal  changes  be  made 
(by  addition,  subtraction,  multiplication,  or  division)  in  both  sides  of  an 
equation,  the  results  will  be  equal. 

Any  term  may  be  changed  from  one  side  of  an  equation  to  another,  pro- 


vided its  sign  be  changed:  a  -j-  b  =  c  -j-  d;  a  =  c  +  d  -  b.  To  solve"  an 
equation  having  one  unknown  quantity,  transpose  all  the  terms  involving 
the  unknown  quantity  to  one  side  of  the  equation,  and  all  the  other  terms 


to  the  other  side;  combine  like  terms,  and  divide  both  sides  by  the  coefficient 
of  the  unknown  quantity. 

Solve  8x  -  29  =  26  -  3#.    Sx  +  3x  =  29  +  26;  ttx  =  55;  x  -  5,  ans. 

Simple  algebraic  problems  containing  one  unknown  quantity  are  solved 
by  making  x  —  the  unknown  quantity,  and  stating  the  conditions  of  the 
problem  in  the  form  of  an  algebraic  equation,  and  then  solving  the  equa- 
tion. What  two  numbers  are  those  whose  sum  is  48  and  difference  14  ?  Let 
x  =  the  smaller  number,  x  +  14  the  greater,  x  +  x  +  14  =  48.  2x  =  34,  x 
=  17;  a; +  14  =  31,  ans. 

Find  a  number  whose  treble  exceeds  50  as  much  as  its  double  falls  short 
of  40.  Let  x  =  the  number.  3x  -  50  =  40  -  2#;  5x  =  90:  x  =  18,  ans.  Prov- 
ing, 54  -  50  =  40  -  36. 


ALGEBRA.  35 

Eq  nations   containing  two   unknown  quantities.—  If  one 

equation  contains  two  unknown  quantities,  x  and  y,  an  indefinite  number  of 
pairs  of  values  of  x  and  y  may  be  found  that  will  satisfy  the  equation,  but  if 
a  second  equation  be  given  only  one  pair  of  values  can  be  found  that  will 
satisfy  both  equations.  Simultaneous  equations,  or  those  that  may  be  satis- 
fied by  the  same  values  of  the  unknown  quantities,  are  solved  by  combining 
tiie  equations  so  as  to  obtain  a  single  equation  containing  only  one  unknown 
quantity.  This  process  is  called  elimination. 

Elimination  by  addition  or  subtraction.  —  Multiply  the  equation  by 
such  numbers  as  will  make  the  coefficients  of  one  of  the  unknown  quanti- 
ties equal  in  the  resulting  equation.  Add  or  subtract  the  resulting  equa- 
tions according  as  they  have  unlike  or  like  signs. 

Solve  J»*  +  80  =  7.    Multiply  by  2:    4x  +  Qy  =  14 

7G  I  4x  —  5y  =  3.    Subtract:  4x  -  by  =    3         lly  =  11;  y  =  1. 

Substituting  value  of  y  in  first  equation,  2x  -f-  3  —  7;  x  =  2. 

Elimination  by  substitution.—  From  one  of  the  equations  obtain  the 
value  of  one  of  the  unknown  quantities  in  terms  of  the  other.  Substitu- 
tute  for  this  unknown  quantity  its  value  in  the  other  equation  and  reduce 
the  resulting  equations. 


=  8.    (1).    From  (1)  we  find  X=J=. 

T&l3xi-7y  =  7.    (2). 

Substitute  this  value  in  (2):  3(*^—  )  -f  7y  =  7;    =  24  -  9y  +  Uy  =  14, 

whence  y  =  —  2.    Substitute  this  value  in  (1):   2x  —  6  =  8;  x  =  7. 

Elimination  by  comparison.  —  From  each  equation  obtain  the  value  of 
one  of  the  unknown  quantities  in  terms  of  the  other.  Form  an  equation 
from  these  equal  values,  and  reduce  this  equation. 

2x-9y  =  11.    (1).    From  (1)  we  find  x  = 


- 
Solve  \ 

\3x-4y  =  7.    (2).    From  (2)  we  find  x  =     \  y  . 
I  » 


Equating  these  values  of  a?,  1!  "^  9?/    =  ;  Wy  =  -  19;  y  =  -  1. 

Substitute  this  value  of  y  in  (1):  2x  -f  9  =  11;  x  =  1. 

If  three  simultaneous  equations  are  given  containing  three  unknown 
quantities,  one  of  the  unknown  quantities  must  be  eliminated  between  two 
pairs  of  the  equations:  then  a  second  between  the  two  resulting  equations. 

Quadratic  equations.—  A  quadratic  equation  contains  the  square 
of  the  unknown  quantity,  but  no  higher  power.  A  pure  quadratic  contains 
the  square  only;  an  affected  quadratic  both  the  square  and  the  first  power. 

To  solve  a  pure  quadratic,  collect  the  unknown  quantities  on  one  side, 
and  the  known  quantities  on  the  other;  divide  by  the  coefficient  of  the  un- 
known quantity  and  extract  the  square  root  of  each  side  of  the  resulting 
equation. 

Solve  3x2  -  15  _=  0.    3x2  =  15;  x*  =  5;  x  -  |/5 

A  root  like  ^5,  which  is  indicated,  but  which  can  be  found  only  approxi- 
mately, is  called  a  surd. 

Solve  3-r2  -f  15  =  0.     3#2  =  -  15;  x*  =  -  5;  x  =  V-  5. 

The  square  root  of  —  5  cannot  be  found  even  approximately,  for  the  square 
of  any  number  positive  or  negative  is  positive;  therefore  a  root  which  is  in- 
dicated, but  cannot  be  found  even  approximately,  is  called  imaginary. 

To  solve  an  affected  quadratic.  —  1.  Convert  the  equation  into  the  form 
a"x"*  ±  2abx  =  c,  multiplying  or  dividing  the  equation  if  necessary,  so  as 
to  make  the  coefficient  of  #2  a  square  number. 

2.  Complete  the  square  of  the  first  member  of  the  equation,  so  as  to  con- 
vert it  to  the  form  of  a2#2  ±  2abx  -f  62,  which  is  the  square  of  the  binomial 
ax  ±  6,  as  follows:  add  to  each  side  of  the  equation  the  square  of  the  quo- 
tient obtained  by  dividing  the  second  term  by  twice  the  square  root  of  the 
first  term. 

3.  Extract  the  square  root  of  each  side  of  the  resulting  equation. 

Solve  3:e2  -  4x  =  32.    To  make  the  coefficient  of  x*  a  square  number, 
multiply  by  3:  9#2  -  12#  =  96;  12x  -s-  (2  x  3#)  =  2;  22  =  4. 
Complete  the  square  :.9.t;2  -  12x  -f  4  =  100.    Extract  the  root:  3x  —  2  =  ± 


36  ALGEBRA. 

10,  whence  x  =  4  or  -  2  2/3.  The  square  root  of  100  is  either  -f  30  or  -  10, 
since  the  square  of  —  10  as  well  as  -j-  !02  =  ICO. 

Problems  involving  quadratic  equations  have  apparently  two  solutions,  as 
a  quadratic  has  two  roots.  Sometimes  both  will  be  true  solutions,  but  gen- 
erally one  only  will  be  a  solution  and  the  other  be  inconsistent  with  the 
conditions  of  ihe  problem. 

The  sum  of  the  squares  of  two  consecutive  positive  numbers  is  481.  Find 
the  numbers. 

Let  x  =  one  number,  x  -f  1  the  other,  x"*  +  (x  +  I)2  =  481.  2#2  -f  2x  -f  1 
=  481. 

x*  -\-  %  =  240.  Completing  the  square,  x*  -f  x  +  0.25  =  240.25.  Extracting 
the  root  we  obtain  x  -j-  0.5  =  ±  !5.5;  x  =  15  or  —  16. 

The  positive  root  gives  for  the  numbers  15  and  16.  The  negative  root  — 
16  is  inconsistent  with  the  conditions  of  the  problem. 

Quadratic  equations  containing  two  unknown  quantities  require  different 
methods  for  their  solution,  according  to  the  form  of  the  equations.  For 
these  methods  reference  must  be  made  to  works  on  algebra. 

Theory  of  exponents.—  \  a,  when  n  is  a  positive  integer  is  one  of  u 

equal  factors  of  a.  \  am  means  a  is  to  be  raised  to  the  with  power  and  the 
nth  root  extracted. 

(V~a)    means  t 
raised  to  the  mth  power. 

«   --          ,  v  -.-yn  m 

y  am  =  VT<*  /       =  cin.    When  the  exponent  is  a  fraction^he  numera- 

tor indicates  a  power,  and  the  denominator  a  root.    cJ  —  V  a<5  =  a3;  eJ  = 

4/a,3  =  a1'5- 

To  extract  the  root  of  a  quantity  raised  to  an  indicated  power,  divide 
the  exponent  by  the  index  of  the  required  root;  as, 

*,  —  ™.  3,-  e 

\  am  —an'  \  a6  =  a3  =  a2. 

Subtracting  1  from  the  exponent  of  a  is  equivalent  to  dividing  by  a  : 


A  number  with  a  negative  exponent  denotes  the  reciprocal  of  the  number 
with  the  corresponding  positive  exponent. 

A  factor  under  the  radical  sign  whose  root  can  be  taken  may,  by  having 
the  root  taken,  be  removed  from  under  the  radical  sign: 

\/a?b    =  I/a2    x    |/6  =  a  tyb. 

A  factor  outside  the  radical  sign  may  be  raised  to  the  corresponding 
power  and  plact-d  under  it: 


Binomial  Theorem.—  To  obtain  any  power,  as  the  nth,  of  an  ex- 
pression of  the  form  x  4-  a 

n    i       ,   n(n-l)«M-2     ,    .   n  (n  -  l)(n  -  2)  a*'3^  , 
(a  +  x)H=an  ±nan-    x  -\  ---  ^  --  x*  -f  -  L  2.  3.  — 

The  following  laws  hold  for  any  term  in  the  expansion  of  (a  +  x)n. 

The  exponent  of  x  is  less  by  one  than  the  number  of  terms. 

The  exponent  of  a  is  n  minus  the  exponent  of  x. 

The  last  factor  of  the  numerator  is  greater  by  one  than  the  exponent  of  a. 

The  last  factor  of  the  denominator  is  the  same  as  the  exponent  of  x. 

In  the  rth  term  the  exponent  of  x  will  be  r  —  1. 

The  exponent  of  a  will  be  n  —  (r  —  1).  or  n  -  r  -f-  1. 

The  last  factor  of  the  numerator  will  be  u  —  r  -f-  2. 

The  last  factor  of  the  denominator  will  be  =  r  —  1. 

Hence  tbe  rth  term  ="<»  ~  ')'»-«)•••<» 


1  . 


GEOMETBICAL   PROBLEMS. 


37 


GEOMETRICAL  PROBLEMS. 


1.  To  bisect  a  straight  HIM-, 
or  an  arc  of  a  circle  (Fig.  ]}.— 
From  the  ends  A^  B,  as  centres,  de- 
scribe arcs  intersecting  at  C  and  Z), 
and  draw  a  line  through  C  and  D 
which  will  bisect  the  line  at  E  or  the 
arc  at  F. 


2.  To  draw  a  perpendicular 
to  a  straight  line,  or  a  radial 
line  to  a  circular  arc.— Same  as 
in  Problem  1.     C 1)  is  perpendicular  i  o 
the  line  A  B,  and  also  radial  to  the  are. . 

3.  To  draw  a  perpendicular 
to  a  straight  line  from  a  given 
point  in  that  line  (Fig.  a).— With 
any  radius,  from  the  given  point  A  in 
the  line  B  C,  cut  the  line  at  B  and  C. 
With  a  longer  radius   describe  arcs 
from  B  and  C,  cutting  each  other  at 
D,  and  draw  the  perpendicular  D  A. 

4.  From  the  end  /  of  a  given 
line  A.  1>  to  erect  a  perpendic- 
ular A.  E  (Fig.  8).— From  any  centre 
F,  above  A  D,  describe  a  circle  passing 
through  the  given  point  A,  and  cut- 
ting the  given  line  at  D.    Draw  D  F 
and  produce  it  to  cut  the  circle  at  E, 
and  draw  the  perpendicular  A  E. 

Second  Method  (Fig.  4). — From  the 
given  point  A  set  off  a  distance  A  E 
equal  to  three  parts,  by  any  scale  ; 
and  on  the  centres  A  and  E,  with  radii 
of  four  and  five  parts  respectively, 
describe  arcs  intersecting  at  C.  Draw 
the  perpendicular  A  C. 

NOTE.— This  method  is  most  useful 
on  very  large  scales,  where  straight 
edges  are  inapplicable.  Any  multiples 
of  the  numbers  3,  4,  5  may  be  taken 
with  the  same  effect  as  6,  8,  10,  or  9, 
12,  15. 

5.  To  draw  a  perpendicular 
to  «   straight  line  from  any 
point  Without  it  (Fig.  5.)— From 
the  point  Ay  with  a  sufficient  radius 
cut  the  given  line  at  F  and  6r,  and 
from  these  points  describe  arcs  cut- 
ting at  E.    Draw  the  perpendicular 
A  E. 


A  B 

FTG.  6. 


6.  To  draw  a  straight  line 
parallel  to  a  given  line,  at  a 
given  distance  apart  (Fig.  (>).— 
From  the  centres  A,  B,  in  the  given 
line,  with  the  given  distance  as  radius, 
describe  arcs  C,  D,  and  draw  the  par- 
allel lines  C  D  touching  the  arcs. 


38 


GEOMETRICAL   PROBLEMS. 
C 


7.  To  divide  a  straight  line 
into  a  number  of* equal  parts 

(Fig.  ?).— To  divide  the  line  A  B  into, 
say,  five  parts,  draw  the  line  A  C  at 
an  angle  from  A;  set  off  five  equal 
parts;  draw  B  5  and  draw  parallels  to 
it  from  the  other  points  of  division  in 
A  C.  These  parallels  divide  A  B  as 
required. 

NOTE.— By  a  similar  process  a  line 
may  be  divided  into  a  number  of  un- 
equal parts;  setting  off  divisions  OM 
A  C,  proportional  by  a  scale  to  the  re- 
quired divisions,  and  drawing  parallel 
cutting  A  B.  The  triangles  .411,  A22, 
.433,  etc.,  are  similar  triangles. 


-  H . 


FIG.  8. 


\ 


8.  Upon  a  straight  line  to 
draw  an  angle  equal  to  a 
given  angle  (Fig.  «.).— Let  A  be  the 

given  angle  and  F  G  the  line.  From 
the  point  A  with  any  radius  describe 
the  arc  D  E.  From  F  with  the  same 
radius  describe  I  H.  Set  off  the  arc 
I H  equal  to  D  E,  and  draw  F  H.  The 
angle  JR'is  equal  to  A,  as  required. 


9.  To    draw   angles   of   60° 

and  30°  (Fig.  9).— From  F,  with 
any  radius  F  I.  describe  an  arc/JEf : 
and  from  I,  with  the  same  radius,  cut 
the  arc  at  H  and  draw  F Hto  form 
the  required  angle  I F  H.  Draw  the 
perpendicular  H  Kto  the  base  line  to 
form  the  angle  of  30°  F  H  K. 


1O.  To  d  raw  an  angle  of  45° 

(Fig.  10).— Set  off  the  distance  F  I; 
draw  the  perpendicular  1 H  equal  to 
IF,  and  join  H Fto  form  the  angle  at 
F.  The  angle  at  H  is  also  45°. 


11.  To  bisect  an  angle  (Fig. 
11).— Let  A  C  B  be  the  angle;  with  C 
as  a  centre  draw  an  arc  cutting  the 
sides  at  A,  B.  From  A  and  B  as 
centres,  describe  arcs  cutting  each 
other  at  D.  Draw  C  D,  dividing  the 
angle  into  two  equal  parts. 


12.  Through  two  given 
points  to  describe  an  arc  of 
a.  circle  with  a  given  radius 

(Fig.  12). — From  the  points  A  and  B 
as  centres,  with  the  given  radius,  de- 
scribe arcs  cutting  at  C ,  and  from 
C  with  the  same  radius  describe  an 


GEOMETRICAL   PROBLEMS. 


39 


FIG.  13. 


FIG.  14. 


FIG.  15. 


13.  To  find  the  centre  of  a 
circle  or  of  an  arc  of  a  circle 

(Fig.  13). — Select  three  points,  A,  B, 
(7,  in  the  circumference,  well  apart; 
with  the  same  radius  describe  arcs 
from  these  three  points,  cutting  each 
other,  and  draw  the  two  lines,  D  E, 
F  G,  through  their  intersections.  The 
point  O,  where  they  cut,  is  the  centre 
of  the  circle  or  arc. 

To  describe  a  circle  passing; 
through  three  given  points. 
— Let  A,  B,  C  be  the  given  points,  and 
proceed  as  in  last  problem  to  find  the 
centre  0,  from  which  the  circle  may 
be  described. 

14.  To  describe  an  arc  of 
a  circle  passing  through 
three  given  points  when 
the  centre  is  not  available 
(Fig.  14).— From  the  extreme  points 
A,  -B,  as  centres,  describe  arcs  A  H. 
B  G.  Through  the  third  point  C 
draw  A  E,  B  F,  cutting  the  arcs. 
Divide  A  F  and  B  E  into  any  num- 
ber of  equal  parts,  and  set  off  a 
series  of  equal  parts  of  the  same 
length  on  the  upper  portions  of  the 
arcs  beyond  the  points  E  F.  Draw 
straight  lines,  B  L,  B  M ,  etc.,  to 
the  divisions  in  A  F,  and  A  /,  A  K, 
etc.,  to  the  divisions  in  E  G.  The 
successive  intersections  JV,  O,  etc., 
of  these  lines  are  points  in  the 
circle  required  between  the  given 

Soints  A  and    C.  which  may  be 
rawnin  ;  similarly  the  remaining 
part  of   the  curve  B  C  may  be 
described.     (See  also  Problem  54.) 

15.  To  draw  a  tangent  to 
a  circle  from  a  given  point 
in  the  circumference  (Fig.  15). 
—Through  the  given  point  A,  draw  the 
radial  line  A  C,  and  a  perpendicular 
to  it,  F  (?,  which  is  the  tangent  re- 
quired. 


16.  To  draw  tangents  to  a 
circle  from  a  point  without 

it  (Fig.  16). — From  A,  with  the  radius 
A  C,  describe  an  arc  BCD,  and  from 
C.  with  a  radius  equal  to  the  diameter 
of  the  circle,  cut  the  arc  at  B  D,  Join 
B  C,  CD,  cutting  the  circle  at  E  F, 
and  draw  A  E,  A  F,  the  tangents. 

NOTE. — When  a  tangent  is  already 
drawn,  the  exact  point  of  contact  may 
be  found  by  drawing  a  perpendicular 
to  it  from  the  centre. 


17.  Between  two  inclined  lines  to  draw  a  series  of  cir- 
cles touching  these  lines  and  touching  each  other  (Fig.  i?). 
—Bisect  the  inclination  of  the  given  lines  A  B,  C  D,  by  the  line  N  O.  From 
a  point  P  in  this  line  draw  the  perpendicular  P  B  to  the  line  A  B,  and 


40 


GEOMETRICAL   PROBLEMS. 
A 


on  P  describe  the  circle  B  D,  touching 
the  lines  and  cutting  the  centre  line 
at  E.  From  E  d  raw  E  F  perpendicular 
to  the  centre  line,  cutting  A  B  at  F, 
and  from  .F  describe  an  arc  E  G,  cut- 
ting A  B  at  G.  Draw  G  H  parallel  to 
B  P,  giving  H,  the  centre  of  the  next 
circle,  to  be  described  with  the  radius 
HE,  and  so  on  for  the  next  circle  IN. 
Inversely,  the  largest  circle  may  be 
described  first,  and  the  smaller  ones 
in  succession.  This  problem  is  of  fre- 
quent use  in  scrollwork. 

18.  Between  two    inclined 
lines  to  draw  a  circular  seg- 
ment tangent  to  the  lines  and 
passing   through   a   point    / 
on  the  line  /   C  which  bisects 
the  angle  of  the  lines  (Fig.  18). 
—  Through  .Fdraw  D  A  at  right  angles 
to  F  C  ;  bisect  the  angles  A  and  D,  as; 
in  Problem  11,  by  lines  cutting  at  C, 
and  from  C  with  radius  C  jPdiaw  the 
arc  H  F  G  required. 

19.  To  draw  a  circular  arc 
that  will  be  tangent  to  two 
given  lines   A  R  and  C  />  in- 
cJiiied   to   one    another,  one 
tangential     point     E     being 
given   (Fig.   19).—  Draw    the    centre 
line  G  F.    From  #draw  E  Fa,t  right 
to  angles  A  B  ;   then  F  is  the  centre1 
of  the  circle  required. 

20.  To  describe  a   circular 
arc  joining  two  circles,  and 
touching   one    of  them  at   a 
given  point  (Fig.  20).—  To  join  the 
circles  A  B,  F  G,  by  an  arc  touching 
one  of  them  at  F,  draw  the  radius  E  F, 
and  produce  it  both  ways.    Set  off  F  H 

ual  ' 


eq 


to  the  radius  A  'C  of  the  other 


circle;  join  C  H  and  bisect  it  with  the 
perpendicular  L  7,  cutting  E  F  at  I. 
On  the  centre  7,  with  radius  IF,  de- 
scribe the  arc  FA  as  required. 


21.  To  draw  a  circle  with  a 
given  radius  i>  that  will  be 
tangent  to  two  given  circles 

A  and  7i  (Fig.  21).—  From  centre 
of  circled  with  radius  equal  R  plus 
radius  of  A,  and  from  centre  of  B  with 
radius  equal  to  R  +  radius  of  B,  draw 
two  arcs  cutting  each  other  in  (7,  which 
will  be  the  centre  of  the  circle  re- 
quired. 


22.  To  construct  an  equi- 
lateral triangle,  the  sides 
being  given  (Fig.  22).— On  the  ends 
of  one  side,  A,  B,  with  A  B  as  radius, 
describe  arcs  cutting  at  C,  and  draw/ 
AC,  CB. 


GEOMETRICAL   PROBLEMS. 


41 


FIG.  23. 


23.  To  construct  a  triangle 
of  unequal  sides  (Big.  23).— On 
either  end  of  the  base  A  Z),  with  the 
side  B  as  radius,  describe  an  arc; 
and  with  the  side  C  as  radius,  on  the 
other  end  of  the  base  as  a  centre,  cut 
the  arc  at  E.  Join  A  E,  D  E. 


FIG.  24. 


FIG.  25. 


A  E       ^     C 

FIG.  27. 


24.  To    construct  a  square 
on  a  given  straight  line  A  B 

(Fig.  24). — At  A  erect  a  perpendicular 
A  C,  as  in  Problem  4.  Lay  off  A  D 
equal  to  A  B  ;  from  D  and  B  as  centres 
with  radius  equal  A  B,  describe  arcs 
cutting  each  other  in  E.  Join  D  E  and 
BE. 


25.  To     construct     a    rect- 
angle with    given  base   JK  F 

and  height  E  H  (Fig.  25).— On  the 
base  E  Fdraw  the  perpendiculars  E  H, 
F  G  equal  to  the  height,  and  join  G  H. 


26.  To  describe  a  circle 
about  a  triangle  (Fig.  26).— 
Bisect  two  sides  A  B,  A  C  of  the  tri- 
angle at  E  F,  and  from  these  points 
draw  perpendiculars  cutting  at  K.  On 
the  centre  K,  with  the  radius  K  A, 
draw  the  circle  A  B  C. 


27.  To  inscribe  a  circle  in 
a  triangle  (Fig.  27).— Bisect  two  of 
the  angles  A,  C,  of  the  triangle  by  lines 
cutting  at  D  ;    from  D  draw  a  per- 
pendicular D  E  to  any  side,  and  with 
D  E  as  radius  describe  a  circle. 

When  the  triangle  is  equilateral, 
draw  a  perpendicular  from  one  of  the 
angles  to  the  opposite  side,  and  from 
the  side  set  off  one  third  of  the  per- 
pendicular. 

28.  To    describe     a    circle 
about   a  square,  and  to   in- 
scribe a  square  in  a  circle  (Fig. 
28). — To  describe  the  circle,  draw  the 
diagonals  A  J5,  C  D  of  the  square,  cut- 
ting at  E.    On  the  centre  E,  with  the 
radius  A  E,  describe  the  circle. 

To  inscribe  the  square.— 
Draw  the  two  diameters,  A  B,  CD,  at 
right  angles,  and  join  the  points  A,  B, 
C  D,  to  form  the  square. 

NOTE. — In  the  same  way  a  circle  may 
be  described  about  a  rectangle. 


42 


GEOMETRICAL   PROBLEMS. 


29.  To  inscribe  a  circle  in  a 
square  (Fig.  29).— To  inscribe  the 
circle,  draw  the  diagonals  A  B,  C  D 
of  the  square,  cutting  at  E',  draw  the 
perpendicular  E  F  to  one  side,  and 
with  the  radius  E  F  describe  the 
circle. 


3O.  To  describe  a  square 
about  a  circle  (Fig.  30). — Draw  two 
diameters  A  B,  CD  at  right  angles. 
With  the  radius  of  the  circle  and  A,  B, 
C  and  D  as  centres,  draw  the  four 
half  circles  which  cross  one  another 
in  the  corners  of  the  square. 


31.  To  inscribe  a  pentagon 
in  a  circle  (Fig.  31).— Draw  diam- 
eters A  C,  B  D  at  right  angles,  cutting 
at  o.  Bisect  A  o  at  E,  arid  from  £J, 
with  radius  E  B,  cut  A  C  at  F  ;  from 
B,  with  radius  B  F,  cut  the  circumfer- 
ence at  G,  H,  and  with  the  same  radius 
step  round  the  circle  to  /  and  K ;  join 
the  points  so  found  to  form  the  penta- 
gon. 


32.  To    construct   a  penta- 
gon on  a  given  line  A.  B  (Fig. 

92). — From  B  erect  a  perpendicular 
B  Chalf  the  length  of  A  B;  join  A  C 
and  prolong  it  to  /),  making  C  D  =  B  C. 
Then  B  D  is  the  radius  of  the  circle 
circumscribing  the  pentagon.  From 
A  and  Bas  centres,  with  B  D  as  radius, 
draw  arcs  cutting  each  other  in  O, 
which  is  the  centre  of  the  circle. 

33.  To  construct  a  hexagon 
upon    a  given    straight   line 

(Fig.  33).  -From  A  and  B,  the  ends  of 
the  given  line,  with  radius  A  B,  de- 
scribe arcs  cutting  at  g  ;  from  g,  with 
the  radius  g  A,  describe  a  circle ;  with 
the  same  radius  set  off  the  arcs  A  G, 
G  F,  and  B  D.  D  E.  Join  the  points  so 
found  to  form  the  hexagon.  The  side 
of  a  hexagon  =  radius  of  its  circum- 
scribed circle. 

34.  To  inscribe  a  hexagon 
in  a  circle  (Fig.  34).— Draw  a  diam- 
eter A  C  B.  From  A  andl?  as  centres, 
with  the  radius  of  the  circle  A  C,  cut 
the  circumference  at  D,  E,  F,  G,  and 
draw  A  D,  D  E,  etc.,  to  form  the  hexa- 
gon.   The  radius  of  the  circle  is  equal 
to  the  side  of  the  hexagon ;  therefore 
the  points  D,  E,  etc.,   may  also  be 
found    by    stepping    the    radius    six 
times  round  the  circle.      The  angle 
between  the  diameter  and  the  sides  of 
a  hexagon  and  also  the  exterior  angle 
between  a  side  and  an  adjacent  side 
prolonged  is  60  degrees;   therefore  a 
hexagon  may  conveniently  be  drawn 
by  the  use  of  a  60-degree  triangle. 


GEOMETRICAL   PROBLEMS. 


43 


35.  To  describe  a  hexagon 
about  a  circle  (Fig.  35).— Draw  a 
diameter  A  D  J3,  and  with  the  radius 
A  D,  on  the  centre  A,  cut  the  circum- 
ference at  C  ;  join  A  C,  and  bisect  it 
with  the  radius  D E  ;  through  .Ed raw 
F  G,  parallel  to  A  (7,  cutting  the  diam- 
eter at  F,  and  with  the  radius  D  F  de- 
scribe the  circumscribing  circle  F  H. 
Within  this  circle  describe  a  hexagon 
by  the  preceding  problem.    A  more 
convenient  method  is  by  use  of  a  60- 
degree  triangle.      Four  of  the  sides 
make  angles  of  60  degrees  with  the 
diameter,  and  the  other  two  are  par- 
allel to  the  diameter. 

36.  To  describe  an  octagon 
oil  a  given  straight  line  •  !•  i_ 

36).— Produce  the  given  line  A  B  both 
wa}7s,  and  draw  perpendiculars  A  E, 
B  F;  bisect  the  external  angles  A  and 
B  by  the  lines  A  H,  B  C,  which  make 
equal  to  A  B.  Draw  C  D  and  //  G  par- 
allel to  A  E,  and  equal  to  A  B  ;  from 
the  centres  G,  D,  with  the  radius  A  B, 
cut  the  perpendiculars  at  E,  F,  and 
draw  E  F  to  complete  the  octagon. 

37.  To    convert    a    square 
into  an  octagon  (Fig.  37).— Draw 
the  diagonals  of  the  square  cutting  at 
e  ;  from  the  corners  A,  B,  C,  Z>,  with 
A  e  as  radius,  describe  arcs  cutting 
the  sides  at  gn,  /&,  km,  and  ol,  and 
join  the  points  so  found  to  form  the 
octagon.    Adjacent  sides  of  an  octa- 
gon make  an  angle  of  135  degrees. 


38.  To  inscribe  an  octagon 
in  a  circle  (Fig.  38).— Draw  two 
diameters,  A  C,  B  D  at  right  angles; 
bisect  the  arcs  A  B,  B  O,  etc.,  at  ef, 
etc.,  and  join  A  e,  e  B,  etc.,  to  form 
the  octagon. 


39.  To  describe  an  octagon 
about  a  circle  (Fig.  39).— Describe 
a  square  about  the  given  circle  A  B  ; 
draw  perpendiculars  h  k.  etc.,  to  the 
diagonals,  touching  the  circle  to  form 
the  octagon. 


4O.  To  describe  a  polygon  of  any  number  of  sides  upon 
a  given  straight  line  (Fig.  40).— Produce  the  given  line  A  B.  and  on  At 


GEOMETRICAL   PROBLEMS. 


FIG.  42. 


with  the  radius  A  B,  describe  a  semi- 
circle; divide  the  semi-circumference 
into  as  many  equal  parts  as  there  are 
to  be  sides  in  the  polygon— say,  in  this 
example,  five  sides.  Draw  lines  from 
A  through  the  divisional  points  D,  ft, 
and  c,  omitting  one  point  a  ;  and  on 
the  centres  B,  D,  with  the  radius  A  B, 
cut  A  b  at  E  and  A  cat  F.  Draw  D  E, 
E  F,  F B  to  complete  the  polygon. 

41.  To  inscribe  a  circle 
within  a  polygon  (Figs.  41, 42).— 
When  the  polygon  has  an  even  number 
of  sides  (Fig.  41),  bisect  two  opposite 
sides  at  A  and  5;  draw  A  B,  and  bisect 
it  at  C  by  a  diagonal  D  E,  and  with 
the  radius  C  A  describe  the  circle. 

When  the  number  of  sides  is  odd 
(Fig.  42),  bisect  two  of  the  .sides  at  A 
and  J9,  and  draw  lines  A  E,  B  D  to  the 
opposite  angles,  intersecting  at  (7; 
from  C,  with  the  radius  C  A,  describe 
the  circle. 


42.  To  describe  a  circle 
without  a  polygon  (Figs.  41,  42). 
—Find  the  centre  (J  as  before,  and  with 
the  radius  C  D  describe  the  circle. 


43.  To  inscribe  a  polygon 
of  any  number  of  sides  with- 
in a  circle  (Fig.  43).— Draw  the 
diameter  AB  and  through  the  centre 
E  draw  the  perpendicular  EC,  cutting 
the  circle  at  F.  Divide  E  F  into  four 
equal  parts,  and  set  off  three  parts 
equal  to  tliose  from  F  to  C.  Divide 
the  diameter  A  B  into  as  many  equal 
parts  as  the  polygon  is  to  have  sides  ; 
and  from  C  draw  CD,  through  the 
second  point  of  division,  cutting  the 
circle  at  D.  Then  A  D  is  equal  to  one 
side  of  the  polygon,  and  by  stepping 
round  the  circumference  with  the 
length  A  D  the  polygon  may  be  com- 
pleted. 


TABLE  OF  POLYGONAL  ANGLES. 


Number 
of  Sides. 

Angle 
at  Centre. 

Number 
of  Sides. 

Angle 
at  Centre. 

Number 
of  Sides. 

Angle 
at  Centre. 

No. 
3 
4 
5 
6 
7 
8 

Degrees. 
120 
90 
72 
60 
Blf 
45 

No. 
9 
10 
11 
i        12 
13 
14 

Degrees. 
40 
36 
32T\ 
30 
27T93 
25$ 

No. 
15 
16 
17 
18 
19 
20 

Degrees. 
24 
22£ 

1* 

19 

18 

GEOMETRICAL   PROBLEMS. 


45 


In  this  table  the  angle  at  the  centre  is  found  by  dividing  360  degrees,  the 
number  of  degrees  in  a  circle,  by  the  number  of 'sides  in  the  polygon;  and 
by  setting  off  round  the  centre  of  the  circle  a  succession  of  angles  by  means 
of  the  protractor,  equal  to  the  angle  in  the  table  due  to  a  given  number  of 
sides,  the  radii  so  drawn  will  divide  the  circumference  into  the  same  number 
of  parts. 

44.  To  describe  an  ellipse 
\\  h en  the  length  and  breadth 
are  given  (Fig.  44).—  A  B,  transverse 
axis;  C  D,  conjugate  axis;  F  G,  foci. 
The  sum  of  the  distances  from  C  to 
F  &i\d  G,  also  the  sum  of  the  distances 
from  F  and  G  to  any  other  point  in 
the  curve,  is  equal  to  the  transverse 
axis.  From  the  centre  C,  with  A  E  as 
radius,  cut  the  axis  A  B  at  .Fand  6r, 
the  foci ;  fix  a  couple  of  pins  into  the 
axis  at  F  and  G,  and  loop  on  a  thread 
or  cord  upon  them  equal  in  length  to 
the  axis  A  B,  so  as  when  stretched  to 
reach  to  the  extremity  C  of  the  con- 
jugate axis,  as  shown  in  dot-lining. 
Place  a  pencil  inside  the  cord  as  at  H\ 
and  guiding  the  pencil  in  this  way, 
keeping  the  cord  equally  in  tension, 
carry  the  pencil  round  the  pins  F,  G, 
and  so  describe  the  ellipse. 

NOTE.— This  method  is  employed  in 
setting  off  elliptical  garden  -  plots, 
walks,  etc. 

2d  Method  (Fig.  45).  —  Along  the 
straight  edge  of  a  slip  of  stiff  paper 
mark  off  a  distance  a  c  equal  to  A  C,  . 
halt'  the  transverse  axis;  and  from  the 
same  point  a  distance  a  b  equal  to 
C  D,  half  the  conjugate  axis.  Place 
the  slip  so  as  to  bring  the  point  b  on 
the  line  A  B  of  the  transverse  axis, 
and  the  point  c  on  the  line  D  E ;  and 
set  off  on  the  drawing  the  position  of 
the  point  a.  Shifting  the  slip  so  that 
the  point  b  travels  on  the  transverse 
axis,  and  the  point  c  on  the  conjugate 
axis,  any  number  of  points  in  the 
curve  may  be  found,  through  which 
the  curve  may  be  traced. 

3d  Method  (Fig.  46).— The  action  of 
the  preceding  method  may  be  em- 
bodied so  as  to  afford  the  means  of 
describing  a  large  curve  continuously 
by  means  of  a  bar  m  fc,  with  steel 
points  m,  /,  fc,  riveted  into  brass  slides 
adjusted  to  the  length  of  the  semi- 
axis  and  fixed  with  set-screws.  A 
rectangular  cross  E  G,  with  guiding- 
slots  is  placed,  coinciding  with  the 
two  axes  of  the  ellipse  A  C  and  B  H. 
By  sliding  the  points  fc,  I  in  the  slots, 
and  carrying  round  the  point  m,  the 
curve  may  be  continuously  described. 
A  pen  or  pencil  may  be  fixed  at  m. 

4th  Method  (Fig.  47).— Bisect  the 
transverse  axis  at  C,  and  through  C 
draw  the  perpendicular  D  E,  making 
C  D  and  C  E  each  equal  to  half  the 
conjugate  axis.  From  D  or  £",  with 
the  radius  A  C,  cut  the  transverse 
axis  at  F,  F',  for  the  foci.  Divide 
A  C  into  a  number  of  parts  at  the 


FIG.  45. 


GEOMETRICAL   PROBLEMS. 


points  1,  2,  3,  etc.  With  the  radius  A  I  on  F  and  F'  as  centres,  describe 
arcs,  and  with  the  radius  B  I  on  the  same  centres  cut  these  arcs  as  shown. 

Repeat  the  operation  for  the  other 
divisions  of  the  transverse  axis.  The 
series  of  intersections  thus  made  are 
points  in  the  curve,  through  which  the 
curve  may  be  traced. 

5th  Method  (Fig.  48).— On  the  two 
axes  A  B,  D  E  &s  diameters,  on  centre 
C,  describe  circles;  from  a  number  of 
points  a,  6,  etc.,  in  the  circumference 
AFB,  draw  radii  cutting  the  inner 
circle  at  a',  fc',  etc.  From  a,  b,  etc., 
draw  perpendiculars  to  AB;  and  from 
a',  b',  etc.,  draw  parallels  to  A  B,  cut- 
ting the  respective  perpendiculars  at 
n,  o,  etc.  The  intersections  are  points 
in  the  curve,  through  which  the  curve 
may  be  traced. 

Qth  Method  (Fig.  49).  — When  the 
transverse  and  conjugate  diameters 
are  given,  A  B,  C  D,  draw  the  tangent 
E  F  parallel  to  A  B.  Produce  C  D, 
and  on  the  centre  G  with  the  radius 
of  half  A  J5,  describe  a  semicircle 
H  D  K ;  from  the  centre  G  draw  any 
number  of  straight  lines  to  the  points 
E,  r.  etc.,  in  the  line  E  F,  cutting  the 
circumference  at  I,  m,  n,  etc.;  from 
the  centre  O  of  the  ellipse  draw 
straight  lines  to  the  points  E,  r,  etc.; 
and  from  the  points  I,  m,  n,  etc.,  draw 
parallels  to  G  C,  cutting  the  lines  O  E, 
O  r,  etc.,  at  £,,  M,  N,  etc.  These  are 
points  in  the  circumference  of  the 
ellipse,  and  the  curve  may  be  traced 
through  them.  Points  in  the  other 
half  of  the  ellipse  are  formed  by  ex- 
tending the  intersecting  lines  as  indi- 
cated in  the  figure. 

45.  To  describe  an  ellipse 
approximately  by  means  of 
circular  arcs.—  First.— With  arcs 
of  two  radii  (Fig.  50).— Find  the  differ- 
ence of  the  two  axes,  and  set  it  off 
from  the  centre  O  to  a  and  c  on  O  A 
and  O  C ;  draw  a  c,  and  set  off  half 
a  c  to  d  ;  draw  d  i  parallel  to  a  c;  set 
off  O  e  equal  to  O  d;  join  e  i,  and  draw 
the  parallels  e  m,  d  m.  From  m,  with 
radius  m  O,  describe  an  arc  through 
C ;  and  from  i  describe  an  arc  through 
D;  from  d  and  e  describe  arcs  through 
A  and  B.  The  four  arcs  form  the 
ellipse  approximately. 

NOTE.— This  method  does  not  apply 
satisfactorily  when  the  conjugate  axis 
is  less  than  two  thirds  of  the  trans- 
verse axis. 

2d  Method  (by  Carl  G.  Earth, 
Fig.  51). —In  Fig.  51  a  b  is  the  major 
and  c  d  the  minor  axis  of  the  ellipse 
to  be  approximated.  Lay  off  b  e  equal 
to  the  semi-minor  axis  c  O,  and  use  a  e 
as  radius  for  the  arc  at  each  extremity 
of  the  minor  axis.  Bisect  e  o  at  /  and 
lay  off  e  g  equal  to  e  f,  and  use  g  b  as 
radius  for  the  arc  at  each  extremity 
of  the  major  axis. 


GEOMETRICAL   PROBLEMS. 


The  method  is  not  considered  applicable  for  cases  in  which  the  minor 
axis  is  less  than  two  thirds  of  the  major. 

3d  Method :  With  arcs  of  three  radii 
(Fig.  52).— On  the  transverse  axis  A  B 
draw  the  rectangle  B  G  on  the  height 
O  C ;  to  the  diagonal  A  C  draw  the 
perpendicular  6r  H  D;  set  off  OK 
equal  to  O  C,  and  describe  a  semi- 
circle on  A  K,  and  produce  O  C  to  L; 
set  off  O  M  equal  to  C  L,  and  from  D 
describe  an  arc  with  radius  D  M :  from 
A,  with  radius  O  Z/,  cut  this  arc  at  a. 
Thus  the  five  centres  Z>,  a,  b,  H,  H' 
are  found,  from  which  the  arcs  are 
described  to  form  the  ellipse. 

NOTE.— This  process  works  well  for 
nearly  all  proportions  of  ellipses.  It 
is  employed  in  striking  out  vaults  and 
stone  bridges. 

•  4th  Method  (by  F.  R.  Honey,  Figs.  53  and  54).— Three  radii  are  employed. 
With  the  shortest  radius  describe  the  two  arcs  which  pass  through  the  ver- 
tices of  the  major  axis,  with  the  longest  the  two  arcs  which  pass  through 
the  vertices  of  the  minor  axis,  and  with  the  third  radius  the  four  arcs  which 
connect  the  former. 

A.  simple  method  of  determining  the  radii  of  curvature  is  illustrated  in 

Fig.  53.  Draw  the  straight 
lines  a  /and  a  c,  forming  any 
angle  at  a.  With  a  as  a  centre, 
and  with  radii  a  b  and  a  c,  re- 
spectively, equal  to  the  semi- 
minor  and  semi-major  axes, 
draw  the  arcs  b  e  and  c  d.  Join 
ed,  arid  through  b  and  c  re- 
spectively draw  b  g  and  c  f 
parallel  to  e  d,  intersecting  a  c 
at  g,  and  af  at/;  af  is  the 
radius  of  curvature  at  the  ver- 
tex of  the  minor  axis;  and  a  g 
the  radius  of  curvature  at  the 
vertex  of  the  major  axis. 

Lay  off  d  h  (Fig.  53)  equal  to  one  eighth  of  b  d.  Join  e  Ji,  and  draw  c  k  and 
b  I  parallel  to  e  h.  Take  a  k  for  the  longest  radius  (=R),al  for  the  shortest 
radius  (=  r),  and  the  arithmetical  mean,  or  one  half  the  sum  of  the  semi-axes, 
for  the  third  radius  (=  p),  and  employ  these  radii  for  the  eight-centred  oval 
as  follows: 

Let  a  b  and  c  d  (Fig.  54) 
be  the  major  and  minor 
axes.  Lay  off  a  e  equal 
to  r,  and  a  f  equal  to  p ; 
also  lay  off  c  g  equal  to  R, 
and  c  h  equal  to  p.  With 
g  as  a  centre  and  g  h  as  a 
radius,  draw  the  arc  h  k; 
with  the  centre  e  and 
radius  e  /  draw  the  arc  /  /c, 
intersecting hk  at  k.  Draw 
the  line  g  k  and  produce  it, 
making  g  I  equal  to  R. 
Draw  k  e  and  produce  it, 
making  k  m  equal  to  p. 
With  the  centre  g  and 
radius  g  c  (=  R)  draw  the 
arc  c  I ;  with  the  centre  k 
and  radius  k  I  (=  p}  draw 
the  arc  I  m,  and  with  the 
centre  e  and  radius  « m 
(=  r)  draw  the  arc  m  a. 

The  remainder  of  the 
work  is  symmetrical  with 
respect  to  the  axes. 


FIG.  54. 


48 


GEOMETRICAL   PROBLEMS. 


E 

«/ 

A 

G 
V 

2] 

\N 

F 

\ 

«/ 

o 

\ 

V 

J 

o 

\ 

V 

1 

o 

\       ^ 

D                 B 

b 

.^a       c 

FIG.  55. 


•  46.  The  Parabola. —A  parabola 
(DA  C,  Fig.  55)  is  a  curve  such  that 
every  point  in  the  curve  is  equally 
distant  from  the  directrix  K  L  and  the 
focus  F.  The  focus  lies  in  the  axis 
A  B  drawn  from  the  vertex  or  head  of 
the  curve  A,  so  as  to  divide  the  figure 
into  two  equal  parts.  The  vertex  A 
is  equidistant  from  the  directrix  and 
the  focus,  or  A  e  =  A  F.  Any  line 
parallel  to  the  axis  is  a  diameter.  A 
straight  line,  as  EG  or  DC,  drawn 
across  the  figure  at  right  angles  to  the 
axis  is  a  double  ordinate,  and  either 
half  of  it  is  an  ordinate.  The  ordinate 
to  the  axis  E  F  G,  drawn  through  the 
focus,  is  called  the  parameter  of  the 
axis.  A  segment  of  the  axis,  reckoned 


from  the  vertex,  is  an  abscissa  of  the 
axis,  and  it  is  an  abscissa  of  the  ordi- 
nate drawn  from  the  base  of  the  ab- 
scissa. Thus,  A  B  is  an  abscissa  of 
the  ordinate  B  C. 

Abscissae  of  a  parabola  are  as  the  squares  of  their  ordinates. 
To  describe  a  parabola  when  an  abscissa  and  its  ordi- 
nate are  given  (Fig.  55).— Bisect  the  given  ordinate  B  Cat  a,  draw  A  a, 
and  then  a  b  perpendicular  to  it,  meeting  the  axis  at  b.  Set  off  A  e,  A  F, 
each  equal  to  B  b]  and  draw  Ke  L  perpendicular  to  the  axis.  Then  K  L  is 
the  directrix  and  F  is  the  focus.  Through  F  and  any  number  of  points,  o,  o, 
etc.,  in  the  axis,  draw  double  ordinates,  n  o  n,  etc  ,  and  from  the  centre  F, 
with  the  radii  Fe,  o  e,  etc.,  cut  the  respective  ordinates  at  E,  G,  n,  n,  etc. 
The  curve  may  be  traced  through  these  points  as  shown. 


%d  Method:  By  means  of  a  square 
and  a  cord  (Fig.  56).— Place  a  straight- 
edge to  the  directrix  E  N,  and  apply 
to  it  a  square  LEG.  Fasten  to  the 
end  G  one  end  of  a  thread  or  cord 
equal  in  length  to  the  edge  E  G,  and 
attach  the  other  end  to  the  focus  F ; 
slide  the  square  along  the  straight- 
edge, holding  the  cord  taut  against  the 
edge  of  the  square  by  a  pencil  Z),  by 
which  the  curve  is  described. 


M  Method :  When  the  height  and 
the  base  are  given  (Fig.  5?).— Let  A  B 
be  the  given  axis,  and  CD  a  double 
ordinate  or  base;  to  describe  a  para- 
bola of  which  the  vertex  is  at  A. 
Through  A  draw  EF parallel  to  CD, 
and  through  C  and  D  draw  C  E  and 
DF  parallel  to  the  axis.  Divide  B  C 
and  B  D  into  any  number  of  equal 
parts,  say  five,  at  a,  b,  etc.,  and  divide 
C  E  and  DF  in  to  the  same  number  of 
parts.  Through  the  points  a,  6,  c,  d  in 
the  base  C  D  on  each  side  of  the  axis 
draw  perpendiculars,  and  through 
a,  6,c,  d  in  CJ^and  DFdraw  lines  to 
the  vertex  A,  cutting  the  perpendicu- 
lars at  e.  /,  g,  h.  These  are  points  in 
the  parabola,  and  the  curve  C  A  D  may 
be  traced  as  shown,  passing  through 
then;. 


FIG.  56. 


A 

—  ^ 

^ 

f 

"e 

L 

J 

^ 

^ 

/r 

!/ 

^ 

FIG.  57 


GEOMETRICAL   PROBLEMS. 


49 


FIG.  58. 


FIG.  59. 


47.  The  Hyperbola  (Fig.  58). — A  hyperbola  is  a  plane  curve,  such 
that  the  difference  of  the  distances  from  any  point  of  it  to  two  fixed  points 

is  equal  to  a  given  distance.    The  fixed 
points  are  called  the  foci. 

To  construct  a  hyperbola. 
—Let  F'  and  B'  be  the  foci,  and  F'  F 
the  distance  between  them.  Take  a 
ruler  longer  than  the  distance  F'  F, 
and  fasten  one  of  its  extremities  at  the 
focus  F'.  At  the  other  extremity,  H, 
attach  a  thread  of  such  a  length  that 
the  length  of  the  ruler  shall  exceed 
the  length  of  the  thread  by  a  given 
distance  A  B.  Attach  the  other  ex- 
tremity of  the  thread  at  the  focus  F. 

Press  a  pencil,  P,  against  the  ruler, 
and  keep  the  thread  constantly  tense, 
while  the  ruler  is  turned  around  F1  as 
a  centre.  The  point  of  the  pencil  will 
describe  one  branch  of  the  curve. 

2d  Method:  By  points  (Fig.  59).— 
From  the  focus  F'  lay  off  a  distance 
F'  N  equal  to  the  transverse  axis,  or 
distance  between  the  two  branches  of 
the  curve,  and  take  any  other  distance, 
as  F'H,  greater  than  F'N. 

With  F'  as  a  centre  and  F'H  as  a 
radius  describe  the  arc  of  a  circle. 
Then  with  .Fas  a  centre  and  N  H  as  a 
radius  describe  an  arc  intersecting 
the  arc  before  described  at  p  and  q. 

Tnese  will  be  points  of  the  hyperbola,  for  F'  q  —  Fq  is  equal  to  the  trans- 
verse axis  A  B. 

If,  with  F  as  a  centre  and  F'  H  as  a  radius,  an  arc  be  described,  and  a 
second  arc  be  described  with  F'  as  a  centre  and  NHas  a  radius,  two  points 
in  the  other  branch  of  the  curve  will  be  determined.  Hence,  by  changing 
the  centres,  each  pair  of  radii  will  determine  two  points  in  each  branch. 

The  Equilateral  Hyperbola.— The  trans  verse  axis  of  a  hyperbola 
is  the  distance,  on  a  line  joining  the  foci,  between  the  two  branches  of  the 
curve.  The  conjugate  axis  is  a  line  perpendicular  to  the  transverse  axis, 
drawn  from  its  centre,  and  of  such  a  length  that  the  diagonal  of  the  rect- 
angle of  the  transverse  and  conjugate  axes  is  equal  to  the  distance  between 
the  foci.  The  diagonals  of  this  rectangle,  indefinitely  prolonged,  are  the 
asymptotes  of  the  hyperbola,  lines  which  the  curve  continually  approaches, 
but  touches  only  at  an  infinite  distance.  If  these  asymptotes  are  perpen- 
dicular to  each  other,  the  hyperbola  is  called  a  rectangular  or  equilateral 
hyperbola.  It  is  a  property  of  this  hyperbola  that  if  the  asymptotes  are 
taken  as  axes  of  a  rectangular  system  of  coordinates  (see  Analytical  Geom- 
etry), the  product  of  the  abscissa  and  ordinate  of  any  point  in  the  curve  is 
equal  to  the  product  of  the  abscissa  and  ordinate  of  any  other  point ;  or,  if 
p  is  the  ordinate  of  any  point  and  v  its  abscissa,  and  p1  and  v^  are  the  ordi- 
nate and  abscissa  of  any  other  point,  pv=p*  vl',  or  pv  =  a  constant. 

48.  The  Cycloid 
(Fig.  60).— If  a  circle  A  d 
be  rolled  along  a  straight 
line  A6,  any  point  of  the 
circumference  as  A  will 
describe  a  curve,  which  is 
called  a  cycloid.  The  circle 
is  called  the  generating 
circle,  and  A  the  generat- 


1     2     3     4     u     w  ~.  -  - , 

™       fin  To  draw  a  cycloid. 

f  IG.  DU.  — Divide  the  circumference 

of  the  generating  circle  into  an  even  number  of  equal  parts,  as  A  1,  12,  etc., 
and  set  off  these  distances  on  the  base.  Through  the  points  1,  2,  3,  etc.,  on 
the  circle  draw  horizontal  lines,  and  on  them  set  off  distances  la  =  ^41, 
26  =  A2,  '\c  =  ^43,  etc.  The  points  A,  a,  6,  c,  etc.,  will  be  points  in  the  cycloid, 
through  which  draw  the  curve. 


50 


GEOMETRIC  AT,    PROBLEMS. 


49.  The  Epicycloid  (Fig.  61)  is 
generated  by  a  point  D  in  one  circle 
D  C  rolling  upon  the  circumference  of 
another  circle  A  C  B,  instead  of  on  a 
flat  surface  or  line;  the  former  being 
the  generating  circle,  and  the  latter 
the  fundamental  circle.  The  generat- 
ing circle  is  shown  in  four  positions,  in 
which  the  generating  point  is  succes- 
sively marked  D,  D',  D",  D'".  A  D'"  B 
is  the  epicycloid. 


FIG.  6! 


y  10 


5O.  The  Hypocycloid  (Fig.  62) 

is  generated  by  a  point  in  the  gener- 
ating circle  rolling  on  the  inside  of  the 
fundamental  circle. 

When  the  generating  circle  =  radius 
of  the  other  circle,  the  hypocycloid 
becomes  a  straight  line. 


51.    The          Tractrix         or 
Schiele's  anti-friction  curve 

(Fig.  63).— #  is  the  radius  of  the  shaft, 
O,  1,2,  etc.,  the  axis.  From  O  set  off 
on  .R  a  small  distance,  o  a;  with  radius 
R  and  centre  a  cut  the  axis  at  1,  join 
a  1,  and  set  off  a  like  small  distance 
«6;  from  b  with  radius  R  cut  axis  at 
2,  join  b  2,  and  so  on,  thus  finding 
^h  which 


points  o,  a,  b,  c,  d,  etc.,  through 
the  curve  is  to  be  drawn. 
FIG.  63. 

52.  The  Spiral.— The  spiral  is  a  curve  described  by  a  point  which 
moves  along  a  straight  line  according  to  any  given  law,  the  line  at  the  same 
time  having  a  uniform  angular  motion.  The  line  is  called  the  radius  vector. 

If  the  radius  vector  increases  directly 
as  the  measuring  angle,  the  spires, 
or  parts  described  in  each  revolution, 
thus  gradually  increasing  their  dis- 
tance from  each  other,  the  curve  is 
known  as  the  spiral  of  Archimedes 
(Fig.  64). 

This  curve  is  commonly  used  for 
cams.    To  describe  it  draw  the  radius 
vector  in  several  different  directions 
f  IG.  o4.  around  the  centre,  with  equal  angles 

between  them;  set  off  the  distances  1,  2,  3,  4,  etc.,  corresponding  to  the  scale 
upon  which  the  curve  is  drawn,  as  shown  in  Fig.  64. 

In  the  common  spiral  (Fig.  64)  the  pitch  is  uniform;  that  is,  the  spires  are 
equidistant.  Such  a  spiral  is  made  by  rolling  up  a  belt  of  uniform  thickness. 


To  construct  a  spiral  with 
four  centres  (Fig.  65).— Given  the 

pitch  of  the  spiral,  construct  a  square 
about  the  centre,  with  the  sum  of  the 
four  sides  equal  to  the  pitch.  Prolong 
the  sides  in  one  direction  as  shown; 
the  corners  are  the  centres  for  each 
arc  of  the  external  angles,  forming  a 
quadrant  of  a  spire. 


Fig.  65. 


GEOMETRICAL   PROBLEMS. 


51 


53.  To  find  the  diameter  of  a  circle  into  which  a  certain 
number  ol  rings  will  fit  on  its  inside  (Fig.  66).— For  instance, 
what  is  the  diameter  of  a  circle  into  which  twelve  i^-inch  rings  will  fit,  as 
per  sketch  ?    Assume   that  we  have  found  the  diameter  of  the  required 

circle,  and  have  drawn  the  rings  inside 
of  it.  Join  the  centres  of  the  rings 
by  straight  lines,  as  shown  :  we  then 
obtain  a  regular  polygon  with  12 
sides,  each  side  being  equal  to  the  di- 
ameter of  a  given  ring.  We  have  now 
to  find  the  diameter  of  a  circle  cir- 
cumscribed about  this  polygon,  and 
add  the  diameter  of  one  ring  to  it;  the 
sum  will  be  the  diameter  of  the  circle 
into  which  the  rings  will  fit.  Through 
the  centres  A  and  D  of  two  adjacent 
rings  draw  the  radii  C  A  and  C  D  ; 
since  the  polygon  has  twelve  sides  the 
angle  A  C  D  =  30°  and  A  C  B  =  15°. 
One  half  of  the  side  A  D  is  equal  to 
A  B.  We  now  give  the  following  pro- 
portion :  The  sine  of  the  angle  ACS 
is  to  A  B  as  1  is  to  the  required  ra- 
dius. From  this  we  get  the  following 
rule  :  Divide  A  B  by  the  sine  of  .the  angle  A  CB  ;  the  quotient  will  be  the 
radius  of  the  circumscribed  circle  ;  add  to  the  corresponding  diameter  the 
diameter  of  one  ring  ;  the  sum  will  be  the  required  diameter  FG. 

54.  To  describe  an  arc  of  a  circle  which   is  too  large  to 
be  d  rawn  by  a  beam  compass,  by  means  of  points  in  the 
arc,  radius  being  given.— Suppose  the  radius  is  20  feet  and  it  is 
desired  to  obtain  five  points  in  an  arc  whose  half  chord  is  4  feet.     Draw  a 
line  equal  to  the  half  chord,  full  size,  or  on  a  smaller  scale  if  more  con- 
venient, and   erect  a  perpendicular  at  one  end,  thus  making  rectangular 
axes  of  coordinates.    Erect  perpendiculars  at  points  1,  2,  3,  and  4  feet  from 
the.  first  perpendicular.    Find  values  of   y  in  the  formula  of  the  circle. 
ra  _|_  yi  —  j£2  Dy  substituting  for  x  the  values  0,  1,  2,  3,  and  4,  etc.,  and  for  Rz 
the_square  of  _the  radius,  or  400.    The  values  will  be  y  =  V R*  -a:2  =  ^400, 
^399,  ^306,  f  391,  ^384;  =  20,          19.975,    19.90,    19.774,    19.596. 
Subtract  the  smallest, 

or  19.596,  leaving  0.404,      0.379,      0.304,    0.178,      0        feet. 

I  jay  off  these  distances  on  the  five  perpendiculars,  as  ordinates  from  the 
half  chord,  and  the  positions  of  five  points  on   the  arc  will  be  found. 

Through    these    the    curve    may   be 
drawn.     (See  also  Problem  14.) 

55.  The  Catenary  is  the  curve 
assumed  by  a  perfectly  flexible  chord 
when  its  ends  are  fastened  at  two 
points,  the  weight  of  a  unit  length 
being  constant. 
The  equation  of  the  catenary  is 


y  —  -Jea_j_e    al    in  which  e  is  the 

base  of  the  Naperian  system  of  log- 
arithms. 
To  plot  the  catenary.— Let  o 

(Fig.  67)  be  the  origin  of  coordinates. 
Assigning  to  a  any  value  as  3,  the 
equation  becomes 


2.     3.     4. 


1. 

FIG.  67. 
To  find  the  lowest  point  of  the  curve. 

(  0        -0 


52 


GEOMETRICAL   PROBLEMS. 


Then  put  a;  =  1; 


=  l-  (1. 396  -f  0.717)  =  3.17. 


=  "(1.9484  0.513)  =  3.69. 

Put  x  —  3,  4,  5,  etc.,  etc.,  and  find  the  corresponding  values  of  y.    For 
each  value  of  y  we  obtain  two  symmetrical  points,  as  for  example  p  and  p*. 
In  this  way,  by  making  a  successively  equal  to  2,  3,  4,  5,  6,  7,  and  8,  the 
curves  of  Fig.  67  were  plotted. 

In  each  case  the  distance  from  the  origin  to  the  lowest  point  of  the  curve 
is  equal  to  a  ;  for  putting  x  =  o,  the  general  equation  reduces  to  y  —  a. 

For  values  of  a  —  6, 7,  and  8  the  catenary  closely  approaches  the  parabola. 
For  derivation  of  the  equation  of  the  catenary  see  Bowser's  Analytic 
Mechanics.  For  comparison  of  the  catenary  with  the  parabola,  see  article 
by  F.  R.  Honey,  Amer.  Machinist,  Feb.  1,  1894. 

56.  The  Involute  is  a  name  given  to  the  curve  which  is  formed  by 

the  end  of  a  string  which  is  unwound 
from  a  cylinder  and  kept  taut ;  con- 
sequently the  string  as  it  is  unwound 
will  always  lie  in  the  direction  of  a 
tangent  to  the  cylinder.  To  describe 
the  involute  of  any  given  circle,  Fig. 
68,  take  any  point  A  on  its  circum- 
ference, draw  a  diameter  AB,  and 
from  B  draw  B  b  perpendicular  to  A  B. 
Make  Bb  equal  in  length  to  half  the 
circumference  of  the  circle.  Divide 
B  b  and  the  semi-circumference  into 
the  same  number  of  equal  parts, 
say  six.  From  each  point  of  division 
1,  2,  3,  etc.,  on  the  circumference  draw 
lines  to  the  centre  C  of  the  circle. 
Then  draw  1  a  perpendicular  to  C 1 ; 
2(1%  perpendicular  to  (72;  and  so  on. 
FIG. 


Make  1  a  equal  to  b  6,  ;    2a2  equal 
to  b  52  ;  3  «3  equal  to  6  b3  ;  and  so  on. 
«3,  etc.,  by  a  curve;    this  curve  will  be  the 

57.  Method  of  plotting  angles  without  using  a  protrac- 
;or. — The  radius  of  a  circle  whose  circumference  is  360  is  57.3  (more  ac- 
jurately  57.296).  Striking  a  semicircle  with  a  radius  57.3  by  any  scale, 
spacers  set  to  10  by  the  same  scale  will  divide  the  arc  into  18  spaces  of  10° 
each,  and  intermediates  can  be  measured  indirectly  at  the  rate  of  1  by  scale 
for  each  1°,  or  interpolated  by  eye  according  to  the  degree  of  accuracy 
required.  The  following  table  shows  the  chords  to  the  above-mentioned 
radius,  for  every  10  degrees  from  0°  up  to  110°.  By  means  of  one  of  these, 


Join  the  *points  A,  a/,  a 
required  involute. 

57 
tor, 
c 


Angle.  Chord. 

1° 0.999 

10° 9.988 

20° 19.899 

30° 29.658 

40° 39.192 

50° 48.429 


Angle.  Chord. 

60° 57.298 

70° 65.727 

80° 73.658 

90° 81.02'.) 

100° 87  782 

110° 93.809 


a  10°  point  is  fixed  upon  the  paper  next  less  than  the  required  angle,  and 
the  remainder  is  laid  off  at  the  rate  of  1  by  scale  for  each  degree. 


GEOMETRICAL     PROPOSITIONS.  53 


GEOMETRICAL   PROPOSITIONS. 

In  a  right-angled  triangle  the  square  on  the  hypothenuse  is  equal  to  the 
sum  of  the  squares  on  the  other  two  sides. 

If  a  triangle  is  equilateral,  it  is  equiangular,  and  vice  versa. 

If  a  straight  line  from  the  vertex  of  an  isosceles  triangle  bisects  the  base, 
it  bisects  the  vertical  angle  and  is  perpendicular  to  the  base. 

If  one  side  of  a  triangle  is  produced,  the  exterior  angle  is  equal  to  the  sum 
of  the  two  interior  and  opposite  angles. 

If  two  triangles  are  mutually  equiangular,  they  are  similar  and  their 
corresponding  sides  are  proportional. 

If  the  sides  of  a  polygon  are  produced  in  the  same  order,  the  sum  of  the 
exterior  angles  equals  four  right  angles. 

In  a  quadrilateral,  the  sum  of  the  interior  angles  equals  four  right  angles. 

In  a  parallelogram,  the  opposite  sides  are  equal  ;  the  opposite  angles 
are  equal;  it  is  bisected  by  its  diagonal;  and  its  diagonals  bisect  each 
other. 

If  three  points  are  not  in  the  same  straight  line,  a  circle  may  be  passed 
through  them. 

If  two  arcs  are  intercepted  on  the  same  circle,  they  are  proportional  to 
the  corresponding  angles  at  the  centre. 

If  two  arcs  are  similar,  they  are  proportional  to  their  radii. 

The  areas  of  two  circles  are  proportional  to  the  squares  of  their  radii. 

If  a  radius  is  perpendicular  to  a  chord,  it  bisects  the  chord  and  it  bisects 
the  arc  subtended  by  the  chord. 

A  straight  line  tangent  to  a  circle  meets  it  in  only  one  point,  and  it  is 
perpendicular  to  the  radius  drawn  to  that  point. 

If  from  a  point  without  a  circle  tangents  are  drawn  to  touch  the  circle, 
there  are  but  two;  they  are  equal,  and  they  make  equal  angles  with  the 
chord  joining  the  tangent  points. 

If  two  lines  are  parallel  chords  or  a  tangent  and  parallel  chord,  they 
intercept  equal  arcs  of  a  circle. 

If  an  angle  at  the  circumference  of  a  circle,  between  two  chords,  is  sub- 
tended by  the  same  arc  as  an  angle  at  the  centre,  between  two  radii,  the 
angle  at  the  circumference  is  equal  to  half  the  angle  at  the  centre. 

If  a  triangle  is  inscribed  in  a  semicircle,  it  is  right-angled. 

If  an  angle  is  formed  by  a  tangent  and  chord,  it  is  measured  by  one  half 
of  the  arc  intercepted  by  the  chord ;  that  is,  it  is  equal  to  half  the  angle  at 
the  centre  subtended  by  the  chord. 

If  two  chords  intersect  each  other  in  a  circle,  the  rectangle  of  the  seg- 
ments of  the  one  equals  the  rectangle  of  the  segments  of  the  other. 

And  if  one  chord  is  a  diameter  and  the  other  perpendicular  to  it,  the 
rectangle  of  the  segments  of  the  diameter  is  equal  to  the  square  on  half  the 
other  chord,  and  the  half  chord  is  a  mean  proportional  between  the  seg- 
ments of  the  diameter. 


54  MENSURATION. 


MENSURATION. 

PLANE  SURFACES. 

Quadrilateral.— A  four-sided  figure. 

Parallelogram.— A  quadrilateral  with  opposite  sides  parallel. 

Varieties.— Square  :  four  sides  equal,  all  angles  right  angles.  Rectangle: 
opposite  sides  equal,  all  angles  right  angles.  Rhombus:  four  sides  equal, 
opposite  angles  equal,  angles  not  right  angles.  Rhomboid:  opposite  sides 
equal,  opposite  angles  equal,  angles  not  right  angles. 

Trapezium.— A  quadrilateral  with  unequal  sides. 

Trapezoid.— A  quadrilateral  with  only  one  pair  of  opposite  sides 
parallel. 

Diagonal  of  a  square  =  |/2  x  side2  =  1.4142  X  side. 

Diag.  of  a  rectangle  =  ^/sum  of  squares  of  two  adjacent  sides. 

Area  of  any  parallelogram  =  base  x  altitude. 

Area  of  rhombus  or  rhomboid  =  product  of  two  adjacent  sides 
X  sine  of  angle  included  between  them. 

Area  of  a  trapezium  =  half  the  product  of  the  diagonal  by  the  sum 
of  the  perpendiculars  let  fall  on  it  from  opposite  angles. 

Area  of  a  trapezoid  =  product  of  half  the  sum  of  the  two  parallel 
sides  by  the  perpendicular  distance  between  them. 

To  find  the  area  of  any  quadrilateral  figure.— Divide  the 
quadrilateral  into  two  triangles;  the  sum  of  the  areas  of  the  triangles  is  the 
area. 

Or,  multiply  half  the  product  of  the  two  diagonals  by  the  sine  of  the  angle 
at  their  intersection. 

To  find  the  area  of  a  quadrilateral  inscribed  in  a  circle. 
— From  half  the  sum  of  the  four  sides  subtract  each  side  severally;  multi- 
ply the  four  remainders  together;  the  square  root  of  the  product  is  the  area. 

Triangle.— A  three-sided  plane  figure. 

Varieties. — Right-angled,  having  one  right  angle;  obtuse-angled,  having 
one  obtuse  angle  ;  isosceles,  having  two  equal  angles  and  two  equal  sides; 
equilateral,  having  three  equal  sides  and  equal  angles. 

The  sum  of  the  three  angles  of  every  triangle  —  180°. 

The  two  acute  angles  of  a  right-angled  triangle  are  complements  of  each 
other. 

Hypothenuse  of  a  right-angled  triangle,  the  side  opposite  the  right  angle. 

—  ^/sum  of  the  squares  of  the  other  two  sides. 
To  find  the  area  of  a  triangle  s 

RULE  1.  Multiply  the  base  by  half  the  altitude. 

RULE  2.  Multiply  half  the  product  of  two  sides  by  the  sine  of  the  included 
angle. 

RULES.  From  half  the  sum  of  the  three  sides  subtract  each  side  severally; 
multiply  together  the  half  sum  and  the  three  remainders,  and  extract  the 
square  root  of  the  product. 

The  area  of  an  equilateral  triangle  is  equal  to  one  fourth  the  square  of  one 

of  its  sides  multiplied  by  the  square  root  of  3,  =  - — 1,  a  being  the  side;  or 

4 
a2  X  .433013. 

Hypothenuse  and  one  side  of  right-angled  triangle  given,  to  find  other  side, 
Required  side  =  V'hyp2  —  given  side2. 

If  the  two  sides  are  equal,  side  =  hyp  -i-  1.4142;  or  hyp  X  .7071. 

Area  of  a  triangle  given,  to  find  base:  Base  =  twice  area  -r-  perpendicular 
height. 

Area  of  a  triangle  given,  to  find  height:  Height  =  twice  area  -4-  base. 

Two  sides  and  base  given,  to  find  perpendicular  height  (in  a  triangle  in 
which  both  of  the  angles  at  the  base  are  acute). 

RULE.— As  the  base  is  to  the  sum  of  the  sides,  so  is  the  difference  of  the 
sides  to  the  difference  of  the  divisions  of  the  base  made  by  drawing  the  per- 
pendicular. Half  this  difference  being  added  to  or  subtracted  from  half 
the  base  will  give  the  two  divisions  thereof.  As  each  side  and  its  opposite 


PLAXE    SURFACES. 


55 


division  of  the  base  constitutes  a  right-angled  triangle,  the  perpendicular  is 
ascertained  by  the  rule  perpendicular  =  Vhyp2  —  base2. 

Polygon.  —  A  plane  figure  having  three  or  more  sides.  Regular  or 
irregular,  according  as  the  sides  or  angles  are  equal  or  unequal.  Polygons 
are  named  from  the  number  of  their  sides  and  angles. 

To  find  the  area  of  an  irregular  polygon.— Draw  diagonals 
dividing  the  polygon  into  triangles,  and  find  the  sum  of  the  areas  of  these 
triangles. 

To  find  the  area  of  a  regular  polygon: 

RULE.— Multiply  the  length  of  a  side  by  the  perpendicular  distance  to  the 
centre;  multiply  the  product  by  the  number  of  sides,  and  divide  it  by  2. 
Or,  multiply  half  the  perimeter  by  the  perpendicular  let  fall  from  the  centre 
on  one  of  the  sides. 

The  perpendicular  from  the  centre  is  equal  to  half  of  one  of  the  sides  of 
the  polygon  multiplied  by  the  cotangent  of  the  angle  subtended  by  the  half 
side. 

The  angle  at  the  centre  =  360°  divided  by  the  number  of  sides. 

TABLE  OF  REGULAR  POLYGONS. 


Radius  of  Cir- 

cumscribed 

T3 

1 

Circle. 

.0- 

«| 

5 

•/" 

t 

II 

IT; 

£  « 

1" 
CO  <D 

i'L 

§ 

I 

11 

P 

55 

o 

35 

1-1 

tc  * 

rt*0  1) 

"S 

D  ._ 

•°  c 

33 

S  5 

II 

tj   OS'S 

Cj  03 

C6 

i 

3 

| 

!§. 

Is 

tuc_3  ;- 

"So 
q 

to 

3 

^ 

S 

OQ 

a 

J 

^ 

5 

3 

Triangle 

.4330127 

2. 

.5773 

.2887 

1.732 

120° 

60° 

4 

Square 

1. 

1.414 

.7071 

.5 

1.4142 

90 

90 

5 

Pentagon 

1.7204774 

1.238 

.8506 

.6882 

1.1756 

72 

108 

6 

Hexagon 

2.5980762 

1.156 

1. 

.866 

1. 

60 

120 

7 

Heptagon 

3.6339124 

1.11 

1.1524 

1.0383 

.8677 

5126' 

128  4-7 

8 

Octagon 

4.8284271 

1.083 

1.3066 

1.2071 

.7653 

45 

135 

9 

Nonagon 

6.1818242 

1.064 

1.4619 

1.3737 

.684 

40 

140 

10 

Decagon 

7.6942088 

1.051 

1.618 

1.5388 

.618 

36 

144 

11 

Undecagon 

9.3656399 

1.042 

1.7747 

1.7028 

.5634 

3243' 

1473-11 

ta 

Dodecagon 

11.1961524 

1.037 

1.9319 

1.866 

.5176 

30 

150 

To  find  the  area  of  a  regular  polygon,  when  the  length 
of  a  side  only  is  given  : 

RULE.— Multiply  the  square  of  the  side  by  the  multiplier  opposite  to  the 
name  of  the  polygon  in  the  table. 

To  find  the  area  of  an  ir- 
regular figure  (Fig.  69).— Draw  or- 
dinates  across  its  breadth  at  equal 
distances  apart,  the  first  and  the  last 
orclinate  each  being  one  half  space 
from  the  ends  of  the  figure.  Find  the 
average  breadth  by  adding  together 
the  lengths  of  these  lines  included  be- 
tween the  boundaries  of  the  figure, 
and  divide  by  the  number  of  the  lines 
added ;  multiply  this  mean  breadth  by 
the  length.  The  greater  the  number 
of  lines  the  nearer  the  approximation. 


]12    34567 
(+ -Length—. 

FIG.  69. 


In  a  figure  of  very  irregular  outline,  as  an  indicator-diagram  from  a  high- 
speed steam-engine,  mean  lines  may  be  substituted  for  the  actual  lines  of  the 
figure,  being  so  traced  as  to  intersect  the  undulations,  so  that  the  total  area 
of  the  spaces  cut  off  may  be  compensated  by  that  of  the  extra  spaces  \\\- 
closed. 


56  MENSURATION. 

2d  Method :  THE  TRAPEZOIDAL  RULE.  —  Divide  the  figure  into  any  suffi- 
cient number  of  equal  parts;  add  half  the  sum  of  the  two  end  ordinates  to 
the  sum  of  all  the  other  ordinates;  divide  by  the  number  of  spaces  (that  is, 
one  less  than  the  number  of  ordinates)  to  obtain  the  mean  ordinate,  and 
multiply  this  by  the  length  to  obtain  the  area. 

3d  Method :  SIMPSON'S  RULE.— Divide  the  length  of  the  figure  into  any 
even  number  of  equal  parts,  at  the  common  distance  D  apart,  and  draw  or- 
dinates through  the  points  of  division  to  touch  the  boundary  lines.  Add 
together  the  first  and  last  ordinates  and  call  the  sum  A ;  add  together  the 
k  even  ordinates  and  call  the  sum  B;  add  together  the  odd  ordinates,  except 
the  first  and  last,  and  call  the  sum  C.  Then, 

area  of  the  figure  =  A  +  4  f  ±—  x  D. 

o 

4th  Method :  DURAND'S  RULE.— Add  together  4/10  the  sum  of  the  first  an  d 
last  ordinates,  1  1/10  the  sum  of  the  second  and  the  next  to  the  last  (or  the 
penultimates),  and  the  sum  of  all  the  intermediate  ordinates.  Multiply  the 
sum  thus  gained  by  the  common  distance  between  the  ordinates  to  obtain 
the  area,  or  divide  this  sum  by  the  number  of  spaces  to  obtain  the  mean  or- 
dinate. 

Prof.  Duraud  describes  the  method  of  obtaining  his  rule  in  Engineering 
News,  Jan.  18,  1894.  He  claims  that  it  is  more  accurate  than  Simpson's  rule, 
and  practically  as  simple  as  the  trapezoidal  rule.  He  thus  describes  its  ap- 
plication for  approximate  integration  of  differential  equations.  Any  defi- 
nite integral  may  be  represented  graphically  by  an  area.  Thus,  let 

Q=fudx 

be  an  integral  in  which  u  is  some  function  of  x,  either  known  or  admitting  of 
computation  or  measurement.  Any  curve  plotted  with  x  as  abscissa  and  u 
as  ordinate  will  then  represent  the  variation  of  u  with  #,  and  the  area  be- 
tween such  curve  and  the  axis  X  will  represent  the  integral  in  question,  no 
matter  how  simple  or  complex  may  be  the  real  nature  of  the  function  u, 

Substituting  in  the  rule  as  above  given  the  word  "volume"  for  "area"  ' 
and  the  word  "  section  "  for  "  ordinate,"  it  becomes  applicable  to  the  deter- 
mination of  volumes  from  equidistant  sections  as  well  as  of  areas  from 
equidistant  ordinates. 

Having  approximately  obtained  an  area  by  the  trapezoidal  rule,  the  area 
by  Durand's  rule  may  be  found  by  adding  algebraically  to  the  sum  of  the 
ordinates  used  in  the  trapezoidal  rule  (that  is,  half  the  sum  of  the  end  ordi- 
nates +  sum  of  the  other  ordinates)  1/10  of  (sum  of  penultimates  — sum  of 
first  and  last)  and  multiplying  by  the  common  distance  between  the  ordi- 
nates. 

5th  Method. — Draw  the  figure  on  cross-section  paper.  Count  the  number 
of  squares  that  are  entirely  included  within  the  boundary;  then  estimate 
the  fractional  parts  of  squares  that  are  cut  by  the  boundary,  add  together 
these  fractions,  and  add  the  sum  to  the  number  of  whole  squares.  The 
result  is  the  area  in  units  of  the  dimensions  of  the  squares.  The  finer  the 
ruling  of  the  cross-section  paper  the  more  accurate  the  result. 

6th  Method.—  Use  a  planimeter. 

7th  Method. — With  a  chemical  balance,  sensitive  to  one  milligram,  draw 
thn  figure  on  paper  of  uniform  thickness  and  cut  it  out  carefully;  weigh  the 
piece  cut  out,  and  compare  its  weight  with  the  weight  per  square  inch  of  the 
paper  as  tested  by  weighing  a  piece  of  rectangular  shape. 


THE   CIRCLE. 


THE:  CIRCLE. 

Circumference  =  diameter  x  3.1416,  nearly;  more  accurately,  3.14159265359. 

Approximations,  ^  =  3.143;  ~  =  3.1415929. 

7  1  lo 

The  ratio  of  circum.  to  diam.  is  represented  by  the  symbol  77  (called  Pi). 


Multiples  of  7T. 
177  =    3.14159265359 

277  =  6.28318530718 
877  =  9.4247779607? 
477  =  12.56637061436 
57r=  15.70796326795 
677  =  18  84955592154 
777  =  21.99114857513 
877  =  25.13274122872 
977  =  28.27433388231 


Multiples  of  -. 

--IT  =  .7853982 
4 

"  x  2  =  1.5707963 
"  x  3  =  2.3561945 
"  x  4  =  3.1415927 
"  x  5=3.9269908 
"  x  6  =  4.7123890 
"  x  7  =  5.4977871 
"  x  8  =  6.2831853 
"  x  9  =  7.0685835 


Ratio  of  diam.  to  circumference  =  reciprocal  of  77  =  0.3183099. 
Reciprocal  of  ^7  =  1 .27324. 


Multiples  of  -. 

77 

—  =    .31831 

77 

—  =    .63662 

77 

3 


^  =  1.27324 
^•  =  1.59155 

Lj.g 


—  =  2.22817 

77 

-  =  2.54648 

77 

-  =  2.86479 

77 

—  =  3.18310 

77 

—  =  3.81972 


77  =  1.570796 


77  =  1.047197 


-77=0.523599 


Diam.  in  ins.  =  13.5405  ^area  in  sq.  ft. 

Area  in  sq.  ft.  =  (diam.  in  inches)2  x  .0054542. 

D  =  diameter,      R  =  radius,       C  =  circumference, 


^77  =  0.261799 
-*TO  =  0.0087266 
—-  =  114.5915 

77 

772  =     9.86960 
-^-  =  0.101321 

772 

^n    =      1.772453 
^/1=     0.564189 

7T 

Log  77=    0.49714987 

Log  ln  =  1.895090 
4 


A  =  area. 
;  =  3.545  V!Z; 


riff 


.7854  ;  =  -^;  =  4R*  x  .7854  ;  =  77 
2 


-i 

;  =  ' 
4 


STJ  nr\. 

2.  =  ^  .  _  .07958C2;  =  --. 
477'  4 


=  0.31831(7;     =2Y~;     =1.12838^; 


;  =  V   ~;     =0.564189^4. 


R  =  £^;  =  0.1591550: 

Areas  of  circles  are  to  each  other  as  the  squares  of  their  diameters. 
To  find  the  length  of  an  arc  of  a  circle : 

RULE  1.  As  360  is  to  the  number  of  degrees  in  the  arc.  so  is  the  circum- 
ference of  the  circle  to  the  length  of  the  arc. 

RULE  2.  Multiply  the  diameter  of  the  circle  by  the  number  of  degrees  in 
the  arc,  and  this  product  by  0.0087^66. 


58 

Relations  of  Arc,  Chord,  Chord  of  Half  the  Arc, 
Versed  Sine,  etc. 

Let  R  =  radius,        D  =  diameter,        Arc  —  length  of  arc, 

Cd  =  chord  of  the  arc,        ch  =  chord  of  half  the  arc. 

V '  =  versed  sine,        D  —  V  =  diarn.  minus  ver.  sin., 

8ch  -  Cd  .  VCd*  +  4r*  x  10F a  . 

Arc  =   — (very  nearly),    =     ~i  5^  +  33^ — -f^'/t,  nearly. 

2ch  x  10F  , 

ArC  =  60D-2TF  4        '  De      y' 
Chord  of  the  arc  =  2 
=  2 

Chord  of  half  the  arc,  ch  = 


Diameter 

Versed  sine 

±j    '      £ 

4 

2  —  Cd2),    if  F  is  greater  than  radius. 


Half  the  chord  of  the  arc  is  a  mean  proportional  between  the  versed  sine 
and  diameter  minus  versed  sine: 


cM  =  VF  x  (D  -   F). 

Length  of  a  Circular  Arc.—  Huyghens's  Approximation. 

Let  C  represent  the  length  of  the  chord  of  the  arc  and  c  the  length  of  the 
chord  of  half  the  arc;  the  length  of  the  arc 

Sc-C 
L  =  —3-' 

Professor  Williamson  shows  that  when  the  arc  subtends  an  angle  of  30°,  the 
radius  being  100,000  feet  (nearly  19  miles),  the  error  by  this  formula  is  about 
two  inches,  or  1/600000  part  of  the  radius.  When  the  length  of  the  arc  is 
equal  to  the  radius,  i.e.,  when  it  subtends  an  angle  of  57°.  3,  the  error  is  less 
than  1/7680  part  of  the  radius.  Therefore,  if  the  radius  is  100.000  feet,  the 

1  00000 
error  is  less  than  -^     -  =  13  feet.    The  error  increases  rapidly  with  the 

increase  of  the  angle  subtended. 

In  the  measurement  of  an  arc  which  is  described  with  a  short  radius  the 
error  is  so  small  that  it  may  be  neglected.  Describing  an  arc  with  a  radius 
of  12  inches  subtending  an  'angle  of  30°,  the  error  is  1/50000  of  an  inch.  For 
57°.  3  the  error  is  less  than  O^-OOIS. 

In  order  to  measure  an  arc  when  it  subtends  a  large  angle,  bisect  it  and 
measure  each  half  as  before—  in  this  case  making  B  =  length  of  the  chord  of 
half  the  arc,  and  b  =  length  of  the  chord  of  one  fourth  the  arc  ;  then 

_  166  -  2ff 
3    ~* 
Relation  of  the  Circle   to  its  Equal,  Inscribed,   and  Cir- 

cumscribed Squares. 

Diameter  of  circle  x   .88623  (    _    .,      -  pnnnl  sniiarp 

Circumference  of  circle  x   .28209  f  - 
Circumference  of  circle  x    1.1284     =  perimeter  of  equal  square. 


TIIK  i<;r^iL>sK.^»«>*5r        59 


Diameter      of      circle     x     .7071  ] 

Circumference  of  circle  x  .22508  y  =  side  of  inscribed  square. 
Area  of  circle  x  .90031-*-  diameter  ) 

Area  of  circle  x  1.2732     =  area  of  circumscribed  square. 

Area  of  circle  x  .63602     =  area  of  inscribed  square. 

Side  of  square  x  1.4142     =  diarn.  of  circumscribed  circle, 

x  4.4428      —  circum.        "  " 

x  1.1284     =  diarn.  of  equal  circle. 

"      x  3.5449     =  circum.          **         ** 

Perimeter  of  square  x          0.88623    = 
Square  inches  x  1.2732     =  circular  inches. 

Sectors  and  Segments.— To  find  the  area  of  a  sector  of  a  circle. 
RULE  1.  Multiply  the  arc  of  the  sector  by  half  its  radius. 
RULE  2.  As  360  is  to  the  number  of  degrees  in  the  arc,  so  is  the  area  of 
the  circle  to  the  area  of  the  sector. 

RULE  3.  Multiply  the  number  of  degrees  in  the  arc  by  the  square  of  the 
radius  and  by  .008727. 

To  find  the  area  of  a  segment  of  a  circle:  Find  the  area  of  the  sector 
which  has  the  same  arc,  and  also  the  area  of  the  triangle  formed  by  the 
chord  of  the  segment  and  the  radii  of  the  sector. 

Then  take  the  sum  of  these  areas,  if  the  segment  is  greater  than  a  semi- 
circle, but  take  their  difference  if  it  is  less. 

R* 
Another  Method:  Area  of  segment  =—  (arc  —  sin  A)  in  which  A  is  the 

central  angle,  R  the  radius,  and  arc  the  length  of  arc  to  radius  1. 

To  find  the  area  of  a  segment  of  a  circle  when  its  chord  and  height  or 
versed  sine  only  are  given.  First  find  radius,  as  follows  : 

1  fsquare  of  half  the  chord  .  ,  ,  "1 
radius  =  -                                          h  height    . 

2  L  height 

2.  Find   the  angle  subtended  by  the  arc,  as  follows: — — — —  —  sine 

radius 

of  half  the  angle.    Take  the  corresponding  angle  from  a  table  of  sines,  and 
double  it  to  get  the  angle  of  the  arc. 

3.  Find  area  of  the  sector  of  which  the  segment  is  a  part ; 

degrees  of  arc 
area  of  sector  =  area  of  circle  x  - — — -— . 

4.  Subtract  area  of  triangle  under  the  segment: 

Area  of  triangle  =  — —   x  (radius  —  height  of  segment). 

The  remainder  is  the  area  of  the  segment. 

When  the  chord,  arc,  and  diameter  are  given,  to  find  the  area.  From  the 
length  of  the  arc  subtract  the  length  of  the  chord.  Multiply  the  remainder 
by  the  radius  or  one-half  diameter;  to  the  product  add  the  chord  multiplied 
by  the  height,  and  divide  the  sum  by  2. 

Another  rule:  Multiply  the  chord 'by  the  height  and  this  product  by  .6834 
plus  one  tenth  of  the  square  of  the  height  divided  by  the  radius. 

To  find  the  chord:  From  the  diameter  subtract  the  height;  multiply  the 
remainder  by  four  times  the  height  and  extract  the  square  root. 

When  the  chords  of  the  arc  and  of  half  the  arc  and  the  versed  sine  are 
given:  To  the  chord  of  the  arc  add  four  thirds  of  the  chord  of  half  the  arc; 
multiply  the  sum  by  the  versed  sine  and  the  product  by  .40426  (approximate). 

Circular  Ring. — To  find  the  area  of  a  ring  included  between  the  cir- 
cumferences of  two  concentric  circles:  Take  the  difference  between  the  areas 
of  the  two  circles;  or,  subtract  the  square  of  the  less  radius  from  the  square 
of  the  greater,  and  multiply  their  difference  by  3.14159. 

The  area  of  the  greater  circle  is  equal  to  7rR2- 
and  the  area  of  the  smaller,  vrr2. 

Their  difference,  or  the  area  of  the  ring,  is  7r(.R2  -  rz). 

The  Ellipse. — Area  of  an  ellipse  =  product  of  its  semi-axes  x  3.14159 

=  product  of  its  axes  x  .785398. 

TJie  Ellipse.— Circumference  (approximate)  —  3.1416  \    — ^ — ,   D  and  d 

being  the  two  axes. 

Trautwine  gives  the  follo\ving  as  more  accurate;  When  the  longer  axis  D 
is  not  more  than  five  times  the  length  of  the  shorter  axis,  d, 


GO  MENSURATION. 

Circumference  =  3.1416  V^i^- 


8.8 

When  D  is  more  than  5d,  the  divisor  8.8  is  to  be  replaced  by  the  following 
divisors : 


8,       9,        10,     12,     14,      16,      18,      20,      30,       40,       50. 

Divisor  =  9,    9.2,    9.3,    9.35,    9.4,    9.5,    9.6,    9.68,    9.75,    9.8,    9.92,    9.98,     10. 

/        ?i2      n*      n*          \ 
Reuleaux  gives  :    Circumference  =  TT  (a  +  b)^l  +-  r  +  ^  +OK"B+-  ••  )»  m 

which  n  =  a  ~    ,  a  and  6  being  the  semi  axes. 

^4?-ea  o/  a  segment  of  an  ellipse  the  base  of  which  is  parallel  to  one  of 
the  axes  of  the  ellipse.  Divide  the  height  of  the  segment  by  the  axis  of 
which  it  is  part,  and  find  the  area  of  a  circular  segment,  in  a  table  of  circu- 
lar segments,  of  which  the  height  is  equal  to  the  quotient;  multiply  the  area 
thus  found  by  the  product  of  the  two  axes  of  the  ellipse. 

Cycloid.— A  curve  generated  by  the  rolling  of  a  circle  on  a  plane. 
Length  of  a  cycloidal  curve  =  4  X  diameter  of  the  generating  circle. 
Length  of  the  base  =  circumference  of  the  generating  circle. 
Area  of  a  cycloid  =  3  X  area  of  generating  circle. 

Helix  (Screw).— A  line  generated  by  the  progressive  rotation  of  a 
point  around  an  axis  and  equidistant  from  its  centre. 

Length  of  a  helix.— To  the  square  of  the  circumference  described  by  the 
generating-point  add  the  square  of  the  distance  advanced  in  one  revolution, 
and  take  the  square  root  of  their  sum  multiplied  by  the  number  of  revolu- 
tions of  the  generating  point.  Or, 

4/(c2  +  h*)n  =  length,  n  being  number  of  revolutions. 

Spirals,— Lines  generated  by  the  progressive  rotation  of  a  point  around 
a  fixed  axis,  with  a  constantly  increasing  distance  from  the  axis. 

A  plane  spiral  is  when  the  point  rotates  in  one  plane. 

A  conical  spiral  is  when  the  point  rotates  around  an  axis  at  a  progressing 
distance  from  its  centre,  and  advancing  in  the  direction  of  the  axis,  as  around 
a  cone. 

Length  of  a  plane  spiral  line. — When  the  distance  between  the  coils  is 
uniform. 

RULE. — Add  together  the  greater  and  less  diameters;  divide  their  sum  by 
2;  multiply  the  quotient  by  3.1416,  and  again  by  the  number  of  revolutions. 
Or,  take  the  mean  of  the  length  of  the  greater  and  less  circumferences  and 
multiply  it  by  the  number  of  revolutions.  Or, 

length  =  irn  — ^ — ,  d  and  d1  being  the  inner  and  outer  diameters. 

Length  of  a  conical  spiral  line. — Add  together  the  greater  and  less  diam- 
eters;'divide  their  sum  by  2  and  multiply  the  quotient  by  3.1416.  To  the 
square  of  the  product  of  this  circumference  and  the  number  of  revolutions 
of  the  spiral  add -the  square  of  the  height  of  its  axis  and  take  the  square 
root  of  the  sum. 


Or,  length  = 


SOLID    BODIES. 

Xlie  Prism*  —  To  find  the  surface  of  a  right  prism  :  Multiply  the  perim- 
eter of  the  base  by  the  altitude  for  the  convex  surface.  To  this  add  the 
areas  of  the  two  ends  when  the  entire  surface  is  required. 

Volume  of  a  prism  =  area  of  its  base  x  its  altitude. 

Tlie  pyramid.—  Convex  surface  of  a  regular  pyramid  =  perimeter  of 
its  base  X  half  the  slant  height.  To  this  add  area  of  the  base  if  the  whole 
surface  is  required. 

Volume  of  a  pyramid  =  area  of  base  X  one  third  of  the  altitude. 


SOLID    BODIES.  61 

To  find  the  surface  of  a  frustum  of  a  regular  pyramid  :  Multiply  half  the 
slant  height  by  the  sum  of  the  perimeters  of  the  two  bases  for  the  convex 
surface.  To  this  add  the  areas  of  the  two  bases  when  the  entire  surface  is 
required. 

To  find  the  volume  of  a  frustum  of  a  pyramid  :  Add  together  the  areas  of 
the  two  bases  and  a  mean  proportional  between  them,  and  multiply  the 
sum  by  one  third  of  the  altitude.  (Mean  proportional  between  two  numbers 
—  square  root  of  their  product.) 

Wedge.— A  wedge  is  a  solid  bounded  by  five  planes,  viz.:  a  rectangular 
base,  two  trapezoids,  or  two  rectangles,  meeting  in  an  edge,  and  two  tri- 
angular ends.  The  altitude  is  the  perpendicular  drawn  from  any  point  in 
the  edge  to  the  plane  of  the  base. 

To  find  the  volume  of  a  ivedt/e  :  Add  the  length  of  the  edge  to  twice  the 
length  of  the  base,  and  multiply  the  sum  by  one  sixth  of  the  product  of  the 
height  of  the  wedge  and  the  breadth  of  the  base. 

Rectangular  prismoid.— A  rectangular  prismoid  is  a  solid  bounded 
by  six  planes,  of  which  the  two  bases  are  rectangles,  having  their  corre- 
sponding sides  parallel,  and  the  four  upright  sides  of  the  solids  are  trape- 
zoids. 

To  find  the  volume  of  a  rectangular  prismoid :  Add  together  the  areas  of 
the  two  bases  and  four  times  the  area  of  a  parallel  section  equally  distant 
from  the  bases,  and  multiply  the  sum  by  one  sixth  of  the  altitude. 

Cylinder.— Convex  surface  of  a  cylinder  —  perimeter  of  base  X  altitude. 
To  this  add  the  areas  of  the  two  ends  when  the  entire  surface  is  required. 
Volume  of  a  cylinder  =  area  of  base  X  altitude. 

Cone.— Convex  surface  of  a  cone  =  circumference  of  base  X  half  the  slant 
side.  To  this  add  the  area  of  the  base  when  the  entire  surface  is  required. 

Volume  of  a  cone  =  area  of  base  X  5  altitude. 

o 

To  find  the  surface  of  a  frustum  of  a  cone  :  Multiply  half  the  side  by  the 
sum  of  the  circumferences  of  the  two  bases  for  the  convex  surface;  to  this 
add  the  areas  of  the  two  bases  when  the  entire  surface  is  required. 

To  find  tJie  volume  of  a  frustum  of  a  cone  :  Add  together  the  areas  of  the 
two  bases  and  a  mean  proportional  between  them,  and  multiply  the  sum 
by  one  third  of  the  altitude. 

Sphere.— To  find  the  surface  of  a  sphere  ;  Multiply  the  diameter  by  the 
chcu inference  of  a  great  circle;  or,  multiply  the  square  of  the  diameter  by 
3.14159. 

Surface  of  sphere  =  4  X  area  of  its  great  circle. 

"       —  convex  surface  of  its  circumscribing  cylinder. 

Surfaces  of  spheres  are  to  each  other  as  the  squares  of  their  diameters. 

To  find  the  volume  of  a  sphere  :  Multiply  the  surface  by  one  third  of  the 
radius;  or,  multiply  the  cube  of  the  diameter  by  I/GTT;  that  is,  by  0.5236. 

Value  of  -Jir  to  10  decimal  places  =  .5385987756, 

The  volume  of  a  sphere  =  2/3  the  volume  of  its  circumscribing  cylinder. 

Volumes  of  spheres  are  to  each  other  as  the  cubes  of  their  diameters. 

Spherical  triangle.  —  To  find  the  area  of  a  spherical  triangle:  Com- 
pute the  surface  of  the  quadrantal  triangle,  or  one  eighth  of  the  surface  of 
the  sphere.  From  the  sum  of  the  three  angles  subtract  two  right  angles; 
divide  the  remainder  by  90,  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

Spherical  polygon.—  To  find  the  area  of  a  spherical  polygon:  Com- 
pute the  surface  of  the  quadrantal  triangle.  From  the  sum  of  all  the  angles 
subtract  the  pro  luct  of  two  right  angles  by  the  number  of  sides  less  two; 
divide  the  remainder  by  90  and  multiply  the  quotient  by  the  area  of  the 
quadrantal  triangle. 

The  prismoid.— The  prismoid  is  a  solid  having  parallel  end  areas,  and 
may  be  composed  of  any  combination  of  prisms,  cylinders,  wedges,  pyra- 
mids, or  cones  or  frustums  of  the  same,  whose  base's  and  apices  lie  in  the 
end  areas. 

Inasmuch  as  cylinders  and  cones  are  but  special  forms  of  prisms  and 
pyramids,  and  warped  surface  solids  may  be  divided  into  elementary  forms 
of  them,  and  since  frustums  may  also  be  subdivided  into  the  elementary 
forms,  it  is  sufficient  to  say  that  all  prismoids  may  be  decomposed  into 
prisms,  wedges,  and  pyramids.  If  a  formula,  can  be  found  which  is  equally 
applicable  to  all  of  these  forms,  then  it  will  apply  to  any  combination  of 
them.  Such  a  formula  is  called 


MENSURATION. 

The  Prismoidal  Formula. 

Let  A  =  area  of  the  base  of  a  prism,  wedge,  or  pyramid; 
,  A^,  Am  =  the  two  end  and  the  middle  areas  of  a  prismoid,  or  of  any  < 

its  elementary  solids; 

h  =  altitude  of  the  prismoid  or  elementary  solid; 
V—  its  volume; 


For  a  prism  AJt  Am  and  A^  are  equal,  =  A\  V=  -xQA  =  hA. 

For  a  wedge  with  parallel  ends,  A*  =  0,  Am  =  -^  ;  V  =  ~(A^  -f  2At)  -  ~- 

For  a  cone  or  pyramid,  A*  =  0,  Am  =  7^1  ;    V  =  -Ju,  +AJ  =  ~. 

<±  O  O 

The  prismoidal  formula  is  a  rigid  formula  for  all  prismoids.  The  only 
approximation  involved  in  its  use  is  in  the  assumption  that  the  given  solid 
may  be  generated  by  a  right  line  moving  over  the  boundaries  of  the  end 
areas. 

The  area  of  the  middle  section  is  never  the  mean  of  the  two  end  areas  if 
the  prismoid  contains  any  pyramids  or  cones  among  its  elementary  forms. 
When  the  three  sections  are  similar  in  form  the  dimensions  of  the  middle 
area  are  always  the  means  of  the  corresponding  end  dimensions.  This  fact 
often  enables  the  dimensions,  and  hence  the  area  of  the  middle  section,  to 
be  computed  from  the  end  areas. 

Polyedrons.—  A  polyedron  is  a  solid  bounded  by  plane  polygons.  A 
regular  poiyedron  is  one  whose  sides  are  all  equal  regular  polygons. 

To  find  the  surface  of  a  regular  poiyedron.—  Multiply  the  area  of  one  of 
the  faces  by  the  number  of  faces  ;  or,  multiply  the  square  of  one  of  the 
edges  by  the  surface  of  a  similar  solid  whose  edge  is  unity. 

A  TABLE  OP  THE  REGULAR  POLYEDRONS  WHOSE  EDGES  ARE  UNITY. 

Names.                                          No.  of  Faces.  Surface.  Volume. 

Tetraedrori  ..........................     4                   1.7320508  0.1178513 

Hexaedron  ...  ...............  .........     6  6.0000000  1  .0000000 

Octaedrou  ...........................     8  3.4(541010  0.4714045 

Dodecaedron  .........................  12  20.6457'288  7.6631189 

Icosaedron  ...........................  20  8.6602540  2.1816950 

To  find  the  volume  of  a  regular  poiyedron.  -Multiply  the 
surface  by  one  third  of  the  perpendicular  let  fall  f  com  the  centre  on  one  of 
the  faces  ;  or,  multiply  the  cube  of  one  of  the  edges  by  the  solidity  of  a 
similar  poiyedron  whose  edge  is  unity. 

Solid  of  revolution.—  The  volume  of  any  solid  of  revolution  is 
equal  to  the  product  of  the  area  of  its  generating  surface  by  the  length  of 
the  path  of  the  centre  of  gravity  of  that  surface. 

The  convex  surface  of  any  solid  of  revolution  is  equal  to  the  product  of 
the  perimeter  of  its  generating  surface  by  the  length  of  path  of  its  centre 
of  gravity. 

Cylindrical    ring.—  Let  d  =  outer   diameter  ;  d'  =  inner  diameter  ; 

-  (d  —  d')  =  thickness  =  t  ;  -  -n  £*  =  sectional  area  ;  -  (d  -(-  d')  =  mean  diam- 
eter =  M  ;  TT  t  =  circumference  of  section  ;  ir  M  —  mean  circumference  of 
ring;  surface  =  irt  X  *  M\  =  -  7r2(d2  -  d'2);  =  9.86965  t  M;  =  2.4674  1  (d2  -d''2); 

volume  =  -*£*  Mir',  =  2.  46741  P  M. 
4 

Spherical  zone.  —  Surface  of  a  spherical  zone  or  segment  of  a  sphere 
=  its  altitude  x  the  circumference  of  a  great  circle  of  the  sphere.  A  great 
circle  is  one  whose  plane  passes  through  the  centre  of  the  sphere. 

Volume  of  a  zone  of  a  sphere.  —  To  the  sum  of  the  squares  of  the  radii 
of  the  ends  add  one  third  of  the  square  of  the  height;  multiply  the  sum 
by  the  height  and  by  1.5708. 

Spherical  segment,—  Volume  of  a  spherical  segment  with  one  base.  — 


SOLID    BODIES.  63 

Multiply  half  the  height  of  the  segment  by  the  area  of  the  base,  and  the 
cube  of  the  height  by  .5236  and  add  the  two  products.  Or,  from  three  times 
the  diameter  of  the  sphere  subtract  twice  the  height  of  the  segment;  multi- 
ply the  difference  by  the  square  of  the  height  and  by  .5286.  Or,  to  three 
times  the  square  of  the  radius  of  the  base  of  the  segment  add  the  square  of 
its  height,  and  multiply  the  sum  by  the  height  and  by  .5236. 

Spheroid  or  ellipsoid.— When  the  revolution  of  the  spheroid  is  about 
the  transverse  diameter  it  is  prolate,  and  when  about  the  conjugate  it  is 
oblate. 

Convex  surface  of  a  segment  of  a  spheroid. — Square  the  diameters  of  the 
spheroid,  and  take  the  square  root  of  half  their  sum  ;  then,  as  the  diameter 
from  which  the  segment  is  cut  is  to  this  root  so  is  the  height  of  the 
segment  to  the  proportionate  height  of  the  segment  to  the  mean  diameter. 
Multiply  the  product  of  the  other  diameter  and  3.1416  by  the  proportionate 
height. 

Convex  surface  of  a  frustum  or  zone  of  a  spheroid. — Proceed  as  by 

Erevious  rule  for  the  surface  of  a  segment,  and  obtain  the  proportionate 
eight  of  the  frustum.    Multiply  the  product  of  the  diameter  parallel  to  the 
base  of  the  frustum  and  3.1416  by  the  proportionate  height  of  the  frustum. 

Volume  of  a  spheroid  is  equal  to  the  product  of  the  square  of  the  revolving 
axis  by  the  fixed  axis  and  by  .5236.  The  volume  of  a  spheroid  is  two  thirds 
of  that  of  the  circumscribing  cylinder. 

Volume  of  a  segment  of  a  spheroid.—!.  When  the  base  is  parallel  to  the 
revolving  axis,  multiply  the  difference  between  three  times  the  fixed  axis 
and  twice  the  height  of  the  segment,  by  the  square  of  the  height  and  by 
.5236.  Multiply  the  product  by  the  square  of  the  revolving  axis,  and  divide 
by  the  square  of  the  fixed  axis. 

2.  When  the  base  is  perpendicular  to  the  revolving  axis,  multiply  the 
difference  between  three  times  the  revolving  axis  and  twice  the  height  of 
the  segment  by  the  square  of  the  height  and  by  .5236.  Multiply  the 
product  by  the  'length  of  the  fixed  axis,  and  divide  by  the  length  of  the 
revolving  axis. 

Volume  of  the  middle  frustum  of  a  spheroid.— 1.  When  the  ends  are 
circular,  or  parallel  to  the  revolving  axis  :  To  twice  the  square  of  the 
middle  diameter  add  the  square  of  the  diameter  of  one  end  ;  multiply  the 
sum  by  the  length  of  the  frustum  and  by  .2618. 

2.  When  the  ends  are  elliptical,  or  perpendicular  to  the  revolving  axis : 
To  twice  the  product  of  the  transverse  and  conjugate  diameters  of  the 
middle  section  add  the  product  of  the  transverse  and  conjugate  diameters 
of  one  end  ;  multiply  the  sum  by  the  length  of  the  frustum  and  by  .2618. 

Spindles.— Figures  generated  by  the  revolution  of  a  plane  area,  when 
the  curve  is  revolved  about  a  chord  perpendicular  to  its  axis,  or  about  its 
double  ordinate.  They  are  designated  by  the  name  of  the  arc  or  curve 
from  which  they  are  generated,  as  Circular,  Elliptic,  Parabolic,  etc.,  etc. 

Convex  surface  of  a  circular  spindle,  zone,  or  segment  of  it  — Rule:  Mul- 
tiply the  length  by  the  radius  of  the  revolving  arc;  multiply  this  arc  by  the 
central  distance,  or  distance  between  the  centre  of  the  spindle  and  centre 
of  the  revolving  arc  ;  subtract  this  product  from  the  former,  double  the 
remainder,  and  multiply  it  by  3.1416 

Volume  of  a  circular  spindle. — Multiply  the  central  distance  by  half  the 
area  of  the  revolving  segment;  subtract  the  product  from  one  third  of  the 
cube  of  half  the  length,  and  multiply  the  remainder  by  12.5664. 

Volume  of  frustum  or  zone  of  a  circular  spindle. — From  the  square  of 
half  the  length  of  the  whole  spindle  take  one  third  of  the  square  of  half  the 
length  ofj  the  frustum,  and  multiply  the  remainder  by  the  said  half  length 
of  the  frustum  ;  multiply  the  central  distance  by  the  revolving  area  which 
generates  the  frustum  ;  subtract  this  product  from  the  former,  and  multi- 
ply the  remainder  by  6.2832. 

Volume  of  a  segment  of  a  circular  spindle.— Subtract  the  length  of  the 
segment  from  the  half  length  of  the  spindle  ;  double  the  remainder  and 
ascertain  the  volume  of  a  middle  frustum  of  this  length  ;  subtract  the 
result  from  the  volume  of  the  whole  spindle  and  halve  the  remainder. 

Volume  of  a  cycloidal  spindle  =  five  eighths  of  the  volume  of  the  circum- 
scribing cylinder.— Multiply  the  product  of  the  square  of  twice  the  diameter 
of  the  generating  circle  and  3.927  by  its  circumference,  and  divide  this  pro- 
duct by  8. 

Parabolic  conoid. — Volume  <>f  a  parabolic  conoid  (generated  by  the 
revolution  of  a  parabola  on  its  axis;.— Multiply  the  area  of  the  base  by  half 
the  height. 


64  MENSURATION. 

Or  multiply  the  square  of  the  diameter  of  the  base  by  the  height  and  by 
.3927. 

Volume  of  a  frustum  of  a  parabolic  conoid.— Multiply  half  the  sum  of 
the  areas  of  the  two  ends  by  the  height. 

Volume  of  a  parabolic  spindle  (generated  by  the  revolution  of  a  parabola 
on  its  base). — Multiply  the  square  of  the  middle  diameter  by  the  length 
and  by  .4189. 

The  volume  of  a  parabolic  spindle  is  to  that  of  a  cylinder  of  the  same 
height  and  diameter  as  8  to  15. 

Volume  of  the  middle  frustum  of  a  parabolic  spindle.— Add  together 
8  times  the  square  of  the  maximum  diameter,  3  times  the  square  of  the  end 
diameter,  and  4  times  the  product  of  the  diameters.  Multiply  the  sum  by 
the  length  of  the  frustum  and  by  .05236. 

This  rule  is  applicable  for  calculating  the  content  of  casks  of  parabolic 
form. 

Casks* — To  find  the  volume  of  a  cask  of  any  form. — Add  together  39 
times  the  square  of  the  bung  diameter,  25  times  the  square  of  the  head 
diameter,  and  26  times  the  product  of  the  diameters.  Multiply  the  sum  by 
the  length,  and  divide  by  31,773  for  the  content  in  Imperial  gallons,  or  by 
26,470  for  U.  S.  gallons. 

This  rule  was  framed  by  Dr.  Hutton,  on  the  supposition  that  the  middle 
third  of  the  length  of  the  cask  was  a  frustum  of  a  parabolic  spindle,  and 
each  outer  third  was  a  frustum  of  a  cone. 

To  find  the  ullage  of  a  cask,  the  quantity  of  liquor  in  it  when  it  is  not  full. 
1.  For  a  lying  cask :  Divide  the  number  of  wet  or  dry  inches  by  the  bung 
diameter  in  inches.  If  the  quotient  is  less  than  .5,  deduct  from  it  one 
fourth  part  of  what  it  wants  of  .5.  If  it  exceeds  .5,  add  to  it  one  fourth  part 
of  the  excess  above  .5.  Multiply  the  remainder  or  the  sum  by  the  whole 
content  of  the  cask.  The  product  is  the  quantity  of  liquor  in  the  cask,  in 
gallons,  when  the  dividend  is  wet  inches;  or  the  empty  space,  if  dry  inches. 

2.  For  a  standing  cask :  Divide  the  number  of  wet  or  dry  inches  by  the 
length  of  the  cask.  If  the  quotient  exceeds  .5,  add  to  it  one  tenth  of  its 
excess  above  .5;  if  less  than  .5,  subtract  from  it  one  tenth  of  what  it  wants 
of  .5.  Multiply  the  sum  or  the  remainder  by  the  whole  content  of  the  cask. 
The  product  is  the  quantity  of  liquor  in  the  cask,  when  the  dividend  is  wefc 
inches;  or  the  empty  space,  if  dry  inches. 

Volume  of  cask  (approximate)  U.  S.  gallons  =  square  of  mean  diam. 
X  length  in  'inches  X  .0034.  Mean  diam.  =  half  the  sum  of  the  bung  and 
head  diams. 

Volume  of  an  irregular  solid.— Suppose  it  divided  into  parts, 
resembling  prisms  or  other  bodies  measurable  by  preceding  rules.  Find 
the  content  of  each  part;  the  sum  of  the  contents  is  the  cubic  contents  of 
the  solid. 

The  content  of  a  small  part  is  found  nearly  by  multiplying  half  the  sum 
of  the  areas  of  each  end  by  the  perpendicular  distance  between  them. 

The  contents  of  small  irregular  solids  may  sometimes  be  found  by  im- 
mersing them  under  water  in  a  prismatic  or  cylindrical  vessel,  and  observ- 
ing the  amount  by  which  the  level  of  the  water  descends  when  the  solid  is 
withdrawn.  The  sectional  area  of  the  vessel  being  multiplied  by  the  descent 
of  the  level  gives  the  cubic  contents. 

Or,  weigh  the  solid  in  air  and  in  water;  the  difference  is  the  weight  of 
water  it  displaces.  Divide  the  weight  in  pounds  by  62.4  to  obtain  volume  in 
cubic  feet,  or  multiply  it  by  27.7  to  obtain  the  volume  in  cubic  inches. 

When  the  solid  is  very  large  and  a  great  degree  of  accuracy  is  not 
requisite,  measure  its  length,  breadth,  and  depth  in  several  (  iiTerent 
places,  and  take  the  mean  of  the  measurement  for  each  dimension,  and 
multiply  the  three  means  together. 

When  the  surface  of  the  solid  is  very  extensive  it  is  better  to  divide  it 
into  triangles,  to  find  the  area  of  each  triangle,  and  to  multiply  it  by  the 
mean  depth  of  the  triangle  for  the  contents  of  each  triangular  portion;  the 
contents  of  the  triangular  sections  are  to  be  added  together, 

The  mean  depth  of  a  triangular  section  is  obtained  by  measuring  the 
depth  at  each  angle,  adding  together  the. three  measurements,  and  taking 
one  third  of  the  sum. 


PLANE   TRIGONOMETRY. 


65 


PLANE    TRIGONOMETRY. 


Trigonometrical  Functions. 

Every  triangle  has  six  parts— three  angles  and  three  sides.  When  any 
three  of  these  parts  are  given,  provided  one  of  them  is  a  side,  the  other 
p.irts  may  be  determined.  By  the  solution  of  a  triangle  is  meant  the  deter- 
mination of  the  unknown  parts  of  a  triangle  when  certain  parts  are  given. 

The  complement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
an^le  or  arc  from  90°. 

In  general,  if  we  represent  any  arc  by  A,  its  complement  is  90°  —  A. 
Hence  the  complement  of  an  arc  that  exceeds  (JU°  is  negative. 

Since  the  two  acute  angles  of  a  right-angled  triangle  are  together  equal  to 
a  right  angle,  each  of  them  is  the  complement  of  the  other. 

The  supplement  of  an  angle  or  arc  is  what  remains  after  subtracting  the 
angle  or  arc  from  180°.  If  A  is  an  arc  its  supplement  is  180°  —  A.  The  sup- 
plement of  an  arc  that  exceeds  180°  is  negative. 

The  sum  of  the  three  angles  of  a  triangle  is  equal  to  180°.  Either  angle  is 
the  supplement  of  the  other  two.  In  a  right-angled  triangle,  the  right  angle 
being  equal  to  90°,  each  of  the  acute  angles  is  the  complement  of  the  other. 

In  all  right-angled  triangles  having  the  same  ocute  angle,  the  sides  have 
to  each  other  the  same  ratio.  These  ratios  have  received  special  names,  as 
follows: 

If  A  is  one  of  the  acute  angles,  a  the  opposite  side,  b  the  adjacent  side, 
and  c  the  hypothenuse. 

The  sine  of  the  angle  A  is  the  quotient  of  the  opposite  side  divided  by  the 

a 
hypothenuse.     Sin.  A  —  — 

The  tangent  of  the  angle  A  is  the  quotient  of  the  opposite  side  divided  by 
a 

the  adjacent  side.    Tang.  A  =  r- 

The  secant  of  the  angle  A  is  the  quotient  of  the  hypothenuse  divided  by 
c 

the  adjacent  side.     Sec.  A  =  r* 

The  cosine,  cotangent,  and  cosecant  of  an  angle  are  respec- 
tively the  sine,  tangent,  and  secant  of  the  complement  of  that  angle.  The 
terms  sine,  cosine,  etc.,  are  called  trigonometrical  functions. 

In  acircle  whose  radius  is  unity,  the  sine  of  an  arc,  or  of  the  angle  at  the 
centre  measured  by  that  arc,  is  the  perpendicular  let  fall  from  one  extrem- 
ity of  the  arc  upon  the  diameter  passing  through  the  other  extremity. 

The  tangent  of  an  arc  is  the  line  irhich.  touches  the  circle  at  one  extrem- 
ity of  the  arc.  and  is  limited  by  the  diameter  (produced)  passing  through 
the  other  extremity. 

The  secant  of  an  arc  is  that  part  of  the  produced  diameter  which  is 
intercepted  bet'i'een  th.e  centre  and  the  tangent. 

The  versed  sine  of  an,  <nc  is  that  part  of  the  diameter  intercepted 
betn:een  the  extremity  of  the  arc  and  the  foot  of  the  sine. 

In  a  circle  whose  radius  is  not  unity,  the  trigonometric  functions  of  an  arc 
will  be  equal  to  the  lines  here  defined,  divided  by  the  radius  of  the  circle. 

It  1C  A  (Fig.  70)  is  an  angle  in  the  first  quadrant,  and  C  F=  radius, 

W  C*  C'  C1  1?  T? 

The  sine  of  the  angle  =  -— f .   Cos  =  ^ 


I A 


CI 


D  L 


TanS'  =  Rad?   Secant  =  Rad/   Cot'  =  Rad.' 


Cosec-  = 


CL 


GA 


Rad/      ersi"-  =  Rod/ 
If  radius  is  1,  then  Rad.  in   the  denominator  is 

omitted,  and  sine  =  F  G,  etc. 
The  sine  of  an  arc  —  half  the  chord  of  twice  the 

arc. 
The  sine  of  the  supplement  of  the  arc  is  the  same 

as  that  of  the  arc  itself,    Sine  of  arc  B  D  F  =  F  (Jr  — 

sin  arc  F  A, 


66 


PLAKE  TKIGOKOMETRY. 


The  tangent  of  the  supplement  is  equal  to  the  tangent  of  the  arc,  but  with 
a  contrary  sign.  Tang.  B  D  F  —  B  M. 

The  secant  of  the  supplement  is  equal  to  the  secant  of  the  arc,  but  with  a 
contrary  sign.  Sec.  B  D  F  =  CM. 

Signs  of  the  functions  in  the  four  quadrants.— If  we 
divide  a  circle  into  four  quadrants  by  a  vertical  and  a  horizontal  diame- 
ter, the  upper  right-hand  quadrant  is  called  the  first,  the  upper  left  the  sec- 
ond, the  lower  left  the  third,  and  the  lower  right  the  fourth.  The  signs  of 
the  functions  in  the  four  quadrants  are  as  follows: 

First  quad.    Second  quad.     Third  quad.    Fourth  quad. 
Sine  and  cosecant,  +  + 

Cosine  and  secant,  4- 

Tangent  and  cotangent,  +  + 

The  values  of  the  functions  are  as  follows  for  the  angles  specified: 


Angle  

0 

30 

45 

60 

qo 

120 

135 

150 

180 

370 

Sine  

0 

1 

1 

V3~ 

1 

V3 

1 

1 

() 

—  1 

Cosine  

1 

2 

£! 

«2 
1 

2 
\ 

0 

2 
1 

Vo 
1 

2 

A/5 

_^A 

,    1 

0 

Tangent 

0 

2 

1 

^2 
1 

2 

Vy 

GO 

—  Vjj 

~*2 
-t 

2 
1 

Cotangent 

V3 

1 

1 

1 

1/3 

0 

00 

Secant    

1 

^3 
2 

«2 

1/3 
2 

GO 

~V~s 

-  1 

l/o 

~  \  3 
2 

QO 
-  1 

0 

Cosecant  .... 
Versed  sine 

GC 

0 

*3 
2 

2-  ^3 

«2 

Ig-j 

2 

V3 
1 

1 

2 

V3 

3 

.  V5 
1/5+1 

1/3 

e 

M^ 

GC 

i 

a 

V-t 

2 

2 

y2 

2 

1 

TRIGONOMETRICAL  FORMULAE. 

The  following  relations  are  deduced  from  the  properties  of  similar  tri- 
angles (Radius  =  1): 

cos  A  :  sin  A  ::  1  :  tan  A,  whence  tan  A  = 


sin  A  :  cos  A  ::  1  :  cot  A,       "    cotan  A  — 
cos  A  :  1          ::  1  :  sec  A,       "        sec  A  =  • 


cos  A* 
cos  ^4 
sin  A* 
1 


sin  ^4  :  1 


::  1  :  cosec  A,  "    cosec  .4  — 


_ 

sin 


tan  ^1  :  1 


::  1  :  cot  A 


tan  ^4  — 


_ 
cot  A' 


The  sum  of  the  square  of  the  sine  of  an  arc  and  the  square  of  its  cosine 
equals  unity.  Sin2  A  +  cos2  .4  =  1. 

Formulae  for  the  functions  of  the  sum  and  difference  ot 
two  angles : 

Let  the  two  angles  be  denoted  by  A  and  B,  their  sum  A  +  S  =  C,  and  their 
difference  A  -  B  by  D. 


sin  (A  -f  B)  ~  sin  A  cos  B  -j-  cos  A  sin 


(1) 


TIUGOXOMETKICAL   FORMULA.  67 

cos/^4-f  B\=  cos  A  cos  B  -  sin  .4  sin  B\    .....  (2) 

sin  (  A  -  B)  =  sin  A  cos  B  -  cos  A  sin  B;    .    .    .    .    .  (3) 

cos  (A  —  13)  =  cos  A  cos  B  -f  sin  A  sin  B  ......  (4) 

From  these  four  formulae  by  addition  and  subtraction  we  obtain 

sin  (A  +  B)  +  sin  (A  -  B)  -  2  sin  A  cos  #;  .....  (5) 

sin  (A  +  B)  -  sin  (J.  —  B)  =  2  cos  J.  sin  #;  .....  (6) 

cos(^.+  #)  +  cos  (.4  -  5)  =  2  cos  .4  cos  #;  .....  (7) 

cos  (4  -  B)  -  cos  U  +  B)  =  2  sin  A  sin  B  ......  (8) 

If  we  put  A  -f  B  -  C,  and  A  -  B  =  D,  then  ^4  =  ~«7  +  D)  and  £  -  -(<?  - 
D),  and  we  have 

sin  (7  +  sin  £>  =  2  sin  ^(C  +  £>)  cos  £(  (7-  D);  .    ...      (9) 


sin  C-sin  £>  =  2  cos    (  <?••!-  Z>)  sin     (6Y-  D);  .    .    .    .    (10) 
cos  <7  +  cosZ)=:  2  cos  ^(C  +  D)  cos  ^(C—  D);  .    .    .    .    (11) 

cosD-  cos  C-  2  sin  ^(O+Z))sin  J(C  -  Z>)  .....    (12) 

Equation  (9)  may  be  enunciated  thus:  The  sum  of  the  sines  of  any  two 
angles  is  equal  to  twice  the  sine  of  half  the  sum  of  the  angles  multiplied  by 
the  cosine  of  half  their  difference.  These  formulae  enable  us  to  transform 
a  sum  or  difference  into  a  product. 

The  sum  of  the  sines  of  two  angles  is  to  their  difference  as  the  tangent  of 
half  the  sum  of  those  angles  is  to  the  tangent  of  half  their  difference. 


sin  A  -  sin  B      g  QQS  l(A  +  p)  ^  1(^  _  p)      t&n  ^  _  ^}* 

The  sum  of  the  cosines  of  two  angles  is  to  their  difference  as  the  cotan- 
gent of  half  the  sum  of  those  angles  is  to  the  tangent  of  half  their  difference. 

c»«A  +  co*B_2COSl(A+B}™*l{A-B)  =  <**jj 
cos  B  - 


_  _  _ 

The  sine  of  the  sum  of  two  angles  is  to  the  sine  of  their  difference  as  the 
sum  of  the  tangents  of  those  angles  is  to  the  difference  of  the  tangents. 

sin  (A  -f  B)  _  tan  A  +  tan  B 


sin  (A  -  B)       tan  A  -  tan  B' 


(15) 


sin  (A  +  B) 
cos  A  cos  B 
sin  (A  -  B) 
cos  A  cos  B 
cos  ( J.  +  ff) 
cos  A  cos  # 
cos  (A  -  B) 
cos  J.  cos  B 


=  tan  .4  +  tan  B] 


=  tan  JL  —  tan  J5; 


=  1  —  tan  A  tan 


-  1  -f  tan  A  tan 


tan  (A  +  B)  = 


tan  (.4  -  5)  = 


cot  ( 


cot  (4  -  J5)  = 


tan  A  +  tan  B  f 
1  —  tan  A  tan  5' 

tan  A  -  tan  B  ^ 
1  +  tan  A  tan  B' 
cot  A  cot  1?  —  1  m 

cot  5  +  cot  A  ' 
cot  .4  cot  B  4-  1 

cot  £  —  cot  4  ' 


68  PLANE   TEIGONOMETEY. 

Solution  of  Plane  Right-angled  Triangles. 

Let  A  and  B  be  the  two  acute  angles  and  C  the  right  angle,  and  a,  b,  and 
c  the  sides  opposite  these  angles,  respectively,  then  we  have 

1.  sin  A  =  cosB  =  -;      3.  tan^l  =  cotJ?  =  ^; 

c  b 

2.  cos  A  =  sin  B  =  -;       4.  cot  A  =  tan  B  =  -. 

c  a 

1.  In  any  plane  right-angled  triangle  the  sine  of  either  of  the  acute  angles 
is  equal  to  the  quotient  of  t lie  opposite  leg  divided  by  the  hypothenuse. 

2.  Tiie  cosine  of  either  of  the  acute  angles  is  equal  to  the  quotient  of  the 
adjacent  leg  divided  by  the  hypothenuse. 

3.  The  tangent  of  either  of  the  acute  angles  is  equal  to  the  quotient  of  the 
opposite  leg  divided  by  the  adjacent  leg. 

4.  The  cotangent  of  either  of  the  acute  angles  is  equal  to  the  quotient  of 
the  adjacent  leg  divided  by  the  opposite  leg. 

5.  The  square  of  the  hypothenuse  equals  the  sum  of  the  squares  of  the 
other  two  sides. 

Solution  of  Oblique-angled  Triangles. 

The  following  propositions  are  pi  oved  in  works  on  plane  trigonometry.  In 
any  plane  triangle — 

Theorem  1.  Tlie  sines  of  the  angles  are  proportional  to  the  opposite  sides. 

Theorem  2.  The  sum  of  any  two  sides  is  to  their  difference  as  the  tangent 
of  half  the  sum  of  the  opposite  angles  is  to  the  tangent  of  half  their  differ- 
ence. 

Theorem  3.  If  from  any  angle  of  a  triangle  a  perpendicular  be  drawn  to 
the  opposite  side  or  base,  the  whole  base  will  be  to  the  sum  of  the  other  two 
sides  as  the  difference  of  those  two  sides  is  to  the  difference  of  the  segments 
of  the  base. 

CASK  I.  Given  two  angles  and  a  side,  to  find  the  third  angle  and  the  other 
two  sides.  1.  The  third  angle  =  180°  —  sum  of  the  two  angles.  2.  The  sides 
may  be  found  by  the  following  proportion  : 

.  The  sine  of  the  anjile  opposite  the  given  side  is  to  the  sine  of  the  angle  op- 
posite the  required  side  as  the  given  side  is  to  the  required  side. 

CASE  II.  Given  two  sides  and  an  angle  opposite  one  of  them,  to  find  the 
third  side  and  the  remaining  angles. 

The  side  opposite  the  given  angle  is  to  the  side  opposite  the  required  angle 
as  the  sine  of  the  given  angle  is  to  the  sine  of  the  required  angle. 

The  third  angle  is  found  by  subtracting  the  sum  of  the  other  two  from  180°, 
and  the  third  side  is  found  as  in  Case  I. 

TASK  III.  Given  two  sides  and  the  included  angle,  to  find  the  third  side  and 
the  remaining  angles. 

The  sum  of  the  required  angles  is  found  by  subtracting  the  given  angle 
from  180°.  The  difference  of  the  required  angles  is  then  found  by  Theorem 
II.  Half  the  difference  added  to  half  the  sum  gives  the  greater  angle,  and 
half  the  difference  subtracted  from  half  the  sum  gives  the  less  angle.  The 
third  side  is  then  found  by  Theorem  I. 

Another  method  : 

Given  the  sides  c,  b.  and  the  included  angle  A,  to  find  the  remaining  side  a 
and  the  remaining  angles  B  and  C. 

From  either  of  the  unknown  angles,  as  JE?,  draw  a  perpendicular  B  e  to  the 
opposite  side. 

Then 

Ae  =  ccosA,    Be  — c  sin  A,    eC—b  —  Ae,    B  c  -5-  e  C  =  tan  C. 

Or,  in  other  words,  solve  Be,  A  e  and  B  e  C  as  right-angled  triangles. 

CASE  IV.  Given  th^  three  sides,  to  find  the  angles. 

Let  fall  a  perpendicular  upon  the  longest  side  from  the  opposite  angle, 
dividing  the  given  tiTuiirle  into  two  right-angled  triangles.  The  two  seg- 
ments of  the  base  ma.v  be  found  by  Theorem  III.  There  will  then  be  given 
the- hypothenuse  and  one  side  of  a  right-angled  triangle,  to  find  the  angles. 

For  areas  of  triangles,  see  Mensuration, 


ANALYTICAL   GEOMETRY.  69 


ANALYTICAL  GEOMETRY. 

Analytical  geometry  is  that  branch  of  Mathematics  which  has  for 
its  object  ihe-  ueterminauou  of  the  forms  and  magnitudes  of  geometrical 
magnitudes  by  menus  of  analysis. 

Ordinal os  and  abscissas.— In  analytical  geometry  two  intersecting 
lines  FF'.  XX'  are  used  as  coordinate  axes, 
XX'  being  the  axis  of  abscissas  or  axis  of  X, 
p    .     and  YY'  the  axis  of  ord mates  or  axis  of  Y. 


~7 


A.  the  intersection,  is  called  the  origin  of  co- 
ordinates. The  distance  of  any  point  P  from 
the  axis  of  Y  measured  parallel  to  the  axis  of 
X  is  called  the  abscissa  of  the  point,  as  AD  or 
CP,  Fig.  71.  Its  distance  from  the  axis  of  X. 
measured  parallel  to  the  axis  of  F,  is  called 
the  ordiriate,  as  AC  or  PD.  The  abscissa  and 
ordinate  taken  together  are  called  the  coor- 
dinates of  the  point  P.  The  angle  of  intersec- 
Y'  tion  is  usually  taken  as  a  right  angle,  in  which 

FIG  71  ^  case  the  axes  of  JCaud  Fare  called  rectangu- 

lar coordinates. 

The  abscissa  of  a  point  is  designated  by  the  letter  x  and  the  ordinate  by  ?/. 
The  equations  of  a  point  are  the  equations  which  express  the  distances  of 
th^  point  from  the  axis.     Tims  x  =  «,  y  =  b  are  the  equations  of  the  point  P. 
Equations  referred  to  rectangular  coordinates.— The  equa- 
tion oi  a  line  expresses  the  relation  wlncn  exists  between  the  coordinates  of 
every  point  of  the  line. 

Equation  of  a  straight  line,  y  =  ax  ±  6,  in  which  a  is  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  X,  and  b  the  distance  above  A  in  which 
the  line  cuts  the  axis  of  F. 

Every  equation  of  the  first  degree  between  two  variables  is  the  equation  of 
a  straight  line,  as  Ay  -f-  Bx  4-  C  =  0,  which  can  be  reduced  to  the  form  y  = 
ax  ±  b. 
Equation  of  ihe  distance  between  two  points: 

D  =  \/(x"  -  x')*  -f  (y"  -  y')*, 

in  which  x'y'.  x"y"  are  the  coordinates  of  the  two  points. 
Equation  of  a  line  passing  through  a  given  point: 

y  —  y'  =  a(x  —  x'), 

in  which  x'y'  are  the  coordinates  of  the  given  point,  a,  the  tangent  of  the 
angle  the  line  makes  with  the  axis  of  x;  being  undetermined,  since  any  num- 
ber of  lines  may  be  drawn  through  a  given  point. 
Equation  of  a  line  passing  through  two  given  points: 


Equation  of  a  line  parallel  to  a  given  line  and  through  a  given  point: 

y  -  y'  =  a(x  -  x'). 
Equation  of  an  angle  F  included  between  two  given  lines: 

a'  —  a 
tang  V  =  — — — — , 

in  which  a  and  a'  are  the  tangents  of  the  angles  the  lines  make  with  th* 
axis  of  abscissas. 
If  the  lines  are  at  right  angles  to  each  other  tang  V  —  oo ,  and 

1  -j-  a'a  =  0. 

Equation  of  an  intersection  of  two  lines,  whose  equations  are 
y  =  ax  -f-  b,        and      y  =  a'x  -\-  b\ 

b  —  b'  ab'  •-  a'b 

x  = — , ,    and     y  =  — 

a  —  a"  a  -  a' 


70  ANALYTICAL   GEOMETRY. 

Equation  of  a  perpendicular  from  a  given  point  to  a  given  line: 

y  -  y'  =  -  ~(x  -  x'). 
Equation  of  the  length  of  the  perpendicular  P: 

y'  -  ax'  -  b 


1/1  X  a2 

The  circle.—  Equation  of  a  circle,  the  origin  of  coordinates  being  at  the 
centre,  auu  radius  =  R  : 

x*  -f  7/2  =  R*. 
If  the  origin  is  at  the  left  extremity  of  the  diameter,  on  the  axis  of  X: 

y*  =  2Rx  -  a;2. 
If  the  origin  is  at  any  point,  and  the  coordinates  of  the  centre  are  x'y'  : 

(x  -  x')*  +  (y  -  2/')2  =  #  2. 

Equation  of  a  tangent  to  a  c'rcle,  the  coordinates  of  the  point  of  tangency 
being  x"y"  and  the  origin  at  the  centre, 

yy"  -f  xx"  =  Rt. 

The  ellipse.  -Equation  of  an  ellipse,  referred  to  rectangular  coordi- 
nates with  axis  at  the  centre: 


in  which  A  is  half  the  transverse  axis  and  B  half  the  conjugate  axis. 

Equation  of  the  ellipse  when  the  origin  is  at  the  vertex  of  the  transverse 
axis  : 


The  eccentricity  of  an  ellipse  is  the  distance  from  the  centre  to  either 
focus,  divided  by  the  semi-transverse  axis,  or 


The  parameter  of  an  ellipse  is  the  double  ordinate  passing  through  the 
focus.  It  is  a  third  proportional  to  the  transverse  axis  and  its  conjugate,  or 

2#2 
2A  :  2B  :  :  2B  :  parameter;  or  parameter  =  —  —  . 

Any  ordinate  of  a  circle  circumscribing  an  ellipse  is  to  the  corresponding 
ordinate  of  the  ellipse  as  the  semi-transverse  axis  to  the  semi-conjugate. 
Any  ordinate  <>f  a  circle  inscribed  in  an  ellipse  is  to  the  corresponding  onii 
nate  of  the  ellipse  as  the  semi-conjugate  axis  to  the  semi-transverse. 

Equation  of  the  tangent  to  an  ellipse,  origin  of  axes  at  the  centre  : 

A*mj"  +  B'^xx"  =  A*B*, 

y'x"  being  the  coordinates  of  the  point  of  tangency. 

Equation  of  the  normal,  passing  through  the  point  of  tangency,  and  per 
pendicular  to  the  tangent: 


The  normal  bisects  the  angle  of  the  two  lines  drawn  from  the  point  of 
tangency  to  the  foci. 

Th*>  li"ps  drawn  from  the  foci  make  equal  angles  with  the  tangent. 

Tfce  parabola.  —  Equation  of  the  parabola  referred  to  rectangular 
coord  males,  the  origin  being  at  the  vertex  of  its  axis,  y2  —-  Xpx,  in  which  2p 
is  the  parameter  or  double  ordinate  through  the  focus. 


ANALYTICAL   GEOMETRY.  71 

The  parameter  is  a  third  proportional  to  any  abscissa  and  its  corresponding 
ordinate,  or 

x  :  y  : :  y  :  2p. 
Equation  of  the  tangent: 

yy"  =  p(x  -f  x"\ 

y''x"  being  coordinates  of  the  point  of  tangency. 
Equation  of  the  normal: 

y" 
y  -  y"  xx  —  —(x  —  x"). 

The  sub  normal,  or  projection  of  the  normal  on  the  axis,  is  constant,  and 
equal  to  half  the  parameter. 

The  tangent  at  any  point  makes  equal  angles  with  the  axis  and  with  the 
linn  drawn  from  the  point  of  tangency  to  the  focus. 

The  hyperbola. —Equation  of  the  hyperbola  referred  to  rectangular 
coo;  diuates,  origin  at  the  centre: 

Aty*  -  BW  =  -  A^B*, 

in  which  A  is  the  semi-transverse  axis  and  B  the  semi-conjugate  axis. 
Equation  when  the  origin  is  at  the  vertex  of  the  transverse  axis: 

7/2  _  ~^(2A  xxx*). 

Conjugate  and  equilateral  hyperbolas.— If  on  the  conjugate 
axis,  as  a  transverse,  and  a  focal  distance  equal  to  \ 'A*  -+-  .Z?2,  we  construct 
the  two  brandies  of  a  hyperbola,  the  two  hyperbolas  thus  constructed  are 
called  conjugate  hyperbolas.  If  the  transverse  and  conjugate  axes  are 
equal,  the  hyperbolas  are  called  equilateral,  in  which  case  y*  —  x*  =  —  A2 
when  A  is  the  transverse  axis,  and  x'1  —  ?/2  =  —  B*  when  B  is  the  trans- 
verse axis. 

The  parameter  of  the  transverse  axis  is  a  third  proportional  to  the  trans- 
verse axis  and  its  conjugate. 

2A  :  2B  : :  2B  :  parameter. 

The  tangent  to  a  hyperbola  bisects  the  angle  of  the  two  lines  drawn  from 
the  point  of  tangency  to  the  foci. 

The  asymptotes  of  a  hyperbola  are  the  diagonals  of  the  rectangle 
described  on  the  axes,  indefinitely  produced  in  both  directions. 

In  an  equilateral  hyperbola  the  asymptotes  make  equal  angles  with  the 
transverse  axis,  and  are  at  right  angles  to  each  other. 

The  asymptotes  continually  approach  the  hyperbola,  and  become  tangent 
to  it  at  an  infinite  distance  from  the  centre. 

Conic  sections.— Every  equation  of  the  second  degree  between  two 
variables  will  represent  either  a  circle,  an  ellipse,  a  parabola  or  a  hyperbola. 
These  curves  are  those  which  are  obtained  by  intersecting  the  surface  of  a 
cone  by  planes,  and  for  this  reason  they  are  called  conic  sections. 

Logarithmic  curve.— A  logarithmic  curve  is  one  in  which  one  of  the 
coordinates  of  any  point  is  the  logarithm  of  the  other. 

The  coordinate  axis  to  which  the  lines  denoting  the  logarithms  are  parallel 
is  called  the  axis  of  logarithms,  and  the  other  the  axis  of  numbers.  If  y  is 
the  axis  of  logarithms  and  x  the  axis  of  numbers,  the  equation  of  the  curva 
is  y  —  log  x. 

If  the  base  of  a  system  of  logarithms  is  a,  we  have  ay  =  x,  in  which  y  is  the 
logarithm  of  x. 

Each  system  of  logarithms  will  give  a  different  logarithmic  curve.  If  y  = 
0,  x  =  1.  Hence  every  logarithmic  curve  will  intersect  the  axis  of  numbers 
at  a  distance  from  the  origin  equal  to  1. 


72  DIFFERENTIAL   CALCULUS. 


DIFFERENTIAL  CALCULUS. 

The  differential  of  a  variable  quantity  is  the  difference  between  any  two 
of  its  consecutive  values;  hence  it  is  indefinitely  small.  It  is  expressed  by 
writing  d  before  the  quantity,  as  dx,  which  is  read  differential  of  x. 

The  term  ~  is  called  the  differential  coefficient  of  y  regarded  as  a  func- 
tion of  x. 

The  differential  of  a  function  is  equal  to  its  differential  coefficient  mul- 
tiplied by  the  differential  of  the  independent  variable;  thus,  ~-dx  =  dy. 

The  limit  of  a  variable  quantity  is  that  value  to  which  it  continually 
approaches  so  as  at  last  to  differ  from  it  by  less  than  any  assignable  quaii 
tity. 

The  differential  coefficient  is  the  limit  of  the  ratio  of  the  increment  of  the 
independent  variable  to  the  increment  of  the  function. 

The  differential  of  a  constant  quantity  is  equal  to  0. 

The  differential  of  a  product  of  a  constant  by  a  variable  is  equal  to  the 
constant  multiplied  by  the  differential  of  the  variable. 

If    u  =  Av,    du  =  Adv. 
In    any  curve  whose   equation  is  y=f(x\  the  differential   coefficient 

-~  =  tan  a:  hence,  the  rate  of  increase  of  the  function,  or  the  ascension  of 
dx 

the  curve  at  any  point,  is  equal  to  the  tangent  of  the  angle  which  the  tangent 
line  makes  with  the  axis  of  abscissas. 
All  the  operations  of  the  Differential  Calculus  comprise  but  two  objects: 

1.  To  find  the  rate  of  change  in  a  function  when  it  passes  from  one  state 
of  value  to  another,  consecutive  with  it. 

2.  To  find  the  actual  change  in  the  function  :  The  rate  of  change  is  the 
differential  coefficient,  and  the  actual  change  the  function. 

Differentials  of  algebraic  functions.— The  differential  of  the 
sum  or  difference  of  any  number  of  functions,  dependent  on  the  same 
variable,  is  equal  to  the  sum  or  difference  ot:  iheir  differentials  taken  sepa- 
rately : 

If    u  =  y  -f  z  —  w,    tin  =  dy  -J-  dz  —  dw. 

The  differential  of  a  product  of  two  functions  dependent  on  the  same 
variable  is  equal  to  the  sum  of  the  products  of  each  by  the  differential  of 
the  other : 

,         d(uv)      du  .  dv 

d(uv)  =  vdu  4-  udv.  --  — . 

uv         u    '    v 

The  differential  of  the  product  of  any  number  of  functions  is  equal  to  the 
sum  of  the  products  which  arise  by  multiplying  the  differential  of  each 
function  by  the  product  of  all  the  others: 

d(uts}  =  tsdu  +  usdt  4-  utds. 

The  differential  of  a  fraction  equals  the  denominator  into  the  differential 
of  the  numerator  minus  the  numerator  into  the  differential  of  the  denom- 
inator, divided  by  the  square  of  the  denominator  : 


\V  '  V'2 

If  the  denominator  is  constant,  dv  =  0,  and  dt  =  — —  =  : — . 

If  the  numerator  is  constant,  du  =  0,  and  dt  xx — 

The  differential  of  the  square  root  of  a  quantity  is  equal  to  the  differen- 
tial of  the  quantity  divided  by  twice  the  square  root  of  the  quantity: 

If    v  —  u*,    or    v 

2  yu 


DIFFERENTIAL   CALCULUS.  73 

The  differential  of  any  power  of  a  function  is  equal  to  the  exponent  multi- 
plied by  the  function  raided  to  a  power  less  one,  multiplied  by  the  different 
tial  of  the  function,  d(un)  =  nun  -  ldu. 

Form ii las  for  differentiating  algebraic  functions* 


e.d  -    = 


ydx  -  xdy 


1.  d  (a)  =  0. 

2.d(ax)=adx.  7.  d  (xm)  =  mx™  ~  >dx. 

jlx_ 
S-d(Vx)~2Vx 

4.  d  (x  —  y)  =  dx  —  dy.  I    --\  —  -  — 

5.  d  (xy)  =  xdy  +  ydx.  *'  tt  \x     ' '  =  ~  I  X  ^ 

To  find  the  differential  of  the  form  u  =  (a  -f-  bxn)m'. 

Multiply  the  exponent  of  the  parenthesis  into  the  exponent  of  the  varia- 
ble within  the  parenthesis,  into  the  coefficient  of  the  variable,  into  the  bi- 
nomial raised  to  a  power  less  1,  into  the  variable  within  the  parenthesis 
raised  to  a  power  less  1,  into  the  differential  of  the  variable. 

du  =  d(a  -f  bxn)m  =  mnb(a  +  bxn)m  ~lxn~  ldx. 

To  find  the  rate  of  change  for  a  given  value  of  the  variable  : 
P'ind  the  differential  coefficient,  and  substitute  the  value  of  the  variable  in 
the  second  member  of  the  equation. 

EXAMPLE. — If  x  is  the  side  of  a  cube  and  u  its  volume,  u  =  x3.  —  =  3x*. 

dx 

Hence  the  rate  of  change  in  the  volume  is  three  times  the  square  of  the 
edge.    If  the  edge  is  denoted  by  1,  the  rate  of  change  is  3. 

Application.  The  coefficient  of  expansion  by  heat  of  the  volume  of  a  body 
is  three  times  the  linear  coefficient  of  expansion.  Thus  if  the  side  of  a  cube 
expands  .001  inch,  its  volume  expands  .003  cubic  inch.  1.0013  =  1.003003001. 

A  partial  differential  coefficient  is  the  differential  coefficient  of 
a  function  of  two  or  more  variables  under  the  supposition  that  only  one  of 
them  has  changed  its  value. 

A  partial  differential  is  the  differential  of  a  function  of  two  or  more  vari- 
ables under  the  supposition  that  only  one  of  them  has  changed  its  value. 

The  total  differential  of  a  function  of  any  number  of  variables  is  equal  to 
tiie  sum  of  the  partial  differentials. 

If  u  =f(xy\  the  partial  differentials  are  -r^dx,  -r-dy. 

ax       ay 

If  u  =  #2  +  y3  —  z,  du  =  -^dx  +  -;-dy  -f  -~dz\  =  2xdx  -(-  3?/2d?/  —  dz. 


Integrals.— An  integral  is  a  functional  expression  derived  from  a 
differential.  Integration  is  the  operation  of  finding  the  primitive  function 
from  the  differential  function.  It  is  indicated  by  the  sign /,  which  is  read 
'•  the  integral  of."  Thus  f2xdx  —  x^  ;  read,  the  integral  of  2xdx  equals  x"*. 

To  integrate  an  expression  of  the  form  mxm~  ldx  or  xmdx,  add  1  to  the 
exponent  of  the  variable,  and  divide  by  the  new  exponent  and  by  the  differ- 
ential of  the  variable:  /  Sx^dx  =  x3.  (Applicable  in  all  cases  except  when 

m  —  —  1.    For  I  x        dx  see  formula  2  page  78.) 

The  integral  of  the  product  of  a  constant  by  the  differential  of  a  vari- 
able is  equal  to  the  constant  multiplied  by  the  integral  of  the  differential: 


faxmdx  =  afxmdx  =  a— ^—.  x 
J  m  -f-  1 


The  integral  of  the  algebraic  sum  of  any  number  of  differentials  is  equal  to 
the  algebraic  sum  of  their  integrals: 

2  b  z3 
du  =  2ax*dx  —  bydy  —  z"*dz;    fdu  =  -ax3  —  -y*  —  -7.-. 

3  #  o 

Since  the  differential  of  a  constant  is  0,  a  constant  connected  with  a  vari- 
able by  the  sign  -f-  or  —  disappears  in  the  differentiation;  thus  d(a  -f-  xm)  — 
dxm  =  ma?m  "  ldx.  Hence  ill  integrating  a  differential  expression  we  must 


74  DIFFERENTIAL   CALCULUS. 

annex  to  the  integral  obtained  a  constant  represented  by  C  to  compensate 
for  the  term  which  may  have  been  lost  in  differentiation.  Thus  if  we  have 
dy  =  adx\  fdy  =  afdx.  Integrating, 

y  =  ax  ±  C. 

The  constant  (7,  which  is  added  to  the  first  integral,  must  have  such  a 
value  as  to  render  the  functional  equation  true  for  every  possible  value  that 
may  be  attributed  to  the  variable.  Hence,  after  having  found  the  first 
integral  equation  and  added  the  constant  C,  if  we  then  make  the  variable 
equal  to  zero,  the  value  which  the  function  assumes  will  be  the  true  value 
of  a 

An  indefinite  integral  is  the  first  integral  obtained  before  the  value  of  the 
constant  Cis  determined. 

A  particular  integral  is  the  integral  after  the  value  of  C  has  been  found. 

A  definite  integral  is  the  integral  corresponding  to  a  given  value  of  the 
variable. 

Integration  between  limits.— Having  found  the  indefinite  inte- 
grcii  ana  the  particular  integral,  the  next  step  is  to  find  the  definite  integral, 
and  then  the  definite  integral  between  given  limits  of  the  variable. 

The  integral  of  a  function,  taken  between  two  limits,  indicated  by  given 
values  of  x,  is  equal  to  the  difference  of  the  definite  integrals  correspond- 
ing to  those  limits.  The  expression 

dx 


J7"=afd 

is  read:  Integral  of  the  differential  of  y,  taken  between  the  limits  x'  and  x"\ 
the  least  limit,  or  the  limit  corresponding  to  the  subtractive  integral,  being 
placed  below. 

Integrate  du  —  $x*dx  between  the  limits  x  =  1  and  x  =  3,  u  being  equal  to 
81  when  x  =  0.    fdu  =  fdx'2dx  =  3#3  -f  O;  C  -  81  when  x  =  0,  then 

/  Xdu  =  3(3)3  -f  81,  minus  3(1)3  -f  81  =  78. 

Integration  of  particular  forms. 

To  integrate  a  differential  of  the  form  du  =  (a  -f  bxn)mxn  ~  ldx. 

1.  If  there  is  a  constant  factor,  place  it  without  the  sign  of  the  integral, 
and  omit  the  power  of  the  variable  without  the  parenthesis  and  the  differ- 
ential ; 

2.  Augment  the  exponent  of  the  parenthesis  by  1,  and  then  divide  this 
quantity,  with  the  exponent  so  increased,  by  the  exponent  of  the  paren- 
thesis, into  the  exponent  of  the  variable  within  the  parenthesis,  into  the  co- 
efficient of  the  variable.    Whence 


J  (m  -f  l)nb 

The  differential  of  an  arc  is  the  hypothenuse  of  a  right-angle  triangle  of 
which  the  base  is  dx  and  the  perpendicular  dy. 

If  z  is  an  arc,  dz  =   ^dx*  +  dy*      z  =f  ]/dx*  +  dy*. 

Quadrature  of  a  plane  figure. 

The  differential  of  the  area  of  a  plane  surf  ace  is  equal  to  the  ordinate  into 
the  differential  of  the  abscissa. 

ds  =  ydx. 

To  apply  the  principle  enunciated  in  the  last  equation,  in  finding  the  area 
of  any  particular  plane  surface  : 

Find  the  value  of  y  in  terms  of  x,  from  the  equation  of  the  bounding  line; 
substitute  this  value  in  the  differential  equation,  and  then  integrate  between 
the  required  limits  of  x. 

Area  of  the  parabola^—  Find  <the  area  of  any  portion  of  the  com- 
mon parabola  whose  equation  is 

y*  =  2px\       whence    y  = 


DIFFERENTIAL  CALCULUS.  75 

Substituting  this  value  of  y  in  the  differential  equation  ds  —  ydx  gives 

r     r  ~,-  r  .      '*v*i>  * 

I   ds=   I    y^pxdx  =  \/2p  I  x^dx  =  —  -"  —  xl  +  C; 


2 

C7. 


Tf  we  estimate  the  area  from  the  principal  vertex,  x  =  0.  y  =  0,  and  (7  =  0; 

and  denoting  the  particular  integral  by  s',  s'  =  r  #//. 

9 

That  is,  the  area  of  any  portion  of  the  parabola,  estimated  from  the  ver- 
tex, is  equal  to  %  of  the  rectangle  of  the  abscissa  and  ordinate  of  the  extreme 
point.  The  curve  is  therefore  quadrable. 

Quadrature  of  surfaces  of  revolution.  —The  differential  of  a 
surface  of  revolution  is  equal  to  the  circumference  of  a  circle  perpendicular 
to  the  axis  into  the  differential  of  the  arc  of  the  meridian  curve. 


in  which  y  is  the  radius  of  a  circle  of  the  bounding  surface  in  a  plane  per- 
pendicular to  the  axis  of  revolution,  and  x  is  the  abscissa,  or  distance  of  the 
plane  from  the  origin  of  coordinate  axes. 

Therefore,  to  find  the  volume  of  any  surface  of  revolution: 

Find  the  value  of  y  and  dy  from  the  equation  of  the  meridian  curve  in 
terms  of  x  and  dx,  then  substitute  these  values  in  the  differential  equation,, 
and  integrate  between  the  proper  limits  of  x. 

By  application  of  this  rule  we  may  find : 

The  curved  surface  of  a  cylinder  equals  the  product  of  the  circumference 
of  the  base  into  the  altitude". 

The  convex  surface  of  a  cone  equals  the  product  of  the  circumference  of 
the  base  into  half  the  slant  height. 

The  surface  of  a  sphere  is  equal  to  the  area  of  four  great  circles,  or  equal 
to  the  curved  surface  of  the  circumscribing  cylinder. 

€11  bat  11  re  of  volumes  of  revolution.— A  volume  of  revolution 
is  a  volume  generated  by  the  revolution  of  a  plane  figure  about  a  fixed  line 
called  the  axis. 

If  we  denote  the  volume  by  V,  dV  =  ny*  dx. 

The  area  of  a  circle  described  by  any  ordinate  y  is  Try2;  hence  the  differ- 
ential of  a  volume  of  revolution  is  equal  to  the  area  of  a  circle  perpendicular 
to  the  axis  into  the  differential  of  the  axis. 

The  differential  of  a  volume  generated  by  the  revolution  of  a  plane  figure 
about  the  axis  of  Y  is  irx'2dy. 

To  find  the  value  of  Ffor  any  given  volume  of  revolution  : 

Find  the  value  of  #2  in  terms  of  x  from  the  equation  of  the  meridian 
curve,  substitute  this  value  in  the  differential  equation,  and  then  integrate 
between  the  required  limits  of  x. 

By  application  of  this  rule  we  may  find: 

The  volume  of  a  cylinder  is  equal  to  the  area  of  the  base  multiplied  by  the 
altitude. 

The  volume  of  a  cone  is  equal  to  the  area  of  the  base  into  one  third  the 
altitude. 

The  volume  of  a  prolate  spheroid  and  of  an  oblate  spheroid  (formed  by 
the  revolution  of  an  ellipse  around  its  transverse  and  its  conjugate  axis  re- 
spectively) are  each  equal  10  two  thirds  of  the  circumscribing  cylinder. 

If  the  axes  are  equal,  the  spheroid  becomes  a  sphere  and  its  volume  = 

"nR1*  x  D  —  --  irD3:  R  being  radius  and  D  diameter. 
o  o 

The  volume  of  a  paraboloid  is  equal  to  half  the  cylinder  having  the  same 
base  and  altitude. 

The  volume  of  a  pyramid  equals  the  area  of  the  base  multiplied  by  one 
third  the  altitude. 

Second,  third,  etc.,  differentials. -The  differential  coefficient 
being  a,  function  of  the  independent  variable,  it  may  be  differentiated,  and 
\ve  thus  obtain  the  second  differential  coefficient: 

d\-jT )  =  -T-.    Dividing  by  dx^  we  have  for  the  second  difl!ere;itia!  cce^l- 


76  DIFFERENTIAL   CALCULUS. 

cient  —  ",  which  is  read:   second  differential  of  u  divided  by  the  square  of 

the  differential  of  x  (or  dx  squared). 

d^u 
The  third  differential  coefficient  -—$  is  read:  third  differential  of  u  divided 

by  dx  cubed. 
The  differentials  of  the  different  orders  are  obtained  by  multiplying  -the 

d3u 
differential  coefficients  by  the  corresponding  powers  of  dx:  thus  —  ~  dx*  = 

third  differential  of  u. 

Sign  of  the  first  differential  coefficient.—  If  we  have  a  curve 
\vnose  equation   is  y  =  fx,  referred  to  rectangular  coordinates,   the  curve 

will  recede  from  the  axis  of  X  when    C~~  is  positive,  and  approach  the 

axis  when  it  is  negative,  when  the  curve  lies  within  the  first  angle  of  the 
coordinate  axes.  For  all  angles  and  every  relation  of  y  and  x  the  curve 
will  recede  from  the  axis  of  JTwheri  the  ordinate  and  first  differential  co- 
efficient have  the  same  sign,  and  approach  it  when  they  have  different 
signs.  If  the  tangent  of  the  curve  becomes  parallel  to  the  axis  of  .X  at  any 

point  -p  —  0.    If  the  tangent  becomes  perpendicular  to  the  axis  of  JTat  any 

point  —  =  co. 

dx 

Sign  of  the  second  differential  coefficient.  -The  second  dif- 
ferential coefficient  has  the  same  sign  as  the  ordinate  when  ihe  curve  is 
convex  toward  the  nxia  of  abscissa  and  a  contrary  sign  when  it  is  concave. 
Jftaclaiirin's  Theorem.—  For  developing  into  a  series  any  function 
of  a  single  variable  as  u  —  A  -J-  Ux  -f  Ox'1  +  />#s  -r  -^'4i  etc.,  in  which  A,  B, 
C,  etc.,  are  independent  of  x: 

/du\  1    /d^u\  1       fd*u\ 

«  =  <»>..  0+(^).V+iTiU*).-o*  '+i—  sWLo*1-*  ete- 

In  applying  the  formula,  omit  the  expressions  x  =  0,  although  the  coeffi- 
cients are  always  found  under  tins  hypothesis. 
EXAMPLES  : 

(a  +  x)n  =  «'"  +  mam  ~  >*  4-  ™  (-^-=-V-  V 


1 


x    .  a:3      a-3 


Taylor's  Theorem.— For  developing  into  a  series  any  function  of  the 

sum  or  difference  of  two  independent  variables,  as  u'  =  f(x  ±  y): 

du  du'  , 

in  which  u  is  what  u'  becomes  when  y  =  0,  —   is  what          becomes  win  n 

y  =  0.  etc. 

maxima  and  minima.— To  find  the  maximum  or  minimum  ralue 
of  a  function  of  a  single  variable: 

1.  Find  the  first  differential  coefficient  of  the  function,  place  it  equal  to  ((. 
and  determine  the  roots  of  the  equation. 

2.  Find  the  second  differential  coefficient,  and  substitute  each  real  root. 
in  succession,  for  the  variable  in  the  second  member  of  the  equation.     Each 
root  which  gives  a  negative  result  will  correspond  to  a  maximum  value  of 
the  function,  and  each  which  gives  a  positive  result  will  correspond  to  a 
minimum  value. 

EXAMPLE.— To  find  the  value  of  x  which  will  render  the  function  y  a 
maximum  or  minimum  in  the  equation  of  the  circle,  ?/2  +  #2  =  R*\ 

—  =  —  ^:  making  -  -  ==  0  gives  x  =?  Q. 
<*#         y  y 


DIFFERENTIAL  CALCULUS.  77 

The  second  differential  coefficient  is:  —^=  —  X    \y  . 

dx  y3 

When  x  =  U,  y  =  R;  hence  -—  |  =  —  —  ,  which  being  negative,  y  is  a  maxi- 

mum for  R  positive. 

In  applying  the  rule  to  practical  examples  we  first  find  an  expression  for 
the  function  which  is  to  be  made  a  maximum  or  minimum. 

2.  If  iu  such  expression   a  constant  quantity  is  found  as  a  factor,  it  may 
be  omitted  in  the  operation;  for  the  product  will  be  a  maximum  or  a  mini- 
mum when  the  variable  factor  is  a  maximum  or  a  minimum. 

3.  Any  value  of  the  independent  variable  which  renders  a  function  a  max- 
imum  or  a  minimum  will  render  any  power  or  root  of  that    function   a 
maximum  or  minimum;  hence  we  may  square  both  members  of  an  equa- 
tion to  free  it  of  radicals  before  differentiating. 

By  these  rul^s  we  may  find: 

The  maximum  rectangle  which  can  be  inscribed  in  a  triangle  is  one  whose 
altitude  is  half  the  altitude  of  the  triangle. 

The  altitude  of  the  maximum  cylinder  which  can  be  inscribed  in  a  cone  is 
one  third  the  altitude  of  the  cone.' 

The  surface  of  a  cylindrical  vessel  of  a  given  volume,  open  at  the  top,  is  a 
minimum  when  the  altitude  equals  half  the  diameter. 

The  altitude  of  a  cylinder  inscribed  in  a  sphere  when  its  convex  surface  is 
a  maximum  is  r  |/2.    r  —  radius. 

The  altitude  of  a  cylinder  inscribed  in  a  sphere  when  the  volume  is  a 

2r 
maximum  is  ~~7-' 

V* 

Differential  of  an  exponential  function. 

If     u  =  ax  ...............    (1) 

then  du  —  dax  —  ax  k  dx,     .........    (2) 

in  which  fc  is  a  constant  dependent  on  a. 

The  relation  between  a  and  k  is  ak  =  e\  whence  a  =  e*,      .....    (3) 

in  which  e  =  2.7182818  .  .  .  the  base  of  the  Naperian   system  of  logarithms. 
Logarithms.  —  The  logarithms  in  the  Naperian  system  are  denoted  by 
Z,  Nap.  log  or  hyperbolic    log,  hyp.  log,  or  loge;  and  in  the  common  system 
always  by  log. 

k  =  Nap.  log  a,    log  a  —  k  log  e  .......    (4) 


og  —  com.   og  x  5. 

If  in  equation  (4)  we  make  a  =  10,  we  have 


1  =  k  log  e,    or    -  =  log  e  =  M  '. 

K 

That  is,  the  modulus  of  the  common  system  is  equal  to  1,  divided  by  the 
Naperian  logarithm  of  the  common  base. 
From  equation  (2)  we  have 

du     da* 

—  =  -  =  kdx. 
u       ax 

If  we  make  a  =  10,  the  base  of  the  common  system,  x  =  log  u,  and 

,.,         .        7         du      1       du 
u(log  u}  =  dx  =  —  x  -  =  —  x  M. 
u        k       u 

That  is,  the  differential  of  a  common  logarithm  of  a  quantity  is  equal  to  the 
differential  of  the  quantity  divided  by  the  quantity,  into  the  modulus. 
If  we  make  a  =  e,  the  base  of  the  Naperian  system,  x  becomes  the  Nape- 


78  DIFFERENTIAL   CALCtTLtTS. 

rian  logarithm  of  u,  and  k  becomes  1  (see  equation  (3));  hence  M  =  1,  and 

d(Nap.  log  u)  =  dx  =  — ;   =  ^. 
a**'  ^ 

That  is,  the  differential  of  a  Naperian  logarithm  of  a  quantity  is  equal  to  the 
differential  of  the  quantity  divided  by  the  quantity;  and  in  the  Naperiau 
system  the  modulus  is  1. 

Since  k  is  the  Naperian  logarithm  of  a,  du  =  ax  I  a  dx.  That  is,  the 
differential  of  a  function  of  the  form  ax  is  equal  to  the  function,  into  the 
Naperian  logarithm  of  the  base  a,  into  the  differential  of  the  exponent. 

If  we  have  a  differential  in  a  fractional  form,  in  which  the  numerator  is 
the  differential  of  the  denominator,  the  integral  is  the  Naperiari  logarithm 
of  the  denominator.  Integrals  of  fractional  differentials  of  other  forms  are 
given  below: 

Differential  forms  which  have  known  integrals;  ex* 
ponential  functions.  (I  —  Nap.  log.) 


/  a 


1.  /  ax  I  a  dx  =  ax  -f-  C; 


2.  A^=    fdxx-i-lx 
J    x      J 

3.  /  (xyx~ldy  +  yx  ly  x  dx)  =  yx  +  <7; 

/»       da?  , 

4-  /     7  =  Z(#  +  /i/a;2  ±  a2)  4-  C; 

«/    y  x2  ±  a2 

s°  /  '          ^  =  l(x  ±a  +  \/xt  ±  2ax)  +  C; 

/^S 


/2/7r//r 
g^g—     = 
0.^^+^ 

J   a:  |/a2  -  *2    •      i^f^?^/  +  ^ 

V^~~~f--*  "  ~  *  V"^**        /  +  C* 


Circular  functions.— Let  a  denote  an  arc  in  the  first  quadrant,  y  fts 
sine,  x  its  cosine,  v  its  versed  sine,  and  t  its  tangent;  and  the  following  nota- 
tion be  employed  to  designate  an  arc  by  any  one  of  its  functions,  viz., 

sin  —1  y  denotes  an  arc  of  which  y  is  the  sine 
cos""1  a;     "  "     *    "        "      x  is  the  cosine, 

tan"1  t      "          "    "    "        "      t  is  the  tangent 


DIFFERENTIAL   CALCULUS. 


79 


<'read  "arc  whose  sine  is  y,"  etc.), — we  have  the  following  differential  forms 
which  have  known  integrals  (r  =  radius): 


cos  z  dz      =  sin  z  -f  C\ 


/-sin 


/'-H-gL.     ^cos-^ftf; 
J    |/1  -  ^ 

—  ,.  =  ver-sin  ~~  l 

|/2v  -  v* 


v  -f-  C\ 


C     rdy     •    =sin-l2/  +  C; 
J    yr*-y* 

—  —          =  cos  ~~  l  x  +  C\ 
|/r2  -  x* 


sin  z  dz  =  ver-sin  z  4-  C; 


COS'2 


=  tan  z  -f  O; 


/rd  v  _ 
tfto-v  +  tf  =  ver-sin  ~ 


/du  _lu  . 

.  =  sm     x  -  -f-  (7; 

|/a2  -  w2  a 

/-<fu  lW   , 

._  =  cos  ~  1  --  4-  (7; 

|/a2  _  ws  a 


y » "+i 


Tlie  cycloid,— If  a  circle  be  rolled  along  a  straight  line,  any  point  of 
the  circumference,  as  P,  will  describe  a  curve  which  is  called  a  cycloid.  The 
circle  is  called  the  generating  circle,  and  Pthe  generating  point. 

The  transcendental  equation  of  the  cycloid  is 


and  the  differential  equation  is  dx  =     /g-~-  - — % 

The  area  of  the  cycloid  is  equal  to  three  times  the  area  of  the  generating 
circle. 

The  surface  described  by  the  arc  of  a  cycloid  when  revolved  about  its  base 
is  equal  to  64  thirds  of  the  generating  circle. 

The  volume  of  the  solid  generated  by  revolving  a  cycloid  about  its  base  is 
equal  to  five  eighths  of  the  circumscribing  cylinder. 

Integral  calculus. — In  the  integral  calculus  we  have  to  return  from 
the  differential  to  the  function  from  which  it  was  derived  A  number  of 
differential  expressions  are  given  above.,  each  of  which  has  a  known  in- 
tegral corresponding  to  it,  and  which  being  differentiated,  will  produce  the 
given  differential. 

In  all  classes  of  functions  any  differential  expression  may  be  integrated 
when  it  is  reduced  to  one  of  the  known  forms;  and  the  operations  of  the 
Integral  calculus  consist  mainly  in  making  such  transformations  of  given 
differential  expressions  as  shall  reduce  them  to  equivalent  ones  whose  in- 
tegrals are  known. 

For  methods  of  making  these  transformations  reference  must  be  made  to 
che  text-books  on  differential  and  integral  calculus. 


80 


MATHEMATICAL   TABLES. 
RECIPROCALS   OF   NUMBERS. 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro-  , 
cal. 

1 

No. 

Recipro- 
cal. 

1 

1.00000000 

64 

.01562500 

127 

.00787402 

190 

.00526316 

253 

.00395257 

2 

.50000000 

5 

.0153S461 

8 

.00781250 

1 

.00523560 

4 

.00393701 

3 

.33333333 

6 

.01515151 

9 

.00775194 

2 

.00520833 

5 

.00392157 

4 

.25000000 

7 

.01492537 

130 

.00769231 

3 

.00518135 

6 

.00390625 

5 

.20000000 

8 

.01470588 

1 

.00763359 

4 

.00515464 

7 

.00389105 

6 

.16666667 

9 

.01449275 

2 

.00757576 

5 

.0051-2820 

8 

.00387597 

7 

.11285714 

70 

.01428571 

3 

.00751880 

6 

.00510204 

9 

.00386100 

8 

.1-2500000 

1 

.01408451 

4 

.00746269 

7 

.00507614 

260 

.00384615 

9 

.11111111 

2 

.01388889 

5 

.00740741 

8 

.00505051 

1 

.00383142 

10 

.10000000 

3 

.01369863 

6 

.00735294 

9 

.00502513 

2 

.00381679 

11 

.09090909 

4 

.01351351 

7 

.00729927 

200 

.00500000 

3 

,00380228 

Id 

.08333333 

g 

.01333333 

8 

.00724638 

1 

.00497512 

4 

.00378788 

.  13 

.07692308 

6 

.01315789 

9 

.00719424 

2 

.00495049 

R 

.00377358 

14 

.07142857 

7 

.01298701 

140 

.00714286 

d 

.00492611 

6 

.00375940 

15 

.06666667 

8 

.01282051 

1 

.00709220 

4 

.00490196 

7 

.00374532 

10 

.06250000 

c 

.01-265823 

t 

.00704225 

5 

.00487805 

8 

.00373134 

17 

.05582353 

80 

.01250000 

£ 

.00699301 

6 

.00485437 

9 

.00371747 

18 

.05555556 

1 

.01234568 

4 

.00694444 

7 

.00483092 

270 

.00370370 

19 

.05263158 

c 

.01219512 

5 

.00689655 

8 

.00480769 

1 

.00369004 

20 

.05000000 

3 

.01204819 

6 

.00684931 

9 

.00478469 

.00367647 

1 

.04761905 

4 

.01190476 

7 

.00680272 

210 

.00476190 

j 

.00366300 

2 

.04545455 

5 

.01176471 

8 

.00675676 

11 

.00473934 

4 

.00364963 

3 

.04347826 

6 

.01162791 

9 

.00671141 

12 

.00471698 

£ 

.00363636 

4 

.04166667 

•j 

.01149425 

150 

.00666667 

13 

.00469484 

6 

.00302319 

5 

.04000000 

8 

.01136364 

1 

.00662252 

H 

.00467290 

r 

.00361011 

6 

.03846154 

9 

.01123595 

c 

.00657895 

15 

.00465116 

8 

.00359712 

7 

.03703704 

90 

.01111111 

o 

.00653595 

16 

.00462963 

9 

.00358423 

8 

.03571429 

1 

.01098901 

4 

.00649351 

17 

.00460829 

280 

.00357143 

9 

.03448276 

2 

.01086956 

5 

.00645161 

18 

.00458716 

1 

.00355872 

30 

.0^333333 

0 

.01075269 

6 

.00641026 

19 

.00456621 

.00354610 

1 

.03225806 

4 

.01063830 

7 

.00636943 

220 

.00454545 

•_ 

.00353357 

2 

.03125000 

5 

01052632 

8 

.0063-2911 

1 

.00452489 

^ 

.00352113 

3 

.03030303 

6 

.01041667 

9 

.00628931 

f 

.00450450 

F 

.00350877 

4 

.02941176 

7 

.01030928 

160 

.00025000 

I 

.00448430 

6 

.00349350 

5 

.02857143 

8 

.01020408 

1 

.00621118 

4 

.00446429 

1 

.00348432 

6 

.02777778 

9 

.01010101 

2 

.00617284 

5 

.00444444 

8 

.00347222 

7 

.02702703 

100 

.01000000 

3 

.00613497 

6 

.00442478 

9 

.00346021 

8 

.02631579 

1 

.00990099 

4 

.00609756 

7 

.00440529 

290 

.00344828 

9 

.02564103 

2 

.00980392 

5 

00606061 

8 

.00438596 

1 

.00343643 

40 

.02500000 

g 

.00970874 

6 

.00602410 

Cj 

.00436681 

2 

.00342466 

1 

.02439024 

4 

.00961538 

7 

.00598802 

230 

.00434783 

c 

.00341297 

2 

.02380952 

FJ 

.00952381 

8 

.00595238 

1 

.00432900 

4 

.00340136 

3 

.02325581 

6 

.00943396 

9 

.00591716 

2 

.00431034 

5 

.00338983 

4 

.02272727 

7 

.00934579 

170 

.00588235 

f\ 

.00429184 

6 

.00337838 

5 

.02222222 

8 

.00925926 

1 

.00584795 

4 

.00427350 

7 

.00336700 

6 

.02173913 

9 

.00917431 

2 

.00581395 

5 

.00425532 

8 

.00335570 

7 

.02127660 

110 

.00909091 

3 

,00578035 

6 

.00423729 

9 

.00334448 

8 

.02083333 

11 

.00900901 

4 

.00574713 

7 

.00421941 

300 

.00333333 

9 

.02040816 

12 

.00892857 

5 

.00571429 

8 

.00420168 

1 

.00332226 

50 

.02000000 

13 

.00884956 

6 

.00568182 

9 

.00418410 

jj 

.00331126 

1 

.01960784 

14 

.00877193 

7 

.00564972 

240 

.00416667 

3 

.00330033 

2 

.01923077 

15 

.00869565 

8 

.00561798 

1 

.00414938 

4 

.00328947 

3 

.01886792 

16 

.00862069 

9 

.00558659 

2 

.00413223 

5 

.00327869 

4 

.01851852 

17 

.00854701 

180 

.00555556 

g 

.00411523 

6 

.00326797 

5 

.01818182 

18 

.0084745S 

1 

.00552486 

4 

.00409836 

7 

.00325733 

6 

.01785714 

19 

.00840336 

2 

.00549451 

5 

.00408163 

8 

,00324675 

7 

.01754386 

120 

.00833333 

j] 

.00546448 

6 

.00406504 

£ 

.00323625 

8 

.01724138 

1 

.00826446 

4 

.00543478 

7 

.00404858 

310 

.00322581 

9 

.01694915 

2 

.00819672 

5 

.00540540 

8 

.00403226 

11 

.00321543 

60 

.01666667 

€ 

.00813008 

6 

.00537634 

9 

.00401606 

12 

,00320513 

1 

.01639344 

4 

.00806452 

7 

.00534759 

250 

.00400000 

13 

.00319489 

2 

.01612903 

K 

.00800000 

8 

.00531914 

1 

.00398406 

14 

.00318471 

3 

.01587302 

6 

.00793651 

9 

.00529100 

2 

.00396825 

15 

.00317460 

RECIPROCALS  OF   NUMBERS. 


81 


No 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

310 

.00316456 

381 

.00262467 

446 

.00224215 

511 

.00195695 

576 

.00173611 

17 

.00315457 

2 

.00261780 

7 

.00223714 

12 

.00195312 

7 

.00173310 

18 

.00314465 

3 

.00261097 

8 

.00223214 

13 

.00194932 

8 

.00173010 

19 

.00313480 

4 

.00260417 

9 

.00222717 

14 

.00194552 

9 

.00172712 

320 

.00313500 

5 

.00259740 

450 

.00222222 

15 

.00194175 

580 

.00172414 

1 

.00311526 

6 

.00259067 

1 

.00221729 

16 

.00193798 

1 

.00172117 

2 

.00310559 

7 

.00258398 

2 

.00221239 

17 

.00193424 

0 

.00171821 

3 

.00309597 

8 

.00257732 

3 

.00220751 

18 

.00193050 

3 

.00171527 

4 

.00308642 

9 

.00257069 

4 

.00220264 

19 

.00192678 

4 

.00171233 

5 

.00307692 

390 

.00256410 

5 

.002197-80 

5-20 

.00192308 

5 

.00170940 

6 

.00306748 

1 

.00255754 

6 

.00219298 

1 

.00191939 

6 

.00170648 

7 

.00305810 

2 

.00255102 

7 

.00218818 

2 

.00191571 

7 

.00170358 

8 

.00304878 

3 

.00254453 

8 

.00218341 

3 

.00191205 

8 

.00170008 

9 

.00303951 

4 

.00253807 

9 

.00217865 

4 

.00190840 

9 

.00169779 

330 

.00303030 

5 

.00253165 

460 

.00217391 

5 

.00190476 

590 

.00169491 

1 

.00302115 

6 

.00252525 

1 

.00216920 

6 

.00190114 

1 

.00169205 

a 

.00301205 

7 

.00251889 

2 

.00216450 

f 

.00189753 

2 

.00168919 

3 

.00300300 

8 

.00251256 

s 

.00215983 

8 

.00189394 

3 

.00168634 

4 

.00299401 

9 

.00250627 

4 

.00215517 

9 

.00189036 

4 

.00168350 

5 

.00298507 

400 

.00250000 

t 

.00215054 

530 

.00188679 

5 

.00168007 

6 

.00297619 

1 

.00249377 

6 

.00214592 

1 

.00188324 

6 

.00167785 

7 

.00296736 

2 

.00248756 

7 

.00214133 

2 

.00187970 

r- 

.00167504 

8 

.00295858 

3 

.00248139 

8 

.00213675 

3 

.00187617 

8 

.00167224 

9 

.00294985 

4 

.00247525 

c 

.00213220 

4 

.00187-266 

9 

.00166945 

340 

.00294118 

5 

.00246914 

470 

.00212766 

5 

.00186916 

600 

.00166667 

1 

.00293255 

6 

.00246305 

1 

.00212314 

6 

.00186567 

1 

.00166389 

2 

.00292398 

7 

.00245700 

2 

.00211864 

7 

.00186220 

2 

.00166113 

3 

.00291545 

8 

.00245098 

* 

.00211416 

8 

.00185874 

3 

.00165837 

4 

.00290698 

9  j  .00244499 

4 

.00210970 

9 

.00185528 

3 

.00165563 

R 

.00289855 

410  .00243902 

5 

.00210526 

540 

.00185185 

5 

.00165289 

6 

.00289017 

11  .00243309 

6 

.00210084 

1 

.C0184S43 

6 

.00165016 

ri 

.00288184 

12  .00242718 

7 

.00209644 

2 

.00184502 

,7 

.00164745 

8 

.00287356 

13  .00242131 

8 

.00201)205 

3 

.00184162 

8 

.00164474 

9 

.00286533 

14:  .00241546 

9 

.00208768 

4 

.00183823 

9 

.00164204 

350 

.00285714 

15  .00240964 

480 

.00208333 

R 

00183486 

610 

.00163934 

1 

.00284900 

16|  .00240385 

1 

.00207900 

e 

.00183150 

11 

.00163666 

2 

.00284091 

17  i  .00239808 

2 

.00207469 

7 

.0018-2815 

12 

.00163399 

3 

.00283286 

18:  .00  .'39234 

'. 

.00207039 

8 

.00182482 

13 

.00163132 

4 

.00282486 

19!  .00238663 

t 

.00206612 

9 

.00182149 

14 

.00162866 

5 

.00281690 

420  .00238095 

5 

.00206186 

£50 

.00181818 

15 

.00162602 

6 

.00280899 

1 

.00237530 

6 

.00205761 

1 

.00181488 

16 

.00162338 

i~ 

.00280112 

2 

.00236967 

1 

.00205339 

2 

.00181159 

17 

.00162075 

8 

.90279330 

3 

.00236407 

8 

.00204918 

£ 

.00180832 

18 

.00161812 

9 

.00278551 

4 

.00235849 

< 

.00204499 

4 

.00180505 

19 

.00161551 

360 

.00277778 

5 

.00235294 

490 

.00204082 

5 

.00180180 

620 

.00161290 

1 

.00277008 

6 

.00234742 

] 

.00-203666 

6 

.00179856 

] 

.00161031 

2 

.00276243 

7 

.00234192 

t 

.00203252 

7 

.00179533 

2 

.00160772 

g 

.00275482 

8 

.00233645 

\ 

.00202840 

8 

.00179211 

I 

.00160514 

4 

.00274725 

9 

.00233100 

i 

.00202429 

9 

.00178891 

f 

.00160256 

5 

.00273973 

430  .00232558 

r 

.00202020 

560 

.00178571 

5 

.00160000 

6 

.00273224 

1 

.00232019 

b 

.00201613 

1 

.00178253 

0 

.00159744 

7 

.00272480 

2 

.00231481 

\ 

.00201207 

2 

.00177936 

7 

.00159490 

8 

.00271739 

3 

.00-230947 

8 

.00200803 

3 

.00177620 

8 

.00159236 

9 

.00271003 

4 

.00230415 

j 

.00200401 

4 

.00177305 

t 

.00158982 

370 

.00270270 

5 

.00229885 

500 

.00200000 

r 

.00176991 

630 

.00158730 

1 

.00269542 

6 

.00-229358 

\ 

.00199601 

6 

.00176678 

.00158479 

5 

.00268817 

7 

.00228833 

< 

.00199203 

7 

.00176367 

c 

.00158228 

3 

.00268096 

8 

.00228310 

J 

.00198807 

8 

.00176056 

3 

.00157978 

4 

.00267380 

9  .00227790 

i 

.00198413 

9 

400175747 

4 

.00157729 

5 

.00266667 

440  i  .00227273 

| 

.001980-20 

570 

,00175439 

5 

.00157480 

6 

.00265957 

1  .00226757 

( 

.00197628 

1 

.00175131 

1 

.00157'233 

7 

.00265252 

2i  .00226244 

7 

.00197239 

2 

.00174825 

7 

.00156986 

8 

.00264550 

3 

.00225734 

8 

.001968oO 

j. 

.00174520 

8 

.00156740 

9 

.00263852 

4 

.00225225 

( 

.00196464 

4 

.00174216 

9 

.00156494 

380 

.C0263158 

5 

.00224719 

510 

.00196078 

1   5 

.00173913 

1  640 

.00156250 

MATHEMATICAL  TABLES. 


No. 

Recipro- 
cal. 

No. 

Recipro 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

641 

.00156006 

706 

.00141643 

771 

.00129702 

836 

.00119617 

901 

.00110988 

2 

.00155763 

7 

.00141443 

2 

.00129534 

7 

.00119474 

2 

.00110865 

3 

.00155521 

8 

.00141243 

3 

.00129366 

8 

.00119332 

3 

.00110742 

4 

.00155279 

9 

.00141044 

4 

.00129199 

9 

.00119189 

4 

.00110619 

5 

.00155039 

710 

.00140845 

5 

.00129032 

840 

.00119048 

5 

.00110497 

6 

.00154799 

11 

.00140647 

6 

.00128866 

1 

.00118906 

6 

.00110375 

r- 

.00154559 

12 

.00140449 

ir 

.00128700 

2 

.00118765 

7 

.00110254 

8 

.00154321 

13 

.00140252 

8 

.00128535 

3 

.00118(>24 

8 

.00110132 

9 

.00154083 

14 

.00140056 

9 

.00128370 

4 

.00118483 

9 

.00110011 

650 

.00153846 

15 

.00139860 

780 

.00128205 

5 

.00118343 

910 

.00109890 

] 

.00153610 

16 

.00139665 

1 

.00128041 

6 

.00118203 

11 

.00109769 

2 

.00153374 

17 

.00139470 

2 

.00127877 

7 

.00118064 

12 

.00109649 

3 

.00153140 

18 

.00139276 

3 

.00127714 

8 

.00117924 

13 

.00109529 

4 

.00152905 

19 

.00139082 

4 

.00127551 

9 

.00117786 

14 

.00109409 

5 

.00152672 

720 

.00138889 

5 

.00127388 

850 

.00117647 

15 

.00109290 

6 

.00152439 

1 

.00138696 

6 

.00127226 

1 

.00117509 

16 

.00109170 

r- 

.0015.2207 

2 

.00138504 

7 

.00127065 

2 

.00117371 

17 

.00109051 

8 

.00151975 

g 

.00138313 

8 

.00126904 

g 

00117233 

18 

.00108932 

9 

.00151745 

4 

.00138121 

9 

.00126743 

4 

.00117096 

19 

.00108814 

660 

.00151515 

£ 

.00137931 

790 

.00126582 

e 

.00116959 

920 

.00108696 

1 

.00151286 

6 

.00137741 

1 

.00126422 

€ 

.00116822 

.00108578 

«• 

.00151057 

•  7 

.00137552 

2 

.00126263 

7 

.00116686 

( 

.00108460 

£ 

.00150830 

8 

.00137363 

3 

.00126103 

8 

.00116550 

{ 

.00108342 

4 

.00150602 

9 

.00137174 

4 

.00125945 

9 

.00116414 

i 

.00108225 

f 

.00  1503  re 

730 

.00136986 

P 

.00125786 

860 

.00116279 

5 

.00108108 

6 

.00150150 

1 

.00136799 

6 

.00125628 

j 

.00116144 

6 

.00107991 

r/ 

.00149925 

f 

.00136612 

7 

.00125470 

f 

.00116009 

.00107875 

8 

.00149701 

j 

.00136426 

8 

.00125313 

«. 

.00115875 

8 

.00107759 

( 

.00149477 

i 

.C0136240 

c 

.00125156 

4 

.00115741 

( 

.00107643 

670 

.00149254 

F 

.00136054 

800 

.00125000 

* 

.00115607 

930 

.00107527 

.00149031 

( 

.00135870 

1 

.00124844 

i 

.00115473 

.00107411 

< 

.00148809 

7 

.00135685 

i 

.00124688 

7 

.00115340 

i 

.00107296 

.00148588 

8 

.00135501 

\ 

.00124533 

8 

.00115207 

.00107181 

t 

.00148368 

9 

.00135318 

L 

.00124378 

( 

.00115075 

i 

.00107066 

5 

.00148148 

740 

.00135135 

5 

.00124224 

870 

.00114942 

I 

.00106952 

I 

.001-17929 

.00134953 

( 

.00124069 

.00114811 

| 

.00106838 

• 

.00147710 

.00134771 

1 

.00123916 

i 

.00114679 

i 

.00106724 

j 

.00147493 

.00134589 

8 

.00123762 

j 

.00114547 

.00106610 

.00147275 

i 

.00134409 

J 

.00123609 

/ 

.00114416 

.00106496 

68< 

.00147059 

j 

.00134228 

810 

.00123457 

j 

.00114286 

941 

.00106383 

.00146843 

I 

.001310-18 

.00123305 

d 

.00114155 

.00106270 

.00146628 

1 

.00133861 

12 

.00123153 

7 

.00114025 

.00106157 

.00146413 

.00133690 

13 

.00123001 

I 

.00113895 

.00106044 

t 

.00146199 

.00133511 

14 

.00122850 

f 

.00113766 

, 

.00105932 

.00145985 

75i 

.0013333: 

15 

.00122699 

880 

.00113636 

.00105820 

i 

.00145773 

.00133156 

16 

.00122549 

; 

.00113507 

i 

.00105708 

• 

.00145560 

2 

.00132979 

17 

.00122399 

2 

.00113379 

i 

.00105597 

.00145349 

.00132802 

18 

.00122249 

.00113250 

.00105485 

.00145137 

t 

.00132626 

19 

.00122100 

i 

.00113122 

.00105374 

69i 

.00144927 

.00132450 

820 

.00121951 

i 

.00112994 

951 

.001052(53 

.00144718 

.00132275 

; 

.00121803 

6 

.00112867 

.00105152 

.00144509 

1 

.00132100 

\ 

.00121654 

\ 

.00112740 

.00105042 

.00144300 

.00131926 

'. 

.00121507 

8 

.00112613 

.00104932 

,: 

.00144092 

; 

.00131752 

i 

.00121359 

9 

.00112486 

< 

.00104822 

I 

.00143885 

760 

.00131579 

5 

.0012121? 

890 

.00112360 

f 

.00104712 

( 

.001436?'8 

.00131406 

6 

.00121065 

1 

.00112233 

6 

.00104602 

7 

.00143472 

2 

.00131234 

7 

.00120919 

2 

.00112108 

'( 

.00104493 

8 

.00143266 

± 

.00131062 

8 

.00120773 

3 

.00111982 

8 

.00104384 

( 

-.00143061 

i 

.00130890 

9 

.00120627 

4 

.00111857 

9 

.00104275 

700 

.00142857 

5 

.00130719 

830 

.00120482 

ft 

.00111732 

960 

.00104167 

1 

.00142653 

6 

.00130548 

1 

.00120337 

€ 

.00111607 

1 

.00104058 

2 

.00142450 

7 

.00130378 

2 

.00120192 

7 

.00111483 

2 

.00103950 

3 

.00142247 

8 

.00130208 

g 

.00120048 

8 

.00111359 

3 

.00103842 

4 

.00142045 

9 

.00130039 

4 

.00119904 

-  9 

.00111235 

4 

.00103734 

5 

.00141844 

770 

.00129870 

5 

.00119760 

900 

.00111111 

5 

.00103627 

RECIPEOCALS  OB   XUMBERS. 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

966 

00103520 

1031 

.000969932 

1096 

.000912409 

1161 

.000861326 

1226 

.000815661 

00103413 

2 

.000968992 

7 

.000911577 

2 

.000860585 

7 

.000814996 

8 

00103306 

3 

.000988054 

8 

.000910747 

3 

.000859845 

8 

.000814332 

9 

00103199 

4 

.000967)18 

9 

.000909918 

4 

.000859106 

9 

.000818670 

970 

00103093 

5 

000966184 

1100 

.000!  109091 

5 

.000858369 

1230 

.000813008 

1 

.00102987 

6 

.000965251 

1 

.00090S265; 

6 

.000857633 

1 

.000812348 

00102881 

.000964320 

2 

.000907441 

7 

.000856898 

2 

.000811688 

3 

.00102775 

81.000963391 

3 

.000906618 

8 

.000856164 

3 

.000811030 

4 

.  00102669 

91.  0009624  64 

4 

.000905797 

9 

.000855432 

4 

.000810373 

.00102564 

1040  .000961538 

5 

.000904977 

1170 

.000854701 

5 

.000809717 

6 

.00102459 

1 

.000960615 

6 

.000904159 

1 

.000853971 

6 

.(X10809061 

r- 

.00102354 

2 

.000959693 

7 

.000903342 

2 

.000853242 

7 

.000*08407 

8 

.00102250 

3 

.000958774 

8 

.000902527 

3 

.000852515 

8 

.000807754 

9 

.00102145 

4 

.000957854 

9 

.000901713 

4 

.000851789 

9 

.000807102 

980 

.00102041 

5 

000956938 

1110 

.000900901 

5  .000851064 

1240 

.000806452 

.00101937 

6 

.000956023 

11 

000900090 

6 

.000850340 

1 

.000805802 

2 

.00101833 

.000955110 

12 

.000899281 

7 

.000849618 

2 

.000805153 

t 

.00101729 

8 

.000954198 

13 

.000898473 

8 

.000848896 

3 

.000804505 

t. 

.00101626 

9 

.000953289 

14 

.000897666 

9 

.000848176 

4 

.000h03858 

f 

.00101523 

1050 

.000952381 

15 

.000896861 

1180 

.000847457 

5 

.000803213 

I 

.00101420 

1 

.000951475 

tfl 

.000896057 

1 

.000846740 

6 

.000802568 

.00101317 

2 

.000950570 

17 

.000895255 

2 

.000846024 

7 

.000801925 

8 

.00101215 

3 

.000949668 

18 

.000894454 

3 

.000845308 

8 

.000801282 

< 

.00101112 

4 

.000948767 

19 

.000893655: 

4 

.000844595 

9 

.000800640 

990 

.00101010 

5 

.000947867 

1120 

.  000892857  j 

5 

.000843882 

1250 

.000800000 

.00100908 

6 

.000946970 

.000892061 

6 

.000843170 

1 

.000799360 

2 

.00100806 

7 

.000946074 

5 

.000891266! 

7 

.000842460 

2 

.000798722 

;: 

.00100705 

8 

.000945180 

• 

.  000890472  i 

8 

.000841751 

3 

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.00100604 

9 

.000944287 

i 

.0008896801 

9 

.000841043 

4 

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1 

.00100502 

1060 

.000943396 

5 

.OOOS88889 

1190 

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5 

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6 

.00100402 

1 

.000942507 

6 

.000888099 

1 

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6 

.000796178 

» 

.00100301 

2 

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1 

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2 

.000838926 

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.00100200 

c 

.000940734 

& 

.000886525 

3 

.000838222 

8 

.000794913 

.00100100 

4 

.000939850 

9 

.000885740 

4 

.000837521 

9 

.000794281 

100! 

.00100000 

5 

.000938967 

1130 

.000884956 

5 

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1260 

.000793651 

.000999001 

6  000938086 

.000884173 

6 

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1 

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7  .000937207 

« 

.000883392 

7 

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t 

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8  .0009:56330 

| 

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8 

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3 

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, 

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9  .000935454 

i 

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9 

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i 

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1070 

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5 

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1200 

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r 

.000790514 

1 

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1 

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6 

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1 

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6 

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2 

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2 

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3 

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8 

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3 

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8 

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4  .000931099 

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4 

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9 

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1010 

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5 

.000930233 

"l!40 

.000877193 

5 

.000829875 

1270 

.000787402 

1 

.000989120 

6 

.000929368 

; 

.000876424 

6 

.0008*918? 

1 

.000786782 

1- 

.000988142 

i 

.000928505 

2 

.000875657 

7 

.000828500 

2 

.000786163 

l: 

.000987167 

8 

.000927644 

j 

.000874891 

8 

.000827815 

3 

.000785546 

H 

.000986193 

9 

.000926784 

t 

.000874126 

9 

.000827130 

^ 

.000784929 

IS 

.000985222 

1080 

.000925926 

f 

.000873362 

1210 

.000826446 

t 

.000784314 

If 

.000984252 

1 

.000925069 

6 

.000872600 

11 

.  000825764 

j 

.000783099 

r 

.000983284 

2 

.000924'-'  14 

1 

.000871840 

12 

.000825082 

.000783085 

18 

.000982318 

8 

.  00092336  1 

8 

.000871080 

13 

.000824402 

8 

.000782473 

lc 

.000981354 

4 

.000922509 

9 

.000870322 

14 

.000823723 

9 

.000781861 

1020 

.000980392 

5 

.000921659 

1150 

.000869565 

15 

.000823045 

1280 

.000781250 

.000979432 

6 

.000920810 

.000868810 

16 

.000822368 

] 

.000780640 

000978474 

r- 

.000919963 

i 

.000868056 

17 

.000821693 

jj 

.000780031 

.000977517 

8 

.000919118 

j 

.000867303 

18 

.000821018 

{ 

.000779423 

, 

.000976562 

9 

000918274 

i 

.000866551 

19 

.000820344 

i 

.000778816 

j 

.000975610 

1090 

.000917431 

t 

.000865801 

1220 

.000819672 

5 

.000778210 

1 

.000974659 

1 

.000916590 

( 

.OOOF65052 

1 

.000819001 

6 

.000777605 

' 

.000973710 

21.000915751 

\ 

.00086-1304 

2 

.000818331 

7 

.000777001 

.000972763 

31.000914913 

8 

.000863558 

3 

.000817661 

8 

.000776397 

1 

.000971817 

4  .000914077 

9 

.OC0862813 

4 

.000816993 

c 

.000775795 

1030 

.000970874 

51.000913242 

IllCO 

.0008620(59 

5 

.000816326 

1290 

.000775194 

MATHEMATICAL   TABLES. 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

!No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

1291 

.000774593 

1356 

.000737463 

1421 

.  000703730 

!1486 

.000672948 

1551 

.000644745 

2  .000773994 

7 

000736920 

2 

.000703235    7 

.000672495 

2 

.000644330 

3  -'.000773395 

8 

.000736377 

3 

00070*741  1  j   8 

.  000672043 

3 

.000043915 

4 

.000772797 

9 

.000735835 

4 

.000702247    9 

.000671592 

4 

.000043501 

5  .000772201 

1360 

.000735294 

5 

.000701754  1490 

.000671141 

5 

.000043087 

6  .000771605 

1 

.000734754 

6 

.000701262 

1 

.000670691 

6 

.00004^073 

7 

.000(71010 

2 

.000734214 

7 

.000700771|l   2 

,000070241 

7 

.000042201 

8 

.000770416 

3 

.000733676 

8 

.010700280 

3 

.  000669792 

8  .000641848 

9 

.000769823 

4 

.  000733  13S 

9 

.000699790' 

4 

.000009344 

9  .000641437 

1300 

.000769231 

5 

.00073  .'601 

1430 

.000699301 

5 

.000008890 

1560 

.000041026 

1 

.000768639 

6 

.000732064 

1 

.000698812! 

6 

.  000008449 

1 

.000040015 

2 

.000768049 

7 

.000731529 

o 

.000698324; 

7 

.000008003 

2 

.000040205 

3 

.000767459 

8 

.000730994 

3 

.  000697  837' 

8  .000667557 

3 

.000039795 

4 

.000766871 

9 

.000730460 

4 

.000697350 

9  .000667111 

4 

.000039386 

5 

.000766283 

1370 

.000729927 

5 

.0006908641  1500  .000066607 

5 

.000038978 

6 

.000765697 

1 

.000729395 

6 

.000696379 

1  .000606223 

6 

.000038570 

7 

.000765111 

2 

.000728863 

7 

.000695894 

2  .000665779 

7 

.000038162 

8 

.  000764526 

3 

.000728332 

8 

000695410 

3 

.000665336 

8 

.000637755 

9 

.0007(53942 

4 

.000727802 

9 

.000094927 

4 

.000004894 

9 

.000637349 

1310 

.000763359 

5 

.000737273 

1440 

.000694444 

5 

.000664452 

1570 

.000636943 

11 

.0007627761 

6 

.000726744 

1 

.000093962 

6 

.000664011 

1 

.000630537 

U 

.000762195' 

.00072621  6  : 

2 

.000693481 

71.000603570 

2  .000636132 

13 

.000761615 

8 

.000725689 

3 

.000093001 

8L000603130 

3  .000635728 

14 

.000761035 

9 

.000725163 

4 

.000692521 

9 

.000602691 

4).  000635324 

15 

.000760456 

1380 

.000724638 

5 

.000092041 

1510 

.000062252 

5  L  000634921 

10 

.00075S878 

1 

.000724113 

6 

.000691563 

11 

.000061813 

6  '.000634518 

17 

000759301 

2 

.000723589 

7 

.000691085! 

12 

.000661376 

71.000634115 

18 

.000758725 

3 

.000723066 

8 

.000690608! 

13 

.000660939 

8  .000633714 

19 

.000758150 

4 

.000722543 

9 

.0006901  31  1 

14 

.000660502 

9  .000033312 

1320 

.000757576 

5 

.000722022 

1450 

.  000089055  i 

15 

.  000660006 

1  580  !.  0006329  11 

1 

000757002 

6 

.000721501 

1 

.000089180; 

16  '.000059631 

1  .000632511 

2 

.000756430 

7 

.000720980 

2 

.000088705 

17  .000059196 

2  '.0000321  11 

3 

.000755858 

8 

.000720461 

3 

.000088231 

18  000658761 

3  .000031712 

4 

.000755287 

9 

.000719942 

4 

.000687758 

19  .000058328 

4  .000031313 

6 

.000754717 

1390 

.000719424 

5 

.  000687  285  j  1  520  !  .  000657895 

5  .000630915 

6 

.0007541-18 

1 

00071H907 

6 

.000080813 

1 

.000657402 

6  i.  00003051  7 

7 

.000753579 

2 

000718391 

7 

.000680341 

2 

.000657030 

7i.000030120 

8 

.000753012 

3 

.000717875 

8 

.000085871 

3 

.000650598 

8  ;.  000029723 

9 

.000752445 

4 

.000717360 

9 

.000(585401 

4 

.000050108 

9  .000029327 

1330 

.000751880 

5 

.000716846 

14HO 

.000084932 

5 

.000055738 

1590  .000028931 

1 

.000751315 

6 

.000716332 

1 

.000684463 

6  .000055308 

1  .000628536 

2 

.000750750: 

7' 

.  000715820 

2 

000083994 

71.000654879 

o 

.000628141 

3 

.000750187 

8 

.000715308 

3 

.000683527 

81.000054450 

3 

.000027740 

4 

.0007496-25 

9 

.000714796 

4 

.000083000 

9  .000654022 

4 

.000027353 

5 

.000749064 

1400 

.000714286 

5 

.000682594 

1530 

.000653595 

5 

.000020959 

6 

.000748503 

1 

.000713776 

6 

.000082128 

1 

.000653168 

G 

.000020506 

.000747943 

2 

.000713267 

7 

.000681663 

o 

.000052742 

7 

.000626174 

8 

.000747384 

3 

.000712758 

8 

.000081199 

3 

.000052310 

8 

.00062578.2 

9 

.  000746826 

4 

.000712251 

9 

.000680735 

4 

.000051890 

9 

.000625391 

1340 

.  000746269 

5 

.000711744 

1470 

.000680272 

5 

.  00005  140f 

1600 

.000625000 

1 

.000745712 

6 

.000711238 

1 

000079810 

6 

.000051042 

2 

.000624219 

2 

.0007'45156 

7 

.000710732 

2 

.000079348 

7 

.000050018 

4 

.000023441 

3 

.000744002 

8 

.000710227 

3 

.000078887 

8 

.000650195 

6 

.000622665 

4 

,000744048 

9 

.000709723 

4 

.000678428 

9 

.000049773 

8 

.000021890 

5 

.000743494 

1410 

.000709220 

5 

.000077900 

1540 

.000649351 

1610 

.000621118 

6 

.000742942 

11 

.000708717 

6 

.000077507 

1 

.000648929 

2 

.000620347 

7 

.000742390 

12 

.000708215 

.000677048 

2 

.000048508 

4 

.000619578 

8 

.000741840 

13 

.000707714 

8 

.000676590 

3 

.000048088 

6 

.000018812 

9 

.000741290 

14 

000707214 

9 

.000676132 

4 

.000(547008 

8 

.000618047 

1350 

.000740741 

15 

.000706714 

1480 

000075076 

5 

.000047249 

1620 

.000617284 

1 

.000740192 

16 

.000706215 

1 

.000075219 

6 

.000046830 

2 

.000010523 

2 

000739645 

17 

.000705716; 

2 

.OOOO.T'04 

7 

.000040412 

4 

.000615703 

3 

.000739098 

18 

.000705219 

3 

.000074309 

8 

.000545995 

6 

.000015006 

4 

.000738552 

19 

.000704722 

4 

.OOOi>73So4 

9 

.000045578 

8 

.000014250 

5 

.000738007, 

1420 

.000704225 

5 

.0006^3401 

1550 

.000045101 

1630 

.000013497 

KEGIPEOCALS   OF   NUMBERS. 


85 


No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

No. 

Recipro- 
cal. 

163.2 

.000612745 

1706 

.000586166 

1780 

.000561798 

1854 

.000539374 

1928 

.000518672 

4 

.000611995 

8 

.000585480 

2 

.000561167 

6 

.000538793 

1930 

.000518135 

0 

.000611247 

1710 

.000584795 

4 

.000560538 

8 

.000538213 

2 

.000517599 

8 

000610500 

12 

.000584112 

6 

.000559910  I860 

.000537634 

4 

.000517063 

1040 

.000609756 

14 

.000583430 

8 

.000559284 

2 

.000537057 

6 

.000516528 

.000609013 

16 

.000582750 

1790 

.000558659 

4 

.000536480 

8 

.000515996 

4 

.000608272 

18 

.000582072 

2 

.000558035 

6 

.000535905 

1940 

.000515464 

6 

.000607533 

1720 

.000581395 

4 

.000557413 

8 

.000535332 

2 

.000514933 

8 

.000606796 

2 

.000580720 

6 

.000556793!  1870 

.000534759 

4 

.000514403 

1650 

.000606061 

4 

.000580046 

8 

.000556174 

2 

.000534188 

6 

.000513874 

2 

.000(505327 

6 

.000579374 

1800 

.000555556  |   4 

.000533618 

8 

.000513347 

.000604595 

8 

.000578704 

2 

.000554939 

6 

.000533049 

1950 

.000512820 

6 

.000603865 

1730 

.000578035 

4 

.000554324 

8 

.000532481 

2 

.000512295 

8 

.000603136 

2 

.000577367 

6 

.000553710 

1880 

.000531915 

4 

.000511770 

1660  .000602410 

4 

.000576701 

8 

.0005530971 

g 

.000531350 

6 

.000511247 

21.000601685 

6 

.000576037 

1810 

.0005524861 

4 

.000530785 

8 

.000510725 

4  .OO.J600932 

8 

.000575374 

12 

.000551876 

6 

.000530222 

K60 

.000510204 

6  .000600240 

1740 

.000574713 

14 

.000551268 

8 

.000529661 

2 

.000509684 

8 

.000599520 

2 

.000574053 

16 

.000550661 

1890 

.000529100 

4 

.(X.  '05091  65 

1670 

.000598802 

4 

.000573394 

18 

.000550055 

2 

.000528541 

6 

.000508647 

2 

.000598086 

6 

.000572737 

1820 

.000549451 

4 

.000527983 

8 

000508130 

4 

.000597371 

8 

.000572082 

2 

.000548848 

6 

.000527426 

1970 

.000507014 

6 

.000596658 

1750 

.000571429 

4 

.0005482461 

8 

.000526870 

2 

.000507099 

8 

.000595947 

2 

.000570776 

6i 

.000547645 

1900 

.000526316 

4 

.000506585 

1680 

.000595238 

4 

.000570125 

8l 

000547046 

2 

.000525762 

6 

.000506073 

2 

.  000594530 

6 

.000569476 

1830! 

.000546448 

4 

.000525210 

8 

.000505561 

4 

.000593824 

8 

.000568828 

2 

.000545851! 

6 

.000524659 

1980 

.000505051 

6 

.000593120 

1760 

.000568182 

4 

.000545555 

8 

.000524109 

2 

.000504541 

8 

.000592417 

2 

.00056753? 

6 

.000544662, 

1910 

.000523560 

4 

.000504032 

1690 

.000591716 

4 

.000566893 

8 

.000544069 

12 

.000523012 

6 

.000503524 

2 

.000591017 

6 

.000566251 

1840! 

.000543478 

14 

.000522466 

8 

.000503018 

4 

.000590319 

8 

.000565611 

2! 

.000542888 

16 

.000521920 

1990 

.000502E13 

6 

.000589622 

1770 

.000^64972 

4 

.000542299 

18 

.000521376 

2 

.000502008 

8 

.000588928 

2 

000564334 

6 

.000541711 

1920 

.000520833 

4 

.000501504 

1700 

.000588235 

4 

.000563698 

8 

.000541125 

g 

.000520291 

6 

.000501002 

2 

4 

.000587544 
.000586854 

6 

8 

.000563063 
.000562430 

1850 

2 

.000540540 
.0005399571 

4 
6 

.000519750 
.0(1051  92  111 

8 
2000 

.000500501 
000500000 

Use  of  reciprocals.— Reciprocals  may  be  conveniently  used  to  facili- 
tate computations  in  long  division.  Instead  of  dividing  as  usual,  multiply 
the  dividend  by  the  reciprocal  of  the  divisor.  The  method  is  especially 
useful  when  many  different  dividends  are  required  to  be  divided  by  the 
same  divisor.  In  this  case  find  the  reciprocal  of  the  divisor,  and  make  a 
small  table  of  its  multiples  up  to  9  times,  and  use  this  as  a  multiplication- 
table  instead  of  actually  performing  the  multiplication  in  each  case. 

EXAMPLE.— 9871  and  several  other  numbers  are  to  be  divided  by  1638.    The 
reciprocal  of  1638  is  .000610500. 
Multiples  of  the 


reciprocal: 


10. 


.0006105 
.0012210 
.0018315 
.0024420 
.0030525 
.0036630 
.0042735 
.0048840 
.0054945 
.0061050 


The  table  of  multiples  is  made  by  continuous  addition 
of  6105.     The  tenth  line  is  written  to  check  the  accurac} 
of  the  addition,  but  it  is  not  afterwards  used. 
Operation: 

Dividend         9871 

Take  from  table  1 0006105 

7 0.042735 

8 00.48S40 

9 005  4945 


Quotient 6.0262455 

Correct  quotient  by  direct  division 6.0262515 

The  result  will  generally  be  correct  to  as  many  figures  as  there  are  signifi- 
cant figures  in  the  reciprocal,  less  one,  and  the  error  of  the  next  figure  will  in 
general  not  exceed  one.  In  the  above  example  the  reciprocal  has  six  sig- 
nificant figures,  6105QO,  and  the  result  is  correct  to  five  places  of  figures, 


86 


MATHEMATICAL   TABLES. 


SQUARES,    CUBES, 


ROOTS    AND    CUBE 


ROOTS   OF    NUMBERS   FROM   .1    TO    160O. 


No. 

Square. 

Cube. 

Sq. 

Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 

Root. 

.1 

.01 

.001 

.3162 

.4642 

3.1 

0.61 

29.791 

1.761 

1.458 

.15 

.0225 

.0034 

.3873 

.5313 

.2 

10.24 

32.768 

1.789 

1.474 

.2 

.04 

.008 

.4472 

.5848 

.3 

10.89 

35.937 

1.817 

1.489 

.25 

.0625 

.0156 

.500 

.6300 

.4 

11.56 

39.304 

1.844 

1.504 

.3 

.09 

027 

.5477 

.6694 

.'5 

12.25 

42.875 

1.871 

1.518 

.35 

.1225 

.0429 

.5916 

.7047 

.6 

12.96 

46.656 

1.897 

1.533 

.4 

.16 

.064 

.6325 

.7368 

7 

13.69 

50.653 

1  .  924 

1.547 

.45 

.2025 

.0911 

.6708 

.7663 

!8 

14.44 

54,872 

1.949 

1.560 

.5 

.25 

.125 

.7071 

.7937 

.9 

15.21 

59.319 

1.975 

1.574 

.55 

.3025 

.1664 

.7416 

.8193 

4. 

16. 

64. 

2. 

1.5874 

.6 

.36 

.216 

.7746 

.8434 

.1 

16.81 

68.921 

2.025 

1.601 

.65 

.4225 

.2746 

.8062 

.8662 

.2 

17.64 

74.088 

2.049 

1.613 

.49 

.343 

.8367 

.8879 

.3 

18.49 

79.507 

2.074 

1.626 

.75 

.5625 

.4219 

.8660 

.9086 

.4 

19.36 

85.184 

2.098 

1.639 

.8 

.64 

.512 

.8944 

.9283 

.5 

20.25 

91.125 

2.121 

1.651 

.85 

.7225 

.6141 

.9219 

.9473 

.6 

21.16 

97.336 

2.145 

1.663 

.9 

.81 

.729 

.9487 

.9655 

.7 

22.09 

103.823 

2.168 

1.675 

.95 

.9025 

.8574 

.9747 

.9830 

.8 

23.04 

110.592 

2.191 

1.687 

1. 

1. 

1. 

1. 

1. 

.9 

24.01 

117.649 

2.214 

1.698 

1.05 

1.1025 

1.158 

1.025 

1.016 

5. 

25. 

125. 

2.2361 

1.7100 

1.1 

1.21 

1.331 

1.049 

1.032 

.1 

26.01 

132.651 

2.258 

1.721 

1.15 

1.3225 

1.521 

1.072 

1.048 

.2 

27.04 

140.608 

2.280 

1.732 

1.2 

1.44 

1.728 

1.095 

1.063 

.3 

28.09 

148.877 

2.302 

1.744 

.25 

1.5625 

1.953 

1.118 

1.077 

.4 

29.16 

157.464 

2.324 

1.754 

!a 

1.69 

2.197 

1.140 

1.091 

.5 

30.25 

166.375 

2.345 

1.765 

.35 

1.8225 

2.460 

1.162 

1.105 

.6 

31.36 

175.616 

2.366 

1.776 

.4 

1.96 

2.744 

1.183 

1.119 

.7 

32.49 

185.193 

2.387 

1.786 

.45 

2.1025 

3.049 

1.204 

1.132 

.8 

33.64 

195.112 

2.408 

1.797 

.5 

2.25 

3.375 

1.2247 

1.1447 

.9 

34.81 

205.379 

2.429 

1.807 

.55 

2.4025 

3.724 

1.245 

1.157 

6. 

36. 

216. 

2.4495 

1.8171 

1.6 

2.56 

4.096 

1.205 

1.170 

.1 

37.21 

226.981 

2.470 

1.827 

1.65 

2.7225 

1  4.492 

1.285 

t.182 

o 

38.44 

238.328 

2.490 

1.837 

1.7 

2.89 

4.913 

1.304 

1.193 

!3 

39.69 

250.047 

2.510 

1.847 

1.75 

3.0625 

5.359 

1.323 

1.205 

.4 

40.96 

262.144 

2.530 

1.857 

1.8 

3.24 

5.832 

1.342 

1.216 

.5 

42.25 

274.625 

2.550 

1.866 

1.85 

3.4225 

6.332 

1.360 

1.228 

.6 

43.56 

287.496 

2.569 

1.876 

1.9 

3.61 

6.859 

1.378 

1.239 

7 

44.89 

300.763 

2.588 

1.885 

1.95 

3.8025 

7.415 

1.396 

1.249 

.8 

46.24 

314.432 

2.608 

1.895 

2. 

4. 

8. 

1.4142 

1.2599 

.9 

47.61 

328.509 

2.627 

1.904 

.1 

4.41 

9.261 

1.449 

1.281 

7. 

49. 

343. 

2.6458 

1.9129 

.2 

4.84 

10.648 

1.483 

1.301 

.1 

50.41 

357.911 

2.665 

1.922 

.3 

5.29 

12.167 

1.517 

1.320 

2 

51.84 

373.248 

2.683 

1.931 

.4 

5.76 

13.8-24 

1.549 

1.339 

!3 

53.29 

389.017 

2.702 

1.940 

.5 

6.25 

15.625 

1.581 

1.357 

.4 

54.76 

405.224 

2.720 

1.949 

.6 

6.76 

17.576 

1.612 

1.375 

.5 

56.25 

421.875 

2.739 

1.957 

.7. 

7.29 

19.683 

1.643 

1.392 

.6 

57.76 

438.976 

2.757 

1.966 

.8 

7.84 

21.952 

1.673 

1.409 

7 

59.29 

456.533 

2.775 

1.975 

.9 

8.41 

24.389 

1.703 

1.426 

',8 

60.84 

474.552 

2.793 

1.983 

3. 

9. 

27. 

1.7321 

1.4422 

.9 

62.41 

493.039 

2.811 

1.992 

SQUARES,  CUBES,,  SQUARE   AND   CUBE   ROOTS.         87 


No. 

Square. 

Cube. 

Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

8. 

64. 

512. 

2.8284 

2 

45 

2025 

91125 

6.7082 

3.5569 

.1 

65.61 

531.441 

2.846 

2'  008 

46 

2116 

97336 

6.7823 

3.5830 

0 

67.24 

551.368 

2.864 

2.017 

47 

2209 

103823 

6.8557 

3.6088 

'.3 

68.89 

571.787 

2.881 

2  025 

48 

2304 

110592 

6.9282 

3.6342 

A 

70.56 

592.704 

2.898 

2.033 

49 

2401 

117649 

7. 

3.6593 

.5 

72.25 

614.125 

2.915 

2.041 

50 

2500 

125000 

.0711 

3.6840 

.6 

73.96 

636.050 

2.933 

2.049 

51 

2601 

132651 

.1414 

3.7084 

.7 

75.09 

658.503 

2.950 

2.057 

52 

2704 

1  40608 

2111 

3.7325 

.8 

77.44 

681.472 

2.966 

2.065 

53 

2809 

148877 

.2801 

3.7563 

.9 

79.21 

704.969 

2.983 

2.072 

54 

2916 

157464 

.3485 

3.7798 

9. 

81. 

729. 

3. 

2.0801 

55 

3025 

166375 

.4162 

3.8030 

.1 

82.81 

753.571  3.017 

2.088 

56 

3136 

17'5616 

.4833 

3.8259 

.2 

84.64 

778.0883.033 

2.095 

57 

3249 

185193 

-.5498 

3.8485 

.3 

86.49 

804.  357  i  3.  050 

2.103 

58 

3364 

195112 

.6158 

3.8709 

.4 

88.36 

830.584 

3.066 

2.110 

59 

3481 

205379 

.6811 

3.8930 

.5 

90.25 

857.375 

3.082 

2.118 

60 

3600 

216000 

.7460 

3.9149 

.6 

92.16 

884.736 

3.098 

2.125 

61 

3721 

226981 

.8102 

3.9305 

.7 

94.09 

912.673 

3.114 

2.133 

62 

3844 

238328 

.8740 

3.9579 

.8 

96.04 

941.192 

3.130 

2.140 

63 

3969 

250047 

.9373 

3.9791 

.9 

98.01 

970.299 

3.146 

2.147 

64 

4096 

262144 

8. 

4. 

10 

100 

1000 

3.1623 

2.1544 

65 

4225 

274625 

8.0623 

4.0-207 

11 

121 

1331 

3.3166 

2.2240 

66 

4356 

287496 

8.1240 

4.0412 

12 

144 

1723 

3.1641 

2.2894 

67 

4489 

300763 

8.1854 

4.0015 

13 

169 

2197 

3.6056 

2.3513 

68 

4624 

314432 

8.2462 

4.0817 

14 

196 

2744 

3.7417 

2.4101 

69 

4761 

328509 

8.3066 

4.1016 

15 

225 

3375 

3.8730 

2.4662 

70 

4900 

343000 

8.3666 

4.1213 

16 

256 

4096 

4. 

2.5198 

71 

5041 

357911 

8  4261 

4.1408 

17 

2S9 

4913 

4.1231 

2.5713 

72 

5184 

373248 

8.4853 

4.1602 

18 

324 

5832 

4.2426 

2.6207 

73 

5329 

389017 

8.5440 

4.1793 

19 

361 

6859 

4.3589 

2.6684 

74 

5476 

405224 

8.6023 

4.1983 

20 

400 

8000 

4.4721 

2.V144 

75 

5625 

421875 

8.6603 

4  2172 

21 

441 

9261 

4.5826 

2  7589 

76 

5776 

438976 

8.7178 

4.2358 

22 

484 

10648 

4.6904 

2.8020 

77 

5929 

456533 

8.7750 

4.2543 

23 

529 

12167 

4.7958 

2.8439 

78 

6084 

474552 

8.8318 

4.2727 

24 

576 

13824 

4.8990 

2.8845 

79 

6241 

493039 

8.8882 

4.2908 

25 

625 

15625 

5. 

2.9240 

80 

6400 

512000 

8.9443 

4.3089 

26 

676 

17576 

5.0990 

2.9625 

81 

6561 

531441 

9. 

4.3267 

27 

729 

19683 

5.1962 

3. 

8-2 

6724 

551368 

9.0554 

4.3445 

28 

784 

21952 

5.2915 

3  0366 

83 

6889 

571787 

9.1104 

4.3621 

29 

841 

24389 

5.3852 

3.0723 

84 

7056 

592704 

9.1652 

4.3795 

30 

900 

27000 

5.4772 

3.1072 

85 

7225 

614125 

9.2195 

4.3968 

31 

961 

29791 

5.5678 

3.1414 

86 

7396 

636056 

9.2736 

4.4140 

32 

1024 

32768 

5.6569 

3.1748 

87 

7569 

658503 

9  3-276 

4.4310 

33 

1089 

35937 

5.7446 

3.2075 

88 

7744 

6S1472 

9.3808 

4.4480 

34 

1156 

39304 

5.8310 

3.2396 

89 

7921 

704969 

9.4340 

4.4647 

35 

1225 

42875 

5.9161 

3.2711 

90 

8100 

729000 

9.4868 

4.4814 

36 

1296 

46656 

6. 

3.3019 

91 

8281 

753571 

9.5394 

4.4979 

37 

1369 

50653 

6.0828 

3.3322 

92 

8464 

778688 

9.5917 

4.5144 

38 

1444 

54872 

6.1644  3.3620 

93 

8649 

804357 

9  6437 

4.5307 

39 

1521 

59319 

6.2450 

3.3912 

94 

8836 

830584 

9.6954 

4  .  5468 

40 

1600 

64000 

6.3246 

3.4200 

95 

9025 

857375 

9  7468 

4.5629 

41 

1681 

68921    6.4031 

3.4482 

96 

9216 

884736 

9.7980 

4.5789 

42 

1764 

74088    6.4807  13.4760 

97 

9409 

912673 

9.8489 

4.5947 

43 

1849 

79507    6  5574  3.5034  " 

98 

9604 

941192 

9.8995 

4.6104 

44 

1936 

85184   '6.6332  13.5303 

99 

9801 

970:299 

9.9499 

4.6261 

88 


MATHEMATICAL   TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

100 

10000 

1000000 

10. 

4.6416 

155 

24025 

3723875 

12.4499 

5.3717 

101 

10201 

1030301 

10.0499 

4.6570 

156 

24336 

3796416 

12.49UO 

5.3832 

10:2 

10404 

1061208 

10.0995 

4.6723 

157 

24649 

3869893 

12.5300 

5.3947 

103 

10(509 

1092727 

10.1489 

4.6875 

158 

24964 

3944312 

12.5698 

5.4061 

104 

10816 

1124864 

10.1980 

4.7027 

159 

25281 

4019679 

12.6095 

5.4175 

105 

11025 

1157625 

10.2470 

4.7177 

160 

25600 

4096000 

12.6491 

5.4288 

106 

112  6 

1191016 

10.2956 

4.7326 

161 

25921 

4173281 

12.688(3 

5.4401 

107 

11449 

1225043 

10.3441 

4.7475 

162 

26244 

4251528 

12.7279 

5  4514 

108 

11664 

1259712 

10.3923 

4.7622 

163 

26569 

4330747 

12.7(571 

5.4626 

109 

11881 

1295029 

10.4403 

4.7769 

164 

26896 

4410944 

12.8062 

5.4737 

110 

12100 

1331000 

10.4881 

4.7914 

165 

27225 

4492125 

12.8452 

5.4848 

111 

12321 

1367631 

10.5357 

4.8059 

166 

27556 

4574296 

12.8841 

5.4959 

112 

12544 

1404928 

10.5830 

4.8203 

167 

27889 

4657463 

12.9228 

5  .  5069 

113 

12769 

1442897 

10.6301 

4.8346 

168 

28224 

4741632 

12.9615 

5.5178 

114 

12996 

1481544 

10.6771 

4.8488 

169 

28561 

4826809 

13.0000 

5.5288 

115 

13225 

1520875 

10.7238 

4.8629 

170 

28900 

4913000 

13.0384 

5.5397 

116 

13456 

1560896 

10.7703 

4.8770 

171 

29241 

5000211 

13.0767 

5.5505 

117 

13889 

1601613 

10.8167 

4.8910 

172 

29584 

5088448 

13.1149 

5.5613 

118 

13924 

1643032 

10.8628 

4.9049 

173 

29929 

5177717 

13.1529 

5.5721 

119 

14161 

1685159 

10.9087 

.4.9187 

174 

30276 

5268024 

13.1909 

5.5828 

120 

14400 

1728000 

10.9545 

4.9324 

175 

30625 

5359375 

13.2288 

5.5934 

121 

14641 

1771561 

11.0000 

4.9461 

176 

30976 

5451776 

'13.2665 

5.6041 

122 

14884 

1815848 

11.0454 

4.9597 

177 

31329 

5545233 

13.3041 

5.6147 

123 

15129 

1860867 

1J.0905 

4.9732 

178 

31684 

5639752 

13.3417 

5.6252 

124 

15376 

1906624 

11.1355 

4.9866 

179 

32041 

5735339 

13.3791 

5.6357 

125 

15625 

1953125 

11.1803 

5.0000 

180 

32400 

5832000 

13.4164 

5.6462 

126 

15876 

2000376 

11.2250 

5.0133 

181 

32761 

5929741 

13.4536 

5.6567 

12V 

16129 

2048383 

11.2694 

5.0265 

182 

33124 

6028568 

13.4907 

5.6671 

128 

16384 

2097152 

11.3137 

5.0397 

183 

33489 

6128487 

13.5277 

5.6774 

129 

16641 

2146689 

11.3578 

5.0528 

184 

33856 

6229504 

13.5647 

5.6877 

130 

16900 

2197000 

11.4018 

5.0658 

185 

34225 

6331625 

13.6015 

5.6980 

131 

17161 

2248091 

11.4455 

5.0788 

186 

34596 

6434856 

13.6382 

5.7083 

132 

17424 

2299968 

11.4891 

5.0916 

187 

34969 

6539203 

13.6748 

5.7185 

133 

17689 

2352637 

11.5326 

5.1045 

188 

35344 

6644672 

13.7113 

5:7287 

134 

17956 

2406104 

11.5758 

5.1172 

189 

35721 

6751269 

13.7477 

5.7388 

135 

18225 

2460375 

11.6190 

5.1299 

190 

36100 

6859000 

13.7840 

5.7489 

136 

18496 

2515456 

11.6619 

5.1426 

191 

36481 

6967871 

13.8203 

5.7590 

137 

18769 

2571353 

11.7047 

5.1551 

J92 

36864 

7077888 

13.8564 

5.7690 

138 

19044 

2628072 

11.7473 

5.1676 

193 

37249 

7189057 

13.8924 

5  7790 

139 

19321 

2685619 

11.7898 

5.1801 

194 

37636 

7301384 

13.9284 

5.7890 

140 

19600 

2744000 

11.8322 

5.1925 

195 

38025 

7414875 

13.9642 

5.7989 

141 

19881 

2803221 

11.8743 

5.2048 

196 

38416 

7529536 

14.0000 

5.8088 

142 

20164 

2863288 

11.9164 

5.2171 

197 

38809 

7645373 

14.0357 

5.8186 

143 

20449 

2924207 

11.9583 

5.2293 

198 

39204 

7762392 

14.0712 

5  .  8285 

144 

50736 

2985984 

12.0000 

5.2415 

199 

39601 

7880599 

14.1067 

5.8383 

145 

21025 

3048625 

12.0416 

5.2536 

200 

40000 

8000000 

14.1421 

5.8480 

146 

21316 

3112136 

12.0830 

5.2656 

201 

40401 

8120601 

14.1774 

5.8578 

147 

21609 

3176523 

12.1244 

5.2776 

202 

40804 

8242408 

14.2127 

5.8675 

148 

21904 

3241792 

12.1655 

5.2896 

203 

41209 

8365427 

14.2478 

5.8771 

149 

32201 

3307949 

12.2066 

5.3015 

204 

41616 

8489664 

14.2829 

5.8808 

150 

22500 

3375000 

12.2474 

5.3133 

205 

42025 

8615125 

14.3178 

5.8964 

151 

22801 

3442951 

12.2882 

5.1251 

206 

42436 

8741816 

14.3527 

5  9059 

152 

23104 

3511808 

12.3288 

5.3368 

207 

42849 

8869743 

14.3875 

5.9155 

153 

23409 

3581577 

12.3693 

5.3185 

208 

43264 

8998912 

14.4222 

5.9250 

154 

23716 

3(552264  112  4097 

5.3601 

209 

43681 

9129329 

14.4568 

5.9345 

SQUARES,,  CUBES,  SQUARE   AKI)   CUBE    ROOTS.         89 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

210 

44100 

9261000 

14.4914 

5.9439 

265 

70225 

18609625 

16.2788 

6  4232 

211 

44521 

9393931 

14.5258 

5.9533 

266 

707..6 

18821096 

16.3095 

6.4312 

212 

44944 

9528128 

14.5602 

5.9627 

267 

71289 

19034163 

16.3401 

6.4393 

213 

45369 

9663597 

14.5945 

5.9721 

268 

71824 

11)248802  !  16.  3707 

6.4473 

214 

45796 

9800344 

14.6287 

5.9814 

269 

72361 

19465109 

16.4012 

6.4553 

215 

46225 

9938375 

14.6629 

5  9907 

270 

72900 

19683000 

16  4317 

6.4633 

216 

46656 

J  0077696 

14.6969 

6.0000 

27! 

73441 

19902511 

16.4621 

6.4713 

217 

47089 

10218313 

14.7309 

6.0092 

272 

73984 

20123648 

16.4924 

6.4792 

218 

47524 

10360232 

14.7648 

6.0185 

273 

74529 

20346417 

10.5227 

6.4872 

219 

47961 

10503459 

14.7986 

6  0277 

274 

75076 

20570824 

16.5529 

6.4951 

220 

48400 

10648000 

14.8324 

6.0368 

275 

75625 

20796875 

16.5831 

6.5030 

221 

48841 

10793861 

14.8661 

6.0459 

276 

76176 

21024576 

16.6132 

6.5108 

222 

49284 

10941048 

14.8997 

6  0550 

277 

7V.729 

21253933 

16.6433 

6.5187 

223 

49729 

11089567 

14  9332 

6.0641 

278 

77284 

21484952 

16.6733 

6.5265 

224 

50176 

11239424 

14.9666 

6.0732 

279 

77841 

21717639 

16.7033 

6.5343 

225 

50625 

11390625 

15.0000 

6.0822 

280 

78400 

21952000 

16.733-2 

6.5421 

226 

51076 

11543176 

15.0333 

6.0912 

281 

78961 

22188041 

16.7631 

6.5499 

22? 

51529 

11697083 

1  5  .  0665 

6  1002 

•282 

79524 

22425768 

16.7929 

6  .  5577 

228 

51984 

11852352 

15.0997 

6.1091 

283 

H0089 

22665187 

16.8226 

6.5654 

229 

52441 

120U8989 

15.1327 

6.1180 

284 

80656 

229U6304 

16.8523 

6.5731 

230 

52900 

12167000 

15.1658 

6.1269 

285 

81225 

23149125 

16.8819 

6.5808 

231 

53361 

12326391 

15.1987 

6.1358 

286 

81796 

23393656 

16.9115 

6.5885 

232 

53824 

12487168 

15.2315 

6.1446 

287 

82369 

23639903 

16.9411 

6.5962 

233 

54289 

12649337 

15.2643 

6.1534 

288 

82944 

,23887872 

16.9706 

6  .  6039 

234 

54756 

12812904 

15.2971 

6.1622 

289 

83521 

24137569 

17.0000 

6.6115 

235 

55225 

12977875 

15.3297 

6.1710 

290 

84100 

24389000 

17.0294 

6.6191 

236 

55696 

13144256 

15.3623 

6.1797 

21)1 

84681 

2464-2171 

17.0587 

6  .  6267 

237 

56169 

13312053 

15  3948 

6.1885 

292 

85264 

24897088 

17.0880 

6.6343 

238 

56644 

13481272 

15  4272 

6.1972 

293 

85849 

25153757 

17.1172 

6.6419 

239 

57121 

13651919 

15.4596 

6.2058 

294 

86436 

25412184 

17.1464 

6.6494 

240 

57600 

13824000 

15.4919 

6.2145 

295 

870-25 

2567-J375 

17.1756 

6.6569 

241 

58081 

13997521 

15.5242 

6.2231 

296 

87616 

25934336 

17.2047 

6  .  6044 

242 

58564 

14172488 

15.5563 

6.2317 

297 

88209 

26198073 

17  2337 

6.6719 

243 

59049 

14348907 

15.5885 

6.2403 

298 

88804 

26463592 

17.2627 

6.  (1794 

244 

59536 

14526784 

15.6205 

6.2488 

299 

89401 

26730899 

17.2916 

6.6869 

245 

60025 

14706125 

15.6525 

6.2573 

3QO 

90000 

27000000 

17.3205 

6.6943 

246 

60516 

14886936 

15.6844 

6.2658 

301 

90601 

27270901 

17.3494 

6.7018 

247 

61009 

15069223 

15.7162 

6.2743 

:50:2 

91204 

27543608 

17.3781 

6.7092 

248 

61504 

15252992 

15.7480 

6.2828 

303 

91809 

27818127 

17.406!) 

6.7166 

249 

62001 

15438249 

15.7797 

6.2912 

304 

92416 

28094464 

17  4356 

6.7240 

250 

62500 

15625000 

15.8114 

6.2996 

305 

93025 

28372625 

17.4642 

6.7313 

251 

6:H001 

15813251 

15.8430 

6.3080 

306 

93636 

28652616 

17.4929 

6.  7387 

252 

63504 

16003008 

15.8745 

6.3164 

307 

94249 

28934443 

17.5214 

6.7460 

25  5 

64009 

16  194^77 

15.90(50 

6.3247 

308 

94864 

29218112 

17.5499 

6.7533 

25  4 

64516 

16387064 

15.9374 

6.3330 

309 

95481 

295036-29 

17.5784 

6.7606 

255 

65025 

16581375 

15.9687 

6.3413 

310 

96100 

29791000 

17.6068 

6.7679 

256 

65536 

16777216 

16.000J 

6.3496 

311 

96721 

30080231 

17.6352 

6  7752 

257 

66049 

16974593 

16.0312 

6.3579 

312 

97344 

303713-28 

17.6635 

6.7824 

258 

66564 

17173512 

16.  06-24 

6.3661 

313 

97969 

30664297 

17.6918 

6  7897 

259 

67081 

17373979 

16.0935 

6.3743 

314 

98596 

30959144 

17.7200 

6.7969 

260 

67600 

17576000 

16.1245 

6.3825 

315 

99225 

31255875 

17.7'482 

6.8041 

261 

68121 

17779581 

16.1555 

6.3907 

316 

99856 

31554496 

17.7764 

6.8113 

262 

686  14 

17984728 

16.1864 

6.3988 

317 

100489 

31855013 

17.8045 

6.8185 

203 

69169 

18191447 

16.2173 

6.4070 

318 

101124 

32157432 

17.8326 

6.8256 

264 

69696 

18399744 

16.2481 

6.4151 

319 

101761 

32461759 

17.8606 

6.8328 

MATHEMATICAL  TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

320 

102400 

32768000 

17.8885 

6.8399 

375 

140625 

52734375 

19.3649 

7.2112 

321 

103041 

33076161 

17.9165 

6  8470 

376 

141376 

53157376 

19.3907 

7  2177 

322 

103684 

33386248 

17.9444 

6.8541 

377 

142129 

53582633 

19.4165 

7.  '2240 

3-33 

104329 

33698267 

17.9722 

6.8612 

378 

142884 

54010152 

19.4422 

7.i!304 

324 

104976 

34012224 

18.0000 

6.8683 

379 

143641 

54439939 

19.4679 

7.2308 

325 

105625 

34328125 

18.0278 

6.8753 

380 

144400 

54872000 

19.4936 

7.2432 

326 

106276 

34645976 

18.0555 

6.8824 

381 

145161 

55306341 

19.5192 

7.2495 

327 

106929 

34965783 

18.0831 

6.8894 

382 

145924 

55742968 

19.5448 

7.2558 

328 

107584 

35287552 

18.1108 

6.8964 

383 

146689 

56181887 

19.5704 

7.2622 

329 

108241 

35611289 

18.1384 

6.9034 

384 

147456 

5G623104 

19.5959 

7.2685 

330 

108900 

35937000 

18.1659 

6.9104 

385 

148225 

57066625 

19.6214 

7.2748 

331 

109561 

36264691 

18.1934 

6.9174 

386 

148996 

57512456 

19.6469 

7.2811 

332 

110224 

36594368 

18.2209 

6.9244 

387 

149769 

57960603 

19.6723 

7.2874 

333 

110889 

36926037 

18.2483 

6.9313 

388 

150544 

58411072 

19.6977 

7.2936 

334 

111556 

37259;  04 

18.2757 

6.9382 

389 

151321 

58863869 

19.7231 

7.2999 

335 

112225 

37595375 

18.3030 

6.9451 

390 

152100 

59319000 

19.7484 

7  3061 

330 

112896 

37933056 

18.3303 

6.9521 

391 

152881 

5977  6471 

19.7737 

7.3124 

337 

113569 

38272753 

18.3576 

6.9589 

392 

153664 

60236288 

19.7990 

7.3186 

338 

114244 

38614472 

18.3848 

6.9658 

393 

154449 

60698457 

19.8242 

7.3248 

339 

114921 

38958219 

18.4120 

6.9727 

394 

155236 

61162984 

19.8494 

7.3310 

340 

115600 

39304000 

18.4391 

6.9795 

395 

156025 

61629875 

19.8746 

7.3372 

341 

116281 

39651821 

18.4662 

6.9864 

396 

156816 

62099136 

19.8997 

7.3434 

342 

116964 

40001688 

18.4932 

6  9932 

397 

157609 

62570773  19.9249 

7.3496 

343 

117649 

40353607 

18.5203 

7.0000 

398 

158404 

63044792 

19.9499 

7.3558 

344 

118336 

40707584 

18.5472 

7.0068 

399 

159201 

63521199 

19.9750 

7.3619 

345 

119025 

41063625 

18.5742 

7.0136 

400 

160000 

64000000 

20  0000 

7.3681 

346 

119716 

41421736 

18.6011 

7.0203 

401 

160!-  01 

64481201 

20  0250 

7.3742 

347 

120409 

41781923 

18.6279 

7.0271 

402 

161604 

64964808 

20.0499 

7.3803 

348 

121104 

42144192 

18.6548 

7.0338 

403 

162409 

65450827 

20  0749 

7.3864 

349 

121801 

42508549 

18.6815 

7.0406 

404 

163216 

65^39264 

yO.0998 

7.3925 

350 

122500 

42875000 

18.7083 

7.0473 

405 

164025 

66430125 

20.1246 

7.3986 

351 

123201 

43243551 

18.7850 

7.0540 

406 

164836 

66923416 

20.1494 

7.4047 

352 

123904 

43614208 

18.7617 

7.0607 

407 

165649 

67419143 

20.1742 

7.4108 

353 

124609 

43986977 

18.7883 

7.0674 

408 

166464 

67917312 

20.1990 

7.4169 

354 

125316 

44361864 

18.8149 

7.0740 

409 

167281 

68417929 

20.2237 

7.4229 

355 

126025 

44738875 

18.8414 

7.0807 

410 

168100 

68921000 

20.2485 

7.4290 

3:>6 

126736 

45118016 

18.8680 

7.0873 

411   168921 

69426531 

20.2731 

7.4350 

357 

127449 

45499293 

18.8944 

7.0940 

412 

169744 

69934528 

20.2978 

7.4410 

358 

128164 

45882712 

18  9209 

7.1006 

413 

170569 

70444997 

20.3224 

7.4470 

359 

128881 

46268279 

18.9473 

7.1072 

414 

171396 

70957944 

20.3470 

7.4530 

360 

129600 

46656000 

18.9737 

7.1138 

415 

172225 

71473375 

20.3715 

7.4590 

361 

130321 

47045881 

19.0000 

7.1204 

416 

173056 

71991296 

20.3961 

7.4650 

362 

131044 

47437928 

19.0263 

7.1269 

417 

173889 

72511713 

20.4206 

7.4710 

363 

131769 

47832147 

17.0526 

7.1335 

418 

174724 

73034632 

20.4450 

7.4770 

364 

132496 

48228544 

19.0788 

7.1400 

419 

175561 

73560059 

20.4695 

7.4829 

365 

133225 

48627125 

19.1050 

7.1466 

420 

176400 

74088000 

20.4939 

7.4889 

366 

133956 

49027896 

19.1311 

7.1531 

421 

177241 

74618461 

20.5183 

7.4948 

367 

134689 

49430863 

19.1572 

7.1596 

422 

178084 

75151448 

20.5426 

7.5007 

368- 

135424 

49836032 

19.1833 

7.1661 

423 

1789:29 

75686967 

20.5670 

7.5067 

369 

136161 

50243409 

19.2094 

7.1726 

424 

179776 

76225024 

20.5913 

7.5126 

370 

136900 

50653000 

19.2354 

7.1791 

425 

180625 

76765625 

20.6155 

7.5185 

371 

137641 

51064811 

19.2614 

7.1855 

426 

181476 

77308776 

20.6398 

7.5244 

372 

138384 

51478848  1  19.  2873 

7.1920 

427 

188329 

77854483 

20.6640 

7.5302 

173 

139129 

51895117 

19.3132 

7.1984 

428 

183184 

78402752 

20.6882 

7.5361 

374 

139876 

52313624 

19.3391 

7.2048 

429  1  184041 

78953589 

20.7123 

7.5420 

SQUARES,  CUBES,  SQUARE   AND   CUBE   BOOTS.        91 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

430 

184900 

79507000 

20.7364 

7.5478 

485 

235225 

114084125 

22.0227 

7.8568 

431 

185761 

80062991 

20.7605 

7.5537 

486 

236196 

114791256 

22.0454 

7.8622 

432 

186624 

80621568 

^0.7846 

7.5595 

487 

237169 

115501303 

22.0681 

7.8676 

433 

187489 

S  11  82737 

20.8087 

7.5654 

488 

238144 

116214272 

22.0907 

7.8730 

434 

188356 

81746504 

20.8327 

7.5712 

489 

239121 

116930169 

22.1133 

7.8784. 

435 

189225 

82312875 

20.8567 

7.5770 

490 

240100 

117649000 

22.1359 

7.8837 

436 

190096 

82881856 

20.8806 

7.5828 

491 

241081  118370771 

~'2.1585 

7.8891 

437 

190969 

83453453 

20.9045 

7.5886 

492 

242064  119095488 

22.1811 

7.8944 

438 

191844 

84027672 

20.9284 

7.5944 

493 

243049  1119823157 

22.2036 

7.8998 

439 

192721 

84604519 

20.9523 

7.6001 

494 

244036  120553784 

22.2261 

7.9051 

440 

193600 

85184000 

20.9762 

7.6059 

495 

245025  121287375 

22.2486 

7.9105 

441 

194481 

85766121 

21.0000 

7.6117 

496 

246016  122023936 

22.2711 

7.9158 

442 

195364 

86350888 

31.0238 

7.6174 

497 

247009  122763473 

22.2935 

7.9211 

443 

196249 

86938307 

21.0476 

7.6232 

498 

248004  123505992 

22.3159 

7.9204 

444 

197136 

87528384 

21.0713 

7.6289 

499 

249001  124251499 

<!2  3383 

7.9317 

445 

198025 

88121125 

21.0950 

7.6346 

500 

250000  125000000 

22.3607 

7.9370 

446 

198916 

88716536 

21.1187 

7.6403 

501 

251001  125751501 

22.3830 

7.9423 

447 

199809 

89314623 

21.1424 

7.6460 

502 

252004  126506008 

22.4054 

7.9476 

448 

200704 

89915392 

21.1660 

7.6517 

503 

253009  127263527 

22.4277 

7.9528 

449 

201  601 

90518849 

21.1896 

7.6574 

504 

254016 

128024064 

22.4499 

7.9581 

450 

202500 

91125000 

21.2132 

7.6631 

505 

255025 

128787625 

22.4722 

7.9634 

451 

203401 

91733851 

21.2368 

7.6688 

506 

256036  129554216 

,22.4944 

7.9686 

452 

204304 

92345408 

21.2603 

7.6744 

507 

257049  130323843 

22.5167 

7.9739 

453 

205209 

92959677 

21.2838 

7.6800 

508 

258064 

131096512 

22.5389 

7.9791 

454 

206116 

93576664 

21.3073 

7.6857 

509 

259081 

131872229 

22.5610 

7.9843 

455 

207025 

94196375 

21.3307 

7.6914 

510 

260100 

132651000 

22.5832 

7.9896 

456 

207936 

94818816 

21.3542 

7.6970 

511 

261121 

133432831 

22.6053 

7.9948 

457 

208849 

95443993 

21.3776 

7.7026 

512 

262144 

134217728 

22.6274 

8.0000 

458 

209764 

96071912 

21.4009 

7.7082 

513 

263169 

135005697 

22.6495 

8.0052 

459 

210681 

96702579 

21.4243 

7.7138 

514 

264196 

135796744 

22.6716 

8.0104 

460 

211600 

97336000 

21.4476 

7.7194 

515 

265225 

136590875 

22.6936 

8.0156 

461 
462 

212521 
213444 

97972181 
98611128 

21.4709 
21.4942 

7.7250 
7.7306 

516 

517 

266256  137388096 
267289  1138188413 

22.7156 
22.7376 

8.0208 
8.0260 

463 

214369 

99252847 

21.5174 

7.7362 

518 

268324  S  138991  832 

22.7596 

8.0311 

464 

215296 

99897344 

21.5407 

7.7418 

519 

269361  139798359 

22.7816 

8.0363 

465 

216225 

100544625 

21.5639 

7.7473 

520 

270400 

140608000 

22.8035 

8.0415 

466 

217156 

101194696 

21.5870 

7.7529 

521 

271441  1141420761 

22.8254 

8.0466 

467 

218089 

101847563 

21.6102 

7.7584 

522 

272484  :  142236648 

22.8473 

8.0517 

468 

219024 

102503232 

21.6333 

7.7639 

523 

273529  143055667 

22.8692 

8.0569 

469 

219961 

103161709 

21.6564 

7.7695 

524 

274576  il438778-,'4 

22.8910 

8.0620 

470 

220900 

103823000 

21.6795 

7.7750 

525 

275625  144703125 

22.9129 

8.0671 

471 

221841 

104487111 

21.7025 

7.7805 

526 

276676  !  145531576 

22.9347 

8.0723 

472 

222784 

105154048 

21.7256 

8.7860 

527 

277729  146363183 

22.9565 

8.0774 

473 

223729 

105823817 

21.7486 

7.7915 

528 

278784  147197952 

22.9783 

8.0825 

474 

224.676 

106496424 

21.7715 

7.7970 

529 

279841  148035889 

23.0000 

8.0876 

475 

225625 

107171875 

21  .  7945 

.8025 

530 

280900  148877000 

23.0217 

8.0927 

476 

226576 

107850176 

21.8174 

".8079 

531 

281961  149721291 

23.0434 

8.0978 

477 

227529 

108531333 

21.8403 

.8134 

532 

283024  150568768 

23.0651 

8.1028 

478 

228484 

109215352 

21.8632 

.8188 

533 

284089  ;  151  41  9437 

23.0868 

8.1079 

479 

229441 

109902239 

21.8861 

.8243 

534 

285156 

152273304 

23.1084 

8.1130 

480 

230400 

110592000 

21  9089 

".8297 

535 

286225 

153130375 

23.1301 

8.1180 

481 

231361 

111284641  21.9317 

".8352 

536 

287296  153990656 

23.1517 

8.1231 

482 

232324 

111980168 

21.9545 

".8406 

537 

288369  154854153 

23.1733 

8.1281 

483 

233289 

112678587 

21.9773 

".8460 

538 

289444 

155720872 

23.1948 

8.1332 

484 

234256 

113379904 

22.0000 

".8514 

539 

290521 

156590819 

23.2164 

8.1382 

MATHEMATICAL  TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

540 

291600 

157464000 

23.2379 

8.1433 

595 

354025 

210644875 

24.3926 

8.4108 

541 

292681 

158340421 

23.2594 

8.1483 

596 

355216 

211708736 

24.4131 

8.4155 

542 

293764 

159220088 

23.2809 

8.1533 

597 

356409 

212776173 

24.4336 

8.4202 

543 

294849 

160103007 

23.3024 

8.1583 

598 

357604 

213847192 

24.4540 

8.4249 

544 

21)5936 

160989184 

23.3238 

8.1633 

599 

358801 

214921799 

24.4745 

8.4296 

545 

297025 

161878625 

23.3452 

8.1683 

6CO 

360000 

21600GOOO 

24.4949 

8  4843 

546 

298116 

162771336 

23  .  3666 

8.1733 

601 

361201 

a  1708  1801 

24.5153 

8.4390 

547 

299209 

163667323 

23.3880 

8.1783 

602 

362404 

218167208 

24.5357 

8.4437 

548 

300304 

164566592 

23.4094 

8.1833 

603 

363609 

219256227 

24.5561 

8.4484 

549 

301401 

165469149 

23.4307 

8.1882 

604 

364816 

220348864 

24.5764 

8.4530 

550 

302500 

166375000 

23.4521 

8.1932 

605 

366025 

221445125 

24.5967 

8.4577 

551 

30360! 

167284151 

23  4734 

8.1982 

606 

367236 

22254501  (i 

24.6171 

8  4623 

552 

304704 

168196608 

23.4947 

8.2031 

607 

368449 

223648543 

24.6374 

8.4670 

553 

305809 

169112377 

23.5160 

8.2081 

608 

369664 

224755712 

24.6577 

8.4716 

554 

306916 

170031464 

23.5372 

8.2130 

609 

370881 

225866529 

24.6779 

8.4763 

555 

308025 

170953875 

23.5584 

8.2180 

610 

372100 

226981000 

24  6982 

8.4809 

556 

309136 

71879616 

23.5797 

8.2229 

611 

373321 

228099131 

24.7184 

8  4  856 

557 

310249 

72808693 

23.6008 

8.2278 

612 

374544 

229220928 

24  7386 

8.4902 

558 

311364 

73741112 

23.6220 

8.2327 

613 

375769 

230346397 

24.7588 

8.4948 

559 

312481 

74676879 

23.6432 

8.2377 

614 

376996 

231475544 

24.7790 

8.4994 

560 

313600 

75616000 

23.6643 

8.2426 

615 

378225 

232608375 

24.7992 

8.5040 

561 

314721 

76558481 

23.6854 

8.2475 

616 

379456 

233744896 

24.8193 

8.5086 

562 

315844 

177504328 

23.7065 

8  2524 

617 

380689 

234885113 

24.8395 

8.5132 

563 

316969 

178453547 

23.7276 

8.2573 

618 

381924 

236029032 

24.8596 

8.5178 

564 

318096 

179406144 

23.7487 

8.2621 

619 

383161 

237176659 

24.8797 

8.5224 

565 

319225 

180362125 

23.7697 

8.2670 

620 

384400 

238328000 

24.8998 

8.5270 

506 

320356 

181321496 

23.7908 

8.2719 

621 

385641 

239483061 

24.9199 

8.5316 

567 

321489 

182284263 

23.8118 

8.2768 

622 

3H6884 

240641848 

24.9399 

8.5362 

568 

322624 

183250432 

23.8328 

8.2816 

623 

388129 

241804367 

24.9600 

8.5408 

569 

323761 

184220009 

23.8537 

8.2865 

624 

389376 

242970624 

24.9800 

8.5453 

570 

324900 

185193000 

23.8747 

8.2913 

625 

390625 

244140625 

25.0000 

8.5499 

571 

326041 

186169411 

23.8956 

8.2962 

626 

391876 

245314376 

25.0200 

8.5544 

572 

327184 

187  1  49248 

23.9165 

8.3010 

627 

393129 

246191883 

25.0400 

8.5590 

573 

328329 

188132517 

23.9374 

8.3059 

628 

394384 

247673152 

25.0599 

8.5635 

574 

329476 

189119224 

23.9583 

8.3107 

629 

395641 

248858189 

25.0799 

8.5681 

575 

330625 

190109375 

23.9792 

8.3155 

630 

396900 

250047000 

25.0998 

8.5726 

576 

331776 

191102976 

24.0000 

8.3203 

631 

398161 

251  239591 

25.1197 

8.5772 

577 

332929 

19-2100033 

21.0208 

8.3251 

632 

399424 

2P.243:)968 

25.1396 

8.5817 

578 

334084 

193  100552 

24.0416 

8.3300 

633 

400689 

253636137 

25.1595 

8.5862 

579 

335241 

194104539 

24.0624 

8.3348 

634 

401956 

254840104 

25.1794 

8.5907 

580 

336400 

195112000 

24.0832 

8.3396 

635 

403225 

256047875 

25.1992 

8.5952 

581 

337561 

196122941 

24.1039 

8.3443 

636 

404496 

257259456 

25.2190 

8  5997 

582 

338724 

197137368 

24.1247 

8.3491 

637 

405769 

258474858 

25.2389 

8.6043 

583 

339889 

198155287 

24.1454 

8.3539 

638 

407044 

259694072 

25.2587 

8.6088 

584 

341056 

199176704 

24.1661 

8.3587 

639 

408321 

260917119 

25.2784 

8.6132 

585 

342225 

200201625 

24.1868 

8.3634 

640 

409600 

262144000 

25.2982 

8.6177 

586 

343396 

201230056 

24.2074 

8.3682 

641 

410881 

26337'4721 

25.3180 

8.6222 

587 

344569 

202262003 

24.2281 

8.3730 

642 

412164 

264609288 

25.3377 

8.62(57 

588 

345744 

203297472 

24.2487 

8.3777 

643 

413449 

265847707 

25.3574 

8.6312 

589 

346921 

204336469 

24.2693 

8.3825 

644 

414736 

267089984 

25.3772 

8.6357 

590 

348100 

205379000 

24.2899 

8.3872 

645 

416025 

268336125 

25.3969 

8.6401 

591 

349281 

2061251)71 

24  31  or 

8.3019 

646 

417316 

269586136 

25.4165 

8  6410 

51)2 

350464 

20747-1(188 

24.3311 

8.3967 

647 

418(509 

270840023 

25.4362 

8.6190 

593 

351649 

208527857 

24.  35  If 

8.4014 

648 

419904 

272097792 

25.4558 

8.  (5535 

594 

352336 

2095*4584 

24.3721 

8.4061 

(549 

421201 

273359449 

25.4755 

8.6579 

SQUARES,  CUBES,,  SQUARE   AND    CUBE    ROOTS.         93 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

650 

422500 

274625000 

25.4951 

8.6624 

705 

497025 

350402625 

26.5518 

8.9001 

651 

<O301 

275894451 

25.5147 

8.0068 

706 

498436 

351895816  26.5707 

8.9043 

65:2 

425104 

277167808 

25.5343 

8.6713 

707 

499849 

353393243 

26  .  5895 

8.9085 

653 

420409 

278415077 

25.5539 

8.6757 

708 

501264 

354894912 

26.0083 

8.9127 

654 

427716 

279726204 

35.5734 

8.6801 

709 

502681 

356400829 

26.6271 

8.9169 

655 

429025 

281011375 

25.5930 

8.6845 

710 

504100 

357911000 

26.645S 

8.9211 

656 

430330 

282300416 

25.6125 

8.6890 

711 

505521 

359425431 

26.6646 

8.9253 

657 

431649 

283593393 

25.6320 

8.6934 

712 

506944 

300944128 

26.6833 

8.9295 

658 

432964 

284890312 

25.6515 

8  6978 

713 

508369 

362467097 

26.7021 

8.9337 

659 

434281 

286191179 

25.6710 

8.7022 

714 

509796 

363994344 

26.7208 

8.9378 

660 

435600 

287496000 

25.6905 

8.7066 

715 

511225 

365525875 

26.7395 

8.9420 

661 

436921 

288804781 

25.7099 

8.7110 

716 

512656 

367061696 

26.7582 

8.9462 

662 

438244 

290117528 

25  7294 

8.7154 

717 

514089 

368601813 

26.7769 

8.9503 

603 

439569 

291434247 

25.7488 

8.7198 

718 

515524 

370146232 

26.7955 

8.9545 

664 

440896 

292754914 

25.7082 

8.7241 

719 

516961 

371694959 

26.8142 

8.9587 

665 

442225 

294079625 

25.7876 

8.7285 

720 

518400 

373248000 

26.8328 

8.9628 

666 

443556 

295408296 

25.8070 

8.7329 

721 

519841 

374805361 

26.8514 

8  9670 

667 

444889 

296740963 

25.8263 

8.7373 

722 

521284 

356367048 

26.8701 

8.9711 

6!5S 

446224 

298077032 

25.8457 

8.7416 

723 

522729 

377933067 

26.8887 

8.9752 

009 

447501 

299418309 

25.8650 

8.7460 

724 

524176 

379503424 

26.9072 

8.9794 

670 

448900 

300763000 

25.8844 

8.7503 

725 

525625 

381078125 

26.9258 

8.9835 

671 

450241 

302111711 

25.9037 

8.7547 

726 

527076 

382657176 

26.9444 

8.987'6 

67:3 

451584 

303404448 

25.9230 

8.7590 

727 

528529 

384240583 

26.9629 

8.9918 

673 

4521)29 

304821217 

25.9422 

8.7634 

728 

529984  385828352 

26.9815 

8.9959 

6T4 

454,276 

300182024 

25.9615 

8.7677 

729 

531441 

387420489 

27.0000 

9.0000 

675 

455625 

307546875 

25.9808 

8.7721 

730 

532900 

389017000 

27  0185 

9  0041 

676 

45(5976 

308915776 

26.0000 

8.7764 

731 

534301  390617891 

27.0370 

9.0082 

677 

458329 

310288733 

26.0192 

8.7807 

732 

535824  392223168 

27.0555 

9.0123 

678 

459084 

311065752 

26.0384 

8.7850 

733 

537289  '393832837 

27.0740 

9.0164 

679 

461041 

313046839 

26.0576 

8.7893 

734 

538756 

39544G904 

27.0924 

9.0205 

680 

462100 

314432000 

26.0768 

8.7937 

735 

540225 

397065375 

27.1109 

9  0246 

681 

403701 

315821241 

20.0960 

8.7980 

736 

541696 

398688256  j  27.  1293 

9  0287 

682 

465124 

317214508 

20.1151 

8.8023 

737 

543169 

400315553  1  27.  1477 

9.0328 

ess 

406489 

318011987 

26.1343 

8.8006 

738 

544044 

401947272  '27  1662 

9.0369 

684 

407856 

320013504 

26.1534 

8.8109 

739 

546121 

403583419 

27.1846 

9.0410 

685 

469225 

321419125 

26.1725J  8.8152 

740 

547600 

405224000 

27.2029 

9.0450 

686 

470596 

322828856 

26.1910 

8.8194 

741 

549801 

400809021 

27.2213 

9.0491 

687 

471909 

324242703 

20.2107 

8.8237 

742 

550564 

408518488 

27.2397 

9.0532 

688 

473344 

325000072 

26.2298 

8.8280 

743 

552049 

410172407 

27.2580 

9.0572 

689 

474721 

327082769 

26.2488 

8.8323 

744 

553536 

411830784 

27.2764 

9.0613 

600 

476100 

328509000 

26.2679 

8.8366 

745 

555025 

413493625 

27.2947 

9.0654 

091 
092 

477481 
478804 

329939371 

331373888 

26.2869  8.8408 
26.3059  8.8451 

740 
747 

556510 
558009 

415160930  J27.3130 
410832723  1  £7.  33  13 

9.0094 
9.0735 

6!  >3 

480249 

332812557 

26.3249 

8.8493 

748 

559504 

418508992  !  27.  3496 

9.0775 

694 

481036 

334255384 

26.3439 

8.8536 

749 

501001 

420189749 

27.3679 

9.0816 

695 

483025 

335702375 

26.3629 

8.8578 

750   562500 

421875000 

27.3861 

9.0856 

690 

484410 

337153536 

20.3818 

8.8621 

751   504001 

423564751 

27  4044 

9.0896 

697 

485809 

338008873 

20.4008 

8.8603 

752   505504 

425259008 

27.4226 

9.0937 

698 

487204 

340008392 

23.4197 

8.8700 

553 

567009 

426957777 

27.4408 

9.0977 

699 

488001 

3*1532099 

26.4386 

8.8748 

754 

568516 

428661064 

27.4591 

9.1017 

700 

490000 

343000000 

26.4575 

8.8790 

755 

570025 

430368875 

27.4773 

9.1057 

701 

491401 

344472101 

26.4764 

8  .  8833 

756 

571536 

432081216 

27.  4955  j  9.1098 

702 

705 

492804 
494:09 

345948408 
347428927 

26.4953 
20.5141 

8.88«o 

8.8917 

758 

573049 
574564 

13379S093  27.5130 
435519512  27.5318 

y.ii3s 
9.1178 

704 

495016 

348913664 

26.53301  8.8959 

759 

576081 

437245479  27.5500 

9.1218 

94 


MATHEMATICAL   TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

760 

577600 

438976000 

27.5681 

9.1258 

815  !  664225 

541343375 

28.5482 

9.3408 

761 

579121 

44071  1081 

27.5862 

9.1298 

81  6  1  665856 

543338490128.5657 

9.3447 

702 

580644 

442450728 

27.6043 

9.1338 

817i  667489 

54533851328.5832 

9.3485 

703 

582169 

444194947 

27.0225 

9.1378 

818  609124 

547343432,28.6007 

9.3523 

704 

583696 

445943744 

27.6405 

9.1418 

819  67'0761 

549353259 

28.0182 

9.3561 

765 

585225 

447697125 

27.6586 

9.1458 

820  '  672400 

551308000 

28.0356 

9.3599 

760 

586756 

449455096 

27.6767 

9.1498 

821  !  674041 

553387001 

28.0531 

9.3637 

767 

588289 

451217663 

27.6948 

9.1537 

822  675684 

555412248 

28.6705 

9.3675 

768 

589824 

452984832 

27.7128 

9.1577 

823  677329 

557441767 

28.0880 

9.3713 

70!) 

591361 

454756609 

27.7308 

9.1617 

824  i  078970 

559470224 

28.7054 

9.3<"51 

:  o 

592900 

456533000 

27.7489 

9.1657 

825  680625 

501515625 

28.7228 

9.3789 

i'  i 

594141 

458314011 

27.7669 

9.1696 

820  682270 

503559976 

28.7402 

9.3827 

7'~v 

595984 

460099648 

27.7849 

9.1736 

827:  083929 

565009283 

28.7576 

9  .  3865 

7  3 

597529 

401889917 

27.8029 

9.1775 

828!  085584 

567003552 

28.7750 

9.3902 

774 

599076 

403684824 

27.8209 

9.1815 

829 

687241 

569722789 

28.7924 

9.3940 

77  5 

600625 

465484375 

27.8388 

9.1855 

830 

688900 

571787000 

28.8097 

9.3978 

776 

602176 

467288576 

27.8568 

9.1894 

831 

690561 

573850191 

28.8271 

9.4016 

777 

603729 

469097433 

27.8747 

9.1933 

832 

692224 

575930308 

28.8444 

9.4053 

778 

005284 

47091095227.8927  9.1973 

S33 

093889  j  578009537 

28.8017 

9.4091 

779 

606841 

47272913927.9106  9.2012 

834 

095550   580093704 

28.8791 

9.4129 

• 

780 

608400 

474552000 

27.9285  9.2052 

835 

697225  582182875 

28.8964 

9.4166 

781 

609961 

476379541 

27.  9464  9.2091 

830 

098896   584277050 

28.9137 

9.4204 

782 

611524 

47821176827.9643  9.2130 

837 

700569  58CJJ7V.253 

28.9310 

9.4241 

783 

613089 

480048687  27  .  9821  9  .  21  70 

838 

702244  5S8480I72 

28  9482 

9.4279 

784 

614056 

481890304 

28.0000  9.2209 

839 

703921  j  590589719 

28.9055 

9.4316 

785 

616225 

483736625 

28.01791  9.2248 

840 

705600  592704000 

28.9828 

9.4354 

786 

617796 

48558765028.0357  9.2287 

841 

707281  i  594K-j:i:i21 

29.0000 

9.4391 

787 

619369 

487443403:28.0535  9.2326 

842 

708904  ;  5969470S8 

29.0172 

9  4429 

7'88 

620944 

489303872:28.0713  9.2365 

843 

710049   599077107 

29.0345 

9.4406 

789 

622521 

491169009 

28.0891  9.2404 

844 

712330 

001211584 

29.0517 

9.4503 

790 

624100 

493039000 

28.1  009  !  9.2443 

845 

714025 

603351125 

29.0689 

9.4541 

791 

025681 

494913671  i2S.  1247;  9.2482 

840 

715710 

005495730 

29.0861 

9.4578 

792 

627264 

496793088126.1425'  9.2521 

847 

717409  !  007645423 

29.1033 

9.4015 

793 

028849 

498677257  j  28  .  1  603  9  .  2500 

848 

719104   60980019229.1204 

9.4652 

794 

630436 

500566184128.1780 

9.2599 

849 

720801   01190004929.1370 

9.4090 

795 

632025 

502459875 

28.1957 

9.2638 

850 

722500 

614125000 

29.1548 

9.4727 

796 

633616 

504358336 

28.2135 

9.2677 

851 

724201 

610295051 

29.1719 

9.4704 

797 

635209 

506261573 

2S.2312 

9.2716 

852 

725904 

01847020829.1800 

9.4801 

798 

636804 

508169592:28.2489  9.2754 

853 

727009  !  62065047729.2062 

9.4838 

799 

038401 

510082399 

28.2666 

9.2793 

854 

729316 

62283580429.2233 

9.4875 

800 
801 

6-10000 
641601 

512000000 
513922401 

28.2843 
28.3019 

9.2832 
9.2870 

855 
856 

731025 
732736 

625026375 
6272220)6 

29.2404 
29  2575 

9.4912 

9.4949 

802 

643204 

515849608liJ8.3196  9.2909 

857 

734449 

02942279329.2740 

9.4986 

803 

644809 

517781627128.3373;  9.2948 

858 

730164 

631628712 

29.2916 

9  5023 

804 

646416 

519718464 

28.3549 

9.2986 

859 

737881 

633839779 

29.3087 

9.5000 

805 

648025 

521660125 

28.3725 

9.3025 

860 

739000 

636056000 

29.3258 

9.5097 

806 
807 

649636 
651249 

523606616!  28.  390  l!  9.3063 
525557943128.4077  9.3102 

861 
862 

741321   638277381 
743044   640503928 

29  3428 
29.3598 

9.5134 
9  5171 

808 

052864 

527514112128.4253  9.3140 

863 

744709   642735047  29.3709 

9.5207 

809 

654481 

529475129 

28.4429,  9.3179 

864 

746490 

644972544 

29.3939 

9.5244 

810 

656100 

531441000 

28.4605  9  3217 

865 

748225 

647214625 

29.4109 

9.5281 

811 

657721 

533411731  28.4781  9.3255 

800 

749950   649401890  29.4279 

9.5317 

812 

659344 

535387328  28  .4956  9  .  3294 

807 

751089 

0517  '143G3'29.  4449 

9.5354 

813 

660969 

537367797 

28.5132  9.3332 

808 

753424 

053972032;  29.  40  18 

9.5391 

814 

662596 

539353144  28  .  5307  9  .  3370 

809 

755101  !  05023490929.4788 

9.5427 

SQUARES,  CUBES,  SQUAEE   AtfD   CUBE   ROOTS.         95 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

870 

756900 

658503000 

29.4958 

9.5464 

925 

855625 

791453125 

30.4138 

9.74% 

871 

758641 

660776311 

29.5127 

9.5501 

926 

857476 

794022776  30.430;. 

9.7470 

872 

760384 

663054848 

29.5296 

9.5537 

927 

859329 

79659798330.4467 

9.7505 

873 

762129 

665338617 

29.5466 

9.5574 

928 

861184 

799178752  30.4631 

9  7540 

874 

763876 

667627624 

29.5635 

9.5610 

929 

863041 

801765089 

30.4795 

9.7575 

875 

765625 

669921875 

29.5804 

9.5647 

930 

864900 

804357000 

30.4959 

9.7610 

876 

767376 

67222137029  5973 

9.5683 

931  866761 

806954491  i  30.  5123 

9.7645 

877 

769129 

6745&5133  29.6142 

9.5719 

932  868624 

809557568  '30.  5287 

9.7680 

878 

770884 

676831)152:29.6311 

9.5756 

933  870489 

812166237)30.5450 

9.7715 

879 

772641 

67915143929.6479 

9.5792 

934 

872356 

814780504 

30.5614 

9.7750 

880 

774400 

68147200029.6648 

9.5828 

935 

874225 

817400375 

30.5778 

9.7785 

8*1 

776161 

083707841 

29.6816 

9.5865 

936  876096 

82002585630.5941 

9.7819 

88  J 

777924 

68(3128968 

29.6085 

9.5901 

937|  877969 

822656953  1  30.  W«6 

9.7854 

88.3 

779689. 

688465387 

29.7153 

9.5937 

938  879844 

82529307230.6268 

9.7889 

884 

781456 

690807104 

29.7321 

9.5973 

939  881721 

827936019 

30.6431 

9.79-24 

885 

783225 

693154125 

29.74891  9.6010 

940  883600 

830584000 

30.6594 

9.7959 

886 

7841)96 

695506456 

29.7658  9.6046 

941  885481 

833237621  30.6757 

9.7993 

887 

786769 

697864103 

29.7825  9.6082 

942  !  887364 

83589688830.6920 

9.8028 

888 

788544 

700227072 

29.7993 

9.6118 

943  889249 

83856180730.7083 

9.8063 

889 

790321 

702595369 

29.8161 

9.6154 

944 

891136 

841232384 

30.7246 

9.8097 

890 

792100 

704969000 

29.8329 

9.6190 

945 

893025 

843908625 

30.7409 

9.8132 

891 

793881 

707347971 

29.8496 

9.6226 

946 

894916 

8-1659053630.7571 

9.8167 

892 

795664 

709732288 

29.8664 

9.6262 

947 

896809 

849278123  30.7734 

9.8201 

893 

797449 

712121957 

29.8831 

9.6298 

948  !  898704 

85  1  97  1?92  ;30.7896 

9.8236 

894 

799236 

714516984 

29.8998 

9.6334 

949 

900601 

854670349 

30.8058 

9.8270 

895 

801025 

716917375 

29.9166 

9.6370 

950 

902500 

857375000 

30.8221 

9.8305 

896 

802816 

719323136 

29.9333 

9.6406 

951;  904401 

860085351  30.8383 

9.8339 

897 

804609 

721734273 

29.9500 

9.6442 

952  906304 

86280  1408;  30.  8545 

9.8374 

898 

806404 

724150792 

29.9666 

9.6477 

953  908209 

86552317730.8707 

9.8408 

899 

808201  726572699 

29.9833 

9  6513 

954  910116 

868250664 

30.8869 

9.8443 

900 

810000 

729000000 

30  0000 

9.6549 

955  912025 

870983875 

30.9031 

9.8477 

901 

811801 

7  31  43:2701  130.0167 

9.6585 

956  913936 

87872281630.9192 

9.8511 

902 

813604 

733870808130.0333 

9.6620 

957  915849 

87646749330.9354 

9.8546 

9031  815409 

736314327  30.0500 

9.6656 

958 

917764 

879217912 

30.9516 

9.8580 

904 

817216 

738763264 

30.0666 

9.6692 

959 

919681 

881974079 

30.9677 

9.8614 

905 

819025 

741217625 

30.0832 

9.6727 

960 

921600 

884736000 

30.9839 

9.8648 

906 

820836 

743677416 

30.0998 

9.8763 

961 

923521 

887503681 

31.0000 

9.8683 

907 

822649 

746142643 

30.1164 

9.67'99 

962 

925444 

890277128 

31.0161 

9.8717 

908 

824464 

748613312 

30.1330 

9.6834 

963 

927369 

893056347 

31.0322 

9.8751 

909 

826281 

751089429 

30.1496 

9.6870 

964 

929296 

895841344 

31.0483 

9.8785 

910 

828100 

753571000 

30.1662 

9.6905 

965 

931225 

898632125 

31.0644 

9.8819 

911 

829921 

756058031 

30.1828 

9.6941 

966 

933156 

901428696 

31.0805 

9.8854 

912 

831744 

758550528 

30.1993 

9.6976 

967 

935089 

904231063 

31.0966 

9.8888 

913 

833569 

761048497 

30.2159 

9.7012 

968 

937024 

907039232 

31.1127 

9.8922 

914 

835396 

763551944 

30.2324 

9.7047 

969 

938961 

909853209 

31  .  1288 

9.8956 

915 

837225 

766060875 

30.2490 

9.7082 

970 

940900 

912673000 

31.1448 

9.8990 

916 

839056 

768575296 

30.2655 

9.7118 

971 

942841 

915498611 

31.1609 

9.9024 

917 

840889 

771095213 

30.2820 

9.7153 

97'2 

944784 

918330048 

31.1769 

9.9058 

918 

842724 

773620632 

30.2985 

9.7188 

973 

946729 

921167317 

31.1929 

9.9092 

919 

844561 

776151559 

30.3150 

9.7224 

974 

948676 

924010424 

Jl.2090 

9.9126 

920 

846400 

778688000 

30.3315 

9.7259 

975 

950625 

926859375 

31.2250 

9.9160 

921 

848241 

781229961 

30.3480 

9.7294 

976 

952576 

929714176 

31.2410 

9.9194 

922 

850084 

783777448 

30.3645 

9.7329 

977 

954529 

932574833 

31.2570 

9  9227 

923 

851929   786330467 

30.3809 

9.7364 

978 

956484 

935441352 

31.2730 

9.9261 

924 

853776  !  788889024  130.3974 

9.7400 

079 

(>5S441  1  938313739 

31.2890 

9.9295 

MATHEMATICAL   TABLES. 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube. 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

980 

960400 

941192000 

31.3050 

9  9329 

1035 

1071225 

1108717875 

32.1714 

10.1153 

981 

962361 

944076141 

31.3209 

9.9363 

1036 

1  073296  i  1  1  1  1  934656  32  .  1  870 

10.1186 

98*2 

964324 

946966168 

31.3369 

9.9396 

1037 

1  075369  11151  57653  32  .  2025 

10.1218 

983 

966289 

949862087 

31.3528 

9.9430 

1038 

1077444J  1  1  18^86872  32  .  2180 

10.1251 

984 

968256 

952763904 

31.3688 

9.9464 

1039 

1079521 

1121622319 

32.2335 

10.1283 

985 

970225 

955671625 

31.3847 

9:9497 

1040 

1081600 

1124864000 

32.2490 

10.1316 

986 

972196 

958585256 

31.4006 

9.9531 

1041 

1083681 

1128111921-32.2645 

10.1348 

987 

974169 

961504803 

31.4166 

9.9565 

1042 

1085764 

113136608832.2800 

10.1381 

988 

976144 

964430272 

31.4325 

9.9598 

1043 

1087849 

11346265U7  32.2955 

10.1413 

989 

978121 

967361669 

31.4484 

9.963-2 

1044 

1089936 

1137893184 

32.3110 

10.1446 

990 

980100 

970-299000 

31.4643 

9.9666 

1045 

1092025 

1141166125 

32.3265 

10.1478 

991 

982081 

^7324-2271 

31.4802 

9.9699 

1046 

1094116 

1144445336  32.3419 

10.1510 

992 

984064 

976191488 

31.4960 

9.9733 

1047 

1096209 

1147730823  38  3574 

10.1543 

993 

986049 

979146657 

31.5119 

9.9766 

1048 

1098304 

115102259232.3728 

10.1575 

91)4 

988036 

982107784 

31.5278 

9.9800 

1049 

1100401 

1154320619  '32.  3883 

10.1607 

995 

990025 

985074875 

31.5436 

9.9833 

1050 

1102500 

115762500032.4037 

10.1640 

990 

992016 

988047936 

31.5595 

9.9866 

1051 

1104601 

1160935651  32.4191 

10.1672 

997 

994009 

991026973 

31.5753 

9.9900 

1052 

1106704 

116425260832.4345 

10.1704 

998 

996004 

994011992 

31.5911 

9  9933 

1053 

1108809 

1167575877  32.4500 

10.1736 

999 

998001 

997002999 

31.6070 

9.9967 

1054 

1110916 

1170905464 

32.4654 

10.1769 

1000 

1000000 

1000000000 

31.6228 

10.0000 

1055 

1113025 

1174241375 

32.4808 

10.1801 

1001 

1002001 

1003003001 

31.6386J10.0033 

1056 

1115136 

117758361632.4962 

10.1833 

1002 

1004004 

1006012008 

31.6544 

10.0067 

1057 

1117249 

118093219332.5115 

10.1865 

1003 

1006009 

1009027027 

31.6702 

10.0100 

1058 

1119364 

118428711232.5269 

10.1897 

1004 

1008016 

1012048064 

31.6860 

10.0133 

1059 

1121481 

1187648379 

32.5423 

10.1929 

1005 

1010025 

1015075125 

31.7017 

10.0166 

1060 

1123600 

1191016000 

32.5576 

10  1961 

1006 

1012036 

1018108216 

31.7175 

10.0200 

1061 

1125721 

1194389981  32.5730 

10.1993 

1007 

1014049 

1021147343 

31.7333 

10  0233 

1062 

1127844 

11977703,28 

32.5883 

10.2025 

1008 

1016064 

1024192512 

31.7490  10.0266 

1063 

11  29969!  120  11  57  04  7 

32  .  6036 

10.2057 

1009 

1018081 

1027243729 

31.7648 

10.0299 

1064 

1132096 

1204550144 

32.6190 

10.2089 

1010 

10-20100 

1030301000 

31.7805 

10.0332 

1065 

1134225 

1207949625 

32.6343 

10.2121 

1011 
1012 

1022121 
1024144 

1033364331 
1036433728 

31.7962 
31.8119 

10.0365 
10.0398 

1066 
1067 

1136356 
1138489 

1211355496 
1214767763 

32.6497 
32  6650 

10.2153 
10.2185 

1013 

1026169 

1039509197|31.8277 

10.0431 

1068 

1140624 

1218186432 

32  .  6803 

10.2217 

1014 

1028196 

1042590744 

31.8434 

10.0465 

1069 

1142761 

1221611509 

32.6956 

10.2249 

1015 

1030225 

1045678375 

31.8591 

10.0498 

1070 

1144900 

1225043000 

32.7109 

10.2281 

1016 

1032256 

1048772096 

31.8748 

10.0531 

1071 

1147041 

1228480911 

32.7261 

10.2313 

1017 

1034289 

1051871913 

31.8904 

10.0563 

1072 

1149184 

1231925248 

32.7414 

10.2345 

1018 

1036324 

1054977832 

31.9061 

10.0596 

1073 

1151329  1235376017 

32.7567 

10.2376 

1019 

1038361 

1058089859 

31.9218 

10.0629 

1074 

1153476 

1238833224 

32.7719 

10.2408 

10-20 

1040400 

1061208000 

31.9374 

10.0662 

1075 

1155625 

1242296875 

32.7872 

10.2440 

1021 
1022 

1042441 

1044484 

1064332261 
1067462648 

31.  9531  (10.0695 
31.9687!  10.  0728 

1076 

1077 

1157776 
1159929 

1245766976 
1249243533 

32.8024 
32.8177 

10.2472 
10.2503 

1023 

1046529 

1070599167 

31.9844 

10.0761 

1078 

1162084 

1252726552 

32.8329 

10.2535 

1024 

1048576 

1073741824 

32.0000 

10.0794 

1079 

1164241 

1256216039 

32.8481 

10.2567 

1025 

1050625 

1076890625 

32.0156 

10.0826 

1080 

1166400 

1259712000 

32.8634 

10.2599 

1026 

1052676 

1080045576 

32.0312 

10.0859 

1081 

1168561 

1263214441 

32.8786 

10.2630 

1027 

1054729 

1083206683 

32.0468 

10.0892 

1082 

1170724 

1266723368 

32.8938 

10.2662 

1028 

1056784 

1086373952 

3-2.0624 

10.0925 

1083 

1172889 

1270238787' 

32.9090 

10.2693 

1029 

1058841 

1089547389 

32.0780 

10.0957 

1084 

1175056 

1273760704 

32.9242 

10.2725 

1030 

1060900 

1092727000 

32.0936 

10.0990 

1085 

1177225 

1277289125 

32.9393 

10.2757 

1031 

1062961 

1095912791 

32.1092 

10.1023 

10861  11  79396  !  1280824056 

32.9545 

10.2788 

1032 

1065024 

1099101768 

32.1248 

10.1055 

1087  11  81  569  11284365503 

32.9697 

10.2820 

10  -S3 

1067089 

1102302937 

32.1403 

10.1088 

10S8  11  83744  [12879  134  7-2 

32.9848 

10.2851 

1034 

1069156 

1105507304 

32.1559 

10.1121 

1089  118592111291467969 

33.0000 

10.2883 

SQUARES,  CUBES,  SQUARE   AND   CUBE    ROOTS.          97 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 

Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1090 

1188100 

1295029000 

33.0151 

10.2914 

1145 

1311025 

1501123625 

33.8378 

10.4617 

1091 

1190281 

1298596571 

33.0303 

10.2946 

1146 

1313316 

1505060136 

33.8526 

10.4647 

1092 

1192464 

1302170688 

33.0454 

10.2977 

1147 

1315609  1509003523 

33.8674 

10.4678 

1093 

1194649 

1305751357 

33.0606 

10.3009 

1148 

1317904)1512953792 

33.8821 

10.4708 

1094 

1196836 

J  309338584 

33.0757 

10.3040 

1149 

1320201 

1516910949 

33.8969 

10.4739 

1095 

1199025 

1312932375 

33.0908 

10.3071 

1150 

1322500 

1520875000 

33.9116 

10.4769 

1096 

1201216 

1316532736 

33  .  1059 

10.3103 

1151 

1324801 

1584845951 

33.9264 

10.4799 

1097 

1203409 

1320139673 

33.1210 

10.3134 

1152 

1327104 

1528823808 

33.9411 

10.4830 

1098 

1205604 

1323753192 

33.1361 

10.3165 

1153 

1329409 

1532808577 

33.9559 

10.4860 

1099 

1207801 

1327373299 

33.1512 

10.3197 

1154 

1331716 

1536800264 

33.9706 

10.4890 

1100 

1210000 

1331000000 

33.1662 

10.3228 

1155 

1334025 

1540798875 

33.9853 

10.4921 

1101 

1212201 

1334633301 

33.1813 

10.3259 

1156 

1336336 

1544804416 

34.0000 

10.4951 

1102 

1214404 

1338273208 

33.1964 

10.3290 

1157 

1338649 

1548816893 

34.0147 

10.4981 

1103 

1216609 

1341919727 

33.2114 

10.3322 

1158 

1340964 

1552836312 

34.0294 

10.5011 

1104 

1218816 

1345572864 

33.2264 

10.3353 

1159 

1343281 

1556862679 

34.0441 

10.5042 

1105 

1221025 

1349232625 

33.2415 

10.3384 

1160 

1345600 

1560896000 

34.0588 

10.5072 

1106 

1223236 

1352899016s  33.  2566 

10.3415 

1161 

1347921 

1564936281 

34.0735|10.5102 

1107 

1225449 

1356572043 

33.2716 

10.3447 

1162 

1350244 

1568983528 

34.0881 

10.5132 

1108 

1227664 

1360251712 

33.2866 

10.3478 

1163 

1352569 

1573037747 

34.1028 

10.5162 

1109 

1229881 

1363938029 

33.3017 

10.3509 

1164 

1354896 

1577098944 

34.1174 

10.5192 

1110 

1232100 

1367631000 

33.3167 

10.3540 

1165 

1357225 

1581167125 

34.1321 

10.5223 

1111 

1234321 

1371330631  33.3317 

10.3571 

1166 

1359556 

1585242296 

34.1467 

10.5253 

1112 

1236544 

137503692833.34(57 

10.3602 

1167 

1361889 

1589324463 

34.1614 

10.5283 

1113 

1238769 

1378749897  33.3617 

10.3633 

1168 

1364224 

1593413632 

34.1760 

10.5313 

1114- 

1240996 

1382469544 

33.3766 

10.3664 

1169 

1366561 

1597509809 

34.1906 

10.5343 

1115 

1243225 

1386195875 

33.3916 

10  3695 

1170 

1368900 

1601613000 

34.2053 

10.5373 

1116 

1245456 

138992889633.4066 

10.3726 

1171 

1371241 

1605723211 

34.2199 

10.5403 

1117 

1247689 

139366861333.4215 

10.3757 

1172 

1373584 

1609840448 

34.2345 

10.5433 

1118 

1249924 

139741503233.4365 

10.3788 

1173 

1375929 

1613964717 

34.2491 

10.5463 

1119 

1252161 

1401168159 

33.4515 

10.3819 

1174 

1378276 

1618096024 

34.2637 

10.5493 

1120 

1254400 

1404928000 

33.4664 

10.3850 

1175 

1380625 

1622234375 

34.2783 

10.5523 

1121 

1256641 

1408694561  33.4813 

10.3881 

1176 

1382976 

1626379776 

34.2929 

10.5553 

1122 

1258884 

141246784833.4963 

10.3912 

1177 

1385329 

1630532233 

34.3074 

10.5583 

1123 

1261129 

141624786733.5112 

10.3943 

1178 

1387684 

1634691752 

34.3220 

10.5612 

1124 

1263376 

1420034624,33.5261 

10.3973 

1179 

1390041 

1638858339 

34.3366 

10.5642 

1125 

1265625 

142382812533.5410 

10.4004 

1180 

1392400 

1643032000 

34.3511 

10.5672 

1126 

1267876 

142762837633.5559 

10.4035 

1181 

1394761 

1647212741 

34.3657 

10.5702 

1127 

1270129 

143143538333.5708 

10.4066 

1182 

1397124 

1651400568 

34.3802 

10.5732 

1128 

1-^72384 

143524915233.5857 

10.4097 

1183 

1399489  1655595487 

34.3948 

10  5762 

1129 

1274641 

143906968933.6006 

10.4127 

1184 

1401856 

1659797504 

34.4093 

10.5791 

| 

1130 

1276900 

144289700033.6155 

10.4158 

1185 

1404225 

1664006625 

34.4238 

10.5821 

1131 

1279161 

1446731091 

33.6303 

10.4189 

1186 

1406596 

1668222856 

34.  43841  10.  5851 

1132 

1281424 

1450571968 

33.645210.4219 

1187 

1408969 

1672446203 

34.4529 

10.5881 

1133 

1283689 

1454419637 

33.  6601  |  10.  4250 

1188 

1411344 

1676676672 

34.4674 

10.5910 

1134 

1285956 

1458274104 

33.6749 

10.4281 

1189 

1413721 

1680914269 

34.4819 

10.5940 

1135 

1288225 

1462135375 

33.6898 

10.4311 

1190 

1416100 

1685159000 

34.4964 

10.5970 

1136 
1137 

1290496 
1292769 

1466003456 
1469678353 

33.7046  10.4342 
33.7174  10.4373 

1191 
1192 

1418481 
1420864 

1689410871 
1693669888 

34.5109 
34.5254 

10.6000 
10.6029 

1138 

1295044 

1473760072 

33.7342 

10.4404 

1193 

1423249 

1697936057 

34.5398 

10.6059 

1139 

1291321 

1477648619 

33.7491 

10.4434 

1194 

1425636 

1702209384 

34.5543 

10.6088 

1140 

1299600 

1481544000 

33.7639 

10.4464 

1195 

1428025 

1706489875 

34.5688 

10.6118 

1741 

1301881 

1485446221 

33.7787 

10.4495 

1196 

1430416 

1710777536 

34.5832 

10.6148 

1142 

1304164 

1489355288 

33.7935  10.4525 

1197 

1432809 

1715072373 

34.5977 

10  6177 

1143 

1306449 

1493271207 

33.808310.4556 

1198 

1435204 

1719374392 

34.6121 

10.  6*07 

1144 

1308736 

1497193984 

33.8231  10.4586-1199 

,437601 

1723683599 

34.6266 

10.6236 

98 


MATHEMATICALwTABLES. 


No. 

1200 
1201 
1202 
1203 
1204 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1440000 
1442401 
1444804 
1447209 
1449616 

172800000034.6410 
1732323601  34.6554 
173665440834.6699 
174099242734.6843 
174533766434.6987 

10.6266 
10.6295 
10.6325 
10.6354 
10.6384 

1255 

1256 
1257 
1258 
1259 

1575025 
1577536 
1580049 
1582564 
1585081 

197665637535.4260 
1981385216  35.4401 
198612159335.4542 
1990865512  35.4683 
199561697935.4824 

10.7'865 
10.7894 
10.7922 
10.7951 
10.7980 

1205 
1206 

1207 
1208 
1209 

1452025 
1454436 
1456849 
1459264 
1461681 

174969012534.7131 

175404981  6  :  34.  7'275 
175841674334.7419 
176279091  2  !  34.  7563 
176717232934.7707 

10.6413 
10.6443 
10.6472 
10.6501 
10.6530 

1260 
1261 
1262 
1263 
1264 

1587600 
•,1590121 
1592644 
1595169 
1597696 

200037600035.4965 
2005142581  35.5106 
200991672835.5246 
201469844?  35.5387 
2019487744,35.5528 

10.8008 
10.8037 
10.80(55 
10.8094 
1U.8122 

1210 
1211 
1212 
1213 
1214 

1464100 
1466521 
1468944 
1471369 
1473796 

1771561000 
1775956931 
1780360128 
178477059? 
1789188344 

34.7851 
34.7994 
34.8138 
34.8281 
34.8425 

10.6560 
10.6590 
10.6619 
10.6648 
10.6678 

1265 

1266 
1267 
1268 
1269 

1600225 
1602756 
1605289 
1607824 
1610361 

2024284625 

2029089096 
2033901163 
20387'20832 
2043548109 

35.5668 
35.5809 
35.5949 
35.6090 
35.6230 

10.8151 
10.8179 
10.8208 
10.8236 
10.8265 

1215 
1216 
121? 
1218 
1219 

1476225 

1478656 
1481089 
1483524 
1485961 

1793613375 
1798045696 
1802485313 
1806932232 
1811386459 

34.8569 
34.8712 
34.8855 
34.8999 
34.9142 

10.6707 
10.6736 
10.6765 
10.67'95 
10.6824 

1270 
1271 
1272 
1273 
1274 

1612900 
1615441 
1617984 
1620529 
1623076 

2048383000 
2053225511 
2058075648 
2062933417 
2067798824 

35.6371 
35.6511 
35.6651 
35.6791 
35.6931 

10.8293 
10.8322 
10.8350 
10  8378 
10.8407 

1220 
1221 
1222 
1223 
1224 

1488400 
1490841 
.1493284 
1495729 
1498176 

1815848000 
1820316861 
1824793048 
1829276567 
1833767424 

34.9285 
34.9428 
34.9571 
34.9714 
34.985? 

10.6853 
10.6882 
10.6911 
10.6940 
10.6970 

1275 
1276 
1277 
1278 
1279 

1625625 
1628176 
1630729 
1633284 
1635841 

2072671875 
2077552576 
2082440933 
2087336952 
2092240639 

35.7071 
35.7211 
35.7351 
35.7491 
35.7631 

10.8435 
10.8463 
10.8492 
10.8520 
10.8548 

1225 

1226 
122? 
1228 
1229 

1500625 
1503076 
1505529 
1507984 
1510441 

1838265625 
1842771176 
1847284083 
1851804352 
1856331989 

35.0000 
35.0143 
35.0286 
35.0428 
35.0571 

10.6999 
10.7028 
10.7057 
10.7086 
10.7115 

1280 
1281 
1282 
1283 
1284 

1638400 
1640961 
1643524 
1646089 
1648656 

2097152000 
2102071041 
2106997768 
2111932187 
2116874304 

35.7771 
35.7911 
35.8050 
35.8190 
35.8329 

10.8577 
10.8605 
10.8633 
10.8661 
10.8690 

12:30 
1231 
1232 
1233 
1234 

1512900 
1515361 
1517824 
1520289 
1522756 

1860867000 
1865409391 
1869959168 
1874516337 
1879080904 

35.0714  10.7144 
35.  0856|  10.  7173 
35.0999;10.7202 
85.1141  10.7281 

35.1283  10.7260 

1285 
1286 

1287 
1288 
1289 

1651225 
1653796 
1656369 
1658944 
1661521 

2121824125 
2126781656 
2131746903 
2136719872 
2141700569 

35.8469 
35.8608 
35.8748 
35.8887 
35.9026 

10.8718 
10.8746 
10.8774 
10.8802 
10.8831 

1235 
1236 
1237 
1238 
1239 

1525225 
1527696 
1530169 
1532644 
1535121 

1883652875 
1888232256 
1892819053 
1897413272 
1902014919 

35.1426  10.7289 
35.156810.7318 
35.1710  10.7347 
35.  1852  j  10.  7376 
35.1994  10.7405 

1290 
1291 
1292 
1293 
1294 

1664100 
1666681 
1669264 
1671849 
1674436 

2146689000 
2151685171 
2156689088 
2161700757 
21667'20184 

35.9166 
35.9305 
35.9444 
35.9583 
35.9722 

10.8859 
10.8887 
10.8915 
10.8943 
10.8971 

1240 
1241 
1242 
1243 
1244 

1537600 
1540081 
1542564 
1545049 
1547536 

1906624000 
1911240521 

1915864488 
1920495907 
1925134784 

35.2136 
35.2278 
35.2420 
35.2562 
35.2704 

10.7434 
10.7463 
10.7491 
10.7520 
10.7549 

1295 

1296 
1297 
1298 
1299 

1677025 
1679616 
1682209 
1684804 
1687401 

2171747375 
217-6782336 

2181825073 
2186875592 
2191933899 

35.9861 
36.0000 
36.0139 
36.0278 
36.0416 

10.8999 
10.9027 
10.9055 
10.9083 
10.9111 

1245 
1240 
1247 
1248 
1249 

1550025 
1552516 
1555009 
1557504 
1560001 

1929781125 
1934434936 
1939096223 
19437'64992 
1948441249 

35.2846 
35.298? 
35  3129 
35.3270 
35.3412 

10.7578 
10.7607 
10.7635 
10.7664 
10.7693 

1300 
1301 
1302 
1303 
1304 

16900002197000000 
1  69260  1!  2202073901 
1695204  2207155608 
1697809221224512? 
1700416  2217342464 

36.0555 
36.0694 
36.0832 
36.0971 
36.1109 

10.9139 
10.9167 
10.9195 
10.9223 
10.9251 

1250 
1S51 
1252 
1253 
1254 

1562500 
1565001 
1567504 
1570009 
1572516 

1953125000 
1957816251 
1962515008 
1967221277 
1971935064 

35.3553 
35.3695 
35.3836 
35.3977 
35.4119 

10.7722 

10.7750 
10.7779 
10  7808 
10  7S37 

1305 
1306 
1307 
1308 
13091 

1703025 
1705636 
17'08249 
1710864 
1  713481  : 

2222447625 
2227560616 
2232681443 
223781.0112 
2242946629 

36.1248 
36.1386 
36.1525 
36.1663 
36.1801 

10.9279 
10.9307 
10.9335 
10.9363 
10.9391 

SQUARES,  CUBES,  SQUARE   AND    CUBE    HOOTS.          99 


No 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1310 

17161002248091000 

36.1939 

10.9418 

1365 

1863225 

2543302125 

36.9459 

11.0929 

1311 

1718721  2253243231 

36.2077 

10.9446 

1366 

1865956  2548895896 

36.9594 

11.0956 

1312 

1721344  2258403328 

36.2215 

10.9474 

1367 

1868689  2554497863 

36.9730 

11.0983 

1313 

1723969  2263571297 

36.2353 

10.9502 

1368 

1871424 

2560108032 

36.9865 

11.1010 

1314 

17265962268747144 

36.2491 

10.9530 

1369 

1874161 

2565726409 

37.0000 

11.1037 

1315 

17292252273930875 

36.2629 

10.9557 

1370 

1876900 

2571353000 

37.0135 

11.1064 

1310 

1731856  2279122496 

36.2767 

10.9585 

1371 

1879641 

2576987811 

37.0270 

11.1091 

131? 

1734489  2284322013 

36.2905 

10.9613 

1372 

1882384 

2582630848 

37.0405 

11.1118 

3318 

1737124  228!)52iU32 

36.3043 

10.9640 

1373 

1885129 

2588282117 

37.0540 

11.1145 

1319 

1739761  2294744759 

36.3180 

10.9668 

1374 

1887876 

2593941624 

37.0675 

11.1172 

1330 

17424002299968000 

36.3318 

10.9696 

1375 

1890625 

2599609375 

37.0810 

11.1199 

13-41 

1745041 

2305199161 

36.3456 

10.9724 

1376 

1893376 

2605285376 

37  0945 

11.1226 

1322 

1747684 

2310438248 

36.3593 

10.9752 

1377 

1896129 

2610969633 

37.1080  11.1253 

1323 

1750829 

2315685267 

36  3731 

10.9779 

1378 

1898884 

2616662152 

37.1214 

11.1280 

1324 

1752976 

2320940224 

36.3868 

10.9807 

1379 

1901641 

2622362939 

37.1349 

11.1307 

1325 

1755625 

2326203125 

36.4005 

10.9834 

1380 

1904400 

2628072000 

37.1484 

11.1334 

1326 

1758276 

2331473976 

36.4143 

10.9862 

1381 

1907161 

2633789341 

37.1618 

11.1361 

1327 

1760929 

2336752783 

36.4280 

10.9890 

1382 

1909924 

2639514968 

37.1753 

1  1  .  1387 

1328 

1763584 

2342039552 

36.4417 

10.9917 

1383 

1912689 

2645248887 

37.1887 

11.1414 

1329 

1766241 

2347334289 

36.4555 

10.9945 

1384 

1915456 

2650991104 

37.2021 

11.1441 

1330 

1768900 

2352637000 

36.4692 

10.9972 

1385 

1918225 

2656741625 

37.2156 

11.1468 

1331 

1771561 

2357947691 

36.4829 

11.0000 

J3S6 

1920996 

2662500456 

37.2290 

11.1495 

1332 

17742-24 

2363266368 

36.4966 

11.01)28 

1387 

1923769 

2668267603 

37.2424 

11.1522 

1333 

1776889 

2368593037 

36.5103 

11.0055 

1388 

1926544 

2674043072 

37.2559 

11.1548 

1334 

1779556 

2373927704 

36.5240 

11.0083 

1389 

1929321 

2679826869 

37.2693 

11.1575 

1335 

1782225 

2379270375 

36.5377 

11.0110 

1390 

1932100 

2685619000 

37.2827 

11.1602 

1336 

1784896 

2384621056 

36.5513 

11.0138 

1391 

1934881 

2691419471 

37.2961 

11.1629 

1337 

1787569 

2389979753 

36.5650 

11.0165 

1392 

1937664 

2697228288 

37.3095 

11.1655 

1338 

1790244 

23:.'5346472 

3(5.5787 

11  0193 

1393 

1940449 

2703045457 

37.3229 

11.1682 

1339 

1792921 

2400721219 

36.5923 

11.0220 

1394 

1943236 

2708870984 

37.3363 

11.1709 

1340 

1795600 

2406104000 

36.6060 

11.0247 

1395 

1946025 

2714704875 

37.3497 

11.1736 

1341 

1798281 

2411494821 

36.  6197!  11.0275 

1396 

1948816 

2720547136 

37.3631 

11.1762 

1342 

1800964 

2416893688 

36.6333  ill.  0302 

1397 

1951609 

2726397773 

37.3765 

11.1789 

1343 

1803649 

2422300607 

36.6469 

11.0330 

1398 

1954404 

2732256792 

37.3898 

11.1816 

1344 

1806336 

2427715584 

36.6606 

11.0357 

1399 

1957201 

2738124199 

37.4032 

11.1842 

1345 

1809025 

2433138625 

36.6742 

11.0384 

1400 

1960000 

2744000000 

7.4166 

11.1869 

1346 

1811716 

2438569736 

56.6879 

11.0412 

1401 

1962801 

2749884201 

37.4299 

11.1896 

1347 

J  81  4409 

2444008923 

36.7015 

11.0439 

1402 

1965604 

2755776808 

37.4433 

11.1922 

1348 

1817104 

2449156192 

36.7151  11.0466 

1403 

1968409 

2761677827 

37.4566 

1  1  .  1949 

1349 

1819801 

245491  1549 

36  .  7287 

11.0494 

1404 

1971216 

2767587264 

37.4700 

11.1975 

1350 

1822500 

2460375000 

36.7423  11.0521 

1405 

1974025 

2773505125 

37.4833 

11.2002 

1351 

1825201 

2465846551 

36.7560  11.0548 

1406 

1976836 

2779431416 

37.4967  11.2028 

1352 

1827904 

2471326208 

36.  7696  ill.  0575 

1407  1979649 

2785366143 

37.5100  11.2055 

1353 

183(1609 

2476813977 

36.  7831  ill.  0603 

1408)  1982464 

2791309312 

37.5233  11.2082 

1354 

1833316 

2482309864 

36.7967 

11.0630 

1409 

1985281 

2797260929 

37.5366 

11.2108 

1355 

1836025 

2487813875 

36.8103 

11.0657 

1410 

1988100 

2803221000 

37.5500 

11.2135 

1356 

1838736 

2493326016 

36.8239 

11.0684 

1411 

1990921 

2809189531 

37.5633 

11.2161 

1357 

1841449 

2498846293 

36.8375ill.0712 

1412 

1993744 

2815166528 

37.  5766111.  2188 

1358 

1844164 

2504374712 

36.8511)11.0739 

1413 

19:*6569 

2821151997 

37.5899 

11.2214 

1359 

1846881 

2509911279 

36.8646 

11.0766 

1414 

1999396 

2827145944 

37.6032 

11.2240 

13GO 

1849600 

2515456000 

36.8782 

11.0793 

1415 

2002225 

2833148375 

37.6165 

11.2267 

1361 

1852321 

2521008881 

36.  89  17111.  0820 

1416 

2005056 

2839159296 

37.6298  11  2293 

1362 

1855044 

2526569928 

36.9053'  11.  0847 

1417 

2007S89 

2845178713 

37.6431  11.2320 

1363 

1857769 

2532139147 

36.  91  88'  11.  0875 

1418 

20  10724 

2851206632 

37.6563111.2346 

1364 

1860496 

2537716544 

36.9324  11.0902 

1419 

20)3561 

2857243059 

37.  6696  '11.  2373 

100 


MATHEMATICAL  TABLES. 


No. 

Square 

Cube. 

J3* 
Rout. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1420 

2016400 

2863288000 

37.6829 

11.2399 

1475 

2175625 

3209046875 

38.4057 

11.383-2 

1421 

2019241 

2869341461  37.6962 

11.2425 

14761  2178576 

3215578176 

38.4187 

11.3858 

1422 

2022084 

287540344837.7094 

11.2452 

1477 

2181529 

3222118333 

38.4318 

11.3883 

1423 

2024929 

288147396737.7227 

11.2478 

1478 

2184484 

3228667352 

38.4448 

11.3909 

1424 

2027776 

2887553024 

37.7359 

11.2505 

1479 

2187441 

3235225239 

38.4578 

11.3935 

1425 

2030625 

2893640625 

37.7492 

11.2531 

1480 

2190400 

3241792000 

38.4708 

11.3960 

1426 

2033476 

289973677637.7624 

11.2557 

1481 

2193361 

3248367641 

38.4838 

11.3986 

1427 

2036329 

2905841483  37.7757 

11.2583 

1482 

2196324 

3254952168 

38.4968 

11.4012 

1428 

2039184 

2911954752 

37.7889 

11.2610 

1483 

2199289 

3261545587 

38.5097 

11.4037 

14*9 

2042041 

2918076589 

37.8021 

11.2636 

1484 

2202256 

3268147904 

38.5227 

11.4063 

1430 

2044900 

2924207000 

37.8153 

11.2662 

1485 

2205225 

3274759125 

38.5357 

11.4089 

1431 

2047761 

2930345991  37.8286 

11.2689 

1486 

2208196 

3281379256 

38.5487 

11.4114 

1432 

2050624 

•293649356837.8418 

11.2715 

1487 

2211169 

3288008303 

38.5616 

11.4140 

1433 

2053489 

2942649731:37.8550 

11.2741 

1488 

2214144 

3294646272 

38.5746 

11.4165 

1434 

2056356 

2948814504 

37.8682 

11.2767 

1489 

2217121 

3301293169 

38.5876 

11.4191 

1435 

2059225 

2954987875 

37.8814 

11.2793 

1490 

2220100 

3307949000 

38.6005 

11.4216 

1436 

2062096 

296116985637.8946 

11.2820 

1491 

2223081 

3314613771 

38.6135 

11.4242 

1437 

2064969 

2967360453  !  37.  9078 

11.2846 

1492 

2226061 

3321287488 

38.6264 

11.4268 

1438 

2067844 

297355967237.9210 

11.2872 

1493 

2229049 

3327970157 

38.6394 

11.4293 

1439 

2070721 

2979767519.37.9342 

11.2898 

1494 

2232036 

3634661784 

38.6523 

11.4319 

1440 

2073600 

2985984000  37.9473 

11.2924 

1495 

2235025 

3341362375 

38.665211.4344 

1441 

2076481 

299220912137.9605 

11.2950 

1496 

2238016 

3348071936 

38.6782 

11.4370 

1442 

2079364 

299844288837.9737 

11.2977 

1497 

2241009 

3354790473 

38.6911 

11.4395 

1443 

2082249 

3004685307  37.9868  11.3003 

1498 

2244004 

3361517992 

38.7040 

11.4421 

1444 

2085136 

3010936384  38  .  0000.  1  1  .  3029 

1499 

2247001 

3368254499 

38.7169 

11.4446 

1445 

2088025 

3017196125  38.0132  11.3055 

1500 

2250000 

3375000000 

38.7298 

11.4471 

1446 

2090916 

3023464536  ,  38  .  0263  1  1  .  308  1 

1501  2253001 

3381754501 

38.7427 

11.4497 

1447 

2093809 

3029741623 

38.0395 

11.3107 

1502  2256004 

3388518008 

38.7556 

11.4522 

1448 

2096704 

3036027392 

38.0526 

11.3133 

1503  2259009 

3395290527 

38.7685 

11.4548 

1449 

2099601 

3042321849 

38.0657 

11.3159 

1504 

2262016 

3402072064 

38.7814 

11.4573 

1450 

2102500 

3048625000 

38.0789 

11.3185 

1505 

2265025 

3408862625 

38.7943 

11.4598 

1451 

2105401 

3054936851 

38.0920 

11.3211 

1506 

2268036 

3415662216 

38.8072 

11.4624 

1452 

2108304 

3061257408 

38.1051 

11.3237 

1507 

2:271049 

3422470843 

38.8201 

11.4649 

1453 

2111209 

3067586677 

38.1182  11.3263 

1508 

2274064 

3429288512 

38.8330 

11.4675 

1454 

2114116 

3073924664 

38.1314 

11.3289 

1509 

2:177081 

3436115229 

38.8458 

11.4700 

1455 

2117025 

3080271375 

38.1445 

11.3315 

1510 

2280100 

3442951000 

38.8587 

11.4725 

1456 

2119936 

30866-26816 

38.1576 

11.3341 

1511 

2283121 

3449795831 

38.8716 

11.4751 

1457 

2122849 

3092990993 

38.1707 

11.3367 

1512 

2286144 

3456649728 

38  8844 

11.4776 

1458 

2125764 

3099363912 

38.1838 

11.3393 

1513 

2289169 

3463512697 

38.8973 

11.4801 

1459 

2128681 

3105745579 

38.1969 

11.3419 

1514 

2292196 

3470384744 

38.9102 

11.4826 

1-1  fiO 

2131600 

3112136000 

38.2099 

11.3445 

1515 

2295225 

3477265875 

38.9230 

11.485-2 

1461 

21345-21 

3118535181 

38.223011.3471 

1516 

2298256 

3484156096 

38.  9358  jl  1.4  877 

146-2 

2137444 

3124943128 

38.2361 

11.3496 

1517 

2:301289 

3491055413 

38.9487  11.4902 

1463 

2140369 

3131359847 

38.2492 

11.3522 

1518 

2304324 

3597963832 

38.9615111.4927 

1464 

2143296 

3137785344 

38.2623 

11.3548 

1519 

2307361 

3504881359 

38.9744 

11.4953 

1465 

2146225 

3144219625 

38.2753 

11.3574 

1520 

2310400 

3511808000 

38.9872 

11.4978 

1466 

2149156 

315066-2696 

3S.2884 

11.3600 

1521 

2313441 

3518743761 

39.0000 

11.5003 

1467 

2152089 

3157114563 

38.3014 

11.3626 

1522 

2316484 

3525688648 

39.0128 

11.5028 

1468 

2155024 

3163575232 

38.3145 

11.3652 

1523 

2319529 

353-2642667 

39.0256 

11.5054 

1469 

2157961 

3170044709 

38.3275 

11.3677 

1524 

2322576 

3539605824 

39.0384 

11.5079 

1470 

2160900 

3176523000 

38.3406 

11.3703 

1525 

2325625 

3546578125 

39.0512 

11.5104 

1471 

2163841 

3183010111 

38.3536 

1  1  .  37  29 

1526 

2328676 

3553559576 

39.0640 

11.5129 

1472 

2166784 

3189506048 

38.3667 

11.3755 

1527 

2331729 

3560550183 

39.0768 

11.5154 

1473 

2169729 

3196010817 

38.3797 

11.3780 

1528 

2334784 

3567549952 

39.0896 

11.5179 

1474 

2172676 

3202524424  3F  .  -3927 

1  1  .  3806 

1529 

2337841 

3574558889 

39.102411.5204 

SQUARES,  CUBES,  SQUARE   AKD   CUBE   ROOTS.      101 


No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

No. 

Square. 

Cube. 

Sq. 
Root. 

Cube 
Root. 

1530 

2340900 

3581577000 

39.1152 

11.5230 

1565 

2449225  3833037125 

39.5601 

11.6102 

1531 

2343961 

3588604291  39.1280 

11.5255 

1566 

24523563840389496 

39.5727 

11.6126 

1532 

2347024 

359564076839.1408 

11.5280 

1567 

24554893847751263 

39.5854 

11.6151 

1533 

2350089 

360268(5437 

39.1535 

11.5305 

1568 

2458624  3855123432 

39.5980 

11.6176 

1534 

2353156 

3609741304 

39.1663 

11.5330 

1569 

246  1  761  3862503009 

39.6106 

11.6200 

1535 

2356225 

361680537539.1791 

11.5355 

1570 

2464900  3869893000 

39.6232 

11.6225 

1536 
1537 

2359296 
2362369 

3623878656  39.1  91  % 
363096115339.2046 

11.5380 
11.5405 

1571 
1572 

2468041  3877292411 
24711  84  !  3884701  248 

39.6358 
39.6485 

11.6250 
11.6274 

1538 

2365444 

363805287239.2173 

11.5430 

1573 

2474329  '38921  195  17 

39.6611 

11.6299 

1539 

2368521 

3645153819 

39.2301 

11.5455 

1574 

24774763899547224 

39.6737 

11.6324 

1540 

2371600 

3652264000 

39.2428 

11.5480 

1575 

2480625  3906984375 

39.6863 

11.6348 

1541 

2374681 

3659383421 

39.2556 

11.5505 

1576 

2483776  3914430976 

39.6989 

11.6373 

1542 

2377764 

366651208839.2683 

11.5530 

1577 

24869293921881033 

39.7115 

11.6398 

1543 

2380849 

3673650007139.2810 

11.5555 

1578 

2490084  3929352552 

39.7240 

11.6422 

1544 

2383936 

3680797184  39.2938 

11.5580 

1579 

2493241 

3936827539 

39.7366 

11.6447 

1545 

2387025 

3687953625 

39.3065 

11.5605 

1580 

2496400  3944312000 

39.7492 

11.6471 

1546 

2390116 

36951  1  9336  39  .  3  1  92  1  1  .  5630 

1581 

2499561  3651805941 

39.7618 

11.6496 

1547 

2393209 

37022943231  39  .  3319  1  1  .  5655 

1582 

2502724  3959309368 

39.7744 

11.6520 

1548 

2396304 

3709478592 

39.3446111.5680 

1583 

2505889  !  3966822287 

39.7869 

11.6545 

1549 

2399401 

3716672149 

39.3573 

11.5705 

1584 

25090563974344704 

39.7995 

11.6570 

1550 

2402500 

3723875000 

39.370011.5729 

1585 

2512225  3981876625 

39.8121 

11.6594 

1551 

2405601 

3731087151  39.3827 

11.5754 

1586 

25153963989418056 

39.824611.6619 

155;! 

2408704 

3738308608 

39.395411.5779 

1587 

2518569  3996969003 

39.837211.66*3 

1553 

2411809 

3745539377 

39.4081  11.5804 

1588 

2521744  4004529472 

39  8497  11.6668 

1554 

2414916 

3752779464 

39.4208  1.1.5829 

1589 

2524921 

4012099469 

39.862311.6692 

1555 

2418025 

3760028875 

39.4335 

11.5854 

1590 

2528100 

4019679000 

39.8748 

11.6717 

1556 

2421136 

3767287616 

39.446211.5879 

1591 

2531281  4027268071 

39.887311.6741 

1557 

2424249 

3774555693  !  39  .  4588  !  1  1  .  5903 

J592 

2534464  4034866688 

39.8999:11.6765 

1558 

2427364 

3781833112 

39.4715  11.5928 

1593 

2537649  '4042474857 

39.  9124  '11.  6790 

1559 

2430481 

3789119879 

39.4842 

11.5953 

1594 

2540836  14050092584 

39.924911.6814 

| 

1560 

2433600 

3796416000 

39  496811.5978 

1595 

2544025  4057719875 

39.937511.7839 

1561 

2436721 

380372  1  48  1  39  5095  ill.  6003 

1596 

2547216'4065356736 

39.950011.6863 

1562 

2439844 

38  1  1036328!  39  .  5221  !  1  1  .  6027 

1597 

25504094073003173 

39.  9625  !1  1.6888 

1563 

2442969 

3818360547!  39  .  5348;  1  1  .  6052 

1598 

25536044080659192 

39.975011.6912 

1564 

2446096 

3825694144139  5474  11.6077 

1599 

2556801  '4088324799 

39.9875 

11.6936 

1600 

2560000  4096000000 

40.000011.6961 

SQUARES  AND  CUBES  OF  DECIMALS. 


No. 

Square. 

Cube. 

No. 

Square. 

Cube. 

No. 

Square. 

Cube. 

.1 

.01 

.001 

.01 

.0001 

.000  001 

.001 

.00  00  01 

.000  000  001 

.2 

.04 

.008 

.02 

.0001 

.000  008 

.002 

.00  00  04 

.000  000  008 

.3 

.09 

.027 

.03 

.0009 

.000  027 

.003 

.00  00  09 

.000  000  027 

.4 

.16 

.064 

.04 

.0016 

.000  064 

.004 

.00  00  16 

.000  000  064 

.5 

.25 

.125 

.05 

.0025 

.000  125 

.005 

•00  00  25 

.000  000  125 

.6 

.36 

.216 

.06 

.0036 

.000  216 

.006 

.00  00  36 

.000  000  216 

.7 

.49 

.343 

.07 

.0049 

.000  343 

.007 

.00  00  49 

.000  000  343 

'.8 

.64 

.512 

.08 

.0064 

.000  512 

.008 

.00  00  64 

.000  000  512 

.9 

.81 

.729 

.09 

.0081 

.000  729 

.009 

.00  00  81 

.000  000  729 

1.0 

1.00 

1.000 

.10 

.0100 

.001  000 

.010 

.00  01  00 

.000  001  000 

1.2 

1.44 

1.728 

.12 

.0144 

.001  728 

.012 

.00  01  44 

.000  001  728 

Note  that  the  square  lias  twice  as  many  decimal  places,  and  the  cube  three 
times  as  many  decimal  places,  as  the  root. 


102  MATHEMATICAL  TABLES. 

FIFTH  ROOTS   AND  FIFTH   POWEMS, 

(Abridged  from  TRAUTWINE.) 


*« 
& 

Power. 

N 
&& 

Power. 

^  G 

o  o 

fctf 

Power. 

N 

o  o 

s« 

Power. 

i,  . 
o  *^ 

\jr  f£ 

Power. 

.10 

.000010 

3.7 

693.440 

9.8 

90392 

21.8  4923597 

40 

102400000 

.15 

.000075 

3,8 

792.352 

9  9 

95099 

22.0  5153632 

41 

115856201 

.20 

.000320 

3.9 

902.242 

lO'.u 

100000 

22.  2  !  5392186 

42 

130691232 

.25 

.000977 

4.0 

1024.00 

10.2 

110408 

22.4   5639493 

43 

147008443 

.30 

.002430 

4.1 

1158.56 

10.4 

121665 

22.6)  5895793 

44 

164916224 

.35 

.005252 

4.2 

1306.91 

10.6 

133823 

22.8  6161327 

45 

184528125 

.40 

.010240 

4.3 

1470.08 

10.8 

146933 

23.0   6436343 

46 

205962976 

.45 

.018453 

4.4 

1649.16 

11.0 

161051 

23.2  6721093 

47 

229345007 

.50 

.031250 

4.5 

1845.28 

11.2 

176234 

23.4  7015834 

48 

254803968 

.55 

.050328 

4.6 

2059.63 

11.4 

192541 

23.6 

7320825 

49 

282475249 

,60 

.077760 

4.7 

2293.45 

11.6 

210131 

23.8 

7636332 

50 

312500000 

.65 

.116029 

4.8 

2548.04 

11.8 

228776 

24.0 

7962624 

51 

345025251 

.70 

168070 

4.9 

2824.75 

12.0 

248832 

24.2  8299976 

52 

380204032 

.75 

,237305 

5.0 

3125.00 

12.2 

270271 

24.  4  !  8648666 

53 

418195493 

.80 

.327680 

5.1 

3450.25 

12.4 

293163 

24.6  9008978 

54 

459165024 

.85 

.443705 

5.2 

3802  04 

12.6 

317580 

24.8  9381200 

55 

503284375 

.90 

.590490 

5.3 

4181.95 

12.8 

343597 

25.  O1  9765625 

56 

550731776 

.05 

.773781 

5.4 

4591.65 

13.0 

371293 

25.2  10162550 

57 

601692057 

1.00 

1.00000 

5.5 

5032.84 

13.2 

400746 

25.4  10572278 

58 

656356768 

1.05 

1.27628 

5.6 

5507.32 

13.4 

432040 

25.61  10995116 

59 

714924299 

1.10 

1.61051 

5.7 

6016.92 

13  6 

465259 

25.8  11431377 

60 

777600000 

1.15 

2.01135 

5.8 

6563.57 

13.8 

500490 

26.0  11881376 

61 

844596301 

1.20 

2.48832 

5.9 

7149.24 

14.0 

537824 

26.2  12345437 

62 

916132832 

1.25 

3.05176 

8.0 

7776.00 

14.2 

577353 

26.4  12823886 

63 

992436543 

1.30 

3.71293 

6.1 

8445.96 

14.4 

619174 

26.6  13317055 

64 

1073741824 

1.35 

4.48403 

6.2 

9161.33 

14  6 

663883 

26.8  13825281 

65 

1160290625 

1.40 

5.37824 

6.3 

9924.37 

14.8 

710082 

27.0  14348907 

66 

1252332576 

1.45 

6.40973 

6  4 

10737 

15.0 

759375 

27.2 

14888280 

67 

1350125107 

1.50 

7.59375 

6.5 

11603 

15  2 

811368 

27^4 

15443752 

68 

1453933568 

1.55 

8.94661 

6.6 

125:23 

15.4 

866171 

27.  6  i  16015681 

69 

1564031349 

1.60 

10.4858 

6.7 

13501 

15.6 

923896 

27.8 

16604430 

70 

1680700000 

1.65 

12.2298 

6.8 

14539 

15.8 

984658 

28.0 

17210368 

71 

1804229351 

1.70 

14.1986 

6.9 

15640 

16.0 

1048576 

28.2 

17833868 

72 

1934917632 

1.75 

16.3141 

7.0 

16807 

16.2 

1115771 

28.4 

18475309 

73 

2073071593 

1.80 

18.8957 

7.1 

18042 

16.4 

J  186367 

28.6 

19135075 

74 

2219006624 

1.85 

21.6700 

7.2 

19349 

16.6 

1260493 

28.8 

19813557 

75 

2373046875 

1.90 

21.7610 

7.3 

20731 

16  8 

1338278 

29.0 

20511149 

76 

2535525376 

1.95 

28.1951 

7.4 

22190 

17.0 

1419857 

29.2 

21228253 

77 

2706784157 

2.00 

32^0^00 

7.5 

23730 

17.2 

1505366 

29.4 

21965275 

78 

2887174368 

2.05 

36.2051 

7.6 

25355 

17.4 

1594947 

29.6 

2272:2628 

79 

3077056399 

2.10 

40.8410 

7.7 

27068 

17.6 

1688742 

29  8 

23500728 

80 

3276800000 

2.15 

45.9101 

7.8 

28872 

17.8 

1786899 

30.0 

24300000 

81 

3486784401 

2  20 

51.5363 

7.9 

30771 

18.0 

1889568 

30.5  26393634 

82 

3707398432 

2.25 

57.6650 

8.0 

32768 

18.2 

1996903 

31.0  28629151   83 

3939040643 

2!  30 

64.3634 

8.1 

34868 

18.4 

2109061 

31.5!  31013642 

84 

4182119424 

2.35 

71.6703 

8  2 

37074 

18.6 

2226203 

32.0  33554432 

85 

4437053125 

2.40 

79.6262 

8.3 

39390 

18.8 

2348493 

32.5  36259082   86 

4704270176 

2.45 

88.2735 

8.4 

41821 

19.0 

2476099 

33.0  39135393  1  87 

4984209207 

2.50 

97.6562 

8.5 

44371 

19.2 

2609193 

33.5  42191410  .  88 

5277319168 

2.55 

107.820 

8.6 

47043 

19.4 

2747949 

34.0  45435424  I  89 

5584059449 

2.60 

118.814 

8.7 

49842 

19.6 

2892547 

3*.  5  48875980  1  90 

5904900000 

2.70 

143.489 

8.8 

52773 

19.8 

3043168 

35.0 

52521875 

91 

6240321451 

2.80 

172.104 

8  9 

55841 

20.0 

3200000 

35.5 

56382167 

92 

6590815232 

2.90 

205.111 

9.0 

59049 

20.2 

3363232 

36.0 

60466176 

93 

6956883693 

3.00 

243.000 

9.1 

62403 

20.4 

3533059 

36.5  64783487 

94 

7339040224 

3.10 

286.292 

9.2 

65908 

20.6 

3709677 

37.0  69343957 

95 

773^809375 

3.20 

335.544 

9.3 

69569 

20.8 

3893289 

37.5  74157715 

96 

8153726976 

3.30 

391.354 

9.4 

73390 

21.0 

4084101 

38.0!  7  9235  J  68 

97 

8587340257 

3.40 

454.354 

9.5 

77378 

21.2 

4282322 

38.5!  84587005 

98 

9039207968 

3.50 

525.219 

9.6 

81537 

21.4 

4488166 

39.0  90224199 

99 

9509900499 

3.60 

604.662 

9.7 

85873 

21.6 

47'01850 

39.5  96158012 

CIRCUMFERENCES   AND   AREAS   OF   CIRCLES.        10:1 


CIRCUMFERENCES  AND   AREAS  OF  CIRCLES. 


Diam. 

Circum, 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

1 

3.14161        0.7854 

65 

204.20 

3318.31 

129 

405.27 

13069.81 

2 

6.2832,        3.1416 

66 

207.34 

3421  .  19 

130 

408.41 

13273.23 

3 

9.4248         7.0686 

67 

210.49 

3525.65 

131 

411.55 

13478.22 

4 

12.5664 

12.5664 

68 

213.63 

3631.68 

132 

414.69 

13684  78 

5 

15.7080 

19.635 

69 

216.77 

3739.28 

133 

417.83 

13892.91 

6 

18.850 

28  274 

70 

219.91 

3848.45 

134 

420.97 

14102  61 

7 

21.991 

38.485 

71 

223.05 

3959.19 

135 

424.12 

14313.88 

8 

25.133 

50.266 

72 

226.19 

4071.50 

136 

427.26 

14526.72 

9 

28.274 

63.617 

73 

229.34 

4185.39 

137 

430.40 

14741.14 

10 

31.416 

78.540 

74 

232.48 

4300  84 

138 

433.54 

14957.12 

11 

34.558 

95.033 

75 

235.62 

4417.86 

139 

436.68 

15174.68 

12 

37.699 

113.10 

76 

238.76 

4536.46 

140 

439.82 

15393.80 

13 

40.841 

132.73 

77 

341.90 

4656.63 

141 

442.96 

15614.50 

14 

43.982 

153.94 

78 

245.04 

4778.36 

142 

446.11 

15836.77 

15 

47.124 

176.71 

79 

248.19 

4901.67 

143 

449.25 

16060.61 

16 

50.265 

201.06 

80 

251.33 

5026.55 

144 

452.39 

16286.02 

17 

53.407 

226.98 

81 

254.47 

5153.00 

145 

455.53 

16513.00 

18 

56.549 

254.47 

82 

257.61 

5281.02 

146 

458.67 

16741.55 

19 

59.690 

283.53 

83 

260.75 

5410.61 

147 

461.81 

16971.67 

20 

62.832 

314.16 

84 

263.89 

5541.77 

148 

464.96 

17203.36 

21 

65.973 

346.36 

85 

267.04 

5674  50 

149 

468.10 

17436  62 

oo 

69.115 

380.13 

86 

270.18 

5808.80 

150 

471.24 

17671.46 

ggj 

72.257 

415.48 

87' 

273.32 

5944.68 

151 

474.38 

17907  86 

24 

75.398 

452.39 

88 

276.46 

6082.12 

152 

477.52 

18145.84 

25 

78.540 

490.87 

89 

279.60 

6221.14 

153 

480.66 

18385.39 

26 

81.681 

530.93 

90 

282.74 

6361.73 

154 

483.81 

18626.50 

27 

84.823 

572.56 

91 

285.88 

6503.88 

155 

486.95 

18869.19 

28 

87.965 

615.75 

92 

289.03 

6647.61 

156 

490.09 

19113.45 

29 

91.106 

660.52 

93 

292.17 

6792.91 

157 

493.23 

19359.28 

30 

94.248 

706.86 

94 

295.31 

6939.78 

158 

496.37 

19606.68 

31 

97.389 

754.77 

95 

298.45 

7088.22 

159 

499.51 

19855.65 

82 

100.53 

804.25 

96 

301  .  59 

7238.23 

ItiO 

502.65 

20106.19 

33 

103.67 

855.30 

97 

304.73 

7389.81 

161 

505.80 

20358.31 

34 

06.81 

907.92 

98 

307.88 

7542.96 

162 

508.94 

20611.99 

35 

09.96 

962.11 

99 

311.02 

7697.69 

163 

512.08 

20867.24 

36 

113.10 

1017.88 

100 

314.16 

7853.98 

164 

515.22 

21124  07 

37 

16.24 

1075.21 

101 

317.30 

8011.85 

165 

518.36 

21382.46 

38 

119.38 

1134.11 

102 

320  44 

8171.28 

166 

521.50 

21642.43 

39 

122.52 

1194.59 

103 

323.58 

8332.29 

167 

524.65 

21903.97 

40 

125.66 

1256.64 

104 

326.73 

8.494.87 

168 

527.79 

22167  08 

41 

128.81 

1320.25 

105 

329  87 

8659.01 

169 

530.93 

22431.76 

42 

131.95 

1385.44 

106 

333.01 

8824.73 

170 

534.07 

22698.01 

43 

135.09 

1452.20 

107 

336.15 

8992.02 

171 

537.21 

22965.83 

44 

138.23 

1520.53 

108 

339.29 

9160.88 

172 

540.35 

23235.22 

45 

141.37 

1590.43 

109 

342.43 

9331.32 

173 

543.50 

23506.18 

46 

144.51 

1661.90 

110 

345.58 

9503.32 

174 

546.64 

23778.71 

47 

147.65 

1734.94 

111 

348.72 

9676.89 

175 

549.78 

24052.82 

48 

150.80 

1809.56 

112 

351.86 

9852.03 

176 

552.92 

24328.49 

49 

153.94 

1885.74 

113 

355.00 

10028.75 

177 

556.06 

24605.74 

50 

157.08 

1963.50 

114 

358.14 

10207.03 

178 

559.20 

24884,56 

51 

160.22 

2042.82 

115 

361.28 

10386  89 

179 

562.35 

25164.94 

52 

163.36 

2123.72 

116 

364.42 

10568.32 

180 

565.49 

25446  90 

53 

166.50 

2206.18 

117 

367.57 

10751.32 

181 

568.63 

25730.43 

54 

169.65 

2290.22 

118 

370.71 

10935.88 

182 

571.77 

26015.53 

55 

172.79 

2375.83 

119 

373.85 

11122.02 

183 

574.91 

26302.20 

56 

175.93 

2463.01 

120 

376.99 

11309.73 

184 

578.05 

26590.44 

57 

179.07 

2551.76 

121 

380.13 

11499.01 

185 

581.19 

26880.25 

58 

182.21 

2642.08 

122 

383.27 

11689.87 

186 

584.34 

27171.63 

59 

185.35 

2733.97 

123 

386.42 

11882.29 

187 

587.48 

27464  .  59 

60 

188.50 

2827.43 

124 

389.56 

12076.28 

188 

51H).(52 

27759.11 

61 

191.64 

2922.47 

125 

392.70 

12271.85 

189 

593.76 

28055.21 

62 

194.78 

3019.07 

126 

395.84 

12468.98 

11)0 

596.90 

28352.87 

63 

197.92 

3117.25 

127 

398.98 

12667.69 

191 

600.04 

28652  11 

64 

201.06 

3216.99 

128 

402.12 

12867.96 

192 

603.19 

28952.92 

104 


MATHEMATICAL   TABLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam.  Circum. 

Area. 

193 

606.33 

29255.30 

260 

816.81 

53092.92 

327 

1027.30 

83981.84 

194 

609.47 

29559.25 

261 

819.96 

53502.11 

328 

1030.44 

84496.28 

195 

612.61 

29864.77 

262 

823.10 

53912.87 

329 

1033.58 

85012.28 

196 

615.75 

30171.86 

263 

826.24 

54825.21 

330 

1036  73 

85529.86 

197 

618.89 

30480.52 

264 

829.38 

54739.11 

331 

1039.87 

86049.01 

198 

622.04 

30790.75 

265 

832.52 

55154.59 

332 

1043.01 

86569.73 

199 

625.18 

31102.55 

266 

835.66 

55571.63 

333 

1046.15 

87092.02 

200 

628.32 

31415.93 

267 

838.81 

55990.25 

334 

1049.29 

87615.88 

201 

631.46 

31730.87 

268 

841.95 

5C.410.44 

335 

1052.43 

88141.31 

202 

634.60 

32047.39 

269 

845.09 

56832.20 

336 

1055.58 

88668.31 

203 

637.74 

32365.47 

270 

848.23 

57255.53 

337 

1058.72 

89196.88 

204 

640.88 

32685.13 

271 

851.37 

57680.43 

338 

1061.86 

89727.03 

205 

644.03 

33006.36 

272 

854.51 

58106.90 

339 

1065.00 

90258.74 

206 

647.17 

33329.16 

273 

857.65 

58534.94 

340 

1068.14 

90792.03 

207 

650.31 

33653.53 

274 

860.80 

58964.55 

341 

1071.28 

91326.88 

208 

653.45 

33979.47 

275 

.863.94 

59395.74 

342 

1074.42 

91863.31 

209 

656.59 

34306.98 

276 

867.08 

59828.49 

343 

1077.57 

92401  .  31 

210 

659.73 

34636.06 

277 

870.22 

60262.82 

344 

1080.71 

92940.88 

211 

662.88 

34966.71 

278 

873.36 

60698.71 

345 

1083.85 

93482.02 

212 

666.02 

35298.94 

279 

876.50 

61136.18 

346 

1080.99 

94024.73 

213 

669.16 

35632.73 

280 

879.65 

61575  22 

347 

1090.13 

94569.01 

214 

672.30 

35968.09 

281 

882.79 

62015.82 

348 

1093.27 

95114.86 

215 

675.44 

36305.03 

282 

885.93 

62458.00 

349 

1096.42 

95662.28 

216 

678.58 

36643.54 

283 

889.07 

62901.75 

350 

1099.56 

96211.28 

217 

681.73 

36983.61 

284 

892.21 

63347.07 

351 

1102.70 

96761.84 

218 

684.87 

37325.26 

285 

895.35 

63793.97 

352 

1105.84 

97313.97 

219 

688.01 

37668.48 

286 

898.50 

64242.43 

353 

1108.98 

97867.68 

220 

091.15 

38013.27 

287 

901.64 

64692.46 

354 

1112.12 

98422.96 

221 

694.29 

38359.63 

288 

904.78 

65144.07 

355 

1115.27 

98979.80 

222 

697.43 

38707.56 

289 

907.92 

65597.24 

356 

1118.41 

99538.22 

223 

700.58 

39057.07 

290 

911.06 

66051.99 

357 

1121.55 

100098.21 

224 

703.72 

39408.14 

291 

914.20 

66508.30 

358 

1124.69 

100059.77 

225 

706.86 

39760.78 

292 

917.35 

669C6.19 

359 

1127.83 

101222.90 

226 

710.00 

40115.00 

293 

920.49 

67425.65 

360 

1130.97 

101787.60 

227 

713.14 

40470.78 

294 

923.63 

67886.68 

361 

1134.11 

102353.87 

228 

716.28 

40828.14 

295 

926.77 

68349.28 

362 

1137.26 

102921.72 

229 

719.42 

41187.07 

296 

929.91 

68813.45 

363 

1140.40 

103491.13 

230 

722.57 

41547.56 

297 

933.05 

69279.19 

364 

1143.54 

104062.12 

231 

725.71 

41909.63 

298 

936.19 

69746.50 

365 

1146.68 

104634.67 

232 

728.85 

42273.27 

299 

939.34 

70215.38 

366 

1149.82 

105208.80' 

233 

731.99 

42638.48 

300 

942.48 

70685.83 

367 

1152.96 

105784.49' 

234 

735.13 

43005.26 

301 

945.62 

71157.86 

368 

1156.11 

106361.76 

235 

738.27 

43373.61 

303 

948.76 

71631.45 

369 

1159.25 

106910  60 

236 

741  .  42 

43743.54 

303 

951.90 

72106.62 

370 

1162.39 

107521.01; 

237 

744.56 

44115.03 

304 

955.04 

72583.36 

371 

1165.53 

108102.99* 

238 

747.70 

44488.09 

305 

958.19 

73061.66 

372 

1168.67 

108686.54 

239 

750.84 

44862.73 

306 

961.33 

73541.54 

373 

1171.81 

109271.66 

240 

753.98 

45238.93 

307 

964.47 

74022.99 

374 

1174.96 

109858.35. 

241 

757.12 

45616.71 

308 

967.61 

74506.01 

375 

1178.10 

110446.62: 

242 

760.27 

45996.06 

309 

970.75 

74990.60 

376 

1181.24 

111036.45- 

243 

763.41 

46376.98 

310 

973.89 

75476.76 

377 

1184.38 

111627.86 

244 

766.55 

46759.47 

311 

977.04 

75964.50 

378 

1187.52 

112220.83- 

245 

769.69 

47143.52 

312 

980.18 

76453.80 

379 

1190  66 

112815.38 

246 

772.83 

47529.16 

313 

983.32 

76944.67 

380 

1193.81 

113411.  4» 

247 

775.97 

47916.36 

314 

986.46 

77437.12 

381 

1196.95 

114009.18 

248 

779.11 

48305.13 

315 

989.60 

77931.13 

382 

1200.09 

114608.44 

249 

782.26 

48695.47 

316 

992.74 

784-26.72 

383 

1203.23 

115209.27 

250 

785.40 

49087.39 

317 

995.88 

78923.88 

384 

1206.37 

115811.67 

251 

788.54 

49480.87 

318 

999.03 

79422.60 

CSS 

12C9.51 

116415.04 

252 

791.68 

49875.92 

319 

1002.17 

79922.90 

386 

1212.65 

117021.18 

253 

794.82 

50272.55 

320 

1005.31 

80424.7? 

387 

1215.80 

117628  30 

254 

797.96 

50670.75 

321   11008.45 

80928.21 

388 

1218.94 

118236:98 

255 

801.11 

51070.52 

322    1011.59 

81433  22 

389 

1222.08 

118847.24 

256 

804.25 

51471.85 

323 

1014.73 

81939.80 

390 

1225.22 

119459.06 

257 

807.39 

51874.76 

324 

1017.88 

82447.96 

391 

1228.36 

120072.46 

258 

810.53 

52279.24 

325 

1021.02 

82957.68 

392 

1231.50 

120687.42 

259 

813.67 

52685.29 

326 

1024.16 

83468.98 

393 

1234.65 

121303.96 

CIRCUMFERENCES   AND    AREAS    OF    CIRCLES.        105 


Diam. 

Circum 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

394 

1237.79 

121922.07 

461 

1448.27 

166913.60 

528 

1658.76 

218956.44 

395 

1240.93 

122541.75 

462 

1451.42 

167638.53 

529 

1661.90 

219786.61 

396 

1244.07 

123163.00 

463 

1454.56 

168365.02 

530 

1665.04 

220618.34 

;i97 

1247.21 

123785.82 

464 

1457.70 

169093.08 

531 

1668.19 

221451.65 

398 

1250.35 

124410.21 

465 

1460.84 

169822.72 

532 

1671.33 

222286.53 

399 

1253.50 

125036.17 

466 

1463.98 

170553.92 

533 

1674.47 

223122.98 

400 

1256.64 

125663.71 

467 

1467.12 

171286.70 

534 

1677.61 

223961.00 

401 

1259.78 

126292.81 

468 

1470.27 

172021.05 

535 

1680.75 

224800.59 

402 

1262.92 

126923.48 

469 

1473.41 

72756.97 

536 

1683.89 

225641.75 

403 

1266.06 

1  27555.  73 

470 

1476.55 

73494.45 

537 

1687.04 

226484.48 

404 

1269.20 

128189.55 

471 

1479.69 

74233.51 

538 

1690.18 

227328.79 

405 

1272.35 

128824.93 

472 

1482.83 

74974.14 

539 

1693.32 

228174.66 

400 

1275.49 

129461.89 

473 

1485.97 

75716.35 

540 

1696.46 

229022.10 

407 

1278.63 

130100.42 

474 

1489.11 

76460  12 

541 

1699.60 

229871.12 

408 

1281.77 

130740.52 

475 

1492.26 

177205.46 

542 

1702.74 

230721.71 

409 

1284.91 

131382.19 

476 

1495.40 

177952.37 

543 

1705.88 

231573.86 

410 

1288.05 

132025.43 

477 

1498.54 

178700.86 

544 

1709.03 

232427.59 

411 

1291.19 

132670.24 

478 

1501.68 

179450.91 

545 

1712.17 

233282.89 

412 

1294.34 

133316.63 

479 

1504.82 

180202.54 

546 

1715.31 

234139.76 

413 

1297.48 

133964.58 

480 

1507.96 

180955.74 

547 

1718.45 

234998.20 

414 

1300.62 

134614.10 

481 

1511.11 

181710.50 

548 

1721.59 

235858.21 

415 

1303.76 

135265.20 

482 

1514.25 

182466.84 

549 

1724.73 

236719.79 

416 

1306.90 

135917.86 

483 

1517.39 

183224.75 

550 

1727.88 

237582.94 

417 

1310.04 

136572.10 

484 

1520.53    183984.23 

551 

1731.02 

238447.67 

418 

1313.19 

137227.91 

485 

1523.67!  184745.28 

552 

1734.16 

239313.96 

419 

1316.33 

137885.29 

486 

1526.81 

185507.90 

553 

1737.30 

240181.83 

420 

1319.47 

138544.24 

487 

1529.96 

186272.10 

554 

1740.44 

241051.26 

421 

1322.61 

139204.76 

488 

1533.10 

187037.86 

555 

1743.58 

241922.27 

422 

1325.75 

139866.85 

489 

1536.24 

187805.19 

556 

1746.73 

242794.85 

423 

1328.89 

140530.51 

490 

1539.38 

188574.10 

557 

1749.87 

243668.99 

424 

1332.04 

141195.74 

491 

1542.52 

189344.57 

558 

1753.01 

244544.71 

425 

1335.18 

141862  54 

492 

1545.66 

190116.62 

559 

1756.15 

245422  00 

426 

1338.32 

142530.92 

493 

1548.81 

190890.24 

560 

1759.29 

246300.86 

427 

1341.46 

143200.86 

494 

1551.95 

191665.43 

561 

1762.43 

247181.30 

428 

1344.60 

143872.38 

495 

1555  09 

192442.18 

562 

1765.58 

248063.30 

429 

1347.74 

144545.46 

496 

1558.23 

193220.51 

563 

176S.72 

248946.87 

430 

1350.88 

145220.12 

497 

1561.37 

194000.41 

564 

1771.86 

249832.01 

431 

1354.03 

145896.35 

498 

1564.51 

194781.89 

565 

1775.00 

250718,73 

432 

1357.17 

146574  15 

499 

1567.65 

195564.93 

566 

1778.14 

251607.01 

433 

1360.31 

147253.52 

500 

1570.80 

196349.54 

567 

1781.28 

252496.87 

434 

1363.45 

147934.46 

501 

1573.94 

197135.72 

568 

1784.42 

253388.30 

435 

1366.59 

148616.97 

502 

1577.08 

197923.48 

569 

1787.57 

254281.29 

436 

1369.73 

149301.05 

503 

1580.22 

198712.80 

570 

1790.71 

255175.86 

437 

1372.88 

149986.70 

504 

1583.36 

1  99503.  70 

571 

1793.85 

256072.00 

438 

1376.02 

150873.93 

505 

1586  50 

200296.17 

572 

1796.99 

256969.71 

439 

1379.16 

151362.72 

506 

1589.65 

201090.20 

573 

1800.13 

257868.99 

440 

1382.30 

152053.08 

507 

1592.79 

201885.81 

574 

1803.27 

258769.85 

411 

1385.44 

152745.02 

508 

1595.93 

202682.99 

575 

1806.42 

259672.27 

442 

1388.58 

153438  53 

509 

1599.07 

203481.74 

576 

1809.56 

260576.26 

443 

1391.73 

154133.60 

510 

1602.21 

204282.06 

577 

1812.70 

261481.83 

444 

1394.87 

154830.25 

511 

1605.35 

205083.95 

578 

1815  84 

262388.96 

445 

1398.01 

155528.47 

512 

1608.50 

205887.42 

579 

1818.98 

263297.67 

446 

1401.15 

156228.26 

513 

1611.64 

206692.45 

580 

1822.12 

264207.94 

447 

1404.29 

156929.62 

514 

1614.78 

207499.05 

581 

1825.27 

265119.79 

448 

1407.43 

157632.55 

515 

1617.92 

208307.23 

582 

1828.41 

266033.21 

449 

1410.58 

158337.06 

516 

1621.06 

209116.97 

583 

1831.55 

266948.20 

450 

1413.72 

159043.13 

517 

1624.  20  1  209928.29 

584 

1834.69 

267864.76 

451 

1416.86 

1597'50.77 

518 

1627.34    210741.18 

585 

1837.83 

2687'82.89 

452 

1420.00 

160459.93 

519 

1630.49    211555.63 

586 

1840.97 

269702.59 

453 

1423.14 

161170.77 

520 

1633.63    212371.66 

587 

1844.11 

270623.86 

454 

1426.28 

161883.13 

521 

1636.77 

213189.26 

588 

1847.26 

271546.70 

455 

1429  42 

162597.05 

522 

1639.91 

214008.43 

589 

1850.40 

272471.12 

456 

1432.57 

163312.55 

523 

1643.05 

214829.17 

590 

1853.54 

273397  .  10 

457 

1435.71 

164029.62 

524 

1616.11)    215651.49 

591 

1856.68 

274324.66 

458 

1438.85 

164748.26 

525 

1649.34    216475.37 

592 

1859.82 

275253.78 

459 

1441.99 

165468.47 

526 

1652.48    217300.82 

593 

1862.96 

276184.48 

400 

1445.13 

166190.25 

527 

1655  62    218127.85 

594 

1866.11 

277116.75 

106 


MATHEMATICAL   TABLES. 


Diam. 

Circum. 

Area. 

Diam- 

Circum. 

Area. 

Dianv  Circum. 

Area. 

595 

1869.25 

278050.58 

663 

2082.88 

345236.69 

731 

2296.50 

419686.15 

596 

1872.39 

278985.99 

664 

2086.02 

346278.91 

732 

2299.65 

420835.19 

597 

1875.53 

279922.97 

665 

2089.16 

347322.70 

733 

2302.79 

421985.79 

598 

1878.67 

280861.52 

666 

2092.30 

348368.07 

734 

2305.93 

423137.97 

599 

1881.81 

281801  65 

667 

2095.44 

349415.00 

735 

2309.07 

424291.72 

600 

1884.96 

282743.34 

668 

2098.58 

350463.51 

736 

2312.21 

425447.04 

601 

1888.10 

283686.60 

669 

2101.73 

351513.59 

737 

2315.35 

426603.94 

602 

1891.24 

284631.44 

670 

2104.87 

352565.24 

738 

2318.50 

427762.40 

603 

1894.38 

285577.84 

671 

2108.01 

353618.45 

739 

2321.64 

428922.43 

604 

1897.52 

286525.82 

672 

2111.15 

354673.24 

740 

2324.78 

430084.03 

605 

1900.66 

287475.36 

673 

2114.29 

355729.60 

741 

2327.92 

431247.21 

606 

1903.81 

288426.48 

674 

2117.43 

356787.54 

742 

2331.06 

432411.95 

607 

1906.95 

289379.17 

675 

2120.58 

357847.04 

743 

2334.20 

433578.27 

608 

1910.09 

290333.43 

676 

2123.72 

358908.11 

744 

2337.34 

434746.16 

609 

1913.23 

291289.26 

677 

2126.86 

359970.75 

745 

2340.49 

435915.62 

610 

1916.37 

292246.66 

678 

2130.00 

361034.97 

746 

2343.63 

437086.64 

611 

1919  51 

293205.63 

679 

2133.14 

362100.75 

747 

2346.77 

438259.24 

612 

1922.65 

294166.17 

680 

2136.28 

363168  11 

748 

2349.91 

439433.41 

613 

1925.80 

295128.28 

681 

2139.42 

364237.04 

749 

2353.05 

440609  16 

-  614 

1928.94 

296091.97 

682 

2142.57 

365307.54 

750 

2356.19 

441786.47 

615 

1932.08 

297057.22 

683 

2145.71 

366379.60 

751 

2359.34 

442965.35 

616 

1935.22 

298024.05 

684 

2148.85 

367453.24 

752 

2362.48 

444145.80 

617 

1938.36 

298992.44 

685 

2151.99 

368528.45 

753 

2365.62 

445327.83 

618 

1941.50 

299962.41 

686 

2155.13 

369605.23 

754 

2368.76 

446511.42 

619 

1944.65 

300933.95 

687 

2158.2? 

370683.59 

755 

2371.90 

447696.59 

620 

1947.79 

301907.05 

688 

2161.42 

371763.51 

756 

2375.04 

448883.32 

621 

1950.93 

302881.73 

689 

2164.56 

372845.00 

757 

2378.19 

450071.63 

622 

1954.07 

303857.98 

690 

2167.70 

373928.07 

758 

2381.33 

451261.51 

623 

1957.21 

304835.80 

691 

2170.84 

375012.70 

759 

2384.47 

452452.96 

624 

1960.35 

305815.20 

692 

2173.98 

376098.91 

760 

2387.61 

453645.98 

625 

1963.50 

306796.16 

693 

2177.12 

377186.68 

761 

2390.75 

454840.57 

626 

1966.64 

307778.69 

694 

2180.27 

378276.03 

762 

2393.89 

456036.73 

627 

1969.78 

308762.79 

695 

2183.41 

379366.95 

763 

S397.04 

457234.46 

628 

1972.92 

309748.47 

696 

2186  55 

380459.44 

764 

2400.18 

458433.77 

629 

1976.06 

310735.71 

697 

21  89!  69 

381553.50 

765 

2403.32 

459634.64 

630 

1979.20 

311724.53 

698 

2192.83 

382649.13 

766 

2406.46 

460837.08 

631 

1982.35 

312714.92 

699 

2195.97 

383746.33 

767 

2409.60 

462041.10 

632 

1985.49 

313706.88 

700 

2199.11 

384845.10 

768 

2412.74 

463246.69 

633 

1988.63 

314700.40 

701 

2202.26 

385945.44 

769 

2415.88 

464453.84 

634 

1991.77 

315695.50 

702 

2205.40 

387047.36 

770 

2419.03 

465662.57 

635 

1994.91 

316692.17 

•703 

2208.54 

388150.84 

771 

2422.17 

466872.87 

636 

1998.05 

317690.42 

704 

2211.68 

389255.90 

772 

2425.31 

468084.74 

637 

2001.19 

318690.23 

705 

2214.82 

390362.52 

773 

2428.45 

469298.18 

638 

2004.34 

319691.61 

706 

2217.96 

391470.72 

774 

2431.59 

470513.19 

639 

2007.48 

320694.56 

707 

2221.11 

392580.49 

775 

2434.73 

471729.77 

640 

2010.62 

321699.09 

708 

2224.25 

393691.82 

776 

2437.88 

472947.92 

641 

2013.76 

322705.18 

709 

2227.39 

394804.73 

777 

2441  .02 

474167.65 

642 

2016.90 

323712.85 

710 

2230.53 

395919.21 

778 

2444.16 

475388.94 

643 

2020.04 

324722.09 

711 

2233.67 

397035.26 

779 

2447.30 

476611.81 

644 

2023.19 

325732.89 

712 

2236.81 

398152.89 

780 

2450.44 

477836.24 

645 

2026.33 

326745.27 

713 

2239.96 

399272.08 

781 

2453.58 

479062.25 

646 

2029.47 

327759.22 

714 

2243.10 

400392.84 

782 

2456.73 

480289.83 

647 

2032.61 

328774.74 

715 

2246.24 

401515.18 

7'83 

2459.87 

481518.97 

648 

2035.75 

329791.83 

716 

2249.38 

402639.08 

7'84 

2463.01 

482749.69 

649 

2038.89 

330810.49 

717 

2252.52 

403764.56 

785 

2466.15 

483981  .  98 

650 

2042.04 

331830.72 

718 

2255.66 

404891.60 

786 

2469.29 

485215.84 

651 

2045.18 

332852.53 

719 

2258.81 

406020.22 

787 

2472.43 

486451.28 

652 

2048.32 

333875.90 

720 

2261.95 

407150.41 

788 

2475.58 

487688.28 

653 

2051.46 

334900.85 

721 

2265.09 

408282.17 

789 

2478.72 

488926.85 

654 

2054.60 

335927.36 

722 

2268.23 

409415.50 

790 

2481.86 

490166.99 

655 

2057.74 

336955.45 

723 

2271.37 

410550.40 

791 

2485.00 

491408.71 

656 

2060.88 

337985.10 

724 

2274.51 

411686.87 

792 

2488.14 

492651.99 

657 

2064.03 

339016.33 

725 

2277.65 

412824.91 

793 

2491.28 

493896.85 

658 

2067.17 

340049.13 

726 

2280.80 

413964.52 

794 

2494.42 

495143.28 

659 

2070.31 

341083.50 

727 

2283.94 

415105.71 

795 

2497.57 

496391.27 

660 

2073.45 

342119.44 

728 

2287.08 

416248.46 

796 

2500.71 

497640.84 

661 

2076.59 

343156.95 

729 

2290.22 

417392.79 

797 

2503.85 

498891.98 

662 

2079.73 

344196.03 

730 

2293.36 

418538.68 

798 

2506.99 

500144.69 

CIRCUMFERENCES   AND   AREAS   OF   CIRCLES.       107 


Diam. 

Circum. 

Area, 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

799 

2510.13 

501398.97 

867 

2723.76 

590375.16 

935 

2937.39    686614.71 

800 

2513.27 

502654.82 

868 

2726.90 

591737.83 

936 

2940.53    688084.19 

801 

2516.42 

503912.25 

869 

2730.04 

593102.06 

937 

2943.  67  j  689555.24 

802 

2519.56 

505171.24 

870 

2733.19 

594467.87 

938 

2946  81 

691027.86 

803 

2522.70 

506431.80 

871 

2736.33 

595835.25 

939 

2949.96 

692502.05 

804 

2525.84 

507693.94 

872 

2739.47 

597204.20 

940 

2953.10 

693977.82 

805 

2528.98 

508957.64 

873 

2742.61 

598574.72 

941 

2956.24 

695455.15 

806 

2532.12 

51022-^.92 

874 

2745.75 

599946.81 

942 

2959.38 

696934.06 

807 

2535.27 

511489.77 

875 

2748.89 

601320.47 

943 

2962.52 

698414.53 

808 

2538.41 

512758.19 

876 

2752.04 

602695.70 

944 

2965.66 

699896.58 

809 

2541.55 

514028.18 

877 

2755.18 

604072.50 

945 

2968.81 

701380.19 

810 

2544.69 

515299.74 

878 

2758.32 

605450.88 

946 

2971.95 

702865.38 

811 

2547.83 

516572.87 

879 

2761.46 

606830.82 

947 

2975.09 

704352.14 

812 

2550.97 

517847.57 

880 

2764.60 

608212.34 

948 

2978.23 

705840.47 

813 

2554.11 

519123.84 

881 

2767.74 

609595.42 

949 

2981.37 

707330.37 

814 

2557.26 

520401  .  68 

882 

2770.88 

610980.08 

950 

2984.51 

708821.84 

815 

2560.40 

521681.10 

883 

2774.03 

612366.31 

951 

2987.65 

710314.88 

816 

2563.54 

522962.08 

884 

2777.17 

613754.11 

952 

2990.80 

711809.50 

817 

2566.68 

524244.63 

885 

27'80.31 

615143.48 

953 

2993.94 

71  3305.  (>8 

818 

2569.82 

525528.76 

886 

2783.45 

616534.42 

954 

2997.08 

714H03.43 

819 

2572.96 

526814.46 

887 

2786.59 

617926.93 

955 

3000.22 

716302.76 

820 

2576.11 

528101.73 

888 

2789.73 

619321.01 

956 

3003.36 

717803.66 

821 

2579.25 

529390.56 

889 

2792.88 

620716.66 

957 

3006.50 

719306.12 

822 

2582.39 

530080.97 

890 

2796.02 

622113.89 

958 

3009.65 

720810.16 

823 

2585.53 

531972.95 

891 

2799.16 

623512.68 

959 

3012.79 

722315.77 

824 

2588.67 

533266.50 

892 

2802.30 

624913.04 

960 

3015.93 

723822.05 

825 

2591.81 

534561.62 

893 

2805.44 

626314.98 

961 

3019.07 

725331.70 

826 

2594.96 

535858.32 

894 

2808.58 

627718.49 

962 

3022.21 

726842.02 

827 

2598.10 

537156.58 

895 

2811.73 

629123.56 

963 

3025.35 

728353.91 

828 

2601.24 

538456.41 

896 

2814.87 

630530.21 

964 

3028.50 

729867.37 

829 

2604.38 

539757.82 

897 

2818.01 

631938.43 

965 

3031.64 

731382.40 

830 

2607.52 

541060,79 

898 

2821.15 

633348.22 

966 

3034.78 

732899.01 

831 

2610.66 

542365.34 

899 

2824.29 

634759.58 

967 

3037.92 

734417.18 

832 

2613.81 

543671.46 

900 

2827.43 

636172.51 

968 

8041.06 

735936.93 

833 

2616.95 

544979.15 

901 

2830.58 

637587.01 

969 

3044.20 

737458.24 

834 

2620.09 

546288.40 

902 

2833.72 

639003.09 

970 

3047.34 

738981.13 

835 

2623.23 

547599.23 

903 

2836.86 

640420.73 

971 

3050.49 

740505,59 

836 

2626.37 

548911.63 

904 

2840.00 

641839.95 

972 

3053.63 

742031.62 

837 

2629.51 

550225.61 

905 

2843.14 

643260.73 

973 

3056.77 

743559.22 

838 

2632.65 

551541.15 

906 

2846.28 

644683.09 

974 

3059.91 

745088.39 

839 

2635.80 

552858.26 

907 

2849.42 

646107.01 

975 

3063.05 

746619.13 

840 

2638.94 

554176.94 

908 

2852.57 

64753?,.  51 

976 

3066.19 

748151.44 

841 

2642.08 

555497.20 

909 

2855.71 

64895^.58 

977 

3069.34 

749685.32 

842 

2645.22 

556819.02 

910 

2858.85 

650388.22 

978 

3072.48 

751220.78 

843 

2648.36 

558142.42 

911 

2861.99 

651818.43 

979 

3075.62 

752757.80 

844 

2651.50 

559467.39 

912 

2865.13 

653250.21 

980 

3078.76 

754296.40 

845 

2654.65 

560793.92 

913 

2868.27 

654683.56 

981 

3081.90 

755836.56 

846 

2657.79 

562122.03 

914 

2871.42 

656118.48 

982 

3085.04 

757378.30 

847 

2660.93 

563451.71 

915 

287'4.56 

657554.98 

983 

3088.19 

758921.61 

848 

2664.07 

564782.96 

916 

2877.70 

658993.04 

984 

3091.33 

760466.48 

849 

2667.21 

566115.78 

917     2880.84 

660432.68 

985 

3094.47 

762012.93 

850 

2670.35 

567450.17 

918     2883.98 

661873.88 

986 

3097.61 

7635G0.95 

851 

2673.50 

568786.14 

919  !  2887.12 

663316.66 

987 

3100.75 

765110.54 

852 

2676.64 

570123.67 

920 

2890.27 

664761.01 

988 

3103.89 

766661.70 

853 

2679.78 

571462.77 

921 

2893.41 

666206.92 

989 

3107.04 

768214.44 

854 

2682.92 

572803.45 

922 

2896.55 

667654.41 

990 

3110.18 

769768.74 

855 

2686.06 

574145.69 

923 

2899.69 

669103.47 

991 

3113.32 

771324.61 

856 

2689.20 

575489.51 

924 

2902.83 

67U554.10 

992 

3116.46 

772882.06 

857 

2692.34 

576834.90 

925 

2905.97 

672006.30 

993 

3119.60 

774441.07 

858 

2695.49 

578181.85 

926 

2909.11 

673460.08 

994 

3122.74 

776001.66 

859 

2698.63 

579530.38 

927 

2912.26 

674915.42 

995 

3125.88 

777563.82 

800 

2701.77 

580880.48 

928 

2915.40 

676372.33 

996 

3129.03 

779127.54 

861 

2704.91 

582232.15 

929 

2918.54 

677830.82 

997 

3132.17 

780692.84 

862 

2708.05 

583585.39 

930     2921.68 

679290.87 

998 

3135.31 

782259.71 

863 

2711.10 

584940.20 

931      2924.82 

680752.50 

999 

3138.45 

783828.15 

864 

2714.34 

586296.59 

932     2927.96 

682215.69 

1000 

3141.59 

785398.16 

865 

2717.48 

587654.54 

933  !  2931.11 

683080.46 

866 

2720  62 

589014.07 

934  !  2934.25 

685146.80 

108 


MATHEMATICAL   TABLES. 


CIRCUMFERENCES    AND    AREAS    OF    CIRCLES 
Advancing  toy  Eighths. 


Diam. 

Circum. 

Area. 

'Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

1/64 

.04909 

.00019 

2  % 

7  4613 

4.4301 

6  M 

19.242 

29.465 

1/32 

.09818 

.00077 

7/16 

7.6576 

4.6664 

& 

19.635 

30.680 

3/64 

.  1472G 

.00173 

k 

7.8540 

4.908? 

% 

20.028 

31.919 

1/16 

.19635 

.00307 

9/16 

8.0503 

5.1572 

^ 

20.420 

33.183 

3/32 

.29452 

.00690 

% 

8.2467 

5.4119 

% 

20.813 

34.472 

Ys 

.39270 

.0122? 

11/16 

8.4430 

5.672? 

% 

21  206 

35.785 

5/32 

.49087 

.01917 

¥4 

8.6394 

5.9396 

xo 

21.598 

37.122 

3/16 

.58905 

.02761 

13/16 

8.8357 

6.2126 

7. 

21.991 

38.485 

7/32 

.(38722 

.03758 

% 

9.0321 

6.4918 

X 

22.384 

39.871 

15/16 

9.2284 

6.7771 

]A 

22.776 

41.282 

v± 

.78540 

.04909 

% 

23.169 

42.718 

9/32 

.88357 

.06-213 

3. 

9.4248 

7.0686 

^ 

23.562 

44.179 

5/16 

.98175 

.07670 

1/16 

9  6211 

7.3662 

P4 

23.955 

45.664 

11/32 

1.0799 

.09281 

H 

9.8175 

7.6699 

M 

24.347 

47.173 

% 

.1781 

.11045 

3/16 

10.014 

7.9798 

% 

24.740 

48.707 

13/32 

.2763 

.12962 

Y4 

10.210 

8.2958 

8. 

25.133 

50.265 

7/16 

.3744 

.15033 

5/16 

10.407 

8.6179 

Ya 

25.525 

51.849 

15/32 

.4726 

.  17257 

% 

10.003 

8.9462 

Y4 

25.918 

53.456 

7/16 

10.799 

9.2806 

% 

2G.311 

55  088 

^ 

5708 

.19635 

fcl 

10.996 

9.6211 

26.704 

56.745 

17/32 

.6690 

.22166 

9/16 

11.192 

9.9678 

% 

27.096 

58.426 

9/16 

.7671 

.24850 

% 

11.388 

10.321 

» 

27.489 

60.132 

19/32 

.8653 

.27688 

11/16 

11.585 

10.680 

% 

27.882 

61.802 

% 

1.9635 

.30680 

K 

11.781 

11.045 

9. 

28.274 

63.617 

21/32 

2.061? 

.33824 

13/16 

11.977 

11.416 

Ys 

28.667 

65.397 

11/16 

2.1598 

.37122 

% 

12.174 

11.793 

29.060 

67.201 

23/32 

2.2580 

.40574 

15/16 

12.3?0 

12.177 

% 

29.452 

69.029 

4. 

12.566 

12.566 

X^j 

23.845 

70.882 

% 

2.3562 

.44179 

1/16 

12.763 

12.962 

% 

30.238 

72.760 

.25/32 

2.4544 

.4793? 

Ys 

12.959 

13.364 

M 

30.631 

74.662 

13/16 

2.5525 

.51849 

3/16 

13.155 

13.772 

7^ 

31.023 

76.589 

27/32 

2.6507 

.55914 

H 

13.352 

14.180 

10. 

31.416 

78.540 

% 

2.7489 

.60132 

5/16 

13.548 

14.60? 

Ys 

31.809 

80.51(5 

29/32 

2.8471 

.64504 

% 

13.744 

15.033 

Y4 

32.201 

82.516 

15/16 

2.9452 

.69029 

7/16 

13.P41 

15.466 

% 

32.594 

84.541 

31/32 

3.0434 

.73708 

H 

14.137 

15.904 

32.987 

86.590 

9/16 

14.334 

16.319 

% 

33.379 

88.664 

1. 

3.1416 

.7854 

% 

14.530 

16.800 

M 

33.772 

90.703 

1/16 

3.3379 

.8866 

11/16 

14.726 

17.257 

% 

34.165- 

92.886 

H 

3.5343 

.9940 

n 

14.923 

17.728 

11. 

34.558 

95.033 

3/16 

3.7306 

1.1075 

13/16 

15.119 

18.190 

Ys 

34.950 

97.205 

H 

3.9270 

1.2272 

Vs 

15.315 

18.665 

35.343 

99.402 

5/16 

4.1233 

1.3530 

15/16 

15  512 

19.147 

% 

35.736 

101.62 

n 

4.3197 

1.4849 

5. 

15.708 

19.635 

^ 

36.128 

103.87 

7/16 

4.5160 

1.6230 

1/16 

15.904 

20.129 

% 

36.521 

106.14 

34 

4.7124 

1.7671 

Ys 

16.101 

20.629 

% 

36.914 

108.43 

9/16 

4.9087 

1.91?5 

3/16 

16.297 

21.135 

% 

37.306 

110.75 

% 

5.1051 

2.0739 

Y* 

16.493 

21.648 

12 

37.699 

113.10 

11/16 

5.3014 

2.2365 

5/16 

16.690 

22.166 

^s 

38.092 

115.47 

H 

5.4978 

2.4053 

% 

16.886 

'<>2.691 

J4 

38.485 

117.86 

13/16 

5.6941 

2.5802 

7/16 

17.082 

23.221 

% 

38.877 

120.28 

% 

5.8905 

2.7612 

H 

17.279 

23.758 

L£ 

39.270 

122.72 

15/16 

6.0868 

2.9483 

9/16 

17.475 

24.301 

% 

39.663 

125.19 

% 

17.671 

24.850 

H 

40.055 

127.68 

2. 

6.2832 

3.1416 

11/16 

17.868 

25.406 

% 

40.448 

130.19 

1/16 

6.4795 

3.3410 

H 

18.064 

25.96? 

13. 

40.841 

132.73 

H 

6.6759 

3.5466 

13-16 

18.261 

26.535 

^8 

41.233 

135.30 

3/16 

6.8722 

3.7583 

% 

18.457 

27.109 

J4 

41.626 

137.89 

u 

7.0686 

3.9761 

15-16 

18.653 

27.688 

% 

42.019 

140.50 

5/16 

7.2649 

4.2000 

6. 

18.850 

28.274 

Y* 

42.412 

143.14 

CIRCUMFERENCES   AHD   AREAS   OF   CIRCLES.        109 


Diam. 

Circum  . 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

13% 

42.804 

145.80 

21% 

68.722 

375.83 

30^ 

94.640 

712.76 

43.197 

148  49 

32. 

69.115 

380.13 

95.033 

718.69 

7X 

43.590 

151.20 

Ys 

69.508 

384.46 

% 

95.426 

724  64 

14. 

43.982 

153.94 

H 

69.900 

388.82 

Yz 

95.819 

730.62 

H 

44.375 

156.70 

% 

70.293 

393.20 

% 

96.211 

736.62 

44.768 

159.48 

1^3 

70.686 

397.61 

M 

96.604 

742.64 

3£ 

45.160 

162.30 

% 

71.079 

402.04 

Vs 

96.997 

748.69 

^ 

45.553 

165.13 

94 

71.471 

406.49 

31. 

97.389 

754.77 

RX 

45.946 

167.99 

% 

71.864 

410.97 

# 

97.782 

760.87 

•AA 

46.338 

170.87 

23. 

72.257 

415.48 

*f 

98.175 

766.99 

7$ 

46.731 

173.78 

Ys 

72.649 

420.00 

98.567 

773.14 

15. 

47.124 

176.71 

H 

73.042 

424.56 

i^j 

98.960 

779.31 

Ys, 

47.517 

179.67 

| 

73.435 

429.13 

% 

99.353 

785.51 

47.909 

182.65 

73.827 

433.74 

% 

99.746 

791.73 

% 

48.302 

185.66 

% 

74.220 

438.36 

ya 

100.138 

797.98 

IX 

48.695 

188.69 

ax 

74.613 

443.01 

32 

100.531 

804.25 

5X 

49.087 

191.75 

% 

75.006 

447.69 

/^ 

100.924 

810.54 

M 

49.480 

194.83 

24. 

75.398 

452.39 

/4 

101.316 

816.86 

/o 

49.873 

197.93 

H 

75.791 

457.11 

% 

101.709 

823.21 

16 

50.265 

201.06 

g 

76.184 

461.86 

IXj 

102.102 

829.58 

/^ 

50.658 

204.22 

% 

76.576 

466.64 

% 

102.494 

835.97 

i^ 

51.051 

207.39 

kjC 

76.969 

471.44 

^4 

102.887 

842.39 

% 

51.414 

210.60 

% 

77.362 

476.26 

% 

103.280 

848.83 

IX 

51.836 

213.82 

94 

77.754 

481.11 

33. 

103.673 

855.30 

% 

52.229 

217.08 

% 

78.147 

485.98 

Ys 

104.065 

861.79 

M 

52.622 

220.35 

25 

78.540 

490.87 

104.458 

868.31 

% 

53.014 

223.65 

i£ 

78.933 

495.79 

% 

104.851 

874.85 

17. 

53.407 

226.98 

^4 

79.325 

500.74 

% 

105.243 

881.41 

% 

53.800 

230.33 

% 

79.718 

505.71 

% 

105.636 

888.00 

54.192 

233.71 

X^jjj 

80.111 

510.71 

M 

106.029 

894.62 

% 

54.585 

237.10 

5/C 

80.503 

515.72 

% 

106.421 

901.26 

/^2 

U4.978 

240.53 

94 

80.896 

520.77 

34. 

106.814 

907.92 

EjX 

55.371 

243.98 

% 

81.289 

525.84 

Ys 

107.207 

914.61 

94 

55.763 

247.45 

26. 

81.681 

530  93 

y* 

107.600 

921.32 

% 

56.156 

250.95 

& 

82.074 

536.05 

H 

107.992 

928.06 

18 

56.549 

254.47 

82.467 

541.19 

108.385 

934.82 

N 

56.941 

258.02 

% 

82  860 

546.35 

% 

108.778 

941.61 

A 

57.334 

261.59 

r& 

83.252 

551.55 

M 

109.170 

948.42 

% 

57.727 

265  .  18 

% 

83.645 

556.76 

% 

109.563 

955.25 

\^ 

58.119 

268.80 

M 

84.038 

562.00 

35. 

109.956 

962.11 

% 

58.512 

272.45 

/8 

84.430 

567.27 

i£ 

110.348 

969.00 

94 

58.905 

276.12 

27 

84.823 

572.56 

M 

110.741 

975.91 

% 

59.298 

.279.81 

M 

85.216 

577.87 

% 

111.134 

982.84 

19. 

59.690 

283.53 

| 

85.608 

583.21 

X£ 

111.527 

989.80 

M 

60.083 

287.27 

86.001 

588.57 

{& 

111.919 

996.78 

i/ 

60.476 

291.04 

i^ 

86.394 

593.96 

% 

112.312 

1003.8 

% 

60.868 

294.83 

% 

86.786 

599.37 

% 

112.705 

1010.8 

/^ 

61.261 

298.65 

94 

87.179 

604.81 

36. 

113.097 

1017.9 

% 

61.654 

302.49 

Xo 

87.572 

610.27 

Ys 

113.490 

1025.0 

34 

62.046 

306.35 

28 

87.965 

615.75 

Y4 

113.883 

1032.1 

% 

62.439 

310.24 

^ 

88.357 

621.26 

% 

114.275 

1039.2 

20 

62.832 

314.16 

^4 

88.750 

626.80 

114.668 

1046.3 

^ 

63.225 

318.10 

n 

89.143 

632.36 

% 

115.061 

1053.5 

63.617 

3:8.06 

89.535 

637.94 

a 

115.454 

1060.7 

% 

64.010 

326.05 

% 

89.928 

643.55 

% 

115.846 

10,68.0 

64.403 

330.06 

% 

90.321 

649.18 

37 

116.239 

1075.2 

g 

64.795 

334.10 

8 

90.713 

654.84 

Ys 

116.632 

1082.5 

94 

65.188 

338.16 

29  i 

91.106 

660.52 

12 

117.024 

1089.8 

% 

65.581 

342.25 

91.499 

666.23 

% 

117.417 

1097.1 

21 

65.973 

346.36 

IX 

91.892 

671  .  96 

Yz 

117.810 

1104.5 

^ 

66.366 

350.50 

% 

92.284     677.71 

% 

118.202 

1111.8 

J>4 

66.759 

354.66 

JX 

92.677    1  683.  49 

% 

118.596 

1119.2 

% 

67.152 

358.84 

9^ 

93.070    ;  689.  30 

H 

118.988 

1126.7 

/^ 

67.544 

363.05 

3x[ 

93.462      695.13 

38. 

119.381 

1134.1 

% 

67.937 

367.28 

% 

93.855    '  700.  98 

H 

119.773 

1141.6 

% 

68.330 

371.54 

30. 

94.248     706  86 

Y4 

120.166 

1149.1 

110 


MATHEMATICAL  TABLES. 


Diam. 

Circurn. 

Area, 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

38% 

120.559 

1156.6 

46% 

146.477 

1707.4 

54% 

172.395 

2365.0 

/4 

120.951 

1164.2 

146.869 

1716.5 

55. 

172.788 

2375.8 

Kg 

121.344 

1171.7 

1 

147.262 

1725.7 

M 

173.180 

2386.6 

M 

121.  T37 

1179.3 

47  \ 

147.655 

1734.9 

M 

173.573 

2397.5 

xo 

122.129 

1186.9 

148.048 

1744.2 

% 

173.966 

2408.3 

39 

122.522 

1194.6 

IX. 

148  440 

1753.5 

IX 

174.358 

2419.2 

xii 

122.915 

1202.3 

% 

148.833 

1762.7 

x6 

174.751 

2430.1 

/4 

123.308 

1210.0 

u 

149.226 

1772.1 

M 

175.144 

2441  .  1 

% 

123.700 

1217.7 

149.618 

1781.4 

% 

175.536 

2452.0 

L£, 

124.093 

1225.4 

3x 

150.011 

1790.8 

56. 

175.929 

2463.0 

7^ 

124.486 

1233.2 

% 

150.404 

1800.1 

Ys 

176.322 

2474  0 

M' 

124.878 

1241.0 

48. 

150.796 

1809.6 

IX, 

176.715 

2485.0 

% 

125.271 

1248.8 

x^ 

151.189 

1819.0 

% 

177.107 

2196.1 

40. 

125.664 

1256.6 

x4 

151.582 

1828.5 

xl3 

177.500 

2507.2 

x6 

126.056 

1264.5 

% 

151.975 

1837.9 

% 

177.893 

2518.3 

126.449 

1272.4 

V£» 

152.367 

1847.5 

M 

178.285 

2529.4 

% 

126.842 

1280.3 

% 

152.760 

1857.0 

xo 

178.678 

2540.6 

IXj 

127.235 

1288.2 

ax. 

153.153 

1866.5 

57 

179.071 

2551.8 

% 

127.627 

1296.2 

% 

153.545 

1876.1 

Ys 

179.463 

2563.0 

% 

128.020 

1304.2 

49. 

153.938 

1885.7 

| 

179.856 

2574.2 

% 

128.413 

1312.2 

Ys 

154.331 

1895.4 

% 

180.249 

2585.4 

41. 

128.805 

1320.3 

154.723 

1905.0 

180.642 

2596.7 

& 

129.198 

1328.3 

% 

155.116 

1914.7 

% 

181.034 

2608.0 

129.591 

1336.4 

L£j 

155.509 

1924.4 

14 

181.427 

2619.4 

% 

129.983 

1344.5 

fy& 

155.902 

1934.2 

% 

181.820 

2630.7 

L£ 

130.376 

1352.7 

ax 

156.294 

1943.9 

58 

182.212 

2(542.1 

% 

130.769 

1360.8 

% 

156.687 

1953.7 

x^ 

182.605 

2653.5 

M 

131.161 

1369.0 

50. 

157.080 

1963.5 

M 

182.998 

2664.9 

% 

131.554 

1377.2 

xl* 

157.472 

1973.3 

% 

183.390 

2676.4 

42. 

131.947 

1385.4 

x4 

157.865 

1983.2 

xij 

183.783 

2687.8 

x6 

132.340 

1393.7 

% 

158.258 

1993.1 

% 

184.176 

2699.3 

H 

132.732 

1402.0 

\t> 

158.650 

2003.0 

M 

184.569 

2710.9 

% 

133.125 

1410.3 

% 

159.043 

2012.9 

% 

184.961 

2722.4 

133.518 

1418.6 

% 

159.436 

2022.  8 

59 

185.354 

2734.0 

fix. 

133.910 

1427.0 

xl 

159.829 

2032.8 

Ys 

185.747 

2745.6 

*M 

134.303 

1435.4 

51 

160.221 

2042.8 

i  ° 

186.139 

2757.2 

% 

134.696 

1443.8 

Ys 

160.614 

2052.8 

s2 

186.532 

2768.8 

43 

135.088 

1452.2 

J4 

161.007 

2062.9 

Y* 

186.925 

2780.5 

x6 

135.481 

1460.7 

161.399 

2073.0 

% 

187.317 

2792.2 

135.874 

1469.1 

Y> 

161.792 

2083.1 

M 

187.710 

2803.9 

% 

136.267 

1477.6 

% 

162.185 

2093.2 

% 

188.103 

2815.7 

IX 

136.659 

1486.2 

a/ 

162.577 

2103.3 

60 

188.496 

2827.4 

% 

137.052 

1494.7 

% 

162.970 

2113.5 

Ys 

188.888 

2839.2 

137.445 

1503.3 

6».    ' 

163.363 

2123.7 

VA 

189.281 

2851.0 

% 

137.837 

1511.9 

163.756 

2133.9 

xl 

189.674 

2862.9 

44. 

138.230 

1520.5 

M 

164.148 

2144.2 

Yz 

190.066 

2874.8 

138.623 

1529.2 

% 

164.541 

2154.5 

190.459 

2886.6 

IX 

139.015 

1537.9 

IX. 

164.934 

2164.8 

3x£ 

190.852 

2898.6 

% 

139.408 

1546.6 

s 

165.326 

2175.1 

% 

191.244 

2910.5 

IX 

139.801 

1555.3 

165.719 

2185.4 

61 

191.637 

2922.5 

fiX 

140  194 

1564.0 

% 

166.112 

2195.8 

Ys 

192.030 

2934.5 

M 

140.586 

1572.8 

53 

166.504 

2206.2 

M 

192.423 

2946.5 

H 

140.979 

1581.6 

x^ 

166.897 

2216.6 

% 

192.815 

2958.5 

45 

141.372 

1590.4 

167.290 

2227.0 

Y& 

193.208 

2970.6 

J4 

141.764 

1599.3 

% 

167.683 

2237.5 

% 

193.601 

2982.7 

xl 

142.157 

1608.2 

xij 

168.075 

2248.0 

M 

193.993 

2994.8 

SX 

142.550 

1617.0 

KX 

168.468 

2258.5 

7X. 

194.386 

3006.9 

IX 

142.942 

1626.0 

ax 

168.861 

2269.1 

62. 

194.779 

3019.1 

fiX 

143.335 

1634.9 

% 

169.253 

2279.6 

7^ 

195.171 

3031.3 

ax 

143.728 

1643.9 

54 

169.646 

2290.2 

M 

195.564 

3043.5 

% 

144.121 

1652.9 

x^ 

170.039 

2300.8 

% 

195.957 

3055.7 

46.8 

144.513 

1661.9 

x4 

170.431 

2311.5 

L/j 

196  350 

3068.0 

144.906 

1670.9 

xl 

170.824 

2322.1 

% 

196.742 

308H.3 

IX 

145.299 

1680.0 

171.217 

2332.8 

KX. 

197.135 

3092.6 

«7 

145.691 

1689.1 

% 

171.609 

2343.5 

% 

197.528 

3104.9 

/^ 

146.084 

1698.2 

M 

172.002 

2354.3 

63 

197.920 

3117.2 

CIRCUMFERENCES   AND   AREAS   OF    CIRCLES.        Ill 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

63  i£ 

198.313 

3129.6 

71% 

224.231 

4001.1 

79% 

250.149 

4979.5 

198.706 

3142.0 

Y* 

224.6-34 

4015.2 

250  542 

4995.2 

% 

199.098 

3154.5 

% 

225.017 

4029.2 

% 

250.935 

5010.9 

Yz 

199.491 

3166.9 

M 

225.409 

4043.3 

80. 

251.327 

5026.5 

K£ 

199.884 

3179.4 

7X 

225.802 

4057.4 

Ys 

251.720 

5042.3 

M 

200.277 

3191.9 

72 

226.195 

4071.5 

252.113 

5058.0 

% 

200.669 

3204.4 

Ys 

226.587 

4085.7 

ty& 

252.506 

5073.8 

64. 

201.062 

3317.0 

A 

226.980 

4099.8 

V% 

252.898 

5089.6 

Ys 

201.455 

3229.6 

ax 

227.373 

4114.0 

% 

253.291 

5105.4 

34 

201.847 

3242.2 

lx> 

227.765 

4128.2 

% 

253.684 

5121.2 

% 

202.240 

3254.8 

% 

228.158 

4142.5 

% 

254.076 

5137.1 

ix 

202.633 

3267.5 

M 

228.551 

4156.8 

81. 

254  469 

5153.0 

ax 

203.025 

3280.1 

% 

2-38.944 

4171.1 

V6 

254.862 

5168.9 

ax 

203.418 

3292.8 

73. 

229.336 

4185.4 

Y4 

255.254 

5184.9 

/o 

203.811 

3305.6 

229.729 

4199.7 

Ys 

255.647 

5200.8 

65 

204.204 

3318.3 

34 

230.122 

4214.1 

256.040 

5216.8 

204.596 

3331.1 

% 

230.514 

4228.5 

% 

256.433 

523-3.8 

IX 

204.989 

3343.9 

IX 

230.907 

4242.9 

ax 

256.825 

5248.9 

MX 

205.382 

3356.7 

5X 

231.300 

4257.4 

% 

257.218 

5264.9 

l/o 

205.774 

3369.6 

M 

231.692 

4271.8 

82. 

257.611 

5281.0 

% 

206.167 

3382.4 

so 

232.085 

4286.3 

258.003 

5297.1 

M 

206.560 

3395.3 

74 

232.478 

4300.8 

/4 

258.396 

5313.3 

% 

206.952 

3408.2 

232.871 

4315.4 

8X 

258.789 

5329.4 

66. 

207.345 

3421.2 

34 

233.263 

4329.9 

Y* 

259.181 

5345.6 

207.738 

3434.2 

% 

283  656 

4344.5 

% 

259.574 

5361.8 

34- 

208.131 

3447.2 

Y> 

234.049 

4359.2 

%L 

259.967 

5378.1 

% 

208.523 

3460.2 

% 

234.441 

4373.8 

% 

260  359 

5394.3 

Via 

208.916 

3473.2 

M 

234.834 

4388.5 

83. 

260.752 

5410  6 

5X 

209.309 

3486.3 

% 

235.227 

4403.1 

Vs 

261.145 

5426.9 

M 

209.701 

8499.4 

75. 

235.619 

4417.9 

34 

261.538 

5443.3 

% 

210.094 

3512.5 

Ys 

236.012 

4432.6 

% 

261.930 

5459.6 

67 

210.487 

3525  7 

Y4 

236.405 

4447.4 

Yn 

262.323 

5476.0 

210.879 

3538.8 

236.798 

4462.2 

5X 

262.716 

5492.4 

i2 

211.272 

3552.0 

Yt 

237.190 

4477.0 

M 

263.108 

5508.8 

a/ 

211.665 

3565.2 

KX 

237.583 

4491.8 

TX 

263.501 

5525.3 

1Z 

212.058 

3578.5 

M 

237.976 

4506.7 

84. 

263.894 

5541.8 

5X 

212.450 

3591.7 

% 

238.368 

4521.5 

/^ 

264.286 

5558.3 

M 

212.843 

3C05.0 

76 

238.761 

4536.5 

34 

264.679 

5574.8 

7X 

213.236 

3618.3 

IX 

239.154 

4551.4 

% 

265.072 

5591.4 

68. 

213.628 

3631.7 

34 

239.546 

4566.4 

34 

265.465 

5607.9 

^s 

214.021 

3645.0 

% 

239.939 

4581.3 

% 

265.857 

5624.5 

Y1 

214.414 

3658.4 

k£ 

240.332 

4596.3 

ax 

266.250 

5641.2 

% 

214.806 

3671.8 

% 

240.725 

4611.4 

% 

266.643 

5657.8 

V& 

215.199 

3685.3 

% 

241.117 

4626.4 

85. 

267.035 

5674.5 

% 

215.592 

3698.7 

% 

241.510 

4641.5 

Ys 

267.428 

5691.2 

M 

215.984 

3712.2 

77. 

241.903 

4656.6 

267.821 

5707.9 

7X 

216.377 

3725.7 

M 

242.295 

4671.8 

% 

268.213 

5724.7 

69. 

216.770 

3739.3 

34 

242.688 

4686.9 

3^ 

268.606 

5741.5 

217.163 

3752.8 

ax 

243.081 

4702.1 

5X 

268.999 

5758.3 

34 

217.555 

3766.4 

Y* 

243.473 

4717.3 

a^ 

269.392 

5775.1 

ax 

217.948 

3780.0 

% 

243.866 

4732.5 

% 

269.784 

5791.9 

~Y& 

218.341 

3793.7 

M 

244.259 

4747.8 

86. 

270.177 

5808.8 

% 

218.733 

3807.3 

% 

244.652 

4763.1 

270.570 

5825.7 

M 

219.126 

3821.0 

78. 

245.044 

4778.4 

34 

270.962 

5842.6 

7X 

219.519 

3834.7 

245.437 

4793.7 

ax 

271.355 

5859.6 

70. 

219.911 

3S48.5 

34 

245.830 

4809.0 

^x 

271.748 

5876.5 

3*4 

220.304 

3862.2 

% 

246.22-3 

4824.4 

% 

272.140 

5893.5 

^4 

220.697 

3876.0 

IX 

246.615 

4839.8 

ax 

272.533 

5910.6 

% 

221.090 

3889.8 

% 

247.008 

4855.2 

% 

272.926 

5927.6 

221.482 

3903.6 

ax 

247.400 

4870.7 

87. 

273.319 

5944.7 

% 

221.875 

3917.5 

% 

247.793 

4886.2 

Vs 

273.711 

5961.8 

ax 

222.268 

3931.4 

79. 

248.186 

4901.7 

34 

274.104 

5978.9 

% 

222.660 

3945.3 

248.579 

4917.2 

ax 

274.497 

5996.0 

71. 

223.053 

3959.2 

34 

248.971 

4932.7 

3^2 

274.889 

6013.2 

223.446 

3973.1 

| 

249  364 

4948.3 

% 

275.282 

6030.4 

/4 

223.838 

3987.1 

249.757 

4963.9 

M 

275.675 

6047.6 

112 


MATHEMATICAL   TABLES. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

87% 

276,067 

6064.9 

92. 

289.027 

6647.6 

96^ 

301.986 

7257.1 

88. 

276.460 

6082  1 

^ 

289.419 

6665.7 

302.378 

7276.0 

i£ 

276.853 

6099.4 

/4 

289.812 

6683.8 

% 

.302.771 

7294.9 

/4 

277.246 

6116.7 

% 

290.205 

6701.9 

L£ 

303.164 

7313.8 

% 

277.638 

6134.1 

/^ 

290.597 

6720.1 

% 

303.556 

7332.8 

l/Q 

278.031 

6151.4 

% 

290.990 

6738.2 

'A/. 

303.949 

7351.8 

% 

278.424 

6168.8 

% 

291.383 

6756.4 

% 

304  .  342 

7370.8 

% 

278.816 

6186.2 

% 

291.775 

6774.7 

97 

304.734 

7389.8 

/Q 

279.209 

6203.7 

93 

292.168 

6792.9 

ix 

305.127 

7408.9 

89. 

279.602 

6221.1 

Ys 

292.561 

6811.2 

IX 

305.520 

7428  .0 

H 

279.994 

6238.6 

29:2.951 

6829.5 

% 

305.913 

7447.1 

IX 

280.387 

6256.1 

% 

293.346 

6847.8 

%2 

306.305 

7406.2 

^8 

280.780 

6273.7 

/^ 

293.739 

68G6.1 

5^ 

306.698 

7485.3 

/^ 

281.173 

6291.2 

% 

^94.13? 

6884.5 

% 

307.091 

7504  .  5 

% 

281.565 

6  08.8 

M 

294.524 

6902.9 

/o 

307.483 

7523.7 

gl 

281.958 

6320.4 

% 

294.917 

6921  .  3 

98 

307.876 

7543.0 

% 

282.351 

6344  .  1 

94 

295.310 

6939.8 

H 

308.269 

7562.2 

90. 

282.743 

6361.7 

YS 

295.702 

6958.2 

& 

308.661 

7581.5 

1^ 

283.136 

6379.4 

296.095 

6976.7 

% 

309.054 

7000.8 

/4 

283.529 

6397.1 

% 

296.488 

6995.3 

y» 

309.447 

7020.1 

% 

283.921 

6414.9 

vz 

296.881 

7013.8 

H 

309  .  840 

7039.5 

V% 

284.314 

6432.6 

% 

297.273 

703  J.  4 

H 

310.232 

7658.9 

% 

284.707 

6450.4 

«M 

297.666 

7051.0 

% 

310.625 

7678.3 

% 

285.100 

6468.2 

H 

298.059 

7069.6 

99 

311.018 

7697.7 

% 

285.492 

6486.0 

95. 

298.451 

7088.2 

Yz 

311.410 

7717.1 

91 

285.885 

6503.9 

Ys 

298.844 

7106.9 

M 

31  1.803 

7736.6 

8 

286.278 

6521.8 

Y± 

299.237 

7125.6 

% 

312.196 

7756.1 

A 

286.670 

6539.7 

299.629 

7144.3 

^2 

312.588 

7775  .  6 

% 

287.063 

6557.6 

Y& 

300.022 

7163.0 

% 

312.981 

7795.2 

3^ 

287.456 

6575.5 

% 

300.415 

7181.8 

M 

313.374 

7814.8 

5X 

287.848 

6593.5 

% 

300.807 

7200.6 

% 

313.767 

7834.4 

M 

288.241 

6611.5 

1 

301.200 

7219.4 

100 

314.159 

7854.0 

% 

288.634 

6629.6 

96. 

301.593 

7238.2 

DECIMALS  OF  A  FOOT  EQUIVALENT  TO  INCHES 
AND   FRACTIONS   OF   AN   INCH. 


Inches. 

0 

Ys 

H 

% 

H 

% 

M 

% 

0 

0 

.01042 

.02083 

.03125 

.04166 

.05208 

.06250 

.07292 

1 

.0833 

.0937 

.1042 

.1146 

.1250 

.1354 

.1459 

.1503 

2 

.1667 

.1771 

.1875 

.1979 

.2083 

.2188 

.2292 

.2390 

3 

.2500 

.2604 

.2708 

.2813 

.2917 

.3021 

.3125 

.3229 

4 

.3333 

.3437 

.3542 

.3646 

.3750 

.3854 

.3958 

.4003 

5 

.4167 

.4271 

.4375 

.4479 

.4583 

.4688 

.4792 

.4896 

6 

.5000 

.5104 

.5208 

.5313 

.5417 

.5521 

.5625 

.5729 

7 

.5833 

.5937 

.6042 

.6146 

.6250 

.6354 

.6459 

.6563 

8 

.6667 

.6771 

.6875 

.6979 

.7083 

.7188 

.7292 

.7396 

9 

.7500 

.7604 

.7708 

.7813 

.7917 

.80:21 

.8125 

.8-229 

10 

.8333 

.8437 

.8542 

.8646 

.8750 

.8854 

.8958 

.9063 

11 

.9167 

.9271 

.9375 

.9479 

.9583 

.9688 

.9792 

.9896 

CIRCUMFERENCES   OF   CIRCLES. 


113 


v^-\!»\a>NPCss»NTj«\x\a>Na>     Vtf^XjO^NpJNrf-NSp 

CSN^xrisciXT-K^JX  1>\1O\»5\        eOX9SNr4\r>S-K»4\lVX 


t— i  TF  co  i?-  a*  1-1  o"<?!  ^r  o  j.--.  os  i—  o^"'*  Iri'^ci'o^o^'Tf  KT^os  o'cf^SV&TIolVo 


g 

X 

& 


& 
c 


^^c^o^;^»^ 

Vco^"Svob>5iT<'^Voo  -g< «?  oo  os  TH  r-i 


7.    *r 


.c: 


»x*l\rf 
XJ\W\ 


3^^JOi~osoo^coAnt'050o^ccot-coooT-ccoiot-ooooi-io3iob 
HTt^ow«ooswggsw.5aor=o»jH^j-oojgocosoo5^go^gooog 


V*\OC\QO\rt'\ 


>  co  o  o»  ^  »a  go  ^  jrj  oo  ^  •<*  t»  o  50 1»  o  co  to  pb  o»  j<s  os  «2 15  50  »-i  r»«fc 

r^T^  T^  W  W  W  CO  CO  CO  ^  "V  ^  «  fo  »O  «D  3  S  <D  J>  1--  £•-  00  00  OO  OS  O»  O 


T-I  C*  CO  Tf  *O  «O  t»  00  OS  O  TH  «  CO  Tj»KS  «O  l^  00  OS  O  T-I  fi 


114 


MATHEMATICAL   TABLES. 


L.ENQTHS  OF  CIRCULAR  ARCS. 

(Degrees  being  given.    Radius  of  Circle  =  1.) 

FORMULA.— Length  of  arc  —    '  X  radius  X  number  of  degrees. 

RULE.— Multiply  the  factor  in  table  for  any  given  number  of  degrees  by 
the  radius. 

EXAMPLE.— Given  a  curve  of  a  radius  of  55  feet  and  an  angle  of  78°  20'. 
What  is  the  length  of  same  in  feet  ? 

Factor  from  table  for  78° 1.3613568 

Factor  from  table  for  20' . .     .0058178 

Factor 1.3671746 

1.3671746  X  55  =  75.19  feet. 


Degrees. 


1 

.0174533 

61 

1.0646508 

121 

2.1118484 

1 

.0002909 

2 

.0349066 

62 

1.0821041 

122 

2.1293017 

2 

.0005818 

3 

.0523599 

63 

1.0995574 

123 

2.1467550 

3 

.0008727 

4 

.0698132 

64 

1.1170107 

124 

2.1642083 

4 

.0011636 

5 

.0872665 

65 

1.1344640 

125 

2.1816616 

5 

.0014544 

6 

.1047198 

66 

1.1519173 

126 

2.1991149 

6 

.0017453 

7 

.1221730 

67 

1.1693706 

127 

2.2165682 

7 

.0020362 

8 

.1396263 

68 

1.1868239 

128 

2.2340214 

8 

.0023271 

9 

.1570796 

69 

1.2042772 

129 

2.2514747 

9 

.0026180 

10 

.1745329 

70 

1.2217305 

130 

2.2689280 

10 

.0029089 

11 

.1919862 

71 

1.2391838 

131 

2.2863813 

11 

.0031998 

12 

.2094395 

72 

1.2566371 

132 

2.3038346 

12 

.0034907 

13 

.2268928 

73 

1.2740904 

133 

2.3212879 

13 

.0037815 

14 

.2443461 

74 

1.2915436 

134 

2.3387412 

14 

.0040724 

15 

.2617994 

75 

1.3089969 

135 

2.3561945 

15 

.00436?3 

16 

.2792527 

76 

1.3264502 

136 

2.3736478 

16 

.0046542 

17 

.2967060 

77 

1.3439035 

137 

2.3911011 

17 

.0049451 

18 

.3141593 

78 

1.3613568 

138 

2.4085544 

18 

.0052369 

19 

.3316126 

79 

1.3788101 

139 

2.4260077 

19 

.0055269 

20 

.3490659 

80 

1.  3962634 

140 

2.4434610 

20 

.0058178 

21 

.3665191 

81 

1.4137167 

141 

2.4609142 

21 

.  006108  J 

22 

.3839724 

82 

1.4311700 

142 

2.4783675 

22 

.0063995 

23 

.4014257 

83 

1.4486233 

143 

2.4958208 

23 

.0066904 

24 

.4188790 

84 

1.4660766 

144 

2.5132741 

24 

.0069813 

25 

.4363323 

85 

1.4835299 

145 

2.5307274 

25 

.007272? 

26 

.4537856 

86 

1.5009832 

146 

2.5481807 

26 

.0075631 

27 

.4712389 

87 

1.5184364 

147 

2.5656340 

27 

.  007854,'  / 

28 

.4886922 

88 

1.5358897 

148 

2.5830873 

28 

.008144\l 

29 

.5061455 

89 

1.5533430 

149 

2.6005406 

29 

.0084358 

30 

.5235988 

90 

1.5707963 

150 

2.6179939 

30 

.0087266 

31 

.5410521 

91 

1.5882496 

151 

2.6354472 

31 

.0090175 

32 

.5585054 

92 

1.6057029 

152 

2.6529005 

32 

.0093084 

33 

.5759587 

93 

1.6231562 

153 

2.6703538 

33 

.0095993 

34 

.5934119 

94 

1.6406095 

154 

2.6878070 

34 

.0098902 

35 

.6108652 

95 

1.6580628 

155 

2.7052603 

35 

.0101811 

36 

.6283185 

96 

1.6755161 

156 

2.7227136 

36 

.0104720 

37 

.6457718 

97 

1.6929694 

157 

2.7401669 

37 

.0107629 

38 

.6632251 

98 

1.7104227 

158 

2.7576202 

38 

.0110538 

39 

.6806784 

99 

1.7278760 

159 

2.7750735 

39 

.0113446 

40 

.6981317 

100 

1.7453293 

160 

2.7925268 

40 

.0116355 

41 

.7155850 

101 

1.7627825 

161 

2.8099801 

41 

.0119264 

42 

.7330383 

102 

1.7802S5X 

162 

2.8274334 

42 

.0122173 

43 

.7504916 

103 

1.7976891 

163 

2.8448867 

43 

.0125082 

44 

.7679449 

104 

1.8151424 

164 

2.8623400 

44 

.0127991 

45 

.7853982 

105 

1.8325957 

165 

2.8797933 

45 

.0130900 

46 

.8028515 

106 

1.8500490 

166 

2.8972466 

46 

.0133809 

47 

.8203047 

107 

1.8675023 

167 

2.9146999 

47 

.0136717 

48 

.8377580 

108 

1.8849556 

168 

2.9321531 

48 

.0139626 

49 

.8552113 

109 

1.9024089 

169 

2.9496064 

49 

.0142535 

50 

.8726646 

110 

1.9198622 

170 

2.9670597 

50 

.0145444 

51 

.8901179 

111 

1.9373155 

171 

2.9845130 

51 

.0148358 

52 

.9075712 

112 

1.9547688 

172 

3.0019663 

52 

.0151262 

53 

.9250245 

113 

1.9722221 

173 

3.0194196 

53 

.0154171 

54 

.9424778 

114 

1.9896753 

174 

3.0368729 

54 

.0157080 

55 

.9599311 

115 

2.0071286 

175 

3.0543202 

55 

.0159989 

56 

.9773844 

116 

2.0245819 

176 

3.0717795 

56 

.0162897 

57' 

.9948377 

117 

2  0420352 

177 

3.0892328 

57 

.0165806 

58 

1.0122910 

118 

2.0594885 

178 

3.1066861 

58 

.0168715 

59 

1.0297443 

119 

2.0769418 

179 

3.1241394 

59 

.0171624 

60 

1.0471976 

120 

2.0943951 

180 

3.1415927 

60 

.0174533 

LENGTHS   OF   CIRCULAR   ARCS. 


115 


LENGTHS  OF  CIRCTJL.AR 

(Diameter  =  1.     Given  the  Chord  and  Height  of  the  Arc.) 

RULE  FOR  USE  OF  THE  TABLE.— Divide  the  height  by  the  chord.  Find  in  the 
column  of  heights  the  number  equal  to  this  quotient.  Take  out  the  corre- 
sponding number  from  the  column  of  lengths.  Multiply  this  last  number 
by  the  length  of  the  given  chord ;  the  product  will  be  length  of  the  arc. 

If  the  arc  is  greater  than  a  semicircle,  first  find  the.  diameter  from  the 
formula,  Diam.  =  (square  of  half  chord  -*-  rise)  +  rise;  the  formula  is  true 
whether  the  arc  exceeds  a  semicircle  or  not.  Then  find  the  circumference. 
From  the  diameter  subtract  the  given  height  of  arc,  the  remainder  will  be 
height  of  the  smaller  arc  of  the  circle;  find  its  length  according  to  the  rule, 
and  subtract  it  from  the  circumference. 


Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

Hgts. 

Lgths. 

.001 

1.00002 

.15 

1.05896 

.238 

1.14480 

.326 

1.26288 

.414 

1.40788 

.005 

1.00007 

.152 

1.06051 

.24 

1.14714 

.328 

1.26588 

.416 

1.41145 

.01 

1.00027 

.154 

1.06209 

.242 

1.14951 

.33 

1.26892 

.418 

1.41503 

.015 

1.00061 

.156 

1.06368 

.244 

1.15189 

.332 

1.27196 

.42 

1.41861 

.02 

1.00107 

.158 

1.06530 

.246 

1.15428 

.334 

1.27502 

.422 

1.42221 

.025 

1.00167 

.16 

1.06693 

.248 

1.15670 

.336 

1.27810 

.424 

1.42583 

.03 

1.00240 

.162 

1.0685H 

.25 

.15912 

.338 

1.28118 

.426 

1.42945 

.035 

1.00327 

.164 

1.07025 

.252 

.16156 

.34 

1.28428 

.428 

1.43309 

.04 

1.00426 

.166 

1.07194 

.254 

.16402 

.342 

1.28739 

.43 

1.43673 

.045 

1.00539 

.168 

1.07365 

.256 

.16650 

.344 

1.29052 

.432 

1.44039 

.05 

1.00665 

.17 

1.07537 

.258 

.16899 

.346 

1.29366 

.434 

1.44405 

.055 

1.00805 

.172 

1.07711 

.26 

.17150 

.348 

1.29681 

.436 

1.44773 

.06 

1.00957 

.174 

1.07888 

.262 

.17403 

.35 

1.29997 

.438 

1.45142 

.065 

1.01123 

.176 

1.08066 

.264 

.17657 

.352 

1.30315 

.44 

1.45512 

.07 

1.01302 

.178 

1.08246 

.266 

.17912 

.354 

1.30634 

.442 

1.45883 

.075 

1.01493 

.18 

1.08428 

.268 

.18169 

.356 

1.30954 

.444 

1.46255 

.08 

1.01698 

.182 

1.08611 

.27 

.18429 

.358 

1.31276 

.446 

1.46628 

.085 

1.01916 

.184 

1.08797 

.272 

.18689 

.36 

1.31599 

.448 

1.47002 

.09 

1.02146 

.186 

1.08984 

.274 

.18951 

.362 

1.31923 

.45 

1.47377 

.095 

1.02389 

.188 

1.09174 

.276 

.19214 

.364 

1.32249 

.452 

1.47753 

.10 

1.02646 

.19 

1.09365 

.278 

.19479 

.366 

1.32577 

.454 

1.48131 

.102 

1.02752 

.192 

1.09557 

.28 

.19746 

.368 

1.32905 

.456 

1.48509 

.104 

1.02860 

.194 

1.09752 

.282 

.20014 

.37 

1.33234 

.458 

1.48889 

.106 

1.02970 

.196 

1.09949 

.284 

.20284 

.372 

1.33564 

.46 

1.49269 

.108 

1.03082 

.198 

1.10147 

.286 

.20555 

.374 

1.33896 

.462 

1.49651 

.11 

1.03196 

.20 

1.10347 

.288 

.20827 

.376 

1.34229 

.464 

1.50033 

.113 

1.03312 

.202 

1.10548 

.29 

.21102 

.378 

1.34563 

.466 

1.50416 

.114 

1.03430 

.204 

1.10752 

.29.2 

.21377 

.38 

1.34899 

.468 

1.50800 

.116 

1.03551 

.206 

1.10958 

.294 

.21654 

.382 

1.35237 

.47 

1.51185 

.118 

1.03872 

.208 

1.11165 

.296 

.21933 

.384 

1.35575 

.472 

1.51571 

.12 

1.03797 

.21 

1.11374 

.298 

.22213 

.386 

1.35914 

.474 

1.51958 

.122 

1.03923 

.212 

1.11584 

.30 

.22495 

.388 

1.36254 

.476 

1.52346 

.124 

1.04051 

.214 

1.11796 

.302 

.22778 

.39 

1.36596 

.478 

1.52736 

.126 

1.04181 

.216 

1.12011 

.304 

.23063 

.392 

1.36939 

.48 

1.53126 

.128 

1.04313 

.218 

1.12225 

.306 

.23349 

.394 

1.37283 

.482 

1.53518 

.13 

1.04447 

.22 

1.12444 

.308 

.23636 

.396 

1.37628 

.484 

1.53910 

'.132 

1.04584 

222 

1.12664 

.31 

.23926 

.398 

1.37974 

.486 

1.54302 

.134 

1.04722 

!224 

1.12885 

.312 

.24216 

.40 

1  .  3832S 

.488 

1.54696 

.136 

1.04862 

.226 

1.13108 

.314 

.24507 

.402 

1.38671 

.49 

1  .55091 

.138 

1.05003 

.228 

1.13331 

.316 

.24801 

.404 

1.39021 

.492 

1.55487 

.14 

1.05147 

.23 

1.13557 

.318 

.25095 

.406 

1.39372 

.494 

1.55854 

.142 

1.05293! 

.232 

1.13785 

.32 

.25391 

.408 

1.39724 

.496 

1.56282 

.144 

1.05441 

.234 

1.14015 

,322 

.25689 

.41 

1.40077 

.498 

1.56681 

.146 

1.05591 

.236 

1.14247 

.324 

.25988 

.412 

1.40432 

.5 

1.57080 

.148 

1.05743 

116 


MATHEMATICAL   TABLES. 


AREAS  OF  THE  SEGMENTS  OF   A   CIRCLE. 

(Diameter       1  ;  Rise  or  Versed  Sine  in  parts  of  Diameter 
being  given.) 

RULE  FOR  USE  OF  THE  TABLE, — Divide  the  rise  or  height  of  the  segment  by 
the  diameter  to  obtain  the  versed  sine.  Multiply  the  area  in  the  table  cor> 
responding  to  this  versed  sine  by  the  square  of  the  diameter. 

If  the  segment  exceeds  a  semicircle  its  area  is  area  of  circle— area  of  seg- 
ment whose  rise  is  (diam.  of  circle— rise  of  given  segment). 

Given  chord  and  rise,  to  find  diameter.  Diam.  =  (square  of  half  chord  -*- 
rise)  4-  rise.  The  half  chord  is  a  mean  proportional  between  the  two  parts 
into  which  the  chord  divides  the  diameter  which  is  perpendicular  to  it. 


Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

.001 

.00004 

.054 

.01646 

.107 

.04514 

.16 

.08111 

.213 

.12235 

.00-2 

.00012 

.055 

.01691 

.108 

.04576 

.161 

.08185 

.214 

.12317 

.003 

.00022 

.056 

.01737 

.109 

.04638 

.162 

.08258 

.215 

.12399 

.004 

.00034 

.057 

.01783 

.11 

.04701 

.163 

.08332 

.216 

.12481 

.005 

.00047 

.058 

.01830 

.111 

.04763 

.164 

.08406 

.217 

.12563 

.006 

.00062 

.059 

.01877 

.112 

.04826 

.165 

.08480 

.218 

.12646 

.007 

.00078 

.06 

.01924 

.113 

.04889 

.166 

.08554 

.219 

.12729 

.008 

.00095 

.061 

.01972 

.114 

.04953 

.167 

.08629 

.22 

.12811 

.009 

.00113 

.062 

.02020 

.115 

.05016 

.168 

.08704 

.221 

.12894 

.01 

.00133 

.063 

.02068 

.116 

.05080 

.169 

.08779 

.222 

.12977 

.011 

.00153 

.064 

.02117 

.117 

.05145 

.17 

.08854 

.223 

.13060 

.012 

.00175 

.065 

.02166 

.118 

.05209 

.171 

.08929 

.224 

.13144 

.013 

.00197 

.066 

.02215 

.119 

.05274 

.172 

.09004 

.225 

.13227 

.014 

.0022 

.067 

.02265 

.12 

.05338 

.173 

.09080 

.226 

.13311 

.015 

.00244 

.068 

.02315 

.121 

.05404 

.174 

.09155 

.227 

.13395 

.016 

.00268 

.069 

.02366 

.122 

.05469 

.175 

.09231 

.228 

.13478 

.017 

.00294 

.07 

.02417 

.123 

.05535 

.176 

.09307 

.229 

.13562 

.018 

.0032 

.071 

.02468 

.124 

.05600 

.177 

.09384 

.23 

.13646 

.019 

.00347 

.072 

.02520 

.125 

.05666 

.178 

.09460 

.231 

.13731 

.02 

.00375 

.073 

.02571 

.126 

.05733 

.179 

.09537 

.232 

.13815 

.021 

.00403 

.074 

.02624 

.127 

.05799 

.18 

.09613 

.233 

.13900 

.022 

.00432 

.075 

.02676 

.128 

.05866 

.181 

.09690 

.234 

.13984 

.023 

.00462 

.076 

.02729 

.129 

.05933 

.182 

.09767 

.235 

.14069 

.024 

.00492 

.077 

.02782 

.13 

.06000 

.183 

.09845 

.236 

.14154 

.025 

.00523 

.078 

.02836 

.131 

.06067 

.184 

.09922 

.237 

.14239 

.026 

.00555 

.079 

.02889 

.132 

.06135 

.185 

.10000 

.238 

.14324 

.027 

.00587 

.08 

.02943 

.133 

.06203 

.186 

.10077 

.239 

.  14409 

.028 

.00619 

.081 

.02998 

.134 

.06271 

.187 

.10155 

.24 

.14494 

.029 

.00653 

.082 

.03053 

.135 

.06339 

.188 

.10233 

.241 

.  14580 

.03 

.00687 

.083 

.03108 

.136 

.06407 

.189 

.10312 

.242 

.14666 

.031 

.00721 

.084 

.03163 

.137 

.06476 

.19 

.10390 

.243 

.14751 

.032 

.00756 

.085 

.03219 

.138 

.06545 

.191 

.10469 

.244 

.14837 

.033 

.00791 

.086 

.03275 

.139 

.06614 

.192 

.10547 

.245 

.14923 

.034 

.00827 

.087 

.03331 

.14 

.06683 

.193 

.10626 

.246 

.15009 

.035 

.00864 

.088 

.03387 

.141 

.06753 

.194 

.10705 

.247 

.15095 

.036 

.00901 

.089 

.03444 

.142 

.06822 

.195 

.10784 

.248 

.15182 

.037 

.00938 

.09 

.03501 

.143 

.06892 

.196 

.10864 

.249 

.15268 

.038 

.00976 

.091 

.03559 

.144 

.069C3 

.197 

.10943 

.25 

.15355 

.039 

.01015 

.092 

.03616 

.145 

.07033 

.198 

.11023 

.251 

.15441 

.04 

.01054 

.093 

.03674 

.146 

.07103 

.199 

.11102 

.252 

.15528 

.041 

.01093 

.094 

.03732 

.147 

.07174 

.2 

.11182 

.253 

.15615 

.042 

.01133 

.095 

.03791 

.148 

.07245 

.201 

.11262 

.254 

.15702 

.043 

.01173 

.096 

.03850 

.149 

.07316 

.202 

.11343 

.255 

.15789 

.044 

.01214 

.097 

,.03909 

.15 

.07387 

.203 

.11423 

.256 

.15876 

.045 

.01255 

.098 

.03968 

.151 

.07459 

.204 

.11504 

.257 

.15964 

.046 

.01297 

.099 

.04028 

.152 

,07531 

.205 

.11584 

.258 

.16051 

.047 

.01339 

.1 

.04087 

.153 

.07603 

.206 

.11665 

.259 

.16139 

.048 

.01382 

.101 

.04148 

.154 

.07675 

.207 

.11746 

.26 

.16226 

.049 

.01425 

.102 

.04208 

.155 

.07747 

.208 

.11827 

.261 

.16314 

.05 

.01468 

.103 

.04269 

.156 

.07819 

.209 

.11908 

.262 

.16402 

.051 

.01512 

.104 

.04330 

.157 

.07892 

.21 

.11990 

.263 

.16490 

.052 

.01556 

.105 

.04391 

.158 

.07965 

.211 

.12071 

.264 

.16578 

.053 

.01601 

.106 

.04452 

.159 

.08038 

.212 

.12153 

.265 

.16666 

AREAS    OF   THE    SEGMENTS   OF    A    CIRCLE. 


Ill 


Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

Versed 
Sine. 

Area. 

.266 

.16755 

.313 

.21015 

.36 

.25455 

.407 

.30024 

.454 

.34676 

.267 

.16843 

.314 

.21108 

.361 

.25551 

.408 

.30122 

.455 

.34776 

.268 

.16932 

.315 

.21201 

.362 

.25647 

.409 

.30220 

.456 

.34876 

.269 

.17020 

.316 

.21294 

.363 

.25743 

.41 

.30319 

.457 

.34975 

.27 

.17109 

.317 

.21387 

.364 

.25839 

.411 

.30417 

.458 

.35075 

.271 

.  7198 

.318 

.21480 

.365 

.25936 

412 

.30516 

.459 

.35175 

.272 

.  7287 

.319 

.21573 

.366 

.26032 

.413 

.30614 

.46 

.35274 

.273 

.  7376 

.32 

.21667 

.367 

.26128 

.414 

.30712 

.461 

.P5374 

.274 

.  7465 

.321 

.21760 

.368 

.26225 

.415 

.30811 

.462 

.35474 

.275 

.  7554 

.322 

.21853 

.369 

.26321 

.416 

.30910 

.463 

.35573 

.276 

.  7644 

.323 

.21947 

.37 

.26418 

.417 

.31008 

.464 

.35673 

.277 

.17733 

.324 

.22040 

.371 

.26514 

.418 

.31107 

.465 

.35773 

.278 

.17823 

.325 

.22134 

.372 

.26611 

.419 

.31205 

.466 

.35873 

.279 

.17912 

.326 

.22228 

.73 

.26708 

.42 

.31304 

.467 

.35972 

.28 

.18002 

.327 

.22322 

.374 

.26805 

.421 

.31403 

.468 

.36072 

.281 

.18092 

.328 

.22415 

.375 

.26901 

.422 

.31502 

.469 

.36172 

.282 

.18182 

.329 

.22509 

.376 

.26998 

.423 

.31600 

.47 

.36272 

.283 

.18272 

.33 

.22603 

.377 

.27095 

.424 

.31699 

.471 

.36372 

.284 

.18362 

.331 

.22697 

.378 

.27192 

.425 

.31798 

.472 

.36471 

.285 

.18452 

.332 

.22792 

.379 

.27289 

.426 

.31697 

.473 

.36571 

.286 

.18542 

.333 

.22886 

.38 

.27386 

.427 

.31996 

.474 

.36671 

.287 

.18633 

.334 

.22980 

.381 

.27483 

428 

.32095 

.475 

.36771 

.288 

.18723 

.335 

.23074 

.382 

.27580 

!429 

.32194 

.476 

.36871 

.289 

.18814 

.336 

.23169 

.383 

.27678 

.43 

.32293 

.477 

.36971 

.29 

.18905 

.337 

.23263 

.384 

.27775 

.431 

.32392 

.478 

.37071 

.291 

.18996 

.338 

.23358 

.385 

.27872 

.432 

.32491 

.479 

.37171 

.292 

.19086 

.339 

.23453 

.386 

.27969 

.433 

.32590 

.48 

.37270 

.293 

.19177 

.34 

.23547 

.387 

.28067 

.434 

.32689 

.481 

.37370 

.294 

.19268 

.341 

.23642 

.388 

.28164 

.435 

.32788 

.482 

.37470 

.295 

.19360 

.342 

.23737 

.389 

.28262 

.436 

.32837 

.483 

.37570 

.296 

.19451 

.343 

.23832 

.39 

.28359 

.437 

.32987 

.484 

.37670 

.297 

.19542 

.344 

.23927 

.391 

.28457 

.438 

.33086 

.485 

.37770 

.298 

.19634 

.345 

.24022 

.392 

.28554 

.439 

.33185 

.486 

.37870 

.299 

.19725 

.346 

.24117 

.393 

.28652 

.44 

.33284 

.487 

.37970 

.8 

.19817 

.347 

.24212 

.394 

.28750 

.441 

.33384 

.488 

.38070 

.301 

.19908 

.348 

.24307 

.395 

.28848 

.442 

.33483 

.489 

.38170 

.30? 

.20000 

.349 

.24403 

.396 

.28945 

.443 

.33582 

.49 

.38270 

.303 

.20092 

.35 

.24498 

.397 

.29043 

.444 

.38682 

.491 

.38370 

.304 

.20184 

.351 

.24593 

.398 

.29141 

.445 

.33781 

.492 

.38470 

.305 

.20276 

.352 

.24689 

.399 

.29239 

.446 

.33880 

.493 

.38570 

.306 

.20368 

.353 

.24784 

.4 

.29337 

.447 

.33980 

.494 

.38670 

.307 

.20460 

.354 

.24880 

.401 

.29435 

.448 

.34079 

.495 

.38770 

.308 

.20553 

.355 

.24976 

.402 

.29533 

.449 

.34179 

.496 

.38870 

.309 

.20645 

.356 

.25071 

.403 

.29631 

.45 

.34278 

.497 

.38970 

.31 

.20738 

.357 

.25167 

.404 

.29729 

.451 

.34378 

.498 

.39070 

.311 

.20830 

.358 

.25263 

.405 

.29827 

.452 

.34477 

.499 

.39170 

.312 

.20923 

.359 

.25359 

.406 

.29926 

.453 

.34577 

.5 

.39270 

For  rules  for  finding  the  area  of  a  segment  see  Mensuration,  page  59. 


118 


MATHEMATICAL   TABLES. 


SPHERES. 

(Some  errors  of  1  in  the  last  figure  only.    From  TRAUTWINE.) 


Diam. 

Sur. 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Solid- 
ity. 

1-32 

.00307 

.00002 

3    y 

33.183 

17.974 

9    % 

306.36 

504.21 

1-16 

.01227 

.00013 

5-16 

34.472 

19.031 

10. 

314.16 

523.60 

3-32 

.02761 

.00043 

% 

35.784 

20.129 

/"^ 

322.06 

543  48 

.04909 

.00102 

7-16 

37.122 

21.268 

IX 

330.06 

563.86 

5-32 

.07670 

.00200 

38.484 

22.449 

% 

338.16 

584.74 

3-16 

.11045 

.00345 

9-16 

39.872 

23.674 

iz 

346.36 

606.13 

7-32 

.15033 

.00548 

&£ 

41.283 

24.942 

% 

354.66 

628.04 

& 

.19635 

.00818 

11-16 

42.719 

26.254 

$4 

363.05  I  650.46 

9-32 

.24851 

.01165 

44.179 

27.611 

% 

371.54 

673.42 

5-16 

.30680 

.01598 

13-16 

45.664 

29.016 

11. 

380.13 

696.91 

11-32 

.37123 

.02127 

47.173 

30.466 

Ys, 

388.83 

720.95 

.44179 

.02761 

15-16 

48.708 

31.965 

Q 

397.61 

745.51 

13-32 

.51848 

.03511 

4. 

50.265 

33.510 

% 

406.49 

770.64 

7-16 

.60132 

.04385 

1^ 

53.456 

36.751 

V% 

415.48 

796.33 

15-32 

.69028 

.05393 

IX- 

56.745 

40.195 

% 

424.50 

822.58 

te 

.78540 

.06545 

% 

60.133 

43.847 

M 

433.73 

849.40 

9-16 

.99403 

.09319 

1^ 

63.617 

47.713 

% 

443.01 

876.79 

1.2272 

.12783 

% 

67.201 

51.801 

12. 

452.39 

904.78 

11-16 

1.4849 

.17014 

ax 

70:883 

56.116 

IX 

471.44 

962.52 

1.7671 

.22089 

% 

74.663 

60.663 

LJ£ 

490.87 

1022.7 

13-16 

2.0739 

.28084 

5. 

78.540 

65.450 

3X 

510.71 

1085.3 

2.4053 

.35077 

82.516 

70.482 

13. 

530.93 

1150.3 

15-16 

2.7611 

.43143 

IX 

86.591 

75.767 

14 

551.55 

1218.0 

1. 

3.1416 

.52360 

% 

90.763 

81.308 

vx 

572.55 

1288.3 

1-16 

3.5466 

.62804 

ix 

95.033 

87.113 

34 

593.95 

1361.2 

& 

3.9761 

.74551 

% 

99.401 

93.189 

14. 

615.75 

1436.8 

3-16 

4.4301 

.87681 

M 

103.87 

99.541 

/4 

637.95 

1515.1 

14 

4.9088 

1.0227 

7Z 

108.44 

106.18 

L<£ 

660.52 

1596.3 

5-16 

5.4119 

1.1839 

6. 

113.10 

113.10 

3X 

683.49    1680.3 

5.9396 

1.3611 

117.87 

120.31 

15. 

706.85 

1767.2 

7-16 

6.4919 

1.5553 

ixj 

122.72 

127.83 

M 

730.63 

1857.0 

7.0686 

1.7671 

% 

127.68 

135.66 

754.77 

1949.8 

9-16 

7.6699 

1.9974 

LXj 

132.73 

143.79 

M 

779.32 

2045.7 

8.2957 

2.2468 

% 

137.89 

152.25 

16. 

804.25 

2144.7 

11-16 

8.9461 

2.5161 

M 

143.14 

161.03 

/4 

829.57 

2246.8 

H 

9.6211 

2.8062 

7X 

148.49 

170.14 

Lj£ 

855.29 

2352.1 

13-16 

10.321 

3.1177 

7. 

153.94 

179.59 

^4 

881.42 

2460.6 

y» 

11.044 

3.4514 

Ys, 

159.49 

189.39 

17. 

907.93' 

2572.4 

15-16 

11.793 

3.8083 

165.13 

199.53 

J4 

934.83 

2687.6 

2. 

12.566 

4.1888 

% 

170.87 

210.03 

8 

962.12 

2806.2 

1-16 

13.364 

4.5939 

±£ 

176.71 

220.89 

989.80 

2928.2 

14.186 

5.0243 

% 

182.66 

232.13 

18. 

1017.9 

3053.6 

3-16 

15.033 

5.4809 

§4 

188.69 

243.73 

1046.4 

3182.6 

Y4 

15.904 

5.9641 

% 

194.83 

255.72 

Yz 

1075.2 

3315.3 

5-16 

16.800 

6.4751 

8. 

201.06 

268.08 

% 

1104.5 

3451.5 

3X 

17.721 

7.0144 

207.39 

280.85 

19. 

1134.1   J3591.4 

7-16 

18.666 

7.5829 

IX 

213.82 

294.01 

1164.2  13735.0 

^ 

19.635 

8.1813 

% 

220.36 

307.58 

i^ 

1194.6 

3882.5 

9-16 

20.629 

8.8103 

1X5 

226.98 

321.56 

M 

1225.4 

4033.7 

K£ 

21.648 

9.4708 

% 

233.71 

335.95 

20. 

1256.7 

4188.8 

11-16 

22.691 

10.164 

3X. 

240.53 

350.77 

IX 

1288.3 

4347.8 

M 

23.758 

10.889 

% 

247.45 

360.02 

Y> 

1320.3 

4510.9 

13-16 

24.850 

11.649 

9. 

254.47 

381.70 

3-4 

1352.7 

4677.9 

% 

25.967 

12.443 

Ys 

261.59 

397.83 

21.  ' 

1385.5 

4849.1 

15-16 

27.109 

13.272 

y 

268.81 

414.41 

/4 

1418.6 

5024.3 

3. 

28.274 

14.137 

% 

270.12 

431.44 

^ 

1452.2 

5203.7 

1-16 

29.465 

15.039 

14    283.53 

448.92 

M 

1486.2 

5387.4 

H 

30.680 

15.979 

% 

291.04 

466.87 

22. 

1520.5 

5575.3 

3-16  ^31.919 

16.957 

% 

298.65 

485.31 

y* 

1555.3 

5767.6 

SPHERES. 


119 


SPH  ERES— ( Continued.) 


Diam. 

Sur- 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Solid- 
ity. 

Diam. 

Sur- 
face. 

Solid- 
ity. 

22  Yz 

1590.4 

5964.1 

40  & 

5153.1 

34783 

70  ^ 

15615 

183471 

M 

1626.0 

6165.2 

41. 

5281.1 

36087 

71. 

15837 

187402 

23. 

1661.9 

637'0.6 

Yz 

5410.7 

37423 

Yz 

16061 

191389 

H 

1698.2 

6580.6 

42. 

5541.9 

38792 

72. 

16286 

195433 

x-2 

1735.0 

6795.2 

YZ 

5674.5 

40194 

H 

16513 

199532 

H 

1772.1 

7014.3 

43. 

5808.8 

41630 

73. 

16742 

203689 

24. 

1809.6 

7238.2 

H 

5944.7 

43099 

H 

16972 

207903 

H 

1847.5 

7466.7 

44. 

6082.1 

44602 

74. 

17204 

212175 

/^ 

1885.8 

7700.1 

Yz 

6221.2 

46141 

Yz 

17437 

216505 

M 

1924.4 

7938.3 

45. 

6361.7 

47713 

75. 

17672 

220894 

25. 

1963.5 

8181.3 

^ 

6503.9 

49321 

H 

17908 

225341 

\A 

2002.9 

8429.2 

46. 

6647.6 

50965 

76. 

18146 

229848 

Vz 

2042.8 

8682.0 

Yz 

6792.9 

52645 

Yz 

18386 

234414 

M 

2083.0 

8939.9 

47. 

6939.9 

54362 

77. 

18626 

239041 

26. 

2123.7 

9202.8 

^ 

7088.3 

56115 

H 

18869 

243728 

/4 

2164.7 

9470.8 

48. 

7238.3 

57906 

73. 

19114 

248475 

/^ 

2206.2 

9744.0 

H 

7389.9 

59734 

Ys 

19360 

253284 

M 

2248.0 

10022 

49. 

7543.1 

61601 

79. 

19607 

258155 

27. 

2290.2 

10306 

Yz 

7697.7 

63506 

^ 

19856 

263088 

M 

2332.8 

10595 

50. 

7854.0 

65450 

80. 

20106 

268083 

J* 

2375.8 

10889 

K 

8011.8 

67433 

H 

20358 

273141 

« 

2419.2 

11189 

51. 

8171.2 

69456 

81. 

20612 

278263 

28. 

2463.0 

11494 

X 

8332.3 

71519 

H 

20867 

283447 

x4 

2507.2 

11805 

52. 

8494.8 

73622 

82. 

21124 

288696 

3^2 

2551.8 

12121 

Y2 

8658.9 

757'67 

W 

21382 

294010 

M 

2596.7 

12443 

53. 

8824.8 

77952 

83. 

21642 

299388 

29. 

2642.1 

12770 

YQ 

8992.0 

80178 

^ 

21904 

304831 

y 

2687.8 

13103 

54. 

9160.8 

82448 

84. 

22167 

310340 

/^ 

2734.0 

13442 

Yz 

9331.2 

84760 

Yz 

22432 

315915 

ax 

2780.5 

13787 

55. 

9503.2 

87114 

85. 

22698 

321556 

30. 

2827.4 

14137 

H 

9676.8 

89511 

H 

22966 

327264 

/4 

2874.8 

14494 

56. 

9852.0 

91953 

86. 

23235 

333039 

i^ 

2922.5 

14856 

ft 

10029 

94438 

24 

23506 

338882 

M: 

2970.6 

15224 

57. 

10207 

96967 

87. 

23779 

344792 

31. 

3019.1 

15599 

K 

10387 

99541 

Yz 

24053 

350771 

M 

3068.0 

15979 

58. 

105C8 

102161 

88. 

24328 

356819 

3117.3 

16366 

& 

10751 

104826 

x1^ 

24606 

362935 

M 

3166.9 

16758 

59. 

10936 

107536 

89. 

24885 

369122 

32. 

3217.0 

17157 

& 

11122 

110294 

^ 

25165 

375378 

/4 

3267.4 

17563 

60. 

11310 

113098 

90. 

25447 

381704 

Yi 

3318.3 

17974 

tf 

11499 

115949 

& 

25730 

388102 

M 

3369.6 

18392 

61. 

11690 

118847 

91. 

26016 

394570 

33. 

3421.2 

18817 

& 

11882 

121794 

^ 

26302 

401109 

M 

3473.3 

19248 

62. 

1^076 

124789 

92. 

26590 

407721 

^ 

3525.7 

19685 

& 

12272 

127832 

^ 

2(5880 

414405 

M 

3578.5 

20129 

63. 

12469 

130925 

93. 

27172 

421161 

34. 

3631.7 

20580 

fcl 

12668 

134067 

^ 

27464 

427991 

M 

3685.3 

21037 

64. 

12868 

137259 

94. 

27759 

434894 

% 

3739.3 

21501 

H 

13070 

140501 

Yz 

28055 

441871 

35. 

3848.5 

22449 

65. 

13273 

143794 

95. 

28353 

448920 

fca 

3959.2 

23425 

*fi 

13478 

147138 

^ 

28652 

456047 

36. 

4071.5 

24429 

66. 

13685 

150533 

96. 

28953 

463248 

H 

4185.5 

25461 

^ 

13893 

153980 

Yz 

29255 

470524 

37. 

4300.9 

26522 

67. 

14103 

157480 

97. 

29559 

477874 

x4 

4417.9 

27612 

N 

14314 

161032 

M 

29865 

485302 

38. 

4536.5 

28731 

68. 

14527 

164637 

98. 

30172 

492808 

^ 

4656.7 

29880 

^ 

14741 

168295 

34 

30481 

500388 

39. 

4778.4 

31059 

69. 

14957 

172007 

99. 

30791 

508047 

^ 

4901.7 

32270 

K 

15175 

175774 

H 

31103 

515785 

40. 

5056.5 

33510 

70. 

15394 

179595 

100. 

31416 

523598 

120 


MATHEMATICAL   TABLES. 


CONTENTS  IN  CUBIC  FEET  AND  U.  S.  OALL.ONS  OF 
PIPES  AND  CYLINDERS  OF  VARIOUS  DIAMETERS 
AND  ONE  FOOT  IN  L.ENGTH. 

1  gallon  =  231  cubic  inches.    1  cubic  foot  =  7.4805  gallons. 


For  1  Foot  in 

For  1  Foot  in 

For  1  Foot  in 

.S 

Length. 

a 

Length. 

.£ 

Length. 

Diameter 
Inches. 

Cubic  Ft. 
also  Area 
in  Sq.  Ft. 

U.S. 
Gals., 
231 
Cu.  In. 

Diametei 
Inches, 

Cubic  Ft. 
also  Area 
in  Sq.  Ft. 

U.S. 

Gals., 
231 
Cu.  In. 

Diametei 
Inches. 

Cubic  Ft. 
also  Area 
in  Sq.  Ft. 

U.S. 
Gals., 
231 
Cu.  In. 

y± 

.0003 

.0025 

6% 

.2485 

1.859 

19 

1.969 

14.73 

5-16 

.0005 

.004 

.2673 

1.999 

1»& 

2.074 

15.51 

% 

.0008 

.0057 

7!4 

.28(57 

2.145 

20 

2.182 

16.32 

7-16 

.001 

.0078 

7^2 

.3068 

2.295 

20J4 

2.292 

17.15 

X 

,0014 

.0102 

7^ 

.3276 

2.45 

21 

2.405 

17.99 

9-16 

.0017 

.0129 

8 

.3491 

2.611 

21W 

2.521 

18.86 

% 

.0021 

.0159 

m 

.3712 

2.777 

22 

2.640 

19.75 

11-16 

.0026 

.0193 

.3941 

2.948 

22^2 

2.761 

20.66 

% 

.0031 

.0230 

8fy± 

.4176 

3.125 

23 

2.885 

21.58 

13-16 

.0036 

.0269 

9' 

.4418 

3.305 

23J4 

3.012 

22.53 

Vs 

.0042 

.0312 

SM 

.4667 

3.491 

24 

3.142 

23.50 

15-16 

.0048 

.0359 

w* 

.4922 

3.682 

25 

3.409 

25.50 

1 

.0055 

.0408 

w 

.5185 

3.879 

26 

3.687 

27.58 

.0085 

.0638 

10 

.5454 

4.08 

27 

3.976 

29.74 

1}| 

.0123 

.0918 

10M 

.5730 

4.286 

28 

4.276 

31.99 

w± 

.0167 

.1249 

10V6 

.6013 

4.498 

29 

4.587 

34.31 

24 

.0218 

.1632 

log 

.6303 

4.715 

30 

4.909 

36.72 

®A 

.0276 

.2066 

11 

.66 

4.937 

31 

5.241 

39.21 

.0341 

.2550 

1114 

.6903 

5.164 

32 

5.585 

41.78 

2% 

.0412 

.3085 

n}4 

.7213 

5.396 

33 

5.940 

44.43 

3 

.0491 

.3672 

11% 

.7530 

5.633 

34 

6.305 

47.16 

.0576 

.4309 

12 

.7854 

5.875 

35 

6.681 

49.98 

3y^2 

.0668 

.4998 

i'4£ 

.8522 

6.375 

36 

7.069 

52.88 

3*M 

.0767 

.5738 

13 

.9218 

6.895 

37 

7.467 

55.86 

4 

.0873 

.6528 

13^ 

.994 

7.436 

38 

7.876 

58.92 

4J4 

.0985 

.7369 

14 

1.069 

7.997 

39 

8.296 

62.06 

4V£ 

.1134 

.8263 

14^ 

1  147 

8.578 

40 

8.727 

65.28 

434 

.1231 

.9206 

15 

.227 

9.180 

41 

9.168 

68.58 

5 

.1364 

1.020 

15^ 

.310 

9.801 

42 

9.6-21 

71.97 

5M 

.1503 

1.125 

16 

.396 

10.44 

43 

10.085 

75.44 

5J4 

.1650 

1.234 

W/2 

.485 

11.11 

44 

10.559 

78.99 

5% 

.1803 

1.349 

17 

.576 

11.79 

45 

11.045 

82.62 

6 

.1963 

1.469 

17^8 

.670 

12.49 

46 

11.541 

86.33 

6^4 

.2131 

1.594 

18 

.768 

13.22 

47 

12.048 

90.13 

3 

.2304 

1.724 

18^ 

.867 

13.96 

48 

12.566 

94.00 

To  find  the  capacity  of  pipes  greater  than  the  largest  given  in  the  table, 
look  in  the  table  for  a  pipe  of  one  half  the  given  size,  and  multiply  its  capac- 
ity by  4;  or  one  of  one  third  its  size,  and  multiply  its  capacity  by  9,  etc. 

To  find  the  weight  of  water  in  any  of  the  given  sizes  multiply  the  capacity 
in  cubic  feet  by  62^  or  the  gallons  by  8^,  or,  if  a  closer  approximation  is 
required,  by  the  weight  of  a  cubic  foot  of  water  at  the  actual  temperature  in 
the  pipe. 

Given  the  dimensions  of  a  cylinder  in  inches,  to  find  its  capacity  in  U.  S. 
gallons:  Square  the  diameter,  multiply  by  the  length  and  by  .0034.  If  d  ^~- 

rJi  v    7854  V  7 
diameter,  I  -  length,  gallons  =  —.   —'^  —  —  =  .0034d2Z. 


CAPACITY   OF   CYLINDKICAL   VESSELS. 


121 


CYLINDRICAL   VESSELS,   TANKS,   CISTERNS,   ETC. 

Diameter  in  Feet  and  Inches,  Area   in  Square  Feet,  and 
U.  S.  Gallons  Capacity  for  One  Foot  in  Depth. 


1  gallon  =  231  cubic  inches  = 


7.4805 


=  0.13368  cubic  feet. 


Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Diam. 

Area. 

Gals. 

Ft.  In. 

Sq.  ft. 

1  foot 
depth. 

Ft.  In. 

Sq.  ft. 

1  foot 
depth. 

Ft.  In. 

Sq.  ft. 

1  foot 
depth. 

1 

.785 

5.87 

5    8 

25.22 

18866 

19 

283.53 

2120.9 

1     1 

.922 

6.89 

5    9 

25.97 

194.25 

19    3 

291.04 

2177.1 

1    2 

.0(39 

8.00 

5  10 

26.73 

199.92 

19    6 

298.65 

2234.0 

1    3 

.227 

9.18 

5  11 

27.49 

205.67 

19    9 

306.35 

2291.7 

1     4 

.396 

10.44 

6 

28.27 

211.51 

20 

314.16 

2350.1 

1    5 

.576 

11.  19 

6    3 

30.68 

229.50 

20    3 

322.06 

2409.2 

1     6 

.767 

13.22 

6    6 

33.18 

248.23 

20    6 

330.06 

2469.  1 

1    7 

1.909 

14.73 

6    9 

35.78 

267.69 

20    9 

33816 

2529.6 

1    8 

2.182 

16.32 

7 

38.48 

287.88 

21 

34636 

2591.0 

1     9 

2.405 

1799 

7    3 

41.28 

308.81 

21    3 

354.66 

2653.0 

1  10 

2.640 

19.75 

7    6 

44.18 

330.43 

21    6 

363.05 

2715.8 

1  11 

2.885 

21.58 

7    9 

47.17 

352.88 

21    9 

371.54 

2779.3 

2 

3.142 

23.50 

8 

50.27 

376.01 

22 

380.13 

2843.6 

2    1 

3.409 

25.50 

8    3 

53.46 

399.88 

22    3 

388.82 

2908.6 

2    2 

3.687 

27.58 

8    6 

56.75 

424.48 

22    6 

397.61 

2974.3 

2    3 

3.976 

29.74 

8    9 

60.13 

449.82 

22    9 

406.49 

3040.8 

2    4 

4.276 

31.99 

9 

6362 

475.89 

23 

415.48 

3108.0 

2    5 

4.587 

3431 

9    3 

6720 

502.70 

23    3 

424.56 

3175.9 

2    6 

4.909 

36.72 

9    6 

70.88 

53024 

23    6 

433.74 

3244.6 

2    7 

5.241 

39.21 

9    9 

74.66 

558.51 

23    9 

44301 

33140 

2    8 

5.585 

41.78 

10 

78.54 

587.52 

24 

452.39 

3384.1 

2    9 

5.940 

44.43 

10    3 

82.52 

617.26 

24    3 

461.86 

3455.0 

2  10 

6.305 

47.16 

10    6 

86.59 

647.74 

24    6 

471.44 

3526.6 

2  11 

6.681 

49.98 

10    9 

90.76 

678.95 

24    9 

481.11 

3598.9 

3 

7.069 

5288 

11 

95.03 

710.90 

25 

490.87 

3672.0 

3    1 

7.467 

55.86 

11    3 

99.40 

743.58 

25    3 

500.74 

3745.8 

3    2 

7.876 

58.92 

11    6 

10387 

776.99 

25    6 

510.71 

38203 

3    3 

8.296 

62.06 

11    9 

108.43 

811.14 

25    9 

520.77 

3895.6 

3    4 

8.727 

65.28 

12 

113.10 

846.03 

26 

530.93 

3971.6 

3    5 

9.168 

68.58 

12    3 

117.86 

881.65 

26    3 

541.19 

4048.4 

3    6 

9.621 

71.97 

12    6 

122.72 

918.00 

26    6 

551.55 

4125.9 

3    7 

10.085 

75.44 

12    9 

127.68 

95509 

26    9 

562.00 

4204.1 

3    8 

10.559 

78.99 

13 

132.73 

992.91 

27 

572.56 

4283.0 

3    9 

11.045 

8262 

13    3 

137.89 

1031.5 

27    3 

583.21 

4362.7 

3  10 

11.541 

86.33 

13    6 

143.14 

1070.8 

27    6 

593.96 

4443.1 

3  11 

12.048 

90.13 

13    9 

148.49 

1110.8 

27    9 

604.81 

4524.3 

4 

12.566 

94.00 

14 

153.94 

1151.5 

28 

615.75 

4606.2 

4    1 

13.095 

97.96 

14    3 

159.48 

1193.0 

28    3 

626.80 

4688.8 

4    2 

13.635 

102.00 

14    6 

165.13 

1235.3 

28    6 

637.94 

47721 

4    3 

14.186 

106.12 

14    9 

170.87 

1278.2 

28    9 

649.18 

4856.2 

4    4 

14.748 

110.32 

15 

176.71 

1321.9 

29 

660.52 

4941.0 

4    5 

15.321 

114.61 

15    3 

18265 

1366.4 

29    3 

671.96 

5026.6 

4    6 

15.90 

118.97 

15    6 

188.69 

1411.5 

29    6 

683.49 

5112.9 

4    7 

16.50 

123.42 

15    9 

194.83 

1457.4 

29    9 

695.13 

5199.9 

4    8 

17.10 

127.95 

16 

201.06 

1E04.1 

30 

706.86 

5287.7 

4    9 

17.72 

132.56 

16    3 

207.39 

1551.4 

30    3 

718.69 

5376.2 

4  10 

18.35 

137.25 

16    6 

213  82 

1599.5 

30    6 

730.62 

54654 

4  11 

18.99 

14202 

16    9 

220.35 

1648.4 

30    9 

742.64 

5555.4 

5 

19.63 

146.88 

17 

2'<?6.98 

1697.9 

31 

754.77 

5646.1 

5    1 

20.29 

151.82 

17    3 

^.'33.71 

1748.2 

31    3 

766.99 

5737.5 

5    2 

20.97 

156.83 

17    6 

240.53 

1799.3 

31    6 

779.31 

5829.7 

5    3 

21.65 

161.93 

17    9 

247.45 

1851.1 

31     9 

791.73 

5922.6 

5    4 

22.34 

167.12 

18 

25447 

1903.6 

32 

804  ^'5 

6016.2: 

5    5 

23.04 

1  72.  38 

18    3 

261.59 

1956.8 

32    3 

816.86 

6110.6 

5    6 

23.76 

177.72 

18    6 

268.80 

2010.8 

32    6 

829.58 

6205.7 

5    7 

24.48 

183.15 

18    9 

276.12 

2065.5 

32    9 

842.39 

6301.5 

122 


MATHEMATICAL 


GALLONS  AND  CUBIC   FEET. 
United  States  Gallons  in  a  given  Number  of  Cubic  Feet. 

1  cubic  foot  =  7.480519  U.  S.  gallons;  1  gallon  =  231  cu.  in.  =  .13368056  cu.  ft. 


Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

0.1 

0.75 

50 

374.0 

8.000 

59,844.2 

02 

1.50 

60 

448.8 

9,000 

67,324.7 

0.3 

2.24 

70 

528.6 

10,000 

74,805.2 

0.4 

2.99 

80 

598.4 

20,000 

149,610.4 

0.5 

3.74 

90 

673.2 

30,000 

224,415.6 

0.6 

4.49 

100 

748.0 

40,000 

299,220.8 

0.7 

5.24 

200 

1,496.1 

50,000 

374,025.9 

0.8 

5.98 

300 

2,244.2 

60,000 

448,831.1 

0.9 

6.73 

400 

2,992.2 

70,000 

523,636.3 

1 

7.48 

500 

3,740.3 

80,000 

598,441.5 

2 

14.96 

600 

4,488.3 

90,000 

673,246.7 

3 

22.44 

700 

5,236.4 

100,000 

748,051.9 

4 

29.92 

800 

5,984.4 

200,000 

1,496,103.8 

5 

37.40 

900 

6,732.5 

300,000 

2,244,155.7 

6 

44.88 

1,000 

7,480.5 

400,000 

2,992,207.6 

7 

52.36 

2,000 

14,961.0 

500,000 

3,740,259.5 

8 

59.84 

3,000 

22,441.6 

600,000 

4,488,311.4 

9 

67.32 

4,000 

29,922.1 

700.000 

5.236,363  3 

10 

74.80 

5,000 

37,402.6 

800,(NK) 

5,984,415.2 

20 

149.6 

6,000 

44,883.1 

900,000 

6,732,467.1 

30 

224.4 

7,000 

52,363.6 

1,000,000 

7,480,519.0 

40 

299.2 

Cubic  Feet  in  a  given  Number  of  Gallons. 


Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

Gallons. 

Cubic  Ft. 

1 

.134 

1,000 

133.681 

1  ,000,000 

133,680.6 

2 

.267 

2,000 

267.361 

2,000,000 

267,361.1 

3 

.401 

3,000 

401.042 

3,000,000 

401,041.7 

4 

.535 

4,000 

534.722 

4,000,000 

534,722.2 

5 

.668 

5,000 

668.403 

5,000,000 

668,402.8 

6 

.802 

6,000 

802.083 

6,000,000 

802,0833 

y 

.936 

7,000 

935.764 

7,000,000 

935,763.9 

8 

1.069 

8,000 

1,069.444 

8,000,000 

1,069,444.4 

9 

1.203 

9,000 

1,203.125 

9,000,000 

1,203,125.0 

10 

1.337 

10,000 

1,336.806 

10,000,000 

1,336,805.6 

NUMBER   OF   SQUAItE   FEET   IN    PLATES. 


123 


NUMBER    OF    SQUARE   FEET  IN   PIRATES  3   TO  32 
FEET   LONG,    AND   1   INCH   WIDE. 

For  other  widths,  multiply  by  the  width  in  inches.     1  sq.  in.  —  .00690  sq.  ft. 


Ft,  and 
In. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

3.    0 

36 

.25 

7.10 

94 

.6528 

13.  8 

152 

1.056 

1 

37 

.*2569 

11 

95 

.6597 

9 

153 

1.063 

2 

38 

.2639 

8.  0 

96 

.6667 

10 

154 

1.069 

3 

39 

.2708 

1 

97 

.6736 

11 

155 

1.076 

4 

40 

.2778 

2 

98 

.6806 

13.  0 

156 

1.083 

5 

41 

.2847 

3 

99 

.6875 

1 

157 

1.09 

G 

42 

.2917 

4 

100 

.6944 

2 

158 

1.097 

7 

43 

.2986 

5 

101 

.7014 

3 

159 

1.104 

8 

44 

.3056 

6 

102 

.7083 

4 

160 

1.114 

9 

45 

.3125 

7 

103 

.7153 

5 

161 

1.118 

10 

46 

.3194 

8 

104 

.7222 

6 

162 

1.125 

11 

47 

.3264 

9 

105 

.7292 

7 

163 

1.132 

4.    0 

48 

.3333 

10 

106 

.7361 

8 

164 

1  .  139 

1 

49 

.3403 

11 

107 

.7431 

9 

165 

1.146 

2 

50 

.3472 

9.  0 

108 

.75 

10 

166 

1.153 

3 

51 

.3542 

1 

109 

.7569 

11 

167 

1.159 

4 

52 

.3611 

2 

110 

.7639 

14.0 

168 

1.167 

5 

53 

.3681 

3 

111 

.7708 

1 

169 

1.174 

6 

54 

.375 

4 

112 

.7778 

2 

170 

1.181 

7 

55 

.3819 

5 

113 

.7847 

3 

171 

1.188 

8 

56 

.3889 

6 

114 

.7917 

4 

172 

1.194 

9 

57 

.3958 

7 

115 

.7986 

5 

173 

1.201 

10 

58 

.4028 

8 

116 

.8056 

6 

174 

1.208 

11 

59 

.4097 

9 

117 

.8125 

7 

175 

1.215 

5.    0 

60 

.4167 

10 

118 

.8194 

8 

176 

1.222 

1 

61 

.4236 

11 

119 

.8264 

9 

177 

1.229 

2 

62 

.4306 

10.0 

120 

.8333 

10 

178 

1.236 

3 

63 

.4375 

1 

121 

.8403 

11 

179 

.243 

4 

64 

.4444 

2 

122 

.8472 

15.  0 

180 

.25 

5 

65 

.4514 

3 

123 

.8542 

1 

181 

.257 

6 

66 

.4583 

4 

124 

.8611 

2 

182 

.264 

7 

67 

.4653 

5 

125 

.8681 

3 

183 

.271 

8 

68 

4722 

6 

126 

.875 

4 

184 

.278 

9 

69 

!4792 

7 

127 

.8819 

5 

185 

.285 

10 

70 

.4861 

8 

128 

.8889 

6 

186 

.292 

11 

71 

.4931 

9 

129 

.8958 

7 

187 

.299 

6.    0 

72 

.5 

10 

130 

.9028 

8 

188 

.306 

1 

73 

.5069 

11 

131 

.9097 

9 

189 

.313 

2 

74 

.5139 

11.0 

132 

.9167 

10 

190 

.319 

3 

75 

.5208 

1 

133 

.9236 

11 

191 

.326 

4 

76 

5278 

2 

134 

.  9306 

16.0 

192 

.333 

5 

77 

'.5347 

3 

135 

.9375 

1 

193 

.34 

6 

78 

.5417 

4 

136 

.9444 

2 

194 

.347 

7 

79 

.5486 

5 

137 

.9514 

3 

195 

.354 

8 

80 

.5556 

6 

138 

.9583 

4 

196 

361 

9 

81 

.5625 

7 

139 

.9653 

5 

197 

.368 

10 

82 

.5694 

8 

140 

.9722 

6 

198 

.375 

11 

83 

.5764 

9 

141 

.9792 

7 

199 

.382 

7.    0 

84 

.5834 

10 

142 

.9861 

8 

200 

.389 

1 

85 

.5903 

11 

143 

.9931 

9 

201 

.396 

2 

86 

.5972 

12.0 

144 

.000 

10 

202 

.403 

3 

87 

.6042 

1 

145 

.007 

11 

203 

.41 

4 

88 

.6111 

2 

146 

.014 

17.0 

201 

.417 

5 

89 

.6181 

3 

147 

.021 

1 

205 

.424 

6 

90 

.625 

4 

148 

.028 

2 

206 

.431 

7 

91 

.6319 

5 

149 

.035 

3 

207 

.438 

8 

92 

.6389 

6 

150 

.042 

4 

208 

.444 

9 

93 

.6458 

7 

151 

049 

5 

209 

.451 

124 


MATHEMATICAL   TABLES. 


SQUARE  FEET  IN 


-(Continued.) 


Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 

Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

Ft.  and 
Ins. 
Long. 

Ins. 
Long. 

Square 
Feet. 

17.  G 

210 

1.458 

22.5 

269 

1.868 

27.4 

328 

2.278 

7 

211 

1.465 

6 

270 

1.875 

5 

329 

2.285 

8 

212 

1.472 

7 

271 

1.882 

6 

330 

2.292 

9 

213 

1.479 

8 

272 

1.889 

7 

331 

2.299 

10 

214 

1.486 

9 

273 

1.896 

8 

332 

2.306 

11 

215 

1.493 

10 

274 

1.903 

9 

333 

2.313 

18.  0 

216 

1.5 

11 

275 

1.91 

10 

334 

2.319 

1 

217 

1.507 

33.  0 

276 

1.917 

11 

335 

2.326 

2 

218 

1.514 

1 

277 

1.924 

28.0 

336 

2.333 

3 

219 

1.521 

2 

278 

1.931 

1 

337 

2.34 

4 

220 

1.528 

3 

279 

1.938 

2 

338 

2.347 

5 

221 

1.535 

4 

280 

1.944 

3 

339 

2.354 

6 

222 

1.542 

5 

281 

1.951 

4 

340 

2.361 

7 

223 

1.549 

6 

282 

1.958 

5 

341 

2.368 

8 

224 

1.556 

7 

283 

1.965 

6 

342 

2.375 

9 

225 

1.563 

8 

284 

1.972 

7 

343 

2.382 

0 

226 

1.569 

9 

285 

1.979 

8 

344 

2.389 

11 

227 

1.576 

10 

286 

1.986 

9 

345 

2.396 

19.0 

228 

1.583 

11 

287 

1  993 

10 

346 

2.403 

1 

229 

1.59 

24.0 

288 

2 

11 

347 

2.41 

2 

230 

1.597 

1 

289 

2^007 

29.  0 

348 

2.417 

3 

231 

1.604 

2 

290 

2.014 

1 

349 

2.424 

4 

232 

1.611 

3 

291 

2.021 

2 

350 

2.4fl 

5 

233 

1.618 

4 

292  )      2  028 

3 

351 

2.438 

6 

234 

1.6-25 

5 

293 

2.035 

4 

352 

2.444 

7 

235 

1.632 

6 

294 

2.042 

5 

353 

2.451 

8 

236 

1.639 

7 

295 

2.049 

6 

354 

2.458 

9 

237 

1.645 

8 

296 

2.056 

7 

355 

2.465 

10 

238 

1.653 

9 

297 

2  063 

8 

356 

2.472 

11 

239 

1.659 

10 

298 

2.069 

9 

357 

2.473 

20.0 

240 

1.667 

11 

299 

2.076 

10 

358 

2.486 

1 

241 

1.674 

25.0 

300 

2.083 

11 

359 

2.4S3 

2 

242 

1.681 

1 

301 

2.09 

30.  0 

360 

2.5 

3 

243 

1.688 

2 

302 

2.097 

1 

361 

2.50T 

4 

244 

1.694 

3 

303 

2.104 

2 

362 

2.514 

5 

245 

1.701 

4 

304 

2.111 

3 

363 

2.521 

6 

246 

1.708 

5 

305 

2.118 

4 

364 

2.528 

7 

247 

1.715 

6 

306 

2.125 

5 

365 

2.535 

8 

248 

1.722 

7 

307 

2.132 

6 

366 

2.542 

9 

249 

1.729 

8 

308 

2.139 

7 

367 

2.549 

10 

250 

1.736 

9 

309 

2.146 

8 

368 

2.556 

11 

251 

1.743 

10 

310 

2.153 

9 

369 

2.563 

21.0 

252 

1.75 

11 

311 

2.16 

10 

370 

2.569 

1 

253 

1.757 

26.  0 

312 

2.167 

11 

371 

2.576 

2 

254 

1.764 

1 

313 

2.174 

31.0 

372 

2.583 

3 

255 

1  771 

2 

314 

2.181 

1 

373 

2.59 

4 

256 

1.778 

3 

315 

2.188 

2 

374 

2.597 

5 

257 

J.785 

4 

316 

2.194 

3 

375 

2.604 

6 

258 

1.792 

5 

317 

2.201 

4 

376 

2.611 

7 

259 

1.799 

6 

318 

2.208 

5 

377 

2.618 

8 

260 

1.806 

7 

319 

2.215 

6 

378 

2.625 

9 

261 

1.813 

8 

3*0 

2  222 

7 

379 

2.632 

10 

262 

1.819 

9 

321 

2.229 

8 

380 

2.639 

11 

263 

1.826 

10 

322 

2.236 

9 

381 

2.646 

22.0 

264 

1.833 

11 

323 

2  243 

10 

382 

2  653 

1 

265 

1.84 

27.0 

324 

2.25 

11 

383 

2.66 

'   2 

266 

1.847 

1 

325 

2.257 

32.0 

384 

2.667 

3 

267 

1.854 

2 

326 

2.264 

1 

385 

2.674 

4 

268 

1.861 

3 

327 

2.271 

2 

386 

2.681 

CAPACITY    OF    RECTANGULAR   TANKS. 


CAPACITIES    OF    RECTANGULAR    TANKS    IN    U. 
GALLONS,    FOR    EACH    FOOT    IN    DEPTH. 

1  cubic  foot  =  7.4805  U.  S.  gallons. 


S. 


Width 
of 
Tank. 

Length  of  Tank. 

feet. 
2 

ft.  in. 
2    6 

feet. 
3 

ft.  in. 
3  6 

feet. 
4 

ft.  in. 
4    C 

feet. 
5 

ft.  in. 
5  6 

feet. 
6 

ft.  in. 
6    6 

feet. 

7 

ft.   in. 

2      G 
3 
3      6 
4 

4      6 
5 
5      6 
6 
6      6 

7 

29.92 

37.40 

46.75 

44.88 
56.10 
67.32 

52.36 
65.45 

78.54 
91.64 

59.84 

74.80 
89.77 
104.73 
119.69 

67.32 

84.16 
100.99 
117.82 
134.65 

151.48 

74.81 
93.51 

112.21 
130.91 
149.61 

168.31 
187.01 

82.29 
102.86 
123.43 
144.00 
164.57 

185.14 
205.71 
22628 

89.7' 
112.2 
.134.6.' 
157.0< 
179.5; 

201.9' 
224.4 
246.8( 
269.3( 

f    97.25 
121.56 
>  145.87 
)  170.18 
J  194.49 

v  218.80 
L  243.11 
5  267.43 
)  291.  74 
316.05 

104,73 
130.91 
157.09 
183.27 
209.45 

235.63 

261.82 
288.00 
314.18 
340.36 

366  54 

Width 
of 
Tank. 

Length  of  Tank. 

ft.  in. 
7      6 

feet. 

8 

ft.  in. 
8    6 

feet. 
9 

ft.  in. 
9  6 

feet. 
10 

ft.  in. 
10  6 

feet. 
11 

ft.  in. 
11    6 

feet. 
12 

ft.   in. 
2 
2      6 
3 
3      6 
4 

4      6 
5 
5      6 
G 
G      6 

7      6 

8 
8      6 
9 

8      6 

10 
10      6 
•il 
11      6 

12 

112.21 
140.26 
168.31 
196.36 
224.41 

252.47 
280.52 
308.57 
336.62 
364.67 

39272 

420.78 

119.69 
149.61 
179.53 
209.45 
239.37 

269.30 
299.22 
329.14 
359.0  5 

388.98 

418.91 

448.83 
478.75 

127.17 
158.96 
190.75 
222.54 
254.34 

286.13 
317.92 
349.71 
381.50 
413.30 

44509 

476.88 
508.67 
540.46 

134.65 

168.31 
202.97 
235.63 
269.30 

302.96 
336.62 
370.28 
403.94 
437.60 

471.27 
504.93 
538.59 
57'2.25 
605.92 

142.13 

177.66 
213.19 
248.73 
284.26 

319.79 
355.32 
390.85 
426.39 
461.92 

497.45 
532.98 
568.51 
604.05 
639.58 

675.11 

149.61 
187.01 
22441 
261.82 
299.22 

336.62 
374.03 
411.43 

448.83 
486.23 

523.64 
561.04 
598.44 
635.84 
673.25 

710.65 
748.05 

157.09 
196.36 
235.63 
274.90 

314.18 

353.45 
392.72 
432.00 
471.27 
510.54 

549.81 
589.08 
628.36 
66763 
706.90 

746.17 
785.45 
824.73 

164.57 
205.71 
246.86 
288.00 
329.14 

370.28 
411.43 
452.57 
493.71 
534.85 

575.99 
617.14 
658.28 
699.42 
740.56 

781.71 
822.86 
864.00 
905.14 

172.05 
215.06 
258.07 
301.09 
344.10 

387.11 
430.13 
473.14 
516.15 
559.16 

602.18 
645.19 
688.20 
731.21 
774.23 

817.24 
860.26 
903.26 
946.27 
989.29 

179.53 
224.41 
269.30 
314.18 
359.06 

403.94 

448.83 
493.71 
538.59 
583.47 

628  36 
673.24 
718.12 
763.00 
807.89 

852.77 
897.66 
942.56 
987.43 
1032.3 

1077.2 

126 


MATHEMATICAL   TABLES. 


NUMBER  OF   BARRELS  (31    1-2  GALLONS)  IN 

CISTERNS  AND  TANKS. 

SI  5  V  231 
1  Barrel  =  31^  gallons  =     '    *    '    =  4.21094  cubic  feet.    Reciprocal  =  .23?4?7C 


Depth 

Diameter  in  Feet. 

in 
Feet. 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1 

4.663 

6.714 

9.139 

11.93' 

'  15.108 

18.652 

22.569 

20.859 

31.522 

36.557 

5 

23.3 

33.6 

45.7 

59.7 

75.5 

93.3 

112.8 

134.3 

157.6 

182.8 

6 

28.0 

40.3 

54.8 

71.6 

90.6 

111.9 

135.4 

161.2 

189.1 

219.3 

7 

32.6 

47.0 

64.0 

83.6 

105.8 

130.6 

158.0 

188.0 

220.7 

255.9 

8 

37.3 

53.7 

73.1 

95.5 

120.9 

149.2 

180.6 

214.9 

252.2 

292.5 

9 

42.0 

60.4 

82.3 

107.4 

136.0 

167.9 

203.1 

241.7 

283.7 

329.0 

10 

46.6 

67.1 

91.4 

119.4 

151.1 

186.5 

225.7 

268.6 

315.2 

365.6 

11 

51.3 

73.9 

100.5 

131.3 

166.2 

205.2 

248  3 

295.4 

346.7 

402.1 

12 

56.0 

80.6 

109.7 

143.2 

181.3 

223.8 

270.8 

322.3 

378.3 

438.7 

13 

60.6 

87.3 

118.8 

155.2 

196.4 

242.5 

293.4 

349.2 

409.8 

475.2 

14 

65.3 

94.0 

127.9 

167.1 

211.5 

261.1 

316.0 

376.0 

441.3 

511.8 

15 

69.9 

100.7 

137.1 

179.1 

226.6 

289.8 

338.5 

402.9 

472.8 

548.4 

16 

74.6 

107.4 

146.2 

191.0 

241.7 

•J98.4 

361.1 

429.7 

504.4 

584.9 

17 

79.3 

114.1 

155.4 

202.9 

256.8 

317.1 

383.7 

456.6 

535.9 

021  .5 

18 

83.9 

120.9 

164.5 

214.9 

271.9 

335.7 

406.2 

483.5 

567.4 

058.0 

19 

88.6 

127.6 

173.6 

226.8 

287.1 

354.4 

428.8 

510.3 

598.9 

694.6 

20 

93  3 

134.3 

182.8 

238.7 

302.2 

373.0 

451.4 

537.2 

030.4 

731.1 

Depth 

Diameter  in  Feet. 

in 
Feet. 

lo 

16 

17 

18 

19 

20 

21 

22 

1 

41.966 

47.748 

53.903 

60.431 

67.332!     74.606 

82.253 

90.273 

5 

209.8 

238.7 

269.5 

302.2 

336.7 

373.0 

411.3 

451.4 

6 

251.8 

286.5 

323.4 

362  6 

404.0 

447.6 

493.5 

541.6 

7 

293.8 

334  2 

377.3 

423.0 

471.3 

522.2 

575.8 

631.9 

8 

335.7 

382.0 

431.2 

483.4 

538.7 

596.8 

658.0 

722.2 

9 

377.7 

429.7 

485  1 

543.9 

606.0 

671.5 

740.3 

812.5 

10 

419.7 

477.5 

539.0 

004.3 

673.3 

740.1 

822  '.5 

902.7 

11 

481.6 

525.2 

592.9 

664.7 

740.7 

8-20.7 

904.8 

993.0 

12 

503.6 

573.0 

040.8 

725.2 

808.0 

895.3 

987.0 

1083.3 

13 

545.6 

620.7 

7'00.7 

785.6 

875.3 

969.9 

1009.3 

1173.5 

14 

587.5 

668.5 

754.6 

846.0 

942.6 

1044.5 

1151.5 

1203.8 

15 

629.5 

716.2 

808.5 

906.5 

101.0.0 

1119.1 

1233.8 

1354.1 

16 

671.5 

764.0 

862.4 

966.9 

1077.3 

1193.7 

1310.0 

1444.4 

17 

713.4 

811.7 

916.4 

1027.3 

1144.6 

1268.3 

1398.3 

1534.5 

18 

755.4 

859.5 

970.3 

1087.8 

1212.0 

1342.9 

1480.6 

1024.9 

19 

797.4 

907.2 

1024.2 

1148.2 

1279.3 

1417.5 

1562.8 

1715.2 

20 

839.3 

955.0 

1078.1 

1208.6 

1346.0 

1492.1 

1045.1 

1805.5 

LOGARITHMS. 


127 


NUMBER    OF    BARRELS    (31    1-2  GALLONS) 
CISTERNS    AND    TANKS.—  Continued. 


IN 


Depth 
in 
Feet. 

Diameter  in  Feet. 

23 

24 

25 

26 

27 

28 

29 

30 

1 

98.666 

107.432 

116.571 

126.083 

135.968 

146.226 

157.858 

167.88? 

5 

493.3 

537.2 

582.9 

630.4 

679.8 

731.1 

784.3 

839.3 

6 

592  0 

644.6 

699.4 

756.5 

815.8 

877.4 

941.1 

1007.2 

7 

690.7 

752.0 

816.0 

882.6 

951.8 

1023.6 

1098.0 

1175.0 

8 

789.3 

859.5 

932.6 

1008.7 

1087.7 

1169.8 

1254.9 

1342.9 

9 

888.0 

9S6.9 

1049.1 

1134.7 

1223.7 

1316.0 

1411.7 

1510.8 

10 

986.7 

1074.3 

1165.7 

1260.8 

1359.7 

1462.2 

1568.6 

1678  6 

11 

1085.3 

1181.8 

1282.3 

1386.9 

1495.6 

1608.5 

1725.4 

1846.5 

33 

1184.0 

1289.2 

1398.8 

1513.0 

1631.6 

1754.7 

1882.3 

2014.4 

13 

1282.7 

1396.6 

1515.4 

1639.1 

1767.6 

1900.9 

2039.2 

2182.2 

14 

1381.  3 

1504  0 

1632.0 

1765.2 

1903.6 

2047.2 

2196.0 

2350.1 

15 

1480.0 

1611.5 

1748.6 

1891.2 

2039.5 

2193.4 

2352.9 

2517.9 

16 

1578.7 

1718.9 

1865.1 

2017.3 

2175.5 

2339.6 

2509.7 

2685.8 

17 

1677.3 

1826.3 

1981.7 

2143.4 

2311.5 

2485.8 

2666.6 

2853.7 

18 

1776.0 

1933.8 

2098.3 

2269.5 

2447.4 

2632.0 

2823.4 

3021.5 

19 

1874.7 

2041.2 

2214.8 

2395.6 

2583.4 

2778.3 

2980.3 

3189.4 

20 

1973.3 

2148.6 

2321.4 

2521.7 

2719.4 

2924.5 

3137.2 

3357.3 

LOGARITHMS. 

Logarithms  (abbreviation  log}.— The  log  of  a  number  is  the  exponent 
of  the  power  to  which  it  is  necessary  to  raise  a  fixed  number  to  produce  the 
given  number.  The  fixed  number  is  called  the  base.  Thus  if  the  base  is  10, 
the  log  of  1000  is  3,  for  10s  =  1000.  There  are  two  systems  of  logs  in  general 
use,  the  common,  in  which  the  base  is  10,  and  the  Naperian,  or  hyperbolic, 
in  which  the  base  is  2.7182818.28  ....  The  Naperian  base  is  commonly  de- 
noted by  e,  as  in  the  equation  ey  =  x,  in  which  y  is  the  Nap.  log  of  x. 

In  any  system  of  logs,  the  log  of  1  is  0;  the  log  of  the  base,  taken  in  that 
system!  is  1.  In  any  system  the  base  of  which  is  greater  than  1,  the  logs  of 
a'll  numbers  greater  than  1  are  positive  and  the  logs  of  all  numbers  less  than 
1  are  negative. 

The  modulus  of  any  system  is  equal  to  the  reciprocal  of  the  Naperian  log 
of  the  base  of  that  system.  The  modulus  of  the  Naperian  sj'stem  is  1,  that 
of  the  common  system  is  .4342945. 

The  log  of  a  number  in  any  system  equals  the  modulus  of  that  system  X 
the  Naperian  log  of  the  number. 

The  hyperbolic  or  Naperian  log  of  any  number  equals  the  common  log 
X  2.3025851. 

Every  log  consists  of  two  parts,  an  entire  part  called  the  characteristic,  or 
index,  and  the  decimal  part,  or  mantissa.  The  mantissa  only  is  given  in  the 
usual  tables  of  common  logs,  with  the  decimal  point  omitted.  The  charac- 
teristic is  found  by  a  simple  rule,  viz.,  it  is  one  less  than  the  number  of 
fisrures  to  the  left  of  the  decimal  point  in  the  number  whose  log  is  to  be 
found.  Thus  the  characteristic  of  numbers  from  1  to  9.99  +  is  0,  from  10  to 
1)9.99  -f  is  1,  from  100  to  999  +  is  2,  from  .1  to  .99  +  is  -  1,  from  .01  to  .099  -±- 
is  —  2,  etc.  Thus 


log  of  2000  is  3.301 03; 
"  "  200  "  2.30103; 
"  "  20  "  1.30103; 
*4  *'  2  "  0.30103; 


log  of  .2  is  -  1.30103; 
"  *'  .02  "  -  2.30103; 
"  '"  .002  "  -  3.30103; 
"  "  .0002  "  -  4.30103. 


128  MATHEMATICAL   TABLES. 

The  minus  sign  is  frequently  written  above  the  characteristic  thus: 
log  .002  =  T?  30103.  The  characteristic  only  is  negative,  the  decimal  part,  or 
mantissa,  being  always  positive. 

When  a  log  consists  of  a  negative  index  and  a  positive  mantissa,  it  is  usual 
to  write  the  negative  sign  over  the  index,  or  else  to  add  10  to  the*index,  and 
to  indicate  the  subtraction  of  10  from  the  resulting  logarithm. 

Thus  log  .2=1 .30103,  and  this  may  be  written  9.30103  -  10. 

In  tables  of  logarithmic  sines,  etc.,  the  —  10  is  generally  omitted,  as  being 
understood. 

Rules  for  use  of  tlie  table  of  Logarithms.-  To  find  the 
log  of  any  whole  number.— For  1  to  100  inclusive  the  log  is  given 
complete  in  the  small  table  on  page  129. 

For  100  to  999  inclusive  the  decimal  part  of  the  log  is  given  opposite  the 
given  number  in  the  column  headed  0  in  the  table  (including  the  two  figures 
to  the  left,  making  six  figures).  Prefix  the  characteristic,  or  index.  2. 

For  1000  to  9999  inclusive  :  The  last  four  figures  of  the  log  are  found 
opposite  the  first  three  figures  of  the  given  number  and  in  the  vertical 
column  headed  with  the  fourth  figure  of  the  given  number  ;  prefix  the  two 
figures  under  column  0.  and  the  index,  which  is  3. 

For  numbers  over  10,000  having  five  or  more  digits  :  Find  the  decimal  part 
of  the  log  for  the  first  four  digits  as  above,  multiply  the  difference  figure 
in  the  last  column  by  the  remaining  digit  or  digits,  and  divide  by  10  if  there 
be  only  one  digit  more,  by  100  if  there  be  two  more,  and  so  on  ;  add  the 
quotient  to  the  log  of  the  first  four  digits  and  prefix  the  index,  which  is  4 
if  there  are  five  digits,  5  if  there  are  six  digits,  and  so  on.  The  table  of  pro- 
portional parts  may  be  used,  as  shown  below. 

To  find  the  log  of  a  decimal  fraction  or  of  a  whole 
number  and  a  decimal.— First  find  the  log  of  the  quantity  as  if  there 
were  no  decimal  point,  then  prefix  the  index  according  to  rule  ;  the  index  is 
one  less  than  the  number  of  figures  to  the  left  of  the  decimal  point. 

Required  log  of  3.141593. 

log  of    3.141        =  0.497068.  Diff.  =  138 

From  proportional  parts  5      =  690 

09    =  1242 

003  =  041 


log    3.141593       0.4'J71498 

To  find  the  number  corresponding  to  a  given  log.— Find 
in  the  table  the  log  nearest  to  the  decimal  part  of  the  given  log  and  take  the 
first  four  digits  of  the  required  number  from  the  column  N  and  the  top  or 
foot  of  the  column  containing  the  log  which  is  the  next  less  than  the  given 
log.  To  find  the  5th  and  6th  digits  subtract  the  log  in  the  table  from  the 

given  log,  multiply  the  difference  by  100,  and  divide  by  the  figure  in  the 
iff.  column  opposite  the  log  ;  annex  the  quotient  to  the  four  digits  already 
found,  and  place  the  decimal  point  according  to  the  rule  ;  the  number  of 
figures  to  the  left  of  the  decimal  point  is  one  greater  than  the  index. 

Find  number  corresponding  to  the  log 0.497150 

Next  lowest  log  in  table  corresponds  to  3141 497068 

Diff.  =  82 

Tabular  diff.  =  138;  82  -*- 138  =  .59  + 

The  index  being  0,  the  number  is  therefore  3.14159  -f. 

To  multiply  two   numbers  by  the  use  of  logarithms.— 

Add  together  the  logs  of  the  two  numbers,  and  find  the  number  whose  log 
is  the  sum. 

To  divide  two  numbers.— Subtract  the  log  of  the  less  from  the 
log  of  the  greater,  and  find  the  number  whose  log  is  the  difference. 

To  raise  a  number  to  any  given  power.— Multiply  the  log  of 
the  number  by  the  exponent  of  the  power,  and  find  the  number  whose  log  is 
the  product.. 

To  find  any  root  of  a  given  number.— Divide  the  log  of  the 
number  by  the  index  of  the  root.  The  quotient  is  the  log  of  the  root. 

To  find  the  reciprocal  of  a  number.— Subtract  the  decimal 
part  of  the  log  of  the  number  from  0,  add  1  to  the  index  and  change  the  sign 
of  the  index.  The  result  is  the  log  of  the  reciprocal. 


LOGARITHMS. 


129 


Required  the  reciprocal  of  3.141593. 

Log  of  3. 141593,  as  found  above 0.4971498 

Subtract  decimal  part  from  0  gives 0.5028502 

Add  1  to  the  index,  and  changing  sign  of  the  index  gives..  T.5028502 
which  is  the  log  of  0.31831 . 

To  find  the  fourth  term  of  a  proportion  by  logarithms. 
—Add  the  logarithms  of  U*e  second  and  third  terms,  and  from  their  sum 
subtract  the  logarithm  of  tLe  first  term. 

When  one  logarithm  is  to  be  subtracted  from  another,  it  may  be  more 
convenient  to  convert  the  subtraction  into  an  addition,  which  may  be  done 
by  first  subtracting  tLo  given  logarithm  from  10,  adding  the  difference  tc  the 
other  logarithm,  and  afterwards  rejecting  the  10. 

The  difference  between  a  given  logarithm  and  10  is  called  its  arithmetical 
complement,  or  cologarithm. 

To  subtract  one  logarithm  from  another  is  the  same  as  to  add  its  comple- 
ment and  then  reject  10  from  the  result.  For  a  —  b  =  10  —  b  +  a  —  10. 

To  work  a  proportion,  then,  by  logarithms,  add  the  complement  of  the 
logarithm  of  the  first  term  to  the  logarithms  of  the  second  and  third  terms. 
The  characteristic  must  afterwards  be  diminished  by  10. 

Example  in  logarithms  with  a  negative  index.  -Solve  by 

logarithms  ( — — )  '    ,  which  means  divide  526  by  1011  and  raise  the  quotient 


to  the  2.45  power. 


log  526  = 
log  1011  = 


2.720986 
3.004751 


Jog  of  quotient  =  —  1 .716235 
Multiply  by  2.45 


-  2.58117,5 
-  2.8  64940 
-^43  2470 
^"1730  477575  =  .20173,  Ans. 


In  multiplying  -  1.7  by  5,  we  say:  5x7—  35,  3  to  carry;  5  x  —  1  =  —  5  less 
{-  y  carried  =  —  2.  In  adding  -  2  -f  8  -f  3  -f  1  carried  from  previous  column, 
we  say:  1  -f-  3  -f  8  =  12,  minus  2  =  10,  set  down  0  and  carry  1;  1+4  —  2  =  3. 

LOGARITHMS  OF  NUMBERS  FROM  1  TO  100. 


N. 

Log. 

N. 

Log.    N. 

Log. 

N. 

Log. 

N. 

Log. 

1 

0.000000 

21 

1.322219 

41 

1.612784 

61 

1.785330 

81 

1.908485 

2 

0.301030 

22 

1.342423 

42 

1.623249 

62 

1.792392 

82 

1.913814 

3 

0.477121 

23 

1.361728 

43 

1.633468 

63 

1.799341 

83 

1.919078 

4 

0.602060 

24 

1.380211 

44 

1.643453 

64 

1.806180 

84 

1.924279 

5 

0.698970 

25 

1.397940 

45 

1.653213 

65 

1.812913 

85 

1.929419 

6 

0.778151 

26 

1.414973   46 

1.662758 

66 

1.819544 

86 

1.934498 

7 

0.845098  1  27 

1.431364 

47 

1.672098 

67 

1.826075 

87 

1.939519 

8 

0.903090   28 

1.447158 

48 

1.681241 

68 

1.832509 

88 

1.944483 

9 

0.954243 

29 

1.462398 

49 

1.690196 

69 

1.838849 

89 

1.949390 

10 

1.000000 

30 

1.477121 

50 

1.698970 

70 

1.845098 

90 

1.954243 

11 

1.041393 

31 

1.491362 

51 

1.707570 

71 

1.851258 

91 

1.959041 

12 

1.079181 

32 

1.505150 

52 

1.716003 

72 

1.857332 

92 

1.963788 

13 

1.113943 

33 

1.518514 

53 

1.724276 

73 

1.863323 

93 

1.968483 

14 

1.146128 

34 

1.531,479 

54 

1.732394 

74 

1.869232 

94 

1.978128 

15 

1.176091 

35 

1.544068 

55 

1.740363 

75 

1.875061 

95 

1.977724 

16 

1.204120 

36 

1.556303 

56 

1.748188 

76 

1.880814 

96 

1.982271 

17 

1.230449 

37 

1.568202 

57 

1.755875 

77 

1.886491 

97 

1.986772 

18 

1.255273 

38 

1.579784 

58 

1.763428 

78 

1.892095 

98 

1.991226 

19 

1.278754 

39 

1.591065 

59  1.770852   79 

1.897627 

99 

1.9956&5 

20 

1.301030 

40 

1.602060 

60  !  1.778151   80 

1.903090 

100 

2.000000 

LOUAK1THMS   OK    KUMBEE8, 


No.  100  L.  000.] 

—  1 
[No.  109  L.  040. 

N.   0 

1 

284 

5 

678 

9 

Diff. 

100  i  000000 

0434 

0868  1301  1734 

2166 

2598  3029  3461 

3891 

432 

1  !   4321 

4751 

5181   5609  6038 

6466 

6894  i  7321  7748 

8174 

426 

2    8600 

9026 

9451   9876 

0300 

0724 

1147  1570  1993 

2415 

AS>A 

3  j  012837 

3259 

3680  4100  4521 

4940 

5360  5779  6197 

6616 

420 

4  1   7033 

7451 

7868  8284  8700 

9116 

953°  9917 

i 

0361 

0775 

.  .  _ 

5  021189 

1603 

2016  2428  2841 

3252 

3664  |  4075  4486 

4896 

412 

6    5306 

5715 

6125  6533  6942 

7350 

7757  8164  8571 

8978 

408 

9789 

i      iW04: 

0195  0600  1004 

1408 

1812  2216  2619 

3O91 

404 

8  033424 

3826 

4227  4628  5029 

5430 

5830  6230  6629  1  7028 

400 

9    7426 

7825 

8223  i  8620  9017 

9414 

9811 

04 

0207  0602  0998 

397 

PROPORTIONAL.  PARTS. 

Diff. 

1 

-  2 

3 

4 

5 

6 

7 

8 

9 

434 

43.4 

86.8 

130.2 

173.6 

217.0 

260.4 

303.8 

347.2 

390.6 

433 

43.3 

86.6 

129.9 

173.2 

216.5 

259.8 

303.1 

346.4 

389.7 

432 

43.2 

86.4 

129.6 

172.8 

216.0 

259.2 

302.4 

345.6 

388.8 

431 

43.1 

86.2 

129.3 

172.4 

215.5 

258.6 

301.7 

344.8 

387.9 

430   43.0 

86.0 

129.0 

172.0 

215.0 

258.0 

301.0 

344.0 

387.0 

429 

42.9 

85.8 

128.7 

171.6 

214.5 

257.4 

300.3 

343.2 

386.1 

428 

42.  S 

85.6 

128.4 

171.2 

214.0 

256.8 

299.6 

342.4 

385.2 

427 

42.7 

85.4 

128.1 

170.8 

213.5 

256.2 

298.9 

341.6 

384.3 

426 

42.6 

85.2 

127.8 

170.4 

213.0 

255.6 

298.2 

340.8 

383.4 

425 

42.5   85.0 

127.5 

170.0 

212.5 

255.0 

297.5 

340.0 

382.5 

424 

42.4 

84.8 

127.2 

169.6 

212.0 

254.4 

296.8 

339.2 

381.6 

423 

42.3 

84.6 

126.9 

169.2 

211.5 

253.8 

296.1 

338.4 

380.7 

422 

42.2 

84.4 

126.6 

168.8 

211.0 

253.2 

295.4 

337.6 

379.8 

421 

42.1 

84.2 

126.3 

168.4 

210.5 

252.6 

294.7 

336.8 

378.9 

420 

42.0 

84.0 

126.0 

168.0 

210.0 

252.0 

294.0 

336.0 

378.0 

419 

41.9 

as.  8 

125.7 

167.6 

209.5 

251.4 

293.3 

335.2 

377.1 

418 

41.8 

83.6 

125.4 

167.2 

209.0 

250.8  |  292.6 

334.4 

37'6.2 

417 

41.7 

83.4 

125.1 

166.8 

208.5 

250.2   291.9 

333.6 

37'5.3 

416 

41.6 

83.2 

124.8 

166.4 

208.0 

249.6  !  291.2 

332.8 

374.4 

415 

41.5 

&3.0 

124.5 

166.0 

207.5   249.0 

290.5 

332.0 

373.5 

414 

41.4 

82.8 

124.2 

165.6 

207.0 

.248.4 

289.8 

331.2 

372.6 

413 

41.3 

82.6 

123.9 

165.2 

206.5 

247.8 

289.1 

330.4 

371.7 

412 

41.2 

82.4 

123.6 

164.8 

206.0   247.2 

288.4 

329.6 

370.8 

411 

41.1 

82.2 

123.3 

164.4 

205.5   246.6 

287.7 

328.8 

369.9 

410 

41.0 

82.0 

123.0 

164.0 

205.0   246.0 

287.0 

328.0 

369.0 

409 

40.9 

81.8 

122.7 

163.6 

204.5   245.4 

286.3 

327.2 

368.1 

408 

40.8 

81.  e 

122.4 

163.2 

204.0   244.8 

285.6 

326.4 

367.2 

407 

40.7 

81.4 

122.1 

162.8 

203.5   244.2 

284.9 

325.6 

366.3 

406 

40.6 

81.2 

121.8 

162.4   203.0   243  6 

284.2 

324.8 

365.4 

405 

40.5 

81.0 

121.5 

162.0 

202.5 

243.0 

283.5 

324.0 

364.5 

404 

40.4 

80.  £ 

; 

121.2 

161.6 

202.0   242.4 

282.8 

323.2 

363.6 

403 

40.3 

so.  e 

> 

120.9 

161.2 

201.5  !  241.8 

282.1 

322.4 

362.7 

402 

40.2 

80.4 

[ 

120.6 

160.8 

201.0   241  2 

281.4 

321.6 

361.8 

401 

40.1 

80.2 

120.3 

160.4 

200.5 

240.6 

280.7 

320.8 

360.9 

400 

40.0 

80-0 

120.0 

160.0 

200.0 

240.0   280.0 

320.0 

360.0 

399 

39.9 

79.  £ 

5 

119.7 

159.6 

199.5   239.4   279.3 

319.2 

&59.1 

398 

39.8 

79.  ( 

> 

119.4 

159.2 

199.0   238.8   278.6 

318.4 

358.2 

397   39.7 

79.^ 

[ 

119.1 

158.8 

198.5  '  238.3   277.9  !  317.6  857.3 

396  !  39.6 

79.2 

118.8 

158.4   198.0   .337.15   277.2  i  316.8  !  356.4 

395   39.5   79.0    118.5 

158.0   197.5   237.0   276.5   316.0  i  355.5 

LOGARITHMS   OF    NUMBERS. 


131 


No 

110  L.  041.] 

[No.  119  L.  078. 

N. 

0 

1 

2 

3          4 

5     1     6 

7 

8 

9       Diff. 

110 

041393 

1787 

2182 

2576     2969 

3362  '  3755 

4148 

4540 

4932  !     393 

1 

5323 

5714 

6105 

6495     6885 

7275  i  7664 

8053 

8442 

8830       390 

2 

9218 

9606 

9993 

0380     0766 

1153 

1538 

1924 

930Q 

9RCH 

qoo 

3 

053078 

3463 

3846 

4230     4613 

4996 

5378 

5760 

6142 

6524 

OOO 

383 

4 

6905 

7286 

7666 

8046     8426 

8805 

9185 

9563 

9942 

5 

4083 

376 

060698 

1075 

1452 

1829     2206 

2582 

2958 

3333 

37'09 

6 

4458 

4832 

5206 

5580     5953 

6326 

6699 

7071 

7443 

7815 

373 

7 

8186 

8557 

8928 

9298     9668 

0038 

0407 

nyr-ft 

1  1  d^ 

•tK-lA 

<Vf\ 

8 

071882 

2250 

2617 

2985     3352 

3718 

4085 

4451 

114O 

4816 

1O14 

5182 

366 

9 

5547 

5912 

6276 

6640     7004 

7368 

7731 

8094 

8457 

8819 

363 

PROPORTIONAL  PARTS. 

Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

395 
394 

39.5 
39.4 

79.0 

78.8 

118.5 
118.2 

158.0 
157.6 

197.5 
197.0 

237.0 
236.4 

276.5 
275.8 

316.0 
315.2 

355.5 
354.6 

393 

39.3 

78.6 

11 

7.9 

157.2 

196.5 

235.8 

275.1 

314.4 

353.7 

392 

39.2 

78.4 

11 

7.6 

156.8  i     196.0 

235 

.2 

21 

74.4 

313.6 

352.8 

391 

39.1 

78.2 

117.3 

156.4 

195.5 

234 

.6 

273.7 

312.8 

351.9 

390 

39.0 

78.  C 

11 

7.0 

156.0       195.0 

234 

.0 

2 

73.0 

312.0 

351.0 

389 

38.9 

77.8 

116.7 

155.6       194.5 

233 

.4 

27'2.3 

311.2 

350.1 

388 

38.8 

77.6 

116.4 

155.2 

194.0 

232.8 

271.6 

310.4 

349.2 

387 

38.7 

77.4 

11 

6.1 

154.8 

193.5 

232 

.2 

2 

70.9 

309.6 

348.3 

386 

38.6 

77.2 

115.8 

154.4  !     193.0 

231.6 

270.2 

308.8     347.4 

385 

38.5 

77.0 

115.5 

154.0 

192.5 

231.0 

269.5 

308.0     346.5 

384 

38.4 

76.  £ 

j 

115.2 

153.6 

192.0 

230.4 

268.8 

307.2     345.6 

383 

38.3 

76.6 

114.9 

153.2 

191.5 

229 

.8 

2 

68.1 

306.4     344.7 

382 

38.2 

76.4 

I 

1] 

4.6 

152.8 

191.0 

229 

.2 

2 

67.4 

305.6     343.8 

381 

38.1 

76.2 

114.3 

152.4 

190,5 

228.6 

266.7 

304.8     342.9 

380 

38.0 

76  '.0 

114.0 

152.0 

190.0 

228.0 

266.0 

304.0     342.0 

37£ 

37.9 

75.  £ 

] 

1] 

3.7 

151.6 

189.5 

227 

.4 

2 

65.3 

303.2 

341.1 

m 

37.8 

75.  ( 

1] 

3.4 

151.2 

189.0 

226 

.8 

2 

64.6 

302.4 

340.2 

377 

37.7 

75.4 

113.1 

150.8 

188.5 

226.2 

263.9 

301.6 

339.3 

376 

37.6 

75.2 

112.8 

150.4 

188.0 

225.6 

263.2 

300.8 

338.4 

375 

37.5 

75.0 

112.5 

150.0 

187.5 

225.0 

262.5 

300.0 

337.5 

374 

37.4 

74.* 

* 

112.2 

149.6 

187.0 

224.4 

261.8 

299.2 

336.6 

37? 

\ 

37.3 

74.  ( 

5 

11 

1.9 

149.2 

186.5 

223 

.8 

2 

61.1 

298.4 

335.7 

372 

37.2 

74.4 

111.6 

148.8 

186.0 

223.2 

260.4 

297.6 

334.8 

371 

37.1 

74.2 

111.3       148.4 

185.5 

222.6 

259.7 

296.8 

333.9 

37( 

) 

37.0 

74.  ( 

) 

11 

1.0       148.0 

185.0 

222 

.0 

2 

59.0 

296.0 

333.0 

369 

36.9 

73.* 

J 

110.7       147.6       184.5 

22] 

.4 

258.3       295.2 

332.1 

3K 

j 

36.8 

73.  ( 

5 

1] 

0.4 

147.2       184.0 

220 

.8 

2 

57.6  j     294.4 

331.2 

36r 

36.7 

73.4 

110.1 

146.8       183.5 

220.2 

256.9  !     293.6 

330.3 

36( 

> 

36.6 

73.5 

I 

1( 

».8       146.4       183.0 

219 

.0 

2 

56.2       292.8 

329.4 

S65 

36.5 

73.0 

109.5       146.0       182.5 

219.0 

255.7       292.0 

328.5 

364 

36.4 

72.* 

! 

109.2       145.6       182.0 

218.4 

254.8  1     291.2 

327.6 

3& 

\ 

36.3 

72.  < 

1( 

)8.9       145.2  i     181.5 

217 

.s 

2 

54.1       290.4 

326.7 

36$ 

> 

36.2 

72  ' 

1 

1( 

)8.6       144.8       181.0 

217 

.2 

2 

53.4  !     289.6 

325.8 

361 

36.1 

72^2 

108.3 

144.4       180.5 

216.6 

252.7  '•     288.8 

324.9 

360 

36.0 

72.0 

108.0 

144.0        180.0 

21(5 

.0       2 

52.0       2H8.0  i  324.0 

359 

35.9 

71.8 

107.7  !     143.6        179.5 

215 

.4  !     XJ51.8        287.2      JJ23.1 

35* 

*       35.8 

71. 

3 

1( 

)7.4        143.2        179.0 

214 

.S   '     2 

50.6        280.  4      322.2 

35 

'       35.7 

71  . 

1 

1( 

)7.1        142.8        ITS.  5 

214 

2    '       J; 

49.9       2S5.I)      &!1.3  ; 

356    j  35.6 

71.2 

106.8       142.4       178.0 

213 

.6       249.2       284.8      320.4  1 

132 


LOGARITHMS  OF   STUMBEB8. 


No.  120  L.  079.] 

[No.  134  L.  130. 

N.         0 

1 

2 

3 

4 

5 

6 

7 

8          9 

Diff. 

1 

I 

120 

UY9181 

9543 

9904 

0266~ 

1  0626 

0987 

1347 

1707 

2067  i  2426         8f!n 

1 

082785 

3144 

3503 

3861 

4219 

!    4576     4934 

5291     5647     6004 

357 

2 

6360 

QQAK 

6716     7071 

7426 

7781 

:    8136 

8490 

8845 

9198     9552 

355 

yyuo 

0258  !  0611 

0963 

1.315 

i    1667 

2018 

2370 

2721     3071 

352 

4 

093422 

3772     4122 

4471 

4820 

5169 

5518 

5806 

6215     6502 

349 

5 

6910 

7257     7604 

7951 

8298 

i  8644 

8990 

9335 

9081    
0026 

346 

6 

100371 

0715     1059 

1403 

1747 

2091 

2434 

2777 

3119     3462 

343 

7 

3804 

4146 

4487 

4828 

5169 

5510 

5851 

6191 

6531      6871 

341 

8 

7210 

7549 

7888 

8227 

8565 

8903 

9241 

9579 

9916   

0°53 

33S 

9  i  110590 

0926     1263 

1599 

1934 

i  2270 

2605 

2940 

3275     3609 

335 

130  I      3943 

4277 

4611 

4944 

5278 

5611 

5943 

6276 

6608     6940 

333 

1  I      7271 

7603 

7934 

8265 

8595 

8926 

9256 

9586 

9915 

|   no  4  K 

330 

2     120574 

0903 

1231 

1560 

1888       2216 

2544 

2871 

3198      3525 

328 

3         3852 

4178 

4504 

4830 

5156    !  5481 

5806 

6131 

6456     6781 

325 

7105 

7429 

7753 

8076 

8399 

8722 

9045 

9368 

9090 

13 

0012  !       323 

PROPORTIONAL,  PARTS. 

Diff. 

1 

2             3 

1 

4 

5 

•  i  - 

8 

9 

355 

35.5 

71.0 

106.5 

142.0 

177.5       213.0       248.5 

284.0     319.  5 

a54 

35.4 

70.8 

106.2 

141.6 

177.0  j     212.4 

247.8 

283.2 

318.6 

353 

35.3 

70.6 

105.9 

141.2 

176.5       211.8 

247.1 

282.4 

317.7 

352 

35.2 

70.4 

lOt 

.0 

] 

L40.8 

176.0       211.2 

246.4 

281.6 

310.8 

351 

35.1 

70.2 

105.3 

140.4 

175.5 

210.0 

245.7 

280.8 

315.9 

350 

35.0 

70.0 

105.0 

140.0 

175.0       210.0 

245.0 

280.0 

315.0 

349 

34.9 

69.8 

104 

.7 

] 

39.6 

174.5  i     209.4 

244.3 

279.2 

314.1 

348 

34.8 

69.6 

104.4 

139.2 

174.0 

208.8 

243.6 

278.4 

313.2 

347 

34.7 

69.4 

104 

.1 

] 

38.8 

173.5 

208.2 

242.9 

277.6 

312.8 

346 

34.6 

69.2 

103.8 

138.4 

173.0 

207.6 

242.2 

270.8 

311.4 

345 

34.5 

69.0 

103.5 

138.0 

172.5 

207.0 

241.5 

276.0 

310.5 

344 

34.4 

68.8 

103.2 

137.6 

172.0 

206.4 

240.8 

275.2 

309.6 

343 

34.3 

68.6 

102 

: 

37.2 

171.5 

205.8 

240.1 

274.4 

308.7 

342 

34.2 

68.4 

102.6 

136.8 

171.0 

205.2 

239.4 

273.0 

307.8 

341 

34.1 

68.2 

102.3 

136.4 

170.5 

204.6 

238.7 

272.8 

300.9 

340 

34.0 

68.0 

102 

.0 

1 

30.0 

170.0 

204.0 

238.0 

272.0 

300.0 

339 

33.9 

67.8 

-  101 

.7 

135.6 

109.5 

203.4 

237.3 

271  2 

305.1 

338 

33.8 

67.6 

,  101 

.4       135.2 

169.0 

202.8 

236.6 

270  •  4 

304.2 

337 

33.7 

67.4 

101 

.1        1 

34.8 

168.5 

202.2 

235.9 

209.0 

303.3 

ase 

33.6 

67.2 

100.8 

134.4 

168.0 

201.6 

235.2 

208.8 

302.4 

335 

33.5 

67.0 

100.5 

134.0 

167.5 

201.0 

234.5 

268.0 

301.5 

a34 

33.4 

66.8 

100 

.2 

1 

as.  6 

167.0 

200.4 

233.8 

267.2 

300.0 

333 

33.3 

66.6 

99.9       133.2 

166.5 

199.8 

233.1 

266.4 

299.7 

332 

as.  2 

66.4 

99.6 

132.8 

160.0 

199.2 

232.4 

205.0 

298.8 

331 

33.1 

66.2 

99 

.3 

1 

32.4 

165.5       198.6  i     231.7 

204.8 

297.9 

330 

33.0 

66.0 

.  99 

.0 

132.0 

165.0  i     198.0       231.0 

204.0 

297.0 

329 

32.9 

65.8 

98 

.7 

• 

31.6 

164.5  /    197.4 

230.3 

203.2 

296.1 

328 

32.8 

65.6 

96 

.4 

1 

31.2 

164.0       196.8 

229.6 

262.4 

295.2 

327 

32.7       65.4 

98.1 

130.8 

163.5       196.2 

228.9 

201.0 

294.3 

326 

32.6 

65.2 

97.8 

130.4 

163.0  i     195.6 

228.2 

260.8 

293.4 

325 

32.5 

65.0 

97.5 

130.0 

162.5 

195.0 

227  5 

200.0 

292.5 

324 

32.4       04.8 

97.2 

1 

29.0 

102.0        l(-)4.4 

J20.8        259.2 

291  .  0 

323 

32.3  I     04.6 

90 

.9 

1 

25).  2 

101.5        193.H         *>0.1    !     258.4 

290.7 

322       32.2  i     64.4 

90.0        128.8        101.0        1SW.2        J25.t       257.0  !  289.8 

LOGARITHMS   OF   NUMBERS. 


133 


No.  135  L.  130.] 

[No.  149  L.  175. 

N. 

0 

1    2 

8 

4 

5 

6 

7 

8    9 

Diff. 

135 

130334 

0655  0977 

1298 

1619 

i  1939  2260 

2580 

2900  3219 

321 

6 

3539 

3858  4177 

4496 

4814  i  5133  5451 

5769 

6086  6403 

318 

7 

6721 

7037  7354 

7671 

7987   8303  8618 

8934 

9249  9564 

316 

g 

9879 

0194  0508 

0822 

1136  ||  1450  !  1763 

2076 

2389  2702 

314 

9 

143015 

3327  i  3639 

3951 

4263 

4574  4885 

5196 

5507  5818 

311 

140 

6128 

6438  6748 

7058 

7367 

7676  !  7985 

8294 

8603  8911 

309 

9219 

9527  9835 

0142 

0449 

0756  1063 

1370 

1676  1982 

OA7 

2 

152288 

2594  2900 

3205 

3510 

3815  4100 

4424 

47'28  5032 

OU< 

305 

3 

5336 

5640  5943 

6246 

6549 

6852  7154 

7457 

7759  8061 

303 

4 

8362 

8664  8965 

9266 

9567 

9868 

0168 

0469 

0769  1068 

301 

5 

161368 

1667  1967 

2266 

2564 

2863  3161 

3460 

3758  4055 

299 

6 

4353 

4650  4947 

5244 

5541 

5838  i  6134 

6430 

6726  7022 

297 

7 

7317 

7613  7908 

8203 

8497 

8792  9086 

9380 

9674  9968 

295 

8 

170262 

0555  0848 

1141 

1434 

1726 

2019 

2311 

2603  2895 

293 

9 

3186 

3478  3769 

4060 

4351 

4641 

4932 

5222 

5512  5802 

291 

PROPORTIONAL  PARTS. 

Diff. 

i 

2 

3 

4 

5 

6 

7 

8 

9 

321 

32.1   64.2 

96 

3 

128.4 

160.5 

192. 

g 

224.7 

256.8 

288.9 

320 

32.0 

64.0 

96 

0 

128.0 

160.0 

192. 

0 

& 

54.0 

256.0 

288.0 

319 

31.9 

63.8 

95.7 

127.6 

159.5 

191. 

4   2$ 

53.3 

255.2 

287.1 

318 

31.8   63.6 

95 

4 

127  2 

159.0 

190. 

8 

2$ 

52.6 

254.4 

286.2 

317 

31.7   63.4 

95 

1 

126^8 

158.5 

190.2 

221.9 

253.6 

285.3 

316 

31.6   63.2 

94 

8 

126.4 

158.0 

189. 

6 

221.2 

252.8 

284.4 

315 

31.5   63.0 

94 

5 

126.0 

157.5 

189. 

0 

& 

50.5 

252.0 

283.5 

314 

31.4   62.8 

94.2 

125.6 

157.0 

188.4 

219.8 

251.2 

282.6 

313 

31.3   62.6 

93 

9 

125.2 

156.5 

187. 

8 

21 

9.1 

250.4 

281.7 

312 

31.2   62.4 

93 

6 

124.8 

156.0 

187.2 

218.4 

249.6 

280.8 

311 

31.1   62.2 

93 

3 

124.4 

155.5 

186. 

6 

217.7 

248.8 

279.9 

310 

31.0 

62.0 

93 

0 

124.0 

155.0 

186. 

0 

21 

7.0 

248.0 

279.0 

309 

30.9  !  61.8    92 

7 

123.6 

'154.5 

185. 

4 

2] 

6.3 

247.2 

278.1 

308 

30.8   61.6    92.4 

123.2 

154.0 

184. 

8 

215.6 

246.4 

277.2 

307 

30.7   61.4    92 

1 

122.8 

153.5 

184. 

2 

2] 

4.9 

245.6 

276.3 

306 

30.6  ''  61.2    91 

8 

122.4 

153.0 

183. 

6 

214.2 

244.8 

275.4 

305 

30.5   61.0    91 

5 

122.0 

152.5 

183 

0 

21 

3.5   244.0 

274,5 

304 

30.4   60.8    91 

2 

121.6 

152.0 

182 

4 

212.8 

243.2 

273.6 

303 

30.3  i  60.6    90 

9 

121.2 

151.5 

181. 

8 

2] 

2.1   242.4 

272.7 

302 

30.2  |  60.4    90 

6 

120.8 

151.0 

181. 

2 

211.4 

241.6 

271.8 

301 

30.1   60.2 

90 

3 

120.4 

150.5 

180. 

(5 

210.7 

240.8 

270.9 

300 

30.0   60.0 

90.0 

120.0 

150.0 

180. 

0 

210.0   240.0 

270.0 

299 

29.9   59.8 

89 

7 

119.6 

149.5 

179 

4 

2( 

)9.3  i  239.2 

269.1 

298 

29.8   59.6 

89 

4 

119.2 

149.0   178. 

8 

208.6  1  238.4 

268.2 

297 

29.7   59.4 

89 

1 

118.8 

148.5   178. 

2( 

)7.9   237.6 

267.3 

296 

29.6  ;  59.2 

88 

8 

118.4 

148.0 

177. 

6 

207.2  i  236.8 

266.4 

295 

29.5   59.0 

88 

5 

118.0 

147.5 

177 

0 

K 

)6.5   236.0 

265.5 

294 

29.4   58.8 

88 

2 

117.6 

147.0 

176.4 

205.8  i  235.2  264.6 

293 

29.3 

58.6 

87.9 

117.2 

146.5 

175. 

8 

205.1   234.4  263.7 

292 

29.2 

58.4 

87 

G 

116.8 

146.0 

175.2 

204.4   233.6 

262.8 

291 

29.1 

58.2 

87 

3 

116.4 

145.5 

174 

6 

203.7 

232.8 

261.9 

290 

29.0 

58.0 

87 

0 

116.0 

145.0 

174 

0 

203.0   232.0 

261.0 

289 

28.9 

57.8 

86 

7 

115.6 

144.5   173 

4 

2( 

)2.3   231.2 

260.1 

288 

28.8  i  57.6 

86 

4 

115.2 

144.0   172 

s 

ac 

)1.6  !  230.4 

259.2 

287 

28.7   57.4 

86 

1 

114.8 

143.5  ;  172.2 

200.9   229.6 

258.3 

286 

28.6 

57.2 

85 

8 

114.4 

143.0   171 

6   200.2   228.8 

257.4 

134 


LOGARITHMS  OF   KUMBKE8. 


!  No.  150  L.  176.] 


[No.  169  L.  230. 


N. 

0 

1 

2 

3   j  * 

5 

6 

7 

8 

9 

Diff. 

150  176091  6381 
1    8977  9264 

6u70 
9552 

6959  7248 
9839 

7536 

7825 

8113 

8401 

8689 

289 

01°6   0413 

0699 

0986 

1272 

1558 

287 

2  181844'  !  2129 

2415 

2700  2985   3270 

3555 

3839 

4123 

4407 

285 

3 

4691 

4975 

5259 

5542  5825  !  6108 

6391 

6674 

6956 

7239 

283 

4 

7521 

7803 

8084 

8366  8647  i  8928 

9209 

9490 

9771 

00^1 

9m 

,  5  190332  0612 

0892 

1171   1451 

1730 

2010 

2289 

2567 

UlfOJ. 

2846 

279 

6 

3-125  3403 

3681 

3959  I  4237 

4514 

4792 

5069 

5346 

5623 

378 

7 

5900  6176 

6453 

6729  j  7005 

7281 

7556 

7832 

8107 

8382 

276 

g 

8657 

8932 

9206 

9481   9755 

0029 

0303 

0577 

0850 

119J. 

i>74 

9 

201397 

1670 

1943 

2216  ;  2488 

2761 

3033 

3305 

3577 

3848 

272 

160 

4120 

4391 

4663 

4934  5204 

5475 

5746 

6016 

6286 

6556 

271 

1 

6826 

7096 

7365 

7634  i  7904 

8173 

8441 

8710 

8979 

9247 

269 

2 

9515 

9783 

0051 

0319  0586 

0853 

1121 

1388 

1654 

1921 

267 

3 

212188 

2454 

2720 

2986  3252 

3518 

3783 

4049 

4314 

4579 

266 

4 

4844 

5109 

5373 

5638  5902 

6166 

6430 

6694 

6957 

7221 

264 

5 

7484 

7747 

8010 

8273  ,  8536 

8798 

9060 

9323 

9585 

9846 

262 

6 

220108 

0370 

0631 

0892  i  1153 

1414 

1675 

1936 

2196 

2456 

261 

7 

2716 

2976 

3236 

3496  3755 

4015 

4274 

4533 

4792 

5051 

259 

8 

5309 

5568 

5826 

6084  i  6342 

6600 

6858 

7115 

7372 

7630 

258 

9 

7887 

8144 

8400 

8657  8913 

9170 

9426 

9682 

9938 

23 

0193 

256 

PROPORTIONAL  PARTS. 

Diff.   1 

2 

3     4 

5 

6 

7 

8     9 

285 

28.5 

57.0 

85.5 

114.0 

142.5   171 

0 

199.5  ! 

228.0 

256.5 

284 

28.4 

56.8 

85 

.2 

113.6 

142.0 

17'0 

4 

198.8  ! 

227.2 

255.6 

283 

28.3 

56.6 

84 

.9 

113.2 

141.5 

169 

8 

198.1  ! 

226.4 

254.7 

282 

28.2 

56.4 

84 

.6 

112.8 

141.0 

169 

2 

197.4  j 

225.6 

253.8 

281 

28.1 

56.2 

84 

.3 

112  4 

140.5 

168 

6 

196.7 

224.8 

252.9 

280 

28.0 

56.0 

84 

.0 

112.0 

140.0 

168.0 

196.0  l 

224.0 

252.0 

279 

27.9 

55.8 

83 

.7 

111.6 

139.5 

167 

4 

195.3  i 

223  2 

251.1 

278 

27.8 

55.6 

83 

.4 

111.2 

139.0 

166 

8 

194.6  I 

222^4 

250.2 

277 

27.7 

55.4 

83 

.1 

110.8 

138.5 

166 

2   193.9 

221.6 

249.3 

276 

27.6 

55.2 

82 

.8 

110.4 

138.0-   165 

6   193.2  i 

220.8 

248.4 

275 

27.5 

55.0 

82 

.5 

110.0 

137.5   165 

0   192.5  I 

220.0 

247.5 

274 

27.4 

54.8 

82 

2 

109.6 

137.0  i  164 

4 

191.8  ! 

219.2 

246.6 

273 

27.3 

54.6 

81 

'.9 

109.2 

136.5 

163 

191.1  ! 

218.4 

245.7 

272 

27.2 

54.4 

81 

.6 

108.8- 

136.0 

163 

2 

190.4 

217.6 

244.8 

271 

27.1 

54.2 

81 

.3 

108.4 

135.5   162 

6   189.7  | 

216.8 

243.9 

270 

27.0 

54.0 

81 

.0 

108.0 

135.0 

162 

0   189.0  ' 

216.0 

243.0 

269 

26.9 

53.8 

80 

.7 

107.6 

134.5 

161 

4 

188.3  ! 

215.2 

242.1 

268 

26.8 

53.6 

80 

.4 

107.2 

134.0   160 

8 

187.6  i 

214.4 

241.2 

267 

26.7 

53.4 

80 

.1 

106.8 

133.5  !  160 

2 

186.9  ! 

213.6 

240.3 

266 

26.6 

53.2 

79.8 

106.4   133.0   159 

6 

186.2  ' 

212.8 

239.4 

265 

26.5 

53.0 

79 

.5 

106.0 

132.5   159 

0 

185.5 

212.0 

238.5 

264 

26.4 

52.8 

79 

.2 

105.6 

132.0   158.4 

184.8 

211.2 

237.6 

263 

26.3   52.6 

78 

.9 

105.2 

131.5   157 

8 

184.1  : 

210.4 

236.7 

262 

26.2 

52.4 

78 

.6 

104.8 

131.0   157.2 

183.4 

209.6 

235.8 

261 

26.1 

52.2 

78 

.3 

104.4 

130.5   156 

6 

182.7 

208.8 

234.9 

260 

26.0   52.0 

78.0 

104.0 

130.0  !  156.0 

182.0 

208.0 

234.0 

259 

25.9  1  51.8 

77 

.7 

103.6   129.5  i  155 

4 

181.3 

207.2 

233.1 

258 

25.8 

51.6 

77 

.4 

103.2   129.0   154 

8 

180.6 

206.4 

232.2 

257 

25.7 

51.4 

77 

.1 

102.8  !  128.5   154 

2  !  179.9 

205.6  !  231.3 

256   25.6   51.2 

76 

.8 

102.4  !  128.0   153.  G   179.2 

204.8  i  230.4 

255 

25.5  ;  51.0    76 

.5    102.0   1*7.5   153 

0  :  178.5 

204.0  i  229.5 

LOGARITHMS  OF  NUMBERS. 


No.  170  L.  230.] 


[No.  189  L.  278. 


N. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Diff. 

170 

230449 

0704 

0960 

1215 

1470 

1724 

1979 

2234 

2488 

2742   255 

1 

2996 

3250 

3504 

3757 

4011 

4264 

4517 

4770 

5023 

5276   253 

2 

5528 

5781 

6033 

6285 

6537 

6789 

7041 

7292  7544 

7795 

252 

8046 

8297 

8548 

8799 

9049 

9299  9550 

9800 

0050 

0300 

250 

4 

240549 

0799 

1048 

1297 

1546 

1795 

2044 

2293 

2541 

2790 

249 

5 

3038 

3286 

3534 

3782 

4030 

4277 

4525 

4772 

5019 

5266 

248 

6 

5513 

5759 

6006 

6252 

6499 

6745 

6991 

7237 

7482 

7728 

246 

7" 

7973 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

0176 

245 

8 

250420 

0664 

0908 

1151   1395 

1638 

1881 

2125 

2368 

2610 

243 

9 

2853 

3096 

3338 

3580  3822 

4064 

4306 

4548 

4790 

5031 

242 

180 

5273 

5514 

5755 

5996 

6237 

6477 

6718 

6958 

7198 

7439 

241 

1 

7679 

7918 

8158 

8398 

8637 

8877 

9116 

9355 

9594 

9833 

.339 

2 

260071 

0310 

0548 

0787 

1025 

1263 

1501 

1739  j  1976 

2214 

238 

3 

2451 

2688 

2925 

3162 

3399 

36136 

3873 

4109 

4346 

4582 

237 

4 

4818 

5054 

5290 

5525 

5761 

5996 

6232 

6467 

6702 

6937 

235 

5 

7172 
9513 

7406 
9746 

7641 
9980 

7875 

8110 

8344 

8578 

8812 

9046 

9279 

234 

0213 

0446 

0679 

0912 

1144 

1377 

1609 

233 

7 

271842 

2074 

2306 

2538 

2770 

3001 

3233 

3464 

3696 

3927 

232 

8 

4158 

4389 

4(520 

4850 

5081 

5311 

5542 

5772 

6002 

6232 

230 

9 

6462 

6692 

6921 

7151 

7380 

7609 

7838 

8067 

8296 

8525 

229 

PROPORTIONAL  PARTS. 

Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

255 

254 

25,5 

25.4 

8:8 

76,5 
76.2 

102,0 
101.6 

127,5 

127.0 

153.0 
152.4 

17S.5 
177.8 

204.0 

203.2 

229.5 
228.6 

253 

25.3 

50.6 

75.9 

101.2 

126.5 

151.8 

177.1 

202.4 

227.7 

252 

25.2 

50.4 

75.6 

100.8 

126.0 

151.2 

176.4 

201.6 

226.8 

251 

25.1 

50.2 

75.3 

100.4 

125.5 

150.6 

175.7 

200.8 

225.9 

250 

25  0 

50.0 

75.0 

100.0 

125.0 

150.0 

175.0 

200.0 

225.0 

249 

24.9 

49.8 

74.7 

99.6 

124.5 

149.4 

17'4.3 

199.2 

224.1 

248 

24.8 

49.6 

74.4 

99.2 

124.0 

148.8 

173.6 

198.4 

223.2 

247 

24.7 

49.4 

74.1 

98.8 

123.5 

148.2 

172.9 

197.6 

222.3 

246 

24.6 

49.2 

73.8 

98.4 

123.0 

147.6 

172.2 

196.8 

221.4 

245 

24.5 

49.0 

73.5 

98.0 

122.5 

147.0 

171.5 

196.0 

220.5 

244 

24.4 

48.8 

73.2 

97.6 

122.0 

146.4 

170.8 

195.2 

219.6 

243 

24.3 

48.6 

72.9 

97.2 

121.5 

145.8 

170.1 

194.4 

218.7 

242 

24.2 

48.4 

72.6 

96.8 

121.0 

145.2 

169.4 

193.6 

217.8 

241 

24.1 

48.2 

72.3 

96.4 

120.5 

144.6 

168.7 

192.8 

216.9 

240 

24.0 

48.0 

72.0 

96.0 

120.0 

144.0 

168.0 

192.0 

216.0 

239 

23.9 

47.8 

71.7 

95.6 

119.5 

143.4 

167.3 

191.2 

215.1 

238 

23.8 

47.6 

71.4 

95.2 

119.0 

142.8 

166.6 

190.4 

214.2 

237 

23.7 

47.4 

71.1 

94.8 

118.5 

142.2 

165.9 

189.6 

213.3 

236 

23.6 

47.2 

70.8 

94.4 

118.0 

141.6 

165.2 

188.8 

212.4 

235 

23.5 

47.0 

70.5 

94.0 

117.5 

141.0 

164.5 

188.0 

211.5 

234 

23.4 

46.8 

70.2 

93.6 

117.0 

140.4 

163.8 

187.2 

210.6 

233 

23.3 

46.6 

69.9 

93.2 

116.5 

139.8 

163.1 

186.4 

209.7 

232 

23.2 

46.4 

69.6 

92.8   116.0 

139.2 

162.4 

185.6 

208.8 

231 

23.1 

46.2 

69.3 

92.4   115.5 

138.6 

161.7 

184.8 

207.9 

230 

23.0 

46.0 

69.0 

92.0   115.0 

138.0 

161.0 

184.0 

207.0 

229 

22.9 

45.8 

68.7 

91.6   114.5 

137.4   160.3 

183  2 

206.1 

228 

22.8 

45.6 

68.4 

91.2   114.0 

136.8   159.6 

182.4 

205.2 

227 

22.7 

45.4 

68.1 

90.8   113.5 

136.2  j  158.9   181.6 

204.3 

226 

22.6 

45.2 

67.8 

90.4  1  113.0 

135.6  j  158  2  ;  180.8  203.4 

136 


LOGARITHMS  OF   JSTUMBERS. 


No.  190  L.  278.]                                 [No.  214  L.  332. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

o 

Diff. 

190 

278754 

8982 

9211 

9439 

9667 

9895 

0123 

0351 

0578 

0806 

228 

1 

281033 

1261 

1488 

1715 

1942 

2169 

2d'J6 

2622 

2849 

3075 

227 

2 

3301 

3527 

3753 

3979 

4205 

4431 

4056 

4882 

5107 

5332 

226 

3 

5557 

5782 

6007 

6232 

6456 

6681 

69J5 

7130 

7354 

7578 

225 

4 

7802 

8026 

8249 

8473 

8696  j  8920 

9143 

9366 

9589 

9812 

223 

5 

290035 

0257 

0480 

0702 

0925  lj  1147 

1369 

1591 

1813 

2034 

222 

6 

2256 

2478  I  2699 

2920 

3141 

3363 

3584 

3804 

40^5 

4246 

221 

7 

4466 

4687  I  4907 

6127 

5:347 

5567 

5787 

6007 

6226  • 

6440 

220 

8 

6665 

6884 

7104 

7323 

7542 

7761 

7979 

8198 

8416 

8635 

219 

9 

8853 

9071 

9289- 

9507 

9725 

9943  !  

n-ifii 

'  0378 

0595 

0813 

218 

200 

301030 

1247 

1464 

1681 

1898 

2114 

2331 

2547 

2764 

2980 

217 

1 

3196 

3412 

3628 

3844 

4059 

4275 

4491 

47'06 

4921 

5136 

216 

2 

5351 

5566 

5781 

5996 

6211 

6425 

6639 

6854 

7068 

7282 

215 

3 

7496 

7710 

7924 

8137 

8351 

8564 

8778 

8991 

9204 

9417 

213 

4 

9630 

9843 

0056 

0268 

0481 

0693 

0906 

1118 

1330 

1542 

91  P 

5 

311754 

1966 

2177 

2389 

2600 

2812 

3023 

3234 

3445 

3650 

AL4 

211 

6 

3867 

4078 

4289 

4499 

4710 

4920 

5130 

5340 

5551 

5700 

210 

7 

5970 

6180 

6390 

6599 

6809 

7018 

7227 

7436 

7646 

7854 

209 

8 

8063 

8272 

8481 

8689 

8898 

9106 

9314 

9522 

9730 

9938 

208 

9 

"320146 

0354 

0562 

0769 

0977 

1184 

1391 

1598 

1805 

2012 

207 

210 

2219 

2426 

2633 

2839 

3046 

3252 

3458 

3665 

3871 

4077 

206 

1 

4282 

4488 

4694 

4899 

5105 

5310 

5510 

5721 

5926 

6131 

205 

2 

6336 

6541 

6745 

6950 

7155 

7359 

7583 

77(57 

7972 

8170 

204 

3 

8380 

8583 

8787 

8991 

9194 

9398 

9601 

9805 

0008 

0211 

?03 

4 

330414 

0617 

0819 

1022 

1225 

1427 

1630 

1832 

2034 

2236 

&V3 

PROPORTIONAL  PARTS. 

Difif. 

1 

2 

3 

4 

5 

6 

7      8 

9 

225 

22.5 

45.0 

67.5 

90.0 

112.5 

135.0 

157.5   180.0 

202.5 

224 

22.4 

44.8 

67.2 

89.6 

112.0 

134.4 

156.8   179.2 

201.0 

223 

22.3 

44.6 

66.9 

89.2 

111.5 

133.8 

156.1   IT'S.  4  200.7 

222 

22.2 

44.4 

66.6 

88.8 

111.0 

133.2 

155.4   177.6  199.8 

221 

22.1 

44.2 

66.3 

88.4 

110.5 

132.6 

154.7   176.8  |  198.9 

220 

22.0 

44.0 

66.0 

88.0 

110.0 

132.0 

154.0   176.0 

198.0 

219 

21.9 

43.8 

65.7 

87.6 

109.5 

131.4 

153.3   175.2 

197.1 

218 

21.8 

43.6 

65.4 

87.2 

109.0 

130.8 

152.6   174.4 

196.2 

217 

21.7 

43.4 

65.1 

86.8 

108.5 

130.2 

151.9   173.6  195.3 

216 

21.6 

43.2 

64.8 

86.4 

108.0 

129.6 

151.2   172.8 

194.4 

215 

21.5 

43.0 

64.5 

86.0 

107.5 

129.0 

150.5   172.0 

193.5 

214 

21.4 

42.8 

64.2 

85.6 

107.0 

128.4 

149.8   171.2 

192.6 

213 

21.3 

42.6 

63.9 

85.2 

106.5 

127.8 

149.1   170.4 

191.7 

212 

21.2 

42.4 

63.6 

84.8  ' 

106.0 

127.2 

148.4   169.6 

190.8 

211 

21.1 

42.2 

63.3 

84.4 

105.5 

126.6 

147.7   168.8 

189.9 

210 

21.0 

42.0 

63.0 

84.0 

105.0 

126.0 

147.0   168.0 

189.0 

209 

20.9 

41.8 

62.7 

83.6 

104.5 

125.4 

146.3   167.2 

188.1 

208 

20.8 

41.6 

62.4 

83.2 

104.0 

124.8 

145.6   166  4 

187.2 

207 

20.7 

41.4 

62.1 

82.8 

103.5 

124.2 

144.9  |  165.6 

186.3 

206 

20.6 

41.2 

61.8 

82.4 

103.0 

123.6 

144.2   164.8 

185.4 

205 

20.5 

4d.O 

C1.5 

82.0 

102.5 

123.0 

143.5   164.0 

184.5 

204 

20.4 

40.8 

61.2 

81.6 

102.0 

122  4 

142.8   163.2 

183.6 

203 

20.3 

40.6 

60.9 

81.2 

101.5 

121.8 

142.1   162.4 

182.7 

202 

20.2   40.4 

60.6 

'.0.8 

101.0   121.2  |  141.4   161.6 

181.8 

LOGARITHMS  OF   NUMBERS. 


137 


No.  215  L.  332.]                                  [No.  239  L.  380. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

215 

332438 

2640 

2842 

3044 

3246 

3447 

3649 

3850 

4051 

4253 

202 

6 

4454 

4055 

4856 

5057 

5257 

5458 

5058 

5859 

6059 

6260 

201 

7 

0400 

6000 

6860 

7060 

7200 

7459 

7059 

7858 

805* 

J 

8257 

200 

8 

8456 

8056 

8855 

9054 

9253 

9451 

9650 

9849 

004r 

f 

09d.fi 

1QQ 

9 

340444 

0642 

0841 

1039 

1237 

1435 

1632 

1830 

2028 

2225 

198 

220 

2423 

2620 

2817 

3014 

3212 

3409 

3606 

3802 

3999 

4196 

197 

1 

4392 

4589 

4785 

4981 

5178 

537'4 

5570 

5706 

5962 

6157 

196 

2 

6353 

6549 

6744 

6939 

7135 

7330 

7525 

7720 

791  1 

> 

8110 

195 

3 

8305 

8500 

8694 

8889 

9083 

9278 

9472 

9666 

986( 

I 

0054 

194 

4 

350248 

0442 

0636 

0829 

1023 

1216 

1410 

1603 

1796 

1989 

193 

5 

2183 

2375 

2568 

2761 

2954 

3147  3339 

3532 

372- 

I 

3916 

193 

6 

4108 

4301 

4493 

4685 

4876 

5068  i  5260 

5452 

5643 

5834 

192 

7 

6026 

6217 

6408 

6599 

67'90 

6981   7172 

7363  75& 

I 

7744 

191 

8 

7935 

8125 

8316 

8506 

8096 

8886  9076 

9266 

9451 

} 

9646 

190 

9 

9835 

0025 

0215 

0404 

0593 

0783  0972 

1161 

1350 

1539 

189 

230 

361728 

1917 

2105 

2294 

2482 

2671  2859 

3048 

3236 

3424 

188 

1 

3612 

3800 

3988 

4176 

4363 

,4551  i  4739 

4926 

5113 

5301 

188 

2 

5488 

5675 

5862 

6049 

6236 

6423  6610 

6796 

698, 

7169 

187 

3 

7356 

7542 

7729 

7915 

8101 

8287 

8473 

8659 

8845 

9030 

186 

9216 

9401 

9587 

9772 

9958 

!  0143 

0328 

0513 

069L 

i 

0883 

185 

5 

371068 

~1253~ 

1437 

1622 

1806 

1991 

2175 

2360 

2544 

2728 

184 

6 

2912 

3096 

3280 

3404 

3647 

3831 

4015 

4198 

4382 

4565 

184 

7 

4748 

4932 

5115 

5298 

5481 

5664 

5846 

6029 

621S 

> 

6394 

183 

8 

6577 

6759 

6942 

7124 

7306 

7488 

7670 

7852 

80& 

i 

8216 

182 

9 

8398 

8580 

8761 

8943 

9124 

9306 

9487 

9668 

984< 

) 

38 

0030 

181 

PROPORTIONAL  PARTS. 

Diff. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

202 
201 

20.2 
20.1 

40.4 
40.2 

60.6 
60.3 

80.8 
80.4 

101.0 
100.5 

121.2 
120.6 

141.4 
140.7 

161.6 
160.8 

181.8 
180.9 

200 

20.0 

40.0 

60.0 

80.0 

100.0 

120.0 

140.0 

160.0 

180.0 

199 

19.9 

39.8 

59.7 

79.6 

99.5 

119.4 

139.3 

159.2 

179.1 

198 

19.8 

39.6 

59.4 

79.2 

99.0 

118.8 

138.6 

158.4 

178.2 

197 

19.7 

39.4 

59.1 

78.8 

98.5 

118.2 

137.9 

157.6 

177.3 

196 

19.6 

39.2 

58.8 

78.4 

98.0 

117.6 

137.2 

156.8 

176.4 

195 

19.5 

39.0 

58.5 

78.0 

97.5 

117.0 

136.5 

156.0 

175.5 

194  • 

19.4 

38.8 

58.2 

77.6 

97.0 

116.4 

135.8 

155.2 

174.6 

193 

19.3 

38.6 

57.9 

77.2 

96.5 

115.8 

135.1 

154.4 

173.7 

192 

19.2 

38.4 

57.6 

76.8 

96.0 

115.2 

134.4 

153.6 

172.8 

191 

19.1 

38.2 

57.3 

76.4 

95.5 

114.6 

133.7 

152.8 

171.9 

190 

19.0 

38.0 

57.0 

76.0 

95.0 

114.0 

133.0 

152.0 

171.0 

189 

18.9 

37.8 

56.7 

75.6 

94.5 

113.4 

132.3 

151.2 

170.1 

188 

18.8 

37.6 

56.4 

75.2 

94.0 

112.8 

131.6 

150.4 

169.2 

187 

18.7 

374 

56.1 

74.8 

93.5 

112.2 

130.9 

149.6 

168.3 

186 

18.6 

37.2 

55.8 

74.4 

93.0 

111.6 

130.2 

148.8 

167.4 

185 

18.5 

37.0 

55.5 

74.0 

92.5 

111.0 

129.5 

148.0 

166.5 

184 

18.4 

36.8 

55.2 

73.6 

92.0 

110.4 

128.8 

147.2 

165.6 

183 

18.3 

36.6 

54.9 

73.2 

91.5 

109.8 

128.1 

146.4 

104.7 

182 

18.2 

36.4 

54.6 

72.8 

91.0 

109.2 

127.4 

145.6 

163.8 

181 

18.1 

36.2 

54.3 

72.4 

90.5   108.6 

126.7 

144.8 

102.9 

180 

18.0 

36.0 

54.0 

72.0 

90.0 

108.0 

126.0 

144.0 

102.0 

179 

17.9 

35.8 

53.7 

71.6 

89.5 

107.4 

125.3 

143.2 

161.1 

138 


LOGARITHMS   OF   LUMBERS. 


No.  240  L.  380.] 

[No.  269  L.  431. 

N. 

240 
1 
2 
3 
4 
5 

6 

8 
9 

250 
1 

2 

3 

4 
5 

6 

7 

8 
9 

260 
1 

3 

4 
5 
6 

7 
8 
9 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

380211 
2017 
3815 
5606 
7390 
9166 

0392 

2197 
3995 
5785 
7568 
9343 

0573 
2377 
4174 
5964 
7746 
9520 

0754 
2557 
4353 
6142 
7924 
9698 

0934 

2737 
4533 
6321 
8101 
9875 

1115 
2917 
4712 
6499 

8279 

1296 
3097 
4891 
6677 
8456 

1476 
3277 
5070 
6856 
8634 

1656 
3456  . 
5.249 
7034 
8811 

1837 
3636 

T428 
7212 
8989 

181 

180 
179 

17'8 
178 

177 
176 
176 
175 
174 
173 

173 
172 
171 
171 
170 
169 

169 
168 
167 

167 
166 
165 

165 
164 
164 
163 
162 
162 

161 

0051 
1817 
3575 
5326 
7071 

8808 

0228 
1993 
3751 
5501 
7245 

8981 

0405 
2169 
3926 
5676 
7419 

9154 

0582 
2345 
4101 

5850 
7592 

9328 

1056 
2777 
4492 
6199 
7901 
9595 

0759 
2521 
4277 
6025 
7766 
9501 

1228 
2949 
4663 
6370 
8070 
9764 

390935 
2697 
4452 
6199 

7940 
9674 

1112 
2873 
4627 
6374 

8114 

9847 

1288 
3048 
4802 
6548 

8287 

1464 
3224 
4977 
6722 

8461 

1641 
3400 
5152 
6896 

8634 

0020 
1745 
3464 
5176 

6881 
8579 

0192 
1917 
3635 
5346 
7051 
8749 

0365 

2089 
.3807 
5517 
7221 
8918 

0538 
2261 
3978 
5688 
7391 
9087 

0711 
2433 
4149 
5858 
7561 
9257 

0883 
2605 
4320 
6029 
7731 
9426 

401401 
3121 
4834 
6540 
8240 
9933 

1573 
3292 
5005 
6710 
8410 

0102 
1788 
3467 

5140 

6807 
8467 

0271 
1956 
3635 

5307 
6973 
8633 

0440 
2124 
3803 

5474 
7139 

8798 

0609 
2293 
3970 

5641 
7306 
8964 

0777 
!  2461 
4137 

5808 
7472 
1  9*29 

4305 

5974 
7638 
9295 

1114 
2796 
4472 

6141 

7804 
9460 

1283 
2964 
4639 

6308 
7970 
9625 

1451 
3132 

4806 

6474 
8135 
9791 

411620 
3300 

4973 
6641 
8301 
9956 

421604 
3246 
4882 
6511 
8135 
9752 
43 

0121 
1768 
3410 
5045 
6674 
8297 
9914 

0286 
1933 
3574 
5208 
6836 
8459 

0451 
2097 
3737 
5371 
6999 
8621 

0616 
2261 
3901 
5534 
7161 
8783 

0781 
2426 
4065 
5697 
7324 
8944 

0945 
2590 
4228 
5860 
7486 
9106 

1110 
2754 
4392 
6023 
7648 
9268 

1275 
2918 
4555 
6186 
7811 
9429 

1439 
3082 
4718 
6349 
7973 
9591 

0075  !  0236 

0398 

i  0559 

0720 

0881 

1042 

1203 

PROPORTIONAL  PARTS. 

Diff. 

1 

2 

35.6 
35.4 
a5.2 
35.0 
34.8 
34.6 
34.4 
34.2 
34.0 

33.8 
33.6 
33.4 
33.2 

as.o 

32.8 
32.6 
32.4 
32.2 

3 

4 

5 

6 

106.8 
106.2 
105.6 
105.0 
104.4 
103.8 
103.2 
102.6 
102.0 

101.4 

100.8 
100.2 
99.6 
99.0 
98.4 
97.8 
97  2 
9G.6 

7 

8 

9 

160.2 
159.3 
158.4 
157.5 
156.6 
155.7 
154.8 
153.9 
153.0 

152.1 
151.2 
150.3 
149.4 
148.5 
147.6 
146.7 
145.8 
144.9 

178 
177 
176 
175 
174 
173 
172 
171 
170 

169 
168 
167 
166 
165 
164 
163 
162 
Idl 

17.8 
17.7 
17.6 
17.5 
17.4 
17.3 
17.2 
17.1 
17.0 

16.9 
16.8 
16.7 
16.6 
16.5 
16.4 
16.3 
16.2 
16.1 

53.4 
53.1 
52.8 
52.5 
52.2 
51.9 
51.6 
51.3 
51.0 

50.7 
50.4 
50.1 
49.8 
49.5 
49.2 
48.9 
48.5 
48.3 

71.2 
70.8 
70.4 
70.0 
69.6 
69.2 
68.8 
68.4 
68.0 

67.6 
67.2 
66.8 
66.4 
66.0 
65.6 
65.2 
64.8 
64.4 

89.0 
88.5 
88.0 
87.5 
87.0 
86.5 
86.0 
85.5 
85.0 

84.5 
84.0 
83.5 
83.0 

82.5 
82.0 
81.5 
81.0 
80  .  5 

124.6 
123.9 
123.2 
122.5 
121.8 
121.1 
120.4 
119.7 
119.0 

118.3 
117.6 
116.9 
116.2 
115.5 
114.8 
114.1 
113.4 
112.7 

142.4 
141.6 
140.8 
140.0 
139.2 
138.4 
137.6 
136.8 
136.0 

135.2 
134.4 
133.6 
132.8 
132.0 
131.2 
130.4 
129.6 
128.8 

LOGARITHMS   OF   HUMBERS. 


139 


No.  270  L.  431.] 

[No.  299  L.  476. 

N. 

0 

1 

2 

3 

4 

1  5 

6 

7 

8 

9 

Diff. 

270 

431364 

1525 

1685 

1848 

2007 

2167 

2328 

24 

88 

2649 

2809 

161 

1 

2969 

3130 

3290 

345 

0 

3610 

3770 

3930 

4C 

'.)() 

4249 

4409 

160 

2 

4569 

4729 

4888 

5048 

5207 

5367 

5526 

5685 

5844 

6004 

159 

3 

6163 

6322 

6481 

664 

0 

6799 

6957 

7116 

7$ 

175 

7433 

7592 

159 

4 

7751 

7909 

8067  8226 

8384 

8542  8701 

$ 

>59 

9017 

9175 

158 

5 

9333 

9491 

9648 

980 

0 

9964 

.  

— 



_ 



j  0122  0279 

0594 

0752 

158 

6 

440909 

1066 

1224 

1381 

1538 

1695  ;  1852 

2009 

2166 

2323 

157 

7 

2480 

2637 

2793 

2950 

3106 

3263 

3419 

3576 

3732 

3889 

157" 

8 

4045 

4201 

4357 

4513 

4669 

4825 

4981 

5137 

5293 

5449 

156 

9 

5604 

5760 

5915 

6071 

6226 

6382 

6537 

6( 

192 

6848 

7003 

155 

280 

7158 

7313 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

155 

1 

8706 

8861 

9015 

9170 

9324 

9478 

9633  9' 

'87' 

9941 

2 

450249 

0403  0557 

0711 

0865 

1018 

1172 

1326 

1479 

1633 

154 

3 

1786 

1940 

2093 

224 

7 

2400 

2553 

2706 

» 

J59 

3012 

3165 

153 

4 

3318 

3471 

3624 

3777 

3930 

4082 

4235 

4387 

4540 

4692 

153 

5 

4845 

4997 

5150 

53C 

2 

5454 

5606 

5758  5< 

)10 

6062 

6214 

152 

6 

6366 

6518 

6670 

6821 

6973 

7125 

727'6 

7428 

7579 

7731 

152 

7 

7882 

8033 

8184 

8336 

8487 

8638 

8789 

8940 

9091 

9242 

151 

3 

9392 

9543 

9694 

9& 

5 

9995 

0116 

0296 

O^ITT 

(  ir 

0597 

0748 

151 

9 

460898 

1048 

1198 

1348 

1499   1649 

1799 

1948 

2098 

2248 

150 

290 

2398 

2548 

2697 

2847 

2997 

3146 

3296 

3445 

3594 

3744 

150 

1 

3893 

4042 

4191 

4340 

4490 

4639 

4788 

4936 

5085 

5234 

149 

2 

5383 

5532 

5680 

58S 

9 

5977  i  6126 

6274 

6- 

123 

6571 

6719 

149 

3 

6868 

7016 

7164 

7312 

7460 

7608 

7756 

7 

)04 

8052 

8200 

148 

4 

8347 
9822 

8495 
9969 

8643 

8790 

8938 

9085  9233 

9380 

9527 

9675 

148 

0116 

0263 

0410 

0557 

0704 

0851 

0998 

1145 

147 

6 

471292 

1438 

1585 

1732 

1878 

2025 

2171 

2318 

2464 

2610 

146 

7 

2756 

2903 

3049 

3195 

3341 

3487 

3633 

3779 

3925 

4071 

146 

8 

4216 

4362 

4508 

46£ 

>3 

4799 

4944 

5090 

& 

335 

5381 

5526 

146 

9 

5C71 

5816 

5962 

6107 

6252 

6397  6542 

6687 

6832 

6976 

145 

i 

PROPORTIONAL  PARTS. 

Diff.   1 

* 

3 

4 

5 

6 

7 

8 

9 

161   16.1 

32.2 

48.3 

64.4 

80.5 

96.6 

112.7 

128.8 

144.9 

160   16.0   32.0 

48.0 

64.0 

80.0 

96.0 

112.0 

128.0 

144.0 

159   15.9 

31.8 

47.7 

63.6 

79.5 

95.4 

111.3 

127.2 

143.1 

158   15.8 

31.6 

47.4 

63.2 

79.0 

94.8 

110.6 

12(5.4 

142.2 

157   15.7 

31.4 

47.1 

62.8 

78.5 

94.2 

109.9 

125.6 

141.3 

156   15.6 

31.2 

46.8 

62.4 

78.0 

93.6 

109.2 

124.8 

140.4 

155   15.5 

31.0 

46.5 

62.0 

77.5 

93.0 

108.5 

124.0 

139.5 

154   15.4 

30.8 

46.2 

61.6 

77.0 

92.4 

107.8 

123.2 

138.6 

153   15.3 

30.6 

45.9 

61.2 

76.5 

91.8 

107.1 

1.22.4 

137.7 

152   15.2 

30.4 

45.6 

60.8 

76.0 

91.2 

106.4 

121.6 

136.8 

151   15.1 

30.2 

45.3 

60.4 

75.5 

90.6 

105.7 

120.8 

135.9 

150   15.0 

30.0 

45.0 

60.0 

75.0 

90.0 

•;os.o 

120.0 

135.0 

149   14.9 

29.8 

44.7 

59.6 

74.5 

89,4 

104.3 

119.2 

134.1 

148   14.8 

29.6 

44.4 

59.2 

74.0 

88.8 

103.6 

118.4 

133.2 

147   14.7 

29.4 

44.1 

58.8 

73.5 

88.2 

102.9 

117.6 

132.3 

146   14.6 

29.2 

43.8 

58.4 

73.0 

87.6 

102.2 

116.8 

131.4 

145   14.5 

29.0 

43.5 

58.0 

72.5 

87.0 

101.5 

116.0 

130.5 

144   14.4 

28.8 

43.2 

57.6 

72.0 

86.4 

100.8 

115.2 

129.6 

143   14.3 

28.6 

42.9 

57.2 

71.5 

85.8 

100.1 

114.4 

128.7 

142   14.2 

28.4 

42.6 

50.8 

71.0 

85.2 

99.4 

113.6 

127.8 

141   14.1 

28.2 

42.3 

56.4 

70.5 

84.6 

98.7 

112.8 

120.9 

1<*0   14.0 

28.0 

42.0 

50.0    70.0 

84.0 

98.0 

112.0 

126.0 

140 


LOGARITHMS   OF   NUMBERS. 


No.  300  L.  477.] 

[No.  339  L.  531. 

N. 

300 
1 

2 
3 
4 
5 
6 

8 
9 

.310 
1 

2 

4 
5 
6 

8 
9 

320 

1 
a 

3 

4 
5 
6 

8 
9 

330 
1 

2 

3 
4 
5 
6 

7 
8 

9 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

145 
144 

144 
143 
143 
142 
142 
141 
141 

140 

140 
139 
139 
139 

138 

138 

137 
137 
136 
136 

136 
1,35 
135 

134 
134 
133 
133 
133 
132 
132 

131 

131 
131 
130 
130 
129 
129 
129 

128 
128 

477121 
8566 

7266 
8711 

7411 
8855 

7555 
8999 

7700 
9143 

7844 
9287 

7989 
9431 

8133  1 
9575 

8278 
9719 

1156 
2588 
4015 
5437 
6855 
8269 
9677 

8422 
9863 

1299 
2731 
4157 
5579 
6997 
8410 
9818 

480007 
1443 
2874 
4300 
5721 
7138 
8551 
9958 

0151 
1586 
3016 
4442 

5863 
7280 
8692 

0294 
1729 
3159 
4585 
6005 
7421 
8833 

0438 

1872 
3302 
4727 
6147 
7563 
8974 

0582 
2016 
3445 
4869 
6289 
7704 
9114 

07'25 
2159 
3587 
5011 
6430 
7845 
9255 

0869 
2302 
3730 
5153  i 
6572 
7986 
9396 

1012 
2445  i 
3872 
5295 
6714 
8127 
9537 

0099 

1502 
2900 
4294 
5683 
7068 
8448 
9824 

0239 

1642 
3040 
4433 

5822 
7206 
8586 
9962 

0380 

1782 
3179 
4572 
5960 
7'344 
8724 

0520 

1922 
3319 
4711 
6099 

7483 
8862 

i  0661 

2062 
3458 
4850 
6238 
7621 
8999 

0801 

2201 
3597 
4989 
6376 
7759 
9137 

0941 

2341 
3737 
5128 
6515 
7897 
9275 

1081 

2481 
3876 
5267 
6653 
8035 
9412 

1222 

2621 
4015 
5406 
6791 
81753 
9550 

491362 
2760 
4155 
5544 
6930 

asu 

9687 

0099 
1470 
2837 
4199 

5557 
6911 
8260 
9606 

0236 
1607 
2973 
4335 

5693 
7046 
8395 
9740 

0374 
1744 
3109 
4471 

5828 
7181 
i  8530 
!  9874 

0511 
1880 
3246 
4607 

5964 
7316 
8664 

0648 
2017 
3382 
4743 

6099 
7451 
8799 

0785 
2154 
3518 

4878 

6234 
7586 
8934 

0922 
2291 
3655 
5014 

6370 

7721 
9068 

501059 
2427 
3791 

5150 
6505 
7856 
9203 

510545 
1883 
3218 
4548 
5874 
7196 

8514 

9828 

1196 
2564 
3927 

5286 
6640 
7991 
9a37 

1333 
2700 
4063 

5421 
6776 
8126 
9471 

0009 
1349 

3684 
4016 
5344 

6668 
7987 

9303 

0143 

1482 
2818 
4149 
547'6 
6800 
8119 

9434 

0277 
1616 
2951 
4282 
5609 
6932 
8251 

9566 

0411 
1750 
3084 
4415 
5741 
7064 
8382 

9697 

0679 
2017 
3351 
4681 
6006 
7328 

8646 
9959 

0813 
2151 
3484 
4813 
6139 
7460 

87'77 

0947 

2284 
3617 
4946 
6271 
7592 

8909 

1081 
2418 
3750 
5079 
6403 
7724 

9040 

1215 
2551 

3883 
5211 
6535 
7855 

9171 

0090 
1400 
2705 
4006 
5304 
6598 
7888 
9174 

0221 
1530 
2835 
4136 
5434 
6727 
8016 
9302 

0353 
1661 
2966 
4266 
5563 
6856 
8145 
9430 

0484 
1792 
3096 
4396 
5693 
6985 
8274 
9559 

0615 
1922 
3226 
4526 

5822 
7114 
8402 
9687 

0745 
2053 
3356 
4656 
5951 
7243 
8531 
9815 

0876 
2183 
3486 
4785 
6081 
7372 
8660 
9943 

1007 
2314 
3616 
4915 
6210 
7501 
8788 

521138 
2444 
3746 
5045 
6339 
7630 
8917 

530200 

1289 
2575 
3876 
5174 
6469 
7759 
9045 

0072 
1351 

0328 

0456 

0584 

0712 

0840 

0968 

1096   1223 

PROPORTIONAL  PARTS. 

Diff.   1 

2 

3 

41.7 
41.4 
41.1 
40.8 
40.5 
40.2 
39.9 
39.6 
89.3 
89.0 
38.7 
38.4 
38.1 

4 

5 

6 

7 

8 

9 

139   13.9 
138   13.8 
137   13.7 
136   13.6 
135   13.5 
134   J3.4 
133   13.3 
132   13.2 
131   13.1 
130   13.0 
129   12.9 
128   12.8 
127   12  7 

27.8 
27.6 
27.4 
27.2 
27.0 
26.8 
26.6 
26.4 
26.2 
26.0 
25.8 
25.6 
25.4 

55.6 
55.2 
54.8 
54.4 
54.0 
53.6 
53.2 
52.8 
52.4 
52.0 
51.6 
51.2 
50.8 

69.5 
69.0 
68.5 
68.0 
67.5 
67.0 
66.5 
66.0 
65.5 
65.0 
64.5 
64.0 
63.5 

83.4 

82.8 
82.2 
81.6 
81.0 
80.4 
79.8 
79.2 
78.6 
78.0 
77.4 
76.8 
76.2 

97.3 
96.6 
95.9 
95.2 
94.5 
93.8 
93.1 
92.4 
91.7 
91.0 
90.3 
89.6 
88.9 

111.2 
110.4 
109.6 
108.8 
108.0 
107.2 
106.4 
105.6 
104.8 
104.0 
103.2 
102.4 
101.6 

125.1 
124.2 
123.3 
122.4 
121.5 
120.6 
119.7 
118.8 
117.9 
117.0 
116.1 
115.2 
114.3 

LOGAH1THMS  OF  NUJtBEfcS. 


141 


No.  340  L.  531.] 

[No.  379  L.  579. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

340 
1 
2 
3 
4 
5 
6 

7 
8 
9 
350 
1 
2 
3 
4 

5 

6 
7 
8 
9 

360 
1 
2 
3 

4 
5 
6 

7 
8 
9 

370 
1 

2 
3 

4 
5 

6 

7 
8 
9 

531479 
2754 
4026 
5294 
6558 
7819 
9076 

1607 
288<J 
4153 
5421 
6685 
7945 
9202 

1734 

3009 
4280 
5547 
6811 
8071 
9327 

1862 
3136 
4407 
5674 
6937 
8197 
9452 

1990  i  2117 
3264   3391 
4534  !:  4661 
5800  |  5927 
7063   7189 
8322  i  8448 
9578   9703 

2245  | 
3518 
4787 
6053 
7315 
8574 
9829 

2372 
3645 
4914 
6180 
7441 
8699 
9954 

2500  !  2627 
3772  3899 
5041  5167 
6306  6432 
7567  7693 
8825  8951 

123 
127 
127 
126 
126 
126 

125 
125 
125 
124 

124 
124 
123 
123 

123 
122 
122 
121 
121 
131 

120 

120 
120 

119 
119 
119 
119 
118 
118 
118 

117 

117 
117 
116 
116 
116 
115 
115 
115 
114 

0079 
1330 
2576 
3820 

5060 
6296 
7529 

8758 
9984 

0204 
1454 
2701 
3944 

5183 
6419 
7652 

8881 

540329 
1579 

2825 

4068 
5307 
6543 

7775 
9003 

0455 
1704 
2950 

4192 
5431 
6666 

7898 
9126 

0580 
1829 
3074 

•±316 
5555 
67'89 

8021 
9249 

0705 
1953 
3199 

4440 
5678 
6913 
8144 
9371 

0830 
2078 
3323 

4564 
5802 
7'036 
8267 
9494 

0955 
2203 
,  3447 

4688 
5925 
7159 
8389 
9616 

1080 
2327 
3571 

4812 
6049 
7282 
8512 
9739 

1205 
2452 
3696 

4936 
6172 
7405 
8635 
9861 

0106 
1328 
2547 
3762 
4973 
6182 

7387 
8589 
9787 

550228 
1450 
2668 
3883 
5094 

6303 
7507 
8709 
9907 

0351 
1572 
2790 
4004 
5215 

6423 

7627 

8829 

0473 
1694 
2911 
4126 
5336 

6544 
7748 
8948 

0595 
1816 
3033 
4247 
5457 

6664 

7868 
9068 

0717 
1938 
3155 
4368 
5578 

6785 

7988 
9188 

0385 
1578 
2769 
3955 
5139 
6320 
7497 

8671 

9842 

0840 
2060 
3276 
4489 
5699 

6905 

8108 
9308 

0962 
2181 
3398 
4610 
5820 

7026 
8228 
9428 

1084 
2303 
3519 
4731 
5940 

7146 
8349 
9548 

1206 
2425 
3640 

4852 
6061 

7267 
8469 
9667 

0026 
1221 
2412 
3600 
4784 
5966 
7144 

8319 
9491 

0146 
1340 
2531 
3718 

4903 
6084 
7262 

8436 
9608 

0265 
1459 
2650 
3837 
5021 
6202 
7379 

8554 
9725 

0504 
1698 
2887 
4074 
5257 
6437 
7614 

8788 
9959 

0624 
1817 
3006 
4192 
5376 
6555 
7732 

8905 

0743 
1936 
3125 
4311 
5494 
6673 
7849 

9023 

0863 
2055 
3244 
4429 
5612 
6791 
7967 

9140 

0982 
2174 
3362 
4548 
5730 
6909 
80&4 

9257 

561101 
2293 
3481 
4666 
5848 
7026 

8202 
9374 

0076 
1243 

2407 
3568 
4726 
5880 
7032 
8181 
9326 

0193 
1359 
2523 
3684 
4841 
5996 
7147 
8295 
9441 

0309 
1476 
2639 
3800 
4957 
6111 
7262 
8410 
9555 

0426 
1592 
2755 
3915 
5072 
6226 
7377 
8525 
9669 

570543 
1709 
2872 
4031 
5188 
6341 
7492 
8639 

0660 
1825 
2988 
4147 
5303 
6457 
7607 
8754 

0776 
1942 
3104 

4263 
5419 
6573 

7722 
8868 

0893 
2058 
3220 
4379 
5534 
6687 
7836 
8983 

1010 
2174 
3336 
4494 
5650 
6802 
7951 
9097 

1126 
2291 
3452 
4610 
5765 
6917 
8066 
9212 

PROPORTIONAL  PARTS. 

DifiP.   1 

2 

3 

4 

5 

6 

7 

8 

9 

128   12.8 
127   12.7 
126   12.6 
125   12.5 
124   12.4 
123   12.3 
122   12.2 
121   12.1 
120   12.0 
119   11.9 

25.6 
25.4 
25.2 
25.0 
24.8 
24.6 
24.4 
24.2 
24.0 
23.8 

38.4 
38.1 
37.8 
37.5 
37.2 
36.9 
36.6 
36.3 
36.0 
35.7 

51.2 
50.8 
50.4 
50.0 
49.6 
49.2 
48.8 
48.4 
48.0 
47.6 

64.0 
63.5 
63.0 
62.5 
62.0 
61.5 
61.0 
60.5 
60.0 
59.5 

76.8 
76.2 
75.6 
75.0 
74.4 
73.8 
73.2 
72.6 
72.0 
71.4 

89.6 

88.9 
88.2 
87.5 
86.8 
86.1 
85.4 
84.7 
84.0 
83.3 

102.4 
101.6 
100.8 
100.0 
99.2 
98.4 
97.6 
96.8 
96.0 
95.2 

115.2 
114.3 
113.4 
112.5 
111.6 
110.7 
109.8 
108.9 
108.0 
107.1 

LOGARITHMS  OF  NUMBERS. 


No.  380.  L.  579.] 

[No.  414  L.  617. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

1 

1 

380 

579784 

9898 

0012 

0126 

0241   0355  0469  0583 

0697 

0811 

114 

1 

580925 

1039 

1153 

1267 

1381 

1495 

1608  i  1722 

1836 

1950 

2 

2063 

2177 

2291 

240 

4 

2518 

2631  2745 

2k 

58 

2972 

3085 

3 

3199 

3312 

3426 

3539 

3652 

3765  3879 

31 

W 

4105 

4218 

4 

4331 

4444 

4557 

467 

0 

4783 

4896 

5009 

5] 

22 

5235 

5348 

113 

5 

5461 

5574 

5686 

579 

9 

5912 

6024 

6137 

6250 

6362 

6475 

6 

6587 

6700 

6812 

692 

5 

7037 

7149 

7262 

7( 

57'4 

7486 

7599 

7 

7711 

7823 

7935 

8047 

8160 

!  8272 

8384 

8496 

8608 

8720 

112 

8 

8832 

8944 

9056 

9167 

9279 

9391 

9503 

9615 

9726 

9838 

9950 

0061 

0173 

0284 

0396 

0507 

0619 

0730 

0842 

0953 

390 

591065 

1176 

1287 

1399 

1510 

1  1621 

1732 

1843 

1955 

2066 

1 

2177 

2288 

2399 

2510 

2621 

i  2732 

2843 

2954 

3064 

3175 

111 

2 

3286 

3397 

3508 

361 

8 

3729 

3840 

3950 

4( 

J61 

4171 

4282 

3 

4393 

4503 

4614 

4724 

4834 

!  4945 

5055 

5165 

5276 

5386 

4 

5496 

5606 

5717 

582 

7 

5937 

1  6047 

6157 

6 

M7 

6377 

6487 

5 

6597 

6707 

6817 

6927 

7037 

7146 

7256 

7366 

7476 

7586 

110 

6 

7695 

7805 

7914 

802 

4 

8134 

8243 

asss 

8> 

i(W 

8572 

8681 

7 
g 

8791 
9883 

8900 
9992 

9009 

9119 

9228 

9337 

9446 

9556 

9665 

9774 

1AQ 

0101 

0210 

C319 

0428 

0537 

0646 

0755 

0864 

lu» 

9 

"600973 

Io82 

1191 

1299 

1408 

1517 

1625 

1734 

1843 

1951 

400 

2060 

2169 

2277 

23? 

() 

2494 

i  2603 

2711 

2819 

2928 

3036 

1 

3144 

3253 

3361 

34C 

9 

a577 

3686 

3794 

3 

M2 

4010 

4118 

108 

2 

4226 

4334 

4442 

4550 

4658 

4766 

4874 

4982 

5089 

5197 

3 

5305 

5413 

5521 

5628 

5736 

5844 

5951 

6059 

6166 

6274 

4 

6381 

6489 

6596 

67C 

4 

6811 

6919 

7026 

7 

133 

7241 

7348 

5 

7455 

7562 

7669 

7777 

7884 

7991 

8098 

8205 

8312 

8419 

107 

6 

8526 

Q^Q4 

8633 
QTH 

8740 

QQAO 

8847 
9914 

8954 

9061 

9167 

9274 

9381 

9488 

yoy^ 

y<  \JL 

youo 

0021 

0128 

0234 

0341 

0447 

0554 

8 

610660 

0767 

0873 

0979 

1086 

1192 

1298 

1405 

1511 

1617 

9 

1723 

1829 

1936 

2042 

2148 

2254 

2360 

2466 

2572 

2678 

106 

410 

2784 

2890 

2996 

3102 

3207 

3313 

3419 

3525 

3630 

3736 

1 

3842 

3947 

4053 

41£ 

»9 

4264 

4370 

4475 

4 

581 

4086 

4792 

2 

4897 

5003 

5108 

5213 

5319 

5424 

5529 

5634 

5740 

6845 

3 

5950 

6055 

6160 

62€ 

5 

6370 

6476 

6581 

6 

ISO 

6790 

6895 

105 

4 

7000 

7105 

7210 

7315 

7420 

7525 

7629 

7734 

7839 

7943 

PROPORTIONAL  PARTS. 

Diff.   1 

2     3 

4 

5 

1 

7 

8 

9 

118   11.8 

23.6    35.4 

47.2 

59.0 

70.8 

82.6 

94.4 

106.2 

117   11.7 

23.4    35.1 

46.8 

58.5 

70.2 

81.9 

98.6 

105.3 

116   11.6 

23.2    34.8 

46.4 

58.0 

69.6 

81.2 

92.8 

104.4 

115   11.5 

23.0    34.5 

46.0 

57.5 

69.0 

80.5 

92.0 

103.5 

114   11.4 

22.8    34.2 

45.6 

57.0 

68.4 

79.8 

91.2 

102.6 

113   11.8 

22.6    33.9 

45.2 

56.5 

67.8 

79.1 

90.4 

101.7 

113   11.2 

22.4   33.6 

44.8 

56.0 

67.2 

78.4 

89.6 

100.8 

111   11.1 

22.9   33.3 

44.4 

55.5 

66.6 

77.7 

88.8 

99.9 

110   11.0 

22.0    33.0 

44.0 

55.0 

66.0 

77.0 

88.0 

99.0 

109   10.9 

21.8    32.7 

43.6 

54.5 

65.4 

76.3 

87.2 

98.1 

108   10.8 

21.6    32.4 

43.2 

54.0 

64.8 

75.6 

86.4 

97.2 

107   10.7 

21.4    32.1 

42.8 

53.5 

64.2 

74.9 

85.6 

96.3 

106   10.6 

21.2   31.8 

42.4 

53.0 

63.6 

74.2 

84.8 

95.4 

105   10.5 

21.0    31.5 

42.0 

52.5 

63.0 

73.5 

84.0 

94.5 

105   10.5 

21.0    31.5 

42.0 

52.5 

63.0 

73.5 

84.0 

94.5 

104   10.4 

20.8    31.2 

41.6 

52.0 

62.4 

72.8 

83.2 

93.6 

LOCiAltlTHMS   OF   XITMBER8. 


143 


No.  415  L.  618.] 


[No.  459  L.  602    I 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

8884 
9928 

0968 
2007 
3042 

4076 
5107 
6135 
7161 
8185 
9206 

9 

Diff. 

415 
6 

7 
8 
9 

420 
1 
2 
3 
4 
5 
6 

7 
8 
9 

430 
1 
2 
3 
4 
5 
6 

r 

8 
9 

440 

1 
2 
3 
4 
5 
6 

7 
8 
9 

450 
1 
2 
3 

4 
5 
6 

7 

8 
,9 

618048 
9093 

8153  8257 
9198  9302 

8362 
9406 

8466 
9511 

0552 
1592 
2628 

3663 
4695 
5724 
6751 

7775 
8797 
9817 

8571 
9615 

0656 
1695 
2732 

3766 
4798 
5827 
6853 
7878 
8900 
9919 

8676 
9719 

8780 
9824 

0864 
1903 
2939 

3973 
5004 
6032 

7058 
8082 
9104 

8989 

0032 
1072 
2110 
3146 

4179 
5210 
6238 
7263 

8287 
9308 

105 
104 

103 
102 

101 
100 

99 

98 

97 
96 

95 

620136 
1176 
2214 

3249 

4282 
5312 
6340 
7366 
8389 
9410 

630428 
1444 
2457 

3468 
4477 

5484 
6488 
7490 
8489 
9486 

0240 
1280 
2318 

3353 

4385 
5415 
6443 
7468 
8491 
9512 

0344 
1384 
2421- 

3456 
4488 
5518 
6546 
7571 
8593 
9613 

0448 
1488 
2525 

3559 
4591 
5621 
6648 
7673 
8695 
9715 

0760 
1799 

2835 

3869 
4901 
5929 
6956 
7980 
9002 

0021 
1038 
2052 
3064 

4074 
5081 

6087 
7089 
8090 
9088 

0123 
1139 
21o3 
3165 

4175 

5182 
6187 
7189 
8190 
9188 

0224 
1241 
2255 
3266 

4276 
5283 

6287 
7290 
8290 
9287 

0826 
1342 
2356 
3367 

4376 

5383 
6388 
7390 
8389 
9387 

0530 
1545 
2559 

3569 

4578 
5584 
6588 
7590 
8589  ' 
9586 

0631 
1647 
2660 

3670 
4679 
5685 
6688 
7690 
8689 
9686 

0733 
1748 
2761 

3771 
4779 

5785 
6789 
7790 
8789 
9785 

0835 
1849 
2862 

3872 
4880 
5886 
6889 
7890 
8888 
9885 

0936 
1951 
2963 

3973 
4981 
5986 
6989 
7990 
8988 
9984 

0084 
1077 
2069 
3058 

4044 
5029 
6011 
6992 
7969 
8945 
9919 

0183 
1177 

2168 
3156 

4143 
5127 
6110 

7089 
8067 
9043 

0016 
0987 
1956 
2923 

3888 
4850 
5810 
6769 
7725 
8679 
9631 

0283 
1276 
2267 
3255 

4242 
5226 
6208 
7187 
8165 
9140 

0113 
1084 
2053 
3019 

3984 
4946 
5906 
6864 
7820 
8774 
9726 

0382 
1375 
2366 
3354 

4340 
5324 
6306 

7285 
8262 
9237 

0210 
1181 
2150 
•3116 

4080 
5042 
6002 
6960 
7916 
8870 
9821 

0771 
1718 
2663 

640481 
1474 
2465 

3453 
4439 
5422 
6404 
7383 
8360 
9335 

0581 
1573 
2563 

3551 
4537 
5521 
6502 
7481 
8458 
9432 

0680 
1672 
2662 

3650 
4636 
5619 
6600 
7579 
8555 
9530 

0779 
1771 
2761 

3749 
4734 
5717 
6698 
7676 
8653 
9627 

0879 
1871 
2860 

3847 
4832 
5815 
6796 

7774 
8750 
9724 

0978 
1970 
2959 

3946 
4931 
5913 
6894 

7872 
8848 
9821 

650308 
1278 
2246 

3213 
4177 
5138 
6098 
7056 
8011 
8965 
9916 

0405 
1375 
2343 

3309 
4273 
5235 
6194 

7152 
8107 
9060 

0502 
1472 
2440 

3405 
4369 
5331 
6290 

7247 
8202 
9155 

0599 
1569 
2536 

3502 
4465 
5427 
6386 
7343 
8298 
9250 

0696 
1666 
2633 

3598 
4562 
5523 
6482 
7438 
8393 
9346 

0793 
1762 
2730 

3695 
4658 
5619 
6577 
7534 
8488 
9441 

0890 
1859 
2826 

3791 
4754 
5715 
6673 
7629 
8584 
9536 

0486 
1434 

2380 

0011 
0960 
1907 

0106 
1055 

2002 

0201 
1150 
2096 

0296 
1245 
2191 

0391 
1339 
2286 

0581 
1529 
2475 

0676 
1623 
2569 

660865 
1813 

PROPORTIONAL  PARTS. 

Diff.   1 

2 

3 

4 

5 

6 

7     8 

9 

105   10.5 
104   10.4 
103   10.3 
102   10.2 
101   10.1 
100  i  10.0 
99    9.9 

21.0 
20.8 
20.6 
20.4 
20.2 
20.0 
19.8 

31.5 
31.2 
30.9 
30.o 
30.3 
30.0 
29.7  . 

42.0 
41.6 
41.2 
40.8 
40.4 
40.0 
39.6 

52.5 
52.0 
51.5 
51.0 
50.5 
50.0 
49.5 

63.0 
62.4 
61.8 
61.2 
60.6 
60.0 
59.4 

73.5    84.0 
72  8    83.2 
72  1    82.4 
71.4  1  81.6 

70  7  !  80.8 
70  0  !  80.0 
69.3    VH.2 

94.5 
93.6 
92.7 
91.8 
90.9 
90.0 
89.1 

144 


LOGARITHMS  OF   NUMBERS. 


No.  460  L.  662.] 

[No.  499  L.  698. 

N. 

0 

1 

2 

8 

4  1 

5 

6 

7 

8 

9 

Diff. 

460 

662758 

2852 

2947 

3041   3135 

3230 

3324  3418  3512 

3607 

1 

3701 

3795 

3889 

3983 

4078 

4172 

4266 

4360  4454 

4548 

2 

4642 

4736 

4830 

495 

24 

5018 

5112 

5206  5299  539 

3 

5487 

94 

3 

5581 

5675 

5769 

5862 

5956 

6050 

6143  6237  i  6331 

6424 

4 

6518 

6612 

6705 

67* 

W 

6892 

6986 

7079 

7173  726 

3 

7360 

5 

7453 

7546 

7640 

7733 

7826 

7920 

8013 

8106  819 

9 

8293 

6 

8386 

8479 

8572 

86( 

35 

8759 

8852 

8945 

9038  |  913 

1 

9224 

9317 

9410 

9503 

95 

)6 

9689 

9782 

9875 

9967 

006 

A 

0153 

93 

8 

670246 

0339 

0431   0524 

0617 

0710 

0802 

0895  !  0988 

1080 

9 

1173 

1265 

1358 

1451 

1543 

1636 

1728 

1821 

1913 

2005 

470 

2098 

2190 

2283 

2375 

2467 

2560 

2652 

2744  2836 

2929 

1 

3021 

3113 

3205  32 

)7 

3390 

3482 

3574 

3666  375 

8 

3850 

2 

3942 

4034 

4126  4218 

4310 

4402 

4494 

4586  467 

7 

4769 

92 

3 

4861 

4953 

5045  5137 

5228 

5320 

5412 

5503  5595 

5687 

4 

5778 

5870 

5962  60 

33 

6145 

6236 

6328 

6419  I  651 

1 

6602 

5 

6694 

6785 

6876 

6968 

7059 

7151 

7242 

7333 

7424 

7516 

6 

7607 

7698 

7789 

781 

SI 

7972 

8063 

8154 

8245 

833 

6 

8427 

7 

8518 

8609 

8700  8791 

8882 

8973 

9064  I  9155 

9246 

9337 

91 

g 

9428 

9519 

9610  Q7 

Wl 

9791 

9882 

9973 

0063 

0154 

0245 

9 

680336 

0426 

0517 

0607 

0698 

0789 

0879 

0970 

1060 

1151 

480  j   1241 

1332 

1422 

1513 

1603 

1693 

1784 

1874 

1964 

2055 

1    2145 

2235 

2326 

2416 

2506 

2596 

2686 

2777 

2867 

2957 

2    3047 

3137 

3227 

3317 

3407 

3497 

3587 

3677 

3767 

3857 

90 

3  ;   3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

4  !   4845 

4935 

5025 

51 

14 

5204 

5294 

5383 

5473 

556 

3 

5652 

5  |   5742 

5831 

5921 

60 

10 

6100 

6189 

6279 

6368 

645 

8 

6547 

6  1   6636 

6726 

6815 

6904 

6994 

7083 

7172 

7261 

7351 

7440 

7  ;   7529 

7618 

7707 

7796 

7886 

7975 

8064 

8153 

8242 

8331 

89 

8    8420 

8509 

8598 

86 

37 

8776 

8865 

8953 

9042 

913 

1 

9220 

9 

9309 

9398 

9486 

95 

"5 

9664 

9753 

9841 

9930 

001 

o 

0107 

490 

690196 

0285 

0373  0462 

0550 

0639 

0728 

0816 

0905 

0993 

1 

1081 

1170 

1258   13 

17 

1435 

1524 

1612 

1700 

178 

9 

1877 

2 

1965 

2053 

214:2   2-230 

2318 

2406 

2494 

2583 

2671 

2759 

3 

2847 

2935 

3023   31 

11 

3199 

3287 

3375 

3463 

355 

1 

3639 

88 

4 

3727 

3815 

3903  !  3991 

4078 

4166 

4254 

4342 

4430 

4517 

5 

4605 

4693 

4781  ;  48G8 

4956 

5044 

5131 

5219 

530 

7 

5394 

6 

5482 

5569 

5657   57 

14 

5832 

5919 

6007 

6094 

618 

•2 

6269 

7 

6356 

6444 

6531  '  66 

IS 

6706 

6793 

6880 

6908 

705 

8 

7142 

8 

7229 

7317 

7404   7491 

7578 

7665 

7752 

7926 

8014 

9 

8100 

8188 

8275   8362 

8449 

8535 

8622 

8709 

8795 

8883 

87 

P 

ROPORTIONAL  PARTS. 

L  ..^  < 

Diff. 

1 

2 

3 

4 

5 

6     7 

3 

9 

98 

9.8 

19.6 

29.4 

39.2 

49.0 

58.8    68.6 

78.4 

88.2 

97 

9.7 

19.4 

29.1 

38.8 

48.5 

58.2    67.9 

77.6 

87.3 

96 

9.6 

19.2 

28.8 

38.4 

48.0 

57.6    67.2 

76.8 

86.4 

95 

9.5 

19.0 

28.5 

38.0 

47.5 

57.0    66.5 

76.0 

85.5 

94 

9.4 

18.8 

28.2 

37.6 

47.0 

56.4    65.8 

75.2 

84.6 

93 

9.3 

18.6 

27.9 

37.2    46.5 

55.8    85.1 

74.4 

83.7 

92 

9.2 

18.4 

27.6 

36.8  |  46.0 

55.2    64.4 

73.6 

82.8 

91 

9.1 

18.2 

27.3 

36.4    45.5 

54.0    63.7 

72.8 

81.9 

90 

9.0 

18.0 

27.0 

36.0    45.0  |  54.0    63.0 

72.0 

81.0 

89 

8.9 

17.8 

26.7 

35.6    44.5  '  53.4    62.3 

71.2 

80.1 

88 

8.8 

17.6 

26.4 

35.2    44.0  i  52.8  *  61.6 

70.4 

79.2 

87 

8.7   17.4 

26.1 

34.*8  j  '43  ."5 

'52.2    60.9 

(59.6 

78:3 

86 

8.6   17.2 

25.8 

34.4  !  43.0 

51.6    60.2 

68.8 

77.4 

LOGARITHMS  OP   NUMBERS. 


145 


—  "                                         — 

No.  500  L.  698.]                                  [No.  544  L.  736. 

N. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Diff. 

500 
1 

2 
3 

4 
5 
6 

7 
8 
9 

510 
1 
2 

3 
4 
5 

6 
7 
8 
9 

520 
1 

4 

6 

8 
9 

530 
1 

2 
3 
4 

G 

7 

8 
9 

540 
1 
2 
3 
4 

698970  9057 
9838  i  9924 

9144 

9231 

9317 

9404 

9491 

9578 

9664 

9751 

0011 
0877 
1741 
2603 
3463 
4322 
5179 
6035 
6888 

7740 
8591 
9440 

0098 
0963 
1827 
2689 
3549 
4408 
5265 
6120 
6974 

7826 
8676 
9524 

0184 
1050 
1913 
2775 
3635  i 
4494 
5350  ! 
6206 
7059 

7911  j 
8761 
9609 

0271 
1136 
1999 
2861 
3721 
4579 
5436 
6291' 
7144 

7996 
8846 
9694 

0358 
1222 
2086 
2947 
3807 
4665 
5522 
6376 
7229 

8081 
8931 
9779 

0444 
1309 
2172 
3033 
3893 
4751 
5607 
6462 
7315 

8166 
90ft 
9863 

0531 
1395 
2258 
3119 
3979 
4837 
5693 
6547 
7400 

8251 
9100 
9948 

0617 
1482 
2344 
3205 
4065 
4922 
5778 
6632 
7485 

8336 
9185 

86 

85 

84 

83 

82 
81 

80 

700704 
1568 
2431 
3291 
4151 
5008 
5864 
6718 

7570 
8421 
9270 

710117 
0963 
1807 
2650 
3491 
4330 
5167 

6003 

6838 
7671 
8502 
9331 

0790 
1654 
2517 
3377 
4236 
5094 
5949 
6803 

7655 

8506 
9355 

0033 
0879 
1723 
2566 
3407 
4246 
5084 
5920 

6754 

7587 
8419 
9248 

0202 
1048 
1892 
2734 
3575 
4414 
5251 

6087 
6921 

7754 
8585 
9414 

0287 
1132 
197'6 
2818 
3659 
4497 
5335 

6170 
7004 

7837 
8668 
9497 

0371 
1217 
2060 
2902 
3742 
4581 
5418 

6254 
7088 
7920 
8751 
9580 

0456  i 
1301  1 
2144  i 
2986 
3826 
4665 
5502 

6337 
7171 

8003 
8834 
9663 

0540 
1385 
2229 
3070 
3910 
4749 
5586 

6421 
7254 

8086 
8917 
9745 

0625 
1470 
2313 
3154 
3994 
4833 
5669 

6504 

7338 
8169 
9000 

9828 

0710 
1554 
2397 
3238 
4078 
4916 
5753 

6588 
7421 
8253 
9083 
9911 

0794 
1639 
2481 
3323 
4162 
5000 
5836 

6671 
7504 
8336 
9165 
9994 

0077 
0903 
1728 
2552 
3374 
4194 

5013 
5830 
6646 
7460 
8273 
9084 
9893 

720159 
0986 
1811 
2634 
3456 

4276 
5095 
5912 
6727 
7541 
8354 
9165 
9974 

0242 
1068 
1893 
2716 
3538 

4358 
5176 
5993 
6809 
7623 
8435 
9246 

0325 
1151 
1975 
2798 
3620 

4440 

5258 
6075 
6890 
7704 
\8516 
9327 

0407 
1233 

2058 
2881 
3702 

4522 
5340 
6156 
6972 

7785 
8597 
9408 

0490 
1316 
2140 
2963 

3784 

4604 
5422 
6238 
7053 

7866 
8678 
9489 

0573 
1398 
2222 
3045 

3866 

4685 
5503 
6320 
7134 
7948 
8759 
9570 

0655 
1481 
2305 
3127 

3948 

4767 
5585 
6401 
7216 
8029 
8841 
9651 

0738 
1563 
2387 
3209 
4030 

4849 
5667 
6483 
7297 
8110 
8922 
9732 

0821 
1646 
2469 
3291 
4112 

4931 
5748 
6564 
7379 
8191 
9003 
9813 

0055 
0863 
1669 

2474 

3278 
4079 
4880 
5679 

0136 
0944 
1750 

2555 
3358 
4160 
4960 
5759 

0217 
1024 
1830 

2635 
3438 
4240 
5040 
5838 

0298 
1105 
1911 

2715 
3518 
4320 
5120 
5918 

0378 
1186 
1991 

2796 
3598 
4400 
5200 
5998 

0459 
1266 
2072 

2876 
3679 
4480 
5279 
6078 

0540 
1347 
2152 

2956 
3759 
4560 
5359 
6157 

0621 
1428 
2233 

3037 
3839 
4640 
5439 
6237 

0702 
1508 
21313 

3117 
3919 
4720 
5519 
6317 

730782 
1589 

2394 
8197 
3999 
4800 
5599 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5 

678 

9 

87    8.7 
86    8.6. 
85    8.5 
84    8.4 

17.4    26.1    34.8 
17.2    25.8    34.4 
17.0    25.5    34.0 
16.8    25.2    33.6 

43.5 
43.0 
42.5 
42.0 

52.2    60.9    69.6 
51.6    60.2    68.8 
51.0    59.5    68.0 
50.4    58.8    67.2 

78.3 
77.4 
76.5 
75.6 

LOGARITHMS  OF   KUHBEK& 


No.  545  L.  736.] 

INo.  584  L.  707. 

N. 

0 

1 

2 

3 

4  ||  6 

6 

7 

8 

9   Diff. 

545  736397  6476  ;  6556 

6635  6715   6795 

6874 

6954  I  7034 

7113 

6    7193  j  7272  7 

352 

743 

1   7511   7'5<>0 

7670 

rr 

"49  7829 

7908 

7    7987  j  8067  8146 

8225 

8305   8384 

8463  8543  8622  8701 

8  j   8781   8860  8939 
9  '   9572  oftfii   urQi 

9018  9097   9177 
9810  9889   9968 

9256  9335 

9414  9493 

0047' 

0126 

0205 

0^84    79 

550  740363 

0442  0521 

0600  0678   0757 

0836 

0915 

0994 

1073 

1    1152 

1230  1309 

138 

8  1467   1546 

1624 

1703 

1782 

1860 

2    1939 

2018  2 

096 

217 

5  2254 

2332 

2411 

189 

2568 

2647 

3    2725 

2804  2 

882 

2961 

3039 

!  3118 

3196 

3275 

3353 

3431 

4    3510 

3588  3667 

3745 

3823 

\  3902 

3980 

4058 

4136  4215 

5    4293 

4371  4 

449 

452 

8 

4606 

4684 

4762 

4 

340 

491£ 

4997 

6 

5075 

5153  5231 

5309 

5387 

5465 

5543 

5621 

5699 

5777 

78 

7 

5855 

5933  fa 

Oil 

608 

9 

6167 

6245 

6323 

6- 

401 

647S 

6556 

8 

6634 

6712  6790  6868 

6945 

7023  7101 

7179  |  7256 

7334 

9 

7412 

7489  7 

567 

7645 

7722 

7800  7878 

7955 

803£ 

8110 

560 

8188 

8266  8343 

8421 

8498 

8576  !  8653 

8731 

880£ 

8885 

1 

8963 

9040  9118  9195 

9272 

9350  \  9427 

9504 

958$ 

9659 

2 

9736 

9814  8 

891  99( 

8 

019^   090O 

A 

TW 

AOK.^ 

<nm 

3 

750508 

0586 

( 

»663 

0740  0817 

0894  !  0971 

VAwl  I 

1048 

UOt>± 

1125 

1202 

4 

1279 

1356 

1 

433 

151 

0  1  1587 

!  16tJ4  !  1741 

1 

318 

189£ 

1972 

5 

2048 

2125 

2202 

227'9 

2356 

2433  2509 

2586 

2663 

2740 

77 

6 

2816 

2893 

2 

970 

304 

7 

3123 

3200  1  3277 

3 

353 

343( 

I 

3506 

7 

3583 

3660 

3736 

3813 

3889 

!  3966  4042 

4119 

4195 

4272 

8 

4348 

4425 

4501 

4578 

4654 

4730  4807 

4883 

4960 

5036 

9 

5112 

5189 

5265 

5341 

5417 

5494  i  5570 

5646 

5722 

5799 

570 

5875 

5951 

6027 

6103 

6180 

6256 

6332 

6408 

6484 

6560 

1 

6636 

6712 

e 

»788 

68e 

4 

6940 

7016  7092  7 

168 

7244 

7320 

76 

2 

7396 

7472 

7548 

7624 

7700 

7775  7851  \  7927 

800; 

5 

8079 

3 

8155 

8230 

£ 

5306 

83£ 

2 

8458 

8533  8609  8 

685 

8761 

8836 

4 

8912 

8988 

9063 

9139  9214 

9290  9366  9441 

9517 

9592 

5 

9668 

9743 

c 

)819 

ggc 

4 

9970 

0045  0121 

0196 

0272 

0347 

6 

760422 

0498 

0573  0649 

0724 

0799  0875 

0950 

1025 

1101 

7 

1176 

1251 

] 

326  14( 

2 

1477 

1552  1627 

1 

702 

177* 

J 

1853 

8 

1928 

2003 

i 

5078  21£ 

3 

2228 

2303  2378 

2 

453 

2521 

1 

2604 

9 

2679 

2754 

2829  2904 

2978 

3053  3128 

3203 

3278 

3353 

7o 

580 

3428 

3503 

3578  !  3653 

3727 

3802  3877 

3952 

4027 

4101 

1 

4176 

4251 

< 

1326  !  4400 

4475 

|  4550  ;  4624 

4699 

4774 

4848 

2 

4923 

4998 

j 

>072  i  514 

7' 

5221 

5296  5370 

5 

445 

552( 

1 

5594 

3 

5669 

5743 

5818 

581 

2 

5966 

1  6041  6115 

6190 

62fr 

I 

6338 

4 

6413 

6487 

( 

>562 

66c 

G 

6710 

6785  I  6859 

6933 

7007 

7082 

PROPORTIONAL  PARTS. 

Diff.   1 

2 

3 

4 

5 

6 

7 

8 

9 

83    8.3 

16.6 

24 

.9 

33.2 

41.5 

49.8 

58.1 

66.4 

74.7 

82    8.2 

16.4 

24.6 

32.8 

41.0 

49.2 

57.4 

65.6 

73.8 

81    8.1 

16.2 

24.3 

32.4 

40.5 

48.6 

56.7 

64.8 

72.9 

80    8.0 

16.0 

24.0 

32.0 

40.0 

48.0 

56.0 

64.0 

72.0 

79    7.9 

15.8 

23.7 

31.6 

39.5 

47.4 

55.3 

63.2 

71.1 

78    7.8 

15.6 

23.4 

31.2 

39.0    46.8 

54.6 

62.4 

70.2 

77    7.7 

15.4 

23.1 

30.0 

38.5    46.2 

53.9 

61.6 

69.3 

76    7.6 

15.2 

22.8 

30.4 

38.0    45.6 

53.2 

60.8 

68.4 

75    7.5 

15.0 

22.5 

30.0 

37.5  '  45.0 

52.5 

60.0 

67.5 

74    7.4 

14.8 

22.2 

29.6 

37.0    44.4 

51.8 

59.2 

66.6 

LOGARITHMS  OF 


147 


No.  585  L.  767.1                                  [No.  629  L.  799. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

585 

767156 

7230  7304  7379 

7453 

7527  7601 

7675 

7749  7823 

6 

7898 

7972  8046  !  8120 

8194 

8268  i  8342 

8416 

8490  8564 

74 

7 

8638 

8712  8786  |  8860 

8934 

9008  9082 

9156 

9230 

9303 

8 

9377 

9451   9525  9599 

9673 

9746  |  9820 

9894 

9968 

0042 

9 

770115 

0189  0263 

0336 

0410 

0484 

0557 

0631 

0705 

0778 

590 

0852 

0926  0999 

1073 

1146 

1220  1293 

1367 

1440 

1514 

1  j 

1587 

1661  i  1734 

1808 

1881 

1955  2028 

2102 

2175 

2248 

2 

2322 

2395  2468 

2542 

2615 

2688  2762 

2835 

2908 

2981 

3 

3055 

3128  3201 

3274 

3348 

3421 

3494 

3567 

3640 

3713 

4 

3786 

3860  3933 

4006 

4079 

|  4152 

4225 

4298 

4371 

4444 

73 

5 

4517 

4590  i  4663 

4736 

4809 

4882 

4955 

5028 

5100 

5173 

6 

5246 

5319  !  5392 

5465 

5538 

5610 

5683 

5756 

5829 

5902 

7 

5974 

6047  !  6120  0193 

6265 

!  6338 

6411 

6483 

6556 

6629 

8 

6701 

6774  !  6846 

6919 

6992 

i  7064 

7137 

7209 

7282 

7354 

9 

7427 

7499 

7572 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

600 

8151 

8224  8296 

8368 

8441 

8513 

8585 

8658 

8730 

8802 

1 

8874 

8947  9019 

9091 

9163 

9236 

9308 

9380 

9452 

9524 

2 

9596 

9669  9741 

9813 

9885 

9957 

0029 

0101 

0173 

9245 

3 

780317 

0389 

0461 

0533 

0605 

0677 

0749 

0821 

0893 

0965 

72 

4 

1037 

1109 

1181 

1253 

1324 

1396 

1468 

1540 

1612 

1684 

5 

1755 

1827 

1899 

1971 

2042 

2114 

2186 

2258 

2329 

2401 

6 

2473 

2544 

2616  2688 

2759 

2831 

2902 

2974 

3046 

3117 

7 

3189 

3260 

3332  !  3403 

3475 

3546 

3618 

3689 

3761 

3832 

8 

3904 

3975 

4046 

4118 

4189 

4261 

4332 

4403 

4475 

4546 

9 

4617 

4689 

4760 

4831 

4902 

4974 

5045 

5116 

5187 

5259 

610 

5330 

5401  5472 

5543 

5615 

5686 

5757 

5828 

5899 

5970 

1 

6041 

6112 

6183 

6254 

6325 

j  6396 

6467 

6538 

6609 

6680 

71 

2 

6751 

6822 

6893 

6964 

7035 

7106 

7177 

7248 

7319 

7390 

3 

7460 

7531 

7602 

7673 

7744 

7815 

7885 

7956 

8027 

8098 

4 

8168 

8239 

8310 

8381 

8451 

8522 

8593 

8663 

8734 

8804 

5 

8875 

8946 

9016 

9087 

9157 

9228 

9299 

9369 

9440 

9510 

6 

9581 

9651 

9722 

9792 

9863 

9933 

0004 

0074 

0144 

0215 

7 

790285 

0356 

0426 

0496 

0567 

0637 

0707 

0778 

0848 

0918 

8 

0988 

1059 

1129 

1199 

1269 

1340 

1410 

1480 

1550 

1620 

9 

1691   1761 

1831 

1901 

1971 

2041 

2111 

2181 

2252 

2322 

620 

2392  2462 

2532 

2602 

2672 

2742 

2812 

2882 

2952 

3022 

70 

1 

3092 

3162 

3231 

3301 

3371 

3441 

3511 

3581 

3651 

3721 

2  1 

3790 

3860 

3930 

4000 

4070 

i  4139 

4209 

4279 

4349 

4418 

3 

4488  4558 

4627 

4697 

4767 

4836 

4906 

4976 

5045 

5115 

4 

5185  5254 

5324 

5393 

5463 

5532 

5602 

5672 

5741 

5811 

5  i 

5880  5949 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

6505 

6  i 

6574  6644 

6713 

6782 

6852 

6921 

6990 

7060 

7129 

7198 

7 

7268  7337 

7406 

7475 

7545 

i  7614 

7683 

7752 

7821 

7890 

8 

7960 

8029 

8098 

8167 

8236 

8305 

8374 

8443 

8513 

8582 

9 

8651 

8720 

8789 

8858 

8927   8996  9065  9134 

9203 

9272 

.69 

PROPORTIONAL  PARTS. 

Diff 

1 

234 

5678 

9 

75 

7.5 

15.0    22.5    30.0 

37.5 

45.0    52.5    60.0 

67.5 

74 

7.4 

14.8    22.2    29.6 

37.0 

44.4    51.8    59.2 

66.6 

73 

7.3 

14.6    21.9    29.2 

36.5 

43.8    51.1    58.4 

65.7 

72 

7.2 

14.4    21.6    28.8 

36.0 

43.2    50.4    57.6 

64.8 

71 

7.1 

14.2    21.3    28.4 

35.5 

42.6    49.7    56.8 

63.9 

70 

7.0 

14.0    21.0    28.0 

35.0 

42.0    49.0    56.0 

63.0 

69 

6.9 

13.8    20.7    27.6 

34.5 

41.4    48.3    55.2 

62.1 

148 


LOGARITHMS  OF  K UMBERS. 


—  ,  ^ 
No.  630  L.  799.]                                [No.  674  L.  829. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

630 

799341 

9409 

9478 

9547 

9616 

9685 

9754 

9823  9892  9961 

1 

800029 

0098 

0167  0236 

0305 

0373 

0442 

0511   0580  !  0648 

2 

0717 

0786 

0854  i  0923 

0992 

1061 

1129 

1198  1266  1335 

3 

1404 

1472 

1541  I  1609 

1678 

1747  1815 

1884 

1952  2021 

4 

2089 

2158 

2226 

2295 

2363 

2432 

2500 

2568 

2637  2705 

5 

2774 

2842 

2910 

2979 

3047 

3116 

3184 

3252 

3321 

3389 

6 

3457 

3525 

3594 

3662 

3730 

3798 

3867 

3935 

4003 

4071 

7 

4139 

4208 

4276 

4J344 

4412 

4480 

4548 

4616 

4685 

4753 

8 

4821 

4889 

4957 

5025 

5093 

5161 

5229 

5297 

5365 

5433 

68 

9 

5501 

5569 

5637 

5705 

5773 

5841 

5908 

5976 

6044 

6112 

640 

806180 

6248 

6316 

6384 

6451 

6519 

6587 

6655 

6723 

6790 

1 

6858 

6926 

6994 

7061 

7129 

7197 

7264 

7332  7400 

7467 

2 

7535 

7603 

7670 

7738 

7'806  1  7873 

7941 

8008 

8076 

8143 

3 

8211 

8279 

8346 

8414 

8481  1  8549 

8616 

8684 

8751 

8818 

4 

8886 

8953 

9021 

9088 

9156 

9223 

9290 

9358 

9425 

9492 

5 

9560 

9627 

9694 

9762 

9829 

9896 

9964 

0031 

0098 

0165 

6 

810233 

0300 

0367 

0434 

0501 

0569 

0636 

0703 

0770 

0837 

7 

0904 

0971 

1039 

1106 

1173 

1240 

1307 

1374 

1441 

1508 

67 

8 

1575 

1642 

1709 

1776 

1843 

1910 

1977 

2044 

2111 

2178 

9 

2245 

2312 

2379 

2445 

2512 

2579 

2646 

2713 

2780 

2847 

650 

2913 

2980 

3047 

3114 

3181 

3247 

3314 

3381 

3448 

3514 

1 

3581 

3648 

3714 

3781 

3848 

3914 

3981 

4048 

4114 

4181 

2 

4248 

4314 

4381 

4447 

4514 

4581 

4647 

4714 

4780 

4847 

3 

4913 

4980 

5046 

5113 

5179 

5246 

5312 

5378 

5445 

5511 

4 

5578 

5644 

5711 

5777 

5843 

5910 

5976 

6042 

6109 

6175 

5 

6241 

6308 

6374 

6440 

6506 

6573 

6639 

6705 

6771 

6838 

6 

6904 

6970 

7036 

7102 

7169 

7235 

T301 

7367 

7433 

7499 

7 

7565 

7631 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8160 

8 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

9 

8885 

8951 

9017 

9083 

9149 

9215 

9281 

9346 

9412 

9478 

DO 

660 

9544 

9610 

9676 

9741 

9807 

9873 

9939 

0004 

0070 

0136 

1 

820201 

0267 

0333 

0399 

0464 

0530 

0595 

0661 

0727 

0792 

2 

0858 

0924 

0989 

1055 

1120 

1186 

1251 

1317 

1382 

1448 

3 

1514 

1579 

1645 

1710 

1775 

1841 

1906 

1972 

2037 

2103 

4 

2168 

2233 

2299 

2364 

2430 

2495 

2560 

2626 

2691 

2756 

5 

2822 

2887 

2952 

3018 

3083 

3148 

3213 

3279 

3344 

3409 

6 

3474 

&539 

3605 

3670 

3735 

3800 

3865 

3930 

3996 

4061 

7 

4126 

4191 

4256 

4321 

4386 

4451 

4516 

4581 

4646 

4711 

65 

8  i   4776 

4841 

4906 

4971 

5036 

5101 

5166 

5231 

5296 

5361 

9 

5426 

5491 

5556 

5621 

5686 

5751 

5815 

5880 

5945 

6010 

670 

6075 

6140 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

1 

6723 

6787 

6852 

6917 

6981 

7046 

7111 

7175 

7240 

7305 

2 

7369 

7434 

7499 

7563 

7628 

7692 

7757 

7821 

7886 

7951 

3 

8015 

8080 

8144 

8209 

8273 

8338 

8402 

8467 

8531 

8595 

4 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9175 

9239 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5 

678 

9 

68    6.8 

13.6    20.4    27.2 

34.0 

40.8    47.6    54.4 

61.2 

67    6.7 

13.4    20.1    26.8 

33.5 

40.2    46.9    53.6 

60.3 

66    6.6 

13.2    19.8    26.4 

33.0 

3d.  6    46.2    52.8 

59.4 

65    6.5 

13.0    19.5    26.0 

32.5 

39.0    45.5    52.0 

58.5 

64    6.4 

12.8    19.2  |  25.6 

32.0 

38,4    44.8    51.2 

57,  a 

LOGARITHMS   OF   NUMBERS. 


149 


No.  675  L.  829.]                                   [No.  719  L.  857. 

N. 

0 

1    2 

*    4 

5 

« 

7 

8 

9 

Diff 

675 

829304 

9368 

9432 

9497 

9561 

9625 

9690 

9754 

9818 

9882 

Q 

9947 

0011 

0075 

0139 

0204 

0268 

0332 

0396 

0460 

0525  1 

7 

830589 

0653 

0717 

0781 

0845 

0909 

0973 

1037 

1102 

1166  i 

8 

1230 

1294 

1358 

1422 

1486 

1  1550 

1614 

1678 

1742 

1806 

64 

9 

1870 

1934 

1998 

2062 

2126  j  2189 

2253 

2317 

2381 

2445 

680 

3509 

2573 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3083 

1 

3147 

3211 

3275 

3338 

3402 

3466 

3530 

3593 

3657 

3721 

2 

3784 

3848 

3912 

3975 

4039 

4103 

4166 

4230 

4294 

4357 

3 

4421 

4484 

4548 

4611 

4675 

4739 

4802 

4866 

4929 

4993 

4 

5056 

5120 

5183 

5247 

5310 

5373 

5437 

5500 

5564 

5627 

5 

5691 

5754 

5817 

5881 

5944 

6007 

6071 

6134 

6197 

6261 

6 

6324 

6387 

6451 

6514 

6577 

6641 

6704 

6767 

6830 

6894 

7 

6957 

7020 

7083 

7146 

7210 

7273 

7336 

7399 

7462 

7525 

8 

7588 

7652 

7715 

7778 

7841 

7904 

7967 

8030 

8093 

8156 

9 

8219 

8282 

8345 

8408 

8471 

8534 

8597 

8660 

8723 

8786 

63 

690 

8849 

8912 

8975 

9038 

9101 

9164 

9227  !  9289 

9352 

9415 

i 

9478 

9541 

9604 

9667 

9729 

9792 

9855  !  QQ1  fi 

9981 

0043 

2 

840106 

0169 

0232 

0294 

0357 

0420 

0482 

0545 

0608 

0671 

3 

0733 

0796 

0859 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

4 

1359 

1422 

1485 

1547 

1610 

1672 

1735 

1797 

1860 

1922 

5 

1985 

2047 

2110 

2172 

2235 

2297 

2360 

2422 

2484 

2547 

6 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3046 

3108 

3170 

ri 

3233 

3295 

3357 

3420 

3482 

3544 

3606 

3669 

3731 

3793 

8 

3855 

3918 

3980 

4042 

4104 

4166 

4229 

4291 

4353 

4415 

9 

4477 

4539 

4601 

4664 

4726 

4788 

4850 

4912 

4974 

5036 

700 

5098 

5160 

5222 

5284 

5346 

5408 

5470 

5532 

5594 

5656 

62 

1 

5718 

5780 

5842 

5904 

5966 

6028 

6090 

6151 

6213 

6275 

2 

6337 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

3 

6955 

7017 

7079 

7141 

7202 

7264 

7326 

7388 

7449  !  7511 

4 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8004 

8066  8128 

5 

8189 

8251 

8312 

8374 

8435 

8497 

8559 

8620  i  8682  8743 

6 

8805 

8866 

8928 

8989 

9051 

9112 

9174 

9235  9297  9358 

7 

9419 

9481 

9542 

9604 

9665 

9726 

9788 

9849 

9911  9972 

8 

850033 

0095 

0]56 

0217 

0279 

0340 

0401 

0462  0524  0585 

9 

0646 

0707 

0769 

0830 

0891 

0952 

1014 

1075 

1136  1197 

710 

1258 

1320 

1381 

1442 

1503 

1564 

1625 

1686 

1747  1809 

1 

1870 

1931 

1992 

2053 

2114 

2175 

2236 

2297 

2358  2419 

2480 

2541 

2602 

2663 

2724 

2785 

2846 

2907 

2968  3029 

61 

3 

3090 

3150 

3211 

3272 

3333 

3394 

3455 

3516 

3577  i  3637 

4 

3698 

3759 

3820 

3881 

3941 

4002 

4063 

4124 

4185  ;  4245 

5 

4306 

4367 

4428 

4488 

4549 

4610 

4670 

4731 

4792  4852 

6    4913 

4974 

5034 

5095 

5156 

5216 

5277 

5337 

5398  5459 

7    5519 

5580 

5640 

5701 

5761 

5822 

5882 

5943 

6003  6064  i 

8 

6124 

6185 

6245 

6306 

6366 

6427  6487 

6548 

6608  I  6668 

9 

6729 

6789  6850 

6910 

6970 

7031   7091 

7152  7212 

7272 

* 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5 

678 

9 

65    6.5 

13.0    19.5    26.0 

32.5 

39.0    45.5    52.0 

58.5 

64    6.4 

12.8    19.2    25.6 

32.0 

38.4    44.8    51.2 

57.6 

63    6.3 

12.6    18.9    25.2 

81.5    37.8    44.1    50.4 

56.7 

62    6.2 

12.4    18.6    24.8 

31.0 

37.2    43.4    49.6 

55.8 

61    6.1 

12.2    18.3    24.4    30.5 

36.6  !  42.7    48.8 

54.9 

60    6.0 

12.0    18.0    24.0    30.0    36.0    42.0    48.0  I 

54.0 

L50 


LOGARITHMS  OF  NUMBERS* 


No.  720  L.  857.]                                   [No.  764  L.  883. 

i 

N. 

0 

1 

2 

3 

4 

6 

6 

1 

8 

9 

Diff. 

720 

&57332 

7393 

7453 

7513 

7574 

7634 

7694 

7755 

7815 

7875 

1 

7935 

7995 

8056 

8116 

8176 

8236 

8297 

8357 

8417 

8477 

2 

8537 

8597 

8657 

8718 

8778 

8838 

8898 

8958 

9018 

9078 

3 

9138 

9198 

9258 

9318 

9379 

9439 

9499 

9559 

9619 

9679 

GO 

9739 

9799 

9859 

9918 

9978 

4 

!  (X)38 

0098 

0158 

0218 

0278 

5 

860338 

0398 

0458 

0518 

0578 

0637 

0697 

0757 

0817 

0877 

6 

0937 

0996 

1056 

1116 

1176 

1236 

1295 

1355 

1415 

1475 

7 

1534 

1594 

1654 

1714 

1773 

1833 

1893 

1952 

2012 

2072 

8 

2131 

2191 

2251 

2310 

2370 

2430 

2489 

2549 

2608 

2668 

9 

2728 

2787 

2847 

2906 

2966 

3025 

3085 

3114 

3204 

3263 

730 

3323 

3382 

3442 

3501 

3561 

3620 

3680 

3739 

3799 

3858 

1 

3917 

3977 

4036 

4096 

4155 

4214 

4274 

4333 

4392 

4452 

2 

4511 

4570 

4630 

4689 

4748 

4808 

4867 

4926 

4985 

5045 

3 

5104 

5163 

5222 

5282 

5341 

5400 

5459 

5519 

5578 

5637 

4 

5696 

5755 

5814 

5874 

5933 

5992 

6051 

6110 

6169 

6228 

5 

6287 

6346 

6405 

6465 

6524 

6583 

G642 

6701 

6760 

6819 

6 

6878 

6937 

6996 

7055 

7114 

7173 

7232 

7291 

7350 

7409 

59 

7  I   7467 

7526 

7585 

7644 

7703 

7762 

7821 

7880 

7939 

7998 

8    8056 

8115 

8174 

8233 

8292 

8350 

8409 

8468 

8527 

8586 

9 

8644 

8703 

8762 

8821 

8879 

8938 

8997 

9056 

9114 

91V3 

740 

9232 

9290 

9349 

9408 

9466 

9525 

9584 

9642 

9701 

9760 

i 

(1W1« 

9877 

9935 

9994 

0053 

0111 

0170 

0228 

0287 

0345 

2 

870404 

0462 

0521 

0579 

0638 

0696 

0755 

0813 

087'2 

0930 

3 

0989 

1047 

1106 

1164 

1223 

1281 

1339 

1398 

1456 

1515 

4  1   1573 

1631 

1690 

1748 

1806 

1865 

1923 

1981 

2040 

2008 

5  |   2156 

2215 

2273 

2331 

2389 

2448 

2506 

2564 

2622 

2681 

6 

2739 

2797 

2855 

2913 

2972 

3030 

3088 

3146 

3204 

3262 

7 

3321 

3379 

3437 

3495 

3553 

3611 

3669 

3727 

3785 

3844 

8 

3902 

3960 

4018 

4076 

4134 

4192 

4250 

4308 

4366 

4424 

58 

9 

4482 

4540 

4598 

4656 

4714 

|  4772 

4830 

4888 

4945 

5003 

750 

5061 

5119 

5177 

5235 

5293 

!  5351 

5409 

5466 

5524 

5582 

1 

5640 

5698 

5756 

5813 

5871 

5929 

5987 

6045 

6102 

6160 

2 

6218 

6276 

6333 

6391 

6449 

6507 

6564 

6622 

6680 

6737 

3 

6795 

6853 

6910 

6968 

7026 

7083 

7141 

7199 

7256 

7314 

4 

7371 

7429 

7487 

7544 

7602 

7659 

7717 

7774 

7832 

7889 

5 

7947 

8004 

8062 

8119 

8177 

82134 

8292 

8349 

8407 

8464 

6 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

8981 

9039 

7 

9096 

QfifiQ 

9153 
9726 

9211 

9784 

9268 
9841 

9325 

9898 

9383 
9956 

9440 

9497 

9555 

9612 

yooy 

0013 

0070 

0127 

0185 

9  !  880242 

0299 

0356 

0413 

0471 

0528 

0585 

0642 

0699 

0756 

760 

0814 

0871 

0928 

0985 

1042 

1099 

1156 

1213 

1271 

1328 

1 

1385 

1442 

1499 

1556 

1613 

:  1670 

1727 

1784 

1841 

1898 

2  1   1955 

2012 

2069 

2126 

2183 

2240 

2297 

2354 

2411 

2468 

57 

3    2525 

2581 

2638 

2695 

2752 

2809 

2866 

2923 

2980 

3037 

4 

3093 

3150 

3207 

3264 

3321 

3377 

3434 

3491 

3548 

3605 

1 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5      G      7      8 

9 

59    5.9 

11.8    17.7    23.6 

29.5    35.4    41.3    47.2 

53.1 

58    5.8   11.  G    17.4    23.2    29.0    b4.8    40.0    46.4 

52.2 

57    5.7   11.4    17.1  j  22.8    28.5    34.2    39.  «)    45.  G 

51.3 

56  ;  5.G   11.2    10.8  i  22.4    28.  0    o-J.G    :%).•>    44.  S 

50.4 

i 

LOGARITHMS   OF   NUMBERS. 


151 


No.  765  L.  883.]                                   [No.  809  L.  908. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

765 

883661 

3718 

3775 

3832 

3888 

3945 

4002 

4059 

4115 

4172 

6 

4229 

4285 

4342 

4399 

4455 

4512. 

4569 

4625 

4682  4739 

7 

4^95 

4852 

4909 

4965 

5022 

5078 

5135 

5192 

5248  5305 

8 

5361 

5418 

5474 

5531 

5587 

5644 

5700 

5757 

5813  5870 

9 

5926 

5983 

6039 

6096 

6152 

6209 

6265 

6321 

6378 

6434 

770 

6491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

1 

7054 

7111 

7167 

7223 

7280 

7336 

7392 

7449 

7505 

7561 

2 

7617 

7674 

7730 

7786 

7842 

7898 

7955 

8011 

8067 

8123 

3 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

8573 

8629 

8685 

4 

8741 

8797 

8853 

8909 

8965 

9021 

9077 

9134 

9190 

9246 

5 
g 

9302 
9862 

9358 
9918 

9414 

9974 

9470 

9526 

9582 

9638 

9694 

9750 

9806 

56 

0030 

0086 

0141 

0197 

0253 

0309 

0365 

7 

890421 

0477 

0533 

0589 

0645 

0700 

0756 

0812 

0868 

0924 

8 

0980 

1035 

1091 

1147 

1203 

1259 

1314 

1370 

1426 

1482 

9 

1537 

1593 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

780 

2095 

2150 

2206 

2262 

2317 

2373 

2429 

2484 

2540 

2595 

1 

2651 

2707 

2762 

2818 

2873 

2929 

2985 

3040 

3096 

3151 

2 

3207 

3262 

3318 

3373 

3429 

3484 

3540 

3595 

3651 

3706 

3 

3762 

3817 

3873 

3928 

3984 

4039 

4094 

4150 

4205 

4261 

4 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

5 

4870 

4925 

4980 

5036 

5091 

5146 

5201 

5257 

5312 

5367 

6 

5423 

5478 

5533 

5588 

5644 

5699 

5754 

5809 

5864 

5920 

7 

5975 

6030 

6085 

6140 

6195 

6251 

6306 

6361 

6416 

6471 

8 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 

9 

7077 

7132 

7187 

7242 

7297 

7352 

7407 

7462 

7517 

7572 

55 

790 

7627 

7682 

7737 

7792 

7847 

7902 

7957 

8012 

8067 

8122 

1 

8176 

8231 

8286 

8341 

8396 

8451 

8506 

8561 

8615 

8670 

2 

8725 

8780 

8835 

8890 

8944 

8999 

9054 

9109 

9164 

9218 

3 

9273 

9821 

9328 

9875 

9383 
9930 

9437 

9985 

9492 

9547 

9602 

9656 

9711 

9766 

0039 

0094 

0149 

0203 

0258 

0312 

5 

900367 

0422 

0476 

0531 

0586 

0640 

0695 

0749 

0804 

0859 

6 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

1295 

1349 

1404 

7 

1458 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

1894 

1948 

8 

2003 

2057 

2112 

2166 

2221 

2275 

2329 

2384 

2438 

2492 

9 

2547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3036 

800 

3090 

3144 

3199 

3253 

3307 

3361 

3416 

3470 

3524 

3578 

1 

3633 

3687 

3741 

3795 

3849 

3904 

3958 

4012 

4066 

4120 

2 

4174 

4229 

4283 

4337 

4391 

4445 

4499 

4553 

4607 

4661 

3 

4716 

4770 

4824 

4878 

4932 

4986 

5040 

5094 

5148 

5202 

KA 

4 

5256 

5310 

5364 

5418 

5472 

5526 

5580 

5634- 

5688 

5742 

O4 

5 

5796 

5850 

5904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

6 

6335 

6389 

6443 

6497 

6551 

6604 

6658 

6712 

6766 

6820 

7 

6874 

6927 

6981 

7035 

7089 

7143 

7196 

7250 

7304 

7358 

8 

7411 

7405 

7519 

7573 

7626 

7680 

7734 

7787 

7841 

7895 

9 

7949 

8002 

8056 

8110 

8163 

8217 

8270  i  8324 

8378 

8431 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5678 

9 

57    5.7 

11.4    17.1    22.8 

28.5    34.2    39.9    45.6 

51.3 

56    5.6 

11.2    16.8    22.4 

28.0  |  33.6    39.2    44.8 

50.4 

55    5.5 

11.0    16.5    22.0 

27.5    33.0    38.5    44.0 

49.5  i 

54    5.4 

10.8  i  16.2    21.6 

27.0  |  32.4  i  37.8    43.2    48.61 

LOGARITHMS   OF    NUMBERS. 


No.  810  L.  908.] 

[No.  854  L.  931. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

810 

908485 

8539 

8592 

8646 

8699  |  8753 

8807  8860 

8914  1  8967 

1 

9021 

9074 

9128 

9181 

.9235   9289 

9342 

9396 

9449  9503 

9556 

9610 

g 

663 

971 

j 

9770 

Q893 

9877  9S 

30 

99& 

1 

nnQ7 

3 

910091 

0144 

0197 

0251 

0304   0358 

0411  0464 

0518  0571 

4 

0624 

067'8 

0 

731 

078 

4 

0838  !  0891 

0944  i  01 

98 

1051 

1104 

5 

1158 

1211 

1 

264 

131 

7' 

1371   1424 

1477  !  Ic 

30 

158-1 

[ 

1637 

6 

1690 

1743 

1797 

1850 

1903  i  1956 

2009  2063 

2116  2169 

r 

2222 

2275 

2 

328 

238 

1 

2435  |  2488 

2541   2£ 

94 

264r 

r  i  2700 

8 

2753 

2806 

2859 

2913 

2966   3019 

3072  3125 

3178 

3231 

9 

3284 

3337 

3390 

3443 

3496   3549 

3602 

3655 

3708 

3761 

53 

820 

3814 

3867 

3920 

3973 

4026 

4079 

4132 

4184 

4237  4290 

1 

4343 

4396 

4 

449 

450 

2 

4555 

4608 

4660 

4' 

13 

476( 

i  4819 

2 

4872 

4925 

4977 

5030 

5083   5136 

5189 

5241  !  5294  !  5347 

3 

5400 

5453 

5 

505 

555 

8 

5611   5664 

571d 

5' 

"69  '  582, 

2  i  5875 

4 

5927 

5980 

I 

033 

6085 

6138   6191 

6243 

6296  6349 

6401 

5 

6454 

6507 

6 

559 

661 

2 

6664  '  6717 

6770 

0! 

322  687 

3 

6927 

6 

6980 

7033 

7085 

7138 

7190   7243 

7295 

7348  1  7400 

7453 

7 

7506 

7558 

r 

611 

766 

3 

7716  '  7768 

7820 

7 

373  i  792 

5 

7978 

8 

8030 

8083 

81  &5 

8188 

8240  1  8293 

8345 

8397  1  8450 

8502 

9 

8555 

8607 

8659 

8712 

8764 

i  8816 

8869 

8921  8973 

9026 

830 

9078 

9130 

S 

183 

9235 

9287  !  9340 

9392 

9444  9496  |  9549 

9601 

9653 

( 

975 

D 

9810  :  9862 

9914 

9 

ifir 

nmo   nn*7i 

2 

920123 

0176 

0228 

0280 

0332 

0384 

0436 

0489 

0541 

0593 

3 

0645 

0697 

C 

749 

08C 

1 

0853 

0906 

0958 

1 

)10 

106 

2 

1114 

M 

4 

1166 

1218 

1270 

1322 

1374 

1426 

1478 

1530 

1582 

1634 

OSS 

5 

1686 

1738 

1 

790 

184 

2 

1894 

1946 

1998 

2 

):,<> 

210 

2 

2154 

6 

2206 

2258 

2310 

2362 

2414 

2466 

2518 

2570 

2622 

2674 

7 

2725 

2777 

S 

829 

28£ 

1 

2933 

2985 

3037 

3 

189 

314 

0 

3192 

8 

3244 

3296 

3348 

ass 

g 

3451 

3503 

3555 

3607 

3658 

3710 

9 

3762 

3814 

5 

1865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

840 

4279 

4331 

4 

1383 

4434 

4486 

4538 

4589 

4641 

4693 

4744 

1 

4796 

4848 

\ 

1899 

49£ 

i 

5003 

5054 

5106 

5 

157 

520 

9 

5261 

2 

5312 

5364 

5415 

5467 

5518 

5570 

5621 

5673 

5725 

5776 

3 

5828 

5879 

5931 

59£ 

2 

6034 

6085 

6137 

6188 

6240 

6291 

4 

6342 

6394 

( 

1445 

641 

7 

6548 

6600 

6651 

6 

702  i  675 

4 

6805 

5 

6857 

6908 

6959 

7011 

7062 

7114 

7165 

7216  7268 

7319 

6 

7370 

7422 

" 

'473 

75$ 

4 

757'6 

7627 

7678 

7 

730 

778 

1 

7832 

7 

7883 

7935 

r 

'986 

8037 

8088 

8140 

8191 

8242 

8293 

8345 

8 

8396 

8447 

I 

5498 

8549 

8601 

8652 

8703 

8754  8805 

8857 

9 

8908 

8959 

9010 

9061 

9112 

9163 

9215 

9266  9317 

9368 

850 

9419 

9470 

9521 

9572 

9623 

1  9674 

9725 

9776  9827 

9879 

9930 

9981 

51 

0032 

0083 

0134 

0185 

0236 

0287 

0338 

0389 

2 

930440 

0491 

0542 

0592 

0643 

0694 

0745 

0796 

0847 

0898 

3 

0949 

1000 

1 

051 

11C 

2 

1153 

1204 

1254 

1 

305  135 

G 

1407 

4 

1458 

1509 

1560 

1610 

1661 

1712 

1763 

1814  i  1865 

1915 

PROPORTIONAL  PARTS. 

Diff.   1 

2 

3 

4 

5 

6 

7 

8 

9 

53    5.3 

10.6 

15.9 

21.2 

26.5 

31.8 

37.1 

42.4    47.7 

52    5.2 

10.4 

15.6 

20.8 

26.0 

31.2 

36.4 

41.6 

46.8 

51    5.1 

10.2 

15.3 

20.4 

25.5 

30.  G 

35.7 

40.8 

45.9 

50    5.0   10.0 

15.0 

20.0 

25.0 

30.0 

35.0 

40.0    45.0 

JLOGAB1THMS   Off   KUMBERS. 


153 


No.  855  L.  931.1 

[No.  899  L.  954 

N. 

0 

1 

2 

3 

4 

6 

6 

7 

8 

y 

Diff. 

355 

931966 

2017  2068 

2118 

2169 

2220  2271 

2322 

2372 

2423 

6 

2474 

2524 

2575 

26 

26 

2677 

1  2727  2778 

2829 

28" 

"9 

2930 

7 

2981 

3031 

3082 

3133 

3183 

3234 

3285  !  3335 

33* 

to 

3437 

8 

3487 

3538 

3589 

3639 

3690 

3740 

3791  3841  |  3892 

3943 

9 

3993 

4044 

4094 

4145 

4195 

4246 

4296  4347 

4397 

4448 

860 

4498 

4549 

4599 

4650 

4700 

4751 

4801  4852 

4902 

4953 

1 

5003  !  5054 

5104 

51 

54 

5205 

5255 

5306  5356 

54( 

Hi 

5457 

2 

5507  5558 

5608 

5658 

5709 

5759 

5809 

5860 

5910 

5960 

3 

6011 

6061 

6111 

61 

02 

6212 

6262 

6313 

6363 

64] 

8 

6463 

4 

6514  6564 

6614 

6665 

6715 

6765 

6815  6865 

6916 

6966 

5 

7016  7066 

7116 

7167 

7217 

7267 

7317  |  7367 

7418 

7468 

6 

7518  7568 

7618 

76 

(58 

7718 

7769 

7819  i  7869 

79] 

9  7969 

7 

8019 

8069 

8119 

8169 

8219 

8269 

8320  :  8370 

8420  8470 

50 

8 

8520 

8570 

8620 

8670 

8720 

8770 

8820  !  8870 

89$ 

20 

8970 

9 

9020 

9070 

9120 

9170 

9220 

9270 

9320  9369 

9419 

9469 

870 

9519 

9569 

9619 

9669 

9719 

9769 

9819  9869 

9918 

9968 

1 

940018 

0068 

0118 

0168  |  0218  il  0267  0317  0367 

0417 

0467 

2 

0516 

0566 

0616 

0666  0716  !  0765 

0815  0865 

0915 

0964 

3    1044 

1064 

1114 

11 

(53 

1213  1  1263 

1313  1362 

14] 

o 

1462 

4 

1511 

1561 

1611 

1660 

1710   1760 

1809  1859 

1909 

1958 

5    2008 

2058 

2107 

2157 

2207  I,1  2256 

2306  2355 

2405 

2455 

6    2504 

2t>54 

2603 

26 

58 

2702  II  2752 

2801  2851 

29( 

)1 

2950 

7    3000 

3049 

3099 

3148 

3198  1  3247 

3297 

3346 

381 

(5 

3445 

8    3495 

3544 

3593 

36 

43 

3692 

3742 

8791 

3841 

88! 

1) 

3939 

9 

3989 

4038 

4088 

4137 

4186 

4236 

4285 

4335 

4£ 

4 

4433 

880 

4483 

4532 

4581 

4631 

4680 

!  4729 

4779 

4828 

4877 

4927 

1 

4976 

5025  5074 

5124 

5173  i  5222 

5272 

5321 

5370 

5419 

2 

5469 

5518 

5567 

56 

16 

5665 

5715 

5764 

5813 

58e 

j> 

5912 

3 

5961 

6010 

6059 

6108 

6157 

6207 

6256 

6305 

6354 

6403 

4 

6452 

6501 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

5 

6943 

6992 

7041 

70 

JO 

7139 

7189 

7238 

7287 

733 

G 

7385 

6 

7434 

7483 

7532 

75 

11 

7630 

7679 

7728 

7777 

782 

G 

7875 

49 

7 

7924 

7973 

8Q22 

8070 

8119 

8168 

8217 

8266 

8315 

8364 

8 

8413 

8462 

8511 

8560 

8608 

8657 

8706 

8755 

8804 

8853 

9 

8902 

8951 

8999 

9048 

9097 

9146 

9195 

9244 

929 

g 

9341 

890 

9390 

9439 

9488 

95 

3(5 

9585 

9634 

9683 

9731 

978 

0 

9829 

9878 

9926 

9975 

00°  1 

0073 

0121 

0170 

0219 

0267 

0316 

2 

950365 

0414 

0462  0511 

0560 

0608 

0657 

0706 

0754 

0803 

3 

0851 

0900 

0949 

0997 

1046 

1095 

1143 

1192 

1240 

1289 

4 

1338 

1386  1435 

14* 

<3 

1532 

1580 

1629 

1677 

172 

G 

1775 

5 

1823 

1872  1920 

1969 

2017  !|  2066 

2114 

2163 

2211 

2260 

6 

2308 

2356  2405 

2453 

2502  ii  2550 

2599 

2647  2696 

2744 

7 

2792 

2841  2889 

29^ 

18 

2986   3034  3083  3131   318 

f) 

3228 

8 

3276 

3325  3373 

34^ 

21 

3470  i  3518 

3566  3615  :  366 

3 

3711 

9 

3760 

3808  3856 

894 

)5 

3953 

4001 

4049  4098  ;  4146 

4194 

i 

PROPORTIONAL  PARTS. 

Diff.   1 

i 

2 

3 

4 

5 

6      7 

8 

9 

51    5.1 
50    5.0 

10.2 
10.0 

15.3 
15.0 

20.4 
20.0 

25.5 
25.0 

30.6    35.7 
30.0    &5.0 

40.8    45.9 
40.0    45.0 

49    4.9 

9.8 

14.7 

19.6 

24.5 

29.4    34.3 

39.2    44.1 

48    4.8    9.6    14.4 

19.2 

24.0 

28.8    33.6 

38.4    43.2 

154 


LOGARITHMS  OF  NUMBERS, 


No  900  L.  954.1                                  [No.  944  L.  975. 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9    Diff. 

900 

954243 

4291 

4339  4387 

4435 

4484 

4532 

4580  I  4628 

4677 

1 

4725 

4773 

4821 

4869 

4918 

4966 

5014  |  5062  5110  5158 

2 

5207 

5255 

5303 

5351 

5399 

5447 

5495  5543  5592  ;  5640 

3 

5688 

5736 

5784 

5832 

5880 

5928 

5976  1  6024  6072  \  6120 

4 

6168 

6216 

6265 

6313 

6361 

6409 

6457 

6505  6553  6601 

5 

6649 

6697 

6745 

6793 

6840 

6888 

6936 

6984 

7032 

7080 

48  • 

0 

7128 

7176 

7224 

7272 

7320 

7368 

7416 

7464 

7512 

7559 

7 

7607 

7655 

7703 

7751 

7799 

7847 

7894 

7942 

7990 

8038 

8 

8086 

8134 

8181 

8229 

8277 

8325 

8373 

8421 

8468  j  8516 

9 

8564 

8612 

8659 

8707 

8755 

8803 

8850 

8898 

8946 

8994 

910 

9041 

9089 

9137 

9185 

9232 

9280 

9328 

9375 

9423 

9471 

1 
2 

9518 
9995 

9566 

9614 

9661 

9709 

9757 

9804 

9852 

9900 

9947 

0042 

0090 

0138 

0185 

0233 

0280 

0328 

0376 

0423 

3 

960471 

0518 

0566 

0613 

0661 

0709 

0756 

0804 

0851 

0899 

4 

0946 

0994 

1041 

1089 

1136 

1184 

1231 

1279 

1326 

1374 

5 

1421 

1469 

1516 

1563 

1611 

1658 

1706 

17'53 

1801 

1848 

6 

1895 

1943 

1990 

2038 

2085 

2132 

2180 

2227 

2275 

2322 

7 

2369 

2417 

2464 

2511 

2559 

2606 

2653 

2701 

2748 

2795 

8 

2843 

2890 

2937 

2985 

3032 

3079 

3126 

3174 

3221 

3268 

9 

3316 

3363 

3410 

3457 

3504 

3552 

3599 

3646 

3693 

3741 

920 

3788 

3835 

3882 

3929 

3977 

4024 

4071 

4118 

4165 

4212 

1 

4260 

4307 

4354 

4401 

4448 

4495 

4542 

4590 

4637 

4684 

2 

4731 

4778 

4825 

4872 

41)19 

4966 

5013 

5061   5108 

5155 

3 

5202 

5249 

5296 

5343 

5390 

5437 

5484 

5531 

5578 

5625 

4 

5672 

5719 

5766 

5813 

5860 

5907 

5954 

6001- 

6048 

6095 

47 

5 

6142 

6189 

6236 

6283 

6329 

6376 

6423 

6470 

6517 

6564 

6 

6611 

6658 

6705 

6752 

6799 

6845 

6892 

6939 

6986 

7033 

7 

7080 

7127 

7173 

7220 

7267 

7314 

7361 

7408 

7454 

7501 

8 

7548 

7595 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

9 

8016 

8062 

8109 

8156 

8203 

8249 

8296 

a343 

8390 

8436 

930 

8483 

8530 

8576 

8623 

8670 

8716 

8763 

8810 

8856 

8903 

1 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9:376 

9323 

9369 

2 

9416 

9463 

9509 

9556 

9602 

9649 

9695 

9742  9789 

9835 

3 

9882 

9928 

9975 

0021 

0068 

0114 

0161 

0207  ft9.M 

0300 

4 

970347 

0393 

0440 

0486 

0583 

0579 

0626 

0672 

0719 

0765 

5 

0812  !  0858 

0904 

0951 

0997 

1044 

1090 

1187 

1183 

1229 

C 

1276 

1322 

1369 

1415 

1461 

1508 

1554 

1601 

1647 

1693 

7 

1740 

1786 

1832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

8 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 

2573 

2619 

9 

2666 

2712 

2758 

2804 

2851 

2897 

2943 

2989 

3035 

3082 

940 

3128 

3174 

3220 

3266 

3313 

a359 

3405 

3451 

3497 

3543 

1 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

3913 

3959 

4005 

2 

4051 

4097 

4143 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

8 

4512 

4558 

4604 

4650 

4696 

4742 

4788 

4834 

4880 

4926 

4 

4972 

5018 

5064 

5110 

5156 

5202 

5248 

5294 

5340 

5386 

46 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5 

678 

9 

47    4.7 

9.4    14.1    18.8 

23.5 

28.2    32.9    37.6 

42.3 

46    4.6 

9.2    13.8    18.4 

23.0 

27.6    32.2    36.8 

41.  4  | 

LOGARITHMS   OF   NUMBERS. 


!  No.  945  L.  975.] 


[No.  989  I,.  <J95. 


N. 

0 

1 

2 

a 

4 

5 

6 

7 

8 

0 

Diff. 

945 

975432 

5478 

5524 

5570 

5616 

5662 

5707 

5753 

5799 

5845 

6 

5891  £937 

5983 

6029 

6075 

6121 

6167 

6212 

6258 

6304 

7 

6350  6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

8 

6808  6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

72.20 

,  9 

7266  7312 

7358 

7403 

7449 

7495 

7541 

7586 

7632 

7678 

950 

7724  7769  7815 

7861 

7906 

7952 

7998 

8043 

8089 

8135 

1 

8181  !  8226  8272 

8317 

8363 

8409 

8454 

8500 

8546 

8591 

2 

8637  ;  8683  8728 

8774 

8819 

8865 

8911 

8956 

9002 

9047 

3 

9093  i  9138 

9184 

9230 

9275 

9321 

9366 

9412 

9457 

9503 

4 

9548  9594  9639 

9685 

9730 

9776  9821 

9867 

9912  9958 

5 

980003  0049 

0094 

0140 

0185 

0231 

0276 

0322 

0367  0412 

6 

C458 

0503  0549 

0594 

0640 

0685 

0730 

0776 

0821 

0867 

7 

0912  0957  1003 

1048 

1093 

1139 

1184 

1229 

1275 

1320 

8 

1366  1411   1456 

1501 

1547 

15S2 

1637 

1683 

1728 

1773 

9 

1819  j  1864  1909 

1954 

2000 

2045 

2090 

2135 

2181 

2226 

900 

2271 

2316 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

1 

2723  2769 

2814 

2859 

2904 

2949 

2994 

3040 

3085 

3130 

3175  3220 

3265 

3310 

3356 

3401 

3446 

3491 

3536 

3581 

3 

3626  i  3671 

3716 

3762 

3807 

3852 

3897 

3942 

3987 

4032 

4 

4077  !  4122 

4167 

4212 

4257 

4S02 

4347 

4392 

4437 

4482 

5 

4527  4572 

4617 

4662 

4707 

4752 

4797 

4842 

4887 

4932 

45 

6 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

7 

5426 

5471 

5516 

5561 

5606 

5651 

5696 

5741 

5786 

5830 

8 

5875 

5920 

5965 

0010 

6055 

6100 

6144 

6189 

6234 

6279 

9 

6324 

6369 

6413 

6458 

6503   6548 

6593 

6637 

0682 

6727 

970 

6772 

6817 

6861 

6906 

6951 

6996 

7040 

7085 

7130 

7175 

1 

7219 

7'264 

7409 

7353 

7398 

7443 

7488 

7532 

7577 

7622 

2 

7666 

7711 

7756 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

3    8113 

8157 

8202 

8247 

8291 

8336 

8381 

8425 

8470 

8514 

4    8559 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

5  i   9005  9049 

9094 

9138 

9183 

9227 

9272 

9316 

9361 

9405 

6    9450  9494 

9539 

9583 

9628 

9672 

9717 

9761 

9806 

9850 

7  1   9895 

9939 

9983 

0028 

0072 

0117 

0161 

0206 

0250 

0294 

8  990333  0383  0428 

0472 

0516 

0561 

0605 

0650 

0694 

0738 

9 

0783 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182 

980 

1226 

1270 

1315 

1359 

1403 

1448 

1492 

1536 

1580 

1625 

1 

1669 

1713 

1758 

1802 

1846 

1890 

1935 

1979 

2023 

2067 

o 

2111 

2156 

2200 

2244 

2288  i 

2333 

2377 

2421 

2465 

2509 

3 

2554 

2598 

2642 

2686 

2730  ; 

2774 

2819 

2863 

2907 

2951 

4 

2995 

3039 

3083 

3127 

3172 

3216 

3260 

3304 

3348 

8392 

5 

3436 

3480 

3524 

35(58 

3613 

3657 

3701 

3745 

3789 

3833 

6 

3877  3921 

3965 

4009 

4053 

4097 

4141 

4185 

4229 

4273 

7 

4317  4361 

4405 

4449 

4493 

4537 

4581 

4625 

4669 

4713 

44 

8 

4757  4801 

4845 

4889 

4933 

4977 

5021 

5065 

5108 

5152 

9 

5196  5240  5284 

5328 

6373 

5410 

5460 

5504 

5547 

5591 

PROPORTIONAL  PARTS. 

Diff.   1 

234 

5 

678 

9 

46    4.6    9.2    13.8  |  18.4 

23.0 

27.6    32.2    30.8 

41.4 

45    4.5 

9.0    13.5  |  18.0 

22.5 

27'.  0    31.5    30.0 

40.5 

44    4.4 

8.8    13.2    17.6 

22^0 

26.4    30.8    35.2    39.6 

43  !  4.3    8.6  !  12.9    17.2 

21.5 

25.8    30.1    34.4    38.7 

156 

No.  990  L.  995.] 


MATHEMATICAL  TABLES. 


[No.  999  L.  991 


N. 


990 
1 
2 
3 

4 
5 


0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Diff. 

996635 

5679 

5723 

5767 

5811 

5854 

5898 

5942 

5986 

6030 

6074 

6117 

6161 

6205 

6249 

6293 

6337 

6380 

6424 

6468 

44 

6512 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

6906 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

7386 

7430 

7474 

7517 

7561 

7605 

7648 

7692 

7736 

7779 

7823 

7867 

7910 

7954 

7998 

8041 

8085 

8129 

8172 

8216 

8259 

8303 

8347 

8390 

8434 

8477 

8521 

8564 

8608 

8652 

8695 

8739 

8782 

8826 

8869 

8913 

8956 

9000 

9043 

9087 

9131 

9174 

9218 

9261 

9305 

9348 

9392 

9435 

9479 

9522 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

9913 

9957 

43 

HYPERBOLIC    LOGARITHMS. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1.01 

.0099 

1.45 

.3716 

1.89 

.6366 

2.33 

.8458 

2.77 

.0188 

1.02 

.0198 

1.46 

.3784 

1.90 

.6419 

2.34 

.8502 

2.78 

.0225 

1.03 

.0296 

1.47 

.3853 

1.91 

.6471 

2.35 

.8544 

2.79 

.0260 

1.04 

.0392 

.48 

.3920 

1.92 

.6523 

2.36 

.8587  i 

2.80 

.0296 

1.05 

.0488 

.49 

.3988 

1.93 

.6575 

2.37 

.8629  i 

2.81 

.0332 

1.06 

.0583 

.50 

.4055 

1.94 

.6627 

2.38 

.8671 

2.82 

.0367 

1.07 

.0677  | 

.51 

.4121 

1.95 

.6678 

2.39 

.8713 

2.83 

.0403 

1.08 

.0770  1 

.52 

.4187 

1.96 

.6729 

2.40 

.8755 

2.84 

.0438 

1.09 

.0862 

.53 

.4253 

1.97 

.6780 

2.41 

.8796 

2.85 

.0473 

1.10 

.0953 

.54 

.4318 

1.98 

.6831 

2.42 

.8838  ! 

2.86 

.0508 

1.11 

.1044 

.55 

.4383 

1.99 

.6881 

2.43 

.8879  ! 

2.87 

.0543 

1.12 

.1133 

.56 

.4447 

2.00 

.6931 

2.44 

.8920 

2.88 

.0578 

1.13 

.1222 

.57 

.4511 

2.01 

.6981 

2.45 

.8961 

2.89 

.0613 

1.14 

.1310 

.58 

.4574 

2.02 

.7031 

2.46 

.9002 

2.90 

.0047 

1.15 

.1398 

.59 

.4637 

2.03 

.7080 

2.47 

.9042 

2.91 

.0682 

1.16 

.1484 

.60 

.4700 

2.04 

.7129 

2.48 

.9083  j 

2.92 

.0716 

1.17 

.1570 

.61 

.4762 

2.05 

.7178 

2.49 

.9123  | 

2.93 

.0750 

1.18 

.1655 

.62 

.4824 

2.06 

.7227 

2.50 

.9163  i 

2.94 

.0784 

1.19 

.1740 

.63 

.4886 

2.07 

.7275 

2.51 

.9203  i 

2.95 

.0813 

1.20 

.1823 

.64 

.4947 

2.08 

.7324 

2.52 

.9243 

2.96 

.0852 

1.21 

.1906 

.65 

.5008 

2.09 

.7372 

2.53 

.9282 

2.97 

.0880 

1.22 

.1988 

.66 

.5068 

2.10 

.7419 

2.54 

.9322 

2.98 

.0919 

1.23 

.2070 

.67 

.5128 

2.11 

.7467 

2.55 

.9361 

2.99 

.0053 

1.24 

.2151 

.68 

.5188 

2.12 

.7514 

2.56 

.9400 

3.00 

.0980 

1.25 

.2231 

.69 

.5247 

2.13 

.7561 

2.57 

.9439  i 

3.01 

.1019 

1.26 

.2311 

.70 

.5306 

2.14 

.7608 

2.58 

.9478  ! 

3.02 

.1053 

1.27 

.2390 

.71 

.5365 

2.15 

.7655 

2.59 

.9517 

3.03 

.1080 

1.28 

.2469 

.72 

.5423 

2.13 

.7701 

2.60 

.9555 

3.04 

.1119 

1.29 

.2546 

.73 

.5481 

2.17 

.7747 

2.61 

.9594 

3.05 

.1151 

1.30 

.2624 

.74 

.5539 

2.18 

.7793 

2.62 

.9632 

3.06 

.1184 

1.31 

.roo 

.75 

.5596 

2.19 

.7839 

2.63 

.9670 

3.07 

.1217 

1.32 

.2776 

.76 

.5653 

2.20 

.7885 

2.64 

.9708  i 

3.08 

.1249 

1.33 

.2852 

.77 

.5710 

2.21 

.7930 

2.65 

.9746 

3.09 

.1282 

1.34 

,2927 

.78 

.5766 

2.22 

.7975 

2.66 

.9783 

3.10 

.1314 

1.35 

1  .3001 

.79 

.5822 

2.23 

.8020 

2.67 

.9821 

3.11 

.1340 

1.36 

.3075 

.80 

.5878 

2.24 

.8065 

2.68 

.9858 

3.12 

.1378 

1.37 

.3148 

.81 

.5933 

2.25 

.8109 

2.69 

.9895 

3.13 

.1410 

i.es 

.3221 

.82 

.5988 

2.26 

.8154 

2.70 

.9933 

3.14 

.1442 

l.b» 

.3293 

.83 

.6043 

2.27 

.8198 

2.71 

.9969 

3.15 

.1474 

:1  .40 

.3365 

.84 

.6098 

2.28 

.8242 

2.72 

1.0006 

3  16 

.1500 

1.41 

.3436 

.85 

.6152 

2.29 

.8286 

2.73 

1.0043 

3.17 

1.1537 

1.42 

.3507 

.86 

.6206 

2.30 

.8329 

2.74 

1.0080 

3.18 

1.1509 

1.43 

.3577 

1.87 

.6259 

2.31 

.8372 

2.75 

1.0116 

3.19 

1.1000 

1.44 

.3646 

1.88 

.6313 

2.32 

.8410 

2.76 

1.0152 

3.20 

1.1632 

HYPERBOLIC   LOGARITHMS. 


Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1  .  1663 

3.87 

1.3533 

4.53 

1.5107 

5.19 

1.6467 

5.85 

1.7664 

1.1694 

3.88 

1.3558 

4.54 

1.5129 

5.20 

1.6487 

5.86 

1.7681 

.1725 

3.89 

1.3584 

4.55 

1.5151 

5.21 

1.6506 

5.87 

1.7699 

.1756 

3.90 

1.3610 

4.56 

1.5173 

5.22 

1.6525 

5.88 

1.7716 

,1787 

3.91 

1.3635 

4.57 

1.5195 

5.23 

1  .6514 

5.89 

1.7733 

.1817 

3.92 

1.3661 

4.58 

1.5217 

5.24 

1.6563 

5.90 

1.7750 

.1848 

3.93 

1.3686 

4.59 

1.5239 

5.25 

1.6582 

5.91 

1.7766 

.1878 

3.94 

1.3712 

4.60 

1.5261 

5.26 

1.6601 

5.92 

.7783 

.1909 

3.95 

1.3737 

4.61 

1.5282 

5.27 

1.6620 

5.93 

.7800 

.1939 

3.96 

1.3762 

4.62 

1.5304 

5.28 

1.6639 

5.94 

.7817 

.1969 

3.97 

1.3788 

4.63 

1.5326 

5.29 

1.6658 

5.95 

.7834 

.1999 

3.98 

1.3813 

4.64 

1.5347 

5.30 

1.6677 

5.96 

.7851 

.2030 

3.99 

1.3838 

4.65 

1.5369 

5.31 

1.6696 

5.97 

.7867 

.2060 

4.00 

1.3863 

4.66 

1.5390 

5.32 

1.6715 

5.98 

.7884 

.2090 

4.01 

1.3888 

4.67 

1.5412 

5.33 

1.6734 

5.99 

.7901 

.2119 

4.02 

1.3913 

4.68 

1.5433 

5.34 

1.6752 

6.00 

.7918 

.2149 

4.03 

1.3938 

4.69 

1.5454 

5.35 

1.6771 

6.01 

.7934 

.2179 

4.04 

1.3962 

4.70 

1.5476 

5.36 

1.6790 

6-02 

.7951 

.2208 

4.05 

1.3987 

4.71 

1.5497 

5.37 

1.6808 

6.03 

.7967 

.2238 

4.06 

1.4012 

4.72 

1.5518 

5.38 

1.6827 

6.04 

.7984 

.2267 

4.07 

1.4036 

4.73 

1.5539 

5.39 

1.6845 

6.05 

.8001 

.2296 

4.08 

1.4061 

4.74 

1.5560 

5.40 

1.6864 

6.06 

.8017 

.2326 

4.09 

1.4085 

4.75 

1.5581 

5.41 

1.6882 

6.07 

.8034 

.2355 

4.10 

1.4110 

4.76 

1.5602 

5.42 

1.6901 

6.08 

.8050 

.2384 

4.11 

1.4134 

4.77 

1.5623 

5.43 

1.6919 

6.09 

.8066 

.2413 

4.12 

1.4159 

4.78 

1.5644 

5.44 

1.6938 

6.10 

.8083 

.2442 

4.13 

1.4183 

4.79 

1.5665 

5.45 

1.6956 

6.11 

.8099 

.2470 

4.14 

1.4207 

4.80 

1.5686 

5.46 

1.6974 

6.12 

.8116 

.2499 

4.15 

1.4231 

4.81 

1  .5707 

5.47 

1.6993 

6.13 

.8132 

.2528 

4.16 

1.4255 

4.82 

1.5728 

5.48 

1.7011 

6.14 

.8148 

.2556 

4.17 

1.4279 

4.83 

1.5748  : 

5.49 

1.7029 

6.15 

.8165 

.2585 

4.18 

1.4303 

4.84 

1.5769 

5.50 

1.7047 

6.16 

.8181 

.2613 

4.19 

1.4327 

4.85 

1.5790 

5.51 

1.7066 

6.17 

.8197 

.2641 

4.20 

1.4351 

4.86 

1.5810 

5.52 

1.7084 

6.18 

.8213 

.2669 

4.21 

1.4375 

4.87 

1.5831 

5.53 

1.7102 

6.19 

.8229 

.2698 

4.22 

1  .4398 

4.88 

1.5851 

5.54 

1.7120 

6.20 

.8245 

.2726 

4.23 

1  .4422 

4.89 

1.5872 

5.55 

1.7138 

6.21 

.8262 

1.2754 

4.24 

1.4446 

4.90 

1.5892 

5.56 

1.7156 

6.22 

.82?'8 

1.2782 

4.25 

1.4469 

4.91 

1.5913 

5.57 

1.7174 

6.23 

.8294 

1.2809 

4.26 

1.4493 

4.92 

1.5933 

5.58 

1.7192 

6.24 

.8310 

1.5837 

4.27 

1.4516 

4.93 

1.5953 

5.59 

1.7210 

6.25 

.8326 

1.2865 

4.28 

1.4540 

4.94 

1.5974 

5.60 

1.7228 

6.26 

.8342 

1.2892 

4.29 

1.4563 

4.95 

1.5994 

5.61 

1.7246 

6.27 

1.8358 

1.2920 

4.30 

1.4586 

4.96 

1.6014 

5.62 

1.7263 

6.28 

1.8374 

1.2947 

4.31 

1.4609 

4.97 

1.6034 

5.63 

1.7281 

6.29 

1.8390 

.2975 

4.32 

1.4633 

4.98 

1.6054 

5.64 

1.7299 

6.30 

1.8405 

.3002 

4.33 

1  .4656 

4.99 

1.6074 

5.65 

1.7317 

6.31 

1.8421 

.3029 

4.34 

1.4679 

5.00 

1.6094 

5.66 

1.7334 

6.32 

1.843? 

.3056 

4.35 

1.4702 

5.01 

1.6114 

5.67 

1.7352 

6.33 

1.8453 

.3083 

4.36 

1.4725 

5.02 

1.6134 

5.68 

1.7370 

6.34 

1.8409 

.3110 

4.37 

1.4748 

5.03 

1.6154 

5.69 

1.7387 

6.35 

1.8485 

.3137 

4.38 

.4770 

5.04 

1.6174 

5.70 

1.7405 

6.36 

1.8500 

.3164 

4.39 

.4793 

5.05 

1.6194  | 

5.71 

1.7422 

6.37 

1.8516 

.3191 

4.40 

.4816 

5.06 

1.6214 

5.72 

1.7440 

6.38 

1.8532 

.3218 

4.41 

.4839 

5.07 

1.6233 

5.73 

1.7457 

6.39 

1.8547 

.3244 

4.42 

.4861 

5.08 

1.6253  ; 

5.74 

1.7475 

6.40 

1.8563 

.3271 

4.43 

.4884 

5.09 

1.6273 

5.75 

1.7492 

6.41 

1.8579 

.3297 

4.44 

.4907 

5.10 

1.6292 

5.76 

1.7509 

6.42 

1.8594 

.3324 

4.45 

.4929 

5.11 

1.6312 

5.77 

1.7527 

6.43 

1.8610 

.3350 

4.46 

.4951 

5.12 

1.6332 

5.78 

1.7544 

6.44 

1.8625 

.3376 

4.47 

.4974 

5.13 

1.6351 

5.79 

1.7561 

6.45 

1.8641 

.3403 

4.48 

.4996 

5.14 

1.6371 

5.80 

1.7579 

6.46 

1.8656 

.3429 

4.49 

.5019 

5.15 

1.6390 

5.81 

1.7596 

6.47 

1.8672 

.3455 

4.50 

.5041 

5.16 

1.6409 

5.82 

1.7613 

6.48 

1.8687 

.3481 

4.51 

.5063 

5.17 

1.6429 

5.83 

1.7630 

6.49 

1.8703 

.3507 

4.52 

.5085 

5.18 

1.6448 

5.84 

1.7647 

6.50 

1.K71S 

158 


MATHEMATICAL   TABLES. 


No. 

Log. 

No. 

Lo^. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

6.51 

.8733 

7.15 

1.9671 

7.79 

2.0528 

8.66 

2.1587 

9.94 

2.2966 

6.52 

.8749 

7.16 

1.9685 

7.80 

2.0541 

8.68 

2.1610 

9.96 

2.2986 

6.53 

.8764 

7.17 

1.9699 

7.81 

2.0554 

8.70 

2.1633 

9.98 

2.3006 

6.54 

.8779 

7.18 

1.9713 

7.82 

2.0567 

8.72 

2.1656 

10.00 

2.3026 

6.55 

.8795 

7.19 

1.9727 

7.83 

2.0580 

8.74 

2.1679 

10.25 

2.3279 

6.56 

.8810 

7.20 

1.9741 

7.84 

2.0592 

8.76 

2.1702 

10.50 

2.3513 

6.57 

.8825 

7.21 

1.9754 

7.85 

2.0605 

8.78 

2.1725 

10.75 

2.3749 

6.58 

.8840 

7.22 

1.9769 

7.86 

2.0618 

8.80 

2.1748 

11.00 

2.3979 

6.59 

.8856 

7.23 

1.9782 

7.87 

2.  0631 

8.82 

2.1770 

11.25 

2.4201 

6.60 

.8871 

7.24 

1.9796 

7.88 

2.0643 

8.84 

2.1793 

11.50 

2.4430 

6.61 

.8886 

7.25 

1.9810 

7.89. 

2.0656 

8.86 

2.1815 

11.75 

2.4636 

6.62 

.8901 

7.26 

1.9824 

7.90 

2.0669 

8.88 

2.1838 

12.00 

2.4849 

6.63 

.8916 

7.27 

1.9838 

7.91 

2.0681 

8.90 

2.1861 

12.25 

2.5052 

6.64 

.8931 

7.28 

1.9851 

7.92 

2.0694 

8.92 

2.1883 

12.50 

2.5262 

6.65 

.8946 

7.29 

1.9865 

7.93 

2.0707 

8.94 

2.1905 

12.75 

2.5455 

6.  60 

.8961 

7.30 

1.9879 

7.94 

2.0719 

8.96 

2.1928 

13.00 

2.5649 

6.67 

.8976 

7.31 

1.9892 

7.95 

2.0732 

8.98 

2.1950 

13.25 

2.5840 

6.68 

.8991 

7.32 

1.9906 

7-96 

2.0744 

9.00 

2.1972 

13.50 

2.6027 

6.69 

.9006 

7-33 

1.9920 

7-97 

2.0757 

9.02 

2.1994 

13.75 

2.6211 

6.70 

.9021 

7.34 

1.9933 

7.98 

2.0769 

9.04 

2.2017 

14.00 

2.6391 

6.71 

.9036 

7.35 

1.9947 

7.99 

2.0782 

9.06 

2.2039 

14.25 

2.6567 

6.72 

.9051 

7.36 

1.9961 

8-00 

2.0794 

9.08 

2.2061 

14.50 

2.6740 

6.73 

.9066 

7.37 

1.9974 

8.01 

2.0807 

9  10 

2.2083 

14.75 

2.6913 

6.74 

.9081 

7.38 

1.9988 

8.02 

2.0819 

9.12 

2.2105 

15.00 

2.7081 

6.75 

.9095 

7.39 

2.0001 

8-03 

2.0832 

9.14 

2.2127 

15.50 

2.7408 

6.76 

.9110 

7.40 

2.0015 

8.04 

2.0844 

9.16 

2.2148 

16.00 

2.7726 

6.77 

.9125 

7.41 

2.0028 

8-05 

2.0857 

9.18 

2.2170 

16.50 

2.8034 

6.78 

.9140 

7.42 

2.0041 

8.06 

2.0869 

9.20 

2.2192 

17.00 

2.8332 

6.79 

.9155 

7.43 

2.0055 

8-07 

2.0882 

9.22 

2.2214 

17.50 

2.8621 

6.80 

.9169 

7.44 

2.0069 

8-08 

2.0894 

9.24 

2.2235 

18.00 

2.8904 

6.81 

.9184 

7.45 

2-0082 

8.09 

2.0906 

9.26 

2.2257 

18.50 

2.9173 

6.82 

.9199 

7.46 

2.0096 

8.10 

2.0919 

9.28 

2.2279 

19.00 

2.9444 

6.83 

.9213 

7.47 

2.0108 

8.11 

2.0931 

9.30 

2.2300 

19.50 

2.9703 

6.84 

.9228 

7.48 

2.0122 

8-12 

2.0943 

9.32 

2.2322 

20.00 

2.9957 

6.85 

.9242 

7.49 

2.0136 

8.13 

2.0956 

9.34 

2.2343 

21 

3.0445 

6.86 

.9257 

7.50 

2.0149 

8.14 

2.0968 

9.36 

2.2364 

22 

3.0910 

6.87 

.9272 

7.51 

2.0162 

8.15 

2.0980 

9.38 

2.2386 

23 

3.1355 

6.88 

.9286 

7.52 

2.0176 

8-16 

2.0992 

9.40 

2.2407 

24 

3.1781 

6.89 

.9301 

7.53 

2.0189 

8.17 

2.1005 

9.42 

2.2428 

25 

3.2189 

6.90 

.9315 

7.54 

2.0202 

8.18 

2.1017 

9.44 

2.2450 

26 

3.2581 

6.91 

.9330 

7.55 

2.0215 

8.19 

2.1029 

9.46 

2.2471 

27 

3.2958 

6.92 

.9344 

7.56 

2.0229 

8.20 

2.1041 

9.48 

2.2492 

28 

3.3322 

6.93 

.9359 

7.57 

2.0242 

8-22 

2.1066 

9.50 

2.2513 

29 

3.3673 

6.94 

.9373 

7.58 

2.0255 

8-24 

2.1090 

9.52 

2.2534 

30 

3.4012 

6.95 

.9387 

7.59 

2.0268 

8-26 

2.1114 

9.54 

2.2555 

31 

3.4340 

6.96 

.9-102 

7.60 

2.0281 

8.28 

2.1138 

9.56 

2.2576 

32 

3.4657 

6.97 

.9416 

7.61 

2.0295 

8.30 

2.1163 

9.58 

2.2597 

33 

3.4965 

6.98 

.9430 

7.62 

2.0308 

8-32 

2.1187 

9.60 

2.2618 

34 

3.5263 

6.99 

.9445 

7.63 

2.0321 

8.34 

2.1211 

9.62 

2.2638 

35 

3.5553 

7.00 

.9459 

7.64 

2.0334 

8.36 

2.1235 

9.64 

2.2659 

36 

3.5835 

7.01 

.9473 

7.65 

2.0347 

8.38 

2.1258 

9.66 

2.2680 

37 

3.6109 

7.02 

.9488 

7.66 

2.0360 

8.40 

2.1282 

9.68 

2.2701 

38 

3.6376 

7.03 

.9502 

7.67 

2.0373 

8.42 

2.1306 

9.70 

2.2721 

39 

'3.6636 

7.04 

.9516 

7.68 

2.0386  ' 

8.44 

2.1330 

9.72 

2.2742 

40 

3.6889 

7.05 

.9530 

7.69 

2.0399 

8.46 

2.1353 

9.74 

2.2762 

!  41 

3.7136 

7.06 

.9544 

7.70 

2.0412 

8.48 

2.1377 

9.76 

2.2783 

i  42 

3.7377 

7.07 

.9559 

7.71 

2.0425 

8.50 

2.1401 

9.78 

2.2803 

43 

3.7612 

7.08 

.9573 

7.72 

2.0438 

8.52 

2.1424 

9.80 

2.2824 

i  44 

3.7842 

7.09 

.9587 

7.73 

2.0451 

8.54 

2.1448 

9.82 

2.2844 

45 

3.8067 

7.10 

.9601 

7.74 

2.0464  i 

8.56 

2.1471 

9.84 

2.2865 

46 

3.8286 

7.11 

.9615 

7.75 

2.0477 

8.58 

2.1494 

9.86 

2.2885 

47 

3.8501 

7.12 

.9629 

7.76 

2.0490 

8.60 

2.1518 

9.88 

2.2905 

48 

3.8712 

7.13 

1.9643 

7.77 

2.0503 

8.62 

2.1541 

9.90 

2.2925 

!  49 

3.8918 

7.14 

1.9657 

7.  738 

2.0516 

8,64 

2.1564 

9.92 

2.2946 

50 

3.9120 

| 

NATURAL   TRIGONOMETRICAL   FUNCTIONS. 


159 


NATURAL   TRIGONOMETRIC  A  I,    FUNCTIONS. 


0 

M. 

Sine. 

Co-Vers.      Cosec. 

Tang. 

Cotan.        Secant. 

Ver.  Sin.  j 

Cosine. 

0 

0 

00000 

1.0000    Infinite 

.00000 

Infinite1  1.0000 

.00000:1.0000     90 

0 

15 

00436 

.99564:229.18 

.00436  229.  18        1.0000 

.00001! 

.99999 

45 

30 

00873 

.99127  114.59 

.00873  114.59        1.0000 

.00004; 

.99996 

30 

45 

01309 

.98691 

76.397 

.01309 

76.390      1.0001 

.00009 

.99991 

15 

1 

0 

01745 

.98255 

57.299 

.01745 

57.290      1.0001 

.00015' 

.99985    89 

0 

15 

02181 

.97819 

•45.840 

.02182 

45.829      1.0002 

.00024 

.99976 

45 

30 

02618 

.97382 

38.202 

.02618 

38.188      1.0003 

.00034 

.99966 

30 

!  45 

030:>  4 

.08946 

32.746 

.03055 

3:2.730      1.0005 

.00047 

.99953 

15 

2       0 

03490 

.96',  10 

28.654 

.03492 

28.636  !   1.0006 

.00061 

.99939    88 

0 

15 

03926    .96074 

25.471 

.03929 

25.452  i   1.0008 

.00077 

.99923 

45 

30 

04362    .95633 

22.926 

.04366 

22.904      1.0009 

.00095 

.99905! 

30 

45 

04798 

.95202 

20.843 

.04803 

20.819      1.0011 

.00115 

.  99885  ! 

15 

3 

0 

05234 

.94766 

19.107 

.05241 

19.081   i   1.0014 

.00137 

.99863   87 

0 

15 

05669 

.94331 

17.639 

.05678 

17.611       1.0016 

.00161 

.99839 

45 

30 

06105 

.93895 

16.380 

.06116 

16.350  i   1.0019 

.00187 

.99813 

30 

45 

06540 

.93460 

15.290 

06554 

15.257  ;    1.0021 

.00214 

.99786 

15 

4 

0 

06976 

.93024 

14.336 

06993    14.301      1.0024 

.00244 

.99756   86 

0 

15 

0»41I 

.92589 

13.494 

07431 

13.457  !•  1.0028 

.00275 

.99725 

45 

30 

07846 

.92154 

12.745 

07870 

12.706      1.0031 

.00308 

.99692 

30 

45 

08281 

.91719 

12.076 

08309 

12.035      1.0034 

.00343 

.99656 

15 

5 

0 

08716 

.91284 

11.474 

08749 

11.430      1.0038 

.00381 

.99619   85 

0 

15 

09150 

.90850 

10.929 

09189    10.8S3  i    1.0042 

.00420 

.99580 

45 

30 

09585 

.90415 

10.433 

09629    10.385  i    1.0046 

.00460 

.995401 

30 

45 

10019 

.89981 

9.9812 

10069      9.9310    1.0051 

.00503 

.99497 

15 

6 

0 

10453 

.89547 

9.5668 

10510 

9.5144    1.0055 

.00548 

.99452 

84 

0 

15 

10887 

.89113 

9.1855 

10952      9.1309    1.0060 

.00594 

.99406 

45 

30 

11320 

.88680 

8.8337 

11393      8.7769    1.0065 

.00643 

.99357 

30 

45 

11754 

.88246 

8.5079 

1  1836 

8.4490    1.0070 

.00693 

.98307 

15 

7 

0 

12187 

.87813 

8.2055 

12278 

8.1443    1.0075 

.00745 

.99255 

83 

0 

15 

12620 

.87380 

7.9240 

12722 

7.8606    1.0081 

.00800 

.99200 

45 

30 

13053 

.86947 

7.6613 

13165      7.5958    1.0086 

.00856 

.99144: 

30 

45 

13485 

.86515 

7.4156 

.136091     7.3479    1.0092 

.00913 

.99086: 

15 

8       0 

13917 

.86083 

7.1853 

.14054 

7.1154    1.0098 

.00973 

.99027!  82 

0 

1  15 

14349 

.85651 

6.9690 

.14499 

6.8969    1.0105 

.01035 

.98965 

45 

30 

14781 

.85219 

6.7655 

.14945      6.6912    1.0111 

.01098 

.98902 

30 

45 

15212 

.84788 

6.5736 

.15391 

6.4971 

1.0118 

.01164 

.98836 

15 

9 

0 

15643 

.84357 

6.3924 

.15838      6.3138 

1.0125 

.01231 

.98769   81 

0 

15 

16074 

.83926 

6.2211 

.16286:     6.1402 

1.0132 

.01300 

.98700! 

45 

30 

16505 

.83495 

6.0589 

.16734      5.9758 

1.0139 

.01371 

.98629 

30 

45 

.16935 

.83065 

5.9049 

.17183      5.8197 

1.0147 

.01444 

.98556 

15 

10 

0 

.17335 

.82635 

5  .  7588 

.17633 

5.6713 

1.0154 

.01519 

.98481 

80 

0 

15 

.17794 

.82206 

5.6198 

.18083      5.5301 

1.0162 

.01596 

.98404 

45 

30 

.18224 

.81776 

5.4874 

.18534      5.3955 

1.0170 

.01675 

.98325 

30 

45 

.18652 

.81348 

5.3612 

.18986      5.2672 

1.0179 

.017551   .98245 

15 

11 

0 

.19081 

.80919 

5.2408 

.19438;     5.1446 

1  .018" 

.01837 

.98163 

79 

0 

15 

.19509 

.80491 

5.1258 

.19891      5.0273 

1.0196 

.01921 

.98079 

45 

30 

.19937 

.80063 

5.0158 

.20345      4.9152 

1.0205 

.02008 

.97992! 

30 

45 

.20364 

.79636 

4.910b 

•20SOO     4.8077 

1.021 

.02095 

.97905! 

15 

12 

0 

.20791 

.79209 

4.8097 

.21256      4.7046 

1.022: 

.02185]   .97815^  78 

0 

15 

.21218 

.78782 

4.7130 

.21712     4.6057 

1.0233 

.02277 

.97723 

45 

30 

.21644 

.78356 

4.6202 

.22169      4.5107 

1.024; 

.02370 

.97639 

30 

45 

.22070 

.77930 

4.5311 

•22628      4.4194 

1.0253 

.02466 

.97534 

15 

13       0 

.22495 

.77505 

4.4454 

•23087!     4.3315 

1.026: 

.02563 

.97437 

77 

0 

15 

.22920 

.77080 

4.363C 

•23547     4.2468 

1.0273 

.02662 

I   .97338 

45 

30 

.23345 

.76655 

4.283" 

•24008      4.1653 

1.0284 

.02763 

.97237 

30 

45 

.23769!    .76231 

4.207$ 

•24470     4.0867 

1.0295 

.02866 

.97134 

15 

14       0 

.24192!   .7580S 

4.133C 

.24933!     4.0108 

1.0306 

.02970 

.97030 

76 

0 

15 

.2461F 

.7538? 

4.062? 

.25397      3.9375 

1.0817 

.03077    .96923 

45 

3Q 

.2503* 

.74965: 

3.993? 

>  .25862     3.8667 

1.032 

.03185 

.96815 

30 

45 

.2546C 

I    .74540 

3.927' 

J  .26338     3.7983 

1.034 

.03295 

!   .98705 

15 

15       0 

.2588', 

.7411* 

3.863" 

'  .26795'     3.7320 

1.0353    .03407 

.96593 

75 

0 

Cosine 

.  Ver.  Sin 

Secant.       Cotan.  1     Tang. 

Cosec. 

Co  -Vers 

Sine. 

o 

M. 

From  75°  to  9O°  read  from  bottom  of* table  upwards. 


160 


MATHEMATICAL   TABLES. 


• 

M. 

Sine. 

Co-Vers. 

Cosec. 

Tang. 

Cotan. 

Secant. 

Ver.  Sin. 

CoSine. 

15 

0 

.25882 

.74118 

3.8637 

.26795 

3.7320 

1.0353 

.03407 

.96598 

75 

0 

15 

.26303 

.73697 

3.8018 

.27263 

3.6680 

1.0365 

.03521 

.96479 

45 

30 

.26724 

.73276 

3.7420 

.27732 

3.6059 

1.0377 

.03637 

.96368 

30 

45 

.27144 

.72856 

3.6840 

.28203 

3.5457 

1.0390 

.03754 

.96246 

15 

16 

0 

.27564 

.72436 

3.6280 

.28674 

3.4874 

1.0403 

.03874 

.96126 

74 

0 

15 

.27983 

.72017 

3.5736 

.29147 

3.4308 

1.0416 

.03995 

.96005 

45 

30 

.28402 

.71598 

3.5209 

.29621 

3.3759 

1.0429 

.04118 

.95882 

30 

45 

.28820 

.71180 

3.4699 

.30096 

3.3226 

1.0443 

.04243 

.95757 

15 

17 

0 

.29237 

.70763 

3.4203 

.30573 

3.2709 

1.0457 

.04370 

.95630 

73 

0 

15 

.29654 

.70346 

3.8722 

.31051 

3.2205 

1.0471 

.04498 

.95502 

45 

30 

.30070 

.69929 

3.3255 

.31530 

3.1716 

1.0485 

.04628 

.95372 

30 

45 

.30486 

.69514 

3.2801 

.32010 

3.1240 

1.0500 

.04760 

.95240 

15 

18 

0 

.30902 

.69098 

3.2361 

.32492 

3.0777 

1.0515 

.04894 

.95106 

72 

0 

15 

.31316 

.68684 

3.1932 

.32975 

3.0826 

1.0530 

.05030 

.94970 

45 

30 

.31730 

.68270 

3.1515 

.33459 

2.9887 

'1.0545 

.05168 

.94832 

30 

45 

.32144 

.67856 

3.1110 

.33945 

2-9459 

1.0560 

.05307 

.94693 

15 

19 

0 

.32557 

.67443 

3.0715 

.34433 

2.U042 

1.0576 

.05448 

.94552 

71 

0 

15 

.32969 

.67031 

3.0331 

.34921 

2.8636 

1.0592 

.05591 

.94409 

45 

30 

.33381 

.66619 

2.9957 

.35412 

2.8239 

1.0fi08 

k  05736 

.94264 

30 

45 

.33792 

.66208 

2.9593 

.35904 

2.7852 

I.t5625 

05882 

.94118 

15 

20 

0 

.34202 

.65798 

2.9288 

.36397 

2-7475 

1  .0642 

.06031 

.93969 

70 

0 

15 

.34612 

.65388 

2.8892 

.36892 

2.7106 

1.0659 

.06181 

.93819 

45 

30 

.35021 

.64979 

2.8554 

.37388 

2.6746 

1.0676 

.06383 

.93667 

30 

45 

.35429 

.64571 

2.8225 

.37887 

2.6395 

1.0694 

.06486 

.93514 

15 

21 

0 

.35837 

.64163 

2.7904 

.38386 

2.6051 

1.0711 

.06642 

.93358 

69 

0 

15 

.36244 

.63756 

2.7591 

.38888 

2-5715 

1.0729 

.06799 

.93201 

45 

30 

.36650 

.63350 

2.7285 

.39391 

2-5386 

1.0748 

.06958 

.93042 

30 

45 

.37056 

.62944 

2.6986 

.39896 

2-5065 

1.0766 

.07119 

.92881 

15 

22 

0 

.37461 

.02539 

2.6695 

.40403 

2.4751 

1.0785 

.07282 

.92718 

68 

0 

15 

.37865 

.62185 

2.6410 

.40911 

2  4443 

1.0804 

.07446 

.92554 

45 

30 

.38:268 

.61732 

2.6131 

.41421 

2-4142 

1.0824 

.07612 

.92388 

30 

45 

.3867J 

.61329 

2.5859 

.41933 

2-3847 

1.0844 

.07780 

.92220 

15 

23 

0 

.39073 

.60927 

2  5593 

.42447 

2-3559 

1.0864 

.07950 

.92050 

67 

0 

15 

.39474 

.60526 

2.5333 

.42963 

2-3276 

1.0884 

.08121 

.91879 

45 

30 

.39875 

.60125 

2.5078 

.43481 

2-2998 

1.0904 

.08294 

.91706 

30 

45 

.40275 

.59725 

2.4829 

.44001 

2  2727 

1.0925 

.08469 

.91531 

15 

24 

0 

.40674 

.59326 

2.4586 

.44523 

2.2460 

1.0946 

.08645 

.91355 

66 

.0 

15 

.41072 

.58928 

2.4848 

.45047 

2.2199 

1.0968 

.08824 

.91176 

45 

30 

.41469 

.58531 

2.4114 

.45573 

2.1943 

1.0989 

.09004 

.90996 

30 

45 

41866 

.58134 

2.3886 

.46101 

2.1692 

1.1011 

.09186 

.90814 

15 

25 

0 

.42262 

.57738 

2.3662 

.46631 

2.1445 

1  .  1084 

.09369 

.90631 

65 

0 

15 

.42657 

.57343 

2.3443 

.47168 

2.1203 

1.1056 

.09554 

.90446 

45 

30 

.43051 

.56949 

2.3228 

.47697 

2-0965 

1  .  1079 

.09741 

.90259 

30 

45 

.43445 

.56555 

2.3018 

.48234 

2.0732 

1.1102 

.09930 

.90070 

15 

26 

0 

.43887 

.56163 

2.2812 

.48773 

2-0503 

1.1120 

.10121 

.89879 

64 

0 

15 

.44229 

.55771 

2.2610 

.49314 

2.0278 

1.1150 

.10313 

.89687 

45 

30 

.44620 

.55380 

2.2412 

.49858 

2.0057 

1.1174 

.10507 

.89493 

3(? 

45 

.45010 

.54990 

2.2217 

.50404 

1.9840 

1.1198 

.  107'02 

.89298 

15 

27 

0 

.45399 

.54601 

2.2027 

.50952 

1.9626 

1.1223 

.10899 

.89101 

63 

0 

15 

.45787 

.54213 

2.1840 

.51503 

1.9413 

1.1248 

.11098 

.88902 

45 

30 

.46175 

.53825 

2.1657 

.52057 

1.9210 

1  .  1274 

.11299 

.88701 

30 

45 

.46561 

.53439 

2.1477 

.52612 

1.9007 

1.1300 

.11501 

.88499 

15 

28 

0 

.469-17 

.53053 

2.1300 

.53171 

1.8807 

1.1326 

.11705 

.88295 

62 

0 

15 

.47332 

.52668 

2.1127 

.53732 

1.8611 

1  .  1352 

.11911 

.88089 

45 

30 

.47716 

.52284 

2.0957 

.  54295 

1.8418 

1.1379 

.12118 

.87882 

30 

45 

.48099 

.51901 

2.0790 

.54862 

1.8228 

1  .  1406 

.12827 

.87673 

15 

29 

0 

.48481 

.51519 

2.0627 

.55431 

1.8040 

1  .  1433 

.  12538 

.87402 

61 

0 

15 

.48862 

.51138 

2.0466 

.56003 

1.7856 

1.1461 

.12750 

.87250 

45 

30 

.49242 

.50758 

2.0308 

.56577 

1.7'675 

1  .  1490 

.129U4 

.87036 

30 

45 

.49622 

.50378 

2.0152 

.57155 

1.7496 

1.1518 

.13180 

.86820 

15 

30 

0 

.50000 

.50000 

2.0000 

.57735 

1.7320 

1  .  1547 

.  13397 

.  86603 

60 

0 

Cosine. 

Ver.  Sin. 

Secant. 

Cotan. 

Tang. 

Cose,. 

Co-Vers. 

Sine. 

° 

M. 

From  60°  to  75°  read  from  bottom  of  table  upwards. 


NATURAL   TRIGONOMETRICAL   FUNCTIONS. 


161 


0 

M. 

Sine. 

Co-Vera. 

'Cosec. 

Tang. 

Cotan. 

Secant. 

Ver.  Sin. 

Cosine. 

30 

0 

.50000 

.50000 

2.0000 

.57735 

1.7320 

.1547 

.13397 

.86603 

60 

0 

15 

.50377 

.49623 

.9859 

.58318 

1.7147 

.1576 

.13616 

.86384 

45 

30 

.50754 

.49246 

.9703 

.58904 

1.6977 

.1606 

.13837 

.86163 

30 

45 

.51129 

.48871 

.9558 

.59494 

1.6808 

.  1636 

.14059 

.85941 

15 

31 

0 

.51504 

.48496 

.9416 

.60086 

1.6643 

.1666 

.14283 

.85717 

59 

0 

15 

.51877 

.48123 

.9276 

.60681 

1.6479 

.1697 

.14509 

.85491 

45 

30 

.52250 

.47750 

.9139 

.61280 

1.6319 

.1728 

.14736 

.85264 

30 

45 

.52621 

.  47379 

.9004 

.61882 

1.6160 

.1760 

.14965 

.85035 

15 

32 

0 

.52992 

.47008 

.8871 

.62487 

1.6003 

.1792 

.15195 

.84805 

58 

0 

15 

.53361 

.46639 

.8740 

.63095 

1.5849 

.1824 

.15427 

.84573 

45 

30 

.53730 

.46270 

.8612 

.63707 

1.5697 

.1857 

.15661 

.84339 

30 

45 

.54097 

.45903 

.8485 

.64322 

1.5547 

.1890 

.15896 

84104 

15 

33 

0 

.54464 

.45536 

.8361 

.64941 

1.5399 

1924 

.16133 

.83867 

57 

0 

15 

.54829 

.45171 

.8238 

65563 

1.5253 

.1958 

.16371 

.83629 

45 

30 

.55194 

.44806 

.8118 

.66188 

1.5108 

'    .1992 

.16611 

.83389 

30 

45 

.55557 

.44443 

.7999 

.66818 

1.4966 

.2027 

.16853 

.83147 

15 

34 

0 

.55919 

.44081 

.7883 

.67451 

1.4826 

.2062 

.17096 

.82904 

56 

0 

15 

.56280 

.43720 

.7768 

.68087 

1.4687 

.2098 

.17341 

.82659 

45 

30 

.56641 

.43359 

.7655 

.68728 

1.4550 

.2134 

.17587 

.82413 

30 

45 

.57000 

.43000 

.      .7544 

.69372 

1.4415 

.2171 

.17835 

.82165 

15 

35 

0 

.57358 

.42642 

.7434 

.70021 

1.4281 

1.2208 

.18085 

.S1915 

55 

0 

15 

.57715 

.42285 

1.7327 

.70673 

1.4150 

1.2245 

.18336 

.81664 

45, 

30 

.58070 

.41930 

t.T&JO 

.71329 

1.4019 

1.2283 

.18588 

.81412 

30 

45 

.58425 

.41575 

1.7116 

.71990 

1.3891 

1.2322 

.18843 

.81157 

15 

36 

0 

'.58779 

.41221 

1.7013 

.72654 

1.3764 

1.2361 

.19098 

.80902 

54 

0 

15 

.59131 

.40869 

1.6912 

.73323 

1.3638 

1.2400 

.19356 

.80644 

45 

30 

.59482 

.40518 

1.6812 

.73996 

1.&514 

1.2440 

.19614 

.80386 

30 

45 

.59832 

.40168 

1.6713 

.74673 

1.3392 

1.2480 

.19875 

.80125 

15 

37 

0 

.60181 

.39819 

1.G616 

.75355 

1.3270 

1.2521 

.20136 

.79864 

53 

0 

15 

.60529 

.39471 

1.0521 

.76042 

1.3151 

1.2563 

.20400 

.79600 

45 

30 

.60876 

.39124 

1  ,G427 

.76733 

1.3032 

1.2605 

.20665 

.79335 

'30 

45 

.61222 

.38778 

1.C334 

.77428 

1.2915 

1.2647 

.20931 

.79069 

15 

38 

0 

.61566 

.38434 

1.0343 

.78129 

1.2799 

1.2690 

.21199 

.78801 

52 

0 

15 

.61909 

.38091 

1.G153 

.78834 

1.2685 

1.2734 

.21468 

.78532 

45 

30 

.62251 

.37749 

1.6064 

.79543 

1.2572 

1.2778 

.21739 

.78261 

3° 

45 

.62592 

.37408 

1.5976 

.80258 

1.2460 

1.2822 

.22012 

.77988 

15 

39 

0 

.02!  132 

.37068 

1.5890 

.80978 

1.2349, 

1.2868 

.22285 

.77715 

51 

0 

15 

.63271/ 

.36729 

1.5805 

.81703 

1.2239 

1.2913 

.22561 

.77439 

45 

30 

.63608 

.36392 

1.5721 

.82434 

1.2131 

1.2960 

.22838 

.77162 

30 

45 

.63944 

.36056 

1.5639 

.83169 

1.2024 

1.3007 

.23116 

.76884 

15 

40 

0 

.64279 

.35721 

1.5557 

.83910 

1.1918 

1.3054 

.23396 

.76604 

50 

0 

15 

.64612 

.35388 

1.5477 

.84656 

1.1812 

1.3102 

.23677 

.76323 

45 

30 

.64945 

.35055 

1.5398 

.85408 

1.1708 

1.3151 

.23959 

.76041 

30 

45 

.65276 

.34724 

1.5320 

.86165 

1.1606 

1.3200 

.24244 

.75756 

15 

41 

0 

.65606 

.34394 

1.5242 

.86929 

1.1504 

1.3250 

.24529 

.75471 

49 

0 

15 

.65935 

.34065 

1.5166 

.87698 

1.1403 

1.3301 

.24816 

.75184 

45 

30 

.66262 

.33738 

1  5092 

.88472 

1.1303 

1.3352 

.25104 

.74896 

30 

45 

.66588 

.33412 

1.5018 

.89253 

1.1204 

1.3404 

.25394 

.74606 

15 

42 

0 

.66913 

.33087 

1.4945 

.90040 

1.1106 

1.3456 

.25686 

.74314 

48 

0 

15 

.67237 

.32763 

1.4873 

.90834 

1.1009 

1.3509 

.25978 

.74022 

45 

30 

.67559 

.32441 

1.4802 

.91633 

1.0913 

1.3563 

.26272 

.73728 

30 

45 

.67880 

.32120 

1.4732 

.92439 

1.0818 

1.3618 

.26568 

.73432 

15 

43 

0 

.68200 

.31800 

1.4663 

93251 

1.0724 

1.3673 

.26865 

.73135 

47 

0 

15 

.68518 

.31482 

1.4595 

.94071 

1.0630 

1.3729 

.27163 

.72837 

45 

30 

.68835 

.31165 

1.4527 

.94896 

1.0538 

1  .3786 

.27463 

.72537 

30 

45 

.69151 

.30849 

1  .4461 

.95729 

1.0446 

1.3843 

.27764 

.72236 

15 

44 

0 

.69466 

.30534 

1.430(5 

.96569 

1.0355 

1.3902 

.28066 

.71934 

46 

0 

15 

.69779 

.30221 

1.4331 

.97416 

1.0265 

1.3961 

.28370 

.71630 

45 

30 

.70091 

.29909 

1.4267 

.98270 

1.0176 

1.4020 

.28675 

.71325 

,30 

45 

.70401 

.29599 

1.4204 

.99131 

1.0088 

1.4081 

.28981 

.71019 

/15 

45 

0 

.70711 

.29289 

1.4142 

1.0000 

1.0000 

1.4142 

.29289 

.70711 

45 

^-0 

Cosine. 

Ver.  Sin. 

Secant. 

Cotan, 

Tang. 

Cosec. 

Co-Vers. 

Sine. 

o 

M. 

From  45°  to  60°  read  from  bottom  of  table  upwards. 


162 


MATHEMATICAL   TABLES. 
LOGARITHMIC  SINES,  ETC. 


Deg. 

Sine. 

Cosec. 

Versin. 

Tangent. 

Cotan. 

Covers. 

Secant. 

Cosine. 

Deg. 

0 

In.Neg. 

Infinite. 

In.Nes. 

In.Ne?. 

[nfinite. 

10.00000 

10.00000 

10.00000 

90 

1 

-8.24186 

11.75814 

G.I  8271 

8.24192 

11.75808 

9.99235 

10.00007 

9.99993 

89 

2 

8.54282 

11.45718 

6.78474 

8.54308 

11.45692 

9.98457 

10.00026 

9.99974 

88 

3 

8.71880 

11.28120 

7.13687 

8.71940 

11.28060 

9.97665 

10.00060 

9.99940 

87 

4 

8.84358 

11.15642 

7.38667 

8.84464 

11.15536 

9.96860 

10.00106 

9.99894 

86 

5 

8.94030 

11.05970 

7.58039 

8.94195 

11.05805 

9.96040 

10.00166 

9.99834 

85 

6 

9.01923 

10.98077 

7.73863 

9.02162 

10.97838 

9.95205 

10.00239 

9.99761 

84 

7 

9.08589 

10.91411 

7.87238 

9.08914 

10.91086 

9.94356 

10.00325 

9.99675 

83 

8 

9.14356 

10.85644 

7.98820 

9.14780 

10.85220 

9.93492 

10.00425 

9.99575 

82 

9 

9.19433 

10.80567 

8.09032 

9.19971 

10.80029 

9.92612 

10.00538 

9.99462 

81 

10 

9.23967 

10.76033 

8.18162 

9.24632 

10.75368 

9.91717 

10.00665 

9.99335 

80 

11 

9.28060 

10.71940 

8.26418 

9.28865 

10.71135 

9.90805 

10.00805 

9.99195 

79 

12 

9.31788 

10.68212 

8.33950 

9.32747 

10.67253 

9.89877 

10.00960 

9.99040 

78 

13 

9.35209 

10.64791 

8.  '40875 

9.36336 

10.63664 

9.88933 

10.01128 

9.98872 

77 

14 

9.38368 

10.61632 

8.47282 

9.39677 

10.60323 

9.87971 

10.01310 

9.98690 

76 

15 

9.41300 

10.58700 

8.53243 

9.42805 

10.57195 

9  86992 

10.01506 

9.98494 

75 

16 

9.44034 

10.55966 

8.58814 

9.45750 

10.54250 

9!  85996 

10.01716 

9.98284 

74 

17 

9.46594 

10.53406 

8.64043 

9.48534 

10.51466 

9.84981 

10.01940 

9.98060 

73 

18 

9.48998 

10.51002 

8.68969 

9.51178 

10.48822 

9.83947 

10.02179 

9.97821 

72 

19 

9.51264 

10.48736 

8.73625 

9.53697 

10.46303 

9.82894 

10.02433 

9.97567 

71 

20 

9.53405 

10.46595 

8.78037 

9.56107 

10.43893 

9.81821 

10.02701 

9.97299 

70 

21 

9.55433 

10.44567 

8.82230 

9.58418 

10.41582 

9.80729 

10.02985 

9.97015 

69 

22 

9.57358 

10.42642 

8.86223 

9.60641 

10.39359 

9.79615 

10.03283 

9.96717 

68 

23 

9.59188 

10.40812 

8.90034 

9.62785 

10.37215 

9.78481 

10.03597 

9.96403 

67 

24 

9.60931 

10.39069 

8.93679 

9.64858 

10.35142 

9.77325 

10.03927 

9.96073 

66 

25 

9.62595 

10.37405 

8.97170 

9.66867 

10.33133 

9.7614C 

10.04272 

9.95728 

65 

26 

9.64184 

10.35816 

9.00521 

9.68818 

10.31182 

9.74945 

10.04634 

9.95366 

64 

27 

9.65705 

10.34295 

9.03740 

9.70717 

10.29283 

9.73720 

10.05012 

9.94988 

63 

28 

9.67161 

10.32839 

9.06838 

9.72567 

10.27433 

9.72471 

10.05407 

9.94593 

,62 

29 

9.68557 

10.31443 

9.09823 

9.74375 

10.25625 

9.71197 

10.05818 

9.94182 

61 

30 

9.6989T 

10:30103 

9.12702 

9.76144 

10.23856 

9.69897 

10.06247 

9.93753 

60 

31 

9.71184 

10.28816 

9.15483 

9.77877 

10.22123 

£.68571 

10.06693 

9.93307 

59 

32 

9.72421 

10.27579 

9.18171 

9.79579 

10.20421 

9.67217 

10.07158 

9.92842 

58 

33 

9.73611 

10.26389 

9.20771 

9.81252 

10.18748 

9.65836 

10.07641 

9.92359 

57 

34 

9.74756 

10.25244 

9.23290 

9.82899 

10.17101 

9.64425 

10.08143 

9.91857 

56 

35 

9.75859 

10.24141 

9.25731 

9.84523 

10.15477 

9.62984 

10.08664 

9.91336 

55 

36 

9.769:32 

10.23078 

9.28099 

9.86126 

10.13874 

9.61512 

10.09204 

9.90796 

54 

8? 

9.77946 

10.22054 

9.30398 

9.87711 

10.12289 

9.60008 

10.09765 

9.90235 

53 

38 

9.78934 

10.21066 

9.32631 

9.89281 

10.10719 

9.58471 

10.10347 

9.89653 

52 

39 

9.79887 

10.20113 

9.34802 

9.90837 

10.09163 

9.56900 

10.10950 

9.89050 

51 

40 

9.80807 

10.19193 

9.36913 

9.92381 

10.07619 

9.55293 

10.11575 

9.88425 

50 

41 

9.81694 

10.18306 

9.38968 

9.93916 

10.06084 

9.53648 

10.12222 

9.87778  49 

42 

9.82551 

10.17449 

9.40969 

9.95444 

10.04556 

9.51966 

10.12893 

9.87107  48 

43 

9.88878 

10.16622 

9.42918 

9.96966 

10.03034 

9.50243 

10.13587 

9.86413  47 

44 

9.84177 

10.15823 

9.44818 

9.98484 

10.01516 

9.48479 

10.14307 

9.85693 

46 

45 

9.84949 

10.15052 

9.46671 

10.00000 

10.00000 

9.46671 

10.15052 

9.84949 

45 

Cosine. 

Secant.  , 

Covers. 

Cotan. 

Tangent. 

Versin. 

Cosec. 

Sine. 

1 

From  45°  to  90°  read  from  bottom  of  table  upwards* 


SPECIFIC   GRAVITY. 


163 


MATERIALS. 

THE    CHEMICAL    ELEMENTS. 

Common  Elements  (42). 


d~- 

O-M 

13  -3 

o   ' 

•3~ 

It 

Name. 

a  -a 

2® 

|t 

Name. 

It 

P 

Name. 

|| 

Al 
Sb 
As 

Aluminum 
Antimony    * 
Arsenic 

27  1 
120  '.4 
75.1 

F 
Au 
H 

Fluorine 
Gold 
Hydrogen 

19. 

197.2 
1.01 

Pd 
P 
Pt 

Palladium 
Phosphorus 
Platinum 

106. 
31. 
194.9 

Ba 

Barium 

137.4 

I 

Iodine 

126.8 

K 

Potassium 

39.1 

Bi 

Bismuth 

208.1 

Ir 

I  rid  iu  m 

193.1 

Si 

Silicon 

28.4 

B 

Boron 

10.9 

Fe 

Iron 

56. 

Ag 

Silver 

107.9 

Br 

Bromine 

79.9 

Pb 

Lead 

206.9 

Na 

Sodium 

23. 

Cd 

Cadmium 

111.9 

Li 

Lithium 

7.03 

Sr 

Strontium 

87.6 

Ca 
C 

Calcium 
Carbon 

40.1 
12. 

Mg 
Mn 

Magnesium 
Manganese 

24.3 

55. 

S 
Sn 

Sulphur 
Tin 

32.1 
119. 

Cl 

Chlorine 

35.4 

Hg 

Mercury 

200. 

Ti 

Titanium 

48.1 

Cr 

Chromium 

52.1 

Ni 

Nickel 

58.7 

W 

Tungsten 

184.8 

Co 

Cobalt 

59. 

N 

Nitrogen 

14. 

Va 

Vanadium 

51.4 

Cu 

Copper 

63.6 

0 

Oxygen 

16. 

Zn 

Zinc 

65.4 

The  atomic  weights  of  many  of  the  elements  vary  in  the  decimal  place  as 
given  by  different  authorities.  The  above  are  tlie  most  recent  values  re- 
ferred to  O  =  16  and  H  =  1.008.  When  H  is  taken  as  1,  O  =  15.879,  and  the 
other  figures  are  diminished  proportionately.  (See  Jour.  Am.  Chem.  /Soc., 
March,  1896.) 

Tne  Rare  Elements  (27). 


Beryllium,  Be. 
Caesium,  Cs. 
Cerium,  Ce. 
Didymium,  D. 
Erbium,  E. 
Gallium,  Ga. 
Germanium,  Ge. 

Glucinum,  G. 
Indium,  In. 
Lanthanum,  La. 
Molybdenum,  Mo. 
Niobium,  Nb, 
Osmium,  Os. 
Rhodium,  R. 

Rubidium,  Rb. 
Ruthenium,  Ru. 
Samarium,  Sm. 
Scandium,  Sc. 
Selenium,  Se. 
Tantalum,  Ta. 
Tellurium,  Te. 

Thallium,  Tl. 
Thorium,  Th. 
Uranium,  U. 
Ytterbium,  Yr. 
Yttrium,  Y. 
Zirconium,  Zr. 

SPECIFIC    GRAVITY. 

The  specific  gravity  of  a  substance  is  its  weight  as  compared  with  the 
weight  of  an  equal  bulk  of  pure  water. 
To  find  the  specific  gravity  of  a  substance. 

W  =  weight  of  body  in  air;  w  =  weight  of  body  submerged  in  water. 

Specific  gravity  =  — — — . 

If  the  substance  be  lighter  than  the  water,  sink  it  by  means  of  a  heavier 
substance,  and  deduct  the  weight  of  the  heavier  substance. 

Specific-gravity  determinations  are  usually  referred  to  the  standard  of  the 
weight  of  water  at  62°  F.,  62.355  Ibs.  per  cubic  foot.  Some  experimenters 
have  used  60°  F.  as  the  standard,  and  others  32°  and  39.1°  F.  There  is  no 
general  agreement. 

Given  sp.  gr.  referred  to  water  at  39.1°  F.,  to  reduce  it  to  the  standard  of 
62°  F.  multiply  it  by  1.00112. 

Given  sp.  gr.  referred  to  water  at  62°  F.,  to  find  weight  per  cubic  foot  mul- 
tiply by  62.355.  Given  weight  per  cubic  foot,  to  find  sp.  gr.  multiply  by 
0.016037.  Given  sp.  gr.,  to  find  weight  per  cubic  inch  multiply  by  .036085, 


164 


MATERIALS. 


Weight  and  Specific  Gravity  of  Metals. 


Specific  Gravity. 
Range  accord- 
ing to 
several 
Authorities. 

Specific  Grav- 
ity.    Approx. 
Mean  Value, 
used  in 
Calculation  of 
Weight. 

Weight 
per 
Cubic 
Foot, 
Ibs. 

Weight 
per 
Cubic 
Inch, 
Ibs. 

Aluminum 

2.56    to    2.71 
6.66    to    6.86 
9.74    to    9.90 

7.8     to     8.6 

8.52    to    8.96 

8.6      to    8.7 
1.58 
5.0 
8.5      to    8.6 
19.245  to  19.361 
8.69    to    8.92 
22.38    to  23. 
6.85    to    7.48 
7.4      to    7.9 
11.07    to  11.44 
7.        to    8. 
1.69    to  1.75 
13.60    to  13.62 
13.58 
13.37    to  13.38 
8.279  to    8.93 
20.33     to  22.07 
0.865 
10.474  to  10.511 
0.97 
7.69*  to    7.9321 
7.291  to    7.409 
5.3 
17.        to  17.6 
6.86    to    7.20 

2.67 
6.76 
9.82 

f8.60 
J  8.40 
1  8.36 
18.20 

8.853 
8.65 

19.258 
8.853 

7.218 
7.70 
11.38 
8. 
1.75 
13.62 
13.58 
13.38 
8.8 
21.5 

10.505 

7.854 
7.350 

7.00 

166.5 
421.6 
612.4 

536.3 
523.8 
521.3 
511.4 

552. 
539. 

1200.9 
552. 
1396. 
450. 
480. 
709.7 
499. 
109. 
849.3 
846.8 
834.4 
548.7 
1347.0 

655.1 

489.6 
458.3 

436.5 

.0963 
.2439 
.3454 

.3103 
.3031 
.3017 
.2959 

.3195 
.3121 

.6919 
.3195 
.8076 
.2604 
.2779 
.4106 
.2887 
.0641 
.4915 
.4900 
.4828 
.3175 
.7758 

.3791 

.2834 
.2652 

.2526 

Antimony    .  . 

Bismuth  
Brass:  Copper  4-  Zinc  1 
80               20    j 
70               30    Y  .  . 
60               40    | 
50               50  J 
T*,.™    o  J  Copper,  95  to  80  » 
ze"JTin,          5  to  20  j" 
Cadmium 

Calcium 

Chromium  .... 

Cobalt 

Gold,  pure  — 
Copper  .  . 

Iron   Cast 

"     Wrought 
Lead  

Manganese 

Magnesium 

Mercury 

(   32° 

•<    60° 

Nickel  
Platinum 

Potassium 

Silver 

Sodium 

Steel  
Tin 

Titanium  ... 

Tungsten 

Zinc  

*  Hard  and  burned. 

t  Very  pure  and  soft.    The  sp.  gr.  decreases  as  the  carbon  is  increased. 

In  the  first  column  of  figures  the  lowest  are  usually  those  of  cast  metals, 
which  are  more  or  less  porous;  the  highest  are  of  metals  finely  rolled  or 
drawn  into  wire. 

Specific  Gravity  of  Liquids  at  6O°  F. 


Acid,  Muriatic 1.200 

kk      Nitric 1.217 

"      Sulphuric 1.849 

Alcohol,  pure 794 

"        95  per  cent 816 

50    "     "     934 

Ammonia,  27.9  per  cent 891 

Bromine 2.97 

Carbon  disulphide 1 .26 

Ether,  Sulphuric 72 

Oil,  Linseed 94 

Compression  of  tlie  following  Fluids  under  a  Pressure  of 
15  Ibs.  per  Square  Inch. 


Oil,  Olive  92 

'    Palm 97 

'    Petroleum 78  to  .88 

'    Rape 92 

'    Turpentine 87 

1    Whale 92 

Tar 1. 

Vinegar 1.08 

Water 1. 

"    sea 1.026  to  1.03 


Water 0000-1663  | 

Alcohol 0000216 


Ether 00006158 

Mercury 00000265 


SPECIFIC   GRAVITY. 


165 


The  Hydrometer. 

The  hydrometer  is  an  instrument  for  determining  the  density  of  liquids. 
It  is  usually  made  of  glass,  and  consists  of  three  parts:  (1)  the  upper  part, 
a  graduated  stem  or  fine  tube  of  uniform  diameter;  (2)  a  bulb,  or  enlarge- 
ment of  the  tube,  containing  air ;  and  (3)  a  small  bulb  at  the  bottom,  con- 
taining shot  or  mercury  which  causes  the  instrument  to  float  in  a  vertical 
position.  The  graduations  are  figures  representing  either  specific  gravities, 
or  the  numbers  of  an  arbitrary  scale,  as  in  Baum6's,  Twaddell's,  Beck's, 
and  other  hydrometers. 

There  is  a  tendency  to  discard  all  hydrometers  with  arbitrary  scales  and 
to  use  only  those  which  read  in  terms  of  the  specific  gravity  directly. 

ISa  nine's  Hydrometer  and  Specific  Gravities  Compared* 


Degrees 
Baume. 

Liquids 
Heavier 
than 
Water, 
sp.  gr. 

Liquids 
Lighter 
than 
Water, 
sp.  gr. 

VI      • 

a.  «x> 

£  £ 

£§ 

p» 

Liquids 
Heavier 
than 
Water, 
sp.  gr. 

Liquids 
Lighter 
than 
Water, 
sp.  gr. 

Degrees 
Baume. 

Liquids 
Heavier 
than 
Water, 
sp.  gr. 

Liquids 
Lighter 
than 
Water, 
sp.  gr. 

o 

1  000 

19 

1  143 

942 

38 

333 

839 

1 

1.007 

20 

1   152 

.936 

89 

345 

.834 

2 

1  013 

21 

1  160 

930 

40 

357 

830 

3 

4 

1.020 
1  027 

22 
23 

1.169 
1  178 

.924 
918 

41 
42 

.369 

382 

.825 
820 

5 

1  034 

24 

1  188 

.913 

44 

407 

.811 

6 

1.041 

25 

1.197 

.907 

46 

.434 

.802 

1  048 

26 

1  206 

.901 

48 

462 

.794 

8 

1.056 

27 

1.216 

.896 

50 

.490 

.785 

9 

1  063 

28 

1  226 

890 

52 

520 

777 

10 
11 
12 
13 
14 

1.070 
1.078 
1.086 
1.094 
1  101 

1.000 
.993 
.986 
.980 
973 

29 
30 
31 
82 
33 

1.236 
1.246 
1.256 
1.267 
1  277 

.885 
.880 
.874 
.869 
864 

54 

56 
58 
60 
65 

.551 
.583 
.617 
.652 

1  747 

.768 
.760 
.753 
.745 

15 

1.109 

.967 

34 

1  288 

.859 

70 

1  854 

16 

1.118 

.960 

35 

1.299 

.854 

75 

1.974 

17 

1.126 

.954 

36 

1.310 

.849 

76 

2.000 

18 

1.134 

.948 

37 

1.322 

.844 

Specific  Gravity  and  Weight  of  Wood. 


Specific  Gravity. 

Weight 

Cubic 
Foot, 
Ibs. 

Specific  Gravity. 

Weight 

Cubic 
Foot, 
Ibs. 

Alder  

Avge. 
0.56  to  0.80       .68 

42 

Hornbeam  .. 

Avge. 
.76  .76 

47 

73  to    .79       .76 

47 

Juniper 

.56  .56 

35 

Ash 

.60  to    .84        .72 

45 

Larch  . 

.56  .56 

35 

Bamboo..  .. 
Beech 

.31  to    .40       .35 
.62  to    .85       .73 

22 

46 

Lignum  vitse 
Linden 

.65  to  1.33  1.00 
.604 

62 
37 

Birch 

.56  to    .74       .65 

41 

Locust. 

.728 

46 

Box,  
Cedar 

.91  to  1.33     1.12 
.49  to    .75        .62 

70 

39 

Mahogany.  .  . 
Maple 

.56  to  1.06  .81 
.57  to  .79  .68 

51 
42 

Cherry  
Chestnut  
Cork. 

.61  to    .72       .66 
.46  to    .66       .56 
.24                     .24 

41 
35 
15 

Mulberry  
Oak,  Live.... 
"     White.. 

.56  to  .90  .73 
.96  to  1.26  1.11 

.69  to  .86  .77 

46 

69 

48 

Cypress  — 
Dogwood   .  . 
Ebony  
Elm  
Fir  
Gum  
Hackmatack 

.41  to    .66       .53 
.76                     .76 
1.13  to  1.33     1.23 
.55  to    .78       .61 
.48  to    .70       .59 
.84  to  1.00       .92 
.59                     .59 

33 
47 
76 
38 
37 
57 
37 

"     Red... 
Pine,  White.. 
4i      Yellow. 
Poplar  
Spruce.   
Sycamore  
Teak  

.73  to  .75  .74 
.35  to  ,55  .45 
.46  to  .76  .61 
.38  to  .58  .48 
.40  to  .50  .45 
.59  to  .62  .60 
.66  to  .98  .82 

46 

28 
38 
30 
28 
37 
51 

Hemlock  ... 
Hickory  
Holly  

.36  to    .41        .38 
.69  to    .94        .77 
.76                     .76 

24 

48 

47 

Walnut  
Willo\v  

.50  to  .67  .58 
.49  to  .59  .54 

36 
34 

166 


MATERIALS. 


Weight  and  Specific  Gravity  of  Stones,  Brick, 
Cement,  etc. 


Pounds  per 
Cubic  Foot. 


Specific 
Gravity. 


Asphaltuin 87 

Brick,  Soft 100 

"      Common 112 

41      Hard 125 

44      Pressed 135 

44      Fire 140  to  150 

Brickwork  in  mortar 100 

"  cement 112 

Cement,  Rosendale,  loose 60 

k4       Portland,        4t    78 

Clay , 120tol50 

Concrete  120  to  140 

Earth,  loose 72  to   80 

rammed 90  to  110 

Emery 250 

Glass 156tol72 

"    flint 180  to  196 

Gneiss   I  ten  ±^  n^n 

Granite  \ 160  to  170 

Gravel 100  to  120 

Gypsum 130  to  150 

Hornblende 200  to  220 

Lime,  quick,  in  bulk 50  to   55 

Limestone 170  to  200 

Magnesia,  Carbonate.. 150 

Marble 160  to  180 

Masonry,  dry  rubble 140  to  160 

dressed 140  to  180 

Mortar 90  to  100 

Pitch 72 

Plaster  of  Paris 74  to   80 

Quartz 165 

Sand 90  to  110 

Sandstone 140  to  150 

Slate 170  to  180 

Stone,  various 135  to  200 

Trap • 170  to  200 

Tile 110tol20 

Soapstone 166  to  175 


1.39 
1.6 
1.79 
2.0 
2.16 

2.24  to  2.4 
1.6 
1.79 
.96 
1.25 

1.92  to  2.4 
1.92  to  2.24 

1.15  to  1.28 
1.44  to  1.76 
4. 

2.5  to  2.75 
2. 88  to  3. 14 

2. 56  to  2.72 

1.6  to  1.92 
2. 08  to  2. 4 
3.2  to  3. 52 

.8  to  .88 
2. 72  to  3. 2 
2.4 

2. 56  to  2. 88 
2. 24  to  2. 56 
2.24  to  2.88 
1.44  to  1.6 
1.15 

1.18  to  1.28 
2.64 

1.44  to  1.76 
2. 24  to  2.4 
2. 72  to  2. 88 

2. 16  to  3.4 
2. 72  to  3.4 
1.76  to  1.92 
2.65  to  2.8 


Specific   Gravity   and   Weight   of  Gases   at   Atmospheric 
Pressure  and  32°  F. 

(For  other  temperatures  and  pressures  see  pp.  459,  479.) 


Density, 

Air  =  1. 


Grammes 
per  Litre. 


Lbs.  per 
Cu.  Ft. 


Cubic  Ft. 
per  Lb. 


Air 


Hydrogen  ................ 

Nitrogen  .................. 

Carbonic  oxide,  CO  ....... 

Carbonic  acid,  CO2  ....... 

Marsh-gas,  methane,  CH4 
Ethylene,  CaH4  ........... 


1.0000 
1.1051 
0.0695 
0.9714 
0.9674 
1.5290 
0.5560 
0.9847 


1.2931 

1.4290 

0.08987 

1.2561 

1.251 

1.977 

0.719 

1.273 


0.08728 
0.08921 
0.00561 
0.07842 
0.07810 
0.12343 
0.04488 
0.07949 


12.387 
11.209 
178.23 
12.752 
12.804 
8.102 
22.301 
12.580 


J'UOlM'kTIKS   OF   THE    USEFUL   METALS.  167 

PROPERTIES  OF  THE  USEFUL    METALS. 

Aluminum.  Al.— Atomic  weight  27.1.  Specific  gravity  2.6  to  2.7. 
The  lightest  of  all  the  useful  metals  except  magnesium.  A  soft,  ductile, 
malleable  metal,  of  a  white  color,  approaching  silver,  but  with  a  bluish  cast. 
Very  non-corrosive.  Tenacity  about  one  third  that  of  wrought-iron.  For- 
merly a  rare  metal,  but  since  1890  its  production  and  use  have  greatly  in- 
creased on  account  of  the  discovery  of  cheap  processes  for  reducing  it  from 
the  ore.  Melts  at  about  1160°  F.  For  further  description  see  Aluminum, 
under  Strength  of  Materials. 

Antimony  (Stibium),  Sb.— At.  wt.  120.4.  Sp.  gr.  6.7  to  6.8.  A  brittle 
metal  of  a  bluish-white  color  ana  highly  crystalline  or  laminated  structure. 
Melts  at  842°  F.  Heated  in  the  open  air  it  burns  with  a  bluish-white  flame. 
Its  chief  use  is  for  the  manufacture  of  certain  alloys,  as  type-metal  (anti- 
mony 1,  lead  4),  britannia  (antimony  1,  tin  9),  and  various  anti-friction 
metals  (see  Alloys).  Cubical  expansion  by  heat  from  32°  to  212°  F.,  0.0070. 
Specific  heat  .050. 

Bismuth,  Bi.— At.  wt.  208.1.  Bismuth  is  of  a  peculiar  light  reddish 
color,  highly  crystalline,  and  so  brittle  that  it  can  readily  be  pulverized.  It 
melts  at  510°  F.,  and  boils  at  about  2MO°  F.  Sp.  gr.  9.823  at  54°  F.,  and 
10.055  just  above  the  melting-point.  Specific  heat  about  .0301  at  ordinary 
temperatures.  Coefficient  of  cubical  expansion  from  32°  to  212°,  0.0040.  Con- 
ductivity for  heat  about  1/56  and  for  electricity  only  about  1/80  of  that  of 
silver.  Its  tensile  strength  is  about  6400  Ibs.  per  square  inch.  Bismuth  ex- 
pands in  cooling,  and  Tribe  has  shown  that  this  expansion  does  not  take 
place  until  after  solidification.  Bismuth  is  the  most  diamagnetic  element 
known,  a  sphere  of  it  being  repelled  by  a  magnet. 

Cadmium,  Cd.— At.  wt.  112.  Sp.  gr.  8.6  to  8.7.  A  bluish-white  metal, 
lustrous,  with  a  fibrous  fracture.  Melts  below  500°  F.  and  volatilizes  at 
about  680°  F.  It  is  used  as  an  ingredient  in  some  fusible  alloys  with  lead, 
tin.  arid  i  ismuth.  Cubical  expansion  from  32°  to  212°  F.,  0.0094. 

Copper,  Cu.— At.  wt.  63.2.  Sp.  gr.  8.81  to  8.95.  Fuses  at  about  1930° 
F.  Distinguished  from  all  other  metals  by  its  reddish  color.  Very  ductile 
and  malleable,  and  its  tenacity  is  next  to  iron.  Tensile  strength  20,000  to 
30,000  Ibs.  per  square  inch.  Heat  conductivity  73.6$  of  that  of  silver,  and  su- 
perior to  that  of  other  metals.  Electric  conductivity  equal  to  that  of  gold 
and  silver.  Expansion  by  heat  from  32°  to  212°  F.,  0.0051  of  its  volume. 
Specific  heat  .093.  (See  Copper  under  Strength  of  Materials:  also  Alloys.) 

Gold  (Aurum),  All.— At.  wt.  197.2.  Sp.  gr.,  when  pure  and  pressed  in  a 
die,  19.34.  Melts  at  about  1915°  F.  The  most  malleable  and  ductile  of  all 
metals.  One  ounce  Troy  may  be  beaten  so  as  to  cover  160  sq.  ft.  of  surface. 
The  average  thickness  of  gold-leaf  is  1/282000  of  an  inch,  or  100  sq.  ft.  per 
ounce.  One  grain  may  be  drawn  into  a  wire  500  ft.  in  length.  The  ductil- 
ity is  destroyed  by  the  presence  of  1/2000  part  of  lead,  bismuth,  or  antimony. 
Gold  is  hardened  by  the  addition  of  silver  or  of  copper.  In  U.  S.  gold  coin 
there  are  90  parts  gold  and  10  parts  of  alloy,  which  is  chiefly  copper  with  a 
little  silver.  By  jewelers  the  fineness  of  gold  is  expressed  in  carats,  pure 
gold  being  24  carats,  three  fourths  fine  18  carats,  etc. 

Iridium. — Iridium  is  one  of  the  rarer  metals.  It  has  a  white  lustre,  re- 
'seinbling  that  of  steel;  its  hardness  is  about  equal  to  that  of  the  ruby;  in 
the  cold  it  is  quite  brittle,  but  at  a  white  heat  it  is  somewhat  malleable.  It 
is  one  of  the  Heaviest  of  metals,  having  a  specific  gravity  ot  aa.38.  It  is  ex- 
tremely infusible  and  almost  absolutely  inoxiclizable. 

For  uses  of  iridium,  methods  of  manufacturing  it,  etc.,  see  paper  by  W.  D. 
Dudley  on  the  "Iridium  Industry,"  Trans.  A.  I.  M.  E.  1884. 

Iron  (Ferrum),  Fe.— At.  wt.  56.  Sp.  gr.:  Cast,  6.85  to  7.48;  Wrought, 
7.4  to  7.9.  Pure  iron  is  extremely  infusible,  its  melting  point  being  above 
3000°  F.,  but  its  fusibility  increases  with  the  addition  of  carbon,  cast  iron  fus- 
ing about  2500°  F.  Conductivity  for  heat  11.9,  and  for  electricity  12  to  14.8, 
silver  being  100.  Expansion  in  bulk  by  heat:  cast  iron  .0033,  and  wrought  iron 
.0035,  from  32°  to  212°  F.  Specific  heat:  cast  iron  .1298,  wrought  iron  .1138, 
steel  .1165.  Cast  iron  exposed  to  continued  heat  becomes  permanently  ex- 
panded 1)4  to  3  per  cent  of  its  length.  Grate-bars  should  therefore  be 
allowed  about  4  per  cent  play.  (For  other  properties  see  Iron  and  Steel 
under  Strength  of  Materials.) 

Lead  (Plumbum),  Pb.— At.  wt.  206.0.  Sp.  gr.  11.07  to  11.44  by  different 
authorities.  Melts  at  about  625°  F.,  softens  and  becomes  pasty  at  about 
til 7°  F.  If  broken  by  a  sudden  blow  when  just  below  the  melting-point  it  is 
quite  brittle  and  the  fracture  appears  crystalline.  Lead  is  very  malleable 


168  MATERIALS. 

and  ductile,  but  its  tenacity  is  such  that  it  can  be  drawn  into  wire  with  great 
difficulty.  Tensile  strength,  1600  to  2400  Ibs.  per  square  inch.  Its  elasticity  is 
very  low,  and  the  metal  flows  under  very  slight  strain.  Lead  dissolves  to 
some  extent  in  pure  water,  but  water  containing  carbonates  or  sulphates 
forms  over  it  a  film  of  insoluble  salt  which  prevents  further  action. 

Magnesium,  Mg.— At.  wt.  24.  Sp.  gr.  1.69  to  1.75.  Silver-white, 
brilliant,  malleable,  and  ductile.  It  is  one  of  the  lightest  of  metals,  weighing 
only  about  two  thirds  as  much  as  aluminum.  In  the  form  of  filings,  wire, 
or  thin  ribbons  it  is  highly  combustible,  burning  with  a  light  of  dazzling 
brilliancy,  useful  for  signal-lights  and  for  flash-lights  for  photographers.  It 
is  nearly  non-corrosive,  a  thin  film  of  carbonate  of  magnesia  forming  on  ex- 
posure to  damp  air,  which  protects  it  from  further  corrosion.  It  maybe 
alloyed  with  aluminum,  5  per  cent  Mg  added  to  Al  giving  about  as  much  in- 
crease of  strength  and  hardness  as  10  per  cent  of  copper.  Cubical  expansion 
by  heat  0.0083,  from  32°  to  212°  F.  Melts  at  1200°  F.  Specific  heat  .25fr 

Manganese,  Mn.-- -At.  wt.  55.  Sp.  gr.  7  to  8.  The  pure  metal  is  not 
used  in  tne  arts,  but  alloys  of  manganese  and  iron,  called  spiegeleisen  when 
containing  below  25  per  cent  of  manganese,  and  ferro-manganese  when  con- 
taining from  25  to  90  per  cent,  are  used  in  the  manufacture  of  steel.  Metallic 
manganese,  when  alloyed  with  iron,  oxidizes  rapidly  in  the  air,  and  its  func- 
tion in  steel  manufacture  is  to  remove  the  oxygen  from  the  bath  of  steel 
whether  it  exists  as  oxide  of  iron  or  as  occluded  gas. 

Mercury  (Hydrargyrum),  Hg.—  At.  wt.  199.8.  A  silver-white  metal,, 
liquid  at  temperatures  above— 3(J°  F.,  and  boils  at  680°  F.  Unchangeable  as, 
gold,  silver,  and  platinum  in  the  atmosphere  at  ordinary  temperatures,  but 
oxidizes  to  the  red  oxide  when  near  its  boiling-point.  Sp.gr.:  when  liquid 
13.58  to  13.59,  when  frozen  14.4  to  14.5.  Easily  tarnished  by  sulphur  fumes, 
also  by  dust,  from  which  it  may  be  freed  by  straining  through  a  cloth.  No 
metarexcept  iron  or  platinum  should  be  allowed  to  touch  mercury.  The 
smallest  portions  of  tin,  lead,  zinc,  and  even  copper  to  a  less  extent,  cause  it 
to  tarnish  and  lose  its  perfect  liquidity.  Coefficient  of  cubical  expansion 
from  32°  to  212°  F.  .018.2;  per  deg.  .000101. 

Nickel,  NI.— At.  wt.  58.3.  Sp.  gr.  8.27  to  8.93.  A  silvery- white  metal 
with  a  strong  lustre,  not  tarnishing  on  exposure  to  the  air.  Ductile,  hard, 
and  as  tenacious  as  iron.  It  is  attracted  to  the  magnet  and  may  be  made 
magnetic  like  iron.  Nickel  is  very  difficult  of  fusion,  melting  at  about 
3000°  F.  Chiefly  used  in  alloys  with  copper,  as  german-silver,  nickel-silver, 
etc.,  and  recently  in  the  manufacture  of  steel  to  increase  its  hardness  and: 
strength,  also  for  nickel-plating.  Cubical  expansion  from  32°  to  212°  F., 
0.0038.  Specific  heat  .109. 

Platinum,  Pt.— At.  wt.  195.  A  whitish  steel-gray  me*al,  malleable;, 
very  ductile,  and  as  unalterable  by  ordinary  agencies  as  gold.  When  fused: 
and  refined  it  is  as  soft  as  copper.  Sp.  gr.  21.15.  It  is  fusible  only  by  the 
pxyhydrogen  blowpipe  or  in  strong  electric  currents.  When  combined  with: 
iridium  it  forms  an  alloy  of  great  hardness,  which  has  been  used  for  gun- 
vents  and  for  standard  weights  and  measures.  The  most  important  uses  of 
platinum  in  the  arts  are  for  vessels  for  chemical  laboratories  and  manufac- 
tories, and  for  the  connecting  wires  in  incandescent  electric  lamps.  Cubical 
expansion  from  32°  to  212°  F.,  0.0027,  less  than  that  of  any  other  metal  ex- 
cept the  rare  metals,  and  almost  the  same  as  glass. 

Silver  (Argentum),  Ag.  — At.  wt.  107.7.  Sp.  gr.  10.1  to  11.1,  according  to> 
condition  and  purity.  It  is  the  whitest  of  the  metals,  very  malleable  and 
ductile,  and  in  hardness  intermediate  between  gold  and  copper.  Melts  at 
about  1750°  F.  Specific  heat  .056.  Cubical  expansion  from  32°  to  212°  F.,, 
0.0058.  As  a  conductor  of  electricity  it  is  equal  to  copper.  As  a  conductor 
of  heat  it  is  superior  to  all  other  metals. 

Tin  (Stannum)  Sii.— At.  wt.  118.  Sp.  gr.  7.293.  White,  lustrous,  soft,, 
malleable,  of  little  strength,  tenacity  about  3500  Ibs.  per  square  inch.  Fuses 
at  442°  F.  Not  sensibly  volatile  when  melted  at  ordinary  heats.  Heat  con- 
ductivity 14.5,  electric  conductivity  12.4;  silver  being  100  in  each  case. 
Expansion  of  volume  by  heat  .0069  from  32°  to  212°  F.  Specific  heat  .055.  Its 
chief  uses  are  for  coating  of  sheet-iron  (called  tin  plate)  and  for  making 
alloys  with  copper  and  other  metals. 

Zinc,  Zn.— At.  wt.  65.  Sp.  gr.  7.14.  Melts  at  780°  F.  Volatilizes  and 
burns  in  the  air  when  melted,  with  bluish-white  fumes  of  zinc  oxide.  It  is 
ductile  and  malleable,  but  to  a  much  less  extent  than  copper,  and  its  tenacity, 
about  5000  to  6000  Ibs.  per  square  inch,  is  about  one  tenth  that  of  wrought 
iron.  It  is  practically  non-corrosive  in  the  atmosphere,  a  thin  film  of  car 
bonate  of  zinc  forming  upon  it.  Cubical  expansion  between  32°  and  212°  F., 


MEASURES  AND  WEIGHTS  OF  VARIOUS  MATERIALS.  169 


0.0088.  Specific  heat  .096.  Electric  conductivity  29,  heat  conductivity  36, 
silver  being  100.  Its  principal  uses  are  for  coating  iron  surfaces,  called 
"  galvanizing,"  and  for  making  brass  and  other  alloys. 

Table  Showing  the  Order  of 
Malleability.      Ductility.     Tenacity.     Infusibility. 

Gold 

Silver 

Aluminum 

Copper 

Tin 

Lead 

Zinc 

Platinum 

Iron 


Platinum 

Iron 

Platinum 

Silver 

Copper 

Iron 

Iron 

Aluminum 

Copper 

Copper 

Platinum 

Gold 

Gold 

Silver 

Silver 

Aluminum 

Zinc 

Aluminum 

Zinc 

Gold 

Zinc 

Tin 

Tin 

Lead 

Lead 


Lead 


Tin 


FORMULA  AND  TABLE  FOR  CALCULATING  THE 
WEIGHT  OF  RODS,  BARS,  PLATES.  TUBES.  AND 
SPHERES  OF  DIFFERENT  MATERIALS. 

Notation  :  b  =  breadth,  t  =  thickness,  s  =  side  of  square,  d  =  external 
diameter,  dl  =  internal  diameter,  all  in  inches. 

Sectional  areas  :  of  square  bars  —  s2;  of  flat  bars  =  bt ;  of  round  rods  = 
.7854d2;  of  tubes  =  .7854(d2  -  dj2)  =  3.1416(d*  —  *2). 

Volume  of  1  foot  in  length  :  of  square  bars  =  12s2;  of  flat  bars  =  126*;  of 
round  bars  =  9.4248d2;  of  tubes  =  9.4248(d2  -  dj2)  =  37.6992(dr  -  *2),  in  cubic 
inches. 

Weight  per  foot  length  =  volume  X  weight  per  cubic  inch  of  the  material. 
Weight  of  a  sphere  =  diam.3  x  .5236  X  weight  per  cubic  inch. 


Material. 

6 

1 

0 

1 

Weight  pel-  cubic 
foot,  Ibs. 

4J  JH     J3< 

5*3  « 

6C5  '- 

I'-a 

Weight  of  Square 
Bars  pei'  foot 
length,  Ibs. 

!>*t 

&C£  rj 

"S«-| 

.2604 
.2779 
.2833 

.3195 

.3029 

.4106 
.0963 
.0945 
.0174 

|| 

||l 
fll 

aT 

I 
«-i  ° 

Cast  iron  
Wrought  Iron  
Steel  

7.218 

7.7 
7.854 

8.855 

8.393 

11.38 
2.67 
2.62 
0.481 

450. 

480. 
489.6 

552. 

523.2 

709.6 
166.5 
163.4 
30.0 

37.5 
40. 
40.8 

46. 

43.6 

59.1 
13.9 
13.6 
2  5 

3.4s2 
3.833s2 

3.633s2 

4.93s2 
1.16s2 
1.13s2 
0.21s2 

3^6* 
3.46* 

3.8336* 

3.6336* 

4.936* 
1.166* 
1.136* 
0.216* 

15-16 
1. 
1.02 

1.15 

1.09 

1.48 
0.347 
0.34 
1-16 

2.454d2 

2!670d2 
3.011d2 

2.854d2 

3.870d2 
0.908d2 
0.891d2 

.1363d' 
.1455d3 
.1484d3 

.1673d3 
.1586d3 

.2150d8 
.0504d3 
.0495d3 
.0091d3 

Copper  &  Bronze  t 
(copper  and  tin)  f 
R  j  65  Copper.. 
tirass  \  35  Zinc  
Lead  

Aluminum 

Glass  .  . 

Pine  Wood,  dry  .  .  . 

For  tubes  use  the  coefficient  of  d2  in  ninth  column,  as  for  rods,  and 
multiply  it  into  (da  —  dj2);  or  take  four  times  this  coefficient  and  multiply  it 
into  (dt  -  *2). 

For  hollow  spheres  use  the  coefficient  of  d3  in  the  last  column  and 
multiply  it  into  (d3  —  d^J. 

MEASURES    AND    WEIGHTS    OF    VARIOUS 
MATERIALS   (APPROXIMATE). 

Brickwork.— Brickwork  is  estimated  by  the  thousand,  and  for  various 
thicknesses  of  wall  runs  as  follows: 

8U-in.  wall,  or  1  brick  in  thickness,  14  bricks  per  superficial  foot. 

12%  "        "      "  1^  "     "          '•  21      " 

17      "        u      "  2      "     "          "  28      "         "  "  «« 

21^  "        4'      "  2^  "     "          "  35      "         "  "  " 

An  ordinary  brick  measures  about  8^4  X  4  X  2  inches,  which  is  equal  to  66 
ioni)ic  inches,  or  26.2  bricks  to  a  cubic  foot.  The  average  weight  is  4^>  Ibs. 


170 


MATERIALS. 


Fuel.— A  bushel  of  bituminous  coal  weighs  76  pounds  and  contains  2688 
cubic  inches  =  1.554  cubic  feet.  29.47  bushels  =  1  gross  ton. 

A  bushel  of  coke  weighs  40  Ibs.  (35  to  42  Ibs.). 

One  acre  of  bituminous  coal  contains  1600  tons  of  2240  Ibs.  per  foot  of 
thickness  of  coal  worked.  15  to  25  per  cent  must  be  deducted  for  waste  in 
mining. 

44.8  cubic  feet  bituminous  coal  when  broken  down =  1  ton,  2240  Ibs. 

42.3     "        "     anthracite      "        "          "  " -  1  ton,  2240  Ibs. 

123      "       "     ofcharcoal  =  1  ton,  2240  Ibs. 

70.9  "        "      "coke >...  =  1  ton,  2240  Ibs. 

1  cubic  foot  of  anthracite  coal =  50  to  55  Ibs. 

1  "  bituminous"    =  45  to  55  Ibs. 

1  Cumberland  coal — =  53  Ibs. 

1  Cannel  coal =  50.3  Ibs. 

1  charcoal  (hardwood), =  18.5  Ibs. 

1  (pine) =18  Ibs. 

A  bushel  of  charcoal.— In  1881  the  American  Charcoal-Iron  Work- 
ers' Association  adopted  for  use  in  its  official  publications  for  the  standard 
bushel  of  charcoal  2748  cubic  inches,  or  20  pounds.  A  ton  of  charcoal  is  to 
be  taken  at  2000  pounds.  This  figure  of  20  pounds  to  the  bushel  was  taken 
as  a  fair  average  of  different  bushels  used  throughout  the  country,  and  it 
has  since  been  established  by  law  in  some  States. 

Ores,  Earths,  etc. 

13  cubic  feet  of  ordinary  gold  or  silver  ore,  in  mine =  1  ton  =  2000  Ibs. 

20     "        "     "  broken  quartz =  1  ton  =  2000  Ibs. 

18  feet  of  gravel  in  bank =1  ton. 

27  cubic  feet  of  gravel  when  dry =  1  ton. 

25     "        "     "  sand =  1  ton. 

18  '*  earth  in  bank  =  1  ton. 

27     "  "       "      when  dry =  1  ton 

17  "  clay 4  =  1  ton. 

Cement.— English  Portland,  sp.  gr.  1.25  to  1.51,  per  bbl. . . .  400  to  430  Ibs. 

Rosendale,  U.  S.,  a  struck  bushel 62  to   70  Ibs. 

Lime.— A  struck  bushel 72  to   75  Ibs. 

Grain.— A  struck  bushel  of  wheat  =  60  Ibs.:  of  corn  =  56  Ibs. ;  of  oats  = 
30  Ibs. 

Salt.— A  struck  bushel  of  salt,  coarse,  Syracuse,  N.  Y.  =  56  Ibs.;  Turk's 
Island  =  76  to  80  Ibs. 

Weight  of  Earth  Filling. 
(From  Howe's  "  Retaining  Walls.") 

Average  weight  in 
Ibs.  per  cubic  foot. 

Earth,  common  loam,  loose 72  to   80 

shaken... 82  to   92 

"      rammed  moderately 90  to  100 

Gravel , 90  to  106 

Sand , 90tol06 

Soft  flowing  mud 104  to  120 

Sand,  perfectly  wet 118  to  129 

COMMERCIAL    SIZES   OF   IRON   BARS. 

Flats. 


Width.        Thickness. 


Width.        Thickness.       Width.      Thickness. 


to  2 


to  2 


WEIGHTS   OF  WROUGHT   IROK   BARS. 


171 


Rounds :  *4  to  \%  inches,  advancing  by  16ths,  and  \%  to  5  inches  by 
8ths. 

Squares  :  5/16  to  1J4  inches,  advancing  by  16ths,  and  1J4  to  3  inches  by 
8tl)s. 

Half  rounds:  7/16,  %  %,  11/16,  %,  1,  \ys,  1^,  %  %  2  inches. 

Hexagons  :  %  to  \\fa  inches,  advancing  by  8ths. 

Ovals :  Y2  X  V^  %  X  5/16,  %X%,%X  7/16  inch. 

Half  ovals  s^X&HX  5/32,  M  X  3/16,  %  X  7/32,  1^  X  ^  M  X  H, 
1%X%  inch. 

Round-edge  flats :  1^  x  J4  1%  X%,iysx%  inch. 

Bands :  ^  to  1^  inches,  advancing  by  8ths,  7  to  16  B.  W.  gauge. 

1J4  to  5  inches,  advancing  by  4ths,  7  to  16  gauge  up  to  3  inches,  4  to  14 
gauge,  3J4  to  5  inches. 

WEIGHTS    OF    SQUARE    AND    ROUND    RARS    OF 
WROUGHT    IRON    IN    POUNDS    PER    LINEAL   FOOT. 

Iron  weighing  480  Ibs.  per  cubic  foot.    For  steel  add  2  per  cent. 


b 

b 

J 

t-t 

®    L-,    «? 

eg 

£ 

s,  • 

| 

d 

Thickness 
Diamete: 
in  Inches 

~f  1     • 

be  3  *  C 

Weight  of 
Round  B 
One  Foo 
Long. 

Thickness 
Diamete] 
in  Indies 

fill 

^  i'o)  ^ 

Thickness 
Diamete 
in  Inches 

||l 

pi 

0 

11/16 

24.08 

18.91 

¥ 

96.30 

75.64 

1/16 

.013 

.010 

k 

25.21 

19.80 

7/16 

98.55 

77.40 

y* 

.052 

.041 

13/16 

26.37 

20.71 

/^ 

100.8 

79.19 

3/18 

.117 

.092 

% 

27.55 

21.64 

9/16 

103.1 

81.00 

/4 

.208 

.164 

15/16 

28.76 

22.59 

% 

105.5 

82.83 

5/16 

.326 
.469 

.256 

.368 

3 

1/16 

30.00 
31.26 

23.56 
24.55 

T 

107.8 
110.2 

84.69 
86.56 

7/16 

.638 

.501 

j/c 

32.55 

25.57 

13/16 

112.6 

88.45 

4 

.833 

.654 

3/16 

33.87 

26.60 

115.1 

90.36 

9/16 

1.055 

.828 

/4 

35.21 

27.65 

15/16 

117.5 

92.29 

5a 

1.302 

1.023 

5/16 

36.58 

28.73 

6 

120.0 

94.25 

11/16 

1.576 

1.237 

37.97 

29.82 

125.1 

98.22 

% 

1.875 

1.473 

7/16 

39.39 

30.94 

/4 

130.2 

102.3 

13/16 

2.201 

1.728 

Y2 

40.83 

32.07 

% 

135.5 

106.4 

7k 

2.552 

2.004 

9/16 

42.30 

33.23 

L£ 

140.8 

110.6 

15/16 

2.930 

2.301 

% 

43.80 

34.40 

% 

146.3 

114.9 

3.333 

2.618 

11/16 

45.33 

35.60 

% 

151.9 

119.3 

1/16 

3.763 

2.955 

46.88 

36.82 

% 

157.6 

123.7 

^ 

4.219 

3.313 

13/16 

48.45 

38.05 

7 

163.3 

128.3 

3/16 

4.701 

3.692 

Vs 

50.05 

39.31 

169.2 

132.9 

M 

5.208 

4.091 

15/16 

51.68 

40.59 

M 

175.2 

137.6 

5/16 

5.742 

4.510 

53.33 

41.89 

a2 

181.3 

142.4 

% 

6.302 

4.950 

1/16 

55.01 

43.21 

i^ 

187.5 

147.3 

7/16 

6.888 

5.410 

^ 

56.72 

44.55 

% 

193.8 

152.2 

^ 

7.500 

5.890 

3/16 

58.45 

45.91 

% 

200.2 

157.2 

9/16 

8.138 

6.392 

^4 

60.21 

47.29 

y& 

206.7 

162.4 

8.802 

6.913 

5/16 

61.99 

48.69 

8 

213.3 

167.6 

11/16 

9.492 

7.455 

63.80 

50.11 

/4 

226.9 

178.2 

k 

10.21 

8.018 

7/16 

65.64 

51.55 

L£ 

240.8 

189.2 

13/16 

10.95 

8.601 

67.50 

53.01 

M 

255.2 

200.4 

% 

11.72 

9.204 

9/16 

69.39 

54.50 

9 

270.0 

212.1 

15/16 

12.51 

9.828 

K£ 

71.30 

56.00 

/4 

285.2 

224.0 

2 

13.33 

10.47 

11/16 

73.24 

57.52 

/^ 

300.8 

236.3 

1/16 

14.18 

11.14 

k 

75.21 

59.07 

*M 

316.9 

248.9 

^k 

15.05 

11.82 

13/16 

77.20 

60.63 

10 

333.3 

261.8 

3/16 

15.95 

12.53 

79.22 

62.22 

ix 

350.2 

275.1 

M 

16.88 

13.25 

15/16 

81.26 

63.82 

^ 

367.5 

288.6 

5/16 

17.83 

14.00 

5 

83.33 

65.45 

3^ 

385.2 

302.5 

18.80 

14.77 

1/16 

85.43 

67.10 

11 

403.3 

316.8 

7/16 

19.80 

15.55 

H 

87.55 

68.76 

/4 

421.9 

331.3 

20.83 

16.36 

3/16 

89.70 

70.45 

% 

440.8 

346.2 

S/16 

21.89 

17.19 

91.88 

72.16 

% 

460.2 

361.4 

22.97 

18.04 

5/16 

94.08 

73.89 

12 

480. 

377. 

172 


MATERIALS. 


N    1 


t>t-QOOso^Mco^oo^^QDoso^^g3co^^g3t-.Qc 
co  L~  GO  oi  o  o  T-i  c*  i  co'  -^  in  ic  ?o  i-I  GO  os  o  o  ~  oi  co  -*  »o  »c  co 

l-H-.l-HT-lT-<r-lr-lT-H^-ll-^7-l1-l(y?0?(??Oj(?jlMC<C^O? 

•t-GOCSOO^OJCO^^iriCO^^QOOiOjHjjglCO^gS 

&e3 
2S 

O»Or-<J.-COOO^O«Cr-ii-COOiTroSr-(L-CO 

^  ^ 

1C  iT5  CO  «O  t-  I-  O  00  GO  Oi  Oi  O  O  TH  T-<  C*  Ci  CO  CO 

OCOCOt^i>t>t^QCGO 


'  ^ 


10? 


WEIGHTS   OF    FLAT   WROUGHT   IROK. 


173 


o 

i 

3 

*-*«          *.**.-*    .ocoo^coo^      oc-  S 

I 

O5  r-iOOiOt-OSr-HOO^^DQOOgl^^gOOO^^^^TJSOO         ^       g          8  °  J>  8 

8 

<M 

-^CO»fii>OOO'?*Tj<iOt>-OST-iOO^'?OQO-r-iiOOD'?^?OOiCOO  O 

.    ^^^i^^^^^^^^^J 

§ 

00 

1 

I     x   •« 

®     *0 

bfi 

*-HTH<KJSiOCO"*Tf<lOCOCOJ>-OOOOG5O5O-'— IOO^»O?OOOO5O  S 

'T!  ^  •  i*r^XS?0(lJ!-4<^S?\>?X(:s:i-*rnr\>  <•,->(— l;X-n-i(^^^-lom^<?=^  Q  ,      ,_ 

^          5"^  B 

S3  e3  »C  1~> 

O       0^0.0000       .000  f        ^ 

i  SE 

^  «M    ^-«t-l«M 

^  ^^w^^^^^^w.^^^^^^^^^^-.^w-^xr^  ^ 

.^) 

^  <5*  $  c*  "'""' 

^  T-t  <M  OO -rP  O  «O  .  i_(^  ^^  ^^^  ^^  ^(^(jJs^J^ 

i 

iT  <^Ti  i^TeSs'Tj^T 

A    g!5  "         W         **  ^         S         S         ^N^XCON^MfiS^!^ 

Hfl^g  ,„,-,„__ o,    j     ^ 


174 


MATERIALS. 


WEIGHT   OF    IRON    AND  STEEI,    SHEETS. 

Weights  per  Square  Foot. 

(For  weights  by  new  U.  S.  Standard  Gauge,  see  page  31.) 


Thickness  by  Birmingham  Gauge. 

Thickness  by  American  (Brown  and 
Sharped)  Gauge. 

No.  of 
Gauge. 

Thick- 
ness  in 
Inches. 

Iron. 

Steel. 

No.  of 
Gauge. 

Thick- 
ness in 
Inches. 

Iron. 

Steel. 

0000 

.454 

18.16 

18.52 

0000 

.46 

18.40 

18.77 

000 

.425 

17.00 

17.34 

000 

.4096 

16.38 

16.71 

00 

.38 

15.20 

15.30 

00 

.3648 

14.59 

14.88 

0 

.34 

13.60 

13.87 

0 

.3249 

13.00 

13.26 

1 

.3 

12.00 

12.24 

1 

.2893 

11.57 

11.80 

2 

.284 

11.36 

11.59 

2 

.2576 

10.30 

10.51 

3 

.259 

10.36 

10.57 

3 

.2294 

9.18 

9.36 

4 

.238 

9.52 

9.71 

4 

.2043 

8.17 

8.34 

5 

.22 

8.80 

8.98 

5 

.1819 

7.28 

7.42 

6 

.203 

8.12 

8.28 

6 

.1620 

6.48 

6.61 

7 

.18 

7.20 

7.34 

7 

.1443 

5.77 

5.89 

8 

.165 

6.60 

6.73 

8 

.1285 

5.14 

5.24 

9 

.148 

5.92 

6.04 

9 

.1144 

4.58 

4.67 

10 

.134 

5.36 

5.47 

10 

.1019 

4.08 

4.16 

11 

.12 

4.80 

4.90 

11 

.0907 

3.63 

3.70 

12 

.109 

4.36 

4.45 

12 

.0808 

3.23 

3.30 

13 

.095 

3.80 

3.88 

13 

.0720 

2.88 

2.94 

14 

.083 

3.32 

3.39 

14 

.0641 

2.56 

2.62 

15 

.072 

2.88 

2.94 

15 

.0571 

2.28 

2.33 

16 

.065 

2.60 

2.65 

16 

.0508 

2.03 

2.07 

17 

.058 

2.32 

2.37 

17 

.0453 

1.81 

1.85 

18 

.049 

.96 

2.00 

18 

.0403 

1.61 

1.64 

19 

.042 

.68 

1.71 

19 

.0359 

1.44 

1.46 

20 

.035 

.40 

1.43 

20 

.0320 

1.28 

1.31 

21 

.032 

.28 

1.31 

21 

.0285 

1.14 

1.16 

22 

.028 

.12 

1.14 

22 

.0253 

1.01 

1.03 

23 

.025 

1.00 

1.02 

23 

.0226 

.904 

.922 

24 

.022 

.88 

.898 

24 

.0201 

.804 

.820 

25 

.02 

.80 

.816 

25 

.0179 

.716 

.730 

26 

.018 

.72 

.734 

26 

.0159 

.636 

.649 

27 

.016 

.64 

.653 

27 

.0142 

.568 

.579 

28 

.014 

.56 

.571 

28 

.0126 

.504 

.514 

29 

.013 

.52 

.530 

29 

.0113 

.452 

.461 

30 

.012 

.48 

.490 

30 

.0100 

.400 

.408 

31 

.01 

.40 

.408 

31 

.0089 

.356 

.363 

32 

.009 

.36 

.367 

32 

.0080 

.320 

.326 

33 

.008 

.32 

.326 

33 

.0071 

.284 

.290 

34 

.007 

.28 

.286 

34 

.0063 

.252 

.257 

35 

.005 

.20 

.204 

35 

.0056 

.224 

.228 

Specific  gravity.. 
Weight  per  cubic 

I 
? 

ron.                 Steel. 
.7                  7.854 
489.6 

foot...               .     480 

"          »      "      inch...                       .2778              .2833 

As  there  are  many  gauges  in  use  differing  from  each  other,  and  even  the 
thicknesses  of  a  certain  specified  gauge,  as  the  Birmingham,  are  not  assumed 
the  same  by  all  manufacturers,  orders  for  sheets  and  wires  should  always 
state  the  weight  per  square  foot,  or  the  thickness  in  thousandths  of  an  inch. 


WEIGHT  OF  PLATE  IRON. 


175 


'c^COiOC^-OSOT—  iCOlOL~OlOT-!COlOC-OSOCOi~ 
OS  QO  t-  «O  »0  JO  Tt  CO  C*  T-(  O  O  Oi  CO  J>  «5  1C  »O  ?O  1-1 


&s 
1s 

*(, 


« 
H-S 

«« 

«8 

fc-S 
jS 

5s 

Hi 

s* 

•i . 
«I 
g* 

*e 


« 

«« 

Hf. 

3* 

Ss 
Sg 


§coco©coco©coco©coeo©coco©coco©coco©coco©coco< 
CCCOi~£.-J>GOGOOOO5OJC5O©T-iO}(?iCO-^'-^'incOCO{-.GOOOOiC 


COJOOO©OOlOt^-©COlOGO©CO  »O~GO  O  CO  tO 
COt>OOO^C^OOiO<»t^COO^C^CO4O^l-OCOlCOC3C>COinc»OCCi 

J^  O  OO  «O  O  CO  CO  O5  <?*  IO  00  TH  i~  OD  T-^  rjJ  t~  O  CO  O  CO  O  GO  1O  i-H  I-  OO  O  «O  <> 

-- 


O  00  t>  »O  CO  OJ  O  CO  t-  O  CO  C?  O 


O  CO  CO  00  rn  T«<  «D  OS  (N  1C  I-  O  CO  O  tX)  i- 

i--- 


CO  OS  Tf  O  1O  O  CO  T-H  i 


CO  OS  Tf  O 

^i-iwco 


©io©io©o©io©io©io©»o©»o©«n©©©©©©©©©©©©©©©© 


o  10  06  o  o*'  ifi  i>  o»  1 

t<T}iTt<iOiOir500 


6  cc  t-  oi  «>  i-  so  o  o  o  -^  o 

--- 


o  o  o  -^  o  co  ad  <w  t 

00i-i^^<NC<OOCO 


I-H  O  QO  i.^  «D 


cCOQ 

1-1  O  O 


?  -f  ?O  CO  O  TH  OO  »n  t^  oi  '-'  CO  O  <O  CO  O  C? 
^CiWOiCOOTOOOOCOCOr^T^TtiT^TriOO 


»OOinO»OOiOOlf3O 

i.-  O  y-l  O  L-  O  OJ  O  L-  »O  CO  O  CO  JO 

OO  t~  »-<  O  CO  (?»  CD  O  CO  l^  TH  10  0 


J>OOOTHCO»0 
i-t  O  O  O>  OO  t- 


CO  «  ,OT  CO  W  O9  T 


oo  GO  os  o  o  T-H'  i-^  o?  co  co  •*  in  >d  eo  eo  «>  ad  ad  o  ->-I  oi  cc  »o  ?o  <>  GO 

i^r^T^«^i^^^i^T-ir-l^-.T-Ki--lr-i(??OJOiO»WCJC^7< 


>  00  00  OS  O5  O  O  O  -r-(  T-*'  (?j  C^  CO  ^  tO  1O  5O  t-'  GO  CS  O  O  r4 


O  O  r4  0»  CO*  -^  O 


176 


MATERIALS. 


WEIGHTS  OF  STEEL.  BLOOMS. 
Soft  steel.    1  cubic  inch  =  0.284  Ib.    1  cubic  foot  =  490.75  Ibs. 


Sizes. 

Lengths. 

1 

1" 

6" 

12" 

18" 

24" 

30" 

36" 

42" 

48" 

54" 

60" 

66" 

12"  x  4" 

13.63 

82 

164 

245 

327 

409 

491 

573 

654 

736 

818 

900 

11   x  6 

18.75 

113 

225 

338 

450 

563 

675 

788 

900 

1013 

1125 

1238 

x  5 

15.62 

94 

188 

281 

375 

469 

562 

656 

750 

843 

937 

1031 

x  4 

12.50 

75 

150 

225 

300 

375 

450 

525 

600 

675 

750 

825 

10   x  7 

19.88 

120 

239 

358 

477 

596 

715 

835 

955 

1074 

1193 

1312 

x  6 

17.04 

102 

204 

307 

409 

511 

613 

716 

818 

920 

1022 

1125 

x  5 

14.20 

85 

170 

256 

341 

426 

511 

596 

682 

767 

852 

937 

x  4 

11.36 

68 

136 

205 

273 

341 

409 

477 

546 

614 

682 

750 

x  3 

8.52 

51 

102 

153 

204 

255 

306 

358 

409 

460 

511 

562 

9  x  7 

17.89 

107 

215 

322 

430 

537 

644 

751 

859 

966 

1073 

1181 

x  6 

15.34 

92 

184 

276 

368 

460 

552 

644 

736 

828 

920 

1012 

x  5 

12.78 

77 

153 

230 

307 

383 

460 

537 

614 

690 

767 

844 

x  4 

10.22 

61 

123 

184 

245 

307 

368 

429 

490 

552 

613 

674 

8x8 

18.18 

109 

218 

327 

436 

545 

655 

764 

873 

982 

1091 

1200 

x  7 

15.9 

95 

191 

286 

382 

477 

572 

668 

763 

859 

954 

1049 

x  6 

13.63 

82 

164 

245 

327 

409 

491 

573 

654 

736 

818 

900 

x  5 

11.36 

68 

136. 

205 

273 

341 

409 

477 

546 

614 

682 

750 

x  4 

9.09 

55 

109 

164 

218 

273 

327 

382 

436 

491 

545 

600 

7x7 

13.92 

83 

167 

251 

334 

418 

501 

585 

668 

752 

835 

919 

x  6 

11.93 

72 

143 

215 

286 

358 

430 

501 

573 

644 

716 

788. 

x  5 

9.94 

60 

119 

179 

238 

298 

358 

417 

477 

536 

596 

656 

x  4 

7.95 

48 

96 

143 

191 

239 

286 

334 

382 

429 

477 

525 

x  3 

5.96 

36 

72 

107 

143 

179 

214 

250 

286 

322 

358 

393 

6^x  &y2 

12. 

72 

144 

216 

388 

360 

432 

504 

576 

648 

720 

7921 

x  4 

7.38 

44 

89 

133 

177 

221 

266 

310 

354 

399 

443 

487 

6x6 

10.22 

61 

123 

184 

245 

307 

368 

429 

490 

551 

613 

674 

x  5 

8.52 

51 

102 

153 

204 

255 

307 

358 

409 

460 

511 

562* 

x  4 

6.82 

41 

82 

123 

164 

204 

245 

286 

327 

368 

409 

450 

x  3 

5.11 

31 

61 

92 

123 

153 

184 

214 

245 

276 

307 

337 

514  x  5% 

8.59 

52 

103 

155 

206 

258 

309 

361 

412 

464 

515 

567 

x  4 

6.25 

37 

75 

112 

150 

188 

225 

262 

300 

337 

375 

412 

5   x  5 

7.10 

43 

85 

128 

170 

213 

256 

298 

341 

383 

426 

469 

x  4 

5.68 

34 

68 

102 

136 

170 

205 

239 

273 

307 

341 

375 

4^x  414 

5.75 

35 

69 

104 

138 

173 

207 

242 

276 

311 

345 

380 

x  4 

5.11 

31 

61 

92 

123  153 

184 

215 

246 

276 

307 

338 

4   x  4 

4.54 

27 

55 

82 

109  136 

164 

191 

218 

246 

272 

300 

x  3^ 

3.97 

24 

48 

72 

96  i  119 

143 

167 

181 

215 

238 

262 

x  3 

3.40 

20 

41 

61 

82  102 

122 

143 

163 

184 

204 

224 

3^  x  3V6 

3.48 

21 

42 

63 

84 

104 

125 

146 

167 

188 

209 

230 

x  3 

2.98 

18 

36 

54 

72 

89 

107 

125 

14:', 

161 

179 

197 

3   x  3 

2.56 

15 

31 

46 

61 

77 

92 

108 

1*3 

138 

154 

169 

SIZES  AHD   WEIGHTS  OF   STRUCTURAL   SHAPES. 


SIX  US  AND  WEIGHTS  OF  STRUCTURAL  SHAPES. 

Minimum  and  Maximum  Weights  and  Dimensions  of 
Carnegie  I-JBeams. 

STEEL  BEAMS. 


Section 

o.s» 
|s| 

Weight  per 
Foot,  in  Ibs. 

Flange  Width. 

Web  Thickness. 

Increase  of 
Web  and 
Flanges  for 

Index. 

pcq"* 

Min. 

Max. 

Min. 

Max. 

Min. 

Max. 

each  Ib.  in- 
crease of 
weight. 

B  1 

24 

80.00 

100.00 

6.95 

7.20 

.50 

.75 

.0123 

B  2 

20 

80.00 

100.00 

7  00 

7.30 

.60 

.90 

.015 

B  3 

20 

64.00 

75.00 

6.25 

6.41 

.50 

.66 

.015 

B  4     !     15 

80.00 

100  00 

6.41 

6.79 

.77 

1.16 

.020 

B  5     I     15 

60.00 

75.00 

6.04 

6.34 

.54 

.84 

.020 

B  6     i     15 

50.00       59.00 

5.75 

5.93 

.45 

.63 

.020 

*B  7 

15 

41.00 

49.00 

5.50 

5.66 

.40 

.56 

.020 

B  8 

12 

40.00  !     56.70 

5.50 

5.91 

.39 

.80 

.025 

*B  9 

12 

32.00 

39.00 

5.25 

5.42 

.35 

.52 

.025 

BIO 

10 

33.00 

40.00 

5.00 

5.21 

.37 

.58 

.029 

Bll 

10 

25.50 

32.00 

4.75 

4.94 

.32 

.51 

.029 

B12 

9 

27.00 

33.00 

4.75 

4.95 

.31 

.51 

.033 

B13 

9 

21.00 

26.00 

4.50 

4.66 

.27 

.43 

.033 

B14 

8 

22.00 

27.00 

4.50 

4.68 

.27 

.45 

.037 

B15 

8 

18.00 

21.70 

4.25 

4.39 

.25 

.39 

.037 

B16 

7 

20.00 

22.00 

4.25 

4.33 

.27 

.35 

.042 

B17 

7 

15.50 

19.00 

4.00 

4.15 

.23 

.38 

.042 

B18 

6 

16.00 

20.00 

3.63 

3.83 

.26 

.46 

.049 

B19 

6 

13.00 

15.00 

3.50 

3.60 

.23 

.34 

.049 

B20 

5 

13.00 

16.00 

3.13 

3.31 

.26 

.44 

.059 

B21 

5 

10.00 

12.00 

3.00 

3.12 

.22 

.33 

.059 

B22 

4 

10.00 

13.00 

2.75 

2.97 

.24 

.46 

.074 

B23 

4 

7.50 

9.00 

2.63 

2.74 

.20 

.31 

.074 

B24 

4 

6.00 

8.00 

2.18 

2.33 

.18 

.33 

.074 

Given  weight  in  pounds  per  foot,  to  find  sectional  area-* 


Iron.        Steel. 
3.4 

.2941 

Given  sectional  area,  to  find  weight  in  Ibs.  per  foot        x    3^         3.4 
"        '*  Ibs.  per  yard      x  10  10.2 


Maximum  and  Minimum  Weights  and  Dimensions  of 
Carnegie  Deck:  Beams. 

STEEL. 


Section 

Depth 
of 

Weight  per 
Foot,  Ibs. 

Flange  Width. 

Web 
Thickness. 

Increase  of 
Web  and 
Flanges  per 

inches. 

Min. 

Max. 

Min. 

Max. 

Min. 

Max. 

crease  of 
weight. 

B100 

10 

27.23 

35.70 

5.25 

5.50 

.38 

.63 

.029 

B101 

9 

26.52 

30.60 

4.94 

5.07 

.44 

.57 

.032 

B102 

8 

20.15 

24.48 

5.00 

5.16 

.31 

.47 

.037 

BIOS 

7 

18.10 

23.46 

4.87 

5.10 

.31 

.54 

.042 

BIOS 

6 

15.30 

18.36 

4.38 

4.53 

.28 

.43 

.049 

178 


MATERIALS. 


weights  and  Dimensions  of  Carnegie  Steel  Channels* 


Sec- 
tion 
Index 

Depth 

of 

inches. 

Weight  per 
Foot,  inlbs. 

Flange  Width, 

Web 

Thickness, 

Increase 
Of  Web 
and 
Flanges 
for  each 
Ib.  in- 
crease of 
weight. 

Min. 

Max. 

Min. 

Max. 

Min. 

Max. 

Cl 
C2 
03 
04 
05 
06 
07 
08 
09 

15 
12 
10 
9 
8 
7 
6 
5 
4 

32.00 
20.00 
15.25 
12.75 
10.00 
8.50 
7.00 
6.00 
5.00 

51  00 
30.25 
23.75 
20.50 
17.25 
14.50 
12.00 
10.25 
8.25 

3.40 

2.90 
2.66 
2.44 
2.20 
2.00 
1.89 
1.78 
1.67 

3.78 
3.15 
2.91 
2.69 
2.47 
2.25 
2.14 
2.03 
1.91 

.40 
.30 
.26 
.24 
.20 
.20 
.19 
.18 
.17 

.78 
.55 
.51 
.49 
.47 
.45 
.44 
.43 
.41 

.020 
.025 
.029 
.033 
.037 
.042 
.049 
.059 
.074 

Weights  and  Dimensions  of  Carnegie  Z-Bars. 


Section 
Index. 

Thickness 
of  Metal. 

Size. 

Weight. 

Flange. 

Web. 

Flange. 

Iron. 

Stee). 

Z  1 

% 

3    14 

6 

3  y& 

15.3 

15.0 

7-16 

3  9-16 

6  1-16 

3  9-16 

18.0 

18.  a 

44 

Y> 

3    % 

6    i^c 

3    % 

20.6 

21.0 

Z  2 

9-16 

3    Y& 

6 

3    H 

22.3 

22.  V 

4* 

% 

3  9-16 

6  1-16 

3  9-16 

24.9 

25.4 

44 

11-16 

3    % 

6    H 

3    % 

27.5 

28.0 

Z  3 

H 

3    ^ 

6 

3    /^ 

28.8 

29.fi 

44 

13-16 

3  9-16 

6  1-16 

3  9-16 

31.3 

32.0 

44 

VB 

3    % 

6    YB 

3    % 

33.9 

34.6 

Z  i  4 

5-16 

3    % 

5 

3    Y± 

11.3 

11.  V 

3  5-16 

5  1-16 

3  5-16 

13.7 

13.9 

44 

7-16 

3    % 

5    X 

8    % 

16.0 

16.4 

Z  5 

Y> 

3    M 

5 

3    J4 

17.5 

17.8 

44 

9-16 

3  5-16 

5  1-16 

3  5-16 

19.8 

20.2 

14 

% 

3    % 

5    % 

3    % 

22.1 

22.6 

Z  6 

11-16 

3    H 

5 

3    J4 

23.2 

23.7 

44 

% 

3  5-16 

5  1-16 

3  5-16 

25.5 

26.0 

14 

13-16 

3    % 

5    & 

33/ 
78 

27.8 

28.3 

Z  7 

Y± 

3  1-16 

4 

3  1-16 

8.0 

8.2 

5-16 

3    K 

4  1-16 

3    K 

10.1 

10.3 

44 

% 

3  3-16 

4    & 

3  3-16 

12.2 

12.4 

Z  8 

T-16 

3  1-16 

4 

3  1-16 

13.5 

13.8 

44 

v*> 

3    ^ 

4  1-16 

3    T£ 

15.5 

15.8 

«* 

9-16 

3  3-16 

4    ^ 

3  3-16 

17.6 

17.9 

Zt9 

% 

3  1-16 

4 

3  1-16 

18.5 

18.9 

« 

11-16 
% 

3  3-16 

4  1-16 
4    fc 

3    YB 
3  3-16 

20.5 
22.5 

20.9 
22.9 

Z10 

y. 

2  11-16 

3 

2  11-16 

6.6 

6.7 

5-16 

2    % 

3  1-16 

2    M 

8.3 

8.4 

Zll 

% 

2  11-16 

3 

2  11-16 

9.5 

9.7 

44 

7-16 

2    % 

3  1-16 

2    M 

11.2 

11.4 

Z12 

9^6 

2  11-16 
2    % 

3 
3  1-16 

2  11-16 
2    9£ 

12.3 
13.9 

12.5 
14.2 

SIZES   AND   WEIGHTS  OB1   STKUCTUIlAL   SHAPES.     179 


Pencoyd   Steel  Angles, 

EVEN  LEGS. 


1. 

Size 

Approximate  Weight  in  Pounds  per  Foot  for  Various 
Thicknesses  in  Inches. 

? 

in 
Inches. 

3. 

3-16 
.1875 

*4 

.25 

5-16 
.3125 

.375 

7-16 
.4375 

% 

9-16 
.5625 

.625 

1M6 
.6875 

* 

.875 

1 
1.00 

120 

6     x6 

14.8 

17.3 

19.9 

22.3 

24.9 

26.5 

29.1 

34.2 

39.3 

121 

5     x5 

12.2 

14.3 

16.4 

18.5 

20.7 

22.8 

25.0 

29.2 

33.4 

192 

4     x4 

8.2 

9.8 

11.3 

13.0 

14.6 

16.1 

17.7 

19.3 

123 

7.1 

8.6 

10.0 

11.4 

12.8 

14.2 

124 

3     x3 

4.9 

6.0 

7.1 

8.3 

9.4 

10.5 

11.6 

125 

2^x2% 

4.5 

5.6 

6.7 

7.8 

8.9 

126 

2*4x2*£ 

3.1 

4.1 

5.1 

6.1 

Y.I 

127 

2*4x2*4 

2.7 

3.6 

4.5 

5.4 

128 

2     x2 

2.44 

3.3 

4.1 

4.9 

129 

l%xl% 

2.14 

2.9 

3.6 

4.4 

130 

JLZ  x  |1Z 

1.16 

1.80 

2.4 

3.0 

3.6 

131 

1*4x1*4 

1.02 

1.53 

2.04 

132 

1     xl 

0.82 

1.16 

1.53 

UNEVEN  LEGS. 


"1 

Size 
inl 
'Inches. 

Approximate  Weight  in  Pounds  per  Foot  for  Various 
Thicknesses  in  Inches. 

^ 

3-16 

M 

5-16 

*A 

7-16 

V>. 

9-16 

% 

11-16 

^ 

% 

1 

% 

.125 

.1875 

.25 

.3125 

.375 

.4375 

.50 

.5625 

.625 

.6875 

.75 

.875 

1.00 

154 
152 

7     x3*£ 
6Ux4 

12.9 

15.0 

17.0 
17.1 

18.9 
19.3 

20.9 
SI.  4 

22.8 
23.6 

24.8 
25.7 

28.6 
30.0 

32.5 
34.3 

140  6     x  4 

12.2 

14.4 

16.4 

18.6 

20.7 

22.8 

24.9 

29.1 

33.3 

151 

6     x3U 

11.5 

13.6 

15.6 

17.6 

19.7 

21.7 

23.8 

27.8 

31.9 

153 

5Ux3U 

11.0 

12.8 

14.6 

16.4 

18.2 

14115     x4 

11.0 

12.8 

14.6 

16.4 

18.2 

20.0 

21.8 

142  5     x  3*£ 

8.7 

10.3 

12.0 

13.6 

15.2 

16.8 

18.5 

20.1 

1435     x3 

8.2 

9.7 

11.2 

12.8 

14.3 

15.8 

17.3 

18.9 

144  4U  x  3 

7.7 

9.2 

10.6 

12.1 

13.6 

15.0 

16.5 

18.0 

145 

7  7 

9.2 

10.6 

12.1 

13.6 

15.0 

16.5 

18.0 

146 

4x3" 

7.1 

8.6 

10.0 

11.4 

12.8 

14.2 

147 

3^x3 

6.6 

7.9 

9.2 

10.5 

11.8 

13.1 

150 

3*J  x  2*£ 

4.9 

6.0 

7.1 

8.3 

9.4 

159 

3*Hjx  ^ 

4.5 

5.6 

6.7 

148 

3     x  2V£ 

4.5 

5.6 

6.7 

7.8 

8.9 

149 

3     x2 

4.1 

5.1 

6.1 

7.1 

8.2 

155 

2*4  x  2 

2.7 

3.6 

4.5 

5.4 

6.3 

7.2 

156 

2*4xl*£ 

2.24 

3.03 

3.8 

4.6 

157 

o      x  \\A 

1.94 

2.7 

3.3 

4.0 

180 


MATERIALS. 


Pencoyd  Tees. 


EVEN  TEES. 


UNEVEN  TEES. 


Chart 
Number. 

Size 
in 
Inches. 

Weight  per 
Foot. 

Chart 
Number. 

Size 
in 
Inches. 

Weight  per 
Foot. 

Iron. 

Steel. 

Iron. 

Steel. 

70 

4     x4 

12.40 

12.65 

107 

5     x4 

14.70 

15.00 

71 

31^x3^ 

10.17 

10.37 

106 

5     x3!4 

16.13 

16.46 

72 

3     x3 

8.33 

8.50 

93 

5     x  2  9-16 

11.03 

11  25 

82 

3     x3 

6.43 

6.56 

92 

5     x  2^ 

10.23 

10.44 

83 

3     x3 

7.53 

7.68 

90 

4*6  x  3**J 

14.83 

15.13 

84 

4.83 

4.93 

109 

4     x  4^6 

13.23 

13.50 

73 

2Vj»  x  2Vij> 

6.50 

6.63 

91 

4     x  3^2 

18.93 

14.21 

74 

2*6  x  2*4 

5.73 

5.85 

94 

4     x3 

8.63 

8  81 

75 

2J4x2^ 

3.90 

3.98 

95 

4     x3 

8.37 

8.53 

76 

2J4  x  2*4 

3.93 

4.01 

96 

4     x2 

6.43 

6.56 

77 

2     x2 

3.47 

3.54 

97 

3     x3^ 

9.37 

9.55 

78 

iM  x  1M 

2.37 

2.41 

98 

3     x2^ 

7.93 

8.09 

79 

l*i2x  1*6 

2.00 

2.04 

110 

3     x  2V6 

5.87 

5.98 

80 

1J4  x  1*4. 

1.50 

1.53 

111 

3     x  2^6 

6.87 

7.00 

81 

1      xl 

1.03 

1.05 

117 

3     x  2^ 

5.00 

5.10 

85 

4     x4 

10.98 

11.19 

99 

3     xl^6 

3.73 

3.81 

105 

2^x2 

7.13 

7.28 

104 

2%  x  1% 

6.53 

6.66 

100 
108 

2*1  x  0  9-16 

3.03 
2.20 

3.09 
2.24 

101 

2     xlj^ 

2.90 

2.96 

112 

2     xl  1-16 

2.07 

2  11 

102 

2     xl 

2.33 

2.38 

103 

2     x   9-16 

2.03 

2.07 

116 

^M  x  1*4 

3.47 

3.54 

113 

1%  x  1  l-K 

1.87 

1.90 

114 

1*6  x    15-16 

1.37 

1.39 

115 

1*4  x    15-16 

1.13 

1.16 

118 

3     x  2^ 

5.92 

6.03 

119 

2%  x  2^6 

5.63 

5.74 

Peiiooyd  Car-Builders'  Channels,  Iron. 


®  5R 

*=  fl 

|«fl 

1 

m 

1 

II 

ri 

|J 

.Sf'^ 

Approximate  Weight  in  Pounds  per 
Foot  for  Each  Thickness  of 
Web,  in  Inches. 

||s 

fc 

c 

c 

Is 

S  fl  cc 

5     c 

ifii 

o 

C3  ^  S 

o 

<D 
02 

"a 
fi 

S 

eg! 

S 

5-16 

H 

7-16 

y* 

9-16 

% 

pil 

55 

13 

8% 

8^ 

29.5 

29.5 

32.2 

34.9 

37.6 

40.3 

.023 

54 

12 

3 

9-3-2 

22.4 

23.6 

26.1 

28.6 

31.1 

33.6 

.025 

33  j^ 

lOVja 

(  3% 

7-16 

23.6 

23.6 

25.8 

.029 

33 

10*6 

(2*6 

5-16 

17.6 

17.6 

19.8 

.029 

Pencoyd  Car-Builders'  Channels,   Steel. 


55 

54 


33 


9-32 
7-16 
5-16 


30.1 

30.1 

32.9 

35.6 

38.4 

41.1 

22.8 

24.1 

26.6 

29.2 

31.7 

34.3 

24.1 

24.1 

26.3 

17.9 

17.9 

20.2 

SIZES  AND  WEIGHTS'  OF  ROOFING  MATERIALS.    181 


SIZES  AND  WEIGHTS  OF  ROOFING  MATERIALS. 

Corrugated  Iron  (Phoenix  Iron  Co.). 


BLACK  IRON. 

GALVANIZED  IRON. 

Thick- 
ness in 
Inches. 

Weight 
in  Lbs. 
per 
Sq.  Ft., 
Flat. 

Weight 
in  Lbs. 

Sq.  Ft.  on 
Roof. 
Flat. 

Weight 
in  Lbs. 
per 
Sq.  Ft.,  on 
Roof. 
Corrugated 

Weight 
in  Lbs. 
per 
Sq.  Ft., 
Flat. 

Weight 
in  Lbs. 
per 
Sq.  Ft. 
on  Roof. 
Flat. 

Weight 
in  Lbs. 
per 
Sq.  Ft.,  on 
Roof. 
Corrugated 

0.065 

2  ..61 

3.03 

3.37 

3.00 

3.50 

3.88 

0.049 

1.97 

2.29 

2.54 

2.37 

2.76 

3  07 

0.035 

1.40 

1.63 

1.82 

1.75 

2.03 

2.26 

0.028 

1.12 

1.31 

1.45 

1.31 

1.53 

1.71 

0.022 

0.88 

1.03 

1.14 

1.06 

1.24 

1.37 

0.018 

0.72 

0.84 

0.93 

0.94 

1.09 

1.21 

The  above  table  is  calculated  for  the  ordinary  size  of  sheet,  which  is  from 
2  to  2*4  feet  wide,  and  from  6  to  8  feet  long,  allowing  4  inches  lap  in  length 
and  2^  inches  in  width  of  sheet. 

The  galvanizing  of  sheet  iron  adds  about  one- third  of  a  pound  to  its  weight 
per  square  foot. 

In  corrugated  iron  made  by  the  Keystone  Bridge  Co.,  the  corrugations  are 


^ne  corruga 

length,  for  the  usual  pitch  of  roof  of  two  to  one.  Sheets  can  be  corrugated 
of  any  length  not  exceeding  ten  feet.  The  most  advantageous  width  is 
80^",  which  (allowing  ^"  for  irregularities)  will  make  eleven  corrugations 
— -  30",  or,  making  allowance  for  laps,  will  cover  24*4"  of  the  surface  of  the 
roof. 

By  actual  trial  it  was  found  that  corrugated  iron  No.  20,  spanning  6  feet, 
will  begin  to  give  a  permanent  deflection  for  a  load  of  30  Ibs.  per  square  foot, 
and  that  it  will  collapse  with  a  load  of  60  Ibs.  per  square  foot.  The  distance 
between  centres  of  purlins  should  therefore  not  exceed  6  feet,  and,  prefer- 
ably, be  less  than  this. 

Terra-Cotta. 

Porous  terra-cotta  roofing  3"  thick  weighs  16  Ibs.  per  square  foot  and  2" 
thick,  12  Ibs.  per  square  foot. 
Ceiling  made  of  the  same  material  2"  thick  weighs  11  Ibs.  per  square  foot. 

Tiles. 

Flat  tiles  6*4"  X  10^"  X  %"  weigh  from  1480  to  1850  Ibs.  per  square  of 
roof,  the  lap  being  one-half  the  length  of  the  tile. 

Tiles  with  grooves  and  fillets  weigh  from  740  to  925  Ibs.  per  square  of  roof. 
Pan-tiles  14^"  X  10^"  laid  10"  to  the  weather,  weigh  850  Ibs.  per  square. 

Tin. 

The  usual  sizes  for  roofing  tin  are  14"  X  20"  and  20"  X  28".  Without 
allowance  for  lap  or  waste,  tin  roofing  weighs  from  50  to  62  Ibs.  per  square. 

Tin  on  the  roof  weighs  from  62  to  75  Ibs.  per  square. 

Roofing  plates  or  terne  plates  (steel  plates  coated  with  an  alloy  of  tin 
and  lead)  are  made  only  in  1C  and  IX  thicknesses  (27  and  29  Birmingham 
gauge).  "Coke"  and  "charcoal'1  tin  plates,  old  names  used  when  iron 
made  with  coke  and  charcoal  was  used  for  the  tinned  plate,  are  still  used  in 
the  trade,  although  steel  plates  have  been  substituted  for  iron ;  a  coke  plate 
now  commonly  meaning  one  made  of  Bessemer  steel,  and  a  charcoal  plate 
one  of  open-hearth  steel.  The  thickness  of  the  tin  coating  on  the  plates 
varies  with  different  "  brands.11 

For  valuable  information  on  Tin  Roofing,  see  circulars  of  Merchant  &  Co., 
Philadelphia. 


182 


MATERIALS. 


TIN   PIRATES.     (TINNED  SHEET  STEEL,.) 

Standard  Stock  Sizes,  with  Number  of  Sheets  and  Net 
Weight  per  Box. 


B.  W. 

Gauge. 

Thickness. 

Size. 

Sheets. 

Net 
Weight 
Ibs. 

B.  W. 

Gauge. 

Thickness. 

Size. 

Sheets. 

Net 
Weight 

29 

1C 

10x14 

225 

108 

29 

1C 

10x^0 

225 

160 

27 

IX 

10x14 

225 

135 

27 

IX 

10x20 

225 

195 

26 

IXX 

10x14 

225 

160 

26 

IXX 

10x20 

225 

222 

29 

1C 

12x12 

225 

110 

29 

1C 

11x22 

225 

190 

27 

IX 

12x12 

225 

138 

27 

IX 

11  x22 

225 

235 

26 

IXX 

12x12 

225 

165 

26 

IXX 

11x22 

225 

275 

29 

1C 

14x20 

112 

108 

29 

1C 

12  x  24 

112 

110 

27 

IX 

14x20 

112 

135 

27 

IX 

12x24 

112 

138 

26 

IXX 

14x20 

112 

160 

26 

IXX 

12x24 

112 

165 

25 

IXXX 

14x20 

112 

180 

29 

1C 

13x26 

112 

132 

•24^ 

IXXXX 

14x20 

112 

200 

27 

IX 

13x26 

112 

162 

29 

1C 

20x28 

112 

216 

26 

IXX 

13x26 

112 

192 

27 

IX 

20x28 

112 

270 

29 

1C 

14x22 

112 

120 

26 

IXX 

20x28 

112 

320 

27 

IX 

14x22 

112 

148 

25 

IXXX 

20x28 

56 

180 

26 

IXX 

14x22 

112 

174 

24^ 

IXXXX 

20x28 

56 

200 

29 

1C 

14x24 

112 

130 

29 

1C 

13x13 

225 

132 

27 

IX 

14x24 

112 

161 

27 

IX 

13x13 

225 

162 

26 

IXX 

14x24 

112 

190 

26 

IXX 

13x13 

225 

192 

29 

1C 

14x28 

112 

155 

29 

1C 

14x14 

225 

155 

27 

IX 

14x28 

112 

193 

27 

IX 

14x14 

225 

193 

26 

IXX 

14  x  28 

112 

230 

26 

IXX 

14x14 

225 

230 

29 

1C 

14x31 

112 

178 

29 

1C 

15x15 

225 

178 

27 

IX 

14x31 

112 

210 

27 

IX 

15x15 

225 

218 

26 

IXX 

14x31 

112 

240 

26 

IXX 

15x15 

225 

260 

27 

IX 

14x56 

56 

185 

29 

1C 

16x16 

225 

200 

26 

IXX 

14  x  56 

56 

220 

27 

IX 

16x  16 

225 

248 

27 

IX 

14x60 

56 

200 

26 

IXX 

16x16 

225 

290 

26 

IXX 

14x60 

56 

240 

29 

1C 

17x17 

225 

230 

29 

1C 

15x21 

112 

120 

27 

IX 

17x17 

225 

289 

27 

IX 

15  x  21 

112 

152 

26 

IXX 

17x17 

225 

340 

26 

IXX 

15x21 

112 

176 

29 

1C 

18x18 

112 

138 

29 

1C 

1(5x19 

m 

120 

27 

IX 

18x18 

112 

158 

27 

IX 

16x19 

112 

147 

26 

IXX 

18x18 

112 

178 

26 

IXX 

16x19 

112 

170 

29 

1C 

20x20 

112 

160 

29 

1C 

16x20 

112 

127 

27 

IX 

20x20 

112 

195 

27 

IX 

16x20 

112 

154 

26 

IXX 

20x20 

112 

222 

26 

IXX 

16x20 

112 

180 

29 

1C 

22x22 

112 

190 

29 

1C 

16x22 

112 

138 

27 

IX 

22x22 

112 

235 

27 

IX 

16x22 

112 

170 

26 

IXX 

22x22 

112 

275 

26 

IXX 

16  x  22 

112 

200 

29 

1C 

24x24 

112 

220 

27 

IX 

24x24 

112 

276 

26 

IXX 

24x24 

112 

330 

B.  w. 

Gauge. 

Thickness. 

Size. 

Sheets. 

Net 
Weight 
Ibs. 

B.  W. 

Gauge. 

Thickness. 

Size. 

Sheets. 

Net 
Weight 
Ibs. 

28 

DC 

12^x17 

100 

94 

23 

DXXX 

15x21 

100 

244 

25 

DX 

12^x17 

100 

122 

22 

DXXXX 

5x21 

100 

275 

24 

DXX 

12^  x  17 

100 

143 

28 

DC 

7x25 

50 

94 

23 

DXXX 

12^x17 

100 

164 

25 

DX 

7x25 

50 

122 

22 

DXXXX 

12^x17 

100 

185 

24 

DXX 

7x25 

50 

143 

28 

DC 

15x21 

100 

130 

23 

DXXX 

7x25 

50 

164 

25 

DX 

15x21 

100 

180 

22 

DXXXX 

17x25 

50 

185 

24 

DXX 

15x21 

100 

213 

TW™  Pi«tA«  110  (  10  x  20, 1C,    80  Ibs.,  IX  100  Ibs.  per  box. 
Plates  112  J14x2o,  1C,  112  Ibs.,  IX  140    "      "      " 
m  a  DOX  |  2()  x  ^  IC?  2o4  ibSi  jx  280    "      "      " 
Tagger's  Tin  and  Iron,  36  and  38  B.  W.  G.,  10  x  14  and  14  x  20,    112  Ibs.  per  box. 


SIZES   AND    WEIGHTS    OF 

Slate, 

Number  and  superficial  area  of  slate  required  for  one  square  of  roof. 
(1  square  =  100  square  feet.) 


Dimensions 
in 
Inches. 

Number 
per 
Square. 

Superficial 
Area  in 
Sq.  Ft. 

Dimensions 
in 
Inches. 

Number 
per 
Square. 

Superficial 
Area  in 
gq.  Ft. 

6x12 
7x  12 

533 
457 

267 

12x18 
10x20 

160 
169 

240 
235 

8x12 

400 

11x20 

!54 

9x12 

355 

12x20 

141 

7x14 
8x  14 

374 
327 

254 

14x20 
16x20 

121 
137 

9x  14 

291 

12x22 

126 

231 

10x14 

261 

14x22 

108 

8x16 
9x16 

277 
246 

246 

12x24 
14x24 

•       114 

98 

228 

10x16 

221 

16  x  24 

86 

9x18 
10x18 

213 
192 

240 

14  x  26 
16x26 

89 

78 

225 

As  slate  is  usually  laid,  the  number  of  square  feet  of  roof  covered  by  one 
slate  can  be  obtained  from  the  following  formula  : 

width  x  (length  —  3  inches) 

— ^~o —  —  —  the  number  of  square  feet  of  roof  covered. 

Weight  of  slate  of  various  lengths  and  thicknesses  required  for  one  square 
of  roof : 


Length 

Weight 

in  Poun 

ds  per  S 

luare  f  o 

p  the  Thi 

ckness. 

Inches. 

W 

3-16" 

H" 

%" 

y^r 

%" 

H" 

12 

483 

724 

967 

1450 

1936 

2419 

2902 

3872 

14 

460 

688 

920 

1379 

1842 

2301 

2760 

3683 

16 

445 

667 

890 

1336 

1784 

2229 

2670 

3567 

18 

434 

650 

869 

1303 

1740 

2174 

2607 

3480 

20 

425 

637 

851 

1276 

1704 

2129 

2553 

3408 

22 

418 

626 

836 

1254 

1675 

2093 

2508 

3350 

24 

412 

617 

825 

1238 

1653 

2066 

2478 

3306 

26 

407 

610 

815 

1222 

1631 

2039 

2445 

3263 

The  weights  given  above  are  based  on  the  number  of  slate  required  for  one 
square  of  roof,  taking  the  weight  of  a  cubic  foot  of  slate  at  175  pounds. 

Pine  Shingles. 

Number  and  weight  of  pine  shingles  required  to  cover  one  square  of 
roof  : 


Number  of 

Number  of 

Weight  in 

Inches 
Exposed  to 
Weather. 

Shingles 
per  Square 
of  Roof. 

Pounds  of 
Shingle  on 
One-square 

Remarks. 

of  Roofs. 

4 

900 
800 

216 
192 

The  number  of  shingles  per  square  is 
for   common    gable-roofs.      For    hip. 

5 

720 

173 

roofs  add  five  per  cent,  to  these  figures. 

5J^j 

655 

157 

The  weights  per  square  are  based  on 

6 

600 

144 

the  number  per  square. 

184 


MATERIALS. 


Skylight  Glass. 

The  weights  of  various  sizes  and  thicknesses  of  fluted  or  rough  plate-glass 
required  for  one  square  of  roof. 


Dimensions  in 
Inches. 


Thickness  in 
Inches. 


Area 
in  Square  Feet. 


Weight  in  Lbs.  ]>er 
Square  of  Roof. 


12x48 
15x60 
20x100 
94  x  156 


3-16 


3.997 

6.246 

13.880 

101.768 


250 

350 
500 
700 


In  the  above  table  no  allowance  is  made  for  lap. 

If  ordinary  window-glass  is  used,  single  thick  glass  (about  1-16")  will  weigh 
about  82  Ibs.  per  square,'  and  double  thick  glass  (about  ^")  will  weigh  about 
164  Ibs.  per  square,  no  allowance  being  made  for  lap.  A  box  of  ordinary 
window-glass  contains  as  nearly  50  square  feet  as  the  size  of  the  panes  will 
admit  of.  Panes  of  any  size  are  made  to  order  by  the  manufacturers,  but  a 
.great  variety  of  sizes  are  usually  kept  in  stock,  ranging  from  6x8  inches  to 
36  x  60  inches. 

APPROXIMATE:  WEIGHTS  OF  VARIOUS  ROOF- 
COVERINGS. 

For  preliminary  estimates  the  weights  of  various  roof  coverings  may  be 
taken  as  tabulated  below: 

•Vamp  Weight  in  Lbs.  per 

Square  of  Roolf. 

Cast-iron  plates  (%"  thick)  1500 

Copper 80-125 

Felt  and  asphalt , 100 

Felt  and  gravel  800-1000 

Iron,  corrugated  100-  375 

Iron,  galvanized,  flat 100-350 

Lath  and  plaster ,    900-1000 

Sheathing,  pine,  1"  thick  yellow,  northern . .  300 

'•       southern..  400 

Spruce,  1"  thick  200 

Sheaihing,  chestnut  or  maple,  1 "  thick 400 

"          ash,  hickory,  or  oak,  V  thick....  500 

Sheet  iron  (1-16"  thick) 300 

"       "          "     andlaths 500 

Shingles,  pine 200 

Slates  ( J4"  thick) 900 

Skylights  (glass  3-16"  to  ^"  thick) , 250-  700 

Sheet  lead 500-  800 

Thatch 650 

Tin 70-  125 

Tiles,  flat 1500-2000 

(grooves  and  fillets) 700-1000 

pan 1000 

with  mortar 2000-3000 

Zinc 100-200 


WEIGHT  OF   CAST-IRON   PIPES   OR 

WEIGHT  OF  CAST-IRON  PIPES  OR  COLUMNS. 

In  libs,  per  Lineal  Foot. 

Cast  iron  =  450  Ibs.  per  cubic  foot. 


Bore. 

Thick, 
of 
Metal. 

Weight 
per  Foot. 

Bore. 

Thick, 
of 
Metal. 

Weight 
per  Foot. 

Bore. 

Thick, 
of 
Metal. 

Weight 
per  Foot. 

Ins. 

lus. 

Lbs. 

Ins. 

Ins. 

Lbs. 

Ins. 

Ins. 

Lbs. 

3 

12.4 

10 

ax 

79.2 

22 

M 

167.5 

*6 

17.2 

10*6 

*6 

54.0 

% 

196.5 

% 

22.2 

% 

682 

23 

*M 

174.9 

3*6 

% 

14.3 

M 

82.8 

% 

205.1 

**> 

19.6 

11 

*6 

56.5 

1 

235.6 

% 

25.3- 

% 

71.3 

24 

% 

182.2 

4 

% 

16.1 

% 

86.5 

% 

213.7 

*6 

22.1 

H^ 

*6 

58.9 

1 

245.4 

% 

28.4 

% 

74.4 

25 

% 

189.6 

4*6 

% 

17.9 

K£ 

90.2 

% 

222.3 

i£ 

24.5 

12 

*6 

61.3 

1 

255.3 

n 

31.5 

% 

77.5 

26 

M 

197.0 

5 

19.8 

94 

93.9 

% 

230.9 

*** 

27.0 

12*6 

*6 

63.8 

i 

265.1 

% 

34.4 

% 

80.5 

27 

M 

204.3 

5*£ 

M 

21.6 

% 

97.6 

% 

239.4 

II 

29.4 

13 

i/o 

66.3 

i 

274.9 

% 

37.6 

% 

83.6 

28 

% 

211.7 

6 

% 

23.5 

% 

101.2 

% 

248.1 

31.8 

14 

*6 

71.2 

i 

284.7 

% 

40.7 

% 

89.7 

29 

M 

219.1 

6*£ 

¥» 

25.3 

% 

108.6 

% 

256.6 

y* 

34.4 

15 

% 

95.9 

i 

294.5 

g 

43.7 

^ 

116.0 

30 

% 

265.2 

7 

27.1 

136.4 

i 

304.3 

iz 

36.8 

16 

% 

102.0 

1*6 

343.7 

% 

46.8 

% 

123.3 

31 

% 

273.8 

?*6 

% 

29.0 

% 

145.0 

i 

314.2 

**> 

39.3 

17 

9s 

108.2 

1*6 

354.8 

s2 

49.9 

3^ 

130.7 

32 

% 

282.4 

8 

M 

30.8 

% 

153.6 

i 

324.0 

*6 

41.7 

18 

% 

114.3 

1|£ 

365.8 

R£ 

52.9 

% 

138.1 

33 

% 

291.0 

8*6 

V*> 

44.2 

% 

162.1 

i 

333.8 

RX 

56.0    • 

19 

% 

120.4 

1*6 

376.9 

M 

68.1 

% 

145.4 

34 

% 

299.6 

9 

46.6 

% 

170.7 

i 

343.7 

5? 

59.1 

20 

% 

126.6 

1*6 

388.0 

% 

71.8 

!% 

152.8 

35 

% 

308.1 

9*6 

i/ 

49.1 

% 

179.3 

l 

353.4 

% 

62.1 

21 

% 

132.7 

1*6 

399.0 

3/ 

75.5 

JJX 

160.1 

36 

% 

316.6 

10 

I/ 

51.5 

% 

187.9 

i 

363.1 

% 

65.2 

22 

% 

138.8 

1*6 

410.0 

The  weight  of  the  two  flanges  may  be  reckoned  =  weight  of  one  foot. 


186 


MATERIALS. 


WEIGHTS  OF  CAST-IRON  PIPE  TO  L.AY  12  FEET 
LENGTH. 

Weights  are  Gross  'Weights,  including  Hub. 

(Calculated  by  F.  H.  Lewis.) 


Thickness. 

Inside  Diameter. 

Inches. 

Equiv. 
Decimals. 

4// 

209 
228 
247 
266 
286 
306 
327 

6" 

8" 

10" 

12" 

14" 

16" 

18" 

20" 

1640 

1810 
1980 
2152 
2324 
2498 
2672 
3024 
3330 

I* 

7-16 
15-32 
H 

17-32 

9-16 
19-32 
% 
11-16 

13-16 

& 

1 

.375 
.40625 
.4375 
.4687 
.5 
.53125 
.5625 
.59375 
.625 
.6875 
.75 
.8125 
.875 
.9375 
1. 
1.125 
1.25 
1.375 

304 
331 
358 
386 
414 
442 
470 
498 

400 
435 
470 
505 
541 
577 
613 
649 
686 

581 
624 
668 
712 
756 
801 
845 
935 
1026 

692 
744 
795 
846 
899 
951 
1003 
1110 
1216 
1324 
1432 

804 
863 
922 
983 
1043 
1103 
1163 
1285 
1408 
1531 
1656 
1783 
1909 

1050 
1118 
1186 
1254 
1322 
1460 
1598 
1738 
1879 
2021 
2163 

1177 
1253 
1329 
1405 
1481 
1635 
1789 
1945 
2101 
2259 
2418 
2738 
3062 

Thickness. 

Inside  Diameter. 

Inches. 

Equiv. 
Decimals. 

22" 

24" 

27" 

30" 

33" 

36" 

42" 

48" 

60" 

11-16 

% 
13-16 

Vs 
15-16 
1 
1« 
1J4 

2  8 

2M 
a? 

2% 

.625 

.6875 
.75 

.8125 
.875 
.9375 

:  !l25 

.25 
.375 
.5 
625 
.75 
.875 
2. 
2.25 
2.5 
2.75 

1799 
1985 
2171 
2359 
2547 
2737 
2927 
3310 
3698 

2160 
2362 
2565 
2769 
2975 
3180 
3598 
4016 
4439 

2422 

2648 
2875 
3103 
3332 
3562 
4027 
4492 
4964 
5439 

2934 
3186 
3437 
3690 
3942 
4456 
4970 
5491 
6012 
6539 

3221 
3496 
3771 
4048 
4325 
4886 
5447 
6015 
6584 
7159 
7737 

3507 

3806 
4105 
4406 
4708 
5316 
5924 
6540 
7158 
7782 
8405 

4426 
4773 
5122 
5472 
6176 
6880 
7591 
8303 
9022 
9742 
10468 
11197 

5442 

5839 
6236 
7034 
7833 
8640 
9447 
10260 
11076 
11898 
12725 
14385 

9742 
10740 
11738 
12744 
13750 
14763 
15776 
17851 
19880 
219.1G 

CAST-IRON    PIPE   FITTINGS. 


187 


CAST-IRON  PIPE  FITTINGS. 

Approximate  Weight. 

Addyston  Pipe  and  Steel  Co.,  Cincinnati,  Ohio. 


Size  in 
Inches. 

Weight 
in  Lbs. 

Size  in 
Inches. 

Weight 
in  Lbs. 

Size  in 
Inches. 

Weight 
in  Lbs. 

Size  in 
Inches. 

Weight 
in  Lbs. 

CROSSES. 

TEES. 

SLEEVES. 

REDUCERS. 

2 
3 
3x2 
4 
4x3 
4x2 
6 
6x4 
6x3 
8 
8x6 
8x4 
8x3 
10 
10x8 
10x6 
10x4 
10x3 
12 
12x10 
12x8 
12x6 
12x4 
12x3 
14x10 
14x8 
14x6 
16 
16x14 
16x12 
16x10 
16x8 
16x6 
16x4 
20 
20  x  12 
20x10 
20x8 
20x6 
20x4 
24 
24x20 
24x6 
30x20 
30x12 
30x8 

40 
104 
90 
150 
114 
110 
200 
150 
150 
325 
265 
265 
225 
510 
415 
388 
338 
350 
700 
650 
615 
540 
525 
495 
750 
635 
570 
1025 
1070 
1025 
1010 
825 
700 
650 
1790 
1370 
1225 
1000 
1000 
1000 
2190 
2020 
1340 
2635 
2250 
1995 

8x3 
10 
10x8 
10x6 
10x4 
10x3 
12 
12  x  10 
12x8 
12x6 
12x4 
14x12 
14x10 
14x8 
14x6 
14x4 
14x3 
16 
16x14 
16x12 
16x10 
16x8 
16x6 
16x4 
20 
20x16 
20x12 
20x10 
20x8 
20  x  6 
20x4 
21  x  10 
24 
24x12 
24x8 
24x6 
30 
30x24 
30  x  20 
30x12 
30x10 
30x6 
36 
36  x  30 
36  x  12 

220 
390 
330 
312 
292 
290 
565 
510 
492 
484 
460 
650 
650 
575 
545 
525 
490 
790 
850 
825 
890 
755 
630 
655 
1375 
1115 
1025 
1090 
900 
875 
845 
1465 
1875 
1425 
1375 
1375 
3025 
2640 
2200 
2035 
2050 
1825 
5140 
4200 
4050 

6 

8 
10 
12 
14 
16 
20 
24 
30 
36 

65 
86 
140 
176 
208 
340 
500 
710 
965 
1500 

10x4 
12x10 
12x8 
12x6 
12x4 
14x12 
14  x  10 
14x8 
14x6 
16x12 
16x10 
20x16 
20x14 
20x12 
20x8 
24  x  20 
30x24 
30x18 
36x30 

128 
278 
254 
250 
250 
475 
430 
340 
285 
475 
435 
690 
575 
540 
300 
745 
1305 
1385 
1730 

90°  ELBOWS. 

2 

3 
4 
6 
8 
10 
12 
14 
16 
20 
24 

14 
34 
48 
110 
145 
225 
370 
450 
525 
900 
1400 

ANGLE  REDUC- 
ERS FOR  GAS. 

6x4 
6x3 

95 

80 

^or45°  BENDS. 

S  PIPES. 

3 
4 
6 
8 
10 
12 
16 
20 
24 
30 

30 
65 
85 
160 
190 
290 
510 
740 
1425 
2000 

4 
6 

90 
190 

PLUGS. 

2 
3 
4 

6 
8 
10 
12 
14 
16 
20 
24 
30 

2 
5 

8 
12 
26 
46 
66 
70 
100 
150 
185 
370 

1-16  or  22^° 
BENDS. 

6 
8 
10 
12 
16 
24 
30 

150 
155 
165 
260 
500 
1280 
1735 

45°  BRANCH 
PIPES. 

CAPS. 

TEES. 

2 
3 
3x2 
4 

4x3 
4x2 
6 
6x4 
6x3 
6x2 
8 
8x6 
8x4 

28 
76 
76 
100 
90 
87 
150 
130 
125 
120 
266 
252 
222 

3 

6x6x4 
8 
8x6 
24 
24  x  24  x  20 
30 
36 

90 
145 
300 
290 
2765 
2145 
4170 
10300 

REDUCERS. 

3 
4 
6 
8 
10 
12 

15 
25 
60 
75 
100 
120 

3x2 
4x3 

4x2 
6x4 
6x3 

8x6 
8x4 
8x3 
10x8 
10x6 

35 
42 
40 
95 
80 
126 
116 
116 
212 
150 

DRIP  BOXES. 

SLEEVES. 

4 

8 
10 
20 

235 
355 
760 
1420 

2 
3 
4 

10 
20 
44 

188 


MATERIALS. 


WEIGHTS  OF  CAST-IRON  WATER-  AND  GAS-PIPE. 

(Addyston  Pipe  and  Steel  Co.,  Cincinnati,  Ohio.) 


.SB" 

Standard  Water-Pipe. 

ai 

<n  ~* 

Standard  Gas-Pipe. 

jat> 
Sw 

Per  Foot. 

Thick- 
ness. 

Per 
Length. 

|| 

GQHH 

Per  Foot. 

Thick- 
ness. 

Per 
Length. 

2 

7 

5-16 

63 

2 

6 

y± 

48 

3 

15 

% 

180 

3 

12fc 

5ll6 

150 

3 

17 

V& 

204 

4 

22 

/^ 

264 

4 

17 

% 

204 

6 

33 

^ 

396 

6 

30 

7-16 

360 

8 

42 

L£ 

504 

8 

40 

7-16 

480 

10 

60 

9-16 

720 

10 

50 

7-16 

600 

12 

75 

9-16 

900 

12 

70 

« 

840 

14 

117 

% 

1400 

14 

84 

9-16 

1000 

16 

125 

i 

1500 

16 

100 

9-16 

1200 

18 

167 

H 

2000 

18 

134 

11-16 

1600 

20 

200 

15-16 

2400 

20 

150 

11-16 

1800 

24 

250 

3000 

24 

184 

% 

2200 

30 

350 

^ 

4200 

30 

250 

1 

3000 

36 

475 

a^ 

5700 

36 

350 

4200 

42 

COO 

% 

7200 

42 

383 

% 

4600 

48 

775 

L£ 

9300 

48 

542 

}L£ 

6500 

60 

1330 

2 

15960 

60 

900 

1% 

10800 

THICKNESS  OF  CAST-IRON  PIPES. 

P.  H.  Baermann,  in  a  paper  read  before  the  Engineers'  Club  of  Phila- 
delphia in  1882,  gave  twenty  different  formulas  for  determining  the  thick- 
ness of  cast-iron  water-pipes  under  pressure.  The  formulas  are  of  three 
classes: 

1.  Depending  upon  the  diameter  only. 

2.  Those  depending  upon  the  diameter  and  head,  and  which  add  a  con- 
stant. 

3.  Those  depending  upon  the  diameter  and  head,  contain  an  additive  or 
subtractive  term  depending  upon  the  diameter,  and  add  a  constant. 

The  more  modern  formulas  are  of  the  third  class,  and  are  as  follows: 

t  =  .000087id  4-  .Old  +  .36 Shedd.  No.  1. 

t  =  .00006/td  -f  .0133d  -f-  .296 Warren  Foundry,  No.  2. 

t  =  .000058/id  -f  .0152d  -f  .312 Francis,  '     No.  3. 

t  =  .0000487* d -t-  .013d  -f-  .32 Dupuit,  No.  4. 

t  =  .00004/id  -f  .1  Vd  +  .15 Box,  No.  5. 

t  =  .000135/id  +  .4  -  .OOlld Whitman,  No.  6. 

t  =  .00006(7i  -f-  230)d  4-  .333  -  ,0033d Fanning,  No.  7. 

t  =  .000157id  -f  .25  -  '.0052d  Meggs,  No.  8. 

In  which  t  =  thickness  in  inches,  h  =  head  in  feet,  d  =  diameter  in  inches. 

Rankine,  "Civil  Engineering,"  p.  721,  says:  "Cast-iron  pipes  should  be 
made  of  a  soft  and  tough  quality  of  iron.  Great  attention  should  be  made 
to  moulding  them  correctly,  so  that  the  thickness  may  be  exactly  uniform  all 
round.  Each  pipe  should  be  tested  for  air-bubbles  and  flaws  by  ringing  it 
with  a  hammer,  and  for  strength  by  exposing  it,  to  double  the  intended 
greatest  working  pressure."  The  rule  for  computing  the  thickness  of  a  pipe 

to  resist  a  given  working  pressure  is  t  =  ~,  where  r  is  the  radius  in  inches, 

p  the  pressure  in  pounds  per  square  inch,  and  /  the  tenacity  of  the  iron  per 
square  inch.  When  /  =  18000,  and  a,  factor  of  safety  of  5  is  used,  the  above 
expressed  in  terms  of  d  and  h  becomes 

<  =  "=lls=-~- 

"There  are  limitations,  however,  arising  from  difficulties  in  casting,  and 
by  the  strain  produced  by  shocks,  which  cause  the  thickness  to  be  made 
greater  than  that  given  by  the  above  formula.'1 


THICKNESS   OF   CAST-IRON    PIPE. 


lS}f 


Thickness  of  Metal  and  Weight  per  Length  for  Different 
Sizes  of  Cast-iron  Pipes  under  Various  Heads  of  Water. 

(Warren  Foundry  and  Machine  Co.) 


50 

Ft.  Head. 

100 

Ft.  Head. 

150 

Ft.  Head. 

200 

Ft.  Head. 

250 

Ft.  Head. 

300 

Ft.  Head. 

Size. 

02 

^ 

* 

-u  "*^ 

%  • 

*£ 

« 

A 

Id 

3 

%~ 

;3 

|3 

II 

£§ 
wg 

>^ 

8*3 

11 

SI 

£-* 

11 

if 

P 

-§£ 
SE 

If 

11 

"£  tic 

*§ 

£4 

P 

II 

If 

gs 

&% 

g* 

*l 

fo 

*s, 

(W 

& 

go 

^  Si 

o> 
A 

g« 

pl, 

3 

.344 

144 

.353 

149 

.362 

153 

.371 

157 

.380 

161 

.390 

166 

4 

.361 

197 

.373 

204 

.385 

211 

.397 

218 

.409 

226 

.421 

235 

5 

.378 

254 

.393 

265 

.408 

275 

.423 

286 

.438 

298 

.453 

309 

6 

.393 

315 

.411 

330 

.429 

345 

.447     361 

.465 

377 

.483 

393 

8 

.422 

445 

.450 

475 

.474 

502 

498     529 

.522 

557 

.546 

584 

10 

.459 

600 

.489 

641 

.519 

682 

.549     723 

.579 

766 

.609 

808 

12 

.491 

768 

.527 

826 

.563 

885 

.599 

944 

.635 

1004 

.671 

1064 

14 

.524 

952 

.566 

1031 

.608 

1111 

.650 

1191 

.692 

1272 

.734 

1352 

16 

.557 

1152 

.604 

1253 

.652 

1360 

.700 

1463 

.748 

1568 

.796 

1673 

18 

.589 

1370 

.643 

1500 

.697 

1630 

.751 

1761 

.805 

1894 

.859 

2026 

20 

.622 

1603 

.682 

1763 

.742 

1924 

.802    2086 

.862 

2248 

.922 

2412 

24 

.687 

2120 

.759 

2349 

.8311  2580 

.903!  2811 

.975 

3045 

1.047 

3279 

30 

.785 

3020 

.875 

3376 

.965 

3735 

1.055    4095 

1.145 

4458 

1.235 

4822 

36 

.882 

4070 

.990 

4581 

1.098 

5096 

1.206 

5013 

1.314 

6133 

1.422 

6656 

42 

.980 

5265 

1.106 

5958 

1  .  232 

6657 

1.358 

7360 

1.484 

8070 

1.610 

8804 

48 

1.078 

6616 

1.222 

7521 

1.366 

8431 

1.510    9340 

1.654 

10269 

1.798 

11195 

All  pipe  cast  vertically  in  dry  sand;  the  3  to  12  inch  in  lengths  of  12  feet, 
all  larger  sizes  in  lengths  of  12  feet  4  inches. 


Safe  Pressures  and  Equivalent  Heads  of  Water  for  Cast- 
iron  Pipe  of  Different  Sizes  and  Thicknesses. 

(Calculated  by  F.  H.  Lewis,  from  Fanning's  Formula.) 


Size  of  Pipe. 


4 

• 

0 

8' 

1( 

" 

12 

// 

14 

\" 

1< 

>" 

1C 

\" 

L>< 

)" 

ness. 

Pi-essure 
in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

Pi-essure 
in  Pounds. 

Head  in 
Feet. 

Pressure 

in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

Pressure 
in  Pounds. 

Head  in 
Feet. 

7-16 
1-2 
8-16 

5-8 

112 

MJ 

258 
516 
774 

49 
124 

.11)9 

97.) 

112 

2sr, 

•j5x 

<Ml 

18 

74 
180 

1S« 

48 

171 

:;<>(> 
429 

41 

89 

1  -v.» 

101 
20f> 

:?<>.< 

24 
62 

1)') 

55 
148 
228 

42 
74 

97 
170 

60 

121 

41 

95 

11-16 

177 

40S 

187 

S16 

ion 

244 

M 

104 

86 

i;.2 

51 

118 

3  A 

>>v>4 

51  K 

174 

401 

i:;s 

SI  6 

11? 

•>:,,x 

»] 

210 

n 

170 

13  16 

21  :> 

188 

170 

MM" 

140 

:-;•';•; 

11C. 

"r>; 

M 

?*1 

7  8 

.)(<) 

574 

202 

4<>r> 

ir,s 

;is? 

141 

:v>-> 

11  '.» 

^>74 

15-16 

234 

•v:s 

1% 

4.v> 

1(16 

::s" 

141 

395 

I 

"('.It 

SIS 

516 

I'M 

440 

ir,4 

37S 

118 

"1C. 

4<»7 

i 

481 

1  1-4 

2,™ 

158<* 

190 


MATERIALS. 


Safe  Pressures,  etc.,  for  Cast-iron  Pipe.— (Continued.) 


Thick- 
ness. 

Size  of  Pipe. 

22" 

24" 

27" 

30" 

33" 

36" 

42" 

48" 

60" 

If 

a, 

Sfe 

K 

1 

Its 

81 

m 

a?  t» 

a 

g4 

L 

g£ 

jn 

g4 

g 

g^ 

j 

-- 

_ 

S 

1 

w^ 

P| 

11 

W 

1§ 

ll 

gi 

11 

11 

^^ 

l| 

££ 

I? 

P 

•U1 

£ 

.l-i 

•S 

^ 

11-16 
3-4 
13-16 
7-8 
15-16 
1 
1  1-8 
1  1-4 
1  3-8 
1  1-2 
1  5-8 
1  3-4 
1  7-8 
2 
2  1-8 
2  1-4 
21-2 
23-4 

40 
60 
80 
101 
121 
142 
182 
224 

92 
138 
184 
233 
279 
327 
419 
516 

30 

49 
68 
86 
105 
124 
161 
199 
237 

69 
113 

157 
198 
-.'I'.' 

37  L 

458 
546 

19 
36 
52 
69 
85 
102 
135 
169 
202 
236 

64 
83 
120 

159 

!!)() 

:?'i"i 
389 

465 
544 

24 
39 
54 
69 
84 
114 
144 
174 
204 
234 

55 
90 
124 
159 
194 
263 
332 
401 
470 
538 

66 
69 
96 
124 

151 

178 
205 
23:5 

97 

151 
22] 
884 

41< 

47: 
537 

32 
44 
57 
82 
107 
132 
157 
182 
207 

74 
101 

131 

IS! 

30 
36! 

II! 

477 

38 
59 
81 
103 
124 
145 
167 
188 
210 

88 
134 

187 

•;si 

43: 
484 

24 
43 
62 
81 
99 
111 

161 

174 

1!).' 
212 

55 
9! 
14: 

187 
221 

31  r 

357 
401 
!4f 

488 

.",4 
4! 

94 

M 

10! 

124 

15-i 
134 

214 

7S 
113 
147 
182 
217 
251 
286 
320 
355 
424 
482 

NOTE.— The  absolute  safe  static  pressure  which  may  be 

2T     S 
put  upon  pipe  is  given  by  the  formula  P  =  -^  X  -r-,  in 

which  formula  P  is  the  pressure  per  square  inch;  T,  the 
thickness  of  the  shell;  S,  the  ultimate  strength  per  square 
inch  of  the  metal  in  tension;  and  Z>,  the  inside  diameter  of 
the  pipe.  In  the  tables  S  is  taken  as  18000  pounds  per 
square  inch,  with  a  working  strain  of  one  fifth  this  amount 
or  3600  pounds  per  square  inch.  The  formula  for  the 

7200  T 
absolute  safe  static  pressure  then  is:  P  =  . 

It  is,  however,  usual  to  allow  for  "  water-ram  "  by  in- 
creasing the  thickness  enough  to  provide  for  100  pounds 
additional  static  pressure,  and,  to  insure  sufficient  metal  for 
good  casting  and  for  wear  and  tear,  a  further  increase 

equal  to  .333(l-^). 
The  expression  for  the  thickness  then  becomes: 


7SOO 


and  for  safe  working  pressure 


The  additional  section  provided  as  above  represents  an 
increased  value  under  static  pressure  for  the  different  sizes 
of  pipe  as  follows  (see  table  in  margin).  So  that  to  test* 
the  pipes  UD  to  one  fifth  of  the  ultimate  strength  of  the 
material,  the  pressures  in  the  marginal  table  should  be 
added  to  the  pressure-values  given  in  the  table  above. 


Size 

of 

Lbs. 

Pipe. 

4" 

676 

6 

476 

8 

346 

10 

316 

12 

276 

14 

248 

16 

226 

18 

209 

20 

196 

22 

185 

24 

176 

27 

165 

30 

156 

33 

149 

36 

143 

42 

133 

48 

126 

60 

116 

SHEET-IRON    HYDRAULIC    PIPE. 


191 


SHEET-IRON   HYJ>RAUMC   PIPE. 

(Pelton  Water-Wheel  Co.) 
Weight  per  foot,  with  safe  head  for  various  sizes  of  double-riveted  pipe. 


Diameter  of 
Pipe. 

CM 
°g 

o3  ft 

gs 

< 

>,a5    2- 

a,  .Q  bC  i3~Z3 
tr  a  3  i  cg,M  £ 
t>  n  53   D  o>   _J 

111  Wl 

*S  O—  '   j^.^O-l  05 

H  £  :o2 

<*->  ^Csj 
O  i*1"^ 

^^a 
A  0>  0> 

to&fl 
g£3 

Diameter  of 
Pipe. 

<M 

°® 

o3  ft 

ES 

m 

Thickness 
of  Iron  by 
Wire  Gauge. 

Safe  Head 
in  Feet  the 
Pipe  will 
stand. 

ofc£" 
s21 

btftO 

££3 

in. 

sq.in. 

B.W.G. 

feet. 

Ibs. 

in. 

sq.in. 

B.G.W. 

feet. 

Ibs. 

3 

7 

18 

400 

2 

18 

254 

16 

165 

1014 

4 

12 

18 

350 

2)4 

18 

254 

14 

252 

20fc 

4 

12 

16 

525 

3 

18 

254 

12 

385 

27J4 

5 

20 

18 

325 

SH 

18 

254 

11 

424 

30 

5 

20 

16 

500 

4)4 

18 

254 

10 

505 

34 

5 

20 

14 

675 

5 

20 

314 

16 

148 

18 

6 

28 

18 

296 

4)4 

20 

314 

14 

227 

22^ 

6 

28 

16 

487 

5% 

20 

314 

12 

346 

30 

6 

28 

14 

743 

pt 

20 

314 

11 

380 

32^ 

7 

38 

18 

254 

20 

314 

10 

456 

361/a 

7 

38 

16 

419 

6% 

22 

380 

16 

135 

20 

7 

38 

14 

640 

gi^ 

22 

380 

14 

206 

24% 

8 

50 

16 

367 

71^3 

22 

380 

12 

316 

32% 

8 

50 

14 

560 

9^3 

22 

380 

11 

347 

35% 

8 

50 

12 

854 

13 

22 

380 

10 

415 

40 

9 

63 

16 

327 

8^ 

24 

452 

14 

188 

27^ 

9 

63 

14 

499 

108 

24 

452 

12 

290 

35g 

9 

63 

12 

761 

uy4 

24 

452 

11 

318 

39 

10 

78 

16 

295 

m 

24 

452 

10 

379 

43^ 

10 

78 

14 

450 

11% 

24 

452 

8 

466 

53 

10 

78 

12 

687 

i* 

26 

530 

14 

175 

2914 

10 

78 

11 

754 

17% 

26 

530 

12 

267 

3$J 

10 

78 

10 

900 

i$i 

26 

530 

11 

294 

42 

11 

95 

16 

269 

9% 

26 

530 

10 

352 

47 

11 

95 

14 

412 

13 

26 

530 

8 

432 

57J4 

11 

95 

12 

626 

I'M 

28 

615 

14 

162 

31J4 

11 

95 

11 

687 

18% 

28 

615 

12 

247 

41^4 

11 

95 

10 

820 

21 

28 

615 

11 

273 

45 

12 

113 

16 

246 

11)4 

28 

615 

10 

327 

50)4 

12 

113 

14 

377 

14 

28 

615 

8 

400 

6$| 

12 

113 

12 

574 

18^ 

30 

706 

12 

231 

44 

12 

113 

11 

630 

19% 

30 

706 

11 

254 

48 

12 

113 

10 

753 

22% 

30 

706 

10 

304 

54 

13 

132 

16 

228 

12 

30 

706 

8 

375 

65 

13 

132 

14 

348 

15 

30 

706 

7 

74 

13 

132 

12 

530 

20 

36 

1017 

11 

58 

13 

132 

11 

583 

22 

36 

1017 

10 

67 

13 

132 

10 

696 

24)6 

36 

1017 

8 

78 

14 

153 

16 

211 

•  13 

36 

1017 

7 

88 

14 

153 

14 

324 

16 

40 

1256 

10 

71 

14 

153 

12 

494 

21  ^ 

40 

1256 

8 

86 

14 

153 

11 

543 

23^ 

40 

1256 

7 

97 

14 

153 

10 

648 

26 

40 

1256 

6 

108 

15 

176 

16 

197 

13% 

40 

1256 

4 

126 

15 

176 

14 

302 

17 

42 

1385 

10 

74^ 

15 

176 

12 

460 

23 

42 

1385 

8 

91 

15 

176 

11 

507 

24^ 

42 

1385 

7 

102 

15 

176 

10 

606 

28 

42 

1385 

6 

114 

Iff 

201 

16 

185 

14)£ 

42 

1385 

4 

133 

1G 

201 

14 

283 

42 

1385 

M 

137 

16 

201 

12 

432 

24)4 

42 

1385 

3 

145 

16 

201 

11 

474 

26)4 

42 

1385 

5-16 

177 

16 

201 

10 

567 

29^ 

42 

1385 

% 

216 

192 


MATERIALS. 


STANDARD  PIPE  FLANGES, 

Adopted  July  18,  1894,  at  a  conference  of  committees  of  the  American 
Society  of  Mechanical  Engineers,  and  the  Master  Steam  and  Hot  Water  Fit- 
ters'  Association,  with  representatives  of  leading  manufacturers  and  users 
of  pipe. 

The  list  is  divided  into  two  groups;  for  medium  and  high  pressures,  the 
first  ranging  up  to  75  Ibs.  per  square  inch,  and  the  second  up  to  200  Ibs. 


10 
4540 
4490 
4320 
5130 
5030 
5000 
4590 
5790 
,  5700 
I  6090 


2040  U4 1 36 
!38 

4  *  1920  V^A^i, 
210014!.' 
2130  H  57^ 


NOTES.— Sizes  up  to  24  inches  are  designed  for  200  Ibs.  or  less. 

Sizes  from  24  to  48  inches  are  divided  into  two  scales,  one  for  200  Ibs.,  the 
other  for  less. 

The  sizes  of  bolts  given  are  for  high  pressure.  For  medium  pressures  the 
diameters  are  J^-inch  less  for  pipes  2  to  20  inches  diameter  inclusive,  and  14 
inch  less  for  larger  sizes,  except  48-inch  pipe,  for  which  the  size  of  bolt  is  \% 
inches. 

When  two  lines  of  figures  occur  under  one  heading,  the  single  columns  up 
to  24  inches  are  for  both  medium  and  high  pressures.  Beginning  with  24 
inches,  the  left-hand  columns  are  for  medium  and  the  right-hand  lines  are 
for  high  pressures. 

The  sudden  increase  in  diameters  at  16  inches  is  due  to  the  possible  inser- 
tion of  wrought-iron  pipe,  making  with  a  nearly  constant  width  of  gasket  a 
greater  diameter  desirable. 

When  wrought-iron  pipe  is  used,  if  thinner  flanges  than  those  given  are 
sufficient,  it  is  proposed  that  bosses  be  used  to  bring  the  nuts  up  to  the 
standard  lengths.  This  avoids  the  use  of  a  reinforcement  around  the  pipe. 

Figures  in  the  third,  fourth,  fifth,  and  last  columns  refer  only  to  pipe  for 
200  Ibs.  pressure. 

In  drilling  valve  flanges  a  vertical  line  parallel  to  the  spindles  should  be 
midway  between  two  holes  on  the  upper  side  of  the  flanges. 


CAST-IROX  PIPE  A:NTB  PIPE  FLANGES. 


193 


DIMENSIONS  OF  PIPE  FLANGES  AND  CAST-IRON 
PIPES. 

(J.  E.  Codman,  Engineers1  Club  of  Philadelphia,  1889.) 


Diameter 
of  Pipe. 

Diamater 
of  Flange. 

ft 

Diamete1" 
of  Bolt 

Number 
of  Bolts. 

Thickness 
of  Flange. 

Thickness 
of  Pipe. 

Weight 
per  foot 
without 
Flange. 

Weight  of 
Flange 
and  Bolts. 

Frac. 

Dec. 

2 

6^ 

4% 

M 

4 

% 

% 

.373 

6.96 

4.41 

3 

71^ 

5% 

% 

4 

% 

13-32 

.396 

11.16 

5.93 

4 

9 

7 

% 

6 

11-16 

7-16 

.420 

15.84 

7.66 

5 

9% 

8 

§4 

6 

M 

7-16 

.443 

21.00 

9.63 

6 

10% 

QL£ 

% 

8 

3^ 

15-32 

.466 

26.64 

11.82 

8 

13J4 

11% 

% 

8 

13-16 

.511 

39.36 

16.91 

10 

\m 

% 

10 

% 

9-16 

.557 

54.00 

23.00 

12 

17% 

15% 

TA 

12 

15-16 

19-32 

.603 

70  56 

30.13 

14 

20 

18 

% 

14 

1 

21-32 

.649 

89.04 

38.34 

16 

22 

20 

% 

16 

1  1-16 

11-16 

.695 

109.44 

47.70 

18 

24 

22*4 

% 

16 

1^6 

M 

.741 

131.76 

58.23 

20 

27 

24  V6 

18 

1  3-16 

25-32 

.787 

156.00 

70.00 

22 

28% 

26^ 

20 

1M 

27-32 

.833 

182.16 

83.05 

24 

31*4 

28% 

22 

1  5-16 

% 

.879 

210.24 

97.42 

26 

3314 

31 

24 

15-16 

.925 

240.24 

113.18 

28 

35i>4 

33J4 

24 

1  7-16 

31-32 

.971 

272.16 

130.35 

30 

38 

35U 

26 

1  9-16 

1 

1.017 

306.00 

149.00 

32 

40 

37^ 

/^J 

28 

1% 

1  1-16 

1.063 

341.76 

169.17 

34 

42^ 

40 

/^ 

30 

1  11-16 

IL/ 

1.109 

379.44 

190.90 

36 

45 

42 

^ 

32 

1% 

1  5-32 

1.155 

419.04 

214.26 

38 

47 

44 

11^ 

32 

1  13-16 

1  3-16 

1.201 

460.56 

239.27 

40 

49 

46 

\\^ 

34 

1% 

1J4 

1.247 

504.00 

266.00 

42 

51  J4 

48*4 

1^ 

34 

1  15-16 

1  5-16 

1.293 

549.36 

294.49 

44 

531^ 

50*4 

1/4 

36 

2 

111-32 

1.339 

596.64 

324.78 

46 

55% 

52% 

114 

38 

2  1-16 

1% 

1.385 

645.84 

356.94 

48 

58 

55 

iM 

40 

-^ 

17-16 

1.431 

696.96 

391.00 

D  =  Diameter  of  pipe.    All  dimensions  in  inches. 
FORMULA.— Thickness  of  flange  =  0.033D  -f  0.56. 
Thickness  of  pipe  =  0.0237)  -f  0  327. 
Weight  of  pipe  per  foot  =  0.24D2  +  3D. 
Weight  of  flange  =  .001  D3  -f  0.1D2  +  D  -f  2. 
Diameter  of  flange  =  1.125Z)  -f  4.25> 
Diameter  of  bolt-circle  =  1.092Z)  -f-  2.566. 
Diameter  of  bolt  =  0.01  ID  -f  0.73, 
Number  of  bolts  -  0.78D  +  2.56. 

PIPE  FLANGES  FOR  HIGH  STEAM-PRESSURE. 

(Chapman  Valve  Mfg.  Co.) 


Size  of 
Pipe. 

Diameter 
of  Flange. 

Number  of 
Bolts. 

Diameter 
of  Bolts. 

Diameter  of 
Bolt  Circle.  • 

Length  of 
Pipe-Thread. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

'46 

7fcf 

6 

% 

5% 

i£ 

3 

9 

6 

% 

6% 

m 

3^ 

9 

7 

% 

34 

1  7-16 

4 

10 

8 

7% 

1  9-16 

4^ 

10^ 

8 

% 

8^ 

1  11-16 

5 

11 

9 

M 

m 

1  13-16 

6 

13 

10 

% 

10% 

1% 

7 

14 

12 

% 

11% 

1  15-16 

8 

15 

12 

% 

13 

2 

9 

16 

13 

% 

14 

2 

10 

1% 

15 

% 

15^4 

2^ 

12 

20 

18 

% 

17JJ 

2^4 

14 

23 

18 

i 

20^4 

2^ 

15 

23^ 

18 

l 

2114 

2% 

194 


MATERIALS. 


STANDARD  SIZES,  ETC.,  OF   WROUGHT-IRON   PIPE. 
For  Water,  Gas,  or  Steam. 

(Briggs  Standard.) 


Diameter  of  Tube. 

Thickness 
of  Metal. 

Internal 
Circum- 
ference. 

External 
Circum- 
ference. 

Length  of 
Pipe  per 
Sq.  Ft.  of 
Inside  Sur- 
face. 

<M 

«M   {->   O 

ilfll 

Internal 
Area. 

External 
Area. 

'§•3:2 
0  G  | 

Actual 
Inside. 

|ll 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Feet. 

Feet. 

Ins. 

Ins. 

.270 

.405 

.068 

.848 

1.272 

14.15 

9.44 

.0572 

.129 

IX 

.364 

.540 

.088 

1.144 

1.696 

10.50 

7.075 

.1041 

.229 

% 

.494 

.675 

.091 

1.552 

2.121 

7.67 

5.657 

.1916 

.358 

/^ 

.623 

.840 

.109 

1.957 

2.652 

6.13 

4.502 

.3048 

.554 

M 

.824 

1.050 

.113 

2.589 

3.299 

4.635 

3.637 

.5333 

.866 

1 

1.048 

1.315 

.134 

3.292 

4.134 

3.679 

2.903 

.8627 

1.357 

J1X 

1.380 

1.660 

.140 

4.335 

5.215 

2.768 

2.301 

1.496 

2.164 

ILjfi 

1.610 

1.900 

.145 

5.061 

5.969 

2  371 

2.01 

2.038 

2.835 

2 

2,067 

2.375 

.154 

6.494 

7.461 

1.848 

1.611 

3.355 

4.430 

2^ 

2.468 

2.875 

.204 

7.754 

9.032 

1.547 

1.328 

4.783 

6.491 

3  ~ 

3.067 

3.500 

.217 

9.636 

10.996 

1.245 

1.091 

7.388 

9.621 

3^*5 

3.548 

4.000 

.226 

11.146 

12.566 

1.077 

.955 

9.887 

12.566 

4 

4.026 

4.500 

.237 

12.648 

14.137 

.949 

.849 

12.730 

15.904 

41^ 

4.508 

5.000 

.246 

14.153 

15.708 

.848 

.765 

15.939 

19.635 

5 

5.045 

5.563 

.259 

15.849 

17.475 

.757 

.629 

19.990 

24.299 

6 

6.065 

6.625 

.280 

19.054 

20  813 

.63 

.577 

28.889 

34.471 

7. 

7.023 

7.6?5 

.301 

22.063 

23.954 

.544 

.505 

38.737 

45.663 

8 

7.982 

8.625 

.322 

25.076 

27.096 

.478 

.444 

50.039 

58.426 

*9 

9.000 

9.688 

.344 

28.277 

30.433 

.425 

.394 

63.633 

73.715 

10 

10.019 

10.750 

.366 

31.475 

33.772 

.381 

.355 

78.838 

90.762 

*  By  the  action  of  the  Manufacturers  of  Wronght-iron  Pipe  and  Boiler 
Tubes,  at  a  meeting  held  in  New  York,  May  9,  1889.  a  change  in  size  of  actual 
outside  diameter  of  9-inch  pipe  was  adopted,  making  the  latter  9.625  instead 
of  9.688  inches,  as  given  in  the  table  of  Briggs1  standard  pipe  diameters. 

For  discussion  of  the  Briggs  Standard  of  Wrought-iron  Pipe  Dimensions, 
see  Report  of  the  Committee  of  the  A.  S.  M.  E.  in  "  Standard  Pipe  and  Pipe 
Threads,"  1886.  Trans.,  Vol.  VIII,  p.  29.  The  figures  in  the  next  to  the  last 
column  are  derived  from  the  formula 

Z>-(0.05D-f  1.9)  X  — , 
n 


in  which  D  =  outside  diameter  of  the  tubes,  and  n  the  number  of  threads  to 
the  inch.    The  figures  in  the  last  column  are  derived  from  the  formula 

0.8—  x  2  4-  d,  or  1.6 \-  d,  in  which  d  is  the  diameter  at  the  bottom  of  the 

thread  at  the  end  of  the  pipe. 

Having  the  taper,  length  of  full-threaded  portion,  and  the  sizes  at  bottom 
and  top  of  thread  at  the  end  of  the  pipe,  as  given  in  the  table,  taps  and  dies 
can  be  made  to  secure  these  points  correctly,  the  length  of  the  imperfect 
threaded  portions  on  the  pipe,  and  the  length  the  tap  is  run  into  the  fittings 
beyond  the  point  at  which  the  size  is  as  given,  or,  in  other  words,  beyond 
the  end  of  the  pipe,  having  no  effect  upon  the  standard.  The  angle  of  the 
thread  is  60°,  and  it  is  slightly  rounded  off  at  top  and  bottom,  so  that,  instead 
of  its  depth  being  equal  to  its  pitch,  as  is  the  case  with  a  full  V-thread,  it  is 

4/5  the  pitch,  or  equal  to  0.8—,  n  being  the  number  of  threads  per  inch. 


PIPE. 


195 


Sizes,  etc.,  of  Wroiaght-iron  Pipe— (Continued.) 


Sizes,  etc. 

Screwed  Ends. 

Nominal 
Inside 
Diameter. 

1-1  £  O  o 

Weight  per 
Foot  of 
Length. 

Contents  in 
U.S. 
Gallons 
per  Foot. 

Weight  of 
Water  per 
Foot  of 
Length. 

Number  of 
Threads 
per  Inch. 

Length  of 
Perfect 
Screw. 

Diameter  of 
Bottom  of 
Thread  at 
End  of  Pipe. 

Diameter  of 
Top  of 
Thread  at 
End  of  Pipe. 

Inch. 

Feet. 

Lbs. 

Lbs. 

No. 

Inch. 

Inches. 

Inches. 

Vs 

2500. 

.243 

.0006 

.005 

27 

.19 

.334 

.393 

1385. 

.422 

.0026 

.021 

18 

.29 

.433 

.522 

% 

751.5 

.561 

.0057 

.047 

18 

30 

.567 

.656 

L£ 

472.4 

.845 

.0102 

.085 

14 

.39 

.701 

.815 

M 

270. 

1.126 

.0230 

.190 

14 

.40 

.911 

1.025 

1 

166.9 

1.670 

.0408 

.349 

11^ 

.51 

1.144 

1.283 

96.25 

2  258 

.0638 

.527 

\\\4t 

.54 

1.488 

1.627 

]1^ 

70.65 

2.694 

.0918 

.760 

11^3 

.55 

1.727 

1.866 

2 

42.36 

3.667 

.1632 

1  .  :  56 

11^2 

.58 

2.2 

2.339 

01/ 

30.11 

5  .  773 

.2550 

2.116 

8 

.89 

2.62 

2.82 

3 

19.49 

7.547 

.3673 

3.049 

8 

.95 

3.241 

3.441 

•J'^ 

14.56 

9.055 

.4998 

4.155 

8 

.00 

3.738 

3.938 

4 

11.31 

10.728 

.6528 

5.405 

8 

.05 

4.235 

4.435 

41^ 

9.03 

12.492 

.8263 

6.851 

8 

.10 

4.732 

4.932 

5  ~ 

7.20 

14.564 

1.020 

8.500 

8 

.16 

5.291 

5.491 

6 

4.98 

18.767 

1.469 

12.312 

8 

.26 

6.346 

6.546 

7 

3.72 

23.410 

1.999 

16.662 

8 

.36 

7.34 

7.54 

8 

2.88 

28.348 

2.611 

21.750 

8 

.46 

8.334 

8.534 

9 

2.26 

34.077 

3.300 

27.,  100 

8 

.57 

9.39 

9.59 

10 

1.80 

40.641 

4.081 

34.000 

8 

.68 

10.445 

10.645 

Taper  of  conical  tube  ends,  1  in  32  to  axis  of  tube  =  %  inch  to  the  foot 
total  taper. 

1  inch  and  below  are  butt-welded,  and  proved  to  300  pounds  per  square  inch 
hydraulic  pressure. 

'1J4  inch  and  above  are  lap- welded,  and  proved  to  500  pounds  per  square 
inch  hydraulic  pressure. 

SIZES    ABOVE  10  INCHES. 
(Morris,  Tasker  &  Co.,  Limited.) 


0) 

£<M$ 

U«M    8 

o> 

o 

o5 

0 

S 

gj 

•'  S 

i 

0) 

5&0   * 

.&O  cS 

.2* 

&  . 

Nominal  Siz 

Actual  Insic 
Diameter. 

Actual  Outs 
Diameter. 

Thickness. 

Internal  Cir 
cumferein 

External  Ci 
cumferen< 

Internal  An 

External  Ai 

Length  of  1: 
per  sq.  ft. 
Inside  Surl 

Length  of  P 
per  sq.  ft. 
Outside  Surj 

Length  of  I 
containing 
cubic  foot 

Weight  per 
of  Length 

in. 

in. 

in. 

in. 

in. 

in. 

?q  in. 

sq.  in. 

ft. 

ft. 

ft. 

Ibs. 

11 

11.224 

12 

.388 

35.26 

37.70 

98.94 

113.10 

.340 

.318 

1.455 

47.73 

12 

12.180 

13 

.41 

38.26 

40.84  116.54 

132.73 

.313 

.293 

1.235 

54.66 

13 

13.136 

14 

.432 

41.27 

43.98  184.58 

153.94 

.290 

.273 

1.069 

61.94 

14 

14.092 

15 

.454 

44.27 

47.12  155.97jl76.72 

.271 

.254 

.923 

70.01 

15 

15.048 

16 

.476 

47.27 

50,27177.87201.06 

.254 

!288 

.809 

78.27 

16 

16.004 

17 

.498 

50.28 

53.41  !  201.  16:226.  98 

.238 

.2-25 

.715 

87.12 

17 

16.960 

18 

.520 

53.28 

56.55225.91  254.47 

.225 

.212 

.638 

96.38 

18 

17.916 

19 

.542 

56.28 

59.69252.10283.53 

.213 

.201 

.571 

106.07 

.19 

18.872 

20 

.564 

59.29 

62.83279.72314.16 

.202 

.191 

.515 

116.21 

20 

19.828 

21 

.586 

62.29 

65.97 

308.77 

346.36 

.192 

.183 

.466 

126.76 

196 


MATERIALS. 


WROUGHT-IRON  WELDED  TUBES,  EXTRA  STRONG. 

Standard  Dimensions. 


Nominal 
Diameter. 

Actual  Out- 
side 
Diameter. 

Thickness, 
Extra 
Strong. 

Thickness, 
Double 
Extra 
Strong. 

Actual  Inside 
Diameter, 
Extra 
Strong. 

Actual  Inside 
Diameter, 
Double  Extra 
Strong. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

1^4 

0.405 

0.100 

0.205 

\A 

0.54 

0  123 

0  294 

*/ 

0.675 

0.127 

0.421 

^ 

0.84 

0.149 

0.298 

0.542 

0.244 

M 

1.05 

0.157 

0.314 

0.736 

0.422 

1 

1.315 

0.182 

0.364 

0.951 

0.587 

1^ 

1.66 

0.194 

0.388 

1.272 

0.884 

IVi* 

1.9 

0.203 

0.406 

1.494 

1.088 

2 

2.375 

0  221 

0.442 

1.933 

1.491 

% 

2.875 

0.280 

0.560 

2.315 

1.755 

3 

3.5 

0  304 

0.608 

2.892 

2.284 

V4 

4.0 

0.321 

0.642 

3.358 

2.716 

± 

4.5 

0.341 

0.682 

3.818 

3.136 

STANDARD    SIZES,    ETC.,  OF    LAP-WELDED    CHAR- 
COAL-IRON   BOILER-TUBES. 

(Morris,  Tasker  &  Co.,  Limited). 


1 

1 

3 

•~1 

M 

f=S| 

H«  ^ 

!"J 

fei 

Q 

s 

H 
•tf 

SI 

Internal 

.External 

coP^|j 

0—3 

0^| 

a  o 

t»i 

IK' 

|| 

|| 

(5*2 

Area. 

Area. 

5^:3 

5*lo; 

5?§ 

fi  "i 

£#£ 

0)  1> 

w 

•§« 

li 

*i 

g&3 

fill 

BgJ 

W 

HH 

02 

M 

w 

M 

A 

>-3 

£ 

Ins. 

Ins. 

Ins.  !  Ins. 

Ins. 

Sq.  In. 

Sq.Ft 

Sq.  In.!  Sq.Ft 

Ft7~ 

Ft. 

Ft. 

Lbs. 

1 

.856 

.072      2.689 

3.142 

.575 

.004 

\785 

.0055 

4.460 

3.819 

4.139 

.708 

1  1-4 

1.106 

.072      3.474 

3.927 

.960 

!0087 

1.227 

.00X5 

3.455 

3.056 

3.255 

.9 

1  1-2 

1.334 

.083      4.191 

4.712 

1.396 

.001)7 

1.767 

.0123 

2.863 

2.547 

2.705 

1.25 

1  3-4 

1.560 

.095      4.901 

1.911 

.0133 

2.405 

.0167 

2.448 

2.183 

2.315 

1.665 

2 

1.804 

.098 

5.667 

li  ''Sit 

2.556 

.0177 

3.142 

.0218 

2.118 

1.909 

2.013 

1.981 

2  1-4 

2.054 

.098 

6.484 

7l  089 

3.314 

.0230 

3.976 

.0276 

1.850 

1.698 

1.774 

2.238 

2  1-2 

2.283 

.109 

7.172 

7.854 

4.094 

.0284 

4.909 

.0341 

1.673 

1.528 

1.600 

2.755 

2  3-4 

2.533 

.109 

7.957 

8.639 

5.039 

.035 

5.940 

.0412 

1.508 

1.390 

1.449 

3.045 

3 

2.783 

.109 

8.743 

9.425 

6.083 

!0425> 

7.069 

.0491 

1.373 

1.273 

1.323 

3.331! 

3  1-4    S.012 

.119 

9.462 

10.210 

7.125 

.0495 

8.296 

.0576 

1.268 

1.175 

1.221 

3.1I5S 

3  1-2|  3.262 

.119 

10.248 

L0.996 

8.357 

.058 

9.621 

.06(58 

1.171 

1.091 

1.131 

4.272 

3  3-41  C.512 

.119 

11.0:::; 

11.781 

9.687 

.0673 

11.045 

.0767 

1.088 

1.018 

1.053 

4.590 

4           3.741 

.130 

11.753 

i-.'.56i; 

10.992 

.0763 

12.566 

.0872 

1.023 

.955 

.989 

5.32 

4  1-2    4.241 

.130 

14.137 

14.126 

.0981 

15.904 

.1104 

.901 

.849 

.875 

6.01 

5 

4.720 

.140 

14.818 

15.708 

17.497 

.1215 

19.635 

.1364 

.809 

.764 

.786 

7.226 

6 

.151 

17.901 

18.819 

25.509 

.1771 

28.274 

.670 

.637 

.653 

9.346 

7 

(-.G57 

.]72  120.914 

21.991 

34.805 

.2417 

38.484 

.'  2'  r.;': 

.574 

.545 

.560 

12.435 

8 

7.636 

.182    23.989 

25.132 

45.795 

.318 

50.265 

.3490 

.500 

.478 

.489 

15.109 

9 

G.615 

.193 

2?.  055 

28.274 

58.291 

.4048 

63.617 

.4418 

.444 

.424 

.434 

18.002 

10 

9.573 

.214 

T  ).074 

31.416 

71.975 

.4<»9S 

78.540 

.5454 

.399 

.382 

.391 

22.19 

11 

10.560 

.22 

33-175 

34  557 

87.479 

.6075 

95.033 

.6601 

.361 

.347 

.354 

25.189 

12 

i  !.:>(•> 

.229 

36.26 

103.749 

.7205 

113.097 

.7854 

.330 

.318 

.324 

:'<S  516 

13 

12.5'M 

.238 

:',9.:u:. 

40^840 

123.187 

.8554 

132.732 

.9213 

.305 

.293 

.299 

32.208 

14 

13.504 

.248 

42.414 

43.982 

143.189 

.9943 

153  938 

LOW) 

.282 

.272 

.277 

.''»5  27  1 

15 

14.482 

.C59 

45.496 

47.124 

164.718 

1.1438 

176.715 

1.227:. 

.263 

.254 

.258 

in  61:.' 

16 

15.458 

.271 

48-562 

50.  -.'65 

187.667 

1.3032 

201.062 

1.188 

.247 

.238 

.242 

45.199 

17 

16.432 

.284 

53.407 

212.227 

1.4738 

226.980 

1.576: 

.232 

.224 

.228 

49  902 

18 

17.416 

.292 

54^714 

56.548 

238.224 

1.C.54: 

254.469  1.76J1 

.219 

.212 

.215 

54.816 

19 

i:;.400 

.3 

57.805 

59.1590 

265.903 

i.84«r 

283.529  i  1.969 

.207 

.200 

.203 

59.4V9 

20 
21 

19.360 
20.320 

.32 
.34 

60.821  62.832 
63.837  65.973 

294.373  2.0443 
324.311  2.2522 

314.159  2.1817 
346.  361  12.4053 

.197 
.188 

.190 
.181 

.193 
.184 

66.7H5 
73.404 

In  estimating  the  effective  steam-heating  or  boiler  surface  of  tubes,  the  surface  v\ 
contact  with  air  or  g-ases  of  combustion  (whether  internal  or  external  to  the  tubes;  is  to 
be  taken. 

For  heating  liquids  by  steam,  supD-lK-jiting  steam,  or  transferring  heat  from  ony 
liquid  or  gas  to  another,  the  mean  surface  of  the  tubes  is  to  be  taken. 


RIVETED   IROW   PIPE. 


197 


To  find  the  square  feet  of  surface,  #,  in  a  tube  of  a  given  length,  L,  in  feet, 
and  diameter,  d,  in  inches,  multiply  the  length  in  feet  by  the  diameter  in 

inches  and  by  .2618.    Or,  8  =  3A4™dL  =  .2618dL.    For  the  diameters  in  the 

table  below,  multiply  the  length  in  feet  by  the  figures  given  opposite  the 
diameter. 


Inches, 
Diameter. 

Square  Feet 
per  Foot 
Length. 

Inches, 
Diameter. 

Square  Feet 
per  Foot 
Length. 

Inches, 
Diameter. 

Square  Feet 
per  Foot 
Length. 

IX 

1  4 
IM 

if! 

2 

.0654 
.1309 
.1963 
.2618 
.3272 
.3927 
.4581 
.5236 

34 

m 

'    3^ 
3% 

.5890 
.6545 
.7199 
.7854 
.8508 
.9163 
.9817 
1.0472 

5 
6 
7 
8 
9 
10 
11 
12 

1.3090 
1.5708 
1.8326 
2.0944 
2.3562 
2.6180 
2.8798 
3.1416 

RIVETED  IRON  PIPE. 

(Abendroth  &  Root  Mfg.  Co.) 

Sheets  punched  and  rolled,  ready  for  riveting,  are  packed  in  convenient 
form  for  shipment.  The  following  table  shows  the  iron  and  rivets  required 
for  punched  and  formed  sheets. 


Number  Square  Feet  of  Iron 
required  to  make  100  Lineal 
Feet  Punched  and  Formed 
Sheets  when  put  together. 

^t^ 
^-efS 

s-gasg 

£f£0£fa 

Number  Square  Feet  of  Iron 
required  to  make  100  Lineal 
Feet  Punched  and  Formed 
Sheets  when  put  together. 

£'1?1H 

^SoSfe 

Diam- 
eter in 
Inches. 

Width  of 
Lap  in 
Inches. 

Square 
Feet. 

"fif-P*     £ 

£#  es  ^"S^  8 
a«w  aS  «  fl-fl 

AO  cs£fo  OSO2 

<5 

Diam- 
eter in 
Inches. 

Width  of 
Lap  in 
Inches. 

Square 
Feet. 

'Z>~%      3 
ES^,  "S^S 
a'w  d  ?  01  c  & 
ao  ce^fe  ajcc 
<i 

3 

1 

90 

1,600 

14 

1*6 

397 

2,800 

4 

1 

116 

1,700 

15 

}l^j 

423 

2,900 

5 

1^> 

150 

1.800 

16 

I& 

45-2 

3,000 

6 

\\/^ 

178 

1,900 

18 

18 

506 

3,200 

7 

1/^J 

206 

2,000 

20 

i| 

562 

3,500 

8 

m 

234 

2,200 

22 

617 

3,700 

9 

i| 

258    • 

2,300 

24 

1^3 

670 

3,900 

10 

289 

2,400 

26 

1^ 

725 

4,100 

11 

1^5 

314 

2,500 

28 

1^ 

779 

4,400 

12 

lj/3 

343 

2,600 

30 

114 

836 

4,600 

13 

369 

2,700 

36 

m 

998 

5,200 

WEIGHT  OF   ONE   SQUARE  FOOT  OF   SHEET-IRON 
FOR  RIVETED   PIPE. 

Thickness  by  tlie  Rirmingliam  Wire-Gauge. 


No.  of 
Gauge. 

Thick- 
ness in 
Decimals 
of  an 
Inch. 

Weight 
in  Ihs  , 
Black. 

Weight 
in  Ibs., 
Galvan- 
ized. 

No.  of 
Gauge. 

Thick- 
ness in 
Decimals 
of  an 
Inch. 

Weight 
in  Ibs., 
Black. 

Weight 
in  Ibs., 
Galvan- 
ized. 

26 
24 
22 
20 

.018 
.02-3 
.028 
.035 

.72 
.88 
1.12 
1.40 

.94 

1.13 
1.38 
1.69 

18 
16 
14 
12 

.049 
.065 
.083 
.109 

1.97 
2.61 
3.33 
4.37 

2.19 
2.82 
3.52 
4.50 

198 


MATERIALS. 


SPIRAL.    RIVETED    PIPE. 

(Abendroth  &  Root  Mfg.  Co  ) 


Thickness. 

Diam- 
eter, 
Inches. 

Approximate  Weight 
in  Ibs.  per  foot  in 
Length. 

Approximate  Burst- 
ing Pressure  in  Ibs. 
per  sq.  in. 

B.  W.  G. 

No. 

Inches. 

26 

.018 

3  to    6 

lbs.= 

24 

.022 

3  to  12 

=  ^of  diam.  in  ins. 

.028 

3  to  14 

=  .4 

20 

.035 

3  to  24 

=  .5 

2700  Ibs.  -^diam.  in  ins. 

18 

.049 

3  to  24 

=  .6 

8600    "   -=-    " 

16 

.065 

6  to  24 

=  .8 

4800    "   --    " 

14 

.083 

8  to  24 

=  1.1 

6400    "  --    " 

The  above  are  black  pipes.  Galvanized  weighs  from  10  to  30  per  cent 
heavier.  Double  Galvanized  Spiral  Riveted  Flanged  Pressure  Pipe,  tested 
to  150  Ibs.  hydraulic  pressure. 


Inside  diameters  inches 

3 

20 

2*4 

4 

20 
3 

SO 
4 

6 

18 
5 

18 
6 

8 
18 

O50DQO 

10 
16 

11 

11 
1G 

l-.J 
Hi 
14 

13114 
16  14 
15|20 

15 

n 

22 

16  ;8 

14   1-1 
24  29 

Thickness,  B.  W.  G  
Nominal  weight  per  foot,  Ibs.  .  . 

DIMENSIONS  OF  SPIRAL.   PIPE   FITTINGS. 

Dimensions  in  Inches. 


Inside 
Diameter. 

Outside 
Diameter 
Flanges. 

Number 
Bolt  Holes 

Diameter 
Bolt  Holes. 

Diameter 
Circles  on 
which  Bolt 
Holes  are 
Drilled. 

Sizes  of 
Bolts. 

ins. 

3 

6 

4 

\t> 

4% 

7-16x1% 

4 

7 

8 

i£ 

5  15-16 

7-16  x  19£ 

5 

8 

8 

y*, 

6  15-16 

7-16x1-% 

6 

8% 

8 

% 

7% 

«xlg 

7 

10 

8 

% 

9 

iA*m 

8 

11 

8 

% 

10 

9 

13 

8 

% 

ny 

^  x  2 

10 

14 

8 

% 

1214 

Ux2 

11 

15 

12 

% 

im 

1/2  x  2 

12 

16 

12 

% 

1414 

13 

17 

12 

% 

n8 

J^x2 

14 

15 

i* 

12 
12 

H 

1  614 

1?  7-16 

jfxtt 

16 

21  3-16 

12 

% 

19J4 

&*%1 

18 

23  Y4 

18 

11-16 

21M 

20 

25  ys 

16 

11-16 

2314 

y^y* 

SEAMLESS   BRASS   TUBE.     IRON-PIPE    SIZES. 

(Randolph  &  Clowes). 
(For  actual  dimensions  see  tables  of  Wrought-iron  Pipe.) 


Nominal 
Size. 

Weight 
per 
Foot,  Ibs. 

Nom- 
inal 
Size. 

Weight 
per 

Foot,  Ibs. 

Nom- 
inal 
Size. 

Weight 
per 

Foot,  Ibs. 

Nom- 
inal 

Si/e. 

Weight 
per 
Foot,  Ibs. 

Y» 

.266 

M 

1.228 

2 

4 

4 

11.719 

M 

.461 

1 

1.837 

2^ 

6.323 

5 

15.935 

% 

.617 

1J4 

2  468 

3 

8.266 

6 

20.690 

y* 

.925 

*H 

3  045 

3& 

9.878 

7 

D5.286 

8 

s:).88i 

BKASS  TUBING  ;    COILED   PIPES. 


199 


SEAMLESS    DRAWN    BRASS-TUBING. 

(Randolph  &  Clowes,  Waterbury,  Conn.) 

Outside  diameter  3-16  to  7%  inches.    Thickness  of  walls  8  to  25  Stubbs* 
Gauge,  length  12  feet.    The  following  are  the  standard  sizes: 

SEAMLESS  DRAWN  BRASS-TUBING. 


Outside 
Diam- 
eter. 

Length 
Feet. 

Stubbs' 
or  Old 
Gauge. 

Outside 
Diam- 
eter. 

Length 
Feet. 

Stubbs' 
or  Old 
Gauge. 

Outside 
Diam- 
eter. 

Length 
Feet. 

Stubbs' 
or  Old 
Gauge. 

H 

12 

20 

m 

12 

14 

2% 

12 

11 

5-16 

12 

19 

12 

14 

2M 

12 

11 

12 

19 

1% 

12 

13 

3 

12 

n 

i/ 

12 

18 

1% 

12 

13 

3^ 

12 

11 

% 

12 

18 

1  13-16 

12 

13 

S2 

12 

11 

a/ 

12 

17 

1% 

12 

12 

4 

10  to  12 

11 

13-16 

12 

17 

1  15-16 

12 

12 

5 

10  to  12 

11 

%    - 

12 

17 

o 

12 

12 

5/4 

10  to  12 

11 

15-16 

12 

17 

2^ 

12 

12 

5/^ 

10  to  12 

11 

1 

12 

16 

2^ 

12 

12 

5% 

10  to  12 

11 

1V£ 

12 

16 

12 

12 

6 

10  to  12 

11 

i§ 

12 

15 

2^ 

12 

11 

COILED    PIPES. 

(National  Pipe-bending  Co.,  New  Haven,  Conn.) 

COILS  OF  STEEL  OR  IRON  PIPE  ;  WELDED  LENGTHS. 


Butt-  welded  Pipe. 

Lap- 
welded 
Pipe. 

Size  of  pipe                                      Inches 

Y4 
2 
6 

% 
% 

7 

Y2 

sy2 

% 

% 

4 

m 

i 

6 
9 

m 

8 
11 

1^ 
12 

14 

2 

18 
18 

Least  outside  diameter  of  coil  contain- 
ing 25  feet  of  pipe  and  less.     .  Inches 
Least  outside  diameter  of  coils  over  25 
feet  arid  not  over  200  feet.  .   .   .Inches 

COILS  OF  SEAMLESS  DRAWN  BRASS  AND  COPPER  TUBING. 


Size  of  tube,  outside 

diameter           Ins 

M 

3^ 

I/ 

ax 

1 

14 

1*6 

11^ 

iax 

g 

gix 

2&X 

2V^ 

Least  outside  diam- 

* 

eter  of  coils  Ins. 

1 

IK 

2 

3 

4 

6 

7 

8 

10 

12 

14 

16 

18 

Welded  solid  drawn-steel  tubes,  imported  by  P.  S.  Justice  &  Co.,  Phila- 
delphia, are  made  in  sizes  from  14  to  4^  inches  external  diameter,  varying 
by  ^ths,  and  with  thickness  of  walls  from  1-16  to  11-16  inches.  The  maxi- 
mum length  is  15  feet. 


200 


MATERIALS. 


WEIGHT    OF    BRASS,    COPPER,    AND    ZINC    TUBING* 

Per  Foot. 

Thickness  by  Brown  &  Sharpens  Gauge. 


Brass,  No.  17. 

I 
Brass,  No.  20. 

Copper, 
Lightning-rod  Tube, 
No.  23. 

Inch. 
5-16 
& 

f 

r 

m 

VA 

\Y± 

2 

p 

Lbs. 
.107 
.157 
.185 
.234 
.266 
.318 
.333 
.377 
.462 
.542 
.675 
.740 
.915 
.     .980 
1.90 
1.506 
2.188 

Inch. 

Ys 
3-16 

Y4 
5-16 

% 
7-16 

Y2 

9-16 
ft 

1H 
41 

Lbs. 
.032 
.039 
.063 
.106 
.126 
.158 
.189 
.208 
.220 
.252 
.284 
.378 
.500 
.580 

Inch. 

*\ 

% 
11-16 

« 

Lbs. 
.162 
.176 
.186 
.211 
.229 

Zinc,  No.  20. 

1  8 

.161 
.185 
.234 
.272 
"311 
.380 
.452 

LEAD  PIPE  IN  LENGTHS  OF  1O  FEET. 


In. 

3-8  Thick. 

5-16  Thick. 

14  Thick. 

3-16 

Thick. 

Ib. 

oz. 

Ib. 

oz. 

Ib. 

oz. 

Ib. 

oz. 

2^ 

17 

0 

14 

0 

11 

0 

8 

0 

3 

20 

0 

16 

0 

12 

0 

9 

0 

3J4 

22 

0 

18 

0 

15 

0 

9 

8 

4 

25 

0 

21 

0 

16 

0 

12 

8 

4^ 

18 

0 

14 

0 

5 

31 

0 

20 

0 

LEAD  WASTE-PIPE. 


1^  in.,  2  Ibs.  per  foot. 

2  "    3  and  4  Ibs.  per  foot. 

3  "3^  and  5  Ibs.  per  foot 


in.,  4  Ibs.  per  foot. 
44  5,  6,  and  8  Ibs. 
6  and  8  Ibs. 


Weight  per  square  foot,  2^,  3, 
Other  weights  rolled  to  order. 


5  in.  8, 10,  and  12  Ibs. 

LEAD  AND  TIN  TUBING. 

inch.  y±  inch. 

SHEET  LEAD. 

Vz,  5,  6,  8,  9,  10  Ibs.  and  upwards. 


BLOCK-TIN  PIPE. 


in  ,  4J4  6J^,  and  8  oz.  per  foot. 
"  6,  7^,  and  10  oz.  " 
"   8  and  10  oz.          " 
"  10  and  12  oz. 


1  in.,  15,  and  18  oz.  per  foot. 
U4  "     P4  and  \Y%  Ibs.     " 
\Y2  "     2'and2V£lbs. 

2  ;'    2^  and  3  Ibs. 


LEAD   PIPE. 


201 


LEAD  AND  TIN-LIN  HI)  LEAD  PIPE. 

(Tatham  &  Bros.,  New  York.) 


Calibre. 

Letter. 

Weight  per 
Foot  and  Rod. 

Thickness  in 
l-100th  In. 

Calibre. 

Letter. 

Weight  per 
Foot  and  Rod. 

H^ 

«.to. 

E 
D 

7     Ibs.  per  rod 
10     oz.  per  foot 

6 

1     in. 

E 
D 

\Y%  Ibs.  per  foot 
2 

10 

11 

" 

C 

12      " 

8 

** 

C 

gix 

14 

" 

B 

1     Ib. 

12 

<» 

B 

gix 

17 

" 

A 

1^4  "          " 

16 

" 

A 

4 

21 

" 

AA 

I}/**  "         " 

19 

" 

AA 

24 

" 

AAA 

1%  "         *' 

27 

*« 

AAA 

g 

30 

7-16  in. 

13     oz. 

1J4  m- 

E 

2 

10 

" 

1     Ib. 

*« 

D 

12 

^!n- 

E 
D 

9     Ibs.  per  rod 
%  Ib.  per  foot 

9 

u 

C 
B 

m 

14 
16 

' 

C 

1      "         " 

11 

'• 

A 

4M 

19 

' 

B 

1M    *         " 

13 

" 

AA 

5% 

25 

' 

l^j    '         " 

" 

AAA 

6M 

' 

A 

1M    '         " 

16 

J1Z  jjl^ 

E 

3 

12 

' 

AA 

2 

19 

k« 

D 

14 

0 

AAA 

3  J    *          " 

25 

u 

C 
B 

5 

17 
19 

%™. 

E 
D 

12       «    per  rod 
'    per  foot 

8 
9 

" 

A 
AA 

f* 

23 
27 

" 

C 

1L£    '         " 

13 

'» 

AAA 

9 

" 

B 

2 

16 

1%  in. 

C 

4 

13 

' 

A 

2J^  "          " 

20 

« 

B 

17 

' 

AA 

2%  "          " 

22 

" 

A 

6V 

21 

' 

AAA 

3^  '           " 

25 

" 

AA 

8V 

27 

%  in. 

E 

1     per  foot 

8 

2     in. 

C 

4% 

15 

' 

D 

iJ4  ' 

10 

" 

B 

6 

18 

' 

C 

1%  '         " 

12 

" 

A 

7 

22 

B 

^/4  '         " 

16 

" 

AA 

9 

27 

' 

A 

3      '           " 

20 

" 

AAA 

' 

AA 

3^  ' 

23 

AAA 

4%  « 

30 

WEIGHT  OF    LEAD  PIPE  WHICH  SHOULD  BE  USED 
FOR   A  GIVEN  HEAD  OF  WATER. 

(Tatham  &  Bros.,  New  York.) 


Head  or 
Number 
of  Feet 
Fall. 

30  ft. 
50ft. 
75  ft. 
100  ft. 
150  ft. 
200  ft. 

Pressure 
per 
sq.  inch. 

Calibre  and  Weight  per  Foot. 

Letter. 

%inch. 

i^inch. 

%  inch. 

%inch. 

1  inch. 

l^in. 

15  Ibs. 
25  Ibs. 
38  Ibs. 
50  Ibs. 
75  Ibs. 
100  Ibs. 

D 
C 
B 
A 
AA 
AAA 

10     oz. 
12     oz. 
1     Ib. 
1^4  Ibs. 

\y2  ibs. 

1%  Ibs. 

Mlb. 
1      Ib. 
1J4  Ibs. 
1%  Ibs. 
2     Ibs. 
3     Ibs. 

1     Ib. 
\Y2  Ibs. 
2     Ibs. 
214  Ibs. 
2%  Ibs. 
3^  Ibs. 

1J4  Ibs. 
1%  Ibs. 
2J4  Ibs. 
3     Ibs. 
3^  Ibs. 
4%  Ibs. 

2  Ibs. 
V/2  Ibs. 
3^  Ibs. 
4  Ibs. 
4%  Ibs. 
6  Ibs. 

214  Ibs. 
3  Ibs. 
3%  Ibs. 
4%1  s. 
6  Ibs. 
6%  Ibs. 

To  find  the  thickness  of  lead  pipe  required  when  the 
head  of  water  is  given.  (Chadwick  Lead  Works). 

RULE.— Multiply  the  head  in  feet  by  size  of  pipe  wanted,  expressed  deci- 
mally, and  divide  by  750;  the  quotient  will  give  thickness  required,  in  one- 
hundredths  of  an  inch. 

EXAMPLE.— Required  thickness  of  half-inch  pipe  for  a  head  of  25  feet. 

25  X  0.50  -v-  750  =0.16  inch. 


202 


MATERIALS. 


----- 


i 


00    CO 

s 


aS 

M 


«Ot>-«Ot~O?i>-OOt—  ICO^'—  '•—  'C 
—  O*  I-  O  «O  00  O»  00  TT  T-I  OS  t-  i 
k 


1C  t^  O  t—  C 

— 


fi 

fc 


5OOOOOOC 


if 

fi  z 

r?   «^ 


o  CO  W  TH  OS  00  J>  CO  CO  O  Tl<  -^  CO  CO  OC i  OJ  OJ  Oi  T-I  T-J  TH  TH 


o 

w 


H 

H 

3 

I 


s 
I 

£ 


. 

&CV2 


_ 

o  5 

Is 

I2 


,OOT,C 


BOLT   COPPER — SHEET   AKD   BAR   BRASS. 


203 


WEIGHT  OF  ROUND  BOLT  COPPER. 

Per  Foot. 


Inches. 

Pounds. 

Inches. 

Pounds. 

Inches. 

Pounds. 

% 

.425 

1 

3.02 

s 

7.99 

1Z 

.756 

1/^c 

3.83 

1M 

9.27 

% 

1.18 

1/4 

4.72 

1% 

10.64 

ax 

1.70 

1% 

5.72 

0 

12.10 

i 

2.31 

if? 

6.81 

WEIGHT    OF    SHEET    AND    BAR    BRASS. 


Thickness, 
Side  or 
Diam. 

Sheets 
per 
sq.  ft. 

Square 
Bars  1 

ft.  long. 

Round 
Bars  1 
ft.  long. 

Thickness, 
Side  or 
Diam. 

Sheets 
per 
sq.  ft. 

Square 
Bars  1 
ft.  long. 

Round 
Bars  1 
ft.  long. 

Inches. 

Inches. 

1-16 

2.72 

.014 

.011 

1  1-16 

46.32 

4.10 

3.22 

Vs 

5.45 

.056 

.045 

m 

49.05 

4.59 

3.61 

3-16 

8.17 

.128 

.100 

1  3-16 

51.77 

5.12 

4.02 

y± 

10  90 

.227 

.178 

IH 

54.50 

5.67 

4.45 

5-16 

13.62 

.355 

.278 

1  5-16 

57.22 

6.26 

4.91 

% 

16.35 

.510 

.401 

1% 

59.95 

6.86 

5.39 

7-16 

19.07 

.695 

.545 

1  7-16 

62.67 

7.50 

5.89 

ti 

21.80 

.907 

.712 

1V6 

65.40 

8.16 

6.41 

9-16 

24.52 

1.15 

.902 

1  9-16 

68.12 

8.86 

6.95 

% 

27.25 

1.42 

1.11 

1% 

70.85 

9.59 

7.53 

11-16 

29.97 

1.72 

1.35 

1  11-16 

73.57 

10.34 

8.12 

M 

32.70 

2.04 

1.60 

1% 

76.30 

11  12 

8.73 

13-16 

35.42 

2.40 

1.88 

1  13-16 

79.02 

11.93 

9.36 

% 

38.15 

2.78 

2.18 

1% 

81.75 

12.76 

10.01 

15-16 

40.87 

3.19 

2.50 

1  15-16 

84.47 

13.63 

10.70 

1 

43.60 

3.63 

2.85 

2 

87.20 

14.52 

11.40 

COMPOSITION    OF    VARIOUS    GRADES   OF    ROLLED 
BRASS,    ETC. 


Trade  Name. 

Copper 

Zinc. 

Tin. 

Lead. 

Nickel. 

Common  high  brass        

61.5 

38  5 

Yellow  metal  

60 

40 

Cartridge  brass.               

66% 

33K 

Low  bra.ss  

80 

20/3 

Clock  brass 

60 

40 

\y2 

Drill  rod  

60 

40 

I^to2 

Spring  brass 

66% 

33*4 

\\& 

18  per  cent  German  silver  

61*5 

20^ 

18 

The  above  table  was  furnished  by  the  superintendent  of  a  mill  in  Connec- 
ticut in  1894.  He  says:  While  each  mill  has  its  own  proportions  for  various 
mixtures,  depending  upon  the  purposes  for  which  the  product  is  intended, 
the  figures  given  are  about  the  average  standard.  Thus,  between  cartridge 
brass  with  33J/3  per  cent  zinc  and  common  high  brass  with  38^  per  cent 
zinc,  there  are  any  number  of  different  mixtures  known  generally  as  "high 
brass,"  or  specifically  as  "spinning  brass,1'  "drawing  brass,"  etc.,  wherein 
*he  amount  of  zinc  is  dependent  upon  the  amount  of  scrap  used  in  the  mix- 
ture, the  degree  of  working  to  which  the  metal  is  to  be  subjected,  etc. 


204 


MATEKIALS. 


AMERICAN  STANDARD  SIZES  OF  DROP-SHOT. 


£§ 

Is 

%i 

Diameter. 

2j 

o£ 

Diameter. 

mv 

si 

Diam- 
eter. 

?i 

IS 

&* 

Is 

Fine  Dust. 

3-100" 

10784 

No.  8 

Trap  Shot 

472 

No.  2.... 

15-100" 

86 

Dust  

4-100 

4565 

8 

9-100" 

399 

1  . 

16-100 

71 

No.  12  

5-100 

2326 

7 

Trap  Shot 

338 

B... 

17-100 

59 

11  

6-100 

1346 

7 

10-100" 

291 

BB  . 

18-100 

50 

10  

Trap  Shot 

1056 

6 

11-100 

218 

BBB 

19-100 

42 

10  

7-1  00" 

848 

5 

12-100 

168 

T  .   . 

20-100 

36 

9  

Trap  Shot 

688 

4 

13-100 

132 

TT.. 

21-100 

31 

9  

8-100" 

568 

3 

14-100 

106 

F.. 

22-100 

27 

FF.. 

23-100 

24 

COMPRESSED  BUCK-SHOT. 


Diameter. 

No.  of  Balls 
to  the  Ib. 

Diameter. 

No.  of  Balls 
to  the  Ib. 

No  3 

25  100" 

284 

No  00... 

34-100" 

115 

"    2 

27-100 

232 

"    000  

C6-100 

98 

•«    1  

30-100 

173 

Balls  

38-100 

85 

"    0 

32  100 

140 

44-100 

50 

SCREW-THREADS,  SELLERS  OR  U.  S.  STANDARD. 

In  1864  a  committee  of  the  Franklin  Institute  recommended  the  adoption 
of  the  system  of  screw-threads  and  bolts  which  was  devised  by  Mr.  William 
Sellers,  of  Philadelphia.  This  same  system  was  subsequently  adopted  ar 
the  standard  by  both  ihe  Army  and  Navy  Departments  of  the  United  States, 
and  by  the  Master  Mechanics'  and  Master  Car  Builders'  Associations,  so 
that  it  may  now  be  regarded,  and  in  fact  is  called,  the  United  States  Stan 
dard. 

The  rule  given  by  Mr.  Sellers  for  proportioning  the  thread  is  as  follows  : 
Divide  the  pitch,  or,  what  is  the  same  thing,  the  side  of  the  thread,  into 
eight  equal  parts;  take  off  one  part  from  the  top  and  fill  in  one  part  in  the 
bottom  of  the  thread;  then  the  flat  top  and  bottom  will  equal  one  eighth  of 
the  pitch,  the  wearing  surface  will  be  three  quarters  of  the  pitch,  and  the 
diameter  of  screw  at  bottom  of  the  thread  will  be  expressed  by  the  for 
mula 

diameter  of  bolt  -  H^-fhi^s  per  inch' 
For  a  sharp  V  thread  with  angle  of  60°  the  formula  is 

diameter  of  bolt — — ^ — '— - — -  • 

no.  of  threads  per  inch 

The  angle  of  the  thread  in  the  Sellers  system  is  60°.    In  the  Whitworth  or 
English  system  it  is  55°,  and  the  point  and  root  of  the  thread  are  rounded. 
Screw-Threads,  United  States  Standard. 


| 

| 

a 

3 

I 

| 

0 

s 

o 

g 
S 

•8 

§ 

g 

5 

s 

q 

PH 

Q 

S 

Q 

£ 

M 

20 

% 

10 

1M 

7 

1  15-16 

5 

2  13-16 

3V, 

5-16 

18 

13-16 

10 

1  5-16 

6 

2 

41^ 

3 

& 

16 
14 

15-16 

9 
9 

jg 

6 
6 

flw 

til 

8  5-16 

IM 

^ 

13 

1 

8 

]^ 

5J^2 

2% 

4 

•^/^ 

3^4 

9-16 

12 

1  1-16 

7 

ig 

5 

21£ 

4 

3^4 

3 

% 

11 

1^£ 

7 

5 

2^4 

4 

4 

3 

11-16 

11 

U.  S.  OR  SELLERS  SYSTEM  OF  SCREW-THREADS.      205 


Screw-Tlireads,  Whitwortn  (English)  Standard. 


1 

A 

3 

| 

o3 

£ 

a 

3 

I 

a 

73 

i 

.d 
o 

ft 

S 

5 

AH 

s 

S 

ft 

P-i 

ft 

P* 

H 

20 

% 

11 

1 

8 

1% 

5 

3 

3J4 

5-16 

18 

11-16 

11 

1^ 

7 

1% 

4^3 

3!4 

3^4 

& 

16 
14 

ri,6 

10 
10 

IM 

7 
6 

2 

$ 

8« 

3M 

8* 

Yz 

12 

% 

9 

i^ 

6 

2V^ 

4 

4 

3 

9  16 

12 

15-16 

9 

1% 

5 

2% 

3^ 

U.  S.  OR  SEINERS  SYSTEM  OF  SCREW-THREADS. 


BOLTS  AND  THREADS. 

HEX.  NUTS  AND  HEADS. 

§ 

S 

"o 

5-d 

3 

*£ 

"o  a 

S  . 

sr 

gr 

j, 

f 

'ft 

H-) 

TSl 

03^4 

P5  03 
°l 

is 

& 

IS- 

s| 

eM 

sf 

a  g> 

11 

l| 

1 

|M 

S^1 

T3 

ce'o'S 

oS.c'S 

O  AH 

oS 

SS 

3W 

2^ 

c!z 

03  'o 

a;£  fi 

^3 

o 

§H 

5 

CH 

ft° 

P 

«i 

CC^'M 

02 

02 

ij 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

Ins. 

M 

20 

7l85 

.0062 

.049 

.027 

y» 

7-16 

37-64 

\A 

3-16 

7-10 

5-16 

18 

.240 

.0074 

.077 

.045 

19-38 

17-32 

11-16 

5-16 

10-12 

% 

16 

.294 

.0078 

.110 

OG8 

11-16 

% 

51-64 

s^ 

5-16 

63-64 

7-16 

14 

.344 

.0089 

.150 

.093 

25-32 

23-32 

9-10 

7-16 

8X 

1  7-64 

/^ 

13 

.400 

.0096 

.196 

.126 

% 

13-1G 

1 

Vl6 

1  15-64 

9-16 

12 

.454 

.0104 

.249 

.162 

31-32 

29-32 

jix 

9-16 

U 

1  23-64 

% 

11 

.507 

.0113 

.307 

.202 

1  1-16 

1 

17-32 

9-16 

34 

10 

.620 

.0125 

.442 

.302 

1/4 

13-16 

1  7-16 

34 

11-16 

1  19-64 

% 

9 

.731 

.0138 

.601 

.420 

1  7-16 

1  21-32 

% 

13-16 

21-32 

1 

8 

.837 

.0156 

.785 

.550 

1$6 

19-16 

1 

15-16 

2  19-64 

l^J 

7 

.940 

.0178 

.994 

.694  l'iiJ-16 

13< 

2  3-32 

m 

1  1-16 

29-16 

1^4 

7 

1.065 

.0178 

1.227 

.893 

2 

1  iu-lG 

25-16    1J| 

13-16 

2  53-64 

1% 

6 

1.160 

.0208 

1.485 

1.057 

23-16 

%y& 

2  17-32  1% 

15-16 

33-32 

ii^j 

6 

1.284 

.0208 

3   .J7 

1.295 

2% 

234         1^ 

17-16 

323-64 

i^ 

51^ 

1.389 

.0227 

2.074 

1.515 

2  9-16 

2J/> 

231-321% 

19-16 

3% 

1% 

5 

1.491 

.0250 

2.405 

1.746 

234 

2  n-16 

33-16    134 

1  11-16!  3'  57-64 

1% 

5 

1.616 

.0250 

2.761 

2.051 

2  15-16  2% 

3  13-32;  1% 

1  13-16    4  5-32 

2 

4/^2 

1.712 

.0277 

3.142 

2.302 

giz 

3  1-16 

3%        2 

1  15-16:  4  27-64 

2J4 

4J4 

1.962 

.0277 

3.976 

3.023 

3^ 

3  7-16 

4  1-16    214 

23-16 

4  61-64 

2jl 

4 

2.176 

.0312 

4.909 

3.719 

3^ 

3  13-16 

27-16 

5  31-64 

2% 

4 

2.426 

.0312 

5.940 

4.620 

iy 

43-16 

429-32234 

211-16 

6 

3 

3^ 

2.629 

.0357 

7.069 

5.428 

4% 

49-16 

5%         3 

2  15-16 

6  17-32 

3/4 

3^2.879 

.0357 

8.296 

6.510 

5 

415-16 

5  13-16  3»4 

33-16 

71-16 

3V<2 

3143.100 

.0384 

9.621 

7.548 

53/£ 

5  5-16 

67-64    3^ 

37-16 

7  39-64 

3^4 

3     13.317 

.0413 

11.045 

8.  641  15^4 

5  11-1C 

621-323% 

3  11-16 

4 

3     3.567 

.0413  12.566 

9.9i)3i6^ 

61-16 

73-32    4 

315-16    841-64 

4/4 

2%  (3.  798 

.0435  14.186 

11.329 

6^ 

67-16 

4  3-16     9  3-16 

41^ 

2344.028 

.0454  15.904 

12.743 

6% 

6  13-16 

7  31-32  4j| 

4  7-16     9  % 

434 

2%  4.  256 

.0476  17.721 

14.226 

73-16 

8  13-32  434 

411-1610^4 

5 

2^4.480 

.0500  19.635 

15.763 

7^ 

7  9  16 

8  27-32  5 

4  15-16  10  49-84 

5^4 

21^4.730 

.050021.648 

17.572 

8 

7  15-16 

99-32    514 

53-16    11  23-64 

5^J2 

2%  4.  953 

.0526:23.758 

19.267 

83/£ 

85-16 

9  23-32  514 

57-16    11% 

534 

2%  5.  203 

.052625.967 

21.262 

834 

811-16 

105-32    534 

5  11-16  12% 

6 

2J4i5.423  .0555  28.274 

23.098 

9^ 

91-16 

10  19-32  6 

5  15-16  1215-16 

I 

L.IMIT  GAUGES    FOR    IRON   FOR  SCREW    THREADS. 

In  adopting  the  Sellers,  or  Franklin  Institute,  or  United  States  Standard, 
as  it  is  variously  called,  a  difficulty  arose  from  the  fact  that  it  is  the  habit 
of  iron  manufacturers  to  make  iron  over- size,  and  as  there  are  no  over-size 


206 


MATERIALS. 


screws  in  the  Sellers  system,  if  iron  is  too  large  it  is  necessary  to  cut  it  away 
with  the  dies.  So  great  is  this  difficulty,  that  the  practice  of  making  taps 
and  dies  over-size  has  become  very  general.  If  the  Sellers  system  is  adopted 
it  is  essential  that  iron  should  be  obtained  of  the  correct  size,  or  very  nearly 
so.  Of  course  no  high  degree  of  precision  is  possible  in  rolling  iron,  and 
when  exact  sizes  were  demanded,  the  question  arose  how  much  allowable 
variationjthere  should  be  f  rom  the  true  size.  It  was  proposed  to  make  limit- 
gauges  for  inspecting  iron  with  two  openings,  one  larger  and  the  other 
smaller  than  the  standard  size,  and  then  specify  that  the  iron  should  enter 
the  large  end  and  not  enter  the  small  one.  The  following  table  of  dimen- 
sions for  the  limit-gauges  was  recommended  by  the  Master  Car-Builders' 
Association  and  adopted  by  letter  ballot  in  1883. 


Size  of 

Size  of 

Size  of 

Size  of 

Size  of 

Large 

Small 

Differ- 

Size of 

Large 

Small 

Differ- 

Iron. 

End  of 

End  of 

ence. 

Iron. 

End  of 

End  of 

ence. 

Gauge. 

Gauge. 

Gauge. 

Gauge. 

Min. 

0.2550 

0.2450 

0.010 

%in. 

0.6330 

0.6170 

0.016 

5-16 

0.3180 

0.3070 

0.011 

&£ 

0.7585 

0.7415 

0.017 

% 

0.3810 

0.3690 

0.012 

% 

0.8840 

0.8660 

0.018 

7-16 

0.4440 

0.4310 

9.013 

1 

1.0095 

0.9905 

0.019 

^ 

0.5070 

0.4930 

0.014 

1^ 

1  .  1350 

1.1150 

0.020 

9-16 

0.5700 

0.5550 

0.015 

1M 

1.2605 

1.2395 

0.021 

Caliper  gauges  with  the  above  dimensions,  and  standard  reference  gauge,'; 
for  testing  them  are  made  by  the  Pratt  &  Whitney  Co. 

THE    MAXIMUM    VARIATION    IN    SIZE    OF     ROUGItt 
IRON    FOR    U.    S.    STANDARD    BOLTS. 

Am.  Mack.,  May  12,  1892. 

By  the  adoption  of  the  Sellers  or  U.  S.  Standard  thread  taps  and  dies  keb{ 
their  size  much  longer  in  use  when  flatted  in  accordance  with  this  system 
than  when  sharp,  though  it  has  been  found  advisable  in  practice  in  moaV 
cases  to  make  the  taps  of  somewhat  larger  outside  diameter  than  the  nom- 
inal size,  thus  carrying  the  threads  further  towards  the  V-shape  and  giving 
corresponding  clearance  to  the  tops  of  the  threads  when  in  the  nuts  or 
tapped  holes. 

Makers  of  taps  and  dies  often  have  calls  for  taps  and  dies,  U.  S.  Standard 
"  for  rough  iron." 

An  examination  of  rough  iron  will  show  that  much  of  it  is  rolled  out  of 
round  to  an  amount  exceeding  the  limit  of  variation  in  size  allowed. 

In  view  of  this  it  may  be  desirable  to  know  what  the  extreme  variation  hi 
iron  may  be,  consistent  with  the  maintenance  of  U.  S.  Standard  threads,  i.e., 
threads  which  are  standard  when  measured  upon  the  angles,  the  only  plact; 
where  it  seems  advisable  to  have  them  fit  closely.  Mr.  Chas.  A.  Baiier,  the 
general  manager  of  the  Warder,  Bushnell  &  Glessner  Co.,  at  Springfield, 
Ohio,  iu  1884  adopted  a  plan  which  may  be  stated  as  follows :  All  bolts, 
whether  cut  from  rough  or  finished  stock,  are  standard  size  at  the  bottom 
and  at  the  sides  or  angles  of  the  threads,  the  variation  for  fit  of  the  nut  and 
allowance  for  wear  of  taps  being  made  in  the  machine  taps.  Nuts  are 
punched  with  holes  of  such  size  as  to  give  85  per  cent  of  a  full  thread,  expe- 
rience showing  that  the  metal  of  wrought  nuts  will  then  crowd  into  the 
threads  of  the  taps  sufficiently  to  give  practically  a  full  thread,  while  if 
punched  smaller  some  of  the  metal  will  be  cut  out  by  the  tap  at  the  bottom 
of  the  threads,  which  is  of  course  undesirable.  Machine  taps  are  mnde 
enough  larger  than  the  nominal  to  bring  the  tops  of  the  threads  up  sharp, 
plus  the  amount  allowed  for  fit  and  wear  of  taps.  This  allows  the  iron  to 
be  enough  above  the  nominal  diameter  to  bring  the  threads  up  full  (sharp; 
at  top,  while  if  it  is  small  the  only  effect  is  to  give  a  flat  at  top  of  threads  ; 
neither  condition  affecting  the  actual  size  of  the  thread  at  the  point  at  which 
it  is  intended  to  bear.  Limit  gauges  are  furnished  to  the  mills,  by  which  the 
iron  is  rolled,  the  maximum  size  being  shown  in  the  third  column  of  the 
table.  The  minimum  diameter  is  not  given,  the  tendency  in  rolling  being 
nearly  always  to  exceed  the  nominal  diameter. 

In  making  the  taps  the  threaded  portion  is  turned  to  the  size  given  in  the 
eighth  column  of  the  table,  which  gives  6  to  7  thousandths  of  an  inch  allow- 
ance for  fit  and  wear  of  tap.  Just  above  the  threaded  portion  of  the  tap  a 


SIZES  OF  SCREW-THREADS  FOR  BOLTS  AND  TAPS.   207 


place  is  turned  to  the  size  given  in  the  ninth  column,  these  sizes  being  the 
same  as  those  of  the  regular  U.  S.  Standard  bolt,  at  the  bottom  of  the 
thread,  plus  the  amount  allowed  for  fit  and  wear  of  tap  ;  or,  in  other  words, 
d'  =  U.  S.  Standard  d  +  (D'  —  D).  Gauges  like  the  one  in  the  cut,  Fig. 
72,  are  furnished  for  this  sizing.  In  finishing  the  threads  of  the  tap  a  tool 


FIG.  72. 

is  used  which  has  a  removable  cutter  finished  accurately  to  gauge  by  grind- 
ing, this  tool  being  correct  U.  S.  Standard  as  to  angle,  and  flat  at  the  point. 
It  is  fed  in  and  the  threads  chased  until  the  flat  point  just  touches  the  por- 
tion of  the  tap  which  has  been  turned  to  size  d'.  Care  having  been  taken 
with  the  form  of  the  tool,  with  its  grinding  on  the  top  fac^  (a  fixture  being 
provided  for  this  to  insure  its  being  ground  properly),  and  also  with  the  set- 
ting of  the  tool  properly  in  the  lathe,  the  result  is  that  the  threads  of  the  tap 
are  correctly  sized  without  further  attention. 

It  is  evident  that  one  of  the  points  of  advantage  of  the  Sellers  system  is 
sacrificed,  i.e.,  instead  of  the  taps  being  flatted  at  the  top  of  the  threads 
they  are  sharp,  and  are  consequently  not  so  durable  as  they  otherwise  would 
be  ;  but  practically  this  disadvantage  is  not  found  to  be  serious,  and  is  far 
overbalanced  by  the  greater  ease  of  getting  iron  within  the  prescribed 
limits  ;  while  any  rough  bolt  when  reduced  in  size  at  the  top  of  the  threads, 
by  filing  or  otherwise,  will  fit  a  hole  tapped  with  the  U.  S.  Standard  hand 
taps,  thus  affording  proof  that  the  two  kinds  of  bolts  or  screws  made  for  the 
two  different  kinds  of  work  are  practically  interchangeable.  By  this  sj'stem 
\"  iron  can  be  .005"  smaller  or  .0108"  larger  than  the  nominal  diameter,  or,  • 
in  other  words,  it  may  have  a  total  variation  of  .0158",  while  \\"  iron  can  be 
.0105"  smaller  or  .0309"  larger  than  nominal — a  total  variation  of  .0414" — 
and  within  these  limits  it  is  found  practicable  to  procure  the  iron. 
STANDARD  SIZES  OF  SCREW-THREADS  FOR  BOLTS 
AND  TAPS. 
(CHAS.  A.  BAUER.) 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

A 

n 

D 

d 

h 

/ 

D'-D 

D' 

d' 

H 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches 

M 

20 

.2608 

.1855 

.0379 

.0062 

.006 

.2668 

.1915 

.2024 

5-16 

18 

.3245 

.2403 

.0421 

.0070 

.006 

.3305 

.2463 

.2589 

% 

16 

.3885 

.2938 

.0474 

.0078 

.006 

.3945 

.2998 

.3139 

7-16 

14 

.4530 

.3447 

.0541 

.0089 

.006 

.4590 

.3507 

.3670 

& 

13 

12 

.5166 
.5805 

.4000 
.4543 

.0582 
.0631 

.0096 
.0104 

.006 
.007 

.5226 

.5875 

.4060 
.4613 

.4236 
.4802 

% 

11 

.6447 

.5069 

.0689 

.0114 

.007 

.6517 

.5139 

.5346 

3^ 

10 

.7717 

.6201 

.0758 

.0125 

.007 

.7787 

.6271 

.6499 

H 

9 

.8991 

.7307 

.0842 

.0139 

.007 

.9061 

.7377 

.7630 

8 

1.0271 

.8376 

.0947 

.0156 

.007 

1.0341 

.8446 

.8731 

i/^ 

7 

1.1559 

.9394 

.1083 

.0179 

.007 

1.1629 

.9464 

.9789 

1*4 

7 

1.2809 

1.0644 

.1083 

.0179 

.007 

1.2879 

1.0714 

1.1039 

.4  =  nominal  diameter  of  bolt. 

D  =  .4  +  -—  • 

D  =  actual  diameter  of  bolt. 

n 

d  —  diameter  of  bolt  at  bottom  of 

d       1      1'2"04 

thread. 

n 

.7577      D-d 

/  =  flat  of  bottom  of  thread. 

n     '         2     ' 

.125 

h  =  depth  of  thread. 

n  ' 

D'  and  d'  —  diameters  of  tap. 

H-  D'      1-288  -  D'       85(2h  > 

H  =  hole  in  nut  before  tapping. 

n     ~            •    t    •/ 

208 


MATERIALS. 


STANDARD  SET-SCREWS  AND  CAP-SCREWS. 

American,  Hartford,  and  Worcester  Machine-Screw  Companies. 
(Compiled  by  W.  S.  Dix.) 


(A) 

(B) 

(C) 

(D) 

(E) 

(F) 

(G) 

Diameter  of  Screw  — 

^ 

3-16 

H 

5-16 

% 

7-16 

L/' 

Threads  per  Inch  
Size  of  Tap  Drill*  

40 
No.  43 

24 

No.  30 

20 
No.  5 

18 
17-64 

21-64 

14 

27-64 

(H) 

(D 

(J) 

(K) 

(L) 

(M) 

(N) 

Diameter  of  Screw..  .  . 

9-16 

% 

M 

% 

1 

u^ 

114 

Threads  per  Inch  
Size  of  Tap  Drill*  .... 

12 
31-64 

11 
17-32 

10 
21-32 

9 
49-64 

8 

7 
63-64 

7 

Set  Screws. 

Hex.  Head  Cap-screws. 

Sq. 

Head  Cap-screws, 

Short 
Diam 
of  Head 

Long 
Diam. 
of  Head 

Lengths 
(under 
Head). 

Short 
Diam. 
of 
Head. 

Long 
Diam, 
of 
Head. 

Lengths 
(under 
Head). 

Short 
Diam. 
of 
Head. 

Long 
Diam. 
of 
Head. 

Lengths 
(under 
Head). 

(C)    M 

.35 

Mto 

3 

7-16 

.51 

%  to  3 

3^ 

.53 

to  3 

(D)  5-16 

.44 

%  to  3^4 

V 

$ 

.58 

94  to  314 

7-16 

.62 

"54 

to  3^4 

(E)    % 

.53 

M  to  314 

9- 

16 

.65 

%to3^ 

/^ 

.71 

:K 

(F)  7-16 

.62 

94  to 

m 

^ 

f 

.72 

94  to 

•'>•"•, 

9-1 

5 

.80 

M 

to  3% 

(G)  y2 

(H)9-16 

.71 
.80 

%  to  4 

M  to  414 

1*36 

.87 
.94 

94  to  4 
94  to  414 

11-16 

.89 
.98 

%  to  4 

%to4H 

(I)     % 

.89 

M  tc 

4V*> 

7, 

XH 

1.01 

1  to 

IL, 

M 

1.06 

1 

to  4V<2 

(J)     % 

.06 

1      to  4% 

1.15 

1^4  to  4% 

% 

1.24 

1  '  } 

to  4% 

(K)    % 

.24 

1*4  to  5 

Jl 

g 

1.30 

1^  to  5 

11^ 

1.60 

1   '    0 

to  5 

(L)    1 
(M)  \ys 

.42 

.60 

1^  to  5 
1%  to  5 

1^ 

I 

1.45 
1.59 

194  to  5 
2  to  5 

*% 

1.77 
1.95 

3 

to  5 
to  5 

(N)    1*4 

.77 

2      to  5 

| 

2 

1.73 

2  to  5 

m 

2.13 

** 

to  5 

Round  and  Filister  Head 
Cap-screws. 

Flat  Head  Cap-screws. 

Button-head  Cap- 
screws. 

Diam.  of 
Head. 

Lengths 
(under 
Head). 

Diam.  of 
Head. 

Lengths 
(including 
Head). 

Diam.  of 
Head. 

Lengths 
(under 
Head). 

(A)      3-16 

9£to2i 

4, 

^ 

MtoL 

7-32  (.225) 

%t 

ol% 

(B)       Y± 

%to2« 

% 

%  to  2 

5 

-16 

H  t 

D2 

(C)       % 

%  to  3 

is 

>-32 

%to2 

/\ 

7 

-16 

M  t 

0214 

(D)      7-16 

%to3M 

^ 

M 

9-16 

94  1 

o2U 

(E)      9-16 

(F)       % 

94  to  3i 

94  to  3« 

% 

1$6 

%  to  3 
1  to  3 

H 

94  to  29! 
%  to  3 

(G)      M 

M  to  4 

% 

114  to  3 

13 

-16 

1  1 

o3 

(H)    13-16 

1  to  4 

tf 

j 

15-16 

1^4  to  3 

(1)         % 

1J4  to  4 

2 

jix 

13£  to  3 

1 

1^  to  3 

(J)          1 

1^4  to  4 

^4 

1% 

f2  to  3 

1 

14 

1%  to  3 

(K)       1^ 

1%  to  5 

(M       1M 

2  to  5 

*  For  cast  iron.    For  numbers  of  twist-drills  see  p.  29. 

Threads  areU.  S.  Standard.  Cap  screws  are  threaded  %  length  up  to  and 
including  1"  diam.  x  4"  long,  and  ^  length  above.  Lengths  increase  by  J4" 
each  regular  size  between  the  limits  given.  Lengths  of  heads,  except  flat 
and  button,  equal  diam.  of  screws. 

The  angle  of  the  cone  of  the  flat-head  screw  is  76°,  the  sides  making  angles 
of  52°  with  the  top. 


STANDAKD   MACHINE   SCREWS. 


209 


STANDARD  MACHINE:  SCREWS. 

(Am.  Screw  Co.'s  Catalogue,  1883,  1892.) 


No. 

Threads  per 
Inch. 

Diam.  of 
Body. 

Diam. 
of  Flat 
Head. 

Diam.  of 
Round 
Head. 

Diam.  of 
Filister 
Head. 

Lengths. 

From 

To 

2 

56 

.0842 

.1631 

.1544 

.1332 

3-16 

X 

3 

48 

.0973 

.1894 

.1786 

.1545 

3-16 

% 

4 

32,  36,  40 

.1105 

.2158 

.2028 

.1747 

3-16 

M 

5 

32,  3fi,  40 

.1236 

.2421 

.2270 

.1985 

3-16 

% 

6 

30,  32 

.1368 

.2684 

.2512 

.2175 

3-16 

i 

7 

30,32 

.1500 

.2947 

.2754 

.2392 

/4 

\\^ 

8 

30,  32 

.1631 

.3210 

.2936 

.2610 

/4 

1% 

9 

24,  30,  32 

.1763 

.3474 

.3238 

.2805 

24 

]% 

10 

24,  30,  32 

.1894 

.3737 

.3480 

.3035 

/4 

ji^j 

12 

20,  24 

.2158 

.4263 

.3922 

.3445 

a/ 

1M 

14 

20,  24 

.2421 

.4790 

.4364 

.3885 

% 

2 

16 

16,  18,  20 

.2684 

.5316 

.4866 

.4300 

% 

2J4 

18 

16,  18 

.2947 

.5842 

.5248 

.4710 

n 

2^ 

20 

16,  18 

.3210 

.6308 

.5690 

.5200 

234 

22 

16,  18 

.3474 

.6894 

.6106 

.5557 

L£ 

3 

24 

14,  16. 

.3737 

.7420 

.6522 

.6005 

Hi 

3 

26 

14,  16 

.4000 

.7420 

.6938 

.6425 

M 

3 

28 

14,  16 

.4263 

.7946 

.7354 

.6920 

% 

3 

30 

14,  16 

.4520 

.8473 

.7770 

.7240 

1 

3 

Lengths  vary  by  16ths  from  3-16  to  ^,  by  Sths  from  ^  to  1^,  by  4ths  from 
U£  to  3. 

SIZES  AND  WEIGHTS    OF   SQUARE  AND 

HEXAGONAL    NUTS. 

United  States  Standard  Sizes.    Chamfered  and  trimmed. 
Punched  to  suit  U.  S.  Standard  Taps. 


1 

'o 
K 

* 

11 

Square. 

Hexagon. 

CM 

1 

lis 

fi^ 

§ 

A 

8 

& 

O 

g 

4 

3 

o 

55? 

§  ® 

$! 

G    72 

«! 

S 

3 

o 

i 

i 
S 

I 

^^ 

1^ 

i* 

o""1 

^'•a 

D 

£> 

k 

13-64 

11-16         9-16 

7270 

.0138 

7615 

.0131 

5-16 

19-32 

5-16 

k 

13-16 

11-16 

4700 

.0231 

5200 

.0192 

% 

11-16 

a/ 

19-64 

1 

13-16 

2350 

.0426 

3000 

.0333 

7-16 

25-32 

7-16 

11-32 

1630 

.0613 

2000 

.050 

LJ£ 

% 

25-64 

Ik 

1  8 

1120 

.0893 

1430 

.070 

9-16 

31-32 

9-16 

29-64 

1% 

ji^ 

890 

.1124 

1100 

.091 

% 

1  1-16 

% 

33-64 

jiz 

^k 

640 

.156 

740 

.135 

M 

Ik 

M 

39-64 

1% 

1    7-16 

380 

.263 

450 

.222 

% 

1  7-16 

% 

47-64 

2    1-16 

1  11-16 

280 

.357 

309 

.324 

i 

1% 

1 

53-64 

2    5-16 

1% 

170 

.588 

216 

.463 

1  13-16 

59-64 

2    9-jJ6 

2    1-16 

130 

.769 

148 

.676 

k 

2 

ik 

1     1-16 

2  13-16 

2    5-16 

96 

1.04 

111 

.901 

•  % 

2  3-16 

1% 

1     5-32 

31^ 

2J^> 

70 

1.43 

85 

1.18 

^ 

2% 

\\^ 

1    9-32 

3% 

2M 

58 

1.72 

68 

1.47 

% 

2  9-16 

]% 

1  13-32 

3% 

2  15-16 

44 

2.27 

56 

1.79 

M 

2% 

iM 

ji^ 

37X 

3    3-16 

34 

2.94 

40 

2.50 

1% 

2  15-16 

1% 

1% 

41^ 

3% 

30 

3.33 

37 

2.70 

2 

31^ 

2 

1  23-32 

4    7-16 

3% 

23 

4.35 

29 

3.45 

2k 

31^2 

2^4 

1  15-16 

4  15-16 

4    1-16 

19 

5.26 

21 

4.76 

2^ 

37^ 

2^ 

2    3-16 

41^ 

12 

8.33 

15 

6.67 

2H 

4k 

2% 

2    7-16 

6  2 

4  15-16 

9 

11.11 

11 

9.09 

3 

4% 

3 

8N 

6^ 

5    5-16 

VA 

13.64 

^ 

11.76 

210 


MATERIALS. 


WEIGHTS    OF   100   BOLTS  WITH    SQUARE    HEADS 

AND    NUTS. 

(Hoopes  &  Townsend's  List.) 


Length  un- 
der Head 
to  Point. 

Diameter  of  Bolts. 

Y±  in.  5-16  in. 

fcin. 

7-16  in. 

V$in. 

%in. 

»in. 

%in. 

lin. 
Ibs. 

1H 

f 

| 
P 

3^ 
4 

? 

* 
^ 

I* 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

Per  inch 
additional. 

Ibs. 
4.00 
4.35 
4.75 
5.15 
5.50 
5.75 
6.25 
7.00 
7.75 
8.50 
9.25 
10.00 
10.75 

Ibs. 
7.00 
7.50 
8.00 
8.50 
9.00 
9.50 
10.00 
11.00 
12.00 
13.00 
14.00 
15.00 
16.00 

Ibs. 
10.50 
11.25 
12.00 
12.75 
13.50 
14.25 
15.00 
16.50 
18.00 
19.50 
21.00 
22.50 
24.00 
25.50 
27.00 
28.50 
30.00 

Ibs. 
15.20 
16.30 
17.40 
18.50 
19.60 
20.70 
21.80 
24.00 
26.20 
28.40 
30.60 
32.80 
35.00 
37.20 
39.40 
41.60 
43.80 
46.00 
48.20 
50.40 
52.60 

Ibs. 
22.50 
23.82 
25.15 
26.47 
27.80 
29.12 
30.45 
33.10 
35.75 
38.40 
41.05 
43.70 
46.35 
49.00 
51.65 
54.30 
59.60 
64.90 
70.20 
75.50 
80.80 
86.10 
91.40 
96.70 
102.00 
107.30 
112.60 
117.90 
123.20 

5.45 

Ibs. 
39.50 
41.62 
43.75 
45.88 
48.00 
50.12 
52.25 
56.50 
60.75 
65.00 
69.25 
73.50 
77.75 
82.00 
86.25 
90.50 
94.75 
103.25 
111.75 
120.25 
128.75 
137.25 
145.75 
154.25 
162.75 
171.00 
179.50 
188.00 
206.50 

8.52 

Ibs. 
63.00 
66.00 
69.00 
72.00 
75.00 
78.00 
81.00 
87.00 
93.10 
99.05 
105.20 
111.25 
117.30 
123.35 
129.40 
135.00 
141.50 
153.60 
165.70 
177.80 
189.90 
202.00 
214.10 
226.20 
238.30 
250.40 
262.60 
274.70 
286.80 

12.27 

Ibs. 

109.00 
113.25 
117.50 
121.75 
126.00 
134.25 
142.50 
151.00 
159.55 
168.00 
176.60 
185.00 
193.65 
202.00 
210.70 
227.75 
224.80 
261.85 
278.90 
295.95 
313.00 
330.05 
347.10 
364.15 
381.20 
398.25 
415.30 

16.70 

163 
169 
174 
180 
185 
196 
207 
218 
229 
240 
251 
262 
273 
284 
295 
317 
339 
360 
382 
404 
426 
448 
470 
492 
514 
536 
558 

21.82 

j-1.37 

2.13 

3.07 

4.18 

TRACK  BOLTS. 

Wiili   United  States  Standard  Hexagon  Nuts. 


Rails  used. 

Bolts. 

Nuts. 

No.  in  Keg, 
200  Ibs. 

Kegs  per  Mile. 

f 

%x4H 

iS 

230 

6.3 

^x4 

1/4 

240 

6. 

45  to  85  Ibs... 

\ 

%x3^ 
Mx3Vl 

if* 

254 
260 

5.7 
5.5 

\ 

M  x  3^4 

18 

266 

5.4 

I 

%x3 

m 

283 

5.1 

30  to  40  Ibs.  .  . 

i 

%x3^ 
%x3 

1  1-16 
1  1-16 
1  1-16 

375 
410 
435 

4. 
3.7 
3.3 

I 

%x2^j 

1  1-16 

465 

3.1 

r 

1^x3 

% 

715 

2. 

20  to  30  Ibs... 

i 

y2*ly4 

Vs 
% 

760 
800 

2. 
2. 

I 

ijx2 

Vs 

820 

2. 

HUTS  AND   BOLT-HEADS— KIVETS. 


211 


WEIGHTS  OF   NUTS   AND   BOLT-HEADS,   IN  POUNDS. 

For  Calculating  the  Weight  of  Longer  Bolts. 


Diameter  of  Bolt,  in  Inches. 

H 

H 

% 

% 

% 

% 

Weight  of  hexagon  nut  and  head. 
Weight  of  square  nut  and  head  .  . 

.017 
.021 

.057 
.069 

.128 
.164 

.267 
.320 

.43 
.55 

.73 

.88 

Diameter  of  Bolt,  in  Inches. 

1 

1M 

itf. 

m 

2 

2H 

3 

Weight  of  hexagon  nut  and  head. 
Weight  of  square  nut  and  head.. 

1.10 
1.81 

2.14 

2.56 

3.78 
4.42 

5.6 
7.0 

8.75 
10.5 

17 

21 

28.8 
36.4 

NUMBER   OF   RIVETS  IN   1OO   POUNDS. 


Lengths 

%in. 

7-16  in. 

J$in. 

9-16  in. 

fcin. 

11-16  in. 

Kin. 

%in. 

H 

1965 

1419 

1092 

944 

665 

% 

1848 

1335 

1027 

846 

597 

YC, 

1692 
1512 

1222 

1092 

940 

840 

763 
726 

538 
512 

450 
415 

1 

m 

m 

3  4 
4  4 

1437 
1368 
1300 
1260 
1200 
1156 
1100 
1031 
999 
945 
900 
828 
779 
743 
715 

1036 
988 
949 
924 
900 
840 
789 
744 
721 
682 
650 
598 
562 
536 
513 

797 
760 
730 
711 
693 
648 
608 
573 
555 
525 
500 
460 
433 
413 
395 

691 
653 
624 
596 

511 
502 
491 
475 
443 
411 
379 
352 
341 
326 

487 
460 
440 
420 
390 
375 
360 
354 
347 
335 
312 
290 
267 
248 
241 
230 

389 
370 
357 
340 
325 
312 
297 
289 
280 
260 
242 
224 
212 
201 
192 
184 

356 
329 
280 
271 
262 
257 
243 
237 
232 
220 
208 
197 
180 
169 
160 
158 

228 
211 
180 
174 
169 
165 
156 
152 
149 
141 
133 
127 
115 
108 
102 
99 

312 

220 

177 

150 

96 

4V/ 

298 

210 

171 

146 

94 

434 

284 

200 

166 

138 

89 

5 

270 

190 

161 

135 

87 

5U 

256 

180 

156 

130 

84 

5U 

244 

172 

151 

124 

80 

5M 

233 

164 

145 

120 

6 

223 

157 

140 

115 

74 

6J4 

213 

150 

138 

111 

71 

6Va 

207 

146 

134 

107 

69 

203 

143 

129 

104 

67 

7 

198 

140 

125 

100 

64 

TURNBUCKLES. 

Turnbuckles  with  right  and  left  threads  are  made  of  standard  sizes.    B  — 


Fio.  73. 

diameter  of  bolt,  O  =  6  'inches  in  all  sizes  of  turnbuckle.    H  =  length  of 
tapped  heads  =  1*4  B.    L=  length  =  6  inches  -f  3  B. 


212 


MATERIALS. 


SIZES  OF   WASHERS. 


Diameter  in 
inches. 

Size  of  Hole,  in 
inches. 

Thickness, 
Birmingham 
Wire-gauge. 

Bolt   in 
inches. 

No.  in  100  Ibs. 

% 

5-16 

No.  16 

H 

29,300 

% 

% 

"    16 

5—16 

18,000 

1 

7-16 

•    14 

% 

7,600 

1/4 

9-16 

11 

/4 

3,300 

1/4 

^ 

11 

9-16 

2,180 

1/4 

11-16 

11 

% 

2,350 

1M 

13-16 

11 

% 

1,680 

2 

31-32 

10 

% 

1,140 

2/4 

1/^6 

8 

1 

580 

254 

1/4 

8 

1/^3 

470 

3 

1% 

7 

1/4 

360 

3 

ig 

"      6 

1% 

360 

TRACK   SPIKES. 


Rails  used. 

Spikes. 

Number  in  Keg, 
200  Ibs. 

Kegs  per  Mile, 
Ties  24  in. 
between  Centres. 

45  to  85 

5^x9-16 

380 

30 

40  "  52 

5     x  9-16 

400 

27 

35  "  40 

5     x^ 

490 

22 

24  "  35 

41^  x  1^ 

550 

20 

24  "  30 

412  x  7-16 

725 

15 

18  "  24 

4     x7-16 

820 

13 

16  "  20 

3^x% 

1250 

9 

14  "  16 

3     x% 

1350 

8 

8  "  12 

31^  xak 

1550 

7 

8  "  10 

2^x5-1  6 

2500 

5 

STREET  RAILWAY  SPIKES. 


Spikes. 

Number  in  Keg,  200  Ibs. 

Kegs  per  Mile,  Ties  24  in. 
between  Centres. 

5^x9-16 
5     x^ 
4J4  x  7-16 

400 
575 
800 

30 
19 
13 

BOAT    SPIKES. 

Number  in  Keg  of  200  Ibs. 


Length. 

H 

5-16 

% 

H 

4  inch. 

2375 

5   ' 

2050 

1230 

940 

6   * 

7   * 

1825 

1175 
990 

800 
650 

450 
375 

8   ' 

880 

600 

335 

9   * 

525 

300 

10   ' 

475 

275 

SPIKES;  CUT  NAILS. 


213 


WROUGHT    SPIKES. 

Number  of  Nails  in  Keg  of  15O  Pounds. 


Size. 

Mm. 

6-16  in. 

«in. 

7-16  in. 

Kin] 

3  inches 

2250 

3/^      ••  • 

1890 

1208 

4        

1650 

1135 

4^ 

1464 

1064 

f 

1380 

930 

742 

0        .  . 

1292 

868 

570 

7 
8       

1161 

662 
635 

482 
455 

445 

384 

306 
256 

9       

573 

424 

300 

240 

10       ..  .. 

391 

270 

222 

11 

249 

203 

12 

236 

180 

WIRE    SPIKES. 


Size. 

Approx.  Size 
of  Wire  Nails. 

Ap.  No. 
in  1  Ib. 

Size. 

Approx.  Size 
of  Wire  Nails. 

Ap.  No. 
in  1  Ib. 

lOd  Spike  .... 

3     in.  No.  7 

50 

60d  Spike  

6     in.  No.  1 

10 

16d      "      

3&           '    6 

35 

6^  in."      

6^    "     "    1 

9 

20d       "       

4               '    5 

26 

7      li  "       .   ... 

7       "    **    0 

7 

30d      *'       

4^           '    4 

20 

8      "  "       

8       "    "    00 

5 

40d      "      ...    . 

5               '3. 

15 

9      *'  "       

9       "    "    00 

4^ 

50d      "       

5^           '    2 

12 

LENGTH   AND  NUMBER  OF   CUT  NAILS   TO  THE 
POUND. 


Size. 

X) 

"So 

5 

Common. 

Clinch. 

§ 

s 

0) 

ft 

Finishing. 

§ 

fe 

Barrel. 

Casing. 

S 

Tobacco. 

Cut  Spikes. 

%     . 

%  in 

800 

%-.' 

500 

2d  

1 

800 

1100 

1000 

376 

3d.  .  . 

\\A 

480 

720 

760 

224 

4d  

ll/2 

288 

523 

368 

180 

398 

5d  

m 

200 

410 

130 

6d....  

i9* 

1G8 

95 

81 

268 

224 

126 

96 

7d  

214 

124 

74 

64 

188 

98 

82 

8d  

m 

88 

62 

•1R 

146 

128 

75 

68 

9d  

$ 

70 

53 

Rfi 

130 

110 

65 

10d  

3 

58 

46 

SO 

102 

91 

55 

28 

12d  

3J4 

44 

42 

94 

76 

71 

40 

16d  

m 

34 

38 

°0 

62 

54 

27 

22 

20d  

4 

23 

33 

16 

54 

40 

141^ 

30d  

4^ 

18 

90 

33 

40d 

5 

14 

27 

qtV 

50d  

5U 

10 

8/J< 

60d  

6 

8 

fi 

214 


MATERIALS. 


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216 


MATERIALS. 


SIX  1C,  WEIGHT,  LENGTH,  AND    STRENGTH  OF  IRON 
WIRE. 

(Trenton  Iron  Co.) 


No.  by 
Wire 
Gauge. 

Diam. 
in  Deci- 
mals of 
One 

Area  of 
Section  in 
Decimals  of 
One  Inch. 

Feet  to 
the 
Pound. 

Weight  of 
One  Mile 
in  pounds. 

Tensile  Strength  (Ap- 
proximate) of  Charcoal 
Iron  Wire  in  Pounds. 

Inch. 

Bright. 

Annealed. 

00000 

.450 

.15904 

1.863 

2833.248 

12598 

9449 

0000 

.400 

.12566 

2.358 

2238.878 

9955 

7466 

000 

.360 

.10179 

2.911 

1813.574 

8124 

6091 

00 

.330 

.08553 

3.465 

1523.861 

6880 

5160 

0 

.305 

.07306 

4.057 

1301.678 

5926 

4445 

1 

.285 

.06379 

4.645 

1136.678 

5226 

3920 

2 

.265 

.05515 

5.374 

982  555 

4570 

3425 

3 

.245 

.04714 

6.286 

839.942 

3948 

2960 

4 

.225 

.03976 

7.454 

708.365 

3374 

2530 

5 

.205 

.03301 

8.976 

588.1  3Q 

2839 

2130 

6 

.190 

.02835 

10.453 

505.084 

2476 

1860 

7 

.175 

.02405 

12.322 

428.472 

2136 

1600 

8 

.160 

.02011 

14.736 

358.3008 

1813 

1360 

9 

.145 

.01651 

17.950 

294.1488 

1507 

1130 

10 

.130 

.01327 

22.333 

236.4384 

1233 

925 

11 

.1175 

.01084 

27.340 

193.1424 

1010 

758 

12 

.105 

.00866 

34.219 

154.2816 

810 

607 

13 

.0925 

.00672 

44  092 

119.7504 

631 

473 

14 

.080 

.00503 

58.916 

89.6016 

474 

356 

15 

.070 

.00385 

7(5.984 

68.5872 

372 

280 

16 

.061 

.00292 

101.488 

52.0080 

292 

220 

17 

.0525 

.00216 

137.174 

38.4912 

222 

165 

18 

.045 

.00159 

186.335 

28.3378 

169 

127 

19 

.040 

.0012566 

235.084 

22.3872 

137 

103 

20 

.035 

.0009621 

308.079 

17.1389 

107 

80 

21 

031 

.0007547 

392.772 

13  4429 

22 

.028 

.0006157 

481.234 

10.9718 

«  0  2"      af      £ 

23 

.025 

.0004909 

603.863 

8.7437 

e??  §     $:   G::      ~ 

24 

.0225 

.0003976 

745.710 

7.0805 

£    J2<w^    ~ 

25 

.020 

.0003142 

943.396 

5.5968 

~MI5'Q  °S3S**    ** 

26 

.018 

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1164.689 

4.5334 

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27 

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1305.670 

4.0439 

^      "g  g       O^_§  go  £ 

28 

.016 

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1476.869 

3.5819 

§^3  £J  cu-^ci  o^S     '^ 

29 

.015 

.0001767 

1676.989 

3.1485 

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30 

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1925.321 

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d     S^'cl  d.061*^     E 

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32 

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4182.508 

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36 

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.00006362 

4657.728 

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37 

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5222.035 

.0111 

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6724.291 

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£<urt«>'$^§Oa'     § 

41 

.007 

.00003848 

7698.253 

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Hf^    M  - 

TESTS   OF  TELEGRAPH   WIKE. 


217 


GALVANIZED  IRON  WIRE  FOR  TELEGRAPH  AND 
TELEPHONE  LINES. 

(Trenton  Iron  Co.) 

WEIGHT  PER  MILE-OHM.—  This  term  is  to  be  understood  as  distinguishing 
the  resistance  of  material  only,  and  means  the  weight  of  such  material  re- 
quired per  mile  to  give  the  resistance  of  one  ohm.  To  ascertain  the  mileage 
resistance  of  any'wire,  divide  the  "weight  per  mile-ohm  "  by  the  weight  of 
the  wire  per  mile.  Thus  in  a  grade  of  Extra  Best  Best,  of  which  the  weight 
per  mile-ohm  is  5000,  the  mileage  resistance  of  No.  6  (weight  per  mile  525 
Ibs.)  would  be  about  9^5  ohms;  and  No.  14  steel  wire,  6500  Ibs.  weight  per 
mile-ohm  (95  Ibs.  weight  per  mile),  would  show  about  69  ohms. 

Sizes  of  Wire  used  in  Telegraph  and  Telephone  Lines. 

No.  4.  Has  not  been  much  used  until  recently;  is  now  used  on  important 
lines  where  the  multiplex  systems  are  applied. 

No.  5.  Little  used  in  the  United  States. 

No.  6.  Used  for  important  circuits  between  cities. 

No.  8.  Medium  size  for  circuits  of  400  miles  or  less. 

No.  9.  For  similar  locations  to  No.  8,  but  on  somewhat  shorter  circuits  ; 
until  lately  was  the  size  most  largely  used  in  this  country. 

Nos.  10,  11.  For  shorter  circuits,  railway  telegraphs,  private  lines,  police 
and  fire-alarm  lines,  etc. 

No.  12.  For  telephone  lines,  police  and  fire-alarm  lines,  etc. 

Nos.  13,  14.  For  telephone  lines  and  short  private  lines:  steel  wire  is  used 
most  generally  in  these  sizes. 

The  coating  of  telegraph  wire  with  zinc  as  a  protection  against  oxidation 
is  now  generally  admitted  to  be  the  most  efficacious  method. 

The  grades  of  line  wire  are  generally  known  to  the  trade  as  "  Extra  Best 
Best  "  (E.  B.  B.),  "  Best  Best  "  (B.  B.).  and  "Steel." 

"  Extra  Best  Best  "  is  made  of  the  very  best  iron,  as  nearly  pure  as  any 
commercial  iron,  soft,  tough,  uniform,  and  of  very  high  conductivity,  its 
weight  per  mile-ohm  being  about  5000  Ibs. 

The  "  Best  Best11  is  of  iron,  showing  in  mechanical  tests  almost  as  good 
results  as  the  E.  B.  B.,  but  not  quite  as  soft,  and  being  somewhat  lower  in 
conductivity;  weight  per  mile-ohm  about  5700  Ibs. 

The  Trenton  "  Steel  "  wire  is  well  suited  for  telephone  or  short  telegraph 
lines,  and  the  weight  per  mile-ohm  is  about  6500  Ibs. 

The  following  are  (approximately)  the  weights  per  mile  of  various  sizes  of 
galvanized  telegraph  wire,  drawn  by  Trenton  Iron  Co.'s  gauge: 

8, 


4,        5,        6,        7, 


9,        10,      11, 


Lbs.    720,    610,    525,    450,    375,    310,    250, 


13,      14. 
160,     125,     95. 


TESTS  OF  TELEGRAPH  WIRE. 

The  following  data  are  taken  from  a  table  given  by  Mr.  Prescott  relating 
to  tests  of  E.  B.  B.  galvanized  wire  furnished  the  Western  Union  Telegraph 
Co.: 


Size 
of 
Wire. 

Diam. 
Parts  of 
One 
Inch. 

Weight. 

Length. 
Feet 
per 
pound. 

Resistance. 
Temp.  75.8°  Fahr. 

Ratio  of 
Breaking 
Weight  to 
Weight 
per  mile. 

Grains, 
per  foot. 

Pounds 
per  mile. 

Feet 
per  ohm. 

Ohms 
per  mile. 

4 

.238 

1043.2 

886.6 

6.00 

958 

5.51 

5 

.220 

891.3 

673.0 

7.85 

727 

7.26 

6 

.203 

758.9 

572.2 

9.20 

618 

8.54 

3.05 

7 

.180 

596.7 

449.9 

11.70 

578 

10.86 

3.40 

8 

.165 

501.4 

378.1 

14.00 

409 

12.92 

3.07 

9 

.148 

403.4 

304.2 

17.4 

328 

16.10 

3.38 

10 

.134 

330.7 

249.4 

21.2 

269 

19.60 

3.37 

11 

.120 

265.2 

200.0 

26.4 

216 

24.42 

2.97 

12 

.109 

218.8 

165.0 

32.0 

179 

29.60 

3.43 

14 

.083 

126.9 

95.7 

55.2 

104 

51.00 

3.05 

JOINTS  IN  TELEGRAPH  WT  IRES.— The  fewer  the  joints  in  a  line  the  better. 
All  joints  should  be  carefully  made  and  well  soldered  over,  for  a  bad  joint 
may  cause  as  much  resistance  to  the  electric  current  as  several  miles  of 
wire. 


218 


MATERIALS. 


ROr-JO 


ti 

w 


fe 

O 

a 


tl 

I 


^8 
fej 

*?** 

§s 

§1 
ii 


O 

% 
to 

- 

g 


I 


-^^^^x^c.r?:^s^rt 

>OO-*-*«CS»i-l«O^t^C^r^'X 


§§§1 


»»OSQC7i~-C--='- 

Jl-i-^CJ-^rHCl^LS 


DIMENSIONS,  WEIGHT,  RESISTANCE  OF  COPPER  WIRE.  2 


s= 


a 


H 


PQ 


.  —    ~  - .  - 


a  ^  -*  cc 

940  —  iN 


\i 


Oocoot~<x 


•< 
-    « 


S?Sow^S^»oSw«5^»^wS§gS«^SS»82wM^SS| 


220 


MATERIALS. 


8 

B 


• 

si 


• 

H« 
=  | 


o 


.§3^§SSS«SSSco^^ 


^rtoSia-^Nt-^-r-OOOCO^OlO^O 


3>  •*  i-H  OS  05  0»  05  OS  l«  00  O  *?  00  r-(  l«  t-  ^  ^  ^H  <N  CC 

HOQecw'^«'t>oi*}idoicr-ioocoo-4t^r-Icc«ocot^-*o6t^ 

r-n-4(N(N«O->*tiC«OOOOS<?«OOiOO}O'-i-5;t-i 


«SSS55SS 


«o-*t^     «o     ifteo-^^os         I-HCJ«^QC  1-1^  as '-JO5  t^;g  *?«o  co  t^c^  ^o§ 


llllll 


HARD-DKAWN   COPPEE   WIRE;    INSULATED   WIRE.     221 


HARD-DRAWN  COPPER  TELEGRAPH  WIRE. 

(J.  A.  Roebling's  Sons  Co.) 
Furnished  in  half-mile  coils,  either  bare  or  insulated. 


Size,  B.  &  S. 
Gauge. 

Resistance  in 
Ohms 
per  Mile. 

Breaking 
Strength. 

Weight 
per  Mile. 

Approximate 
Size  of  E.B.  B. 
Iron  Wire 
equal  to 
Copper. 

9 

4.30 

625 

209 

2     t? 

10 

5.40 

525 

166 

3     § 

11 

6.90 

420 

131 

4     I 

12 

8.70 

330 

104 

6  a 

13 

10.90 

270 

83 

6^3 

14 

13.70 

213 

66 

8     Q 

15 

17.40 

170 

52 

9     2 

16 

22.10 

130 

41 

10    <g 

CD 

In  handling  this  wire  the  greatest  care  should  be  observed  to  avoid  kinks, 
bends,  scratches,  or  cuts.  Joints  should  be  made  only  with  Mclntire  Con- 
nectors. 

On  account  of  its  conductivity  being  about  five  times  that  of  Ex.  B.  B. 
Iron  Wire,  and  its  breaking  strength  over  three  times  its  weight  per  mile, 
copper  may  be  used  of  which  the  section  is  smaller  and  the  weight  less  than 
an  equivalent  iron  wire,  allowing  a  greater  number  of  wires  to  be  strung  on 
the  poles. 

Besides  this  advantage,  the  reduction  of  section  materially  decreases  the 
electrostatic  capacity,  while  its  non-magnetic  character  lessens  the  self-in- 
duction of  the  line,  both  of  which  features  tend  to  increase  the  possible 
speed  of  signalling  in  telegraphing,  and  to  give  greater  clearness  of  enunci- 
ation over  telephone  lines,  especially  those  of  great  length. 
INSULATED    COPPER    WIRES. 
Weight  per  10OO  feet. 


«s, 

«3 

«O 

Weather- 
proof 
Line 
Wire. 

Under- 
writers1 
Line 
Wire. 

o58> 

*§ 
MO 

Weather- 
proof 
Line 
Wire. 

Under- 
writers' 
Line 
Wire. 

»& 

$1 

pqO 

Weather- 
proof 
Line 
Wire. 

Under- 
writers' 
Line 
Wire. 

0000 
000 
00 
0 

1 

2 
3 
4 

671. 
537. 
426. 
342. 
274. 
220. 
178. 
141. 

701. 
565. 
447. 
364. 
294. 
241. 
185. 
147. 

5 
6 

8 
9 
10 
11 
12 

115. 
93. 
77. 
64. 
53. 
44. 
37. 
30. 

121. 
99. 
80. 
67. 
54. 
45. 
37. 
31. 

13 
14 
15 
16 
17 
18 
19 
20 

26. 
20.5 
17. 
14. 
12. 
10.75 
9. 
7.5 

26.5 
22. 
20. 
15. 
13. 
11. 
10. 
8. 

LEAD-ENCASED  ANTI-INDtJCTION  TELEPHONE  AND 
TELEGRAPH  CABLES.      (Roebling's.) 


PLAIN  CABLES,  LEAD 
ENCASED. 

FOR  METALLIC  CIRCUIT. 

FOR  TELEGRAPH  CIR- 
CUITS. 

No.  of 
Wires. 

Size  Wire 
B.  &  S.  Gauge. 

No.  of 
Pairs. 

Size  Wire 
B.  &  S.  Gauge. 

No.  of 
Wires. 

Size  Wire 
B.  &  S.  Gauge. 

4 

10 
50 
100 

18 
18 
18 
•18 
18 

5 
15 
25 
50 
75 

18 
18 
18 
18 
18 

3 

4 
7 
10 
20 
50 
100 

14 
14 
14 
14 
14 
14 
14 

222 


MATERIALS. 


FLEXIBLE  CABLES. 


Area 
Circ. 
Mils. 

No.  of 
Wires. 

Size 
Wire 
B.&S. 
Gauge. 

Approxim- 
ate Size  of 
Equivalent 
Solid  Wire. 

Area 
Circ. 
Mils. 

No.  of 
Wires. 

Size 
Wire 
B.&S. 
Gauge. 

m 

v'ti^ 

Ifl* 

|&gi 

15699.6 

49 

25 

8  B.  &  S. 

272410.6 

133 

17 

522. 

24963.0 

49 

23 

6 

433154.4 

133 

15 

658 

39693.9 

49 

21 

4        « 

688727.2 

133 

13 

830. 

63116.9 

49 

19 

2 

868-176.7 

133 

12 

932. 

1095145.3 

133 

11 

1016. 

210964.6 

103 

17 

459. 

420127.2 

129 

15 

649. 

657656.8 

127 

13 

811. 

835827.2 

128 

12 

914. 

1062198.9 

129 

11 

1035. 

WEATHERPROOF  AERIAL  CABLES. 


No.  of  Con- 

Weight per 
Conductor 

No.  of  Con- 

Weight per 
Conductor 

No.  of  Con- 

Weight per 
Conductor 

ductors. 

per  1000 

ductors. 

per  1000 

ductors. 

'       per  1000 

feet. 

feet. 

feet. 

1 

10.75  Ibs. 

8 

9.25  Ibs. 

15 

9.25  Ibs. 

2 

18.00 

9 

9.25     " 

16 

9.25    " 

3 

13.00 

10 

9.25     " 

17 

9.25     " 

4 

10.75 

11 

9.25     " 

18 

9.25     " 

5 

10.00 

12 

9  25     k< 

19 

9.25     " 

6 

9.50 

13 

9.25     " 

20 

9.25     " 

7 

9.25 

14 

9.25     " 

LEAD-ENCASED  ELECTRIC-LIGHT  CABLES. 
Single  Wires. 

(J.  A.  Koebling's  Sons  Co.) 


Size, 
B.&S. 
Gauge. 

Diameter 
of  Solid  Cop- 
per Wire. 
Mils. 

Area. 
Circular 
Mils. 

Nearest  Ap- 
proximate 
Birming- 
ham Wire- 
gauge  No. 

Approxi- 
mate 
Weight 
pei*  Foot 
of  Cable. 
Oz. 

Approxi- 
mate 
Diameter 
of  Cable. 
Mils. 

20 

31.96 

1021. 

21 

1.63 

170 

19 

35.39 

1252. 

20 

1.70 

175 

18 

40.30 

1624. 

19 

1.75 

180 

17 

45.25 

2048. 

18^ 

1.84 

185 

16 

50.82 

2583. 

18 

3.00 

245 

15 

57.07 

3257. 

17 

3.20 

250 

14 

64.08 

4107. 

16 

3.38 

255 

13 

71.96 

5178. 

15 

3.56 

265 

12 

80.80 

6530. 

14 

5.00 

310 

11 

90.74 

8234. 

13^ 

5.23 

320 

10 

101.89 

10381. 

12^ 

5.68 

335 

9 

114.23 

13094. 

11^2 

5.95 

345 

8 

128.49 

16509. 

10^2 

6.35 

360 

7 

144.28 

20816. 

9 

6.90 

375 

As  tested  by  the  Bell  Telephone  Co.  of  Philadelphia,  the  insulation  may 
be  stated  at  2000  megohms  per  mile,  \uth  an  electrostatic  capacity  of  .14 
microfarad. 


STEEL  WIRE   CABLES. 


223 


GALVANIZED   STEEL-WIRE   STRAND. 

For  Smokestack  Guys,  Signal  Strand,  etc. 

(J.  A.  Roebling's  Sons  Co.) 
This  strand  is  composed  of  7  wires,  twisted  together  into  a  single  strand. 


c 

£  . 

•a 

. 

3J  . 

T3 

m 

s 

P-tu 

-«  &*5 

CO 

0) 

&"£ 

•2  c  5 

u 

1 

£fe 

S"5  S 

% 

1 

Sfe 

|5  B 

P 

g 

If 

•^3  a>  ^ 

^ 

.5 

•So 

*-2  g  ^ 

*• 

s 

SW^Q 

£> 

ft 

£T 

HPQr^ 

iii. 

Ibs. 

Ibs. 

in. 

Ibs. 

Ibs. 

No.  8 

HJ 

52 

8.320 

No.  15 

/4 

10 

1,600 

9 

15-32 

42 

6,720 

16 

7-32 

8 

1,280 

10 

7-16 

36 

5,720 

17 

3-16 

6 

960 

1  ! 

^8 

29 

4.640 

18 

11-64 

4  3-10 

688 

li? 

5-16 

21 

3,360 

19 

9-64 

3  3-10 

528 

13 

9-32 

16 

2,580 

20 

J^ 

2  4-10 

384 

14 

17-64 

12 

1,920 

21 

3-32 

2 

320 

For  special  purposes  these  strands  can  be  made  of  50  to  100  per  cent 
greater  tensile  strength.  When  used  to  run  over  sheaves  or  pulleys  the  use 
of  soft-iron  stock  is  advisable. 

FLEXIBLE  STEEL-WIRE  CABLES  FOR  VESSELS. 
(Trenton  Iron  Co.,  1886.) 

With  numerous  disadvantages,  the  system  of  working  ships'  anchors  with 
chain  cables  is  still  in  vogue.  A  heavy  chain  cable  contributes  to  the  hold- 
ing-power of  the  anchor,  and  the  facility  of  increasing  that  resistance  by 
paying  out  the  cable  is  prized  as  an  advantage.  The  requisite  holding- 
power  is  obtained,  however,  by  the  combined  action  of  a  comparatively 
light  anchor  and  a  correspondingly  great  mass  of  chain  of  little  service  in 
proportion  to  its  weight  or  to  the  weight  of  the  anchor.  If  the  weight  and 
size  of  the  anchor  were  increased  so  as  to  give  the  greatest  holding-power 
required,  and  it  were  attached  by  means  of  a  light  wire  cable,  the  combined 
weight  of  the  cable  and  anchor  would  be  much  less  than  the  total  weight  of 
the  chain  and  anchor,  and  the  facility  of  handling  would  be  much  greater. 
English  shipbuilders  have  taken  the  initiative  in  this  direction,  and  many  of 
the  largest  and  most  serviceable  vessels  afloat  are  fitted  with  steel-wire 
cables.  They  have  given  complete  satisfaction. 

The  Trenton  Iron  Co/s  cables  are  made  of  crucible  cast-steel  wire,  and 
guaranteed  to  fulfil  Lloyd's  requirements.  They  are  composed  of  72  wires 
subdivided  into  six  strands  of  twelve  wires  each.  In  order  to  obtain  great 
flexibility,  hempen  centres  are  introduced  in  the  strands  as  well  as  in  the 
completed  cable. 

FLEXIBLE  STEEL-WIRE  HAWSERS. 

These  hawsers  are  extensively  used,  They  are  made  with  six  strands  of 
twelve  wires  each,  hemp  centres  being  inserted  in  the  individual  strands  as 
well  as  in  the  completed  rope.  The  material  employed  is  crucible  cast  steel, 
galvanized,  and  guaranteed  to  fulfil  Lloyd's  requirements.  They  are  only 
one  third  the  weight  of  hempen  hawsers;  arid  are  sufficiently  pliable  to  work 
round  any  bitts  to  which  hempen  rope  of  equivalent  strength  can  be  applied. 

13-inch  tarred  Russian  hemp  hawser  weighs  about  39  Ibs.  per  fathom. 

10-inch  white  manila  hawser  weighs  about  20  Ibs.  per  fathom. 

1^-inch  stud  chain  weighs  about  08  Ibs.  per  fathom. 

4-inch  galvanized  steel  hawser  weighs  about  12  Ibs.  per  fathom. 

Each  of  the  above  named  has  about  the  same  tensile  strength. 


224 


MATERIALS. 


SPECIFICATIONS  FOR  GALVANIZED  IRON  WIRE. 

Issued,  by  the  British  Postal  Telegraph  Authorities. 


Weight  per  Mile. 

Diameter. 

Tests  for  Strength  and 
Ductility. 

^•d  s-* 

72 

£ 

"o 

1 
.22 

"o 
g 

go 

25 

III 

•Q  U 

•g 

p  P 

Allowed. 

1 

Allowed. 

IH 

&£ 

JQ 

.SsP  1 

H| 

1. 

H| 

1?1 

|| 

p 

CO 

p 

1| 

^.3 

'5  c 

"o  p 

"53  g 

'o  p 

tc«  ® 

&JC^ 

GC 

1 

CQ^ 

d 

^^ 

d 

^rP 

0*  " 

?  oS 

Qj 

& 

& 

fcUD^ 

523 

tc-^ 

2 

.9    CD 

p  'Jl 

•^•s 

'3 

p 

| 

'3 

S 

§ 

| 

a 

1" 

g* 

g 

B 

g 

|§ 

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5 

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p 
1 

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PQ 

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"a 

><! 

'5 

'B 

o 

'p 

0 

p 

M 

Q 

§ 

CO 

s 

i 

1 

§ 

fe 

s 

fa 

s 

1 

Ibs. 

Ibs. 

Ibs. 

mils. 

mils. 

mils. 

Ibs. 

Ibs. 

Ibs. 

ohms. 

800 

767 

833 

242 

237 

247 

2480 

15 

2550 

14 

2620 

13 

6.75 

5400 

600 

571 

629 

209 

204 

214 

1860 

17 

1910 

16 

1960 

15 

9.00 

5400 

450 

424 

477 

181 

176 

186 

1390 

19 

1  4--.>r> 

18 

1460 

17 

12.00 

5400 

400 

377 

424 

171 

166 

176 

1240 

21 

1270 

20 

1300 

19 

13.50 

5400 

200 

190 

213 

121 

118 

125 

620 

30 

638 

28 

655 

26 

27.00 

5400 

STRENGTH  OF  PIANO-WIRE. 

The  average  strength  of  English  piano- wire  is  given  as  follows  by  Web' 
ster,  Horsf als  &  Lean : 


Numbers 

Equivalents 

Ultimate 

Numbers 

Equivalents 

Ultimate. 

in  Music- 

in  Fractions 

Tensile 

in  Music- 

in  Fractions 

Tensile 

wire 

of  Inches  in 

Strength  in 

wire 

of  inches  in 

Strength  in 

Gauge. 

Diameters. 

Pounds. 

Gauge. 

Diameters. 

Pounds. 

12 

.029 

225 

18 

.041 

395 

13 

.031 

250 

19 

.043 

425 

14 

.033 

285 

20 

.045 

500 

15 

.035 

305 

21 

.047 

540 

16 

.037 

340 

22 

.052 

650 

17 

.039 

360 

These  strengths  range  from  300,000  to  340,000  Ibs.  per  sq.  in.  The  compo- 
sition of  this  wire  is  as  follows:  Carbon,  0.570;  silicon,  0.090;  sulphur,  0.011; 
phosphorus,  0.018;  manganese,  0.425. 

«  PLOUGH "-STEEI,   WIRE. 

The  term  "plough,"  given  in  England  to  steel  wire  of  high  quality,  was 
derived  from  the  fact  that  such  wire  is  used  for  the  construction  of  ropes 
used  for  ploughing  purposes.  It  is  to  be  hoped  that  the  term  will  not  be 
used  in  this  country,  as  it  tends  to  confusion  qf  terms.  Plough-steel  is 
known  here  in  some  steel- works  as  the  quality  of  plate  steel  used  for  the 
mould-boards  of  ploughs,  for  which  a  very  ordinary  grade  is  good  enough. 

Experiments  by  Dr.  Percy  on  the  English  plough-steel  (so-called)  gave  the 
following  results:  Specific  gravity,  7.814;  carbon,  0.828  per  cent;  manga- 
nese, 0.587  per  cent;  silicon,  0.143  per  cent;  sulphur,  0.009  per  cent;  phos- 
phorus, nil;  copper,  0.030  per  cent.  No  traces  of  chromium,  titanium,  or 
tungsten  were  found.  The  breaking  strains  of  the  wire  were  as  follows: 

Diameter,  inch 093  .132  .159  .191 

Pounds  per  sq.  inch 344,960       257,600       224,000       201,600 

The  elongation  was  only  from  0.75  to  1.1  per  cent. 


SPECIFICATIONS  FOR  HAKD-DRAWX  COPPER  WIRE.   225 


WIRES  OF  DIFFERENT  METALS  AND  ALLOYS. 

(J.  Bucknall  Smith's  Treatise  on  Wire.) 

Brass  Wire  is  commonly  composed  of  an  alloy  of  1  3/4  to  2  parts  of 
copper  to  1  part  of  zinc.  The  tensile  strength  ranges  from  20  to  40  tons  per 
square  inch,  increasing  with  the  percentage  of  zinc  in  the  alloy. 

German  or  Nickel  Silver,  an  alloy  of  <•<  pper,  zinc,  and  nickel,  is 
practically  brass  whitened  by  the  addition  of  nickel.  It  has  been  drawn  into 
wire  as  fine  as  ,002"  diam. 

Platinum  wire  may  be  drawn  into  the  finest  sizes.  On  account  of  its 
high  price  its  use  is  practically  confined  to  pecia!  scientific  instruments  and 
electrical  appliances  in  which  resistances  to  high  temperature,  oxygen,  and 
acids  are  essential.  It  expands  less  than  other  metals  when  heated,  whicn 
property  permits  its  bein<?  sealed  in  glass  without  fear"  of  cracking.  It  is 
therefore  used  in  incandescent  electric  lamps. 

Phosphor-bronze  Wire  contains  from  2  to  6  per  cent  of  tin  and 
from  1/20  to  1/8  per  cent  of  phosphorus.  The  presence  of  phosphorus  is 
detrimental  to  electric  conductivity. 

"  Delta-metal  "  wire  is  made  from  an  alloy  of  copper,  iron,  and  zinc. 
Its  strength  ranges  from  45  to  62  tons  per  square  inch.  It  is  used  for  some 
kinds  of  wire  rope,  also  for  wire  gauze.  It  is  not  subject  to  deposits  of  ver- 
digris. It  has  great  toughness,  even  when  its  tensile  strength  is  over  60 
tons  per  square  inch. 

Aluminum  Wire.  —  Specific  gravity  .268.  Tmsile  strength  only 
about  10  tons  per  square  inch.  It  has  been  drawn  as  fine  as  11,400  yards  to 
the  ounce,  or  .042  grains  per  yard, 

Aluminum  Bronze,  90  copper,  10  aluminum,  has  7  igh  strength  and 
ductility;  is  inoxidizable,  sonorous.  Its  electric  conductivity  is  12.6  per  cent 
of  that  of  pure  copper. 

Silicon  Bronze,  patented  in  1882  by  L.  Weiler  of  Paris,  is  made  as 
follows:  Fluosilicate  of  potash,  pounded  glass,  chloride  of  sodium  and  cal- 
cium, carbonate  of  soda  and  lime,  are  heated  in  a  plumbago  crucible,  and 
ufter  the  reaction  takes  place  the  contents  are  thrown  into  the  molten 
bronze  to  be  treated.  Silicon-bronze  wire  has  a  conductivity  of  from  40  to  • 
98  per  cent  of  that  of  copper  wire  and  four  times  more  than  thajt  of  iron, 
while  its  tensile  strength  is  nearly  that  of  steel,  or  28  to  55  tons  per  square 
iaoh  of  section.  The  conductivity  decreases  as  the  tensile  strength  in- 
creases. Wire  whose  conductivity  equals  >5  per  cent  of  that  of  pure  copper 
gives  a  tensile  strength  of  28  tons  per  square  inch,  but  when  its  conductivity 
h*  34  per  cent  of  pure  copper,  its  strength  is  50  tons  per  square  inch.  It  is 
being  largely  used  for  telegraph  wires.  Ii  Ins  great  resistance  to  oxidation. 

Ordinary  Drawn  and  Annealed  Copper  Wire  has  a  strength 
f\t  from  15  to  20  tons  per  square  inch. 

SPECIFICATIONS  FOR  HARD-DRAWN  COPPER 
WIRE. 

The  British  Post  Office  authorities  require  that  hard-drawn  copper  wire 
supplied  to  them  shall  be  of  the  lengths,  sizes,  weights,  strengths,  and  con- 
ductivities as  set  forth  in  the  annexed  table. 


be 

^^ 

Weight  per  Stalute 
Mile. 

Approximate  Equiva- 
lent Diameter. 

1 

^•1 

111 

|fa. 

o>  ^ 

!§w 

2*5.6 

^|.§ 

pco 

^*d 

g 

s 

-g 

d 

o 

'  g'S 

~  fl 

c  &,  ^  ^ 

=  ^<w 

"3T3 

3 
1 

d 

1 

1 
d 

05 

3 

£ 
o 

'x 

'5 

!§•- 

1111 

«GG 

i 

CO 

^ 

^ 

i 

^H 

s 

S 

Ibs. 

Ibs. 

Ibs. 

mils. 

mils. 

mils. 

Ibs. 

ohms. 

Ibs. 

100 
150 
200 

146^| 
195 

102^ 

153% 
205 

79 
97 
112 

78 
95)4 
110K> 

80 
98 

330 

490 
650 

30 
25 
20 

9.10 
6.05 
4.53 

50 
50 
50 

400 

390 

410 

158 

155K2 

160^ 

1300 

10 

2.27 

50 

226 


MATERIALS. 


WIRE   ROPES. 

List  adopted  by  manufacturers  in  1892.    See  pamphlets  of  Trenton  Iron 
Co.,  John  A.  Roebling's  Sons  Co.,  and  other  makers. 

Pliable  Hoisting  Rope. 

With  6  strands  of  19  wires  each. 
IRON. 


B 

c      , 

CM 

s  « 

1 

0 

§ 

p3 

'§"" 

c'o 

'%  a 

0 
O       s3 

II 

| 

2 

**     8* 

OQO 

oo 

^^  of  • 

O  D 

1 

Diameter 

Circumf* 
inches. 

|§1. 

.i.    02 

s§ 

M 

•SJ 

ftOJO 

2  °8 

^Sj'si 

lals 

Min.  Size 
or  Sheav 

1 

2*4 

6% 

8.00 

74 

15 

14 

13 

2 

2 

6 

6.30 

65 

13 

13 

12 

3 

1^ 

51^ 

5.25 

54 

11 

12 

10 

4 

1% 

5 

4.10 

44 

9 

11 

5 

l/'ij 

454 

3.65 

39 

8 

10 

71^ 

51^ 

1% 

4% 

3.00 

33 

glZ 

nix 

7 

6 

1/4 

4 

2.50 

27 

51^ 

8^ 

6^ 

7 

Jl^c 

3/^ 

2.00 

20 

4 

7J^ 

6 

8 

1 

3/^ 

1.58 

16 

3 

gi^ 

5/4 

9 

2M 

1.20 

11.50 

51^ 

4Vi» 

10 

% 

2J4 

0.88 

8.64 

1% 

4% 

4 

9-16 

2 

0.60 
0.44 

5.13 
4.27 

!g 

3M 

% 

10% 

/^ 

1^ 

0.35 

3.48 

3  a 

2^4 

10a 

7-16 

1% 

0.29 

3.00 

a^ 

2% 

2 

10% 

% 

iH 

0.26 

2.50 

5 

2H 

IK 

CAST   STEEL. 


1 

^A 

6^ 

8.00 

155 

31 

2 

2 

6 

6.30 

125 

25 

8 

3 

5.25 

106 

21 

714 

4 

1% 

5 

4.10 

86 

17 

15 

gix 

5 

\\^ 

4^4 

3.65 

77 

15 

14 

55/ 

5)4 

1% 

4^2 

3.00 

63 

12 

13 

5^ 

6 

1J4 

4 

2.50 

52 

10 

12 

5 

7 

ji^ 

2.00 

42 

8 

11 

41^ 

8 

1 

3/^ 

1.58 

33 

6 

9^ 

4 

9 

% 

2% 

1.20 

25 

5 

8J^ 

3/^ 

10 

^ 

2*4 

0.88 

'      18 

3^ 

7 

3 

% 

2 

0.60 

12 

21^ 

5% 

2^4 

10  % 

9-16 

\0/fa 

0.44 

9 

1^ 

5 

1% 

IOM 

^ 

1^> 

0.35 

7 

1 

4^> 

1^1 

10a 

7-16 

1% 

0.29 

51^3 

M 

3% 

1/4 

% 

i« 

0.26 

4« 

g 

3« 

1 

Cable-Traction  Ropes. 

According  to  English  practice,  cable-traction  ropes,  of  about  3^  in.  in 
circumference,  are  commonly  constructed  with  six  strands  of  seven  or  fif- 
teen wires,  the  lays  in  the  strands  varying  from,  say,  3  in.  to  3^£  in.,  and  the 
lays  in  the  ropes  from,  say,  7^  in.  to  9  in.  In  the  United  States,  however, 
strands  of  nineteen  wires  are  generally  preferred  as  being  more  flexible; 
but,  on  the  other  hand,  the  smaller  external  wires  wear  out  more  rapidly. 
The  Market  street  Street  Railway  Company,  San  Francisco,  has  used  ropes 
1J4  i°-  m  diameter,  composed  of  six  strands  of  nineteen  steel  wires,  weighing 
2lj  Ibs.  per  foot,  the  longest  continuous  length  being  24,125  ft.  The  Chicago 
City  Railroad  Company  has  employed  cables  of  identical  construction,  the 
longest  length  being  27,700  ft.  On  the  New  York  and  Brooklyn  Bridge  cable- 
railway  steel  ropes  of  11,500  ft.  long,  containing  114  wires,  have  been  used. 


WIRE   EOPES. 


227 


Transmission  and  Standing  Rope. 

With  6  strands  of  7  wires  each. 
IRON. 


I 

o 


<D  A 


£*o< 
t.  -s  «   . 


a  4* 

ii 

IS 


11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 


•*/» 

ft 


3.37 
2.77 
2.28 
1.82 
1.50 
1.12 
0.88 
0.70 
0.57 
0.41 
0.31 
0.23 
0.19 
0.16 
0.125 


36 
30 
25 
20 
16 

12.3 

8.8 

7.6 

5.8 

4.1 

2.83 

2.13 

1.65 

1.38 

1.03 


CAST  STEEL. 


11 

yx 

4% 

3.37 

62 

13 

13 

8^ 

12 

1^ 

414 

2.77 

52 

10 

12 

8 

13 

1J4 

m 

2.28 

44 

9 

11 

7/4 

14 

l/^ 

3% 

1.82 

36 

7^ 

10 

6^ 

15 

i 

3 

1.50 

30 

6 

9 

5% 

16 

% 

2% 

1.12 

22 

4/^£ 

8 

5 

17 

% 

m 

0.88 

17 

3^> 

7 

4^ 

18 

11-16 

0.70 

14 

3  ~ 

6 

4 

19 

££ 

i|| 

0.57 

11 

2/4 

5tf 

3/^j 

20 

'9-16 

0.41 

8 

1M 

4% 

3 

21 

V£ 

]% 

0.31 

6 

]i^ 

4 

2^ 

22 

7-16 

\\/s 

0.23 

41^ 

\\A 

3^ 

2V4 

23 

% 

\\/fa 

0.19 

4 

1 

314 

2 

24 

5-16 

\ 

0.16 

3 

34 

234 

1^4 

25 

9-32 

% 

0.12 

2 

K3 

2^ 

18 

Plough-Steel  Rope. 

Wire  ropes  of  very  high  tensile  strength,  which  are  ordinarily  called 
"Plough-steel  Ropes,"  are  made  of  a  high  grade  of  crucible  steel,  which, 
when  put  in  the  form  of  wire,  will  bear  a  strain  of  from  100  to  150  tons  per 
square  inch. 

Where  it  is  necessary  to  use  very  long  or  very  heavy  ropes,  a  reduction  of 
the  dead  weight  of  ropes  becomes'a  matter  of  serious  'consideration. 

It  is  advisable  to  reduce  all  bends  to  a  minimum,  and  to  use  somewhat 
larger  drums  or  sheaves  than  are  suitable  for  an  ordinary  crucible  rope  hav- 
ing a  strength  of  60  to  80  tons  per  square  inch.  Before  using  Plough-steel 
Ropes  it  is  best  to  have  advice  on  the  subject  of  adaptability. 


228 


MATERIALS. 


Plough-Steel  Rope. 

With  6  strands  of  19  wires  each. 


Trade 
Number. 

Diameter  in 
inches. 

Weight  pei- 
foot  in 
pounds. 

Breaking 
Strain  in 
tons  of 
2000  Ibs. 

Proper  Work- 
ing Load. 

Min.  Size  of 
Drum  or 
Sheave  in 
feet. 

1 

2^ 

8.00 

240 

46 

9 

2 

2 

6.30 

189 

37 

8 

3 

1M 

5.25 

157 

31 

~M 

4 

i^ 

4.10 

123 

25 

6 

5 

1^4 

3.65 

110 

22 

5^ 

5^ 

•]% 

3.00 

90 

18 

5^ 

6 

51^ 

2.50 

75 

15 

5 

7 

ji^ 

2.00 

60 

12 

4J/J2 

8 

i 

1.58 

47 

9 

4J4 

9 

% 

1.20 

37 

7 

m 

10 

% 

0.88 

27 

5 

m 

10J4 

% 

0.60 

18 

m 

3 

10^ 

9-16 

0.44 

13 

2 

2^ 

10% 

J* 

0.85 

10 

m 

2 

Witli  7  Wires  to  the  Strand. 


15 

1 

1.50 

45 

9 

5^ 

16 

% 

1.12 

33 

6/-13 

5 

17 

H 

0.88 

25 

4^ 

4 

18 

11-16 

0  70 

21 

4 

3^ 

19 

% 

0.57 

16 

3M 

3 

20 

9-16 

0.41 

12 

2 

m 

21 

y* 

0.31 

9 

]i^ 

y& 

22 

7-16 

0.23 

5 

3/ 

2 

23 

% 

0.19 

4 

M 

1^ 

Galvanized  Iron  l¥ire  Rope. 

For  Ships'  Rigging  and  Guys  for  Derricks. 
CHARCOAL  ROPE. 


Circum- 
ference 
in  inches. 

Weight 
per  Fath- 
om in 
pounds. 

Cir.  of 
new 
Manila 
Rope  of 
equal 
Strength. 

Break- 
ing 
Strain 
in  tons 
of  2000 
pounds 

Circum- 
ference 
in  inches 

Weight 
per 

Fathom 
in 
pounds. 

Cir.  of 
new 
Manila 
Rope  of 
equal 
Strength. 

Break- 
ing 
Strain 
in  tons 
of  2000 
pounds 

BH 

26J4 

11 

43 

01^ 

»H 

Fj 

9 

5^ 

24^ 

10t£ 

40 

2J4 

4y% 

4-M 

8 

5 

22 

10 

35 

g 

3^1 

4J^ 

7 

4% 

21 

9^ 

33 

1% 

K 

3% 

5 

4^ 

19 

9 

30 

m 

2 

3 

3^ 

4! 

16^5 

8^ 

26 

m 

1% 

'-/^ 

2^ 

4 
3% 

14M 
12% 

8 

23 
20 

$ 

1 

Sf 

s* 

3^ 

IO-H 

6i/£ 

16 

% 

% 

i2 

1 

3J4 

9^ 

6 

14 

9l 

^ 

i|i 

« 

3 

8 

5M 

12 

% 

% 

iy 

% 

2% 

6% 

5^ 

10 

?• 

y* 

iH 

% 

WIRE   ROPES. 


229 


Galvanized  Cast-steel  Yacht  Rigging. 


Circum- 
ference 
in  inches. 

Weight 
per  Fath- 
om in 
pounds. 

Cir.   of 
new 
Manilla 
Rope  of 
equal 
Strength. 

Break- 
ing 
Strain 
in  tons 
of  2000 
pounds 

Circum- 
ference 
in  inches 

Weight 
per 
Fathom 
in 
pounds. 

Cir.  of 
new 
Manilla 
Rope  of 
equal 
Strength. 

Break- 
ing 
Strain 
in  tons 
of  2000 
pounds 

4 

14*4 

13 

66 

2 

3J4 

^ 

14 

3^ 

10% 

11 

43 

W* 

2U 

5*4 

10 

3 

8 

yi^ 

32 

1/^2 

2 

4M 

8 

2M 

6% 

»! 

27 

1% 

1% 

4^ 

6^ 

8* 

5$ 

8 

22 

iu 

lf| 

3M 

5^j 

4 

4^ 

7 

18 

i 

% 

3 

3^ 

Steel  Hawsers. 

For  Mooring,  Sea,  and  Lake  Towing. 


Size  of 

Size  of 

Circumfer- 

Breaking 

Manilla  Haw- 

Circumfer- 

Breaking 

Manilla  Haw- 

ence. 

Strength. 

ser  of  equal 

Strength. 

ence. 

Strength. 

ser  of  equal 
Strength. 

Inches. 

Tons. 

Inches. 

Inches. 

Tons. 

Inches. 

2« 

15 

6^ 

3^ 

29 

9 

2M 

18 

7 

4 

35 

10 

3 

22 

m 

Steel  Flat  Ropes. 

(J.  A.  Roebling's  Sons  Co.) 

Steel-wire  Flat  Ropes  are  composed  of  a  number  of  strands,  alternately 
twisted  to  the  right  and  left,  laid  alongside  of  each  other,  and  sewed  together 
with  soft  iron  wires,  These  ropes  are  used  at  times  in  place  of  round  ropes 
in  the  shafts  of  mines.  They  wind  upon  themselves  on  a  narrow  winding- 
drum,  which  takes  up  less  room  than  one  necessary  for  a  round  rope.  The 
soft-iron  sewing-wires  wear  out  sooner  than  the  steel  strands,  and  then  it 
becomes  necessary  to  sew  the  rope  with  new  iron  wires. 


Width   and 
Thickness 
in  inches. 

Weight  per 
foot   in 
pounds. 

Strength  in 
pounds. 

Width  and 
Thickness 
in  inches. 

Weight  per 
foot   in 
pounds. 

Strength  in 
pounds. 

%  x2 

1.19 

35,700 

^x3 

2.38 

71,400 

|gx2i^ 

1.86 

55,800 

y^zy* 

2.97 

89,000 

2.00 

60,000 

1^x4 

3.30 

99,000 

9fi.x8K 

2.50 

75,000 

y^^A 

4.00 

120,000 

%x4 

2.86 

85,800 

3^x5 

4.27 

128,000 

%x4^ 

3.12 

93,600 

^x5^ 

4.82 

144.600 

%  x  5 

3.40 

100,000 

*i*6 

5.10 

153,000 

%X5>2 

3.90 

110,000 

3^x7 

5.90 

177,000 

For  safe  working  load  allow  from  one  fifth  to  one  seventh  of  the  breaking 
stress. 

"  Lang  Lay"  Rope. 

In  wire  rope,  as  ordinarily  made,  the  component  strands  are  laid  up  into 
rope  in  a  direction  opposite  to  that  in  which  the  wires  are  laid  into  strands; 
that  is,  if  the  wires  in  the  strands  are  laid  from  right  to  left,  the  strands  are 
laid  into  rope  from  left  to  right.  In  the  '"  Lang  Lay,'1  sometimes  known  as 
"Universal  Lay,1'  the  wires  are  laid  into  strands  and  the  strands  into  rope 
in  the  same  direction;  that  is,  if  the  wire  is  laid  in  the  strands  from  right  to 
left,  the  strands  are  also  laid  into  rope  from  right  to  left.  Its  use  has  been 
found  desirable  under  certain  conditions  and  for  certain  purposes,  mostly 
for  haulage  plants,  inclined  planes,  and  street  railway  cables,  although  it 
has  also  been  used  for  vertical  hoists  in  mines,  etc.  Its  advantages  are  that 


'230 


MATERIALS. 


GALVANIZED  STEEL  CABLES. 
For  Suspension  Bridges.    (Roebling's.) 


I 

.S 

to 

1 

inches. 

£  <?< 

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o 

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£ 

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1 

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11.3 

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10 

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100 

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65 

3.7 

COMPARATIVE  STRENGTHS  OF  FLEXIBLE  GAL- 
VANIZED STEEL-WIRE  HAWSERS, 

With  Chain    Cable,  Tarred    Russian    Hemp,   and  White 
Manila  Ropes.    (Trenton  Iron  Co.) 


Patent  Flexible 

Steel-wire    Hawsers 

and  Cables. 


Chain  Cable. 


Tarred   Rus- 

sian  Hemp 

Rope. 


White 
Manilla 

Ropes. 


5^23 
"  "33 


7 

8 

9 
12 
15 
23)4 


3 

•'•'>( 

3-K  9 
1-2 
15 
18 
2'-2 
20 
33 
39 
64 
74 
88 
37  102 
41  1116 
47  130 
53  150 


-£-d 


17  8-10 
23  7-10 
27 

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77^ 

94^ 
107  1-10 

134% 


5 

7 
9 

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14 
6^ 

20 

24^ 
29 
34 

no 

60 

72 

89 
106 
115 
125 


sy2 13 


15 

10^18 


WIRE  HOPES.  231 

it  is  somewhat  more  flexible  than  rope  of  the  same  diameter  and  composed 
of  the  same  number  of  wires  laid  up  in  the  ordinary  manner;  and  (especi- 
ally) that  owing  to  the  fact  that  the  wires  are  laid  more  axially  in  the  rope, 
longer  surfaces  of  the  wire  are  exposed  to  wear,  and  the  endurance  of  the 
rope  is  thereby  increased.  (Trenton  Iron  Co.) 

Notes  on  the  Use  of  Wire  Rope. 
(J.  A.  Roebling's  Sons  Co.) 

Two  kinds  of  wire  rope  are  manufactured.  The  most  pliable  variety  con- 
tains nineteen  wires  in  the  strand,  and  is  generally  used  for  hoisting  and 
running  rope.  The  ropes  with  twelve  wires  and  seven  wires  in  the  strand 
are  stiff er,  and  are  better  adapted  for  standing  rope,  guys,  and  rigging.  Or- 
ders should  state  the  use  of  the  rope,  and  advice  will  be  given.  Ropes  are 
made  up  to  three  inches  in  diameter,  upon  application. 

For  safe  working  load,  allow  one  fifth  to  one  seventh  of  the  ultimate 
strength,  according  to  speed,  so  as  to  get  good  wear  from  the  rope.  When 
substituting  wire  rope  for  hemp  rope,  it  is  good  economy  to  allow  for  the 
former  the  same  weight  per  foot  which  experience  has  approved  for  the 
latter. 

Wire  rope  is  as  pliable  as  new  hemp  rope  of  the  same  strength;  the  for- 
mer will  therefore  run  over  the  same-sized  sheaves  and  pulleys  as  the  latter. 
But  the  greater  the  diameter  of  the  sheaves,  pulleys,  or  drums,  the  longer 
wire  rope  will  last.  The  minimum  size  of  drum  is  given  in  the  table. 

Experience  has  demonstrated  that  the  wear  increases  with  the  speed.  It 
is,  therefore,  better  to  increase  the  load  than  the  speed. 

Wire  rope  is  manufactured  either  with  a  wire  or  a  hemp  centre.  The  lat- 
ter is  more  pliable  than  the  former,  and  will  wear  better  where  there  is 
short  bending.  Orders  should  specify  what  kind  of  centre  is  wanted. 

Wire  rope  must  not  be  coiled  or  uncoiled  like  hemp  rope. 

When  mounted  on  a  reel,  the  latter  should  be  mounted  on  a  spindle  or  flat 
turn-table  to  pay  off  the  rope.  When  forwarded  in  a  small  coil,  without  reel, 
roll  it  over  the  ground  like  a  wheel,  and  run  off  the  rope  in  that  way.  All 
untwisting  or  kinking  must  be  avoided. 

To  preserve  wire  rope,  apply  raw  linseed-oil  with  a  piece  of  sheepskin, 
wool  inside;  or  mix  the  oil  with  equal  parts  of  Spanish  brown  or  lamp-black. 

To  preserve  wire  rope  under  water  or  under  ground,  take  mineral  or  vege- 
table tar,  and  add  one  bushel  of  fresh-slacked  lime  to  one  barrel  of  tar, 
which  will  neutralize  the  acid.  Boil  it  well,  and  saturate  the  rope  with  the 
hot  tar.  To  give  the  mixture  body,  add  some  sawdust. 

In  no  case  should  galvanized  rope  be  used  for  running  rope.  One  day's 
use  scrapes  off  the  coating  of  zinc,  and  rusting  proceeds  with  twice  the 
rapidity. 

The  grooves  of  cast-iron  pulleys  and  sheaves  should  be  filled  with  well- 
seasoned  blocks  of  hard  wood,  set  on  end,  to  be  renewed  when  worn  out. 
This  end-wood  will  save  wear  and  increase  adhesion.  The  smaller  pulleys 
or  rollers  which  support  the  ropes  on  inclined  planes  should  be  constructed 
on  the  same  plan.  When  large  sheaves  run  with  very  great  velocity,  the 
grooves  should  be  lined  with  leather,  set  on  end,  or  with  India  rubber.  This 
is  done  in  the  case  of  sheaves  used  in  the  transmission  of  power  between 
distant  points  by  means  of  rope,  which  frequently  runs  at  the  rate  of  4000 
feet  per  minute. 

Steel  ropes  are  taking  the  place  of  iron  ropes,  where  it  is  a  special  object 
to  combine  lightness  with  strength. 

But  in  substituting  a  steel  rope  for  an  iron  running  rope,  the  object  in  view 
should  be  to  gain  an  increased  wear  from  the  rope  rather  than  to  reduce  the 
size. 

Locked  \Virc  Rope. 

Fig.  74  shows  what  is  known  as  the  Patent  Locked  Wire  Rope,  made  by 
the  Trenton  Iron  Co.  It  is  claimed  to  wear  two  to  three  times  as  long  as  an 


FIG.  74. 

ordinary  wire  rope  of  equal  diameter  and  of  like  material.    Sizes  made  are 
from  ^3  to  \y%  inches  diameter. 


232 


MATERIALS. 


CRANE  CHAINS. 

(Pencoyd  Iron  Works.) 


"  D.  B.  G."  Special  Crane. 

Crane. 

& 

a 

s,  . 

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fee 

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44968 

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60480    120960 

40320 

The  distance  from  centre  of  one  link  to  centre  of  next  is  equal  to  the  in- 
side length  of  link,  but  in  practice  1/32  inch  is  allowed  for  weld.  This  is  ap- 
proximate, and  where  exactness  is  required,  chain  should  be  made  so. 

FOR  CHAIN  SHEAVES. — The  diameter,  if  possible,  should  be  not  less  than 
twenty  times  the  diameter  of  chain  used. 

EXAMPLE.— For  1-inch  chain  use  20-inch  sheaves. 

WEIGHTS  OF   LOGS,  LUMBER,  ETC. 
Weight  of  Green  Logs  to  Scale  1,000  Feet,  Board  Measure. 

Yellow  pine  (Southern) . .     8,000  to  10,000  Ibs. 

Norway  pine  (Michigan) 7,000  to    8,000    " 

WMtepineCMich^n)]^^^;;;;;;;-;;;;;;;;;;-;;;    Wgto   £000    ;; 

White  pine  CPennsylvania),  bark  off 5,000  to    6,000    " 

Hemlock  (Pennsy Iva iiia),  bark  off 6,000  to    7,000    " 

Four  acres  of  water  are  required  to  store  1,000,000  feet  of  logs. 
Weiglit  of  1,OOO  Feet  of  Lumber,  Board  Measure. 

Yellow  or  Norway  pine .,,'. Dry,  3,000  Ibs.        Green,  5.000  Ibs. 

White  pine "      2,500    "  4,000    " 

Weiglit  of  1  Cord  of  Seasoned  Wood,  128  Clibic  Feet  per 

Cord. 

Hickory  or  sugar  maple 4,500  )bs. 

Whiteoak 3,850    " 

Beech,  red  oak  or  black  oak 3,250    " 

Poplar,  chestnut  or  elm 2,350    " 

Pine  (white  or  Norway) 2,000    " 

Hemlock  bark,  dry 2,200    " 


SIZES   OF   FIRE-BKICK. 


233 


SIZES  OF  FIRE-BRICK. 

9-inch  straight 9  x  4U  x  2V£  inches. 

Soap 9x2^ 

Checker 9x3 

2-inch 9x4}/ 

Split ...   9x41, 

Jamb 9x4^ 

No.  1  key 9x2^thickx4^to4inches 

wide. 

113  bricks  to  circle  12  feet  inside  diam. 

No.  2  key 9  x  2^  thick  x  4]4  to  3^ 

inches  wide. 

63  bricks  to  circle  6  ft.  inside  diam. 

No.  3  key 9x2^   thick  x  4^   to    3 

inches  wide. 

38  bricks  to  circle  3  ft.  inside  diam. 

No.  4  key 9x2)^  thick   x  4^  to  2*4 

inches  wide. 

25  bricks  to  circle  1^  ft.  inside  diam. 
No.  1  wedge  (or  bullhead).  9x4^  wide  x  2^  to  2  in. 
thick,  tapering  lengthwise. 

98  bricks  to  circle  5  ft.  inside  diam. 

No.  2  wedge 9  x  4^  x  2^  to  1  ^  in.  thick. 

60  bricks  to  circle  2^  ft.  inside  diam. 

No.  1  arch 9x4)^x2^  to  2  in.   thick, 

tapering  breadthwise. 

72  bricks  to  circle  4  ft.  inside  diam. 

No.  2  arch 9  x  4*4  x  2J^  to  1^. 

42  bricks  to  circle  2  ft.  inside  diam. 

No.  1  skew 9  to  7  x  4J^  to  2J^. 

Bevel  on  one  end. 

No.  2skew 9 x 2^ x 4^  to  2^. 

Equal  bevel  on  both  edges. 

No.  3  skew 9  x  2^  x  4^  to  1^. 

Taper  on  one  edge. 

24  inch  circle 8J4  to  5%  x  4^  x  2^. 

Edges  curved,  9  bricks  line  a  24-inch  circle. 

36-inch  circle  8%  to  6^  x  4^  x  2^. 

13  bricks  line  a  36-ii)ch  circle. 

48-inch  circle 8%  to  7J4  x  4^  x  2^. 

17  bricks  line  a  48-inch  circle. 

13^-inch  straight 13^  x  %  x  6. 

13^-inch  key  No.  1 13^  x  2^  x  6  to  5  inch. 

90  bricks  turn  a  12-ft.  circle. 

13^-inch  key  No.  2 13^  x  2^  x  6  to  4%  inch. 

52  bricks  turn  a  6-ft.  circle. 

Bridge  wall,  No.  1 13  x  6^  x  6. 

Bridge  wall,  No.  2 13x6^x3. 

Mill  tile  18,20,or24x6x3. 

Stock-hole  tiles 18,  20,  or  24  x  9  x  4. 

18-inch  block  18x9x6. 

Flat  back  9x6x 2^. 

Flat  back  arch 9  x  6  x  3^  to  2^. 

22-inch  radius,  56  bricks  to  circle. 

Locomotive  tile 32  x  10  x  3. 

34x10x3. 
34x  8x3. 
36  x  8x3. 
40x10x3. 

Tiles,  slabs,  and  blocks,  various  sizes  12  to  30  inches 
long,  8  to  30  inches  wide,  2  to  6  inches  thick. 
Cupola  brick,  4  and  6  inches  high,  4  and  6  inches  radial  width,  to  line  shells 
23  to  66  in  diameter. 

A  9-inch  straight  brick  weighs  7  Ibs.  and  contains  100  cubic  inches.  (=120 
Ibs.  per  cubic  foot.  Specific  gravity  1.93.) 

One  cubic  foot  of  wall  requires  17  9Tinch  bricks,  one  cubic  yard  requires 
460.  Where  keys,  wedges,  and  other  "  shapes  "  are  used,  add  10  per  cent  in 
estimating  the  number  required. 


36  in.  Circle 


234 


MATERIALS. 


One  ton  of  fire-clay  should  be  sufficient  to  lay  3000  ordinary  bricks.  To 
secure  the  best  results,  fire-bricks  should  be  laid  in  the  same  clay  from  which 
they  are  manufactured.  It  should  be  used  as  a  thin  paste,  and  not  as  mor 
tar.  The  thinner  the  joint  the  better  the  furnace  wall.  In  ordering  bricks 
the  service  for  which  they  are  required  should  be  stated. 


NUMBER    OF    FIRE-BRICK    REQUIRED    FOR 
VARIOUS    CIRCLES. 


fl  £ 
1*2 

5  '5 

KEY  BRICKS. 

ARCH  BRICKS. 

WEDGE  BRICKS. 

•«* 

6 
& 

co' 

d 
fc 

<N 

o* 

fc 

6 
fc 

1 

o 
E-i 

oi 

6 
X 

o 
& 

OS 

1 

01 

0 

5 

0* 

& 

o» 

i 
1 

ft.  in. 
1  6 
2  0 
2  6 
3  0 
3  6 
4  0 
4  6 
5  0 
5  6 
6  0 
6  6 
7  0 
7  6 
8  0 
8  6 
9  0 
9  6 
10  0 
10  6 
11  0 
11  6 
12  0 
12  6 

25 

17 
9 

25 
30 
34 
38 
42 
46 
51 
55 
59 
63 
67 
71 
76 
80 
84 
88 
92 
97 
101 
105 
109 
113 
117 

13 
25 
38 
32 
25 
19 
13 
6 

10 
21 
32 
42 
53 
63 
58 
52 
47 
42 
37 
31 
26 
21 
16 
11 
5 

9 
19 
29 
38 
47 
57 
66 
76 
85 
94 
104 
113 
113 

42 

31 
21 
10 

'is 

36 
54 

72 
•72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 

42 
49 
57 
64 
72 
80 
87 
95 
102 
110 
117 
125 
132 
140 
147 
155 
162 
170 
177 
185 
193 

60 
48 
36 
24 
12 

20 
40 
59 
79 

98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 

60 
68 
76 
83 
91 
98 
106 
113 
121 
128 
136 
144 
151 
159 
166 
174 
181 
189 
196 
304 

"'s' 

15 
23 
30 
38 
45 
53 
60 
68 
75 
83 
90 
98 
105 
113 
121 

'"% 

15 
23 
30 
38 
46 
53 
61 
68 
76 
83 
91 
98 
106 

For  larger  circles  than  12  feet  use  113  No.  1  Key,  and  as  many  9-inch  brick 
as  may  be  needed  in  addition. 


ANALYSES  OF  MX.   SAVAGE  FIRE-CLAY. 


(1) 

1871 

Mass. 
Institute  of 
Technology. 

50  457 

(2) 
1877. 
Report  on 
Clays  of 
New  Jersey 
Prof.  G.H.  Cook. 

56.80      Silica  

(8) 
1878. 
Second 
Geological 
Survey  of 
Pennsylvania. 

44.395 

(4) 

1885. 

(2  samples) 
Dr.  Otto 
Wuth. 

56.15 

35.904 

30.08      Alumina  

33.558 

33.295 

1.15      Titanic  acid 

,  i  530 

1.504 

1.12      Peroxide  iron 

1.080 

0.59 

0.133 

trace 

0.17 

0.018 

.            Magnesia 

....        0.108 

0.115 

trace 

0.80      Potash  (alkalies). 

0.247 

12.744 

10  .  50     Water  and  inorg. 

matter.      14.575 

9.68 

100,760 

100,450 

100.493 

1QO,000 

MAGNESIA  BRICKS.  235 

MAUNISSIA.    BRICKS. 

"Foreign  Abstracts  "  of  the  Institution  of  Civil  Engineers,  1893,  gives  a 
paper  by  C.  Bischof  on  the  production  of  magnesia  bricks.  The  material 
most  in  favor  at  present  is  the  magnesite  of  Styria,  which,  although  less 
pure  considered  as  a  source  of  magnesia  than  the  Greek,  has  the  property 
of  fritting  at  a  high  temperature  without  melting.  The  composition  of  the 
two  substances,  in  the  natural  and  burnt  states,  is  as  follows: 

Magnesite.  Styrian.  Greek. 

Carbonate  of  magnesia 90.0  to  96. 0#  94.46# 

"  "    lime 0.5  to    2.0  4.49 

"  "    iron  3.0  to    6.0  FeO  0.08 

Silica 1.0  0.52 

Manganous  oxide 0.5  Water  0.54 

Burnt  Magnesite. 

Magnesia 77.6  82.46-95.36 

Lime 7.3  0.83—10.92 

Alumina  and  ferric  oxide 13.0  0.56—  3.54 

Silica 1.2  0.73-7.98 

At  a  red  heat  magnesium  carbonate  is  decomposed  into  carbonic  acid  and 
caustic  magnesia,  which  resembles  lime  in  becoming  hydrated  and  recar- 
bonated  when  exposed  to  the  air,  and  possesses  a  certain  plasticity,  so  that 
it  can  be  moulded  when  subjected  to  a  heavy  pressure.  By  long-continued 
or  stronger  heating  the  material  becomes  dead-burnt,  giving  a  form  of  mag- 
nesia of  high  density,  sp.  gr.  3.8,  as  compared  with  3.0  in  the  plastic  form, 
which  is  unalterable  in  the  air  but  devoid  of  plasticity.  A  mixture  of  two 
volumes  of  dead-burnt  with  one  of  plastic  magnesia  can  be  moulded  into 
bricks  which  contract  but  little  in  firing.  Other  binding  materials  that  have 
been  used  are:  clay  up  to  10  or  15  per  cent;  gas -tar,  perfectly  freed  from 
water,  soda,  silica,  vinegar  as  a  solution  of  magnesium  acetate  which  is 
readily  decomposed  by  heat,  and  carbolates  of  alkalies  or  lime.  Among 
magnesium  compounds  a  weak  solution  of  magnesium  chloride  may  also  be 
used.  For  setting  the  bricks  lightly  burnt,  caustic  magnesia,  with  a  small 
proportion  of  silica  to  render  it  less  refractory,  is  recommended.  The 
strength  of  the  bricks  may  be  increased  by  adding  iron,  either  as  oxide  or 
silicate.  If  a  porous  product  is  required,  sawdust  or  starch  may  be  added 
to  the  mixture.  When  dead-burnt  magnesia  is  used  alone,  soda  is  said  to  be 
the  best  binding  material. 

See  also  papers  by  A.  E.  Hunt,  Trans.  A.  I.  M.  E.,  xvi,  720,  and  oy  T.  Egles- 
ton,  Trans.  A.  I.  M.  E.,  xiv.  458. 

Asbestos.— J.  T.  Donald,  Eng.  and  M.  Jour.,  June  27,  1891. 

ANALYSIS. 

Canadian. 

Italian.  Broughton.  Templeton. 

Silica , 40.30#  40.57£           40.52# 

Magnesia 43.37  41.50            42.05 

Ferrous  oxide 87  2.81              1.97 

Alumina 2.27  .90              2.10 

Water 13.72  13.55             13.46 


100.53  99.33  100.10 

Chemical  analysis  throws  light  upon  an  important  point  in  connection 
with  asbestos,  i.e.,  the  cause  of  the  harshness  of  the  fibre  of  some  varieties. 
Asbestos  is  principally  a  hydrous  silicate  of  magnesia,  i.e.,  silicate  of  mag- 
nesia combined  with  water.  When  harsh  fibre  is  analyzed  it  is  found  to 
contain  less  water  than  the  soft  fibre.  In  fibre  of  very  fine  quality  from 
Black  Lake  analysis  showed  14.38$  of  water,  while  a  harsh-fibred  sample 
gave  only  11.70#.  If  soft  fibre  be  heated  to  a  temperature  that  will  drive  off 
a  portion  of  the  combined  water,  there  results  a  substance  so  brittle  that  it 
may  be  crumbled  between  thumb  and  finger.  There  is  evidently  some  con- 
nection between  the  consistency  of  the  fibre  and  the  amount  of  water  in.  its 
composition. 


236  STRENGTH   OF   MATERIALS. 


STRENGTH  OP  MATERIALS. 

Stress  and  Strain.— There  is  much  confusion  among  writers  on 
strength  of  materials  as  to  the  definition  of  these  terms.  An  external  force 
applied  to  a  body,  so  as  to  pull  it  apart,  is  resisted  by  an  internal  force,  or 
resistance,  and  the  action  of  these  forces  causes  a  displacement  of  the  mole- 
cules, or  deformation.  By  some  writers  the  external  force  is  called  a  stress, 
and  the  internal  force  a  strain;  others  call  the  external  force  a  strain,  and 
the  internal  force  a  stress:  this  confusion  of  terms  is  not  of  importance,  as 
the  words  stress  and  strain  are  quite  commonly  used  synonymously,  but  the 
use  of  the  word  strain  to  mean  molecular  displacement,  deformation,  or  dis- 
tortion, as  is  the  custom  of  some,  is  a  corruption  of  the  language.  See  En- 
gineering News,  June  23,  1892.  Definitions  by  leading  authorities  are  given 
below. 

Stress.—A  stress  is  a  force  which  acts  in  the  interior  of  a  body,  and  re- 
sists the  external  forces  which  tend  to  change  its  shape.  A  deformation  is 
the  amount  of  change  of  shape  of  a  body  caused  by  the  stress.  The  word 
strain  is  often  used  as  synonymous  with  stress  and  sometimes  it  is  also  used 
to  designate  the  deformation.  (Merriman.) 

The  force  by  which  the  molecules  of  a  body  resist  a  strain  at  any  point  is 
called  the  stress  at  that  point. 

The  summation  of  the  displacements  of  the  molecules  of  a  body  for  a 
given  point  is  called  the  distortion  or  strain  at  the  point  considered.  (Burr). 

Stresses  are  the  forces  which  are  applied  to  bodies  to  bring  into  action 
their  elastic  and  cohesive  properties.  These  forces  cause  alterations  of  the 
forms  of  the  bodies  upon  which  they  act.  Strain  is  a  name  given  to  the 
kind  of  alteration  produced  by  the  stresses.  The  distinction  between  stress 
and  strain  is  not  always  observed,  one  being  used  for  the  other.  (Wood.) 

Stresses  are  of  different  kinds,  viz.  :  tensile,  compressive,  transverse,  tor- 
si<  nal,  emd.  shearing  stresses. 

A  tensile  stress,  or  pull,  is  a  force  tending  to  elongate  a  piece.  A  com- 
pressive stress,  or  push,  is  a  force  tending  to  shorten  it.  A  transverse  stress 
tends  to  bend  it.  A  torsional  stress  tends  to  twist  it.  A  shearing  stress 
tends  to  force  one  part  of  it  to  slide  over  tlie  adjacent  ]i art- 
Tensile,  compressive,  and  shearing  stresses  are  called  simple  stresses. 
Transverse  stress  is  compounded  of  tensile  and  compressive  stresses,  and 
torsional  of  tensile  and  shearing  stresses. 

To  these  five  varieties  of  stresses  might  be  added  tearing  stress,  which  is 
either  tensile  or  shearing,  but  in  which  the  resistance  of  different  portions 
of  the  material  are  brought  into  play  in  detail,  or  one  after  the  other,  in- 
stead of  simultaneously,  as  in  the  simple  stresses. 

Effects  of  Stresses.— The  following  general  laws  for  cases  of  simple 
tension  or  compression  have  been  established  by  experiment.  (Merrirnan): 

1.  When  a  small  stress  is  applied  to  a  body,  a  small  deformation  is  pro- 
duced, and  on  the  removal  of  the  stress  the  body  springs  back  to  its  original 
form.    For  small  stresses,  then,  materials  may  be  regarded  as  perfectly 
elastic. 

2.  Under  small  stresses  the  deformations  are  approximately  proportional 
to  the  forces  or  stresses  which  produce  them,  and  also  approximately  pro- 
portional to  the  length  of  the  bar  or  body. 

3.  When  the  stress  is  great  enough  a  deformation  is  produced  which  is 
partly  permanent,   that  is,  the  body  does  not  spring  back  entirely   to  its 
original  form  on  removal  of  the  stress.    This  permanent  part  is  termed  a 
set.    In  such  cases  the  deformations  are  not  proportional  to  the  stress. 

4.  When  the  stress  is  greater  still  the  deformation  rapidly  increases  and 
the  body  finally  ruptures. 

5.  A  sudden  stress,  or  shock,  is  more  injurious  than  a  steady  stress  or  than 
a  stress  gradually  applied. 

Elastic  I^irnit.—  The  elastic  limit  is  defined  as  that  point  at  which  the 
deformations  cease  to  be  proportional  to  the  stresses,  or,  the  point  at  which 
the  rate  of  stretch  (or  other  deformation)  begins  to  increase.  It  is  also 
defined  as  the  point  at  which  the  first  permanent  set  becomes  visible.  The 
last  definition  is  not  considered  as  good  as  the  first,  as  it  is  found  that  with 
some  materials  a  set  occurs  with  any  load,  no  matter  how  small,  and  that 
with  others  a  set  which  might  be  called  permanent  vanishes  with  lapse  of 
time>  and  as  it  is  impossible  to  get  the  point  of  first  set  without  removing 


STRESS  AND  STRAIN.  237 

the  whole  load  after  each  increase  of  load,  which  is  frequently  inconvenient. 
The  elastic  limit,  defined,  however,  as  the  point  at  which  the  extensions  be- 
gin to  increase  at  a  higher  ratio  than  the  applied  stresses,  usually  corresponds 
very  nearly  with  the  point  of  first  measurable  permanent  set. 

Yield-point. — The  term  yield-point  has  recently  been  introduced  into 
the  literature  of  the  strength  of  materials.  It  is  defined  as  that  point  at 
which  the  rate  of  stretch  suddenly  increases  rapidly.  The  difference  be- 
tween the  elastic  limit,  strictly  defined  as  the  point  at  which  the  rate  of 
stretch  begins  to  increase,  and  the  yield-point,  at  which  the  rate  increases 
suddenly,  may  in  some  cases  be  considerable.  This  difference,  however,  will 
not  be  discovered  in  short  test-pieces  unless  the  readings  of  elongations  are 

made  by  an  exceedingly  fine  instrument,  as  a  micrometer  reading  to 

of  an  inch.  In  using  a  coarser  instrument,  such  as  calipers  reading  to  1/100 
of  an  inch,  the  elastic  limit  and  the  yield-point  will  appear  to  be  simultane- 
ous. Unfortunately  for  precision  of  language,  the  term  yield-point  was  not 
introduced  until  long  after  the  term  elastic  limit  had  been  almost  univer- 
sally adopted  to  signify  the  same  physical  fact  which  is  now  defined  by  the 
term  yield-point,  that  is,  not  the  point  at  which  the  first  change  in  rate, 
observable  cnly  by  a  microscope,  occurs,  but  that  later  point  (more  or  less 
indefinite  as  to  its  precise  position)  at  which  the  increase  is  great  enough  to 
be  seen  by  the  naked  eye.  A  most  convenient  method  of  determining  the 
point  at  which  a  sudden  increase  of  rate  of  stretch  occurs  in  short  speci- 
mens, when  a  testing-machine  in  which  the  pulling  is  done  by  screws  is 
used,  is  to  note  the  weight  on  the  beam  at  the  instant  that  the  beam  "  drops." 
During  the  earlier  portion  of  the  test,  as  the  extension  is  steadily  increased 
by  the  uniform  but  slow  rotation  of  the  screws,  the  poise  is  moved  steadily 
along  the  beam  to  keep  it  in  equipoise;  suddenly  a  point  is  reached  at  which 
the  beam  drops,  and  will  not  rise  until  the  elongation  has  been  considerably 
increased  by  the  further  rotation  of  the  screws,  the  advancing  of  the  poise 
meanwhile  being  suspended.  This  point  corresponds  practically  to  the  point 
at  which  the  rate  of  elongation  suddenly  increases,  and  to  the  point  at 
which  an  appreciable  permanent  set  is  first  found.  It  is  also  the  point  which 
has  hitherto  been  called  in  practice  and  in  text-books  the  elastic  limit,  and 
it  will  probably  continue  to  be  so  called,  although  the  use  of  the  newer  term 
"yield-point"  for  it,  and  the  restriction  of  the  term  elastic  limit  to  mean 
the  earlier  point  at  which  the  rate  of  stretch  begins  to  increase,  as  determin- 
able  only  by  micrometric  measurements,  is  more  precise  and  scientific. 

In  tables  of  strength  of  materials  hereafter  given,  the  term  elastic  limit  is 
used  in  its  customary  meaning,  the  point  at  which  the  rate  of  stress  has  be- 
gun to  increase,  as  observable  by  ordinary  instruments  or  by  the  drop  of 
the  beam.  With  this  definition  it  is  practically  synonymous  with  yield- 
point. 

Coefficient  (or  Modulus)  of  Elasticity.— This  is  a  term  express- 
ing the  relation  between  the  amount  of  extension  or  compression  of  a  mate- 
rial and  the  load  producing  that  extension  or  compression. 

It  may  be  defined  as  the  load  per  unit  of  section  divided  by  the  extension 
per  unit  of  length;  or  the  reciprocal  of  the  fraction  expressing  the  elonga- 
tion per  inch  of  length,  divided  by  the  pounds  per  square  inch  of  section 
producing  that  elongation. 

Let  P  be  the  applied  load,  k  the  sectional  area  of  the  piece,  I  the  length  of 
the  part  extended,  A  the  amount  of  the  extension,  and  Ethe  coefficient  of 
elasticity.  Then 

p 

—  =  the  load  on  a  unit  of  section ; 

j  =  the  elongation  of  a  unit  of  length. x 

w     P  -   A       Pl 
E="l~f'-l  =  Wx' 

The  coefficient  of  elasticity  is  sometimes  defined  as  the  figure  expressing 
the  load  which  would  be  necessary  to  elongate  a  piece  of  one  square  inch 
section  to  double  its  original  length,  provided  the  piece  would  not  break,  and 
the  ratio  of  extension  to  the  force  producing  it  remained  constant.  This 
definition  follows  from  the  formula  above  given,  thus:  If  k  =  one  square 
inch,  I  and  ^  each  =  one  inch,  then  E  —  P. 

Within  the  elastic  limit,  when  the  deformations  are  proportional  to  the 


238  STRENGTH  0$  MATERIALS. 

stresses,  the  coefficient  of  elasticity  is  constant,  but  beyond  the  elastic  limit 
it  decreases  rapidly. 

In  cast  iron  there  is  generally  no  apparent  limit  of  elasticity,  the  deforma- 
tions increasing  at  a  faster  rate  than  the  stresses,  and  a  permanent  set  being 
produced  by  small  loads.  The  coefficient  of  elasticity  therefore  is  not  con- 
stant during  any  portion  of  a  test,  but  grows  smaller  as  the  load  increases. 
The  same  is  true  in  the  case  of  timber.  In  wrought  iron  and  steel,  however, 
there  is  a  well-defined  elastic  limit,  and  the  coefficient  of  elasticity  within 
that  limit  is  nearly  constant. 

Resilience,  or  Work  of  Resistance  of  a  Material.— Within 
the  elastic  limit,  the  resistance  increasing  uniformly  from  zero  stress  to  the 
stress  at  the  elastic  limit,  the  work  done  by  a  load  applied  gradually  is  equal 
to  one  half  the  product  of  the  final  stress  by  the  extension  or  other  deforma- 
tion. Beyond  the  elastic  limit,  the  extensions  increasing  more  rapidly  than 
the  loads,  and  ihe  strain  diagram  approximating  a  parabolic  form,  the  work 
is  approximately  equal  to  two  thirds  the  product  of  the  maximum  stress  by 
the  extension. 

The  amount  of  work  required  to  break  a  bar,  measured  usually  in  inch- 
pounds,  is  called  its  resilience;  the  work  required  to  strain  it  to  the  elastic 
limit  is  called  its  elastic  resilience, 

Under  a  load  applied  suddenly  the  momentary  elastic  distortion  is  equal 
to  twice  that  caused  by  the  same  load  applied  gradually. 

When  a  solid  material  is  exposed  to  percussive  stress,  as  when  a  weight 
falls  upon  a  beam  transversely,  the  work  of  resistance  is  measured  by  the 
product  of  the  weight  into  the  total  fall. 

Elevation  of  Ultimate  Resistance  and  Elastic  Limit.— It 
was  first  observed  by  Prof.  R.  H.  Tliurston,  and  Commander  L.  A.  Beards- 
lee,  U.  S.  N.,  independently,  in  1873,  that  if  wrought  iron  be  subjected  to  a 
stress  beyond  its  elastic  limit,  but  not  beyond  its  ultimate  resistance,  and 
then  allowed  to  "  rest "  for  a  definite  interval  of  time,  a  considerable  in- 
crease of  elastic  limit  and  ultimate  resistance  may  be  experienced.  In  other 
words,  the  application  of  stress  and  subsequent  "  rest  "  increases  the  resist- 
ance of  wrought  iron. 

This  "  rest "  may  be  an  entire  release  from  stress  or  a  simple  holding  the 
test-piece  at  a  given  intensity  of  stress. 

Commander  Beardslee  prepared  twelve  specimens  and  subjected  them  to 
an  intensity  of  stress  equal  to  the  ultimate  resistance  of  the  material,  with- 
out breaking  the  specimens.  These  were  then  allowed  to  rest,  entirely  free 
from  stress,  from  24  to  30  hours,  after  which  period  they  were  again  stressed 
until  broken.  The  gain  in  ultimate  resistance  by  the  rest  was  found  to  vary 
from  4.4  to  17  per  cent. 

This  elevation  of  elastic  and  ultimate  resistance  appears  to  be  peculiar  to 
iron  and  steel:  it  has  not  been  found  in  other  metals. 

Relation  of  the  Elastic  Limit  to  Endurance  under  Re- 
peated Stresses  (condensed  from  Engineering,  August  7,  1891). — 
When  engineers  first  began  to  test  materials,  it  was  soon  recognized  that 
if  a  specimen  was  loaded  beyond  a  certain  point  it  did  not  recover  its  origi- 
nal dimensions  on  removing  the  load,  but  took  a  permanent  set;  this  point 
was  called  the  elastic  limit.  Since  below  this  point  a  bar  appeared  to  recover 
completely  its  original  form  and  dimensions  on  removing  the  load,  it  ap- 

Seared  obvious  that  it  had  not  been  injured  by  the  load,  and  hence  the  work- 
ig  load  might  be  deduced  from  the  elastic  limit  by  using  a  small  factor  of 
safety. 

Experience  showed,  however,  that  in  many  cases  a  bar  would  not  carry 
safely  a  stress  anywhere  near  the  elastic  limit  of  the  material  as  determined 
by  these  experiments,  and  the  whole  theory  of  any  connection  between  the 
elastic  limit  of  a  bar  and  its  working  load  became  almost  discredited,  and 
engineers  employed  the  ultimate  strength  only  in  deducing  the  safe  working 
load  to  which  their  structures  might  be  subjected.  Still,  as  experience  accu- 
mulated it  was  observed  that  a  higher  factor  of  safety  was  required  for  a  live 
load  than  for  a  dead  one. 

-In  1871  Wohler  published  the  results  of  a  number  of  experiments  on  bars 
of  iron  and  steel  subjected  to  live  loads.  In  these  experiments  the  stresses 
were  put  on  and  removed  from  the  specimens  without  impact,  but  it  was, 
nevertheless,  found  that  the  breaking  stress  of  the  materials  was  in  every 
case  much  below  the  statical  breaking  load.  Thus,  a  bar  of  Krupp's  axle 
steel  having  a  tenacity  of  49  tons  per  square  inch  broke  with  a  stress  of  28.6 
tons  per  square  inch,  when  the  load  was  completely  removed  and  replaced 
without  impact  170,000  times.  These  experiments  were  made  on  a  large 


STKESS  AOT)  STRA1K.  239 

number  of  different  brands  of  iron  and  steel,  and  the  results  were  concor- 
dant in  showing  that  a  bar  would  break  with  an  alternating  stress  of  only, 
say,  one  third  the  statical  breaking  strength  of  the  material,  if  the  repetitions 
of  stress  were  sufficiently  numerous.  At  the  same  time,  however,  it  ap- 
peared from  the  general  trend  of  the  experiments  that  a  bar  would  stand  an 
indefinite  number  of  alternations  of  stress,  provided  the  stress  was  kept 
below  the  limit. 

Prof.  Bauschinger  defines  the  elastic  limit  as  the  point  at  which  stress 
ceases  to  be  sensibly  proportional  to  strain,  the  latter  being  measured  with 

a  mirror  apparatus  reading  to  r:n^;th  of  a  millimetre,  or   about  .,/w../A  in. 

500U  100000 

This  limit  is  always  below  the  yield-point,  and  may  on  occasion  be  zero.  On 
loading  a  bar  above  the  yield-point,  this  point  rises  with  the  stress,  and  the 
rise  continues  for  weeks,  months,  and  possibly  for  years  if  the  bar  is  left  at 
rest  under  its  load.  On  the  other  hand,  when  a  bar  is  loaded  beyond  its  true 
elastic  limit,  but  below  its  yield-point,  this  limit  rises,  but  reaches  a  maxi- 
mum as  the  yield-point,  is  approached,  and  then  falls  rapidly,  reaching  even 
to  zero.  On  leaving  the  bar  at  rest  under  a  stress  exceeding  that  of  its 
primitive  breaking-down  point  the  elastic  limit  begins  to  rise  again,  and 
may,  if  left  a  sufficient  time,  rise  to  a  point  much  exceeding  its  previous 
value. 

This  property  of  the  elastic  limit  of  changing  with  the  history  of  a  bar  has 
done  more  to  discredit  it  than  anything  else,  nevertheless  it  now  seems  as  if 
it,  owing  to  this  very  property,  were  once  more  to  take  its  former  place  in 
the  estimation  of  engineers,  and  this  time  with  fixity  of  tenure.  It  had  long 
been  known  that  the  limit  of  elasticity  might  be  raised,  as  we  have  said,  to 
almost  any  point  within  the  breaking  load  of  a  bar.  Thus,  in  some  experi- 
ments by  Professor  Styffe,  the  elastic  limit  of  a  puddled-steel  bar  was  raised 
16,000  Ibs.  by  subjecting  the  bar  to  a  load  exceeding  its  primitive  elastic 
limit. 

A  bar  has  two  limits  of  elasticity,  one  for  tension  and  one  for  compression. 
Bauschinger  loaded  a  number  of  bars  in  tension  until  stress  ceased  to  be 
sensibly  proportional  to  strain.  The  load  was  then  removed  and  the  bar 
tested  in  compression  until  the  elastic  limit  in  this  direction  had  been  ex- 
ceeded. This  process  raises  the  elastic  limit  in  compression,  as  would  be 
found  on  testing  the  bar  in  compression  a  second  time.  In  place  of  this, 
however,  it  was  now  again  tested  in  tension,  when  it  was  found  that  the 
artificial  raising  of  the  limit  in  compression  had  lowered  that  in  tension  be- 
low its  previous  value.  By  repeating  the  process  of  alternately  testing  in 
tension  and  compression,  the  two  limits  took  up  points  at  equal  distances 
from  the  line  of  no  load,  both  in  tension  and  compression.  These  limits 
Bauschinger  calls  natural  elastic  limits  of  the  bar,  which  for  wrought  iron 
correspond  to  a  stress  of  about  8^  tons  per  square  iach,  but  this  is  practically 
the  limiting  load  to  which  a  bar  of  the  same  material  can  be  strained  alter- 
nately in  tension  and  compression,  without  breaking  when  the  loading  is 
repeated  sufficiently  often,  as  determined  by  Wohler's  method. 

As  received  from  the  rolls  the  elastic  limit  of  the  bar  in  tension  is  above 
the  natural  elastic  limit  of  the  bar  as  defined  by  Bauschinger,  having  been 
artificially  raised  by  the  deformations  to  which  it  has  been  subjected  in  the 
process  of  manufacture.  Hence,  when  subjected  to  alternating  stresses, 
the  limit  in  tension  is  immediately  lowered,  while  that  in  compression  is 
raised  until  they  both  correspond  to  equal  loads.  Hence,  in  Wohler's  ex- 
periments, in  which  the  bars  broke  at  loads  nominally  below  the  elastic 
limits  of  the  material,  there  is  every  reason  for  concluding  that  the  loads 
were  really  greater  than  true  elastic  limits  of  the  material.  This  is  con- 
firmed by  tests  on  the  connecting-rods  of  engines,  which  of  course  work 
under  alternating  stresses  of  equal  intensity.  Careful  experiments  on  old 
rods  show  that  the  elastic  limit  in  compression  is  the  same  as  that  in  ten- 
sion, and  that  both  are  far  below  the  tension  elastic  limit  of  the  material  as 
received  from  the  rolls. 

The  common  opinion  that  straining  a  metal  beyond  its  elastic  limit  injures 
it  appears  to  be  untrue.  It  is  not  the  mere  straining  of  a  metal  beyond  one 
elastic  limit  that  injures  it,  but  the  straining,  many  times  repeated,  beyond 
its  two  elastic  limits.  Sir  Benjamin  Baker  has  shown  that  in  bending  a  shell 
plate  for  a  boiler  the  metal  is  of  necessity  strained  beyond  its  elastic  limit, 
so  that  stresses  of  as  much  as  7  tons  to  15  tons  per  square  inch  may  obtain 
in  it  as  it  comes  from  the  rolls,  and  unless  the  plate  is  annealed,  these 
stresses  will  still  exist  after  it  has  been  built  into  the  boiler.  In  such  a  case, 
however,  when  exposed  to  the  additional  stress  due  to  the  pressure  inside 


240  STRENGTH   OF  MATERIALS. 

the  boiler,  the  overstrained  portions  of  the  plate  will  relieve  themselves  by 
stretching  and  taking  a  permanent  set,  so  that  probably  after  a  year's  work- 
ing very  little  difference  could  be  detected  in  the  stresses  in  a  plate  built  in- 
to the  boiler  as  it  came  from  the  bending  rolls,  and  in  one  which  had  been 
annealed,  before  riveting  into  place,  and  the  first,  in  spite  of  its  having  been 
strained  beyond  its  elastic  limits,  and  not  subsequently  annealed,  would  be 
as  strong  as  the  other. 

Resistance  of  Metals  to  Repeated  Shocks. 

More  than  twelve  years  were  spent  by  Wohler  at  the  instance  of  the  Prus- 
sian Government  in  experimenting  upon  the  resistance  of  iron  and  steel  to 
repeated  stresses.  The  results  of  his  experiments  are  expressed  in  what  is 
known  as  Wohler's  law,  which  is  given  in  the  following  words  in  Dubois's 
translation  of  Weyrauch: 

'•  Rupture  may  be  caused  not  only  by  a  steady  load  which  exceeds  the 
carrying  strength,  but  also  by  repeated  applications  of  stresses,  none  of 
which  are  equal  to  the  carrying  strength.  The  differences  of  these  stresses 
are  measures  of  the  disturbance  of  continuity,  in  so  far  as  by  their  increase 
the  minimum  stress  which  is  still  necessary  for  rupture  diminishes." 

A  practical  illustration  of  the  meaning  of  the  first  portion  of  this  law  may 
I  e  given  thus:  If  50,000  pounds  once  applied  will  just  break  a  bar  of  iron  or 
ste^l,  a  stress  very  much  less  than  50,000  pounds  will  break  it  if  repeated 
sufficiently  often. 

This  is  fully  confirmed  by  the  experiments  of  Fairbairn  and  Spangenberg, 
as  well  as  those  of  Wohler;  and,  as  is  remarked  by  Weyrauch,  it  may  be 
considered  as  a  long-known  result  of  common  experience.  It  partially  ac- 
counts for  what  Mr.  Holley  has  called  the  "  intrinsically  ridiculous  factor  of 
safety  of  six." 

Another  "long-known  result  of  experience"  is  the  fact  that  rupture  may 
be  caused  by  a  succession  of  shocks  or  impacts,  none  of  which  alone  would 
be  sufficient  to  cause  it.  Iron  axles,  the  piston-rods  of  steam  hammers,  and 
other  pieces  of  metal  subject  to  continuously  repeated  shocks,  invariably 
break  after  a  certain  length  of  service.  They  have  a  "life  "  which  is  lim- 
ited. 

Several  years  ago  Fairbairn  wrote:  "  We  know  that  in  some  cases  wrought 
iron  subjected  to  continuous  vibration  assumes  a  crystalline  structure,  and 
that  the  cohesive  powers  are  much  deteriorated,  but  we  are  ignorant  of  the 
causes  of  this  change.*"  We  are  still  ignorant,  not  only  of  the  causes  of  this 
change,  but  of  the  conditions  under  which  it  takes  place.  Who  knows 
whether  wrought  iron  subjected  to  very  slight  continuous  vibration  will  en- 
dure forever?  or  whether  to  insure  final  rupture  each  of  the  continuous  small 
shocks  must  amount  at  least  to  a  certain  percentage  of  single  heavy  shock 
(both  measured  in  foot-pounds),  which  would  cause  rupture  with  one  applica- 
tion ?  Wohler  found  in  testing  iron  by  repeated  stresses  (not  impacts)  that 
in  one  case  400,000  applications  of  a  stress  of  500  centners  to  the  square  inch 
caused  rupture,  while  a  similar  bar  remained  sound  after  48,000,000  applica- 
tions of  a  stress  of  300  centners  to  the  square  inch  (1  centner  =  110.2  Ibs.). 

Who  knows  whether  or  not  a  similar  law  holds  true  in  regard  to  repeated 
shocks  ?  Suppose  that  a  bar  of  iron  would  break  under  a  single  impact  of 
1000  foot-pounds,  how  many  times  would  it  be  likely  to  bear  the  repetition 
of  100  foot-pounds,  or  would  it  be  safe  to  allow  it  to  remain  for  fifty  years 
subjected  to  a  continual  succession  of  blows  of  even  10  foot-pounds  each  ? 

Mr.  William  Metcalf  published  in  the  Metallurgical  Review,  Dec.  1877,  the 
results  of  some  tests  of  the  life  of  steel  of  different  percentages  of  carbon 
under  impact.  Some  small  steel  pitmans  were  made,  the  specifications  for 
which  required  that  the  unloaded  machine  should  run  4J^  hours  at  the  rate 
of  1200  revolutions  per  minute  before  breaking. 

The  steel  was  all  of  uniform  quality,  except  as  to  carbon.  Here  are  the 
results;  The 

.30  C.  ran  1  h.  21  m.    Heated  and  bent  before  breaking. 

.49  C.    "    1  h.  28  m.,        "         "      "         "  " 

.43  C.    "    4  h.  57  m.    Broke  without  heating. 

.65  C.    "   3  h.  50  m.    Broke  at  weld  where  imperfect. 

.800.    "    5h.  40m. 

.84  C.     "  18  h. 

.87  C.    Broke  in  weld  near  the  end. 

.96  C.    Ran  4.55  m.,  and  the  machine  broke  down. 

Some  other  experiments  by  Mr.  Metcalf  confirmed  his  conclusion,  viz. 


STEESS  AND   STRAIN.  241 

that  high-carbon  steel  was  better  adapted  to  resist  repeated  shocks  and  vi- 
brations than  low-carbon  steel. 

These  results,  however,  would  scarcely  be  sufficient  to  induce  any  en- 
gineer to  use  .84  carbon  steei  in  a  car-axle  or  a  bridge-rod.  Further  experi- 
ments are  needed  to  confirm  or  overthrow  them. 

(See  description  of  proposed  apparatus  for  such  an  investigation  in  the 
author's  paper  in  Trans.  A.  I.  M.  E.,  vol.  viii.,  p.  76,  from  which  the  above 
extract  is  taken.) 

Stresses  Produced  by  Suddenly  Applied  Forces  and 
Shocks. 

(Mansfield  Merriman,  R.  R.  &  Eng.  Jour.,  Dec.  1889.) 
Let  P  be  the  weight  which  is  dropped  from  a  height  h  upon  the  end  of  a 
bar,  and  let  y  be  the  maximum  elongation  which  is  produced.    The  work 
performed  by  the  falling  weight,  then,  is 

W=P(h  +  y\ 

and  this  must  equal  the  internal  work  of  the  resisting  molecular  stresses. 
The  stress  in  the  bar,  which  is  at  first  0,  increases  up  to  a  certain  limit  Q, 
which  is  greater  than  P;  and  if  the  elastic  limit  be  not  exceeded  the  elonga- 
tion increases  uniformly  with  the  stress,  so  that  the  internal  work  is  equal 
to  the  mean  stress  1/2Q  multiplied  by  the  total  elongation  y,  or 

W=l/2Qy. 
Whence,  neglecting  the  work  that  may  be  dissipated  in  heat, 


If  e  be  the  elongation  due  to  the  static  load  P,  within  the  elastic  limit 
y  =   ^  e;  whence 


........  (1) 

which  gives  the  momentary  maximum  stress.    Substituting  this  value  of  Q, 
there  results 


which  is  the  value  of  the  momentary  maximum  elongation. 

A  shock  results  when  the  force  P,  before  its  action  on  the  bar,  is  moving 
with  velocity,  as  is  the  case  when  a  weight  P  falls  from  a  height  h.  The 
above  formulas  show  that  this  height  h  may  be  small  it  e  is  a.  small  quan- 
tity, and  yet  very  great  stresses  and  deformations  be  produced.  For  in- 
stance, let  h  =  4e,  then  Q  =  4P  and  y  =  4e  ;  also  let  h  =  12e,  then  Q  =  6P 
and  y  —  6  e.  Or  take  a  wrought-iron  bar  1  in.  square  and  5  ft.  long:  under  a 
steady  load  of  5000  Ibs.  this  will  be  compressed  about  0.0012  in.,  supposing 
that  no  lateral  flexure  occurs;  but  if  a  weight  of  5000  Ibs.  drops  upon  its  end 
from  the  small  height  of  0.0048  in.  there  will  be  produced  the  stress  of  20,000 
Ibs. 

A  suddenly  applied  force  is  one  which  acts  with  the  uniform  intensity  P 
upon  the  end  of  the  bar,  but  which  has  no  velocity  before  acting  upon  it. 
This  corresponds  to  the  case  of  h  —  0  in  the  above  formulas,  and  gives  Q  = 
2P  and  y  =  2e  for  the  maximum  stress  and  maximum  deformation.  Prob- 
ably the  action  of  a  rapidly-moving  train  upon  a  bridge  produces  stresses 
of  this  character. 

Increasing  the  Tensile  Strength  of  Iron  Bars  toy  Twist- 
ing them.— Ernest  L.  Ransome  of  San  Francisco  has  obtained  an  English 
Patent,  No.  16231  of  1888,  for  an  '•  improvement  in  strengthening  and  testing 
wrought  metal  and  steel  rods  or  bars,  consisting  in  twisting  the  same  in  a 
cold  state.  .  .  .  Any  defect  in  the  lamination  of  the  metal  which  would 
otherwise  be  concealed  is  revealed  by  twisting,  and  imperfections  are  shown 
at  once.  The  treatment  may  be  applied  to  bolts,  suspension-rods  or  bars 
subjected  to  tensile  strength  of  any  description." 

Results  of  tests  of  this  process  were  reported  by  Lieutenant  F.  P.  Gilmore, 
U.  S.  N.,  in  a  paper  read  before  the  Technical  Society  of  the  Pacific  Coast, 
published  in  the  Transactions  of  the  Society  for  the  month  of  December. 
1888. 

Tests  were  also  made  in  1889  in  the  University  of  California.  The  exper- 
iments include  trials  with  thirty-nine  bars,  twenty-nine  of  which  were  va- 


243 


STRENGTH   OF   MATEEIALS. 


riously  twisted,  from  three-eighths  of  one  turn  to  six  turns  per  foot.  The 
test-pieces  were  cut  from  one  and  the  same  bar,  and  accurately  measured 
and  numbered.  From  each  lot  two  pieces  without  twist  were  tested  for  ten- 
sile strength  and  ductility.  One  group  of  each  set  was  twisted  until  the 
pieces  broke,  as  a  guide  for  the  amount  of  twist  to  be  given  those  to  be 
tested  for  tensile  strain. 

The  following  is  the  result  of  one  set  of  Lieut.  Gilmore's  tests,  on  iron 
bars  8  in.  long,  .719  in.  diameter. 


No.  of 
Bars. 

Conditions. 

Twists 
in 
Turns. 

Twists 
per  ft. 

Tensile 
Strength. 

Tensile 
per  sq.  in. 

Gain  per 
cent. 

2 

Not  twisted. 

0 

0 

22,000 

54,180 

2 

Twisted  cold. 

K 

H 

23,900 

59,020 

9 

2 

It                    <C 

i 

m 

25,800 

63,500 

17 

2 

il            tl 

2 

3 

26,300 

64,750 

19 

1 

((                   4< 

2^ 

m 

26,400 

65,000 

20 

TENSILE  STRENGTH. 

The  following  data  are  usually  obtained  in  testing  by  tension  in  a  testing- 
machine  a  sample  of  a  material  of  construction : 

The  load  and  the  amount  of  extension  at  the  elastic  limit. 

The  maximum  load  applied  before  rupture. 

The  elongation  of  the  piece,  measured  between  gauge-marks  placed  a 
stated  distance  apart  before  the  test;  and  the  reduction  of  area  at  the 
point  of  fracture. 

The  load  at  the  elastic  limit  and  the  maximum  load  are  recorded  in  pounds 
per  square  inch  of  the  original  area.  The  elongation  is  recorded  as  a  per- 
centage of  the  stated  length  between  the  gauge-marks,  and  the  reduction 
area  as  a  percentage  of  the  original  area.  The  coefficient  of  elasticity  is  cal- 
culated from  the  ratio  the  extension  within  the  elastic  limit  per  inch  of 
length  bears  to  the  load  per  square  inch  producing  that  extension. 

On  account  of  the  difficulty  of  making  accurate  measurements  of  the  f  rac- 
t u  red  area  of  a  test-piece,  and  of  the  fact  that  elongation  is  more  valuable 
than  reduction  of  area  as  a  measure  of  ductility  and  of  resilience  or  work 
of  resistance  before  rupture,  modern  experimenters  are  abandoning  the 
custom  of  reporting  reduction  of  area.  The  "  strength  per  square  inch  of 
fractured  section  "  formerly  frequently  used  in  reporting  tests  is  now  almost 
entirely  abandoned.  The  data  now  calculated  from  the  results  of  a  tensile 
test  for  commercial  purposes  are:  1.  Tensile  strength  in  pounds  per  square 
inch  of  original  area.  2.  Elongation  per  cent  of  a  stated  length  between 
gauge-mark?,  usually  8  inches.  3.  Elastic  limit  in  pounds  per  square  inch 
of  original  area. 

The  short  or  grooved  test  specimen  gives  with  most  metals,  especially 
with  wrought  iron  and  steel,  an  apparent  tensile  strength  much  higher 
than  the  real  strength.  This  form  of  test-piece  is  now  almost  entirely  aban- 
doned. 

The  following  results  of  the  tests  of  six  specimens  from  the  same  1*4"  steel 
bar  illustrate  the  apparent  elevation  of  elastic  limit  and  the  changes  in 
other  properties  due  to  change  in  length  of  stems  which  were  turned  down 
in  each  specimen  to  .798"  diameter.  (Jas.  E.  Howard,  Eng.  Congress  1893 
Section  G.) 


Description  of  Stem. 

Elastic  Limit, 
Lbs.  per  Sq.  In. 

Tensile  Strength, 
Lbs.  per  Sq.  In. 

Contraction  of 
Area,  per  cent. 

1  00"  long    

64  900 

94,400 

49.0 

.50      4i     
.25      "              .... 

65,320 
68  000 

97,800 
102  420 

43.4 
39  6 

Semicircular  groove, 
A"  radius  

75,000 

116,380 

31.6 

Semicircular  groove, 
y^'  radius  

86,000,  about 

134,960 

23.0 

V-shaped  groove  

90,000,  about 

117,000 

Indeterminate. 

TENSILE  STRENGTH. 


243 


Tests  plate  made  by  the  author  in  1879  of  straight  and  grooved  test-pieces 
of  boiler-plate  steel  cut  from  the  same  gave  the  following  results  : 
5  straight  pieces,  56,605  to  59,012  Ibs.  T.  S.    Aver.  57,566  Ibs. 
4  grooved      "        64,341  to  67,400  "        "  "       65,452  " 

Excess  of  the  short  or  grooved  specimen,  21  per  cent,  or  12,114  Ibs. 

Measurement  of  Elongation.— In  order  to  be  able  to  compare 
records  of  elongation,  it  is  necessary  not  only  to  have  a  uniform  length  of 
section  between  gauge-marks  (say  8  inches),  but  to  adopt  a  uniform  method 
of  measuring  the  elongation  to  compensate  for  the  difference  between  the 
apparent  elongation  when  the  piece  breaks  near  one  of  the  gauge-marks, 
and  when  it  breaks  midway  between  them.  The  following  method  is  rec- 
ommended (Trans.  A.  S.  M.  E.,  vol.  xi.,  p.  622): 

Mark  on  the  specimen  divisions  of  1/2  inch  each.  After  fracture  measure 
from  the  point  of  fracture  the  length  of  8  of  the  marked  spaces  on  each 
fractured  portion  (or  7  +  on  one  side  and  8  -f-  on  the  other  if  the  fracture  is 
not  at  one  of  the  marks).  The  sum  of  these  measurements,  less  8  inches,  is 
the  elongation  of  8  inches  of  the  original  length.  If  the  fracture  is  so 
near  one  end  of  the  specimen  that  7  + spaces  are  not  left  on  the  shorter 
portion,  then  take  the  measurement  of  as  many  spaces  (with  the  fractional 
part  next  to  the  fracture)  as  are  left,  and  for  the  spaces  lacking  add  the 
measurement  of  as  many  corresponding  spaces  of  the  longer  portion  as  are 
necessary  to  make  the  7+  spaces. 

Shapes  of  Specimens  for  Tensile  Tests.— The  shapes  shown 
in  Fig.  75  were  recommended  by  the  author  in  1882  when  he  was  connected 

|< 16-'to  -20" • — --  > 

No.  1.    Square  or  flat  bar,  as 
rolled. 


No.  2.    Round  bar,  as  rolled. 


No.  3.  Standard  shape  for 
flats  or  squares.  Fillets  y% 
inch  radius. 


No.  4.  Standard  shape  for 
rounds.  Fillets  ^  in.  radius. 

No.  5.  Government  shape  for 
marine  boiler-plates  of  iron. 
Not  recommended  for  other 

,   ., ,  tests,  as  results  are  generally 

in  error. 

FIG.  75. 

with  the  Pittsburgh  Testing  Laboratory.  They  are  now  in  most  general 
use,  the  earlier  forms,  with  5  inches  or  less  in  length  between  shoulders, 
being  almost  entirely  abandoned. 

Precautions  Required  in  making  Tensile  Tests.— The 
testing-machine  itself  should  be  tested,  to  determine  whether  its  weighing 
apparatus  is  accurate,  and  whether  it  is  so  made  and  adjusted  that  in  the 
test  of  a  properly  made  specimen  the  line  of  strain  of  the  testing-machine 
is  absolutely  in  line  with  the  axis  of  the  specimen. 

The  specimen  should  be  so  shaped  that  it  will  not  give  an  incorrect  record 
of  strength. 

It  should  be  of  uniform  minimum  section  for  not  less  than  five  inches  of 
its  length. 

Regard  must  be  had  to  the  time  occupied  in  making  tests  of  certain  mate- 
rials. Wrought  iron  and  soft  steel  can  be  made  to  show  a  higher  than  their 
actual  apparent  strength  by  keeping  them  under  strain  for  a  great  length 

In  testing  soft  alloys,  copper,  tin,  zinc,  and  the  like,  which  flow  under  con- 
stant strain  their  highest  apparent  strength  is  obtained  by  testing  them 
rapidly.  In  recording  tests  of  such  materials  the  length  of  time  occupied  in 
the  test  should  be  stated. 


16-'to-20— - 


244  STRENGTH   OF  MATERIALS. 

For  very  accurate  measurements  of  elongation,  corresponding  to  incre- 
ments of  load  during  the  tests,  the  electric  contact  micrometer,  described 
in  Trans.  A.  S.  M.  E.,  vol.  vi.,  p.  479,  will  be  found  convenient.  When  read- 
ings of  elongation  are  then  taken  during  the  test,  a  strain  diagram  may  be 
plotted  from  the  reading,  which  is  useful  in  comparing  the  qualities  of  dif- 
ferent specimens.  Such  strain  diagrams  are  made  automatically  by  the  new 
Olsen  testing-machine,  described  in  Jour.  Frank.  Inst.  1891. 

The  coefficient  of  elasticity  should  be  deduced  from  measurement  ob- 
served between  fixed  increments  of  load  per  unit  section,  say  between  2000 
and  12,000  pounds  per  square  inch  or  between  1000  and  11,000  pounds  instead 
of  between  0  and  10,000  pounds. 

COMPRESSIVE    STRENGTH. 

What  is  meant  by  the  term  "eompressive  strength  "  has  not  yet  been 
settled  by  the  authorities,  and  there  exists  more  confusion  in  regard  to  this 
term  than  in  regard  to  any  other  used  by  writers  on  strength  of  materials. 
The  reason  of  this  may  be  easily  explained.  The  effect  of  a  cornpressive 
stress  upon  a  material  varies  with  the  nature  of  the  material,  and  with  the 
shape  and  size  of  the  specimen  tested.  While  the  effect  of  a  tensile  stress  is 
to  produce  rupture  or  separation  of  particles  in  the  direction  of  the  line  of 
strain,  the  effect  of  a  compressive  stress  on  a  piece  of  material  may  be  either 
to  cause  it  to  fly  into  splinters,  to  separate  into  two  or  more  wedge-shaped 
pieces  and  fly  apart,  to  bulge,  buckle,  or  bend,  or  to  flatten  out  and  utterly  re- 
sist rupture  or  separation  of  particles.  A  piece  of  speculum  metal  under 
compressive  stress  will  exhibit  no  change  of  appearance  until  rupture  takes 
place,  and  then  it  will  fiy  to  pieces  as  suddenly  as  if  blown  apart  by  gun- 
powder. A  piece  of  cast  iron  or  of  stone  will  generally  split  into  wed^e- 
shaped  fragments.  A  piece  of  wrought  iron  will  buckle  or  bend.  A  piece  of 
wood  or  zinc  may  bulge,  but  its  action  will  depend  upon  its  shape  and  si::e. 
A  piece  of  lead  will  flatten  out  and  resist  compression  till  the  last  degree; 
that  is,  the  more  it  is  compressed  the  greater  becomes  its  resistance. 

Air  and  other  gaseous  bodies  are  compressible  to  any  extent  as  long  as 
they  retain  the  gaseous  condition.  Water  not  confined  in  a  vessel  is  com- 

Sressed  by  its  own  weight  to  the  thickness  of  a  mere  film,  while  when  con- 
ned in  a  vessel  it  is  almost  incompressible. 

It  is  probable,  although  it  has  not  been  determined  experimentally,  that 
solid  bodies  when  confined  are  at  least  as  incompressible  as  water.  When 
they  are  not  confined,  the  effect  of  a  compressive  stress  is  not  only  to 
shorten  them,  but  also  to  increase  their  lateral  dimensions  or  bulge  them. 
Lateral  strains  are  therefore  induced  by  compressive  stresses. 

The  weight  per  square  inch  of  original  section  required  to  produce  any 
given  amount  or  percentage  of  shortening  of  any  material  is  not  a  constant 
quantity,  but  varies  with  both  the  length  and  the  sectional  area,  with  the 
shape  of  this  sectional  area,  and  with  the  relation  of  the  area  to  the  length. 
The  "  compressive  strength'1  of  a  material,  if  this  term  be  supposed  to  mean 
the  weight  in  pounds  per  square  inch  necessary  to  cause  rupture,  may  vary 
with  every  size  and  shape  of  specimen  experimented  upon.  Still  more  diffi- 
cult would  it  be  to  state  what  is  the  "  compressive  strength  "  of  a  material 
which  does  not  rupture  at  all,  but  flattens  out.  Suppose  we  are  testing  a 
cylinder  of  a  soft  metal  like  lead,  two  inches  in  length  and  one  inch  in  diam- 
eter, a  certain  weight  will  shorten  it  one  per  cent,  another  weight  ten  per 
cent,  another  fifty  per  cent,  but  no  weight  that  we  can  place  upon  it  will 
rupture  it,  for  it  will  flatten  out  to  a  thin  sheet.  What,  then,  is  its  compres- 
sive strength  ?  Again,  a  similar  cylinder  of  soft  wrought  iron  would  prob- 
ably compress  a  few  per  cent,  bulging  evenly  all  around;  it  would  then  com- 
mence to  bend,  but  at  first  the  bend  would  be  imperceptible  to  the  eye  and 
too  small  to  be  measured.  Soon  this  bend  would  be  great  enough  to  be 
noticed,  and  finally  the  piece  might  be  bent  nearly  double,  or  otherwise  dis- 
torted. What  is  the  "compressive  strength1'  of  this  piece  of  iron  ?  Is  it 
the  weight  per  square  inch  which  compresses  the  piece  one  per  cent  or  five 
per  cent,  that  which  causes  the  first  bending  (impossible  to  be  discovered), 
or  that  which  causes  a  perceptible  bend  ? 

As  showing  the  confusion  concerning  the  definitions  of  compressive 
strength,  the  following  statements  from  different  authorities  on  the  strength 
of  wrought  iron  are  of  interest. 

Wood's  Resistance  of  Materials  states,  "comparatively  few  experiments 
have  been  made  to  determine  how  much  wrought  iron  will  sustain  at  the 
point  of  crushing.  Hodgkinson  gives  65,000,  Rondulet  70,800,  Weisbach  72,000 


COMPKESSIVE   STRENGTH.  245 

Rankine  30,000  to  40,000.  It  is  generally  assumed  that  wrought  iron  will  resist 
about  two  thirds  as  much  crushing  as  to  tension,  but  the  experiments  fail 
to  give  a  very  definite  ratio." 

Mr.  Whipple,  in  his  treatise  on  bridge-building,  states  that  a  bar  of  good 
wrought  iron  will  sustain  a  tensile  strain  of  about  60,000  pounds  per  square 
inch,  and  a  compressive  strain,  in  pieces  of  a  length  not  exceeding  twice  the 
least  diameter,  of  about  90,000  pounds. 

The  following  values,  said  to  be  deduced  from  the  experiments  of  Major 
Wade,  Hodgkinson,  and  Capt.  Meigs,  are  given  by  Haswell  : 

American  wrought  iron  .............................  127,720  Ibs. 

"  (mean)  ......................    85,500    " 


Stoney  states  that  the  strength  of  short  pillars  of  any  given  material,  all 
having  the  same  diameter,  does  not  vary  much,  provided  the  length  of  the 
piece  is  not  less  than  one  and  does  not  exceed  four  or  five  diameters,  and 
that  the  weight  which  will  just  crush  a  short  prism  whose  base  equals  one 
square  inch,  and  whose  height  is  not  less  than  1  to  \y%  and  does  not  exceed 
4  or  5  diameters,  is  called  the  crushing  strength  of  the  material.  It  would 
be  well  if  experimenters  would  all  agree  upon  some  such  definition  of  the 
term  "  crushing  strength,1'  and  insist  that  all  experiments  which  are  made 
for  the  purpose  of  testing  the  relative  values  of  different  materials  in  com- 
pression be  made  on  specimens  of  exactly  the  same  shape  and  size.  An 
arbitrary  size  and  shape  should  be  assumed  and  agreed  upon  for  this  pur- 
pose. The  size  mentioned  by  Stoney  is  definite  as  regards  area  of  section, 
viz.,  one  square  inch,  but  is  indefinite  as  regards  length,  viz.,  from  one  to 
five  diameters.  In  some  metals  a  specimen  five  diameters  long  would  bend, 
and  give  a  much  lower  apparent  strength  than  a  specimen  having  a  length  of 
one  diameter.  The  words  "  will  just  crush  "  are  also  indefinite  for  ductile 
materials,  in  which  the  resistance  increases  without  limit  if  the  piece  tested 
does  not  bend.  In  such  cases  the  weight  which  causes  a  certain  percentage 
of  compression,  as  five,  ten,  or  fifty  per  cent,  should  be  assumed  as  the 
crushing  strength. 

For  future  experiments  on  crushing  strength  three  things  are  desirable  : 
First,  an  arbitrary  standard  shape  and  size  of  test  specimen  for  comparison 
of  all  materials.  Secondly,  a  standard  limit  of  compression  for  ductile 
materials,  which  shall  be  considered  equivalent  to  fracture  in  brittle  mate- 
rials. Thirdly,  an  accurate  knowledge  of  the  relation  of  the  crushing 
strength  of  a  specimen  of  standard  shape  and  size  to  the  crushing  strength 
of  specimens  of  all  other  shapes  and  sizes.  The  latter  can  only  be 
secured  by  a  very  extensive  and  accurate  series  of  experiments  upon  all 
kinds  of  materials,  and  on  specimens  of  a  great  number  of  different  shapes 
and  sizes. 

The  author  proposes,  as  a  standard  shape  and  size,  for  a  compressive  test 
specimen  for  all  metals,  a  cylinder  one  inch  in  length,  and  one  half  square 
inch  in  sectional  area,  or  0.798  inch  diameter;  and  for  the  limit  of  compres- 
sion equivalent  to  fracture,  ten  per  cent  of  the  original  length.  The  term 
"compressive  strength,"  or  "compressive  strength  of  standard  specimen," 
would  then  mean  the  weight  per  square  inch  required  to  fracture  by  com- 
pressive stress  a  cylinder  one  inch  long  and  0.798  inch  diameter,  or  to 
reduce  its  length  to  0.9  inch  if  fracture  does  not  take  place  before  that  reduc- 
tion in  length  is  reached.  If  such  a  standard,  or  any  standard  size  whatever, 
had  been  used  by  the  earlier  authorities  on  the  strength  of  materials,  we 
never  would  have  had  such  discrepancies  in  their  statements  in  regard  to 
the  compressive  strength  of  wrought  iron  as  those  given  above. 

The  reasons  why  this  particular  size  is  recommended  are  :  that  the  sectional 
area,  one-half  square  inch,  is  as  large  as  can  be  taken  in  the  ordinary  test- 
ing-machines of  100,000  pounds  capacity,  to  include  all  the  ordinary  metals 
of  construction,  cast  and  wrought  iron,  and  the  softer  steels;  and  that  the 
length,  one  inch,  is  convenient  for  calculation  of  percentage  of  compression. 
If  the  length  were  made  two  inches,  many  materials  would  bend  in  testing, 
and  give  incorrect  results.  Even  in  cast  iron  Hodgkinson  found  as  the  mean 
of  several  experiments  on  various  grades,  tested  in  specimens  %  inch  in 
height,  a  compressive  strength  per  square  inch  of  94,730  pounds,  while  the 
mean  of  the  same  number  of  specimens  of  the  same  irons  tested  in  pieces  1^ 
inches  in  height  was  only  88,800  pounds.  The  best  size  and  shape  of  standard 
specimen  should,  however,  be  settled  upon  only  after  consultation  and, 
agreement  among  several  authorities, 


246 


STRENGTH  OE  MATERIALS. 


The  Committee  on  Standard  Tests  of  the  American  Society  of  Mechanical 
Engineers  say  (vol.  xi.,  p.  624) : 

"  Although  compression  tests  have  heretofore  been  made  on  diminutive 
sample  pieces,  it  is  highly  desirable  that  tests  be  also  made  on  long  pieces 
from  10  to  20  diameters  in  length,  corresponding  more  nearly  with  actual 
practice,  in  order  that  elastic  strain  and  change  of  shape  may  be  determined 
by  using  proper  measuring  apparatus. 

The  elastic  limit,  modulus  or  coefficient  of  elasticity,  maximum  and  ulti- 
mate resistances,  should  be  determined,  as  well  as  the  increase  of  section  at 
various  points,  viz.,  at  bearing  surfaces  and  at  crippling  point. 

The  use  of  long  compression-test  pieces  is  recommended,  because  the  in- 
vestigation of  short  cubes  or  cylinders  has  led  to  no  direct  application  of 
the  constants  obtained  by  their  use  in  computation  of  actual  structures, 
which  have  always  been  and  are  now  designed  according  to  empirical  for- 
mulae obtained  from  a  few  tests  of  long  columns." 

COLUMNS,  PILLARS,  OR  STRUTS. 
Hodgkinsoii's  Formula  for  Columns. 

P  =  crushing  weight  in  pounds;  d  =  exterior  diameter  in  inches;  dl  =  in- 
terior diameter  in  inches ;  L  =  length  in  feet. 


Kind  of  Column. 

Solid    cylindrical    col-  ) 

umns  of  cast  iron ) 

Hollow  cylindrical  col-  ) 

umns  of  cast  iron ) 

Solid  cylindrical  col- ) 

umns  of  wrought  iron.  ) 
Solid  square  pillar  of  ) 

Dantzic  oak  (dry) ) 

Solid  square  pillar  of  ) 

red  deal  (dry) ) 


Both  ends  rounded,  the 
length  of  the  column 
exceeding  15  times 
its  diameter. 


P= 


£1-7 


/' 

P  =  95,850^- 


Both  ends  flat,  the 
length  of  the  column 
exceeding  30  times 
its  diameter. 

(£3.55 

P  =  98,920-^r 


» =  299,600 


(73-55 

— 


P  =  24,540— 
P=17,51fl£ 


The  above  formulae  apply  only  in  cases  in  which  the  length  is  so  great  that 
the  column  breaks  by  bending  and  not  by  simple  crushing.  If  the  column 
be  shorter  than  that  given  in  the  table,  and  more  than  four  or  five  times  its 
diameter,  the  strength  is  found  by  the  following  formula  : 

PCK 


~  P  -f-  MCJT 

in  which  P=  the  value  given  by  the  preceding  formulae,  K=  the  transverse 
section  of  the  column  in  square  inches,  C  —  the  ultimate  compressive  resis- 
tance of  the  material,  and  W  —  the  crushing  strength  of  the  column. 

Hodgkinson's  experiments  were  made  upon  comparatively  short  columns, 
the  greatest  length  of  cast-iron  columns  being  60^  inches,  of  wrought  iron 
90%  inches. 

The  following  are  some  of  his  conclusions: 

1.  In  all  long  pillars  of  the  same  dimensions,  when  the  force  is  applied  in 
the  direction  of  the  axis,  the  strength  of  one  which  has  flat  ends  is  about 
three  times  as  great  as  one  with  roun  Jed  ends. 

2.  The  strength  of  a  pillar  with  one  end  rounded  and  the  other  flat  is  an 
arithmetical  mean  between  the  two  given  in  the  preceding  case  of  the  same 
dimensions. 

3.  The  strength  of  a  pillar  having  both  ends  firmly  fixed  is  the  same  as 
one  of  half  the  length  with  both  ends  rounded. 

4.  The  strength  of  a  pillar  is  not  increased  more  thai}  one  seventh  by  en- 
larging it  at  the  middle, 


MOMENT  OF  IKERTIA  AND  RADIUS  OF  GYRATION.  247 

Gordon's  formulae  deduced  from  Hodgkinson's  experiments  are  more 
generally  used  than  Hodgkinson's  own.    They  are: 

fS 
Columns  with  both  ends  fixed  or  flat,  P  =  —  -  -  ; 


Columns  with  one  end  flat,  the  other  end  round,  P f^- — a; 

l  +  lUtoja 

Columns  with  both  ends  round,  or  hinged,  P  =  -     * 

S  =  area  of  cross-section  in  inches; 

P—  ultimate  resistance  of  column,  in  pounds; 

/  =  crushing  strength  of  the  material  in  Ibs.  per  square  inch; 

r  =  least  radius  of  gyration,  in  inches,  r»  =  Moment  of  inertia; 

area  of  section    ' 
I  =  length  of  column  in  inches; 
a  =  a  coefficient  depending  upon  the  material; 

/  and  a  are  usually  taken  as  constants;  they  are  really  empirical  variables, 
dependent  upon  the  dimensions  and  character  of  the  column  as  well  as  upon 
the  material.    (Burr.) 
For  solid  wrought-iron  columns,  values  commonly  taken  are:  /  =  36,000  to 


=  3600 
For  solid  cast-iron  columns,  /  =  80,000,  a  =  r-^. 

For  hollow  cast-iron  columns,  fixed  ends,  p  =    ,.  80<00°  —  ?  j  _  length  and 

14-  —  — 
800  d2 

d  =  diameter  in  the  same  unit,  and  p  =  strength  in  Ibs.  per  square  inch. 
Sir  Benjamin  Baker  gives, 

For  mild  steel,     /  =  67,000  Ibs.,  a  =  ' 

For  strong  steel,  /  =  114,000  Ibs.,  a  = 

Mr.  Burr  considers  these  only  loose  approximations  for  the  ultimate  resis- 
tances. 
For  dry  timber  Rankine  gives/  =  7200  Ibs.,  a  =  1/3000. 

MOMENT  OF  INERTIA  AND  RADIUS  OF  GYRATION. 

The  moment  of  inertia  of  a  section  is  the  sum  of  the  products  of 
each  elementary  area  of  the  section  into  the  square  of  its  distance  from  an 
assumed  axis  of  rotation,  as  the  neutral  axis. 

The  radius  of  gyration  of  the  section  equals  the  square  root  of  the 
quotient  of  the  moment  of  inertia  divided  by  the  area  of  the  section.  If 
R  =  radius  of  gyration,  1=  moment  of  inertia  and  A  =  area, 


The  moments  of  inertia  of  various  sections  are  as  follows: 
d  —  diameter,  or  outside  diameter;   dj  —  inside  diameter;  6  =  breadth; 
h  =  depth;  61%  ft.,  inside  breadth  and  diameter; 

Solid  rectangle  I  =  l/12b/i3 ;  Hollow  rectangle  7  =  1/1 2(bh*  —  b^i3)  5 

Solid  square     1=  1/1264;  Hollow  square       1=  1/12(64  -  6,4); 

Solid  cylinder   1=  l/647rd4;  Hollow  cylinder    1=  l/647r(d4  -  c^4). 

Moments  of  Inertia  and  Radius  of  Gyration  for  Various 
Sections,  and  their  Use  in  the  Formulas  for  Strength  of 
Girders  and  Columns.— The  strength  of  sections  to  resist  strains, 
either  as  girders  or  as  columns,  depends  not  only  on  the  area  but  also  on  the 
form  of  the  section,  and  the  property  of  the  section  which  forms  the  basis 
of  the  constants  used  in  the  formulas  for  strength  of  girders  and  columns 
to  express  the  effect  of  the  form,  is  its  moment  of  inertia  about  its  neutral 
axis.  Thus  the  moment  of  resistance  of  any  section  to  transverse  bending 


248  STRENGTH   OF   MATERIALS. 

is  its  moment  of  inertia  divided  by  the  distance  from  the  neutral  axis  to 
the  fibres  farthest  removed  from  that  axis;  or 

Moment  of  inertia  ,,      I 

Moment  of  resistance  =  extreme  flbre  trom  axis  .     M=  -. 


Moment  of*  Inertia  of  Compound  Shapes.  (Pencoyd  Iron 
Works.)  —  The  moment  of  inertia  of  any  section  about  any  axis  is  equal  to  the 
I  about  a  parallel  axis  passing  through  its  centre  of  gravity  +  (the  area  of 
the  section  X  the  square  of  the  distance  between  the  axes). 

By  this  rule,  the  moments  of  inertia  or  radii  of  gyration  of  any  single  sec- 
tions being  known,  corresponding  values  may  be  obtained  for  any  combiia- 
tion  of  these  sections. 

Radius  of  Gyration  of  Compound  Shapes.—  In  the  case  of  a 
pair  of  any  shape  without  a  web  the  value  of  R  can  always  be  found  with- 
out considering  the  moment  of  inertia. 

The  radius  of  gyration  for  any  section  around  an  axis  parallel  to  another 
axis  passing  through  its  centre  of  gravity  is  found  as  follows: 

Let  r  =  radius  of  gyration  around  axis  through  centre  of  gravity;  R  = 
radius  of  gyration  around  another  axis  parallel  to  above;  d  =  distance  be- 
tween axes: 

R=  \/d?  -f  r2. 

When  r  is  small,  E  may  be  taken  as  equal  to  d  without  material  error. 
Graphical  Method  for  Finding  Radius  of  Gyration.—  Ben  j. 

F.  La  Hue,  Eng.  News,  Feb.  2,  1893,  gives  a  short  graphical  method  for 
finding  the  radius  of  gyration  of  hollow,  cylindrical,  and  rectangular  col- 
umns, as  follows: 

For  cylindrical  columns: 

Lay  off  to  a  scale  of  4  (or  40)  a  right-angled  triangle,  in  which  the  base 
equals  the  outer  diameter,  and  the  altitude  equals  the  inner  diameter  of  the 
column,  or  vice  versa.  The  hypothenuse,  measured  to  a  scale  of  unity  (or 
10),  will  be  the  radius  of  gyration  sought. 

This  depends  upon  the  formula 

Mom.  of  Inertia        <D2  -f  da 


Area  4 

in  which  A  =  area  and  D  =  diameter  of  outer  circle,  a  =  area  and  d  =  dia- 
meter of  inner  circle,  and  G  =  radius  of  gyration.  4/D2  -f  d2  is  the  expres- 
sion for  the  hypothenuse  of  a  right-angled  triangle,  in  which  D  and  d  are  the 
base  and  altitude. 

The  sectional  area  of  a  hollow  round  column  is  .7854(D2  —  d2).  By  con- 
structing a  right-angled  triangle  in  which  D  equals  the  hypothenuse  and  d 
equals  the  altitude,  the  base  will  equal  4/D2  —  d2.  Calling  the  value  of  this 
expression  for  the  base  B,  the  area  will  equal  .7854J92. 

Value  of  G  for  square  columns: 

Lay  off  as  before,  but  using  a  scale  of  10,  a  right-angled  triangle  of  which 
the  base  equals  D  or  the  side  of  the  outer  square,  and  the  altitude  equals  d, 
the  side  of  the  inner  square.  With  a  scale  of  3  measure  the  hypothenuse, 
which  will  be,  approximately,  the  radius  of  gyration. 

This  process  for  square  columns  gives  an  excess  of  slightly  more  than  4#. 
By  deducting  4%  from  the  result,  a  close  approximation  will  be  obtained. 

A  very  close  result  is  also  obtained  by  measuring  the  hypothenuse  with 
the  same  scale  by  which  the  base  and  altitude  were  laid  off,  and  multiplying 
by  the  decimal  0.29;  more  exactly,  the  decimal  is  0.28867. 

The  formula  is 


G  —      /Mom-  of  inertia 
~  \  Area 

This  may  also  be  applied  to  any  rectangular  column  by  using  the  lesser 
diameters  of  an  unsupported  column,  and  the  greater  diameters  if  the  col- 
umn is  supported  in  the  direction  of  its  least  dimensions. 

ELEMENTS  OF  USUAL.  SECTIONS. 

Moments  refer  to  horizontal  axis  through  centre  of  gravity.  This  table  is 
intended  for  convenient  application  where  extreme  accuracy  is  not  impor- 
tant. Some  of  the  terms  are  only  approximate ;  those  marked  *  are  correct. 
Values  for  radius  of  gyration  in  flanged  beams  apply  to  standard  minimum 
sections  only.  A  =  area  of  section;  b  =  breadth;  h  =  depth;  D  =  diameter. 


ELEMENTS  OF   USUAL  SECTIONS. 


249 


Shape  of  Section. 

Moment 
of  Inertia. 

Moment 
of 
Resistance. 

Square  of 
Least 
Radius  of 
Gyration. 

Least 
Radius  of 
Gyration. 

t 

£~  5fc 

Solid  Rect- 
angle. 

bh*  * 

bh** 

(Least  side)2* 

Least  side  * 

•12 

6 

12 

3.46 

7J& 

f 

Hollow  Rect- 
angle. 

bh^-b.h^  * 
12 

bht-b^** 

h*  +  h^  * 

/i-f  ft1 

-B; 

Qh 

12 

4.89 

1 

0 

Solid  Circle. 

AD*  * 
16 

AD* 

8 

D*  * 

16 

D* 
4 

|^-D—  1 

Hollow  Circle. 
A,  area  of 
large  section  • 
a,  area  of 
small  section. 

AD*  -ad* 

AD*  -ad* 

D*  +  d** 

D-f  cZ 
5.64 

16 

8D 

16 

-A3 

Solid  Triangle. 

6/1* 
36 

bh* 
24 

The  least  of 
of  the  two: 
h*       b* 

r8°r24 

The  least  of 
the  two: 
h           b 

4^4  °r  4^9 

o 

^-6-H 

Even  Angle. 

Ah* 
10.2 

Ah 

7.2 

b* 
25 

6 
5 

1       *< 

Uneven  Angle. 

Ah* 

^7i 

(hb)* 

hb 

9.5 

6.5 

I3(h*  +  62) 

2.6(/i  4-  6) 

-g 

Even  Cross. 

Ah* 
19 

Ah 
9.5 

7l2 

22.5 

h 
4.74 

ill 

Even  Tee. 

.47i* 
11.1 

.4/1 
8 

b* 
22.5 

6 
4.74 

fe^ 

+-h  -H 

I  Beam. 

Ah* 
6.66 

.4/1 
3.2 

62 
21 

6 

4.58 

Channel. 

Ah* 
7.34 

Ah 
3.67 

6« 
1^5 

6 
3.54 

50 

1B9 

h-fc-H 

Deck  Beam. 

Ah* 
"(Uf 

^Ifc 
4 

62 

36.5 

i 

b 

6 

Distance  of  base  from  centre  of  gravity,  solid  triangle,  |;  even  angle,  -4  ; 

0  3.0 

uneven  angle,  gg ;  even  tee,  ^-Q;  deck  beam,  — ;  all  other  shapes  given  in 
the  table,  --  or  — -. 


250 


STRENGTH  OF  MATERIALS. 


Solid  Cast-iron  Columns. 

Hurst  gives  the  following  table,  based  on  Hodgkinson's  formula  (tons  of 
2240  Ibs.). 

The  figures  are  the  safe  load  or  <fo  of  the  breaking  weight  in  tons,  for  solid 
columns,  ends  flat  and  fixed. 


G  CQ 

"*  i> 

I! 

•**  hH 

Length  of  Column  in  Feet. 

6. 

8. 

10. 

12. 

14. 

16. 

18. 

20. 

25. 

1J* 

.82 

.50 

.34 

.25 

.19 

.15 

.13 

.11 

.07 

1M 

1.43 

.87 

.60 

.44 

.34 

.27 

.22 

.18 

.13 

2 

2.31 

1.41 

.97 

.71 

.55 

.44 

.36 

.30 

.20 

2^4 

3.52 

2.16 

1.48 

1.08 

.83 

.67 

.54 

.46 

.31 

gi/ 

5.15 

3.16 

2.16 

1.58 

1.22 

.97 

.80 

.66 

.56 

2% 

7.26 

4.45 

3.05 

2.23 

1.72 

1.37 

1.12 

.94 

.64 

3 

9.93 

6.09 

4.17 

3.06 

2.35 

1.87 

1.53 

1.28 

.88 

3^ 

17.29 

10.60 

7.26 

5.32 

4.10 

3.26 

2.67 

2.23 

1.53 

4 

27.96 

17.15 

11.73 

8.61 

6.62 

5.28 

4.32 

3.61 

2.47 

4U 

42.73 

26.20 

17.93 

13.15 

10.12 

8.07 

6.60 

5.52 

3.78 

5^ 

62.44 

38.29 

26.20 

19.22 

14.79 

11.79 

9.65 

8.06 

5.52 

5U 

88.00 

53.97 

36.93 

27.09 

20.84 

16.61 

13.60 

11.37 

7.78 

6 

120.4 

73.82 

50.51 

37.05 

28.51 

22.72 

18.60 

15.55 

10.64 

6^ 

160.6 

98.47 

67.38 

49.43 

38.03 

30.31 

24.81 

20.74 

14.19 

7 

209.7 

128.6 

87.98 

64.53 

49.66 

39.57 

32.33 

27.08 

18.53 

7J6 

268.8 

164.8 

112.8 

82.73 

63.66 

50.73 

41.53 

34.72 

23.76 

8^ 

339.1 

207.9 

142.3 

104.4 

80.31 

64.00 

52.39 

43.80 

29.97 

8^ 

421.8 

258.6 

177.0 

129.8 

99.90 

79.61 

65.16 

54.48 

37.28 

Q 

518.2 

317.7 

217.4 

159.5 

122.7 

97.80 

80.05 

66.92 

45.80 

% 

629.5 

386.0 

264.2 

193.8 

149.1 

118.8 

97.25 

81.70 

55.64 

10 

757.2 

464.3 

317.7 

233.1 

179.3 

142.9 

117.0 

97.79 

66.92 

10^ 

902.6 

553.5 

378.7 

277.8 

213.8 

170.3 

139.4 

116.6 

79.77 

11 

1067.1 

654.4 

447.8 

328.5 

252.7 

201.4 

164.9 

137.8 

94.31 

11U 

1252.3 

767.9 

525.5 

385.4 

296.6 

236.4 

193.5 

161.7 

110.7 

12XS 

1459.6 

895.1 

612.5 

449.3 

345.7 

275.5 

225.5 

188.5 

129.0 

The  correction  for  short  columns  should  be  applied  where  the  length  is 
less  than  30  diameters. 

SO 
Strength  in  tons  of  short  columns  =  , 

S  being  the  strength  for  long  columns  given  in  the  above  table,  and  C  =  49 
times  the  sectional  area  of  the  metal  in  inches. 

Hollow  Columns.—  The  strength  nearly  equals  the  difference  be- 
tween that  of  two  solid  columns  the  diameters  of  which  are  equal  to  the 
external  and  internal  diameters  of  the  hollow  one. 

Ultimate  Strength  of  Hollow,  Cylindrical  Wrought  and 


Cast-iron  Columns,  when  fixed  at  the  en 

(Pottsville  Iron  and  Steel  Co.) 

Computed  by  Gordon's  formula,  p  — — 


ugh 
ds. 


p  =  Ultimate  strength  in  Ibs.  per  square  inch; 

j  =  Ti£±U?oSV  f  *>*  ">  -»e  units; 

f  _  j  40,000  Ibs.  for  wrought-iron;  | 
*  ~  I  80,000  Ibs.  for  cast-iron;  f 
C  =  1/3000  for  wrought-iron,  and  1/800  for  cast-iron. 


COLUMNS,   PILLARS,    OR  STRUTS. 

80000 
For  cast-iron,        p  = 


For  wrought-iron,  p  = 


251 


40000 


1+3000\d) 

HOLLOW  CYLINDRICAL  COLUMNS. 


Ratio 

Maximum  Load  per  sq.  in. 

Safe  Load  per  square  inch. 

of  Length  to 

Diameter. 

I 
~h 

Cast  Iron. 

Wrought  Iron. 

Cast  Iron, 
Factor  of  6. 

Wrought  Iron, 
Factor  of  4. 

8 

74075 

39164 

12346 

9791 

10 

71110 

38710 

11851 

9677 

12 

67796 

38168 

11299 

9542 

14 

64256 

37546 

10709 

9386 

16 

60606 

36854 

10101 

9213 

18 

56938 

36100 

9489 

9025 

20 

53332 

35294 

8889 

8823 

22 

49845 

34442 

8307 

8610 

24 

46510 

C3556 

7751 

8389 

26 

43360 

32642 

7226 

8161 

28 

40404 

31712 

6734 

7928 

30 

37646 

30768 

6274 

7692 

32 

35088 

29820 

5848 

7455 

34 

32718 

28874 

5453 

7218 

36 

30584 

27932 

5097 

6983 

38 

28520 

27002 

4753 

6750 

40 

26666 

26086 

4444 

6522 

42 

24962 

25188 

4160 

6297 

44 

23396 

24310 

3899 

6077 

46 

21946 

23454 

3658 

5863 

48 

20618 

22620 

3436 

5655 

50 

19392 

21818 

3262 

5454 

52 

18282 

21036 

3047 

5259 

54 

17222 

20284 

2870 

5071 

56 

16260 

19556 

2710 

4889 

58 

15368 

18856 

2561 

4714 

60 

14544 

18180 

2424 

4545 

Ultimate  Strength  of  Wrought-iron  Columns. 

p  =  ultimate  strength  per  square  inch; 
I  =  length  of  column  in  inches; 
r  =  least  radius  of  gyration  in  inches. 

40000 
For  square  end-bearings,  v  = 


+ 


For  one  pin  and  one  square  bearing,    p  =  • 


40000 


For  two  pin-bearings, 


1 

30000 
40000 


1  + 


—  t-V 

20000\rJ 


For  safe  working  load  on  these  columns  use  a  factor  of  4  when  used  in 
buildings,  or  when  subjected  to  dead  load  only;  but  when  used  in  bridges 
the  factor  should  be  5. 


252 


STRENGTH   OF   MATERIALS. 


WROUGHT-IRON  COLUMNS. 


Ultimate  Strength  in  Ibs. 
per  square  inch. 

Safe  Strength  in  Ibs.  per 
square  inch—  Factor  of  5. 

I 

I 

r 

r 

Square 
Ends. 

Pin  and 
Square 
End. 

Pin 

Ends. 

Square 
Ends. 

Pin  and 
Square 
End. 

Pin 

Ends. 

10 

39944 

39866 

39800 

10 

7989 

7973 

7960 

15 

39776 

39702 

39554 

15 

7955 

7940 

7911 

20 

39604 

39472 

39214 

20 

7921 

7894 

7843 

25 

39384 

39182 

38788 

25 

7877 

7836 

7758 

30 

39118 

38834 

38278 

30 

7821 

7767 

7656 

35 

38810 

38430 

37690 

35 

7762 

7686 

7538 

40 

38460 

37974 

37036 

40 

7692 

7595 

7407 

45 

38072 

37470 

36322 

45 

7614 

7494 

7264 

50 

37646 

36928 

35525 

50 

7529 

7386 

7105 

55 

37186 

36336 

34744 

55 

7437 

7267 

6949 

60 

36697 

35714 

33898 

60 

7339 

7143 

6780 

65 

36182 

34478 

33024 

65 

7236 

6896 

6605 

TO 

35634 

34384 

32128 

70 

7127 

6877 

6426 

75 

35076 

33682 

31218 

75 

7015 

6736 

6244 

80 

34482 

32966 

30288 

80 

6896 

6593 

6058 

85 

33883 

32236 

29384 

85 

6777 

6447 

5877 

90 

33264 

31496 

28470 

90 

6653 

6299 

5694 

95 

32636 

30750 

27562 

95 

6527 

6150 

5512 

100 

32000 

30000 

26666 

100 

6400 

6000 

5333 

105 

31357 

29250 

25786 

105 

6271 

5850 

3157 

1 

Maximum    Permissible    Stresses  in  columns  used  in  buildings. 

(Building  Ordinances  of  City  of  Chicago,  1893.) 
Maximum  permissible  loads  : 
For  cast-iron  round  columns  : 


lOOOOa 


I  =  length  of  column  in  inches; 
d  =  diameter  of  column  in  inches; 
a  =  area  of  column  in  square  inches. 


For  cast-iron  rectangular  columns; 

lOOOOa  I  and  a  as  before; 

72     •  d  =  least  horizontal  dimension  of  column. 


8=  • 


For  riveted  or  other  forms  of  wrought-iron  columns: 

12000a  I  =  and  a  as  before; 

"  —         — £2 *        r  =  least  radius  of  gyration  in  inches. 

1^~    36000r2 
For  riveted  or  other  steel  columns,  if  less  than  60r  in  length: 

S  =  17,000 .    I  and  r  as  before. 

r 

If  more  than  60r  in  length: 

S  --=  13,500a.    a  as  before. 
For  wooden  posts: 

ac  a  =  area  of  post  in  square  inches; 


1  + 


d  =  least  side  of  rectangular  post  in  inche 
I  =  length  of  post  in  inches; 

(  600  for  white  or  Norway  pine; 
C=  •<  800  for  oak; 

(  900  for  long-leaf  yellow  pine. 


HOLLOW   CYLINDRICAL   CAST   IRON   COLUMNS.     253 


SAFE   LOAD  OF  HOI.L.OW  CYLINDRICAL,  CAST-IRON 
COLUMNS.     (New  Jersey  Steel  Iron  Co.) 

(One  fifth  the  breaking  weight.) 

The  following  tables  give  the  safe  load  in  tons  of  2,000  Ibs.,  for  columns 
having  capitals  and  bases  accurately  turned  to  a  true  plane,  and  having  a 
perfectly  fair  bearing  on  these  surfaces.  In  the  case  of  columns  having 
turned  ends,  but  set  only  with  the  degree  of  care  usual  in  ordinary  building, 
only  one  half  of  these  loads  should  be  taken;  and  for  columns  not  turned  at 
all,  or  having  rounded  ends,  one  third  of  these  amounts  should  be  taken  for 
the  safe  load.  Columns  having  one  end  accurately  turned  to  a  true  plane, 
and  the  other  rounded,  may  be  loaded  to  two  thirds  the  amount  given  in  the 
tables. 

Safe  Load,  In  Tons  of   2000  Ibs.   for  Cast-iron  Columns 
with  Turned  Capitals  and  Bases. 


Outside 
Diameter, 
3  inches. 

-±3 

«w 

_g 

&JD 

a 

2 

Outside 
Diameter, 
3  inches. 

Length  in  ft. 

Outside 
Diameter, 
4  inches. 

Length  in  ft. 

Outside 
Diameter, 
4  inches. 

Thickness  in 
inches. 

Thickness  in 
inches. 

Thickness    in 
inches. 

Thickness   in 
inches. 

M 

H 

1 

% 

H 

1 

K 

H 

1 

ik 

M 

H 

1 

Ik 

12.8 
10.9 
8.9 
7.5 
6.4 
5.4 
4.8 
4.2 
3.7 
3.4 

15.9 
13.0 
10.7 
8.9 
7.6 
6.6 
5.7 
5.0 
4.5 
4.0 

17.2 
14.0 
11.4 
9.6 
8.1 
7.0 
6.1 
5.4 
4.8 
4.3 

17 
18 
19 
20 
31 
22 
23 
2-1 
25 

3.0 
2.8 
2.5 
2.3 
2.1 
1.9 
1.8 
1.7 
1.6 

3.6 
3.3 
3.0 
2.7 
2.5 
2.3 
2.1 
2.0 
1.9 

3.9 
3.5 
3.2 
2.9 
2.7 
2.5 
2.3 
2.1 
2.0 

7 
8 
9 
10 
11 
12 
13 
14 
15 
16 

24.9 
21.7 
19.0 
17.4 
14.8 
12.7 
11.1 
9.8 
8.7 
7.8 

32.9 
28.4 
24.8 
22.0 
18.7 
16.2 
14.1 
12.4 
11.1 
9.9 

38.3 
33.0 

28.7 
24.9 
21.1 
18.2 
15.9 
14.0 
12.5 
11.2 

41.7 
35.8 
81.0 
26.3 
22.4 
19.3 
16.8 
14.9 
13.2 
11.8 

17 
18 
19 
20 
21 
22 
23 
24 
25 

7.0 
6.4 
5.8 
5.3 
4.9 
4.6 
4.2 
3.9 
3.7 

8.9 
8.1 
7.4 
6.8 
6.2 
5.8 
5.3 
5.0 
4.6 

10.1 
9.1 
8.3 
7.6 
7.0 
6.5 
6.0 
5.6 
5.2 

10.7 
9.7 
8.8 
8.1 
7.5 
6.9 
6.4 
5.9 
5.5 

j 

Outside  Diameter, 

Outside  Diameter, 

Outside  Diameter, 

c 

5  inches. 

6  inches. 

7  inches. 

I 

Thickness  in  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

1 

% 

M 

1 

Ik 

H 

1 

IK 

1« 

H 

1 

ik 

IK 

7 

39.5 

53.8 

65.0 

73.3 

77.3 

95.5 

110.3 

122.1 

102.4 

128.7 

150T7 

169.4 

8 

35.1 

47.6 

57.3 

64.4 

69.7 

85.7 

98.7 

108.8 

93.6 

117.0 

136.9 

153.5 

9 

31.3 

42.3 

50.7 

56.8 

62.8 

77.1 

88.5 

97.3 

85.6 

106.7 

124.6 

139.3 

10 

28.0 

37.7 

45.1 

50.4 

56.9 

69.6 

79.6 

87.4 

78.4 

97.5 

113.5 

126.6 

11 

25  2133.8 

40  3 

44.9 

51.6 

63.0 

71.9 

78.7 

71.8 

89.2 

103.6 

115.3 

13 

22.7 

30.5 

36.2 

40.3 

46.9 

57.2 

65.2 

71.2 

66.0 

81.7 

94.8 

105.3 

13 

21.0 

27.6 

32.2 

35.2 

42.9 

52.1 

59  3 

64.6 

60.7 

75.1 

87.0 

96.5 

14 

18.5 

24.3 

28.3 

31.0 

39.3 

47.6 

54.1 

58.9 

56.0 

69.2 

80.0 

88.6 

15 

16.o 

21.6 

25.2 

27.6 

36.8 

43.9 

49.0 

52.6 

51.8 

63.9 

73.8 

81.6 

16 

14.8 

19.4 

22.6 

24.7 

33.0 

39.4 

44.0 

47.2 

48.1 

59.2 

68.2 

75.4 

17 

13.3 

17.5 

20.4 

22.3 

29.8 

35.5 

39.7 

42.5 

44.6 

54.9 

63.2 

69.8 

18 

12.1 

15.9 

18.5 

20.2 

27.0 

32.2 

36.0 

38.6 

42.0 

50.9 

57.8 

63.0 

19 

11.0 

14.5 

16.9 

18.4 

24.6 

29.4 

32.8 

35.2 

38.3 

46.4 

52.7 

57.4 

20 

10.1 

13.3 

15.4 

16.9 

22.6 

26.9 

30  1 

32.3 

35.1 

42.5 

48.3 

52.6 

21 

9.3 

12.2 

14.2 

15.5 

20.8 

24.8 

27.7 

29.7 

32.3 

39.1 

44.5 

48.4 

22 

8.6 

11.3 

13.1 

14.4 

19.2 

22.9 

25.6 

27.4 

29.8 

36.2 

41.1 

44.7 

23 

8.0 

10.5 

12.2 

13.3 

17.8 

21.2 

23.7 

25.4 

27.7 

33.5 

38.1 

41.5 

24 

7.4 

9.7 

11.3 

12.4 

16.6 

19.7 

22.1 

23.7 

25.7 

31.2 

35.4 

38.6 

25 

6.9 

9.1 

10.6 

11.5 

15.4 

18.4 

20.6 

22.1 

24.0 

29.1 

33.1 

36.0 

254 


STRENGTH   OF   MATERIALS. 


Safe  Load,  in  Tons  of  2000  Ibs.  for  Cast-iron  Columns 
with  Turned  Capitals  and  Bases. 


^J 

Outside  Diameter, 

Outside  Diameter. 

Outside  Diameter, 

8  inches. 

9  inches. 

10  inches. 

.s 

£ 
ti 

Thickness  in  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

1 

u 

1 

IK 

Ifc 

i 

1 

m 

m 

H 

1 

m 

Ifc 

7 

128.3 

162.6 

193.0 

219.5 

154.8 

197.7 

236.6 

271.4 

181.6 

233.4 

280.9 

324.2 

8 

118.7 

150.1 

177.7 

201.6 

144.7 

184.5 

220.2 

252.0 

171.1 

219.5 

263.8 

303.!) 

9 

109.8 

138.5 

163.6 

185.2 

135.0 

171.8 

204.7 

233.9 

160.9 

206.2 

247.3 

284.5 

10 

101.5 

127.8 

150.7 

170.2 

126.0 

160.0 

190.3 

217.0 

151.2 

193.4 

231.6 

266.0 

11 

94.0 

118.0 

139.0 

156.7 

117.5 

149.0 

177.0 

201.4 

142.0 

181.4 

216.9 

248.7 

w 

87.0 

109.21128.2 

144.3 

109.6 

138.8 

164.5 

187.0 

133.4 

170.1 

203.1 

23<!.ti 

13 

80.7 

101.1 

118.5 

133.2 

102.4 

129.4 

153.2 

173.9 

125.3 

159.6 

190.3 

217.7 

14 

75.0 

93.8 

109.8 

123.2 

95.7 

120.8 

142.8 

161.9 

117.8 

149.8 

178.4 

203.8 

15 

69..  8 

87.1 

101.9 

114.2 

89.5 

112.9 

133.3 

150.9 

110.8 

140.7 

167.5 

191.1 

1(5 

65.0 

81.1 

94.7 

106.1 

83.9 

105.7 

124.6 

140.9 

104.3 

132.4 

157.3 

179.3 

17 

60.7 

75.7 

88.3 

98.7 

78.7 

99.0 

116.7 

131.8 

98.3 

124.6 

148.0 

168.5 

IS 

56.8 

70.7 

§2'4 

92.1 

73.9 

92.9 

109.4 

123.5 

92.7 

117.4 

139.3 

158.5 

19 

53.2 

66.2 

77.1 

86.1 

69.6 

87.4 

102.7 

115.9 

87.5 

110.8 

131.3 

149.3 

20 

51.1 

62.7 

72.1 

79.5 

65.5 

82.3 

96.7 

108.9 

82.7 

104.6 

124.0 

140.8 

21 

47.0 

57.7 

66.4 

73.2 

61.8 

75.5 

91.0 

102.6 

78.3 

99.0 

117.2 

133.0 

22 

43.5 

53.3 

61.3 

67.6 

58.4 

73.2 

85.9 

96.7 

74.2 

93.7 

110.9 

125.8 

23 

40.3 

49.4 

56.8 

62.7 

55.9 

69.3 

80.4 

89.5 

70.4 

88.9 

105.1 

119.1 

24 

37.5 

46.0 

52  9 

58.3 

52.0 

64.4 

74.8 

83.3 

66.9 

84.3 

99.7 

112.9 

25 

35.0 

42.9 

49  '.3 

54.4 

48.5 

60.1 

69.8 

77.7 

64.9 

81.0 

94.2 

106.3 

Outside  Diameter, 

Outside  Diameter, 

•  Outside  Diameter, 

11  inches. 

12  inches. 

13  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

1 

IK 

Ifc 

2 

1 

IK 

m 

2 

1 

m 

V/2 

2 

269.4 

325.9 

377.6 

469.5 

305.3 

370.8 

431.7 

540.9 

341.5 

414.4 

485.7 

612.7 

255.1 

308.1 

356.8 

442.2 

290.9 

352.8 

410.2 

512.8 

327.0 

396.3 

464.1 

583  9 

241.2 

290.8 

336.3 

415.6 

276.6 

335.0 

389.1 

485.0 

312.4 

378.4 

442.5 

555.5 

227.8 

274.2 

316.7 

390.3 

262.7 

317.7 

368.6 

458.3 

298.0 

360.6 

421.3 

527.8 

214.9 

258.4 

298.1 

366.3 

249.2 

301.0 

348.8 

432.9 

284.0 

343.4 

400.6 

501.1 

202.7 

243.5 

280.5 

343.9 

236.3 

285.1 

330.0 

408.6 

270.5 

326.7 

380.8 

475.3 

191.2 

229.4 

264.0 

322.8 

223.9 

270.0 

312.2 

385.7 

257.5 

310.8 

361.8 

450.7 

180.5 

216.2 

248.5 

303.3 

212.3 

255.6 

295.3 

364.1 

245.0 

295.5 

343.7 

427.4 

170.3 

203.9 

234.1 

285.1 

201.2 

242.1 

279.4 

343.9 

233.2 

281.1 

326.5 

405.4 

160.9 

192.4 

220.7 

268.3 

190.8 

229.4 

264.5 

325.0 

222.0 

267.3 

310.3 

384.6 

152.1 

181.7 

208.2 

252.7 

181.1 

217.5 

250.6 

307.4 

211.3 

254.4 

295.0 

365.1 

143.9 

171.7 

196.7 

238.3 

171.9 

206.3 

237.5 

290.9 

201.3 

242.1 

280.5 

346.7 

136.2 

162.5 

185.9 

225.0 

163.3 

195.8 

225.3 

275.6 

191.8 

230.6 

267.0 

329.5 

129.1 

153.9 

176.0 

212.6 

155.2 

186.0 

213.9 

261.3 

182.8 

219.7 

254.2 

313.3 

122.4 

145.9 

166.7 

201.2 

147.7 

176.9 

203.2 

247.9 

174.4 

209.5 

242.2 

298.2 

116.3 

138.4 

158.1 

190.6 

140.6 

168.3 

193.3 

235.5 

166.5 

199.9 

230.9 

284.0 

110.5 

131.5 

150.1 

180.7 

134.0 

160.3 

184.0 

224.0 

159.0 

190.8 

220.4 

270.7 

105.2 

125.1 

142.7 

171.6 

127.8 

152.8 

175.3 

213.2 

152.0 

182.3 

210.4 

258.3 

[100,9 

119.1 

135  7 

163.1 

122.0 

145.8  1167.1 

203.1 

145.4 

174.3 

201.0 

246.6 

ECCENTRIC  LOADING  OF  COLUMNS. 


255 


Safe  Load  of  Cast-iron  Columns— (Continued). 


Outside  Diameter, 

Outside  Diameter, 

Outside  Diameter, 

14  inches. 

15  inches. 

16  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

Thickness  in  inches. 

1 

w 

IK 

2 

1 

IK 

m 

2 

1 

l* 

IK 

2 

377.7 

461.1 

539.9 

684.6 

413.7 

506.1 

594.0 

"56.7 

449.8 

551.1 

648.0 

828.6 

363.1 

442.8 

518.0 

655.9 

399.3 

487.9 

572.2 

^27.7 

435.3 

532.8 

626.3 

799.8 

348.5 

424.4 

496.3 

627.0 

384.4 

469.5 

550.1 

698.4 

420.5 

514.4 

604.1 

770.4 

333.8 

406.3 

474.6 

598.5 

369.7 

451.0 

528.2 

669.3 

405.6 

496.0 

581.8 

740.9 

319.4 

388.5 

453.4(570.7 

355.1 

433.0 

506.3 

640.9 

390.6 

477.4 

559.8 

711.7 

305.4 

371.1 

432.6543.6 

340.6 

415.0 

485.0 

612.8 

376.0 

459.3 

538.0 

683.4 

-m.B 

354.3 

412.7J517.7 

326.6 

397.6 

464.5 

585.9 

361.6 

441.2 

516.7 

655.1 

278.8 

338.2 

393.6|493.0 

318.0 

380.7 

444.4 

559.7 

347.6 

423.8 

495.9 

628.0 

•J<56.2 

322.7 

375.3 

469.4 

299.9 

364.5 

425.2 

534.9 

333.9 

406.9 

475.9 

601.8 

254.3 

308.0 

357.9 

446.9 

287.2 

348.9 

406.7 

510.9 

320.7 

390.6 

456.6 

576.6 

242.9 

294.0 

341.4 

425.7 

275.1 

334.0 

389.1 

488.1 

308.0 

374.9 

438.0 

552.5 

232.0 

280.6 

325.6 

405.5 

263.6 

319.7 

372.2 

466.5 

295.8 

359.9 

420.1 

529.4 

221.7 

268.0 

310.8 

386.5 

252.5 

306.2 

356.2 

445.9 

284.1 

345.4 

403.0    507.3 

212.0 

256.1 

296.7 

368.6 

242.0 

293.3 

341.0 

426.3 

272.9 

331.6 

386.8 

486.3 

202.7 

244.7 

283.5 

351.8 

232.0 

281.0 

326.5 

407.8 

262.1 

318.4 

371.2 

466  2 

194.0 

234.0 

270.9 

335.9 

222.5 

269.3    1312.8 

390.3 

251.9 

305.9 

356.4 

447.2 

185.7 

224.0 

259.1 

320.9 

213.4 

258.3 

299.8 

373.7 

242.2 

293.9 

342.3 

429.1 

177.9 

214.4 

248.0 

306.8 

204.9 

247.8 

287.5 

358.1 

232.9 

282.5 

328.8 

411.9 

170.5 

205.4 

237.5 

294.1 

196.7 

237.8 

275.9 

343.2 

224.0 

271.6 

316.1 

395.6 

ECCENTRIC  LOADING  OF  COLUMNS. 

In  a  given  rectangular  cross-section,  such  as  a  masonry  joint  under  press- 
ure, the  stress  will  be  distributed  uniformly  over  the  section  only  when  the 
resultant  passes  through  the  centre  of  the  section ;  any  deviation  from  such 
a  central  position  will  bring  a  maximum  unit  pressure  to  one  edge  and  a 
minimum  to  the  other;  when  the  distance  of  the  resultant  from  one  edge  is 
one  third  of  the  entire  width  of  the  joint,  the  pressure  at  the  nearer  edge  is 
twice  the  mean  pressure,  while  that  at  the  farther  edge  is  zero,  and  that 
when  the  resultant  approaches  still  nearer  to  the  edge  the  pressure  at  the 


the  pressure  at  the  nearer  edge,  when  the  resultant  approaches  it  nearer 
than  one  third  of  the  width,  increases  very  rapidly  and  dangerously,  becom- 
ing theoretically  infinite  when  the  resultant  reaches  the  edge. 

With  a  given  position  of  the  resultant  relatively  to  one  edge  of  the  joint  or 
section,  a  similar  redistribution  of  the  pressures  throughout  the  section  may 
be  brought  about  by  simply  adding  to  tor  diminishing  the  width  of  the 
section. 

Let  P  =  the  total  pressure  on  any  section  of  a  bar  of  uniform  thickness. 

w  =  the  width  of  that  section  =  the  area  of  the  section,  when  thickness 

p 

p  =  —  =  the  mean  unit  pressure  on  the  section. 

M  —  the  maximum  unit  pressure  on  the  section. 
m  —  the  minimum  unit  pressure  on  the  section. 

d  —  the  eccentricity  of  the  resultant  =  its  distance  from  the  centre  of 
the  section. 


Then  M  -  p  (l  4 ~  )  and  m  =  p  (l  -  ^). 


When  d  =  -  w  then  M  =  2p  and  m  =  O. 

When  d  is  greater  than  l/6w,  the  resultant  in  that  case  being  less  than 
one  third  of  the  width  from  one  edge,  p  becomes  negative.  (J.  C.  Traut- 
wine,  Jr.,  Engineering  News,  Nov.  23, 1893.) 


256 


STKEKGTH   OF   MATERIALS. 
BUILT    COLUMNS. 


From  experiments  by  T.  D.  Lovett,  discussed  by  Burr,  the  values  of /and 
a  in  several  cases  are  determined,  giving  empirical  forms  of  Gordon's  for- 
mula as  follows:  p  =  pounds  crushing  strength  per  square  inch  of  section, 
I  =  length  of  column  in  inches,  r  =  radius  of  gyration  in  inches. 


Keystone 


Open.  Square 

FIG.  76. 


Fhocnix       Am.Br.Co. 


Flat  Ends. 


Keystone 
Columns. 

39,500 
"*"  18,300  r2 


Square 
Columns. 

39,000 
*~  35,000  r 


(4) 


Phcenix 
Columns. 

42,000 
1       V 


American  Bridge 
Co.  Columns. 


r(8) 


36.000 


p- 


36,000 

1 
" 18,300  r2 


^  50,000  r2 
Flat  Ends,  Swelled* 


1  + 


1       Z2 


(9) 


46,000  r2 


I  (2) 


Pin  Ends. 


39,000 

«  ,  .  1   - 
^  17.000  r2 


(5) 


42,000 

1  .   *   *- 

•  22,700  r2 


•(7) 


36,000 

1   l__ 
"21,500  r2 


(10) 


36,000 

1   [_ 
"  15,000  r2 


Pin  Ends,  Swelled. 


(3) 


P  = 


Round  Ends. 

42,000 


1   Z2 
12,500  r2 


(8) 


36,000 


(11) 


11,500  r2 


With  great  variations  of  stress  a  factor  of  safety  of  as  high  as  6  or  8  may 
be  used,  or  it  may  be  as  low  as  3  or  4,  if  the  condition  of  stress  is  uniform  or 
essentially  so. 

Burr  gives  the  following  general  principles  which  govern  the  resistance  of 
built  columns  : 

The  material  should  be  disposed  as  far  as  possible  from  the  neutral  axis 
of  the  cross-section,  thereby  increasing  ?-; 

There  should  be  no  initial  internal  stress; 

The  individual  portions  of  the  column  should  be  mutually  supporting; 

The  individual  portions  of  the  column  should  be  so  firmly  secured  to  each 
other/that  no  relative  motion  can  take  place,  in  order  that  the  column  may 
fail  as  a  whole,  thus  maintaining  the  original  value  of  r. 

Stoney  says:  "When  the  length  of  a  rectangular  wronght-iron  tubular 
column  does  not  exceed  30  times  its  least  breadth,  it  fails  by  the  bulging  or 
buckling  of  a  short  portion  of  the  plates,  not  by  the  flexure  of  the  pillar  as  a 
whole." 

In  Trans.  A.  S.  C.  E.,  Oct.  1880,  are  given  the  following  formulae  for  the 
Ultimate  resistance  of  wrought-iron  columns  designed  by  C.  Shaler  Smith : 


BUILT   COLUMNS. 


257 


Square 
Columji. 

38,500 
— p 

1  +  5820  d* 


38,500 


Flat  Ends. 


PhcBnix 
Column. 

42,500 


American  Bridge 
Co.  Column. 


T*  (15) 


36,500 


(18) 


1500  d2  ^3750 

One  Pin  End. 

40,000 


Common 
Column. 

36,500 


1  + 


1     j2 
2700  d2 


(21) 


36,500 


-- 

3000  d2 


37,500 


2250  d2 


2250  d2 


1500  d2 


Two  Pin  Ends. 

36,600  36,500 


1 

1500  d2 


(17) 


(20) 


14- 


36,500 
1 


(23) 


1200 


The  "  common  "  column  consists  of  two  channels,  opposite,  with  flanges 
outward,  with  a  plate  on  one  side  and  a  lattice  on  the  other. 

The  formula  for  "  square  "  columns  may  be  used  without  much  error  for 
the  common-chord  section  composed  of  two  channel-bars  and  plates,  with 
the  axis  of  the  pin  passing  through  the  centre  of  gravity  of  the  cross- 
section.  (Burr). 

Compression  members  composed  of  two  channels  connected  by  zigzag 
bracing  may  be  treated  by  formulae  4  and  5,  using  /  =  36,000  instead  of 
39,000. 

Experiments  on  full-sized  Phoenix  columns  in  1873  showed  a  close  agree- 
ment of  the  results  with  formulae  6-8.  Experiments  on  full-sized  Phoenix 
columns  on  the  Watertown  testing-machine  in  1881  showed  considerable  dis- 
crepancies when  the  value  of  l-*-r  became  comparatively  small.  The  fol- 
lowing modified  form  of  Gordon's  formula  gave  tolerable  results  through 
the  whole  range  of  experiments  : 


Phcenix  columns,  flat  end,    p  = 


40,000  (l  -f  y) 


1  -f  50,000 


j2  ' 
r2 


Plotting  results  of  three  series  of  experiments  on  Phoenix  columns,  a 
more  simple  formula  than  Gordon's  is  reached  as  follows  : 


Phoenix  columns,  flat  ends,  p  =  39,640  -  46-,  when  I  - 


r  is  from  30  to  140; 


p  =  64,700  -  4600  y  I  when  I  -4-  r  is  less  than  30. 
r 


Dimensions  of  Phcenix  Columns. 

(Phcenix  Iron  Co.) 

The  dimensions  are  subject  to  slight  variations,  which  are  unavoidable  in 
rolling  iron  shapes. 

The  weights  of  columns  given  are  those  of  the  4,  6,  or  8  segments  of 
which  they  are  composed.  The  rivet-heads  add  from  2  to  5  per  cent  to  the 
weights  given.  Rivets  are  spaced  3,  4,  or  6  inches  apart  from  centre  to 
centre,  and  somewhat  more  closely  at  the  ends  than  towards  the  centre  of 
the  column. 

G  columns  have  8  segments,  E  columns  6  segments,  (7,  Z?2,  U1,  and  A  have 
4  segments.  Least  radius  of  gyration  =  D  X  .3636. 


258 


Phoenix  Column*. 


One  Segment. 

Diameters  in  inches. 

One  Column. 

Safe 

j§ 

i 

£ 

K      - 

Load  in 

.a 

o  ^ 

f->  oj 

ga 

net  tons 

1  - 

.S'o 

•§ 

03 

o  * 

s. 

la"^  oJ 

for 

•*•*  o3 

1 

1 

^  he 

«w  c"^ 

+=  § 

P3  2^5 

16-feet 

11 

|| 

1 

O 

-I 

ill 

!& 

1-1 

Lengths. 

F  . 

£& 

•e 

^ 

qfa 

,«.  ~ 

t£"" 

3^ 

3-16 

9V 

f 

4 

6    1-16 

3.8 

12.6 

1.45 

17.72 

1-i, 

12' 

A 

3%      1 

6    3-16 
6    5-16 

4.8 
5.8 

16.0 
19.3 

.50 
1.55 

22.65 
27.66 

17 

I 

4% 

6    7-16 

6.8 

22.6 

.59 

32.58 

J4 

16 

5    5-16 

8    1-16 

6.4 

21.3 

.92 

32.00 

5-16 

19^ 

5    7-16 

8% 

7.8 

26.0 

.96 

39.15 

23 

i 

5    9-16 

8M 

9.2 

30.6 

2.02 

46.45 

*f-16 
|tf 

5* 

33^ 

B 

«H 

5  11-16 
5  13-16 
5  15-16 

8    7-16 

10.6 
12.0 
13.4 

35.3 
40.0 
44.6 

2.07 
2.11 
2.16 

53.72 
61.08 
68.48 

37 

6    1-16 

8% 

14.8 

49.3 

2.20 

70.88 

1,6 

2214 

f 

6    7-16 
6    9-16 

9V 

7.4 
9.0 

24.6 
30.0 

2.34 
2.39 

45.72 
55.77 

J16 

B, 

6  11-16 
6  13-16 

9  Vl6 

10.6 
12.2 

35.3 
40.6 

2.43 

2.48 

65.82 
75.95 

34^ 

5jt 

6  15-16 

9V£ 

13.8 

46.0 

2.52 

86.08 

9-16 

38V> 

7    1-16 

9% 

15.4 

51.3 

2.57 

96.30 

% 

42^ 

[ 

7    3-16 

9  11-16 

17.0 

56.6 

2.61 

106.49 

M 

25U 

{ 

7  11-16 

11     9-16 

10.2 

34. 

2.80 

64.41 

5-16 

31 

7  13-16 

11% 

12.4 

41.3 

2.85 

78.45 

% 

36 

7  15-16 

11  11-16 

14.4 

48.0 

2.90 

91.28 

7-16 

41 

8    1-16 

11% 

16.4 

54.6 

2.94 

104.09 

1-16 

46 
51 

8    3-16 
8    5-16 

11  13-16 

18.4 
20  4 

61.3 
68. 

2.98 
3.03 

116.94 
129.87 

11-16 

56 
62 

7°* 

8    7-16 
8    9-16 

12 
12    1-16 

22.4 

24.8 

74.6 

82.6 

3.08 
3.12 

142.83 

158.34 

% 

68 

8  11-16 

12    3-16 

27.2 

90.6 

3.16 

173.86 

13-16 

73 

8  13-16 

12    5-16 

29.2 

97.3 

3.21 

186.93 

% 

78 

8  15-16 

12    7-16 

31.2 

104. 

3.26 

200.02 

1 

89 

9    3-16 

12    9-lb 

35.6 

118.6 

3.34 

228.72 

Iff 

99 
109 

I 

9    7-16 
9  11-16 

12% 

12  15-16 

39.  C> 
43.6 

132. 
145.3 

3.43 
3.52 

255.02 

281.41 

IX 

28 

JJ1X 

15    7-16 

16.8 

56. 

4.18 

109.88 

5-16 

321^ 

11% 

15    9-16 

19.5 

65. 

4.23 

127.64 

% 

37 

11% 

15  11-16 

22.2 

74. 

4.28 

145.48 

7-16 

42 

11% 

15  13-16 

25.2 

84. 

4.32 

165.21 

J4 

47 

12 

15% 

28.2 

94. 

4.36 

184.98 

9-16 

52 

12% 

16 

31.2 

104. 

4.40 

205.33 

% 

57 

E 

12^4 

16    1-16 

34.2       114. 

4.45 

224.64 

11-16 

62 

11 

12% 

16    3-16 

37.2 

124. 

4.50 

244.53 

13-16 

68 
73 

1<H 

16    5-16 
16    7-16 

40.8 
43.8 

136. 
146. 

4.55 
4.60 

268.37 
288.30 

% 

78 

12% 

16% 

46.8 

156. 

4.64 

308.16 

1 

88 

13 

16% 

52.8 

176. 

4.73 

348.15 

1% 

98 

13*4 

17 

58.8 

196. 

4.82 

388.15 

1M 

108 

I 

13^2 

17    3-16 

64.8 

216. 

4.91 

428.26 

5-16 

31 

f 

15 

19% 

24.8 

82.6 

5.45 

164.87 

% 

36 

] 

15% 

19J4 

28.8 

96. 

5.50 

101.54 

7-16 

41 

G 

15J4 

19% 

32.8 

109.3 

5.55 

218.25 

H 

46 

15% 

19    7-16 

36.8 

122.6 

5.59 

244.95 

9-16 

51 

15% 

40.8 

136. 

5.63 

271.69 

% 

56 

. 

15% 

19% 

44.8 

149.3 

5.68 

298.45 

FORMULAE    FOR   IRON   AND    STEEL   STRUTS. 


259 


One  Segment. 

Diameters  in  inches. 

One  Column. 

Safe 

cs 

j§ 

$ 

£J 

S3  fl" 

Load  in 

p  o1. 

^    n 

^3  ° 

net  tons 

$ 

a  w 

II 

f& 

6 

2 
"8 

a 

I 

2 

i 

it 

s|< 
s|| 

S.'S 

i! 

D  « 

!ll 

for 
16-feet 
Lengths. 

flf 

|| 

^ 

Q 

Qfe 

^^.= 

fe-2 

j"-2 

11-16 

61 

r 

15% 

19% 

48.8 

162.6 

5.72 

325.21 

% 

66 

19% 

52.8 

176. 

5.77 

352.02 

13-16 

71 

16            20 

56.8 

189.3 

5.82 

378.85 

% 

76 

G 

16%         20% 

60.8 

202.6 

5.87 

405.70 

1 

86 

14%    i 

16%         203/6 

68.8 

229.3 

5.95 

464.38 

1% 

96 

16%         20% 

76.8 

256. 

6.04 

513.17 

1J4 

106 

i 

16%        120% 

84.8 

282.6 

6.14 

567.06 

1% 

116 

I 

17%        |21 

92.8 

309.3 

6.23 

620.98 

Working  Formulae  for  Wro  light-iron  and  Steel  Struts 
of  various  Forms.—  Burr  gives  the  following  practical  formulae,  which 
he  believes  to  possess  advantages  over  Gordon's: 

PJ  —  Working 
p  =  Ultimate  Strength  = 

Strength,  1/5  Ultimate, 

Ibs.  per  sq.  in.  Ibs.  per  sq. 

Kind  of  Strut.  of  Section.  in.  of  Section. 

Flat  and  fixed  end  iron  angles  and  tees  44000-140  —    (1)       8800-28  —    (2) 

r  r 

Hinged-end  iron  angles  and  tees  .......  46000—175  —    (3)       9200—35  —    (4) 

Flat-end  iron  channels  and  I  beams  .  .  .  .40000-  1  10  —    (5)       8000-22  —    (6) 

r  r 

Flat-end  mild-steel  angles  ..............  52000-180—    (7)      10400-36—    (8) 

Flat-end  high-steel  angles  ..............  76000-  290  —    (9)      15200-58  —    (10) 


Pin-end  solid  wrought  iron  columns  ____  32000-  80  — 


32000-277  - 
d  J 


6400 


—16  — 

• 


6400-55  — 
d  J 


Equations  (1)  to  (4)  are  to  be  used  only  between  —  =  40  and  —  =  200 

r  r 

(5)  and  (6)      "    "  "      "        "         "  "  =  20    "    "   =200 

(7)  to  (10)       "    "   "      »        "         "  »  =  40    "     "   =200 

(11)  and  (12)  "     MM      "        "         "  «  =  20    "    "=200 

or     ~  =    6  and  ^-  =    65 
d  d 

Steel  columns,  properly  made,  of  steel  ranging  in  specimens  from  65,000  to 
73,000  Ibs.  per  square  inch  should  give  a  resistance  25  to  33  per  cent  in  ex- 
cess of  that  of  wrought-iron  columns  with  the  same  value  of  I  H-  r.  provided 
that  ratio  does  not  exceed  140. 

The  unsupported  width  of  a  plate  in  a  compression  member  should  not 
exceed  30  times  its  thickness. 

In  built  columns  the  transverse  distance  between  centre  lines  of  rivets 
securing  plates  to  angles  or  channels,  etc.,  should  not  exceed  35  times  the 
plate  thickness.  If  this  width  is  exceeded,  longitudinal  buckling  of  the 


260 


STRENGTH    OF   MATERIALS. 


plate  takes  place,  and  the  column  ceases  to  fail  as  a  whole,  but  yields  in 
detail. 

The  same  tests  show  that  the  thickness  of  the  leg  of  an  angle  to  which 
latticing  is  riveted  should  not  be  less  than  1/9  of  the  length  of  that  leg  or 
side  if  the  column  is  purely  and  wholly  a  compression  member.  The  above 
limit  may  be  passed  somewhat  in  stiff  ties  and  compression  members  de- 
signed to  carry  transverse  loads. 

The  panel  points  of  latticing  should  not  be  separated  by  a  greater  distance 
than  60  times  the  thickness  of  the  angle-leg  to  which  the  latticing  is  riveted, 
if  the  column  is  wholly  a  compression  member. 

The  rivet  pitch  should  never  exceed  16  times  the  thickness  of  the  thinnest 
metal  pierced  by  the  rivet,  and  if  the  plates  are  very  thick  it  should  never 
nearly  equal  that  value. 

Merriman's  Rational  Formula  for  Columns  (Eng.  News, 
>July  19,  1894). 


7r2.fi;   r2 


(2) 


B  —  unit-load  on  the  column  =  total  load  P  -4-  area  of  cross-section  A ; 
C  =  maximum  compressive  unit-stress  on  the  concave  side  of  the  column ; 
I  =  length  of  the  column;  r  =  least  radius  of  gyration  of  the  cross-section; 
E  =  coefficient  of  elasticity  of  the  material;  n  =•  1  for  both  ends  round; 
n  =  4/9  for  one  end  round  and  one  fixed;  n  =  %  for  both  ends  fixed.  This 
formula  is  for  use  with  strains  within  the  elastic  limit  only:  it  does  not 
hold  good  when  the  strain  C  exceeds  the  elastic  limit. 

Prof.  Merrimau  takes  the  mean  value  of  E  for  timber  =  1,500,000,  for  cast 
iron  =  15,000,000,  for  wrought-iron  =  25,000,000,  and  for  steel  =  30,000,000, 
and  7T2  =  10  as  a  close  enough  approximation.  With  these  values  he  com- 
putes the  following  tables  from  formula  (1): 

I.— Wrought-iron  Columns  with  Round  Ends. 


Unit- 
load. 


Maximum  Compressive  Unit-stress  C. 


—  or  B. 
A 

7  =  a> 

1  =  40 
r 

1  =  60 
r 

1  =  80 
r 

l  =  :oo 

t 

—  =  120 
r 

1=,40 
r 

1  =  160 

r 

5.000 
6,000 
7,000 
8,000 

5,040 
6,055 

7,080 
8,100 

5,170 
6,240 
7,330 
8,430 

5,390 
6,560 
7,780 
9,040 

5,730 
7,090 
8,530 
10,060 

6,250 
7,890 
9,720 
11,660 

6,980 
9,090 
11,610 
14,640 

8,220 
11,330 
15,510 
21,460 

10,250 
15,560 
24,720 

9,000 

9,130 

9,550 

10,340 

11,690 

14,060 

18,380 

10,000 
11.000 

10,160 
11,200 

10,680 
11,750 

11,680 
13,070 

13,440 
15  310 

16,670 
19640 

23,090 

12,000 

12,240 

13  000 

14  500 

17320 

23  080 

13,000 

13,280 

14,180 

15,990 

19480 

STRENGTH  OF  WROUGHT  IRON  AND  STEEL  COLUMNS.  261 


II.— Wrouglit-iron  Columns  with  Fixed  Ends. 


Unit- 
load. 

Maximum  Compressive  Unit-stress  C. 

—  or  B. 

A 

1  =  20 
r 

1  =  40 

1  =  60 

1.80 

-=100 

—  =  120 

L  =  1401!  =  160 

0,000 
7,000 
8,000 
9,000 
10,000 
11,000 
12,000 
13,000 
14,000 

6,010 
7,020 
8,025 
9,030 
10,040 
11,050 
12,060 
13,070 
14,080 

6,060 
7,080 
8,100 
9,130 
10,160 
11,200 
12,240 
13,280 
14,320 

6,130 
7,180 
8,240 
9,300 
10,370 
11,450 
12,540 
13,640 
14,740 

6,240 
7,330 
8,430 
9,550 
10,710 
11,830 
13,000 
14,210 
15,380 

6,380 
7,530 
8,700 
9,890 
11,110 
12,360 
13,640 
14,940 
16,280 

6,570 
7,780 
9,040 
10,340 
11,680 
13,070 
14,510 
15,990 
17,530 

6,800 
8,110 
9,490 
10,930 
12,440 
14,020 
15,690 
17,440 
19,290 

7,090 
8,530 
10,060 
11,690 
13,440 
15,310 
17,320 
19,480 
21,820 

III.— Steel  Columns  with  Round  Ends. 


Unit- 
load. 

Maximum  Compressive  Unit-stress  C. 

—  or  B. 
A 

l  =  2o 

T 

1  =  40 

T 

1  =  60 

r 

1  =  80 
r 

1.100 
r 

1  =120 
r 

1  =  140 
r 

1  =  160 
r 

6,000 
7,000 
8,000 
9,000 
10,000 
11,000 
12,000 
13,000 
14,000 

6,050 
7,070 
8,090 
9,110 
10,130 
11,160 
12,200 
13,330 
14,250 

6,200 
7,270 
8,380 
9,450 
10,560 
11,690 
12,820 
13,970 
15,130 

6,470 
7,650 
8,770 
10,090 
11,360 
12,670 
14,020 
15,400 
16,830 

6,880 
8,230 
9,650 
11,140 
12,710 
14,370 
16,130 
18,000 
19,960 

7,500 
9,130 
10,870 
12,850 
15,000 
17,370 
20,000 
22,940 
26,250 

8,430 
10,540 
12,900 
15.850 
19,230 
23,300 
28,300 

9,870 
12,900 
16,760 
20,930 

28,850 

12,300 
17,400 
24,590 

IV.— Steel  Columns  with  Fixed  Ends. 


Unit- 
load. 

Maximum  Compressive  Unit-stress  C. 

™  or  B. 

1  =  30 
r 

1  =  40 

1=60 
r 

1  =  80 
r 

1  =  100 
r 

f-» 

1=140 

r 

1=  160 
r 

7,000 
8,000 
9,000 
10,000 
11,000 
12,000 
13,000 
14,000 
15,000 

7,020 
8,020 
9,030 
10,030 
11,040 
12,050 
13,060 
14,070 
15,080 

7,070 
8,090 
9,110 
10,130 
11,100 
12,200 
13,230 
14,250 
15,310 

7,150 
8,200 
9,250 
10,310 
11,380 
12,450 
13,530 
14,610 
15,710 

7,270 

8,380 
9,450 
10,560 
11,690 
12,820 
13,970 
15,130 
16,310 

7,430 
8,570 
9,730 
10,910 
12,110 
13.330 
14^580 
15,850 
17,140 

7,650 
8,770 
10,090 
11,360 
12,670 
14,020 
15,400 
16,830 
18,290 

7,900 
9,200 
10,550 
11,810 
13,410 
14,930 
16,500 
18,150 
19,870 

8,230 
9,650 
11,140 
12,710 
14,370 
16,130 
17,990 
19,960 
22,060 

The  design  of  the  cross-section  of  a  column  to  carry  a  given  load  with 
maximum  unit-stress  C  may  be  made  by  assuming  dimensions,  and  then 


262  STRENGTH   OF   MATERIALS. 


bre 
Ar 


HI  oe  snort ened. 

The  formula  (1)  may  be  put  in  another  form  which  in  some  cases  will  ab- 
reviate  the  numerical  work.  For  B  substitute  its  value  P-*-  A,  and  for 
r2  write  /,  the  least  moment  of  inertia  of  the  cross-section ;  then 


" 


in  which  I  and  ?-2  are  to  be  determined. 

For  example,  let  it  be  required  to  find  the  size  of  a  square  oak  column 
with  fixed  ends  when  loaded  with  24,000  Ibs.  and  16  ft.  long,  so  that  the 
maximum  compressive  stress  C  shall  be  1000  Ibs.  per  square  inch.  Here 
/  =  24,000,  C  =  1000,  n  =  *4,  7r2  =  10,  E  =  1,500,000,  I  -  16  X  12,  and  (3)  be- 
comes 

I  -  24r2  =  14.75. 

Now  let  x  be  the  side  of  the  square;  then 

1=  -g     and    r2  =  ^, 

so  that  the  equation  reduces  to  x4  —  24#2  =  177,  from  which  x1*  is  found  to  be 
29.92  sq.  in.,  and  the  side  x  =  5.47  in.  Thus  the  unit-load  B  is  about  802 
Ibs.  per  square  inch. 

WORKING  STRAINS  ALLOWED  IN   BRIDGE 
MEMBERS. 

Theodore  Cooper  gives  the  following  in  his  Bridge  Specifications  : 
Compression  members  shall  be  so  proportioned  that  the  maximum  load 
shall  in  no  case  cause  a  greater  strain  than  that  determined  by  the  follow- 
ing formula : 

8000 
P  — — for  square-end  compression  members  ; 

~*~  40,000r2 

8000 
P  =  —    — _ for  compression  members  with  one  pin  and  one  square  end ; 

1  +  30,000r2 

P—  —    — — —  for  compression  members  with  pin-bearings; 
1  ~*~  20,000r2 

(These  values  may  be  increased  in  bridges  over  150  ft.  span.  See  Cooper's 
Specifications.) 

P  =  the  allowed  compression  per  square  inch  of  cross-section; 
I  —  the  length  of  compression  member,  in  inches; 
r  =  the  least  radius  of  gyration  of  the  section  in  inches. 

No  compression  member,  however,  shall  have  a  length  exceeding  45  times 
its  least  width. 

The  Phoenix  Bridge  Company  give  the  following  : 

The  greatest  working  stresses  in  wrought-iron  compression  members  of 
spans  150  feet  in  length  and  under  shall  be  the  following: 

Flat  Ends.                  Pin  Ends. 
8400                              8400 
Phoenix  column P—  —    — ™ —        P  = ^ — 


'    *n  nnrws  ' 


30,000r2 


8000                               7800 
Latticed  or  common  column P  = — —        P  = ==- 


!   , 

T 


—- 
40,000r2  T  80,000r» 


Angle-iron  struts  ..................  P=9000-3o|         P  =  9000  -  34  ^ 


WORKING  STRAINS  ALLOWED  IN  BRIDGE  MEMBERS.  2G3 

Upper  chords  shall  be  proportioned  by  the  flat-end  formula. 

A  mean  between  flat-end  and  pin-end  results  shall  be  used  for  one  pin  end 
and  one  flat  end. 

Lateral  and  transverse  struts  shall  be  designed  by  taking  working  stresses 
equal  to  one  and  four  tenths  those  given  by  the  preceding  formulae. 

Working  Stresses  allowed  in  Bridge  Tension  Members. 

(Theodore  Cooper's  Specifications.) 

All  parts  of  the  structure  shall  be  so  proportioned  that  the  maximum 
loads  shall  in  no  case  cause  a  greater  tension  than  the  following  (except  in 
spans  exceeding  150  feet)  : 

Pounds  per 

sq.  in. 
On  lateral  bracing  .............  .................................  15,000 

On  solid  rolled  beams,  used  as  cross  floor-beams  and  stringers.    9,000 
On  bottom  chords  and  main  diagonals  (forged  eye-bars)  .....  10,000 

On  bottom  chords  and  main  diagonals  (plates  or  shapes),  net 

section  ............................................   ........     8,000 

On  counter  rods  anfi  long  verticals  (forged  eye-bars)  ..........     8,000 

On  counter  and  long  verticals  (plates  or  shapes),  net  section..    6,500 
On  bottom  flange  of  riveted  cross-girders,  net  section  ........     8,000 

On  bottom  flange  of  riveted  longitudinal  plate  girders  over 

20  ft.  long,  net  section  ...    ...............................     8,000 

On  bottom  flange  of  riveted  longitudinal  plate  girders  under 

20  ft.  long,  net  section  ....................................    7,000 

On  floor-beam  hangers,  and  other  simitar  members  liable  to 

sudden  loading  (bar  iron  with  forged  ends)  ................     6,000 

On  floor  beam  hangers,  and  other  similar  members  liable  to 

sudden  loading  (plates  or  shapes),  net  section  .............     5,000 

Members  subject  to  alternate  strains  of  tension  and  compression  shall  be 
proportioned  to  resist  each  kind  of  strain.     Both  of  the  strains  shall,  how- 
ever, be  considered  as  increased  by  an  amount  equal  to  8/10  of  the  least  of 
the  two  strains,  for  determining  the  sectional  area  by  the  above  allowed 
strains. 

The  Phoenix  Bridge  Company  specify  :  The  greatest  working  stresses  in 
all  wrought-iron  tensile  members  of  railway  spans  150  feet  in  length  and 
under,  shall  be  as  follows: 

Pounds  per 

sq.  in. 
In  counter  web  members.  .................................  ....    8,000 

In  long  verticals  ..............................................    8,000 

In  main-web  and  lower-chord  members  (eye-bars)  .............  10,000 

In  suspension  loops  .............................................     7,000 

In  suspension  plates  (net  section)  ..................     ..........    7,000 

In  tension  members  of  lateral  and  transverse  bracing  .........  15,000 

In  counter  rods  and  long  verticals  of  lattice  girders  (net  sec- 

tion) ...........................................  .............    7,000 

In  lower  chords  and  main  tension  members  o  *  lattice  girders 

(net  section)  ........     .....................................    8,000 

In  bottom  flange  of  plate  girders  (net  section)  .  ,  ...............    8,000 

In  bottom  flange  of  rolled  beams  ...........  .  .................    8,000 

In  angle-iron  lateral  ties  (net  section)  .........................  12,000 

In  spans  over  150  feet  in  length,  the  greatest  working  tensile  stresses  per 
square  inch  of  wrought  iron,  lower-chord  and  end  main-web  eye-bars,  shall 
be 

min'   total  stress\ 


whenever  this  quantity  exceeds  10,000. 

Working  Stresses  for  Steel. 

The  greatest  allowed  working  stresses  for  steel  tension  members,  for 
spans  of  200  feet  in  length  and  less,  shall  be  as  follows  : 


264  STRENGTH   OF   MATERIALS. 

Pounds  per 
sq.  in. 

In  counter  web  members 10,500 

In  long  verticals 10,000 

In  all  main- web  and  lower-chord  eye-bars *   13,200 

In  plate  hangers  (net  section) 9,000 

In  tension  members  of  lateral  and  transverse  bracing 19,000 

In  steel-angle  lateral  ties  (net  section) 15,000 

For  spans  over  200  feet  in  length  the  greatest  allowed  working  stresses 
per  square  inch,  in  lower-chord  and  end  main-web  eye-bars,  shall  be  taken  at 

,  min.  total  stress  \ 


~  max.  total  stress/ 

whenever  this  quantity  exceeds  13,200. 

The  greatest  allowable  stress  in  the  main-web  eye-bars  nearest  the  centre 
of  such  spans  shall  be  taken  at  13,200  pounds  per  square  inch  ;  and  those 
for  the  intermediate  eye-bars  shall  be  found  by  direct  interpolation  between 
the  preceding  values. 

The  greatest  allowable  working  stresses  in  steel  plate  and  lattice  girders 
and  rolled  beams  shall  be  taken  as  follows  : 

Pounds  per 
sq. in. 

Upper  flange  of  plate  girders  (gross  section) 10,000 

Lower  flange  of  plate  girders  (net  section) 10,000 

In  counters  and  long  verticals  of  lattice  girders  (net  section) . .     9,000 
In  lower  chords  and  main  diagonals  of  lattice  girders  (net 

section) 10,000 

In  bottom  flanges  of  rolled  beams 10,000 

In  top  flanges  of  rolled  beams 10,000 

RESISTANCE  OF  HOLLOW  CYLINDERS  TO 
COLLAPSE. 

Fairbairn's  empirical  formula  (Phil.  Trans.  1858)  is 

p  =  9,675,600  **'^-  , (1) 

where  p  =  pressure  in  Ibs.  per  square  inch,  t  =  thickness  of  cylinder,  d  = 
diameter,  and  I  =  length,  all  in  inches  ;  or, 

**•!• 

p  =  806,600  -=-p  if  L  is  in  feet (2) 

He  recommends  the  simpler  formula 

p  =  9,675,600**,.    .  .  (3> 

la 

as  sufficiently  accurate  for  practical  purposes,  for  tubes  of  considerable 
diameter  and  length. 

The  diameters  of  Fairbairn's  experimental  tubes  were  4",  6",  8",  10",  and 
12",  and  their  lengths,  between  the  cast-iron  ends,  ranged  between  19  inches 
and  60  inches. 

His  formula  (3)  has  been  generally  accepted  as  the  basis  of  rules  for 
ascertaining  the  strength  of  boiler-flues.  In  some  cases,  however,  limits  are 
fixed  to  its  application  by  a  supplementary  formula. 

Lloyd's  Register  contains  the  following  formula  for  the  strength  of  circular 
boiler-flues,  viz., 

_  89,600*2 

Ld 

The  English  Board  of  Trade  prescribes  the  following  formula  for  circular 
flues,  when  the  longitudinal  joints  are  welded,  or  made  with  riveted  butt- 
straps,  viz., 

'=£SS *> 

For  lap-joints  and  for  inferior  workmanship  the  numerical  factor  may  be 
reduced  as  low  as  60,000. 


RESISTANCE  OF  HOLLOW  CYLINDERS  TO  COLLAPSE.  265 

The  rules  of  Lloyd's  Register,  as  well  as  those  of  the  Board  of  Trade,  pre- 
scribe further,  that  in  no  case  the  value  of  P  must  exceed  the  amount  given 
by  the  following  equation,  viz., 

QAAA« 

(6) 

In  formulae  (4),  (5),  (6)  P  is  the  highest  working  pressure  in  pounds  per 
square  inch,  t  and  d  are  the  thickness  and  diameter  in  inches,  L  is  the 
length  of  the  flue  in  feet  measured  between  the  strengthening  rings,  in  case 
it  is  fitted  with  such.  Formula  (4)  is  the  same  as  formula  (3),  with  a  factor 
of  safety  of  9.  In  formula  (5)  the  length  L  is  increased  by  1  ;  the  influence 
which  this  addition  has  on  the  value  of  P  is,  of  course,  greater  for  short 
tubes  than  for  long  ones. 

Nystrom  has  deduced  from  Fairbairn's  experiments  the  following  formula 
for  the  collapsing  strength  of  flues  : 


where  p,  t,  and  d  have  the  same  meaning  as  in  formula  (1),  L  is  the  length  in 
feet,  and  T  is  the  tensile  strength  of  the  metal  in  pounds  per  square  inch. 

If  we  assign  to  T  the  value  50,000,  and  express  the  length  of  the  flue  in 
inches,  equation  (7)  assumes  the  following  form,  viz., 

p  -  692,800  -¥— .  .  (8) 

dVl 

Nystrom  considers  a  factor  of  safety  of  4  sufficient  in  applying  his  formula. 
(See  "  A  New  Treatise  on  Steam  Engineering,"  by  J.  W.  Nystrom,  p.  106.) 

Formula  (1),  (4),  and  (8)  have  the  common  defect  that  they  make  the 
collapsing  pressure  decrease  indefinitely  with  increase  of  length,  and  vice 
versa.  M.  Love  has  deduced  from  Fairbairn's  experiments  an  equation  of 
a  different  form,  which,  reduced  to  English  measures,  is  as  follows,  viz., 

p  =5,358, 150  ^  +  41,906^+ 1323  j, (9) 

where  the  notation  is  the  same  as  in  formula  (1) . 

D.  K.  Clark,  in  his  "  Manual  of  Rules,"  etc.,  p.  696,  gives  the  dimensions  of 
six  flues,  selected  from  the  reports  of  the  Manchester  Steam-Users  Associa- 
tion, 1862-69,  which  collapsed  while  in  actual  use  in  boilers.  These  flues 
varied  from  24  to  60  inches  in  diameter,  and  from  3-16  to  %  inch  in  thickness. 
They  consisted  of  rings  of  plates  riveted  together,  with  one  or  two  longitud- 
inal seams,  but  all  of  them  unfortified  by  intermediate  flanges  or  strength- 
ening rings.  At  the  collapsing  pressures  the  flues  experienced  compressions 
ranging  from  1.53  to  2.17  tons,  or  a  mean  compression  of  1.82  tons  per  square 
inch  of  section.  From  these  data  Clark  deduced  the  following  formula 
"for  the  average  resisting  force  of  common  boiler-flues,"  viz., 

„  =  (,(«£»_  WO) (,0) 

where  p  is  the  collapsing  pressure  in  pounds  per  square  inch,  and  d  and  t 
are  the  diameter  and  thickness  expressed  in  inches. 

C.  R.  Roelker,  in  Van  Nostrand's  Magazine,  March,  1881,  discussing  the 
above  and  other  formulae,  shows  that  experimental  data  are  as  yet  insuffi- 
cient to  determine  the  value  of  any  of  the  formulae.  He  says  that  Nystrom's 
formula,  (8),  gives  a  closer  agreement  of  the  calculated  with  the  actual  col- 
lapsing pressures  in  experiments  on  flues  of  every  description  than  any  of 
the  other  formulae. 

Collapsing  Pressure  of  Plain  Iron  Tubes  or  Flues. 

(Clark,  S.  E.,  vol.  i.  p.  643.) 

The  resistance  to  collapse  of  plain-riveted  flues  is  directly  as  the  square  of 
the  thickness  of  the  plate,  and  inversely  as  the  square  of  the  diameter.  The 
support  of  the  two  ends  of  the  flue  does  not  practically  extend  over  a  length 
of  tube  greater  than  twice  or  three  times  the  diameter.  The  collapsing 
pressure  of  long  tubes  is  therefore  practically  independent  of  the  length. 


266  STRENGTH   OF   MATERIALS. 

Instances  of  collapsed  flues  of  Cornish  and  Lancashire  boilers  collated  by 
Clark,  showed  that  the  resistance  to  collapse  of  flues  of  %-inch  plates,  18  to 
43  feet  long,  and  30  to  50  inches  diameter,  varied  as  the  1.75  power  of  the 
diameter.  Thus, 

for  diameters  of 30    35  40  45  50     inches, 

the  collapsing  pressures  were 76    58  45  37  30     Ibs.  per  sq.  in; 

for   7-16-inch    plates   the    collapsing 

pressures  were - 60  49  42 

For  collapsing  pressures  of  plain  iron  flue-tubes  of  Cornish  and  Lanca 
shire  steam-boilers,  Clark  gives: 

_  200,000*2 


P  =  collapsing  pressure,  in  pounds  per  square  inch; 
t  =  thickness  of  the  plates  of  the  furnace  tube,  in  inches. 
d  =  internal  diameter  of  the  furnace  tube,  in  inches. 

For  short  lengths  the  longitudinal  tensile  resistance  may  be  effective  in 
augmenting  the  resistance  to  collapse.  Flues  efficiently  fortified  by  flange- 
joints  or  hoops  at  intervals  of  3  feet  may  be  enabled  to  resist  from  50  Ibs. 
to  60  Ibs.  or  70  Ibs.  pressure  per  square  inch  more  than  plain  tubes,  accord- 
ing to  the  thickness  of  the  plates. 

Strength  of  Small  Tubes.—  The  collapsing  resistance  of  solid- 
drawn  tubes  of  small  diameter,  and  from  .134  inch  to  .109  inch  in  thickness, 
nas  been  tested  experimentally  by  Messrs.  J.  Russell  &  Sons.  The  results 
lor  wrought-iron  tubes  varied  from  14.33  to  20.07  tons  per  square-inch  sec- 
tion of  the  metal,  averaging  18.20  tons,  as  against  17.57  to  24.28  tons,  averag- 
ing 22.40  tons,  for  the  bursting  pressure. 

(For  strength  of  Segmental  Crowns  of  Furnaces  and  Cylinders  see  Clark, 
S.  E.,  vol.  i,  pp.  649-651  and  pp.  627,  628.) 

Formula  for  Corrugated  Furnaces  (Eng'g,  July  24,  1891,  p. 
!02).—  As  the  result  of  a  series  of  experiments  on  the  resistance  to  collapse 
of  Fox's  corrugated  furnaces,  the  Board  of  Trade  and  Lloyd's  Registry 
altered  their  formulae  for  these  furnaces  in  1891  as  follows: 

Board  of  Trade  formula  is  altered  from 


T  =  thickness  in  inches; 

D  =  mean  diameter  of  furnace; 

WP  =  working  pressure  in  pounds  per  square  inch. 

Lloyd's  formula  is  altered  from 

1000  XCT*)  =Trpto1284X(r«)    =  T|rl, 

T  =  thickness  in  sixteenths  of  an  inch  ; 

D  =  greatest  diameter  of  furnace; 

WP  =  working  pressure  in  pounds  per  square  inch. 

TRANSVERSE    STRENGTH. 

In  transverse  tests  the  strength  of  bars  of  rectangular  section  is  found  to 
vary  directly  as  the  breadth  of  the  specimen  tested,  as  the  square  of  its 
depth,  and  inversely  as  its  length.  The  deflection  under  any  load  varies  as 
vhe  cube  of  the  length,  and  inversely  as  the  breadth  and  as  the  cube  of  the 
depth.  Represented  algebraically,  if  S  =  the  strength  and  D  the  deflection, 
I  the  length,  b  the  breadth,  and  d  the  depth, 

fed2  J3 

S  varies  as  —  r-  and  D  varies  as  r-^. 
I  od3 

For  the  purpose  of  reducing  the  strength  of  pieces  of  various  sizes  to 
a  common  standard,  the  term  modulus  of  rupture  (represented  by  R)  is 
Used.  Jts  value  is  obtained  by  experiment  on  a  bar  of  rectangular  section 


TRANSVERSE   STRENGTH.  267 

Is  and  loaded 
ues  in  the  following  formula  : 


supported  at  the  ends  and  loaded  in  the  middle  and  substituting  numerical 

value 


8  PI 


in  which  P  =  the  breaking  load  in  pounds,  Z  =  the  length  in  inches,  6  the 
breadth,  and  d  the  depth. 

The  modulus  of  rupture  is  sometimes  defined  as  the  strain  at  the  instant 
of  rupture  upon  a  unit  of  the  section  which  is  most  remote  from  the  neutral 
axis  on  the  side  which  first  ruptures.  This  definition,  however,  is  based 
upon  a  theory  which  is  yet  in  dispute  among  authorities,  and  it  is  better  to 
define  it  as  a  numerical  value,  or  experimental  constant,  found  by  the  ap- 
plication of  the  formula  above  given. 

From  the  above  formula,  making  I  12  inches,  and  b  and  d  each  1  inch,  it 
follows  that  the  modulus  of  rupture  is  18  times  the  load  required  to  break  a 
bar  one  inch  square,  supported  at  two  points  one  foot  apart,  the  load  being 
applied  in  the  middle. 

..       span  in  feet  X  load  at  middle  in  Ibs. 

Coefficient  of  transverse  strength  =  ~  —  -j-=- 

breadth  in  inches  X  (depth  in  inches)2. 

=—  th  of  the  modulus  of  rupture. 
lo 

Fundamental  Formula?  for  Flexure  of  Beams  (Merriman). 

Resisting  shear  =  vertical  shear; 

Resisting  moment  =  bending  moment; 

Sum  of  tensile  stresses  =  sum  of  compressive  stresses; 

Resisting  shear  =  algebraic  sum  of  all  the  vertical  components  of  the  in- 
ternal stresses  at  any  section  of  the  beam. 

Tf  A  be  the  area  of  the  section  and  5s  the  shearing  unit  stress,  then  resist- 
ing shear  =  ASs;  and  if  the  vertical  shear  =  F,  then  V  =  ASs. 

The  vertical  shear  is  the  algebraic  sum  of  all  the  external  vertical  forces 
on  one  side  of  the  section  considered.  It  is  equal  to  the  reaction  of  one  sup- 
port, considered  as  a  force  acting  upward,  minus  the  sum  of  all  the  vertical 
downward  forces  acting  between  the  support  and  the  section. 

The  resisting  moment  —  algebraic  sum  of  all  the  moments  of  the  inter- 
nal horizontal  stresses  at  any  section  with  reference  to  a  point  in  that  sec- 

tion, =  —  ,  in  which  S  =  the  horizontal  unit  stress,  tensile  or  compressive 

as  the  case  may  be,  upon  the  fibre  most  remote  from  the  neutral  axis,  c  = 
the  shortest  distance  from  that  fibre  to  said  axis,  and  I  =  the  moment  of 
inertia  of  the  cross-section  with  reference  to  that  axis. 

The  bending  moment  M  is  the  algebraic  sum  of  the  moment  of  the  ex- 
ternal forces  on  one  side  of  the  section  with  reference  to  a  point  in  that  sec- 
tion =  moment  of  the  reaction  of  one  support  minus  sum  of  moments  of 
loads  between  the  support  and  the  section  considered. 


The  bending  moment  is  a  compound  quantity  =  product  of  a  force  by  the 
distance  of  its  point  of  application  from  the  section  considered,  the  distance 
being  measured  on  a  line  drawn  from  the  section  perpendicular  to  the 
direction  of  the  action  of  the  force. 

Concerning  the  above  formula,  Prof.  Merriman,  Eng.  News,  July  21,  1894, 
says:  The  formula  just  quoted  is  true  when  the  unit-stress  /S  on  the  part  of 
the  beam  farthest  from  the  neutral  axis  is  within  the  elastic  limit  of  the 
material.  It  is  not  true  when  this  limit  is  exceeded,  because  then  the  neutral 
axis  does  not  pass  through  the  centre  of  gravity  of  the  cross-section,  and 
because  also  the  different  longitudinal  stresses  are  not  proportional  to  their 
distances  from  that  axis,  these  two  requirements  being  involved  in  the  de- 
duction of  the  formula.  But  in  all  cases  of  design  the  permissible  unit- 
stresses  should  not  exceed  the  elastic  limit,  and  hence  the  formula  applies 
rationally,  without  regarding  the  ultimate  strength  of  the  material  or  any 
of  the  circumstances  regarding  rupture.  Indeed  so  great  reliance  is  placed 
upon  this  formula  that  the  practice  of  testing  beams  by  rupture  has  been 
almost  entirely  abandoned,  and  the  allowable  unit-stresses  fire  mainly  de- 
rived from  tensile  and  compressive  tests. 


268 


STRENGTH   OF   MATERIALS. 


S  o  c. 

I  £ 


s  . 


1-1  l!D 


l    2  — 

^ 


II  II 


II 

fc 


,    - 

£    .2  - 


•g 

M 

S 


!°  ~ 

a  s 
S     §   ^o 

1     1  |l 

S      g    o  5 

I  i  T 


APPROXIMATE  SAFE  LOADS  LN"  LBS.  OX  STEEL  BEAMS.    209 


Formulae  for  Transverse  Strength  of  Beams.— Referring  to 
table  on  preceding  page, 

P  =  load  at  middle; 

W—  total  load,  distributed  uniformly; 
I  =  length,  b  =  breadth,  d  =  depth,  in  inches; 

E  =  modulus  of  elasticity; 

R  =  modulus  of  rupture,  or  stress  per  square  inch  of  extreme  fibre; 

/  =  moment  of  inertia; 

c  =  distance  between  neutral  axis  and  extreme  fibre. 

For  breaking  load  of  circular  section,  replace  bd2  by  0.59d3. 

For  good  wrought  iron  the  value  of  R  is  about  80,000,  for  steel  about  120,000, 
the  percentage  of  carbon  apparently  having  no  influence.  (Thurston,  Iron 
and  Steel,  p.  491).  . 

For  cast  iron  the  value  of  R  varies  greatly  according  to  quality.  Thurston 
found  45,740  and  67,980  in  No.  2  and  No.  4  cast  iron,  respectively. 

For  beams  fixed  at  both  ends  and  loaded  in  the  middle,  Barlow,  by  experi- 
ment, found  the  maximum  moment  of  stress  =  1/QPl  instead  of  }&Pl,  the 
result  given  by  theory.  Prof.  Wood  (Resist.  Matls.  p.  155)  says  of  this  case: 
The  phenomena  are  of  too  complex  a  character  to  admit  of  a  thorough  and 
exact  analysis,  and  it  is  probably  safer  to  accept  the  results  of  Mr.  Barlow 
in  practice  than  to  depend  upon  theoretical  results. 

APPROXIMATE:  GREATEST  SAFE  LOADS  IN  LBS.  ON 

STEEL  BEAMS.    (Pencoyd  Iron  Works.) 

Based  on  fibre  strains  of  16,800  Ibs.  for  steel.  (For  iron  the  loads  should  be 
one  sixth  less,  corresponding  to  a  fibre  strain  of  14,000  Ibs.  per  square  inch). 
L  =  length  in  feet  between  supports;  a  =  interior  area  in  square 

A  =  sectional  area  of  beam  in  square  inches; 

inches;  d  =  interior  depth  in  inches. 

D  =  depth  of  beam  in  inches.  w  =  working  load  in  net  tons. 


Shape  of 

Greatest  Safe 

Load  in  Pounds. 

Deflection 

in  Inches. 

Section. 

Load  in 
Middle. 

Load 
Distributed. 

Load  in 
Middle. 

Load 
Distributed. 

Solid  Rect- 

940^4 D 

1880  AD 

wL3 

wL* 

angle. 

L 

L 

32AD* 

52AD* 

HollowRect- 

340(AD-ad) 

mQ(AD-ad) 

wL* 

wL* 

angle. 

L 

L 

32UZ)2-ad2) 

52(AD*-ad*) 

Solid  Cylin 

700AD 

14QOAD 

tvL3 

wL* 

der. 

L 

L 

24AD* 

38AD* 

Hollow 

7QO(AD-ad) 

UOO(AD-ad) 

wL* 

wL* 

Cylinder. 

L 

L 

24UD*-ad2) 

38(^Z)2-ad2) 

Even-legged 

930AD 

mo  AD 

w£3 

wL3 

Tee. 

L 

L 

32AD* 

52AD* 

Channel  or 

WOO  AD 

3200AD 

wL* 

ivL* 

Zbar. 

L 

L 

53AD* 

85AD* 

U50AD 

2900  AD 

wL* 

wL3 

L 

L 

50AD* 

SOAD* 

1WOAD 

3560.41) 

wL* 

wL3 

I  Beam. 

L 

L 

58AD* 

93^Z)a 

I 

II 

III 

IV 

V 

270 


STRENGTH   OP   MATERIALS. 


The  above  formulae  for  the  strength  and  stiffness  of  rolled  beams  of  va- 
rious sections  are  intended  for  convenient  application  in  cases  where 
strict  accuracy  is  not  required. 

The  rules  for  rectangular  and  circular  sections  are  correct,  while  those  for 
the  flanged  sections  are  approximate,  and  limited  in  their  application  to  the 
standard  shapes  as  given  in  the  Pencoyd  tables.  When  the  section  of  any 
beam  is  increased  above  the  standard  minimum  dimensions,  the  flanges  re- 
maining unaltered,  and  the  web  alone  being  thickened,  the  tendency  will  be 
for  the  load  as  found  by  the  rules  to  be  in  excess  of  the  actual;  but  within 
the  limits  that  it  is  possible  to  vary  any  section  in  the  rolling,  the  rules 
will  apply  without  any  serious  inaccuracy. 

The  calculated  safe  loads  will  be  approximately  one  half  of  loads  that 
would  injure  the  elasticity  of  the  materials. 

The  rules  for  deflection  apply  to  any  load  below  the  elastic  limit,  or  less 
than  double  the  greatest  safe  load  by  the  rules. 

If  the  beams  are  long  without  lateral  support,  reduce  the  loads  for  the 
ratios  of  width  to  span  as  follows : 


Length  of  Beam. 
20  times  flange  width. 


40 
50 
60 
70 


Proportion  of  Calculated  Load 
forming  Greatest  Safe  Load. 

Whole  calculated  load. 
9-10 
8-10 
7-10 
&-10 
5-10 


These  rules  apply  to  beams  supported  at  each  end.  For  beams  supported 
otherwise,  alter  the  coefficients  of  the  table  as  described  below,  referring  to 
the  respective  columns  indicated  by  number. 

Changes  of  Coefficients  for  Special  Forms  of  Beams. 


Kind  of  Beam. 

Coefficient  for  Safe 
Load. 

Coefficient  for  Deflec- 
tion. 

Fixed  at  one  end,  loaded 
at  the  other. 

One  fourth  of  the  coeffi- 
cient, col.  II. 

One  sixteenth  of  the  co- 
efficient of  col.  IV. 

Fixed  at  one  end,  load 
evenly  distributed. 

One  fourth  of  the  coeffi- 
cient of  col.  III. 

Five  forty-eighths  of  the 
coefficient  of  col.  V. 

Both  ends  rigidly  fixed, 
or  a  continuous  beam, 
with  a  load  in  middle. 

Twice  the  coefficient  of 
col.  II. 

Four  times    the  coeffi- 
cient of  col.  IV. 

Both  ends  rigidly  fixed, 
or  a  continuous  beam, 
with  load  evenly  dis- 
tributed. 

One  and  one-half  times 
the  coefficient  of  col. 
III. 

Five  times  the  coefficient 
of  col.  V. 

ELASTIC  RESILIENCE. 

In  a  rectangular  beam  tested  by  transverse  stress,  supported  at  the  ends 
and  loaded  in  the  middle. 

2  Rbd* . 

1     PI* 


~  4  Eod*   ' 

in  which,  if  P  is  the  load  in  pounds  at  the  elastic  limit,  R  =  the  modulus  of 
transverse  strength,  or  the  strain  on  the  extreme  fibre,  at  the  elastic  limit, 
E=  modulus  of  elasticity,  A  =  deflection,  I,  6,  and  d  =  length,  breadth,  and 
depth  in  inches.  Substituting  for  P  in  (2)  its  value  in  (1),  we  have 


8  Ed ' 


15  K  A  MS  OF  UNIFORM  STRENGTH  THROUGHOUT  LENGTH.  271 


The  elastic  resilience  =  half  the  product  of  the  load  and  deflection  = 
and  the  elastic  resilience  per  cubic  inch 


2  Ibd 
Substituting  the  values  of  P  and  A,  this  reduces  to  elastic  resilience  per 

cubic   inch  =  7^-^,,  which  is  independent  of  the  dimensions:  and  therefore 

lo  Mi 

the  elastic  resilience  per  cubic  inch  for  transverse  strain  may  be  used  as  a 
modulus  expressing  one  valuable  quality  of  a  material. 
Similarly  for  tension: 

Let  P  =  tensile  stress  in  pounds  per  square  inch  at  the  elastic  limit; 
e  =  elongation  per  unit  of  length  at  the  elastic  limit; 
E  =  modulus  of  elasticity  =  P  -+-  e:  whence  e  =  P-i-  E. 

i  pa 
Then  elastic  resilience  per  cubic  inch  =  ^>Pe  =  -  — . 

6    E 

BEAMS  OF  UNIFORM  STRENGTH  THROUGHOUT 
THEIR  LENGTH. 

The  section  is  supposed  in  all  cases  to  be  rectangular  throughout.  The 
beams  shown  in  plan  are  of  uniform  depth  throughout.  Those  shown  in 
elevation  are  of  uniform  breadth  throughout. 

B  =  breadth  of  beam.    D  =  depth  of  beam. 
-  ""•""  Fixed  at  one  end,  loaded  at  the  other; 

curve  parabola,  vertex  at  loaded  end ;  BD* 
proportional  to  distance  from  loaded  end. 
The  beam  may  be  reversed,  so  that  the  up- 
per edge  is  parabolic,  or  both  edges  may  be 
parabolic. 

Fixed  at  one  end,  loaded  at  the  other; 
triangle,  apex  at  loaded  end;  BD*  propor- 
tional to  the  distance  from  the  loaded  end. 

Fixed  at  one  end;  load  distributed;  tri- 
angle, apex  at  unsupported  end;  BD*  pro- 
portional to  square  of  distance  from  unsup- 
ported end. 

Fixed  atone  end;  load  distributed;  curves 
two  parabolas,  vertices  touching  each  other 
at  unsupported  end;  BD*  proportional  to 
distance  from  unsupported  end. 

Supported  at  both  ends;  load  at  any  one 
point;  two  parabolas,  vertices  at  the  points 
of  support,  bases  at  point  loaded ;  BD*  pro- 
portional to  distance  from  nearest  point  of 
support.  The  upper  edge  or  both  edges 
may  also  be  parabolic. 

Supported  at  both  ends;  load  at  any  one 
point;  two  triangles,  apices  at  points  of  sup- 
port, bases  at  point  loaded;  BD*  propor- 
tional to  distance  from  the  nearest  point  of 
support. 

Supported  at  both  ends;  load  distributed; 
curves  two  parabolas,  vertices  at  the  middle 
of  the  beam;  bases  centre  line  of  beam;  BD* 
proportional  to  product  of  distances  from 
points  of  support. 

Supported  at  both  ends;  load  distributed; 
curve  semi-ellipse;  BD*  proportional  to  the 
product  of  the  distances  from  the  points  of 
support. 


272  STRENGTH   OF   MATERIALS. 

PROPERTIES  OF  ROLLED  STRUCTURAL.    SHAPES. 

Explanation  of  Tables  of  the  Properties  of  Carnegie 
I  Beams,  Channels,  and  Z  Bars. 

The  tables  of  I  beams  are  calculated  for  the  minimum  weight  to  which 
each  pattern  can  be  rolled.  The  tables  of  channels  are  calculated  for  the 
minimum  and  maximum  weights  of  the  various  shapes,  while  the  properties 
of  Z  bars  are  given  for  thicknesses  differing  by  1/16  inch. 

Columns  11  and  13,  in  the  tables  for  I  beams  and  channels,  give  coefficients 
by  the  help  of  which  the  safe  uniformly-distributed  load  may  readily  be  de- 
termined. To  do  this,  divide  the  coefficient  given  by  the  span  or  distance 
between  supports  in  feet.  If  the  weight  of  the  section  is  intermediate  be- 
tween the  minimum  and  maximum  weights  given,  add  to  the  coefficient 
for  the  minimum  weight  the  value  given  in  columns  12  or  14  (for  one  pound 
increase  of  weight),  multiplied  by  the  number  of  pounds  the  section  is 
heavier  than  the  minimum. 

If  a  section  is  to  be  selected  (as  will  usually  be  the  case)  intended  to 
carry  a  certain  load,  for  a  length  of  span  already  determined  on,  ascertain 
the  coefficient  which  this  load  and  span  will  require,  and  refer  to  the  table 
for  a  section  having  a  coefficient  of  this  value.  The  coefficient  is  obtained 
by  multiplying  the  load,  in  pounds  uniformly  distributed,  by  the  span 
length  in  feet. 

In  case  the  load  is  not  imiformly  distributed,  but  is  concentrated  at  the 
middle  of  the  span,  multiply  the  load  by  2  and  then  consider  it  as  uni- 
formly distributed.  The  deflection  will  be  8/10  of  the  deflection  for  the 
latter  load. 

For  other  cases  of  loading  obtain  the  bending  moment  in  foot-pounds;  this 
multiplied  by  8  will  give  the  coefficient  required. 

If  the  loads  are  quiescent,  the  coefficients  for  a  fibre  strain  of  16,000  Ibs 
per  square  inch  for  steel  and  12,000  Ibs.  for  iron  may  be  used  ;  but  if 
moving  loads  are  to  be  provided  for,  the  coefficients  for  12,500  and  10,000 
Ibs.,"  respectively,  should  be  taken.  Inasmuch  as  the  effects  of  impact  may 
be  very  considerable  (the  strains  produced  in  an  unyielding,  inelastic 
material  by  a  load  suddenly  applied  being  double  those  produced  by  the 
same  load  in  a  quiescent  state),  it  will  sometimes  be  advisable  to  use  still 
smaller  fibre  strains  than  those  given  in  the  tables.  In  such  cases  the  co- 
efficients can  readily  be  determined  by  proportion.  Thus,  for  a  fiber  strain 
of  8000  Ibs.  per  square  inch  the  coefficient  will  equal  the  coefficient  for 
10,000  Ibs.  fibre  strain,  from  the  table,  multiplied  by  8/10. 

The  moments  of  resistance  given  in  column  9  are  used  to  determine  the 
fibre  strain  per  square  inch  in  a  beam,  or  other  shape,  subjected  to  bending 
or  transverse  strains,  by  dividing  the  same  into  the  bending  moment 
expressed  in  inch-pounds. 

For  Carnegie  Z  bars,  C9mplete  tables  of  moments  of  inertia,  moments  of 
resistance,  radii  of  gyration,  and  values  of  the  coefficients  (C)  are  given  for 
thicknesses  varying  by  1/16  inch.  These  coefficients  may  be  applied,  as 
explained  above,  for  cases  where  the  Z  bars  are  subjected  to  transverse 
loading,  as,  for  example,  in  the  case  of  roof-purlins. 

For  more  complete  and  detailed  information  concerning  structural  shapes, 
consult  the  pocket-books  and  circulars  issued  by  the  manufacturers. 

[A  more  correct  term  for  what  is  called  "  moment  of  resistance"  above, 
and  also  in  the  tables  on  pages  274-277,  is  "  moment  of  resisting  area."— J.  B. 
Johnson,  Eng'g  Netvs,  Feb.  27,  1896.  Reuleaux  calls  it  "section  modulus'' 
or  section  factor.] 


PROPERTIES   OF   IIOLLED   STRUCTUKAL   SHAPES.    273 


tn  Load  of  1OO  Ibs.  per  square  foot. 

re  to  Centre  of  Beams. 

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For  any  other  load  than  100  Ibs.  per  square  foot,  divide  the  spacing  given  by  the  ratio  the  given  load  per  square  foot  bears  to  100. 
Thus  for  a  load  of  150  Ibs.  per  square  foot  divide  by  1.5.  Maximum  fibre  strain,  16.000  Ibs.  per  square  inch. 
Only  figures  above  the  cross  lines  should  be  used  for  plastered  ceilings,  so  that  the  deflection  will  not  cause  cracking  of  the  plaster. 

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Spacing  of  Carnegie  I  Beams  for  Uiiifori 

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STREKGTH   OF    MATERIALS. 


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PROPERTIES   OF    CARKEGIE   CHAttXELS— STEEL.    275 


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276 


STREKGTH   OF   MATERIALS. 


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PROPERTIES   OF   CARNEGIE   Z    BARS. 


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278 


STRENGTH    OF   MATERIALS. 


TRENTON  IRON  REAMS  AND  CHANNELS. 

(New  Jersey  Steel  and  Iron  Co.) 


V 

S.8 

jjjr 

* 

is 

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bo 

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I  Beams. 

Channels. 

20 
20 

272 

200 

P 

11-16 

1,320,000 
990,000 

15 
15 

190 
120 

4% 
4 

^4 

625,000 
401,000 

15^ 
15  3-16 

200 
150 

5% 

2.6 

748,000 
551,000 

ii/ 

140 
70 

4 
3 

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.33 

381,000 
200,100 

15^ 

125 

5 

.42 

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io4 

60 

2% 

134,750 

170 

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10 

48 

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5-16 

102,000 

12W 

125 

4.8 

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377,000 

9 

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146,000 

12 

120 

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375,000 

9 

50 

31^ 

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104,000 

12 

96 

5/4 

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306,000 

8 

45 

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88,950 

135 

5 

.47 

360,000 

8 

33 

2  2 

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65,800 

io^<a 

105 

I1  •> 

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286,000 

7 

36 

31^ 

62,000 

9 

90 
125 

$1 

5-16 
.57 

250,000 
268,000 

7 
6 

25^ 
45 

^ 

4.20 
.40 

39,500 
58,300 

9 

85 

4J*j 

% 

199.000 

6 

33 

2^4 

.28 

45,700 

9 

70 

4 

.3 

167,000 

6 

22^ 

1% 

.18 

33,680 

8 

80 

41^ 

% 

168,000 

5 

19 

•JKZ 

.20 

22,800 

8 

65 

4 

.3 

135.000 

4 

\\/ 

.20 

15,700 

7 

55 

3% 

.3 

101,000 

3 

15 

\y2 

.20 

10,500 

6 
6 

120 
90 

5 

S 

172,000 
132,000 

Deck  Beams. 

6 

50 

gj/ 

.3 

76,800 

6 

40 

3 

62,600 

5 

40 

3 

5^16 

49,100 

8 

65 

4J^2 

% 

91,800 

5 

30 

2% 

38,700 

7 

55 

4^ 

5-16 

63,500 

4 

37 

3 

5-16 

36,800 

4 

30 

2% 

N 

30,100 

4 

18 

2 

3-16 

18,000 

Trenton  Beams  and  Channels. 

To  find  which  beam,  supported  at  both  ends,  will  be  required  to  support 
with  safety  a  given  uniformly  distributed  load: 

Multiply  the  load  in  pounds  by  the  span  in  feet,  and  take  the  beam  whose 
"  Coefficient  for  Strength  "  is  nearest  to  and  exceeds  the  number  so  found. 
The  weight  of  the  beam  itself  should  be  included  in  the  load. 

The  deflection  in  inches,  for  such  distributed  load,  will  be  found  by  divid- 
ing the  square  of  the  span  taken  in  feet,  by  70  times  the  depth  of  the  beam, 
taken  in  inches,  for  iron  beams,  and  by  52.5  times  the  depth  for  steel. 

EXAMPLE.—  Which  beam  will  be  required  to  support  a  uniformly  distrib- 
uted load  of  12  tons  (-  24,000  Ibs.)  on  a  span  of  15  feet  ? 

24,000  X  15  =  360,000,  which  is  less  than  the  coefficient  of  the  12^-inch  125- 
Ib.  iron  beam.  The  weight  of  the  beam  itself  would  be  625  Ibs.,  which,  ad- 
ded to  the  load  and  multiplied  by  the  span,  would  still  give  a  product  less 
than  the  coefficient;  thus, 

24,625  X  15  =  369,375. 

The  deflection  will  be 


The  safe  distributed  load  for  each  beam  can  be  found  by  dividing  the  co- 
efficient by  the  span  hi  feet,  and  subtracting  the  weight  of  the  beam. 


TREXTOlSr   ANGLE-BARS. 


279 


When  the  load  is  concentrated  entirely  at  the  centre  of  the  span,  one  half 
of  this  amount  must  be  taken. 

The  beams  must  be  secured  against  yielding  sideways,  or  the  safe  loads 
will  be  much  less. 

For  beams  used  with  plastered  ceilings,  the  deflection  allowed  should  not 
exceed  1/30  inch  per  foot  of  span,  to  avoid  cracking  of  the  plaster. 

TRENTON  ANGLE-BARS. 


Si/e  of 
Bar. 

Approximate  Weight,  in  pounds  per  yard,  for 
each  thickness  in  inches. 

Coeff.  for 
Transverse 
Strength. 

6     x6 

4^x4^ 

4     x4 

3^x3^ 

3     x3 
2%x2% 

2^x2^ 
2MX2M 
2     x2 
194  xl« 

imm 

1*4*1*4 

1      xl 

%x    % 
%x   % 

7/16 
37.5 

2886 
24.8 

>& 

5/16 
16.2 

11*9 

y± 

10.6 

7/32 
8.3 
3/16 
6.21 
5.27 

H 
2.97 
2.34 
2  03 
1.72 

57^5 
42.5 
716 
33  1 
28.7 
5/16 
17.7 
% 
19.2 
5/16 
14.7 
9/32 
11.9 

J4 
9.4 

7/32 
7.18 
6.09 
5/32 
3.66 
2.88 
2.48 
2.09 

9/16 
64.3 
47.5 

H 

37.5 
32.5 

t& 

13/32 
20.7 
11/32 
16.0 
5/16 
13.1 
9/32 
10.4 

8.13 
6.88 
3/16 
4  34 
3.40 
2.93 
2.46 

% 
71.1 
52.3 
9/16 
41.8 
36.2 
7/16 
24.4 
7/16 
22.2 

i& 

11/32 
14  3 
5/16 
11.5 
9/32 
9  05 
7.64 
7/32 
4.99 
3.91 

11/16 
77.8 
57.2 
% 
46.1 
39.8 

•fc 

15/32 
23.6 
13/32 
18.6 
% 
15  5 
11/32 
12.6 
5/16 
9.96 
8.40 

*& 

4.38 

A 

61.9 

11/16 
50.5 
43.4 

9/16 
30.6 

2r*o 

7/16 
20.0 
13/32 
16.8 
% 
13  6 
ll/,2 
10  .8 
9.13 

13/16 
91.0 

•& 

Thinnest  Bar. 
36,900  Ibs. 
18,000    " 

12,184    " 
9,200    " 

4,611    " 
4,710    " 
3,156    " 
2,530    " 
1,752    " 

1,150    " 
832    " 

393    " 

246    " 
186    " 
133    " 

,& 

& 

17/32 
26.3 
15/32 
21.2 

7/16 
17.8 

11/16 
36.5 

Sft 
& 

ifc 

Uneven    Legs. 


'  

7/16 

^ 

9/16 

« 

11/16 

M 

f  30,680,  6"  way. 

6     x4 

41.8 

47.5 

53.1 

58.6 

64.0 

69.4 

1  14,750,  4"       ' 

% 

(  18,353,  5"       * 

5     x8^ 

30.5 

35.3 

40.0 

44.7 

19.2 

53.7 

58  1 

1    9,651,  314"   ' 

4^x3 

26.7 

30.9 

35.0 

ft9.^ 

43.0 

46.8 

50.6 

j  14,580,  4^"    ' 

1    7,020,  3" 

5/16 

% 

7/^) 

/^> 

9/16 

% 

11/16 

j    9,850,  4"       ' 

4     x3 

20.9 

24.8 

28.7 

3275 

36.2 

39.8 

43.4 

1    5,871,  3"       ' 

M 

j    6,180,  3^"   ' 

3^x3 

15  6 

19.3 

^3,0 

26.5 

30.0 

33.4 

36.7 

40  0 

1    4,710,3''       * 

3^x2^ 

14.4 

17.7 

21.1 

24.4 

27.5 

30.6 

33.6 

36.5 

j    6,037,  3^"    ' 

1    3,296,  2^"  " 

H 

j    5,515,  314"  " 

31^  x  \y% 

11% 

"j    1,148,  1^"  " 

3     x2^ 

y± 

13.1 

1  5/16 
16.2 

11/32 
17.7 

i£ 

13/32 
20  7 

7/16 
22.2 

2590 

0/16 
27.7 

(    4.490,  3"      " 
1    3.S38,  2^"" 

7/32 

y± 

9/32 

5/16 

% 

7/16 

H 

j    3,833,  3"      il 

3     x2 

10.4 

11  9 

13.3 

14.6 

17.3 

20.0 

22.5 

{    1,850,  2"      " 

280 


STRENGTH   OF   MATERIALS. 


TRENTON  TEE  BARS. 


Designation  of 
Bar. 

Approximate  Weight,  in  pounds,   per 
yard,  for  each  thickness  in  inches. 

Coefficient 
for  Transverse 
Strength. 

Table.       Leg. 
4"     x4" 
3&"x3U" 
3"     x  3" 

au"*au" 
8j|''x3ji" 

2"     x2" 
W  x  W 

W'xiS" 

1'       xl" 
5'       x  2*£" 
3'      x  2" 
2^'  x  3" 
2'       x  3" 
2'       x  1*6" 

2j4"xi*|" 

2"     xl" 
1J$"  x  1" 

*£"  37.5  Ibs. 
*£"  32-5    " 
*£"  27.5     " 
%"  17.3    " 

Thinnest  Bar 
15,800  Ibs. 
10,550 
6,680 
3,850 
3,087 
1.970 
1,033 
596 
268 
6,344 
2,540 
6,404 
6,173       ' 
1,355       ' 
604       ' 
457       ' 
421       ' 

7-16"  28.7  Ibs. 
%"  21.1    " 
5-16"  14.7    " 
5-16"  13  09  tk 
*4"     9.4     " 
*4"    6.68  " 
7-32"    4.87  " 
5-32"    2.80  " 

5-16"  11.5    " 

*4"    5.5     " 
3-16"    3.3    " 
*6"  35.0    " 
%"  17.3    " 

5-16"  14.6  Ibs. 
§'  19.2    " 
'  17.3    " 
'    9.1     " 

*4"  7.4  " 

*4"    6.5    " 
*4"    5.6    " 

SIZE  OF  BEAMS,   AND   THEIR  DISTANCE  APART, 

Suitable  for  Floors  having  Loads  per  square 
foot  from  10O  Ibs.  to  300  Ibs. 

(New  Jersey  Steel  and  Iron  Co.) 


Load  per 
sq.  ft. 
100  Ibs. 

Load  per 
sq.  ft. 
150  Ibs. 

Load  per 
sq.  ft. 
200  Ibs. 

Load  per 
sq.  ft. 
250  Ibs. 

Load  per 
sq.  ft. 
300  Ibs. 

1 

5 

i 

Hg 

a 

« 

a 

,q 

« 

, 

~ 

§ 

5 

§3 

t«  O 

•S 

P 

c  o 

.SP 

!« 

E  o 

11 

If  . 

c  ?5 

®% 

^  a 

«w  *j 

«w  -w 

So 

02 

as,  ill 

15 

1)  <B 

y  £ 

e  £ 

82 

G  •£ 

55 

CM  •" 

-o  | 
c  ^» 

0° 

iS 

cS 

oj  v,        Jg  C    • 

il 

||| 

II 

||g 

II 

si 

0 

33      '5 

9 

s 

53 

5 

02 

S"^ 

CQ 

5^ 

in.     Ib. 

feet 

in.     Ib. 

feet 

in.     Ib. 

feet 

in.     Ib.ifeet 

in.      Ib. 

feet 

fi  j 

4        30 

4.6 

4       30 

3.1 

5       30 

3.0 

6       40 

3.9 

6        40 

3.2 

8  j 

5        30 

5.9 

5       30 

4.0 

6       40 

4.8 

6        50 

4.7 

5        50 

3.9 

5       30     3.8 

6        40 

4.1 

6       40 

3.0 

6        50 

3.0 

7        55 

3.3 

10  j 

5        40     4.8 

6        50 

5.0 

6        50 

3.7 

7        55 

4.0 

8        65 

4.4 

10   f 

6        40j     4.2 

6        50 

3.4 

7        55 

3.4 

8        65 

3.6 

8        65 

3.0 

12, 

6        50     5.2 

7        55 

4.6 

8       65 

4.5 

9        70 

4.5 

9        70 

3.8 

( 

7        55 

5.0 

7        55 

3.3 

8        65 

3.3 

9        70 

3.3 

9        85|  3.3 

1 

8        65 

6.7 

8        65 

4.5 

9        70 

4.1 

10*6    90 

5.0 

10*6    90  1  4.2 

i 

8        65 

5.0 

8        65 

3.3 

9        85 

3.7 

10U    90  1 

3.8 

10*6  105 

3.6 

i 

9        70 

6.3 

9        70 

4.2 

10*6  90 

4.7 

10U  105 

4.3 

12*4  125 

4.8 

j 

9        70 

4.9 

9        85 

3.9 

10*6  105 

4.2    10*6  105i 

3.4 

10*6  135 

3.6 

lo  -J 

9        85 

5.9 

10*6    90 

4.9 

12        96 

4.6 

12*4  1251 

4.5 

12*4  125 

3.7 

( 

10*6    90 

6.0 

10*6  105 

4.5 

10*6  105 

3.4 

12*4  125 

3.6 

12*4  125 

3.0 

20] 

1  ^^4  1  25 

6.0 

12*4  125 

4.5 

12*4  1^0 

4.9 

15      150 

4.4 

10*6    90 

4  9 

12        96 

4.0 

12*4  125 

3.7 

1214  125; 

3.0 

12*4  170 

3.3 

22] 

10*6  105 

5^6 

12*4  125 

4.9 

15      125 

4.5 

15      125 

3.6 

15      150 

3.6 

12        96 

5.0 

12*4  125 

4.1 

12*4  125 

3.0 

12*4  170, 

3.3 

15      150 

3.0 

24] 

12*4  125     6.1 

15      125 

5.0 

15      150 

4.5 

15      150; 

3.6 

15      200 

4.1 

o<t  3 

12*4  125!     5.1 

15      125 

4.3 

15      150 

3.8 

15      150 

30 

15      200 

3.5 

st>  < 

15      150 

5.1 

15      200 

5.2 

15      200! 

4.2 

20      200 

4.7 

1 

15""i25 

"55 

15      150 

4.3 

15      200 

4.4 

15      200i 

3.5 

^0      200 

3.9 

28  j 

15      200 

5.9 

20      200 

6.0 

20      200| 

4.8 

20      272 

5.3 

15""i50 

"5^6 

15      150 

3.7 

15      200 

3.8 

20      200! 

4.1 

20      200 

3.4 

I 

15      200     5.1 

20      200 

5.2 

20      272 

5.5 

20      272 

4.C 

TORSIOKAL   STRENGTH.  281 

FLOORING  MATERIAL. 

For  fire-proof  flooring,  the  space  between  the  floor-beams  may  be  spanned 
with  brick  arches,  or  with  hollow  brick  made  especially  for  the  purpose,  the 
latter  being  much  lighter  than  ordinary  brick. 

Arches  4  inches  deep  of  solid  brick  weigh  about  70  Ibs.  per  square  foot, 
including  the  concrete  levelling  material,  and  substantial  floors  are  thus 
made  up  to  6  feet  span  of  arch,  or  much  greater  span  if  the  skew  backs  at 
the  springing  of  the  arch  are  made  deeper,  the  rise  of  the  arch  being  prefer- 
ably not  less  than  1/10  of  the  span.  Hollow  brick  for  floors  are  usually  in 
depth  about  ^  of  the  span,  and  are  used  up  to,  and  even  exceeding,  spans 
of  10  feet.  The  weight  of  the  latter  material  will  vary  from  20  Ibs.  per 
square  foot  for  3-foot  spans  up  to  60  Ibs.  per  square  foot  for  spans  of  10  feet. 
Full  particulars  of  this  construction  are  given  by  the  manufacturers.  For 
supporting  brick  floors  the  beams  should  be  securely  tied  with  rods  to  resist 
the  lateral  pressure. 

In  the  following  cases  the  loads,  in  addition  to  the  weight  of  the  floor 
itself,  may  be  assumed  as: 

For  street  bridges  for  general  public  traffic 80  Ibs.  per  sq.  ft. 

For  floors  of  dwellings  40  Ibs.        "     " 

For  churches,  theatres,  and  ball-rooms 80  Ibs.       "     " 

For  hay-lofts 80  Ibs.       "     " 

For  storage  of  grain  100  Ibs. 

For  warehouses  and  general  merchandise 250  Ibs,       " 

For  factories 200  to  400  Ibs. 

For  snow  thirty  inches  deep .   ...     16  Ibs. 

For  maximum  pressure  of  wind  50  Ibs. 

For  brick  walls 112  Ibs.  per  cu.  ft. 

For  masonry  walls 116-144  Ibs. 

Roofs,  allowing  thirty  pounds  per  square  foot  for  wind  and  snow: 
For  corrugated  iron  laid  directly  on  the  purlins. . .     37  Ibs.  per  sq.  ft. 

For  corrugated  iron  laid  on  boards 40  Ibs.       "     " 

For  slate  nailed  to  laths 43  Ibs. 

For  slate  nailed  on  boards 46  Ibs. 

If  plastered  below  the  rafters,  the  weight  will  be  about  ten  pounds  per 
square  foot  additional. 

TIE-RODS  FOR   BEAMS  SUPPORTING  BRICK 
ARCHES. 

The  horizontal  thrust  of  brick  arches  is  as  follows: 

-^— — —  =  pressure  in  pounds,  per  lineal  foot  of  arch: 
K 

W  =  load  in  pounds,  per  square  foot; 
8  =  span  of  arch  in  feet; 
R  ==  rise  in  inches. 

Place  the  tie-rods  as  low  through  the  webs  of  the  beams  as  possible  and 
spaced  so  that  the  pressure  of  arches  as  obtained  above  will  not  produce  a 
greater  stress  than  15,000  Ibs.  per  square  inch  of  the  least  section  of  the  bolt. 

TORSION  AX   STRENGTH. 

Let  a  horizontal  shaft  of  diameter  —  d  be  fixed  at  one  end,  and  at  the 
other  or  free  end,  at  a  distance  =  I  from  the  fixed  end,  let  there  be  fixed  a 
horizontal  lever  arm  with  a  weight  =  P  acting  at  a  distance  =  a  from  the 
axis  of  the  shaft  so  as  to  twist  it;  then  Pa  =  moment  of  the  applied  force. 

Resisting  moment  =  twisting  moment  —  — ,  in  which  8=  unit  shearing 

resistance,  J  =  polar  moment  of  inertia  of  the  section  with  respect  to  the 
axis,  and  c  —  distance  of  the  most  remote  fibre  from  the  axis,  in  a  cross- 
section.  For  a  circle  with  diameter  d, 


__  ^o^o.   „_  ,      1Pa 

16 


282  STRENGTH   OF   MATERIALS. 

For  hollow  shafts  of  external  diameter  d  and  internal  diameter  dlt 

Pa  =  .I963^/liS;  „ 

d 

For  a  square  whose  side  =  d, 


For  a  rectangle  whose  sides  are  b  and 


c  6  V  6V+  d^ 

The  above  formulae  are  based  on  the  supposition  that  the  shearing  resist- 
ance at  any  point  of  the  cross-section  is  proportional  to  its  distance  from  the 
axis;  but  this  is  true  only  within  the  elastic  limit.  In  materials  capable  of 
flow,  while  the  particles  near  the  axis  are  strained  within  the  elastic  limit 
those  at  some  distance  within  the  circumference  may  be  strained  nearly  to 
the  ultimate  resistance,  so  that  the  total  resistance"  is  something  greater 
than  that  calculated  by  the  formulae.  (See  Thurston,  "  Matls.  of  Eng.,"  Part 
II.  p.  527.)  Saint  Veriant  finds  for  square  shafts  Pa  =  0.281d3S  (Rankine, 
"Mach.  and  Millwork,"  p.  504).  For  working  strength,  however,  the  for- 
mulae may  be  used,  with  S  taken  at  the  safe  working  unit  resistance. 

The  ultimate  torsional  shearing  resistance  S  is  about  the  same  as  the  di- 
rect shearing  resistance,  and  may  be  taken  at  20,000  to  25,000  Ibs.  per  square 
inch  for  cast  iron,  45,000  Ibs.  for  wrought  iron,  and  50,000  to  150,000  Ibs.  for 
steel,  according  to  its  carbon  and  temper.  Large  factors  of  safety  should 
be  taken,  especially  when  the  direction  of  stress  is  reversed,  as  in  reversing 
engines,  and  when  the  torsional  stress  is  combined  with  other  stresses,  as  is 
usual  in  shafting.  (See  "Shafting.1') 

Elastic  Resistance  to  Torsion.—  Let  I  =  length  of  bar  being 
twisted,  d  —  diameter,  P  —  force  applied  at  the  extremity  of  a  lever  arm 
of  length  =  a,  Pa  =  twisting  moment,  G  —  torsional  modulus  of  elasticity, 
0  =  angle  through  which  the  free  end  of  the  shaft  is  twisted,  measured  in 
arc  of  radius  =  1. 

For  a  cylindrical  shaft 

pn  _  »«<W4  .  0  _  32Pal  .  _  32Pal  .  32 

pa-~'  ~"'  -' 


If  a  =  angle  of  torsion  in  degrees, 

_    an  _  1800  _  180  X  33Pal    _  583.6PaZ 

180  '  TT  7T2d4(r  d46r 

The  value  of  G  is  given  by  different  authorities  as  from  ^  to  2/5  of  E,  the 
modulus  of  elasticity  for  tension. 

COMBINED  STRESSES. 
(From  Merriman's  "Strength  of  Materials.") 

Combined  Tension  and  Flexure.— Let  A  =  the  area  of  a  bar 
subjected  to  both  tension  and  flexure,  P=  tensile  stress  applied  at  the  ends, 
P~-A  =  unit  tensile  stress,  8  =  unit  stress  at  the  fibre  on  the  tensile  side  most 
remote  from  the  neutral  axis,  due  to  flexure  alone,  then  maximum  tensile 
unit  stress  =  (P-*-A)+  S.  A  beam  to  resist  combined  tension  and  flexure 
should  be  designed  so  that  ( P -=-  A)  -f  8  shall  not  exceed  the  proper  allow- 
able working  unit  stress. 

Combined  Compression  and  Flexure.— If  P -±-A  —  unit  stress 
due  to  compression  alone,  and  <S  =  unit  compressive  stress  at  fibre  most 
remote  from  neutral  axis,  due  to  flexure  alone,  then  maximum  compressive 
unit  stress 


Combined  Tension  (or  Compression)  and  Shear.— If  ap- 


STRENGTH  OF  FLAT  PLATES.          283 

plied  tension  (or  compression)  unit  stress  =  p,  applied  shearing  unit  stress 
=  v,  then  from  the  combined  action  of  the  two  forces 


Max.  S  =  ±  4/^2  +  J4P2»       Maximum  shearing  unit  stress; 
Max.  t  =  }£p  -j-  Vv%  +  J4p2,    Maximum  tensile  (or  compressive)  unit  stress. 


Combined  Flexure  and  Torsion.—  If  £  =  greatest  unit  stress 
due  to  flexure  alone,  and  Ss  =  greatest  torsional  shearing  unit  stress  due  to 
torsion  alone,  then  for  the  combined  stresses 

Max.  tension  or  compression  unit  stress  /  =  $£S  +  V<Ss2 
Max.  shear  s  =  ±  \/S 


Formula  for  diameter  of  a  round  shaft  subjected  to  transverse  load  while 
transmitting  a  given  horse-power  (see  also  Shafts  of  Engines): 


ie  sate  allowable  tensile  or  compressive  working  strengtn  or  tue  iraterial. 

Combined  Compression  and  Torsion.— For  a  vertical  round 
shaft  carrying  a  load  and  also  transmitting  a  given  horse-power,  the  result- 
ant maximum  compressive  unit  stress 


16P2 


in  which  P  is  the  load.    From  this  the  diameter  d  may  be  found  when  t  and 
thn  other  data  are  given. 
Stress  due  to  Temperature.—  Let  I  =  length  of  a  bar,  A  =  its  sec- 

tional area,  c  =  coefficient  of  linear  expansion  for  one  degree,  t  —  rise  or 
fall  in  temperature  in  degrees,  E  =  modulus  of  elasticity,  A  the  change  of 
length  due  to  the  rise  or  fall  t;  if  the  bar  is  free  to  expand  or  contract,  A  .-= 
ctl. 

If  th.3  bar  is  held  so  as  to  prevent  its  expansion  or  contraction  the  stress 
produced  by  the  change  of  temperature  =  S  =  ActE.  The  following  are 
average  values  of  the  coefficients  of  linear  expansion  for  a  change  in  temper- 
ature of  one  degree  Fahrenheit: 

For  brick  and  stone.  .  .  .a  =  0.0000050, 

For  cast  iron  ...........  a  =  0.0000062, 

For  wrought  iron  .......  a  =  0  .  0000067, 

For  steel  ................  a  =  0.0000065. 

The  stress  due  to  temperature  should  be  added  to  or  subtracted  from  the 
stress  caused  by  other  external  forces  according  as  it  acts  to  increase  or  to 
relieve  the  existing  stress. 

What  stress  will  be  caused  in  a  steel  bar  1  inch  square  in  area  by  a  change 
of  temperature  of  100°  F.  ?  S  =  ActE  =  I  X  .0000065  X  100  X  30,000,000  = 
19,500  Ibs.  Suppose  the  bar  is  under  tension  of  19,500  Ibs.  between  rigid  abut- 
ments before  the  change  in  temperature  takes  place,  a  cooling  of  100°  F. 
will  double  the  tension,  and  a  heating  of  100°  will  reduce  the  tension  to  zero. 

STRENGTH  OF  FLAT  PLATES. 

For  a  circular  plate  supported  at  the  edge,  uniformly  loaded,  according  to 
Grashof, 

5  r2 


For  a  circular  plate  fixed  at  the  edge,  uniformly  loaded, 


in  which  /denotes  the  working  stress;  r,  the  radius  in  inches;  £,  the  thick 
ness  in  inches;  and  p,  the  pressure  in  pounds  per  square  inch. 


284  STRENGTH   OF  MATERIALS. 

For  mathematical  discussion,  see  Lanza,  "Applied  Mechanics,"  p.  900,  etc. 
Lanza  gives  the  following  table,  using  a  factor  of  safety  of  8,  with  tensile 
strength  of  cast  iron  20,000,  of  wrought  iron  40,000,  and  of  steel  80,000  : 

Supported.  Fixed. 

Cast  iron  ............  t  =  .0182570r  \fp  t  =  .0163300r  Vp 

Wrought  iron  ........  t  =  .0117850r  \/p  t  =  .0105410r  \/p 

Steel  .................  t  =  .0091287r  \'p  t  =  .0081649r  \/p 

For  a  circular  plate   supported  at  the  edge,  and  loaded  with  a  concen- 
trated load  P  applied  at  a  circumference  the  radius  of  which  is  r0: 


for          —  =    10         20         30         40         50; 
'•o 

c  =  4.07      5.00       5.53      5.92      6.22; 


The  above  formulas  are  deduced  from  theoretical  considerations,  and  give 
thicknesses  much  greater  than  are  generally  used  in  steam-engine  cylinder- 
heads.  (See  empirical  formulas  under  Dimensions  of  Parts  of  Engines.)  The 
theoretical  formulae  seem  to  be  based  on  incorrect  or  incomplete  hypoth- 
eses, but  they  err  in  the  direction  of  safety. 

The  Strength  of  Unstayed  Flat  Surfaces.— Robert  Wilson 
(Eng'g,  Sept.  24,  1877)  draws  attention  to  the  apparent  discrepancy  between 
the  results  of  theoretical  investigations  and  of  actual  experiments  on  the 
strength  of  unstayed  flat  surfaces  of  boiler-plate,  such  as  the  unstayed  flat 
crowns  of  domes  and  of  vertical  boilers. 

Rankine's  "  Civil  Engineering"  gives  the  following  rules  for  the  strength 
of  a  circular  plate  supported  all  round  the  edge,  prefaced  by  the  remark 
that  "  the  formula  is  founded  on  a  theory  which  is  only  approximately  true, 
but  which  nevertheless  may  be  considered  to  involve  no  error  of  practical 
importance:" 

_  Wb  _  P63 
M  ~  ~foT  -  ~24~' 
Here 

M  =  greatest  bending  moment ; 

W=  total  load  uniformly  distributed  =  -  '  w; 

b  =  diameter  of  plate  in  inches  ; 
P  =  bursting  pressure  in  pounds  per  square  inch. 
Calling  t  the  thickness  in  inches,  for  a  plate  supported  round  the  edges, 

i  p;,2 

M  =  4  42,0006 J8;  .'.    -  —  =  7000*2. 

b  24 


For  a  plate  fixed  round  the  edges, 


2  P62  _       *2  X  63.000 

—  =  7000<2;    whence  P=  —         —  , 

3  24  ?'2 

where  r  =  radius  of  the  plate. 
Dr.  Grashof  gives  a  formula  from  which  we  have  the  following  rule: 

<2  x  72,000 
r2 

This  formula  of  Grashof  s  has  been  adopted  by  Professor  Unwin  in  his 
u  Elements  of  Machine  Design."  These  formulae  by  Rankine  and  Grashof 
may  be  regarded  as  being  practically  the  same. 

On  trying  to  make  the  rules  given  by  these  authorities  agree  with  the 
results  of  his  experience  of  the  strength  of  unstayed  flat  ends  of  c3Tlindrical 
boilers  and  domes  that  had  given  way  after  long  use,  Mr.  Wilson  was  led  to 
believe  that  the  above  rules  give  the  breaking  strength  much  lower  than  it 


STRENGTH  OF  FLAT  PLATES.          285 

actually  is.  He  describes  a  number  of  experiments  made  by  Mr.  Nichols  of 
Kirkstall,  which  gave  results  varying  widely  from  each  other,  as  the  method 
of  supporting  the  edges  of  the  plate  was  varied,  and  also  varying  widely 
from  the  calculated  bursting  pressures,  the  actual  results  being  in  all  case's 
very  much  the  higher. 
Some  conclusions  drawn  from  these  results  are: 

1.  Although  the  bursting  pressure  has  been  found  to  be  so  high,  boiler- 
makers  must  be  warned  against  attaching  any  importance  to  this,  since  the 
plates  deflected  almost  as  soon  as  any  pressure  was  put  upon  them  and 
sprang  back  again  on  the  pressure  being  taken  off.    This  springing  of  the 
plate  in  the  course  of  time  inevitably  results  in  grooving  or  channelling, 
which,  especially  when  aided  by  the  action  of  the  corrosive  acids  in  the 
water  or  steam,  will  in  time  reduce  the  thickness  of  the  plate,  and  bring 
about  the  destruction  of  an  unstayed  surface  at  a  very  low  pressure. 

2.  Since  flat  plates  commence  to  deflect  at  very  low  pressures,  they  should 
never  be  used  without  stays;  but  it  is  better  to  dish  the  plates  when  they  are 
not  stayed  by  flues,  tubes,  etc. 

3.  Against  the  commonly  accepted  opinion  that  the  limit  of  elasticity 
should  never  be  reached  in  testing  a  boiler  or  other  structure,  these  experi- 
ments show  that  an  exception  should  be  made  in  the  case  of  an  unstayed 
flat  end-plate  of  a  boiler,  which  will  be  safer  when  it  has  assumed  a  perma- 
nent set  that  will  prevent  its  becoming  grooved  by  the  continual  variation 
of  pressure  in  working.    The  hydraulic  pressure  in  this  case  simply  does 
what  should  have  been  done  before  the  plate  was  fixed,  that  is,  dishes  it. 

4.  These  experiments  appear  to  show  that  the  mode  of  attaching  by  flange 
or  by  an  inside  or  outside  angle-iron  exerts  an  important  influence  on  the 
manner  in  which  the  plate  is  strained  by  the  pressure. 

When  the  plate  is  secured  to  an  angle-iron,  the  stretching  under  pressure  is, 
to  a  certain  extent,  concentrated  at  the  line  of  rivet-holes,  and  the  plate  par- 
takes rather  of  a  beam  supported  than  fixed  round  the  edge.  Instead  of  the 
strength  increasing  as  the  square  of  the  thickness,  when  the  plate  is  attached 
by  an  angle-iron,  it  is  probable  that  the  strength  does  not  increase  even 
directly  as  the  thickness,  since  the  plate  gives  way  simply  by  stretching  at 
the  rivet-holes,  and  the  thicker  the  plate,  the  less  uniformly  is  the  strain 
borne  by  the  different  layers  of  which  the  plate  may  be  considered  to  be 
made  up.  When  the  plate  is  flanged,  the  flange  becomes  compressed  by  the 
pressure  against  the  body  of  the  plate,  and  near  the  rim,  as  shown  by  the 
contrary  flexure,  the  inside  of  the  plate  is  stretched  more  than  the  outside, 
and  it  may  be  by  a  kind  of  shearing  action  that  the  plate  gives  way  along 
the  line  where  the  crushing  and  stretching  meet. 

5.  These  tests  appear  to  show  that  the  rules  deduced  from  the  theoretical 
investigations  of  Lame,  Rankine,  and  Grashof  are  not  confirmed  by  experi- 
ment, and  are  therefore  not  trustworthy. 

Unbraced  Wrought-iron.  Heads  of  Boilers,  etc.  (The  Loco- 
motive, Feb.  1890). — Few  experiments  have  been  made  on  the  strength  of 
flat  heads,  and  our  knowledge  of  them  comes  largely  from  theory.  Experi- 
ments have  been  made  on  small  plates  1-16  of  an  inch  thick,  yet  the  data  so 
obtained  cannot  be  considered  satisfactory  when  we  consider'the  far  thicker 
heads  that  are  used  in  practice,  although  the  results  agreed  well  with  Ran- 
kine's  formula.  Mr.  Nichols  has  made  experiments  on  larger  heads,  and 
from  them  he  has  deduced  the  following  rule:  "  To  find  the  proper  thick- 
ness for  a  flat  unstayed  head,  multiply  the  area  of  the  head  by  the  pressure 
per  square  inch  that  it  is  to  bear  safely,  and  multiply  this  by  the  desired 
factor  of  safety  (say  8);  then  divide  the  product  by  ten  times  the  tensile 
strength  of  the  material  used  for  the  head."  His  rule  for  finding  the  burst- 
ing pressure  when  the  dimensions  of  the  head  are  given  is:  "  Multiply  the 
thickness  of  the  end-plate  in  inches  by  ten  times  the  tensile  strength  of  the 
material  used,  and  divide  the  product  by  the  area  of  the  head  in  inches." 

In  Mr.  Nichols's  experiments  the  average  tensile  strength  of  the  iron  used 
for  the  heads  was  44,800  pounds.  The  results  he  obtained  are  given  below, 
with  the  calculated  pressure,  by  his  rule,  for  comparison. 

1.  An  unstayed  flat  boiler-head  is  34^  inches  in  diameter  and  9-16  inch 
thick.    What  is  its  bursting  pressure?    The  area  of  a  circle  34^  inches  in 
diameter  is  935  square  inches;  then  9-10  X  44,800  X  10  =  252,000,  and  252,000  -r- 
935  —  270  pounds,  the  calculated  bursting  pressure.    The  head  actually  burst 
at  280  pounds. 

2.  Head  34^  inches   in  diameter   and   %    inch    thick.     The    area  =  935 
square  inches;  then,  %  X  44,800  X  10  =  168,000,  and  108,000  -*-  935  =  180 pounds, 
calculated  bursting  pressure.    This  head  actually  burst  at  200  pounds. 


286  STRENGTH    OF   MATERIALS. 

3.  Head  26J4  inches  in  diameter,  and  %  inch  thick.    The  area  541  square 
inches.    Then,   %  x  41,800  x  10  =  168,000,   and  168,000  -=-  541  =  311   pounds. 
This  head  burst  at  370  pounds. 

4.  Head   28J4   inches   in   diameter  and  %  inch   thick.    The  area  =  638 
square   inches;    then,    %  x  44,800  X  10  =  168,000,    and    168,000 -=- 638  =  263 
pounds.    The  actual  bursting  pressure  was  300  pounds. 

In  the  third  experiment,  the  amount  the  plate  bulged  under  different 
pressures  was  as  follows  : 

At  pounds  per  sq.  in 10        20        40         80         120         140         170         200 

Plate  bulged 1/32     1/16       ^        y±          %          y»          %          % 

The  pressure  was  now  reduced  to  zero,  "  and  the  end  sprang  back  3-16 
inch,  leaving  it  with  a  permanent  set  of  9-16  inch.  The  pressure  of  200  Ibs. 
was  again  applied  on  36  separate  occasions  during  an  interval  of  five  days, 
the  bulging  and  permanent  set  being  noted  on  each  occasion,  but  without 
any  appreciable  difference  from  that  noted  above. 

The  experiments  described  were  confined  to  plates  not  widely  different  in 
their  dimensions,  so  that  Mr.  Nichols's  rule  cannot  be  relied  upon  for  heads 
that  depart  much  from  the  proportions  given  in  the  examples. 

Thickness  of  Flat  Cast-iron  Plates  to  resist  Bursting 
Pressures.— Capt.  John  Ericsson  (Church's  Life  of  Ericsson;  gave  me 
following  rules:  The  proper  thickness  of  a  square  cast-iron  plate  will  be  ob- 
tained by  the  following:  Multiply  the  side  in  feet  (or  decimals  of  a  foot)  by 
34  of  the  pressure  in  pounds  and  divide  by  850  times  the  side  in  inches;  the 
quotient  is  the  square  of  the  thickness  in  inches. 

For  a  circular  plate,  multiply  11-14  of  the  diameter  in  feet  by  14  of  the 
pressure  on  the  plate  in  pounds.  Divide  by  850  times  11-14  of  the  diameter 
in  inches.  [Extract  the  square  root.] 

Prof.  Wm.  Harkness,  Eng'g  News,  Sept.  5, 1895,  shows  that  these  rules  can 
be  put  in  a  more  convenient  form,  thus: 

For  square  plates    T  =  0.00495S  1/p, 
and 

For  circular  plates  T  =  0.00439Z)  |/p, 

where  T  —  thickness  of  plate,  S  =  side  of  the  square,  D  =  diameter  of  the 
circle,  and  p  =  pressure  in  Ibs.  per  sq.  in.  Professor  Harkness,  however, 
doubts  the  value  of  the  rules,  and  says  that  no  satisfactory  theoretical  solu- 
tion has  yet  been  obtained. 

Strength  of  Stayed  Surfaces.— A  flat  plate  of  thickness  t  is  sup- 
ported uniformly  by  stays  whose  distance  from  centre  to  centre  is  cr,  uniform 
load  p  Ibs.  per  square'  inch.  Each  stay  supports  pa2  Ibs.  The  greatest 
stress  on  the  plate  is 


SPHERICAL  SHELLS  AND  DOMED  BOILER-HEADS. 

To  find  the  Thickness  of  a  Spherical  Shell  to  resist  a 
given  Pressure.— Let  d  =  diameter  in  inches,  and  p  the  internal  press- 
ure per  square  inch.  The  total  pressure  which  tends  to  produce  rupture 
around  the  great  circle  will  be  347r^2P-  Let  S  —  safe  tensile  stress  per 
square  inch,  and  t  the  thickness  of  metal  in  inches;  then  the  resistance  to  the 
pressure  will  be  ndtS.  Since  the  resistance  must  be  equal  to  the  pressure. 

YAtrd^p  =  irdtS.    Whence  t  =  ~=r. 
48 

The  same  rule  is  used  for  finding  the  thickness  of  a  hemispherical  head 
to  a  cylinder,  as  of  a  cylindrical  boiler. 

Thickness  of  a  Domed  Head  of  a  boiler.— If  S  =  safe  tensile 
stress  per  square  inch,  d  =  diameter  of  the  shell  in  inches,  and  t  =  thickness 
of  the  shell,  t  =  pd  -5-  2S  ;  but  the  thickness  of  a  hemispherical  head  of  the 
same  diameter  is/  =  pd-^-48.  Hence  if  we  make  the  radius  of  curvature 
of  a  domed  head  equal  to  the  diameter  of  the  boiler,  we  shall  have  t  = 

~-  =  *—,  or  the  thickness  of  such  a  domed  head  will  be  equal  to  the  thick- 

4o         26 

ness  of  the  shell. 


THICK    CYLINDERS    UNDER   TENSION. 


28? 


Stresses   in    Steel  Plating   due  to   Water-pressure,  as  in 

plating  of  vessels  and  bulkheads  (Engineering,  May  22,  1891,  page  629). 

Mr.  J.  A.  Yates  has  made  calculations  of  the  stresses  to  which  steel  plates 
are  subjected  by  external  water-pressure,  and  arrives  at  the  following  con- 
clusions : 

Assume  2a  inches  to  be  the  distance  between  the  frames  or  other  rigid 
supports,  and  let  d  represent  the  depth  in  feet,  below  the  surface  of  the 
water,  of  the  plate  under  consideration,  t  =  thickness  of  plate  in  inches, 
D  the  deflection  from  a  straight  line  under  pressure  in  inches,  and  P=  stress 
per  square  inch  of  section. 

For  outer  bottom  and  ballast- tank  plating,  a  =  420- ,  D  should   not  be 

a 

2a          P 
greater  than  .05  — ,  and  —  not  greater  than  2  to  3  tons  ;  while  for  bulkheads, 

etc.,  a  =  2352-,  D  should  not  be  greater  than  .1—,  and  —  not  greater  than 

7  tons.    To  illustrate  the  application  of  these  formulae  the  following  cases 
have  been  taken : 


For  Outer  Bottom,  etc. 

For  Bulkheads,  etc. 

Thick- 
ness of 
Plating. 

Depth 
below 
Water. 

Spacing  of 
Frames  should 
not  exceed 

Thick- 
ness of 
Plating 

Depth  of 
Water. 

Maximum  Spac- 
ing of  Rigid 
Stiffeners. 

in. 

ft. 

in. 

in. 

ft. 

ft.         in. 

20 

About  21 

L£ 

20 

9    10 

\/ 

10 

'       42 

% 

20 

7      4 

% 

18 

'       18 

% 

10 

14      8 

% 

9 

1       36 

% 

20 

4    10 

\A 

10 

*       20 

/4 

10 

9      8 

% 

5 

'       40 

™ 

10 

4    10 

It  would  appear  that  the  course  which  should  be  followed  in  stiffening 
bulkheads  is  to  fit  substantially  rigid  stiffening  frames  at  comparatively 
wide  intervals,  and  only  work  such  light  angles  between  as  are  necessary 
for  making  a  fair  job  of  the  bulkhead. 

THICK    HOLLOW   CYLINDERS  UNDER  TENSION* 

Burr,  "  Elasticity  and  Resistance  of  Materials,"  p.  36,  gives 
t  =  thickness;  r  =  interior  radius  ; 

(/h+p\?         \       h  —  maximum  allowable  hoop  tension  at  the 
t  =  r  •(  ^  _      I    -  interior  of  the  cylinder; 

p  =  intensity  of  interior  pressure. 

Merriman  gives 

s  =  unit  stress  at  inner  edge  of  the  annulus; 
r  =  interior  radius  ;  t  =  thickness  ; 
I  =  length. 

rt 

The  total  stress  over  the  area  2tl  —  2sl  — — (1) 

f"-f-t 

The  total  interior  pressure  which  tends  to  rupture  the  cylinder  is  2rl  XP- 
If  p  be  the  unit  pressure,  then  p  =  ^—^,  from  which  one  of  the  quantities 
s,  p,  r,  or  t  can  be  found  when  the  other  three  are  given. 


s-p 


288  STRENGTH    OF   MATERIALS. 

In  eq.  (1),  if  t  be  neglected  in  comparison  with  r,  it  reduces  to  2slt,  which 
is  the  same  as  the  formula  for  thin  cylinders.  If  t  =  r,  it  becomes  sit,  or 
only  half  the  resistance  of  the  thin  cylinder. 

The  formulae  given  by  Burr  and  by  Merriman  are  quite  different,  as  will 
be  seen  by  the  following  example  :  Let  maximum  unit  stress  at  the  inner 
edge  of  the  annul  us  =  8000  Ibs.  per  square  inch,  radius  of  cylinder  =  4  inches. 
interior  pressure  =  4000  Ibs.  per  square  inch.  Required  the  thickness. 

By  Burr,  t  =  4\  (S  -  400o)*  "  1  I  =  4  (  ^  ~  l)  =  2'928  inches' 


By  Merriman,  t  =       bWo  =  4  inches' 

Limit  to  Useful  Thickness  of  Hollow  Cylinders  (Encfg, 
Jan.  4,  1884).—  Professor  Barlow  lays  down  the  law  of  the  resisting  powers 
of  thick  cylinders  as  follows  : 

"  In  a  homogeneous  cylinder,  if  the  metal  is  incompressible,  the  tension 
on  every  concentric  layer,  caused  by  an  internal  pressure,  varies  inversely 
as  the  square  of  its  distance  from  the  centre/' 

Suppose  a  twelve-inch  gun  to  have  walls  15  inches  thick. 

Pressure  on  exterior  _  _6*_  _ 
Pressure  on  interior  ~~  21  2  ~~ 

So  that  if  the  stress  on  the  interior  is  12*4  tons  per  square  inch,  the  stress 
on  the  exterior  is  only  1  ton. 

Let  s  =  the  stress  on  the  inner  layer,  and  Sj  that  at  a  distance  x  from  the 
axis  ;  r  =  internal  radius,  R  =  external  radius. 


The  whole  stress  on  a  section  1  inch  long,  extending  from  the  interior  to 
the  exterior  surface,  is  8=  sr  x  —  ^—> 

K 
In  a  12-inch  gun,  let  a  =  40  tons,  r  —  6  in.,  R  =  21  in. 

S  =  40  X  6  X  6 


Suppose  now  we  go  on  adding  metal  to  the  gun  outside:  then  R  will  be- 
come so  large  compared  with  r,  that  R  —  r  will  approach  the  value  R,  so 

that  the  fraction  —  =—  becomes  nearly  unity. 

K 

Hence  for  an  infinitely  thick  cylinder  the  useful  strength  could  never 
exceed  Sr  (in  this  case  240  tons). 

Barlow's  formula  agrees  with  the  one  given  by  Merriman. 
Another  statement  of  the  gun  problem  is  as  follows  :  Using  the  formula 

st 


s  =  40  tons,  t  =  15  in.,  r  =  6  in.,  p  =  4°  ^  1  -  =  28f  tons  per  sq.   in.,  28f  X 

radius  =  172  tons,  the  pressure  to  be  resisted  by  a  section  1  inch  long  of  the 
thickness  of  the  gun  on  one  side.  Suppose  thickness  were  doubled,  making 

40  X  30 
t  =  30  in.:  p  =  —    ;  —  =  33^  tons,  or  an  increase  of  only  16  per  cent. 

OO 

For  short  cast-iron  cylinders,  such  as  are  used  in  hydraulic  presses,  it  is 
doubtful  if  the  above  formulae  hold  true,  since  the  strength  of  the  cylindri- 
cal portion  is  reinforced  by  the  end.  In  that  case  the  bursting  strength 
would  be  higher  than  that  calculated  by  the  formula.  A  rule  used  in 
practice  for  such  presses  is  to  make  the  thickness  ±=  1/10  of  the  inner  cir- 
cumference, for  pressures  of  3000  to  4000  Ibs.  per  square  inch.  The  latter 
pressure  would  bring  a  stress  upon  the  inner  layer  of  10,350  Ibs.  per  square 
inch,  as  calculated'  by  the  formula;  which  would  necessitate  the  use  of  the 
best  charcoal-iron  to  make  the  press  reasonably  safe, 


HOLDING-POWER  OF  NAILS,  SPIKES,  AND  SCREWS.  289 

THIN  CYLINDERS   UNDER  TENSION. 

Let  p  =  safe  working  pressure  in  Ibs.  per  sq.  in.; 
d  =  diameter  in  inches; 

T  =  tensile  strength  of  the  material,  Ibs.  per  sq.  in.; 
t  —  thickness  in  inches; 
/  =  factor  of  safety  ; 
c  =  ratio  of  strength  of  riveted  joint  to  strength  of  solid  plate. 


If  T  =  50000,  /  =  5,  and  c  =  0.7;  then 

HOOCtf.  dp 

d  14000' 

The  above  represents  the  strength  resisting  rupture  along  a  longitudinal 
seam.  For  resistance  to  rupture  in  a  circumferential  seam,  due  to  pressure 

on  the  ends  of  the  cylinder,  we  have    *      =  —  ^  —  ; 

47Yc 
whence  p  =  —  . 

Or  the  strength  to  resist  rupture  around  a  circumference  is  twice  as  great 
as  that  to  resist  rupture  longitudinally  ;  hence  boilers  are  commonly  single- 
riveted  in  the  circumferential  seams  and  double-riveted  in  the  longitudinal 
seams. 

HOLLOW  COPPER  BALLS. 

Hollow  copper  balls  are  used  as  floats  in  boilers  or  tanks,  to  control  feed 
and  discharge  valves,  and  regulate  the  water-level. 

They  are  spun  up  in  halves  from  sheet  copper,  and  a  rib  is  formed  on  one 
half.  Into  this  rib  the  other  half  fits,  and  the  two  are  then  soldered  or 
brazed  together.  In  order  to  facilitate  the  brazing,  a  hole  is  left  on  one  side 
of  the  ball,  to  allow  air  to  pass  freely  in  or  out;  and  this  hole  is  made  use  of 
afterwards  to  secure  the  float  to  its  stem.  The  original  thickness  of  the 
metal  may  be  anything  up  to  about  1-16  of  an  inch,  if  the  spinning  is  done 
on  a  hand  lathe,  though  thicker  metal  may  be  used  when  special  machinery 
is  provided  for  forming  it.  In  the  process  of  spinning,  the  metal  is  thinned 
down  in  places  by  stretching;  but  the  thinnest  place  is  neither  at  the  equator 
of  the  ball  (i.e.,  along  the  rib)  nor  at  the  poles.  The  thinnest  points  lie  along 
two  circles,  passing  around  the  ball  parallel  to  the  rib,  one  on  each  side  of  it, 
from  a  third  to  a  half  of  the  way  to  the  poles.  Along  these  lines  the  thick- 
ness may  be  10,  15,  or  20  per  cent  less  than  elsewhere,  the  reduction  depend 
ing  somewhat  on  the  skill  of  the  workman. 

The  Locomotive  for  October,  1891,  gives  two  empirical  rules  for  determin- 
ing the  thickness  of  a  copper  ball  which  is  to  work  under  an  external 
pressure,  as  follows: 

diameter  in  inches  X  pressure  in  pounds  per  sq.  in. 

1.  Thickness  =  -  16,00o 

2.  Thickness  =    diameter  X 


1240 

These  rules  give  the  same  result  for  a  pressure  of  166  Ibs.  only.    Example: 
Required  the  thickness  of  a  5-inch  copper  ball  to  sustain 

Pressures  of 50      100      150      166      200      250  Ibs.  per  sq.  in. 

Answ er  by  first  rule. ,.   .0156  .0312  .0469  .0519  .0625  .0781  inch. 
Answer  by  second  rule  .0285  .0403  .0494  .0518  .0570  .0637 

HOLDING-POWER    OF    NAILS.    SPIKES.    AND 
SCREWS. 

(A.  W.  Wright,  Western  Society  of  Engineers,  1881.) 
Spikes.— Spikes  driven  into  dry  cedar  (cut  18  months): 

Size  of  spikes 5  X  M  in.  sq.  6  X  M  6  X  M  5  X % 

Length  driven  in 4^4  in.          5  in.      5  in.    414  in. 

Pounds  resistance  to  drawing.  Av'ge,  Ibs.  857 

(  Max.  "  1159  923         2129      1556 

From  6  to  9  tests  each j  Min     „  766  766        mo       687 


290  STRENGTH    OF    MATERIALS. 

A.  M.  Wellington  found  the  force  required  to  draw  spikes  9/16  X  9/16  in., 
driven  4J4  inches  into  seasoned  oak,  to  be  4281  Ibs.;  same  spikes, etc.,  in  un- 
seasoned oak,  6523  Ibs. 

44  Professor  W.  R.  Johnson  found  that  a  plain  spike  %  inch  square 
driven  3%  inches  into  seasoned  Jersey  yellow  pine  or  unseasoned  chestnut 
required  about  2000  Ibs.  force  to  extract  it;  from  seasoned  white  oak  about 
4000  and  from  well-seasoned  locust  6000  Ibs." 

Experiments  in  Germany,  by  Funk,  give  from  2465  to  3940  Ibs.  (mean  of 
many  experiments  about  3000  Ibs.)  as  the  force  necessary  to  extract  a  plain 
i^-inch  square  iron  spike  6  inches  long,  wedge-pointed  for  one  inch  and 
driven  4J4  inches  into  white  or  yellow  pine.  When  driven  5  inches  the  force 
required  was  about  1/10  part  greater.  Similar  spikes  9/16  inches  square,  7 
inches  long,  driven  6  inches  deep,  required  from  3700  to  6745  Ibs.  to  extract 
them  from  pine;  the  mean  of  the  results  being  4873  Ibs.  In  all  cases  about 
twice  as  much  force  was  required  to  extract  them  from  oak.  The  spikes 
were  all  driven  across  the  grain  of  the  wood.  When  driven  with  the  grain, 
spikes  or  nails  do  not  hold  with  more  than  half  as  much  force. 

Boards  of  oak  or  pine  nailed  together  by  from  4  to  16  tenpennj'  common  cut 
nails  and  then  pulled  apart  in  a  direction  lengthwise  of  the  boards,  and 
across  the  nails,  tending  to  break  the  latter  in  two  by  a  shearing  action, 
averaged  about  300  to  400  Ibs.  per  nail  to  separate  them,  as  the  result  of 
many  trials. 

Resistance  of  Drift-bolts  in  Timber.— Tests  made  by  Rust  and 
Coolidge,  in  1878. 

Pounds. 

1st  Test.   1  in.  square  iron  drove  30  in.  in  white  pine,  15/16-in.  hole 26,400 

2d      "       1  in.  round      "        "       34"    "        "        "      13/16-in.     "    16,806 

3d      "       1  in.  square    44        44       18  "    "        "        "      15/16-in.    "    14,600 

4th    "       1  in.  round      44        "       22"    "      "        "      13/16-in.     "    13,200 

5th    44       1  in.  round      "        4t       34  4'    "Norway  pine, 13/16-in.     "    18,720 

6th    44       1  in.  square    4i        44       30  "    "        "        "      15/16-in.     "    19,200 

7th    44       1  in.  square    "        44       18"    "        44        44      15/16-in.     "    15.600 

8th    "       1  in.  round      "  22  "    "        4'        "      13/16-in.     "    14,400 

NOTE. — In  test  No.  6  drift-bolts  were  not  driven  properly,  holes  not  being 
in  line,  and  a  piece  of  timber  split  out  in  driving. 
Force  required  to  draw  Screws  out  of  Norway  Pine. 

%"  diam.  drive  screw  4  in.  in  wood.  Power  required,  average  2424  Ibs 

"•        "      4  threads  per  in.  Sin.  in  wood.        44  "  "        2743 

44      D'blethr'd,3perm.,4in.  in  "  "        2730 

44        44       Lag-screw,  7  per  in.,  1*4  "    "  "         1465 

"       6    "     "   2^  "    44  "  "  "         2026 

Y%  inch  R.R.  spike 5  2191 

Force  required  to  draw  Wood  Screws  out  of  Dry  Wood, 

—Tests  made  by  Mr.  Bevan.  The  screws  were  about  two  inches  in  length, 
.22  diameter  at  the  exterior  of  the  threads,  .15  diameter  at  the  bottom,  the 
depth  of  the  worm  or  thread  being  .035  and  the  number  of  threads  in  one 
inch  equal  12.  They  were  passed  tli rough  pieces  of  wood  half  an  inch  in 
thickness  and  drawn  out  by  the  weights  stated:  Beech,  460  Ibs.:  ash,  790 
Ibs.:  oak,  760  Ibs.;  mahogany,  770  Ibs. ;  elm,  665  Ibs.:  sycamore,  830  Ibs. 

Tests  of  Lag-screws  in  Various  Woods  were  made  by  A.  J. 
Cox,  University  of  Iowa,  1891: 

Q.  Size     T        H     Max.       -^ 

Kind  of  Wood.  a»r*L        Hol«     Y ,T  T£    Resist.    J*£ 

rew-      bored.    l     lie>      Ibs. 

Seasoned  white  oak %  in.         ^>in.    4U  in.     8037          3 

44 9/16"       7/16"      3      rt       6480  1 

44          4< Yz  "  %  "     414"       8780  2 

Yellow-pine  stick K"          ^  "     4~"       3800          2 

White  cedar,  unseasoned JJ'*1          Hs  "     4      "       3405          2 

In  figuring  area  for  lag-screws,  the  surface  of  a  cylinder  whose  diameter  is 
equal  to  that  of  the  screw  was  taken.  The  length  of  the  screw  part  in  each 
case  was  4  inches. — Engineering  Neics,  1891. 

Cut  versus  Wire  Nails.— Experiments  were  made  at  the  Watertown 
Arsenal  in  1893  on  the  comparative  direct  tensile  adhesion,  in  pine  and 
spruce,  of  cut  and  wire  nails.  The  results  are  stated  by  Prof.  W.  H.  Bun- 
as follows: 


HOLDING-POWER  OF  NAILS,  SPIKES,  AND  SCREWS.   291 


There  were  58  series  of  tests,  ten  pairs  of  nails  (a  cut  and  a  wire  nail  in  each) 
being  used,  making  a  total  of  1160  nails  drawn.  The  tests  were  made  in 
spruce  wood  in  most  instances,  but  some  extra  ones  were  made  in  white 
pine,  with  "box  nails.1'  The  nails  were  of  all  sizes,  varying  from  1^  inches  to 
6  inches  in  length.  In  every  case  the  cut  nails  showed  the  superior  holding 
strength  by  a  large  percentage.  In  spruce,  in  nine  different  sizes  of  nails, 
both  standard  and  light  weight,  the  ratio  of  tenacity  of  cut  to  wire  nail 
was  about  3  to  2,  or,  as  he  terms  it,  "a  superiority  of  47.45$  of  the  former." 
With  the  "  finishing1"  nails  the  ratio  was  roughly  3.5  to  2;  superiority  72$. 
With  box  nails  (1*4  to  4  inches  long)  the  ratio  was  roughly  3  to  2;  superiority 
51$.  The  mean  superiority  in  spruce  wood  was  61$.  In  white  pine,  cut  nails, 
driven  with  taper  along  the  grain,  showed  a  superiority  of  100$,  and  with 
taper  across  the  grain  of  135$.  Also  when  the  nails  were  driven  in  the  end 
of  the  stick,  i.e.,  along  the  grain,  the  superiority  of  cut  nails  was  100$,  or  the 
ratio  of  cut  to  wire  was  2  to  1.  The  total  of  the  results  showed  the  ratio  of 
tenacity  to  be  about  3.2  to  2  for  the  harder  wood,  and  about  2  to  1  for  the 
softer,  and  for  the  whole  taken  together  the  ratio  was  3.5  to  2.  We  are 
led  to  conclude  that  under  these  circumslances  the  cut  nail  is  superior  to 
the  wire  nail  in  direct  tensile  holding-power  by  72.74$. 

Nail-holding  Power  of  Various  Woods. 
(Watertown  Experiments.) 

Holding-power  per  square  inch  of 
Kind  of  Wood.  Size  of  Nail.    < Surface  in  Wood,  Ibs. 

Wire   Nail.      Cut  Nail.       Mean/ 

8d  ]  f          450 

9  "  455 

White  pine -|          J-0  \\  167  *£        [      405 

363 
60  "          J  I          340 

f  8  "          1  f           695 

Yellow  pine.   .  . . .  -!          !2  "          [•          318        •{          155         I-      662 

ou  I  oyo 

I  60  "  J  I  604 

(  8"  )  (  1340  ) 

White  oak  <  20"  V  940        -{  1292  V     1216 

|  60"  )  I  1018  j 

Chestnut j          650°;;  ?64        j.       683 

Laurel j          £  "  [          651         -j         }™         [     1200 

Nail-holding  Power  of  Various  Woods. 

(F.  W.  Clay's  Experiments.    Eng'g  News,  Jan.  11,  1894.) 

w^_rl  / Tenacity  of  6d   nails » 

Plain.    Barbed.  Blued.      Mean. 

White  pine 106  94  135  111 

Yellow  pine 190  130  270  196 

Basswood 78  132  219  143 

White  oak 226  300  555  360 

Hemlock 141  201  319  220 

Tests  made  at  the  University  of  Illinois  gave  the  resistance  of  a  1-in.  round 
rod  in  a  15/16-inch  hole  perpendicular  to  the  grain,  as  6000  Ibs.  per  lin.  ft.  in 
pine  and  15,600  Ibs.  in  oak.     Experiments  made  at  the  East  River  Bridge 
gave  resistances  of  12,000  and  15,000  Ibs.  per  lin.  ft.  for  a  1-in.  round  rod  iu 
holes  15/1 6-in.  and  14/16-in.  diameter,  respectively,  in  Georgia  pine. 
Holding-power  of  Bolts  in  White  Pine. 
(Eng'g  News,  September  26,  1891.) 

Round.  Square. 

Lbs.  Lbs. 

Average  of  all  plain  1-in.  bolts 8224  8200 

Average  of  all  plain  bolts,  %  to  \ys  in 7805  8110 

Average  of  all  bolts 8383  8598 

Round  drift-bolts  should  be  driven  in  holes  13/16  of  their  diameter,  and 
square  drift-bolte  in  holes  whose  diameter  is  14/16  of  the  side  of  the  square, 


292 


STRENGTH    OF   MATERIALS. 


STRENGTH  OF  WROUGHT  IRON  BOL.TS. 

(Computed  by  A.  F.  Nagle.) 


• 

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Stress  upon  Bolt  upon  Basis  of 

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460 

580 

810 

1160 

5800 

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.15 

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600 

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1130 

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4000 

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3680 

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10640 

14200 

17730 

24830 

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4.43 

13290 

17720 

22150 

31000 

44300 

186000 

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52000 

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21760 

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28860 

38500 

48100 

67350 

96200 

385000 

When  it  is  known  what  load  is  to  be  put  upon  a  bolt,  and  the  judgment  of 
the  engineer  has  determined  what  stress  is  safe  to  put  upon  the  iron,  look 
down  in  the  proper  column  of  said  stress  until  the  required  load  is  found. 
The  area  at  the  bottom  of  the  thread  will  give  the  equivalent  area  of  a  flat 
bar  to  that  of  the  bolt. 

Effect  of  Initial  Strain  in  Bolts.— Suppose  that  bolts  are  used 
to  connect  two  parts  of  a  machine  and  that  they  are  screwed  up  tightly  be- 
fore the  effective  load  conies  on  the  connected  parts.  Let  Pj  —  the  initial 
tension  on  a  bolt  due  to  screwing  up,  and  P2  =  the  load  afterwards  added. 
The  greatest  load  may  vary  but  little 'from  Pj  or  P2,  according  as  the 
former  or  the  latter  is  greater,  or  it  may  approach  the  value  Pl  -f-  P2,  de- 
pending upon  the  relative  rigidity  of  the  bolts  and  of  the  parts  connected. 
Where  rigid  flanges  are  bolted  together,  metal  to  metal,  it  is  probable  that 
the  extension  of  the  bolts  with  any  additional  tension  relieves  the  initial 
tension,  and  that  the  total  tension  is  Pj  or  P2,  but  in  cases  where  elastic 
packing,  as  india  rubber,  is  interposed,  the  extension  of  the  bolts  may  very 
little  affect  the  initial  tension,  and  the  total  strain  may  be  nearly  Pl  -f-  P2. 
Since  the  latter  assumption  is  more  unfavorable  to  the  resistance  of  the 
bolt,  this  contingency  should  usually  be  provided  for.  (See  Unwin, ''Ele- 
ments of  Machine  Design  "  for  demonstration.) 

STAND-PIPES  AND  THEIR  DESIGN. 

(Freeman  C.  Coffin,  New  England  Waterworks  Assoc.,  Enq.  News,  March 
16,  1893.)  See  also  papers  by  A.  H.  Rowland,  Eng.  Club  of  Phil.  1887;  B.  F. 
Stephens,  Arner.  Water  Works  Assoc.,  Eng.  News,  Oct.  6  and  13,  1888;  W. 
Kiersted,  Rensselaer  Soc.  of  Civil  Eng.,  Eng'g  Record.  April  25  and  May  2, 
1891.  and  W.  D.  Pence,  Eng.  Neivs,  April  and  May,  1894. 

The  question  of  diameter  is  almost  entirely  independent  of  that  of  height. 
The  efficient  capacity  must  be  measured  by  the  length  from  the  high-water 
line  to  a  point  below  which  it  is  undesirable  to  draw  the  water  on  account  of 
loss  of  pressure  for  fire-supply,  whether  that  point  is  the  actual  bottom  of 
the  stand-pipe  or  above  it.  This  allowable  fluctuation  ought  not  to  exceed 
50  ft.,  in  most  cases.  This  makes  the  diameter  dependent  upon  two  condi- 


eter, 

st. 
> 

Wind,  40  Ibs. 
per  sq.  ft. 
45 

Wind,  50  Ibs. 
per  sq.  ft. 
35 

....     70 

55 

)     

150 

SO 

160 

AKD  THEIR  DESIGH.  293 

tions,  the  first  of  which  is  the  amount  of  the  consumption  during  the  ordi- 
nary interval  between  the  stopping  and  starting  of  the  pumps.  This  should 
never  draw  the  water  below  a  point  that  will  give  a  good  fire  stream  and 
leave  a  margin  for  still  further  draught  for  fires.  The  second  condition  is 
the  maximum  number  of  fire  streams  and  their  size  which  it  is  considered 
necessary  to  provide  for,  and  the  maximum  length  of  time  which  they  are 
liable  to'  have  to  run  before  the  pumps  can  be  relied  upon  to  reinforce 
them. 

Another  reason  for  making  the  diameter  large  is  to  provide  for  stability 
against  wind-pressure  when  empty. 

The  following  table  gives  the  height  of  stand-pipes  beyond  which  they  are 
not  safe  against  wind-pressures  of  40  and  50  Ibs.  per  square  foot.  The  area 
of  surface  taken  is  the  height  multiplied  by  one  half  the  diameter. 

Heights  of  Stand-pipe  that  will  Resist  Wind-pressure 
by  its  Weight  alone,  when  Empty. 

Diamete 
feet. 
20. 
25. 
30. 
35.. 

To  have  the  above  degree  of  stability  the  stand-pipes  must  be  designed 
with  the  outside  angle-iron  at  the  bottom  connection. 

Any  form  of  anchorage  that  depends  upon  connections  with  the  sid3 
plates  near  the  bottom  is  unsafe.  By  suitable  guys  the  wind-pressure  is  re- 
sisted by  tension  in  the  guys,  and  the  stand-pipe  is  relieved  from  wind 
strains  that  tend  to  overthrow  it.  The  guys. should  be  attached  to  a  baud 
of  angle  or  other  shaped  iron  that  completely  encircles  the  tank,  and  rests 
upon  some  sort  of  bracket  or  projection,  and  not  be  riveted  to  the  tank. 
They  should  be  anchored  at  a  distance  f  rom  the  base  equal  to  the  height  of 
the  point  at  which  they  are  attached,  if  possible. 

The  best  plan  is  to  build  the  stand-pipe  of  such  diameter  that  it  will  resist 
the  wind  by  its  own  stability. 

Thickness  of  the  Side  Plates. 

The  pressure  on  the  sides  is  outward,  and  due  alone  to  the  weight  of  the 
water,  or  pressure  per  square  inch,  and  increases  in  direct  ratio  to  the 
height,  and  also  to  the  diameter.  The  strain  upon  a  section  1  inch  in  height 
at  any  point  is  the  total  strain  at  that  point  divided  by  two — for  each  side  is 
supposed  to  bear  the  strain  equally.  The  total  pressure  at  any  point  is 
equal  to  the  diameter  in  inches,  multiplied  by  the  pressure  per  square  inch, 
due  to  the  height  at  that  point.  It  may  be  expressed  as  follows: 

H  =  height  in  feet,  and  /  =  factor  of  safety; 

d  =  diameter  in  inches; 

p  -=  pressure  in  Ibs.  per  square  inch; 
.434  =  p  for  1  ft.  in  height; 

s  =  tensile  strength  of  material  per  square  inch; 

T  —  thickness  of  plate. 

Then  the  total  strain  on  each  side  per  vertical  inch 

T  —  '- 
»;-.'::.;*  2s  2s  ' 

Mr,  Coffin  takes/  =  5,  not  counting  reduction  of  strength  of  joint,  equiv- 
alent to  an  actual  factor  of  safety  of  8  if  the  strength  of  the  riveted  joint  is 
taken  as  GO  per  cent  of  that  of  the  plate. 

The  amount  of  the  wind  strain  per  square  inch  of  metal  at  any  joint  can 
be  found  by  the  following  formula,  in  which 

H  —  height  of  stand-pipe  in  feet  above  joint; 

T  —  thickness  of  plate  in  inches; 

p  —  wind -pressure  per  square  foot: 
W  —  wind-pressure  per  foot  in  height  above  joint; 
W  =  Dp  where  D  is  the  diameter  in  feet; 
in  =  average  leverage  or  movement  about  neutral  axis 

or  central  points  in  the  circumference;  or, 
m  =  sine  of  45°,  or  .707  times  the  radius  in  feet. 


294 


STRENGTH    OF    MATERIALS. 


Then  the  strain  per  square  inch  of  plate 


(Hw)- 


II 


circ.  in  ft.  x  mT 

Mr.  Coffin  gives  a  number  of  diagrams  useful  in  the  design  of  stand-pipes, 
together  with  a  number  of  instances  of  failures,  with  discussion  of  their 
probable  causes. 

Mr.  Kiersted's  paper  contains  the  following  :  Among  the  most  prominent 
strains  a  stand-pipe  has  to  bear  are:  that  due  to  the  static  pressure  of  the 
water,  that  due  to  the  overturning  effect  of  the  wind  on  an  empty  stand- 
pipe,  and  that  due  to  the  collapsing  effect,  on  the  upper  rings,  of  violent 
wind  storms. 

For  the  thickness  of  metal  to  withstand  safely  the  static  pressure  of 
water,  let 

t  =  thickness  of  the  plate  iron  in  inches; 
H  =  height  of  stand-pipe  in  feet; 
D  =  diameter  of  stand-pipe  in  feet. 

Then,  assuming  a  tensile  strength  of  48,000  Ibs.  per  square  inch,  a  factor 
of  safety  of  4,  and  efficiency  of  double-riveted  lap-joint  equalling  0.6  of  the 
strength  of  the  solid  plate, 

t=.^HXD;         „=-» 


stand-pipe  is  empty. 
Formula  for  wind-pressure  of  50  pounds  per  square  foot,  when 

d  =  diameter  of  stand-pipe  in  inches; 
x  —  any  unknown  height  of  stand-pipe; 

x  =  \/80irdt  =  15.85  \/dT. 

The  following  table  is  calculated  by  these  formulae.    The  stand-pipe  is 
intended  to  be  self -sustaining;  that  is,  without  guys  or  stiff  eners. 

Heights  of  Stand-pipes  for  Various  Diameters  and 
Thicknesses  of  Plates. 


Thickness  of 
Plate  in  Frac- 
tions of  an  Inch. 

Diameters  in  Feet. 

5 

6 

7 

8 

9 

10 

12 

14 

15 

|U 

18 

20 

25 

3-16. 

50 
55 
60 
70 
75 
80 
85 

55 

65 
75 
80 
90 
95 

60 

'76' 
80 
90 
95 
100 

65 

75 
85 
95 
100 
110 
115 

55 
65 
75 
90 
100 
110 
115 
125 
130 

50 
60 
70 
85 

too 

115 
120 
130 
135 
145 
150 

35 
50 
55 
70 
85 
100 
115 
130 
145 
155 
165 

'40 
50 
60 
75 
85 
100 
110 
120 
135 
145 
160 

'  40 
45 
55 
70 
80 
90 
100 
115 
125 
135 
150 
160 

7-32  

4  16 

40 
50 
65 
75 
85 
95 
105 
120 
130 
140 
150 
160 

35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 

35 
40 
50 
60 
70 
80 
85 
95 
105 
110 
120 
130 
140 

25 

35 
40 
45 
55 
60 
65 
75 
80 
90 
95 
105 
110 

5_16  

6  16 

7-16 

8--16  

9-16  

10-16. 

11-16  

12-16  

13  16 

14-16  

15-16  

16-16  

Heights  to  nearest  5  feet.    Rings  are  to  build  5  feet  vertically. 

Failures  of  Stand-pipes  have  been  numerous  in  recent  years.  A 
list  showing  23  important  failures  inside  of  nine  years  is  given  in  a  paper  by 
Prof.  W.  D.  Pence,  Eng'g.  News,  April  5,  12,  19  and  26,  May  3,  10  and  24,  and 
June  7,  1894.  His  discussion  of  the  probable  causes  of  the  failures  is  most 
valuable. 


WHOUGHT-IRON   AKD   STEEL    WATER-PIPES.         295 

Kenneth  Allen,  Engineers  Club  of  Philadelphia,  1886,  gives  the  following 
rules  for  thickness  of  plates  for  stand  pipes. 

Assume:  Wrought  iron  plate  T.  S.  48,000  pounds  in  direction  of  fibre,  and 
T.  S.  45,000  pounds  across  the  fibre.  Strength  of  single  riveted  joint  .4  that 
of  the  plate,  and  of  double  riveted  joint,  .7  that  of  the  plate  ;  wind  pressure 
=  50  pounds  per  square  foot ;  safety  factor  =  3. 

Let  h,  =  total  height  in  feet  ;  r  =  outer  radius  in  feet  ;  r'  =  inner  radius 
in  feet ;  p  =  pressure  per  square  inch  ;  t  =  thickness  in  inches  ;  d  =  outer 
diameter  in  feet. 

Then  for  pipe  filled  and  longitudinal  seams  double  riveted 

_        pr  X  12          _    hd  f 
~  48,000  X.7XM  "  4801' 

and  for  pipe  empty  and  lateral  seams,  single  riveted,  we  have  by  equating 
moments  : 

50  X  2r  (|)a  =  144  X  6000  (r4  -  r'4)  '-^,  whence  r4  --  r'4  =  ~^. 
Table  showing  required  Thickness  of  Bottom  Plate. 


Height  in 


Diameter. 


Feet. 

5  feet. 

10  feet. 

15  feet. 

20  feet. 

25  feet. 

30  feet. 

50 

t  7-64* 

Vs  * 

11-64* 

15-64 

19-64 

23-64 

60 

t  11-64* 

9-64* 

7-32 

9-32 

23-64 

27-64 

70 

t  7-32 

11-64* 

y± 

21-64 

13-32 

31-64 

80 

t!9-64 

3-16 

9-32 

% 

15-32 

9-16 

90 

t  % 

7-32 

5-16 

27-64 

17-32 

% 

100 

t29-64 

t!5-64 

23-64 

15-32 

37-64 

45-64 

125 

t23-64 

7-16 

37-64 

47-64 

7/8 

150 

t33-64 

17-32 

45-64 

% 

1  3-64 

175 

tll-16 

39-64 

13-16 

1  1-32 

1  7-32 

200 

t29-32 

45-64 

15-16 

1  11-64 

1  25-64 

*The  minimum  thickness  should  =  3-16". 

N.B.— Dimensions  marked  t  determined  by  wind-pressure. 

Water  Tower  at  Yonkers,  N.  Y.— This  tower,  with  a  pipe  122  feet 
high  and  20  feet  diameter,  is  described  in  Engineering  News,  May  18,  1892. 

The  thickness  of  the  lower  rings  is  11-16  of  an  inch,  based  on  a  tensile 
strength  of  60,000  Ibs.  per  square  inch  of  metal,  allowing  65$  for  the  strength 
of  riveted  joints,  using  a  factor  of  safety  of  3^  and  adding  a  constant  of 
%  inch.  The  plates  diminish  in  thickness  by  1-16  inch  to  the  last  four 
plates  at  the  top,  which  are  %  iuch  thick. 

The  contract  for  steel  requires  an  elastic  limit  of  at  least  33,000  Ibs.  per 
square  inch  ;  an  ultimate  tensile  strength  of  from  56,000  to  66,000  Ibs.  per 
square  inch  ;  an  elongation  in  8  inches  of  at  least  20$,  and  a  reduction  of 
area  of  at  least  45$.  The  inspection  of  the  work  was  made  by  the  Pittsburgh 
Testing  Laboratory.  According  to  their  report  the  actual  conditions  de- 
veloped were  as  follows :  Elastic  limit  from  34,020  to  39,420  ;  the  tensile 
strength  from  58,330  to  65,390  ;  the  elongation  in  8  inches  from  22j^  to  32$  ; 
reduction  in  area  from  52.72  to  71.32$  ;  17  plates  out  of  141  were  rejected  in 
the  inspection. 

WROUGHT-IRON  AND  STEEL.  WATER-PIPES. 

Riveted  Steel  Water-pipes  (Engineering  News,  Oct.  11,  1890,  and 
Aug.  1,  1891.) — The  use  of  riveted  wrought-iron  pipe  has  been  common  in 
the  Pacific  States  for  many  years,  the  largest  being  a  44-inch  conduit  in 
connection  with  the  works  of  the  Spring  Valley  Water  Co.,  which  supplies 
San  Francisco.  The  use  of  wrought  iron  and  steel  pipe  has  been  neces- 
sary in  the  West,  owing  to  the  extremely  high  pressures  to  be  withstood 
and  the  difficulties  of  transportation.  As  an  example  :  In  connection  with 


296  StREHGTil   OF   MATERIALS. 

the  water  supply  of  Virginia  City  and  Gold  Hill,  Nev.,  there  was  laid  in 
1872  an  llJ/6-inch  riveted  wrought-iron  pipe,  a  part  of  which  is  under  a  head 
of  1720  feet". 

In  the  East,  the  most  important  example  of  the  use  of  riveted  steel  water 
pipe  is  that  of  the  East  Jersey  Water  Co.,  which  supplies  the  city  of  Newark. 
The  contract  provided  for  a  maximum  high  service  supply  of  25,000,000  gal- 
lons daily.  In  this  case  21  miles  of  48-inch  pipe  was  laid,  some  of  it  under  340 
feet  head.  The  plates  from  which  the  pipe  is  made  are  about  13  feet  long 
by  7  feet  wide,  open-hearth  steel.  Four  plates  are  used  to  make  one  section 
of  pipe  about  27  feet  long.  The  pipe  is  riveted  longitudinally  with  a  double 
row,  and  at  the  end  joints  with  a  single  row  of  rivets  of  varying  diameter, 
corresponding  to  the  thickness  of  the  steel  plates.  Before  being  rolled  into 
the  trench,  two  of  the  27-feet  lengths  are  riveted  together,  thus  diminishing 
still  further  the  number  of  joints  to  be  made  in  the  trench  and  the  extra 
excavation  to  give  room  for  jointing.  All  changes  in  the  grade  of  the  pipe- 
line are  made  by  10°  curves  and  all  changes  in  line  by  'iy%,  5,  ?J^  and  10° 
curves.  To  lay  on  curved  lines  a  standard  bevel  was  used,  and  the  different 
curves  are  secured  by  varying  the  number  of  beveled  joints  used  on  a 
certain  length  of  pipe. 

The  thickness  of  the  plates  varies  with  the  pressure,  but  only  three  thick- 
nesses are  used,  J4,  5-16,  and  %  inches,  the  pipe  made  of  these  thicknesses 
having  a  weight  of  160,  185,  and  225  ibs.  per  foot,  respectively.  At  the  works 
all  the  pipe  was  tested  to  pressure  1J4  times  that  to  which  it  is  to  be  sub- 
jected when  in  place. 

Mannesman!!  Tubes  for  High  Pressures.— At  the  Mannes- 
mariu  Works  at  Kornotau,  Hungary,  more  than  600  tons  or  25  miles  of  3-inch 
and  4-inch  tubes  averaging  J4  inch  in  thickness  have  been  successfully 
tested  to  a  pressure  of  2000  Ibs.  per  square  inch.  These  tubes  were  intended 
for  a  high-pressure  water-main  in  a  Chilian  nitrate  district. 

This  great  tensile  strength  is  probably  due  to  the  fact  that,  in  addition  to 
being  much  more  worked  than  most  metal,  the  fibres  of  the  metal  run 
spirally,  as  has  been  proved  by  microscopic  examination.  While  cast-iron 
tubes  will  hardly  stand  more  than  200  Ibs.  per  square  inch,  and  welded  tubes 
are  not  safe  above  1000  Ibs.  per  square  inch,  the  Mannesmann  tube  easily 
withstands  2000  Ibs.  per  square  inch.  The  length  up  to  which  they  can 
be  readily  made  is  shown  by  the  fact  that  a  coil  of  3-inch  tube  70  feet  long 
was  made  recently. 

For  description  of  the  process  of  making  Mannesmann  tubes  see  Trans. 
A.  I.  M.  E  ,  vol.  xix.,  384. 

STRENGTH  OF  VARIOUS  MATERIALS.    EXTRACTS 
FROM  KIRK  ALLY'S  TESTS. 

The  recent  publication,  in  a  book  by  W.  G.  Kirkaldy,  of  the  results  of  many 
thousand  tests  made  during  a  quarter  of  a  century  by  his  father,  David  Kir- 
kaldy, has  made  an  important  contribution  to  oiir  knowledge  concerning 
the  range  of  variation  in  strength  of  numerous  materials.  A  condensed 
abstract  of  these  results  was  published  in"the  American  Machinist,  May  11 
and  18, 1893,  from  which  the  following  still  further  condensed  extracts  are 
taken: 

The  figures  for  tensile  and  compressive  strength,  or,  as  Kirkaldy  calls 
them,  pulling  and  thrusting  stress,  are  given  in  pounds  per  square  inch  of 
original  section,  and  for  bending  strength  in  pounds  of  actual  stress  or 
pounds  per  BD"*  (breadth  X  square  of  depth)  for  length  of  36  inches  between 
supports.  The  contraction  of  area  is  given  as  a  percentage  of  the  original 
area,  and  the  extension  as  a  percentage.!!!  a  length  of  10  inches,  except  when 
otherwise  stated.  The  abbreviations  T.  S.,  E.  L.,  Contr.,  and  Ext.  are  used 
for  the  sake  of  brevity,  to  represent  tensile  strength,  elastic  limit,  and  per- 
centages of  contraction  of  area,  and  elongation,  respectively. 

Cast  Iron.— 44  tests:  T.  S.  15,468  to  28,740  pounds;  17  of  these  were  un- 
sound, the  strength  ranging  from  15,468  to  24,357  pounds.  Average  of  all, 
23,805  pounds. 

Thrusting  stress,  specimens  2  inches  long,  1.34  to  1.5  in.  diameter;  43  tests, 
all  sound,  94,352  to  131,912;  one,  unsound,  93,759;  average  of  all,  113,825. 

Bending  stress,  bars  about  1  in.  wide  by  2  in,  deep,  cast  on  edge.  Ulti- 
mate stress  2876  to  3854;  stress  per  ED*  —  725  to  892;  average,  820.  Average 
modulus  of  rupture,  R,  =  stress  per  BD*  X  length,  =  29,520.  Ultimate  de- 
flection, .29  to  .40  in.;  average  .34  inch. 

Other  tests  of  cast  iron,  460  tests,  16  lots  from  various  sources,  gave  re- 


EXTRACTS   FROM   KIRKALDY^S   TESTS.  297 

suits  with  total  range  as  follows:  Pulling  stress,  12,688  to  33,616  pounds; 
thrusting  stress,  66,363  to  175,950  pounds;  bending  stress,  per  £D2,  505  to 
H28  pounds;  modulus  of  rupture,  R,  18,180  to  40,608.  Ultimate  deflection, 
.21  to  .45  inch. 

The  specimen  which  was  the  highest  in  thrusting  stress  was  also  the  high- 
est in  bending,  arid  showed  the  greatest  deflection,  but  its  tensile  strength 
was  only  26,502. 

The  specimen  with  the  highest  tensile  strength  had  a  thrusting  stress  of 
143,939,  and  a  bending  strength,  per  #D2,  of  979  pounds  with  0.41  deflection. 
The  specimen  lowest  in  T.  S.  was  also  lowest  in  thrusting  and  bending,  but 
gave  .38  deflection.  The  specimen  which  gave  .21  deflection  had  T.  S.,  19,188; 
thrusting.  104.281;  and  bending,  561. 

Iron  Castings.— 69  tests;  tensile  strength,  10,416  to  31,652;  thrusting 
stress,  ultimate  per  square  inch,  53,502  to  132,031. 

Channel  Irons. — Tests  of  18  pieces  cut  from  channel  irons.  T.  S. 
40,693  to  53,141  pounds  per  square  inch;  contr.  of  area  from  3.9  to  32.5  %. 
Ext.  in  10  in.  from  2.1  to  22.5  %.  The  fractures  ranged  all  the  way  from  100$ 
fibrous  to  100$  crystalline.  The  highest  T.  S.,  53,141,  with  8.1  %  contr.  and 
5.3  %  ext.,  was  100  %  crystalline;  the  lowest  T.  S.,  40,693,  with  3.9  contr.  and 
2  1  %  ext.,  was  75  %  crystalline.  All  the  fibrous  irons  showed  from  12.2  to 
22.5  %  ext.,  17.3  to  32.5  contr.,  and  T.  S.  from  43,426  to  49,615.  The  fibrous 
irons  are  therefore  of  medium  tensile  strength  and  high  ductility.  The 
crystalline  irons  are  of  variable  T.  S.,  highest  to  lowest,  and  low  ductility. 

ILowmoor  Iron  Bars.— Three  rolled  bars  2^  inches  diameter;  ten- 
sile tests:  elastic,  23,200  to  24,200;  ultimate,  50,875  to  51,905;  contraction,  44.4 
to  42.5;  extension,  29.2  to  24.3.  Three  hammered  bars,  4V£  inches  diameter, 
elastic  25,100  to  24,200;  ultimate,  46,810  to  49,223;  contraction,  20.7  to  46.5; 
extension,  10.8  to  31.6.  Fractures  of  all,  100  per  cent  fibrous.  In  the  ham- 
mered bars  the  lowest  T.  S.  was  accompanied  by  lowest  ductility. 

Iron  Bars,  Various.— Of  a  lot  of  80  bars  of  various  sizes,  some  rolled, 
and  some  hammered  (the  above  Lowmoor  bars  included)  the  lowest  T.  S. 
(except  one)  40,808  pounds  per  square  inch,  was  shown  by  the  Swedish 
"hoop  L "  bar  314  inches  diameter,  rolled.  Its  elastic  limit  was  19,150 
pounds;  contraction  68.7  %  and  extension  37.7$  in  10  inches.  It  was  also 
the  most  ductile  of  all  the  bars  tested,  and  was  100$  fibrous.  The  highest 
T.  S.,  60,780  pounds,  with  elastic  limit,  29,400;  coutr.,  36.6;  and  ext.,  24.3  $, 
was  shown  by  a  kt  Farnley  "  2-inch  bar,  rolled.  It  was  also  100$  fibrous. 
The  lowest  ductility  2.6$  contr.,  and  4.1  $  ext.,  was  shown  by  a  3%-inch 
hammered  bar,  without  brand.  It  also  had  the  lowest  T.  S.,  40,278  pounds, 
but  rather  high  elastic  limit,  25,700  pounds.  Its  fracture  was  95  %  crystal- 
line. Thus  of  the  two  bars  showing  the  lowest  T.  S.,  one  was  the  most  duc- 
tile and  the  other  the  least  ductile  in  the  whole  series  of  80  bars. 

Generally,  high  ductility  is  accompanied  by  low  tensile  strength,  as  in  the 
Swedish  bars,  but  the  Farnley  bars  showed  a  combination  of  high  ductility 
and  high  tensile  strength. 

Iioeomotlve  Forcings,  Iron.— 17  tests:  average,  E.  L.,  30,420;  T.  S., 
50.521;  contr.,  36.5;  ext.  in  i<)  inches,  23.8. 

Broken  Anchor  Forgings,  Iron.— 4  tests:  average,  E,  L.,  23,825; 
T.  S..  40,083;  contr.,  3.0;  ext.  in  10  inches,  3.8. 

Kirkaldy  places  these  two  irons  in  contrast  to  show  the  difference  between 
good  and  bad  work.  The  broken  anchor  material,  he  says,  is  of  a  most 
treacherous  character,  and  a  disgrace  to  any  manufacturer. 

Iron  Plate  Girder.  —Tensile  tests  of  pieces  cut  from  a  riveted  iron 
girder  after  twenty  years'1  service  in  a  railway  bridge.  Top  plate,  average 
of  3  tests,  E.  L.,  26,600;  T.  S.,  40,806;  contr.  161;  ext.  in  10  inches,  7.8. 
Bottom  plate,  average  of  3  tests,  E.  L.,  31,200;  T.  S.,  44,288;  contr.,  13.3;  ext. 
in  10  inches,  6.3.  Web-plate,  average  of  3  tests,  E.  L.,  28,000;  T.  S.,  45,902; 
contr.,  15  9;  ext.  in  10  inches,  8.9.  Fractures  all  fibrous.  The  results  of  30 
*.ests  from  different  parts  of  the  girder  prove  that  the  iron  has  undergone 
40  change  during  twenty  years  of  use. 

Steel  Plates.— Six  plates  100  inches  long,  2  inches  wide,  thickness  vari- 
ous, .36  to  .97  inch  T.  S.,  55,485  to  60,805;  E.  L.,  29,600  to  33,200;  contr.,  52.9 
to  59.5;  ext.,  17.05  to  18.57. 

Steel  Bridge  JLinks.— 40  links  from  Hammersmith  Bridge,  1886. 


298 


STRENGTH    OF    MATERIALS. 


Fracture. 


Average  of  all 

Lowest  T.  S 

Highest  T.  S.  and  E.  L.... 

Lowest  E.  L 

Greatest  Contraction  .... 

Greatest  Extension 

Least  Contr.  and  Ext 


67,294 
60,753 
75,986 
64,044 
63,745 
65,980 
63,980 


38,294 
36,030 
44,166 
32,441 
38.118 
36,792 
39,017 


34.5* 
30.1 
31.2 
34.7 

52.8 

40.8 

6.0 


15.51 
12.42 
13.43 
15.46 

17.78 
6.62 


15 

30 

100 

35 

0 


70* 
85 
70 
0 
65 
100 


The  ratio  of  elastic  to  ultimate  strength  ranged  from  50.6  to  65.2  per  cent; 
average,  56.9  per  cent. 

Extension  in  lengths  of  100  inches.  At  10,000  Ibs.  per  sq.  in.,  .018  to  .024; 
mean,  .020  iuch;  at  20.000  Ibs.  per  sq.  in.  .049  to  .063;  mean,  .055  inch;  at 
30,000  Ibs.  per  sq.  in.,  .083  to  .100;  mean,  .090;  set  at  30,000  pounds  per  sq.  in., 
Oto  .002;  mean,  0. 

The  mean  extension  between  10,000  to  30,000  Ibs.  per  sq.  in.  increased  regu- 
larly at  the  rate  of  .007  inch  for  each  2000  Ibs.  per  sq.  in.  increment  of  strain. 
This  corresponds  to  a  modulus  of  elasticity  of  28,511,4^9.  The  least  increase 
of  extension  for  an  increase  of  load  of  20,000  Ibs.  per  sq.  in.,  .065  inch,  cor- 
responds to  a  modulus  of  elasticity  of  30,769,231,  and  the  greatest,  .076  inch, 
to  a  modulus  of  26,315,789. 

Steel  Rails.— Bending  tests,  5  feet  between  supports,  11  tests  of  flange 
rails  72  pounds  per  yard,  4.63  inches  high. 

Elastic  stress.   Ultimate  stress.  Deflection  at  50,000  Ultimate 

Pounds.                Pounds.  Pounds.  Deflection. 

Hardest.  ..          34,200                     60,960  3.24  ins.  Sins. 

Softest....          32,000                     56,740  3.76    "  8  " 

Mean 32,763                     59,209  3.53    "  8  " 

All  uncracked  at  8  inches  deflection. 

Pulling  tests  of  pieces  cut  from  same  rails.  Mean  results. 

Elastic  Ultimate  Contraction  of 

Stress.           Pounds.  area  of  frac-  Extension 

per  sq.  in.  per  sq.  in.  ture.  in  10  ins. 

Top  of  rails 44,200              83,110  19.9*  13.5*    ' 

Botton  of  rails 40,900              77,820  30.9*  22.8* 

Steel  Tires. — Tensile  tests  of  specimens  cut  from  steel  tires. 

KRUPP  STEEL.— 262  Tests. 

Ext.   in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 69,250  119,079  31.9  18.1 

Mean 52,869  104,112  29.5  19.7 

Lowest 41,700  90,523  45.5  23.7 

VICKERS,  SONS  &  Co.— 70  Tests. 

Ext.  in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 58,600  120,789  11.8  8.4 

Mean 51,066  101,264  17.6  12.4 

Lowest 43,700  87,697  24.7  16.0 

Note  the  correspondence  between  Krupp's  and  Vickers1  steels  as  to  ten- 
sile strength  and  elastic  limit,  and  their  great  difference  in  contraction  and 
elongation.  The  fractures  of  the  Krupp  steel  averaged  22  per  cent  silky, 
78  per  cent  granular;  of  the  Vicker  steel,  7  per  cent  silky,  93  per  cent  granu- 
lar. 


EXTRACTS   FROM   KIRKALDY?S   TESTS.  299 

Steel  Axles.— Tensile  tests  of  specimens  cut  from  steel  axles. 
PATENT  SHAFT  AND  AXLE  TREE  Co.— 157  Tests. 

Ext.   in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 49,800  99,009  21.1  16.0 

Mean...   36,267  72,099  33.0  23.6 

Lowest 31,800  61,382  34.8  25.3 

VICKERS,  SONS  &  Co.— 125  Tests. 

Ext.   in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 42,600  83,701  18.9  13.2 

Mean 37,618  70,572  41.6  27.5 

Lowest 30,250  56,388  49.0  37.2 

The  average  fracture  of  Patent  Shaft  and  Axle  Tree  Co.  steel  was  33  per 
cent  silky,  67  per  cent  granular. 

The  average  fracture  of  Vickers'  steel  was  88  per  cent  silky,  12  per  cent 
granular. 

Tensile  tests  of  specimens  cut  from  locomotive  crank  axles. 
VICKERS'.— 82  Tests,  1879. 

Ext.   in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 26,700  68,057  28.3  18.4 

Mean 24,146  57,922  32.9  24.0 

Lowest 21,700  50,195  52.7  36.2 

VICKERS'.— 78  Tests,  1884. 

Ext.  in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 27,600  64,873  27.0  20.8 

Mean 23,573  56,207  32 .7  25.9 

Lowest 17,600  47,695  35.0  27.2 

FRIED.  KRUPP.-43  Tests,  1889. 

Ext.   in 
E.  L.  T.  S.  Contr.  5  inches. 

Highest 31,650  66,868  48.6  35.6 

Mean 29,491  61 ,774  47.7  32.3 

Lowest 21,950  55,172  55.3  35.6 

Steel  Propeller  Shafts.— Tensile  tests  of  pieces  cut  from  two  shafts, 
mean  of  four  tests  each.  Hollow  shaft,  Whitworth,  T.  S.,  61,290;  E.  L., 
30,575;  contr.,  52.8;  ext.  in  10  inches,  28.6.  Solid  Shaft,  Vickers',  T.  S., 
46,870;  E.  L.  20,425;  contr.,  44.4;  ext.  in  10  inches,  30.7. 

Thrusting  tests,  Whitworth,  ultimate,  56,201;  elastic,  29,300;  set  at  30,000 
Ibs.,  0.18  per  cent;  set  at  40,000  IDS.,  2.04  per  cent;  set  at  50,000  Ibs.,  3.82  per 

£6Ht. 

Thrusting  tests,  Vickers',  ultimate,  44,602;  elastic,  22,250;  set  at  30,000  Ibs., 
2.29  per  cent;  set  at  40,000  Ibs.,  4.69  per  cent. 

Shearing  strength  of  the  Whitworth  shaft,  mean  of  four  tests,  was  40,654 
Ibs.  per  square  inch,  or  66.3  per  cent  of  the  pulling  stress.  Specific  gravity 
of  the  Whitworth  steel,  7.867:  of  the  Vickers',  7.856. 

Spring  Steel.— Untempered,  6  tests,  average,  E.  L.,  67,916;  T.  S., 
115,668;  contr.,  37.8;  ext.  in  10  inches,  16.6.  Spring  steel  untempered.  15 
tests,  average,  E.  L.,  38,785;  T.  S.,  69,496;  contr.,  19.1;  ext.  in  10  inches,  29.8. 
These  two  lots  were  shipped  for  the  same  purpose,  viz.,  railway  carriage 
leaf  springs. 

Steel  Castings.— 44  tests,  E.  L.,  31,816  to  35,567;  T.  S.,  54,928  to  63,840; 
coutr.,  1.67  to  15.8;  ext.,  1.45  to  15.1.  Note  the  great  variation  in  ductility. 
The  steel  of  the  highest  strength  was  also  the  most  ductile. 

Riveted  Joints,  Pulling  Tests  of  Riveted  Steel  Plates, 

Triple  Riveted  L.ap  Joints,  Machine  Riveted, 

Holes  Drilled. 

Plates,  width  and  thickn  ss,  inches  : 

13.50  X  .25        13.00  X  .51        11.75  X  .78        12.25  X  1.01        14,00  X  .77 
Plates,  gross  sectional  area  square  inches  : 

3.375  6.63  9.165  12.372  10.780 

Stress,  total,  pounds  : 

199,320  332,640  423,180  528,000  455,21Q 


300  STRENGTH   OF   MATERIALS. 

Stress  per  square  inch  of  gross  area,  joint : 

59,058  50,172  46,173  42,696  42,227 

Stress  per  square  inch  of  plates,  solid  : 

70,765  65,300  64,050  62,280  68,045 

Ratio  of  strength  of  joint  to  solid  plate  : 

83.46  76.83  72.09  68.55  62.06 

Ratio  net  area  of  plate  to  gross  : 

73.4  65.5  62.7  64.7  72.9 

Where  fractured  : 

plate  at  plate  at  plate  at  plate  at  rivets 

holes.  holes.  holes.  holes.  sheared. 

Rivets,  diameter,  area  and  number : 

.45,  .159,  24         .64,  .321,21        .95,  .708,  12        1.08,  .916,  12       .95,  .708, 12 
Rivets,  total  area : 

3.816  6.741  8.496  10.992  8.496 

Strength  of  "Weld*.— Tensile  tests  to  determine  ratio  of  strength  of 
weld  to  solid  bar. 

IRON  TIE  BARS.— 28  Tests. 

Strength  of  solid  bars  varied  from ...  43,201  to  57,065  Ibs. 

Strenth  of  welded  bars  varied  from 17,816  to  44,586  Ibs. 

Ratio  of  weld  to  solid  varied  from 37.0  to79.1# 

IRON  PLATES.— 7  Tests. 

Strength  of  solid  plate  from 44,851  to  47,481  Ibs. 

Strength  of  welded  plate  from 26,442  to  38,931  Ibs. 

Ratio  of  weld  to  solid 57.7  to  83.9$ 

CHAIN  LINKS.— 216  Tests. 

Strength  of  solid  bar  from 49,122  to  57,875  Ibs. 

Strength  of  welded  bar  from .  39,575  to  48,824  Ibs. 

Ratio  of  weld  to  solid 72.1  to  95. 4# 

IRON  BARS.— Hand  and  Electric  Machine  Welded. 

32  tests,  solid  iron,  average 52,444 

17     •'     electri-  welded,  average 46,836  ratio  89. Ig 

19     "     hand  "        46,899     "     89. 3£ 

STEEL  BARS  AND  PLATES.— 14  Tests. 

Strength  of  solid 54,226  to  64,580 

Strength  of  weld 28,553  to  46,019 

Ratio  weld  to  solid 52. 6  to  82.1* 

The  ratio  of  weld  to  solid  in  all  the  tests  ranging  from  37.0  to  95.4  is  proof 
of  the  great  variation  of  workmanship  in  welding. 

Cast  Copper.— 4  tests,  average,  E.  L.,  5900;  T.  S.,  24,781;  ccntr.,  24.5; 
ext.,  21.8. 

Copper  Plates.— As  rolled,  22  tests,  .26  to  .75  in.  thick;  E.  L.,9766  to 
18,650;  T.  S.,  30,993  to  34,281;  contr.,  31.1  to  57.6;  ext.,  39.9  to  52.2.  The  va- 
riation in  elastic  limit  is  due  to  difference  in  the  heat  at  which  the  plates 
were  finished.  Annealing  reduces  the  T.  S.  only  about  1000  pounds,  but  the 
E.  L.  from  3000  to  7000  pounds. 

Another  series,  .38  to  .52  thick;  148  tests,  T.  S.,  29,099  t9  31,924;  contr.,  28.7 
to  56.7;  ext.  io  10  inches,  28.1  to  41.8.  Note  the  uniformity  in  tensile 
strength. 

Drawn  Copper.— 74  tests  (0.88  to  1.08  inch  diameter);  T.  S.,  31,634  to 
40,557;  contr.,  37.5  to  64.1 ;  ext.  in  10  inches,  5.8  to  48.2. 

Bronze  from  a  Propeller  Blade.— Means  of  two  tests  each  from 
centre  and  edge.  Central  portion  (sp.  gr.  8.320).  E.  L.,  7550;  T.  S.,  26,312; 
contr.,  25.4;  ext.  in  10  inches,  32.8.  Edge  portion  (sp.  gr.  8550).  E.  L.,  8950; 
T.  S.,  35,960;  contr.,  37.8;  ext.  in  10  inches,  47.9. 

Cast  German  Silver.— 10  tests:  E.  L.,  13,400  to  29,100;  T.  S.,  23,714  to 
46,540;  contr.,  3.2  to  21.5;  ext.  in  10  inclrs,  0.6  to  10.2. 

Thin  Sheet  Metal.— Tensile  Strength. 

German  silver,  2  lots  75,816  to  87,129 

Brotize,  4  lots 73,380  to  92,086 

Brass,  2  lots , 44,398  to  58,188 

Copper,91ots 30,470  to  48,450 

Iron,  13  lots,  lengthway 44,331  to  59,484 

Iron,  13  lots,  crossway'. 39,838  to  57,350 

Steel,  6  lots 49,253  to  78,251 

Steel,  6  lots,  crossway , 55,948  to  80,799 


EXTRACTS   FROM   RIRKALDY  S  TESTS. 


301 


Wire.— Tensile  Strength. 

German  silver,  5  lots 81 ,735  to  92,224 

Bronze,  1  lot ..  78,049 

Brass,  as  drawn,  4  lots 81,114  to  98,578 

Copper,  as  drawn,  3  lots 37,607  to  46,494 

Copper  annealed,  3  lots 34,936  to  45,210 

Copper  (another  lot),  4  lots  35,052  to  62,-190 

Copper  (extension  36.4  to  0.6$). 

Irou,81ots 59,246  to  97,908 

Iron  (extension  15.1  to  0.7$). 

Steel,  8  lots ..  103,272  to  318,823 

The  Steel  of  318,823  T.  S.  was  .047  inch  diam.,  and  had  an  extension  of  only 
0.3  per  cent;  that  of  103,272  T.  S,  was  .107  inch  diarn.  and  had  an  extension 
of  2.2  per  cent.  One  lot  of  .044  inch  diam.  had  267,114  T,  S.,  and  5.2  per  cent 
extension. 

"Wire  Ropes. 

Selected  Tests  Showing  Range  of  Variation. 


1 

h 

Strands. 

38 

£  * 

ftg 

t-t'ej 

v  g 

tl  bD    • 

Description. 

P 

j| 

6  as 

*O  CD 

.25  •« 

Hemp  Core. 

|P 

a 

r 

02 

C  *; 

o 

Galvanized. 

7  70 

53.00 

6 

19 

.1563 

Main 

339  780 

Ungalvanized  

7  '.00 

53.10 

7 

19 

.1495 

Main  and  Strands 

314^860 

Ungalvanized  — 

6.38 

42.50 

7 

19 

.1347 

Wire  Core 

295,920 

Galvanized  

7.10 

37.57 

6 

30 

.1004 

Main  and  Strands 

272,750 

Ungalvanized  

6.18 

40.46 

7 

19 

.1302 

Wire  Core 

268,470 

Ungalvanized.  .  .  . 

6.19 

40.33 

7 

19 

.1316 

Wire  Core 

221,820 

Galvanized  

4.92 

20.86 

6 

30 

.0728 

Main  and  Strands 

190,890 

Galvanized  

5.36 

18.94 

6 

12 

.1104 

Main  and  Strands 

136,550 

Galvanized  . 

4.82 

,'1.50 

6 

.1693 

Main 

129,710 

Ungalvanized  

3.65 

12.21 

6 

19 

.0755 

Main 

110,180 

Ungalvanized.  .  .  . 

3.50 

12.65 

7 

7 

.122 

Wire  Core 

101,440 

Ungalvanized  
Galvanized  

3.8'J 
4.11 

14.12 
11.35 

6 
6 

7 
12 

.135 

.080 

Main 
Main  and  Strands 

98,670 
75,110 

Galvanized  

3.31 

7.27 

6 

12 

.068 

Main  and  Strands 

55,095 

Ungalvanized  

3.02 

8.62 

6 

7 

.105 

Main 

49,555 

Ungalvanized.  .  .  . 

2.68 

6.26 

6 

6 

.0963 

Main  and  Strands 

41,205 

Galvanized  

2.87 

5.43 

6 

12 

.0560 

Main  and  Strands 

38,555 

Galvanized  

'2.46 

3.85  |   6 

12 

.0472 

Main  and  Strands 

28,075 

Ungalvanized.  .  .  . 

1.75 

2.801   6 

7 

.0619 

Main 

24,552 

Galvanized  

2.04 

2.72 

6 

12 

.0378 

Main  and  Strands 

20,415 

Galvanized  

1.76 

1.85 

6 

12 

.0305 

Main 

14,634 

Hemp  Ropes,  Untarred.— 15  tests  of  ropes  from  1.53  to  6.90  inches 
circumference,  weighing  0.42  to  7.77  pounds  per  fathom,  showed  an  ultim- 
ate strength  of  from  1670  to  33,808  pounds,  the  strength  per  fathom  weight 
varying  from  2872  to  5534  pounds. 

Hemp  Ropes,  Tarred.  -15  tests  of  ropes  from  1.44  to  7.12  inches 
circumference,  weighing  from  0.38  to  10.39  pounds  per  fathom,  showed  an 
ultimate  strength  of  from  1046  to  31,549  pounds,  the  strength  per  fathom 
weisrht  varying  from  1767  to  5149  pounds. 

Cotton  Ropes,— 5  ropes,  2.48  to  6.51  inches  circumference,  1.08  to  8.17 
pounds  per  fathom.  Strength  3089  to  23,258  pounds,  or  2474  to  3346  pounds 
per  fathom  weight. 

Manila  Ropes.— 35  tests:  1.19  to  8.90  inches  circumference,  0.20  to 
11.40  pounds  per  fathom.  Strength  1280  to  65,550  pounds,  or  3003  to  7394 
pounds  per  fathom  weight. 


302 


STRENGTH   OF   MATERIALS. 


Belting. 

No.  of  Tensile  strength 

lots.  per  square  inch. 

11  Leather,  single,  ordinary  tanned  3248  to  4824 

4  Leather,  single,  Helvetia , , 5631  to  5944 

7  Leather,  double,  ordinary  tanned 2160  to  3572 

8  Leather,  double  Helvetia.... 4078  to  5412 

6  Cotton,  solid  woven 5648  to  8869 

14  Cotton,  folded,  stitched    4570  to  7750 

1  Flax,  solid,  woven 9946 

1  Flax,  folded,  stitched 6389 

6  Hair,  solid,  woven 3852  to  5159 

2  Rubber,  solid,  woven 4271  to  4343 

Canvas.— 35  lots:    Strength,  lengthwise,  113  to  408  pounds  per  inch; 

crossways,  191  to  468  pounds  per  inch. 

The  grades  are  numbered  1  to  6,  but  the  weights  are  not  given.  The 
strengths  vary  considerably,  even  in  the  same  number. 

JXIarbles. — Crushing  strength  of  various  marbles.  38  tests,  8  kinds. 
Specimens  were  6-inch  cubes,  or  columns  4  to  6  inches  diameter,  and  6  and 

12  inches  high.    Range  7542  to  13,720  pounds  per  square  inch. 
Granite.— Crushing  strength,  17  tests;  square  columns  4X4  and  6x4, 

4  to  24  inches  high,  3  kinds.  Crushing  strength  ranges  10,026  to  13,271 
pounds  per  square  inch.  (Very  uniform.) 

Stones.— (Probably  sandstone,  local  names  only  given.)  11  kinds,  42 
tests,  6x6,  columns  12,  18  and  24  inches  high.  Crushing  strength  ranges 
from  2105  to  12,122.  The  strength  of  the  column  24  inches  long  is  generally 
from  10  to  20  per  cent  less  than  that  of  the  6-inch  cube. 

Stones. — (Probably  sandstone)  tested  for  London  &  Northwestern  Rail- 
way. 16  lots,  3  to  6  tests  in  a  lot.  Mean  results  of  each  lot  ranged  from 
3785  to  11,956  pounds.  The  variation  is  chiefly  due  to  the  stones  being  from 
different  lots.  The  different  specimens  in  each  lot  gave  results  which  gen- 
erally agreed  within  30  per  cent. 

Bricks.— Crushing  strength,  8  lots;  6  tests  in  each  lot;  mean  results 
ranged  from  1835  to  9209  pounds  per  square  inch.  The  maximum  variation 
in  the  specimens  of  one  lot  was  over  100  per  cent  of  the  lowest.  In  the  most 
uniform  lot  the  variation  was  less  than  20  per  cent. 

Wood.— Transverse  and  Thrusting  Tests. 


Thrust- 

3 

1 

Sizes  abt.  in 
square. 

Span, 
inches. 

Ultimate 
Stress. 

$== 

LW 

ing 
Stress 
per  sq. 

in. 

45,856 

1096 

3586 

Pitch  pine  

10 

llj'jjj  to  12^ 

144 

to 

to 

to 

80,520 

1403 

5438 

37,948 

657 

2478 

Dantzic  fir 

12 

12     to  13 

144 

to 

to 

to 

54,152 

790 

3423 

32,856 

1505 

2473 

English  oak 

Q 

4^  X  12 

120 

to 

to 

to 

39,084 

1779 

4437 

American  white 

23,624 

1190 

2656 

oak    

5 

4^  X  12 

120 

to 

to 

to 

26,952 

1372 

3899 

Demerara  greeriheart,  9  tests  (thrusting) 8169  to  10,785 

Oregon  pine,  2  tests 5888  and  7284 

Honduras  mahogany,  1  test 6769 

Tobasco  mahogany,  1  test 5978 

Norway  spruce,  2  tests  5259  and  5494 

American  yellow  pine,  2  tests 3875  and  3993 

English  ash,  1  test 3025 

Portland  Cement.- (Austrian.)    Cross-sections  of  specimens  2x2^ 
inches  for  pulling  tests  only ;  cubes,  3x3  inches  for  thrusting  tests;  weight, 


MISCELLANEOUS  TESTS   OF   MATERIALS. 


303 


US. 8  pounds  per  imperial  bushel;  residue,  0.7  per  cent  with  sieve  2500  meshes 
per  square  inch;  38.8  per  cent  by  volume  of  water  required  for  mixing;  time 
of  setting,  7  days;  10  tests  to  each  lot.  The  mean  results  in  Ibs.  per  sq.  in. 
were  as  follows: 

Cement  Cement        1  Cement,      1  Cement,        1  Cement, 

alone,  alone,  2  Sand,  3  Sand,  4  Sand, 

Age.  Pulling.         Thrusting.    Thrusting.    Thrusting.       Thrusting. 

10  days  376  2910  893  407  228 

20  days  420  3342  1023  494  275 

30  days  451  3724  1172  594  338 

Portland    Cement.  —Various  samples   pulling  tests,  2  X  2*^>  inches 
cross-section,  all  aged  10  days,  180  tests;  ranges  87  to  643  pounds  per  square 

TENSILE  STRENGTH  OF  WIRE. 

(From  J.  Bucknall  Smith's  Treatise  on  Wire.) 
Tons  per  sq. 
in.  sectional 
area. 

Black  or  annealed  iron  wire 25 

Bright  hard  drawn 35 

Bessemer,  steel  wire 40 

Mild  Siemens-Martin  steel  wire 60 

High  carbon  ditto  (or  "  improved  ") 80 


Pounds  per 
sq.  in.  sec- 
tional area. 
56,000 
78,400 
89,600 
134,000 
179,200 
224,000 
268,800 


Crucible  cast-steel  "  improved  "  wire 100 

"  Improved  "  cast-steel  "  plough  " 120 

Special  qualities  of  tempered  and  improved  cast- 
steel  wire  may  attain 150  to  170     336,000  to  380,800 

MISCELLANEOUS   TESTS    OF    MATERIALS. 
Reports  of  Work  of  the  Watertowii  Testing-machine  in 

1883. 
TESTS  OF  RIVETED  JOINTS,   IRON  AND  STEEL  PLATES. 


1 

* 

8' 

1 

': 

|i|^ 

^s-S 

o 

E 

s 

fc|  . 

11 

s 

o>  ^ 

S*»S'*>  OB 

O)  CfC 

1-5  *->' 

CO 

„  0) 

-£ffi£ 

E.S 

> 

^  *  o3  .S  13 

J3  °°  3 

*o  S 

1 

<t>*o 

£^"0 

-fl^ 

S 

P5i£j 

»«Sg| 

^  0)  ft 

OP 

a 

"S.S 

.5^  3 

§1 

•^  a 

»S*-i  oS  ° 
~        C  3  ft 

3i  &    - 

w  t- 

^ 

a 

ft  p-rH 

o 

*s'^ 

'S^  O 

.Is 

•« 

§ 

3 

PH 

" 

s 

3.2   Q   02 

C^§.5 

o 

H 

5 

AH 

EH^53 

^s 

1 

% 

11-16 

•M 

10U 

6 

1% 

39,300 

47,180 

47.0  ± 

% 

11-16 

% 

10J| 

6 

•"M 

41,000 

47,180 

49.0  J 

/^ 

M 

13-16 

10 

5 

2 

35,650 

44,615 

45.6  J 

Vis 

94 

13-16 

10 

5 

o 

35,150 

44,615 

44.9  £ 

% 

11-16 

^/ 

10 

5 

2 

46,360 

47,180 

59.9  § 

% 

11-16 

M 

10 

5 

2 

46.875 

47,180 

60.5  § 

i^ 

M 

13-16 

10 

5 

2 

46,400 

44,615 

59.4  § 

/^> 

M 

13-16 

10 

5 

2 

46,140 

44,615 

59.2  § 

% 

i 

1  1-16 

lO^-ijj 

4 

2% 

44,260 

44,635 

57.2  § 

% 

i 

1  1-16 

lOJ^ 

4 

2% 

42,350 

44,635 

54.9  § 

M 

i/^ 

1  3-16 

11.9 

4 

2.9 

42,310 

46,590 

52.1  § 

M 

i/^ 

1  3-16 

11.9 

4 

2.9 

41,920 

46,590 

51.7  § 

!      ^ 

M 

13-16 

10^ 

6 

iM 

61,270 

53.330 

59.5  J 

% 

M 

1.3-16 

\®y> 

6 

1% 

60,830 

53,330 

59.1  $ 

l/£ 

15-16 

1 

10 

5 

2 

47,530 

57,215 

40.2  t 

^2 

15-16 

1 

10 

5 

2 

49,840 

57,215 

42.3  J 

% 

11-16 

H 

10 

5 

2 

62,770 

53,330 

71.7  § 

% 

11-16 

H 

10 

5 

2 

61,210 

53,330 

69.8  § 

/4 

15-16 

l 

10 

5 

2 

68,920 

57,215 

57.1  ^ 

^ 

15-16 

i 

10 

5 

2 

66,710 

57,215 

55.0  § 

% 

1 

1  1-16 

91^ 

4 

2% 

62,180 

52,445 

63.4  § 

1 

1 

1  1-16 
1  3-16 

ioa 

4 
4 

it! 

62,590 
54,650 

52,445 
51,545 

63.8  § 
54.0  § 

g 

lf| 

1  3-16 

10 

4 

2^ 

54,200 

51,545 

53.4  § 

*Iron. 


t  Steel. 


Lap-joint. 


§  Butt-joint. 


304 


STRENGTH   OF   MATERIALS. 


The  efficiency  of  the  joints  is  found  by  dividing  the  maximum  tensile 
stress  on  the  gross  sectional  area  of  plate  by  the  tensile  strength  of  the 
material. 

COMPRESSION  TESTS  OF  3  X  3  INCH  WROUGHT-IRON  BARS. 


Length,  inches. 

Tested  with  Two  Pin  Ends,  Pins 
\Y%  inch  in  Diameter. 

Tested  with  One 
Flat  and  One  Pin 
End,  Ultimate 
Compressive 
Strength,  pounds 
per  square  inch. 

Ultimate  Com- 
pressive  Strength 
pounds  per  square 
inch. 

Tested  with  Two 
Flat  Ends,  Ulti- 
mate Compressive 
Strength,  pounds 
per  square  inch. 

30  

j  28,260 
131,990 
I  26,310 
1  26,640 
j  24,030 
1  25,380 
i  20,660 
1  20,200 
j  16,520 
1  17,840 
(  13,010 
\  15,700 

60  

90  

\  26,780 
1  25,580 
j  23,010 
1  22,450 

j  25,120 
1  25,190 
j  22,450 
\  21,870 

120 

150  

180  

Tested   with  two  pin- 
ends.  Length  of  bars  - 
120  inches. 


Diameter  Ult.  Comp.  Str., 

of  Pins.  per  sq.  in. ,  Ibs. 

M  inch 16,250 

!)*  inches 17,740 

J%      "        21,400 

214      "       22,210 


TENSILE  TEST  OF  SIX  STEEL  EYE-BARS. 

COMPARED  WITH  SMALL  TEST  INGOTS. 

The  steel  was  made  by  the  Cambria  Iron  Company,  and  the  eye-bar  heads 
made  by  Keystone  Bridge  Company  by  upsetting  and  hammering.  All  the 
bars  were  made  from  one  ingot.  Two  test  pieces,  %-inch  round,  rolled  from 
a  test-ingot,  gave  elastic  limit  48,040  and  42,210  pounds;  tensile  strength, 
73,150  and  69,470  pounds,  and  elongation  in  8  inches,  22.4  and  25.6  per  cent. 


.074  to  .0 


Gauged 
Length, 
inches. 

160 

160 

160 

800 

200 

200 

200 


Elastic 

limit,  Ibs. 

per  sq.  in. 

37,480 

36,650 

37,600 
35,810 
33,230 
37,640 


Tensile 
strength  per 
sq.  in.,  Ibs. 
67,800 
64,000 
71,560 
68,720 
65,850 
64,410 
68,290 


Elongation 

per  cent,  in 

Gauged  Length. 

15.8 

6.96 

8.6 

12.3 

12.0 

16.4 

13.9 


The  average  tensile  strength  of  the  %-inch  test  pieces  was  71,310  Ibs.,  that 
of  the  eye-bars  67,230  Ibs.,  a  decrease  of  5.7$.  The  average  elastic  limit  of 
the  test  pieces  was  45,150  Ibs.,  that  of  the  eye-bars  36,402  Ibs.,  a  decrease  of 
19.4$.  The  elastic  limit  of  the  test  pieces  was  63.3$  of  the  ultimate  strength, 
that  of  the  eye-bars  54.2$  of  the  ultimate  strength. 


MISCELLANEOUS   TESTS   OF   MATERIALS. 


305 


COMPRESSION  OF  WROUGHT-IRON  COLUMNS,   LATTICED  BOX 
AND  SOLID  WEB. 

ALL  TESTED  WITH  PIN  ENDS. 


| 

tf 

!•§ 

%*\; 

t* 

Columns  made  of 

a 
a 

& 

"eS'a] 

§1 

'-3  3 

53  S'o 

;n 

5°a 

Ifff 

3 

<D  CO 

£° 

02  «n 

6  inch  channel  solid  web      

10  0 

9831 

432 

30,220 

6  "                           "        "    

15.0 

9.977 

592 

21,050 

20  0 

9  762 

755 

16220 

0     tl                         U                         t<                H 

20  0 

16281 

1,290 

22,540 

g     <(                         11                         U                U 

26  8 

16  141 

1  645 

17,570 

8-inch  channels,  with  5-16-in.  continuous 

plates 

26  8 

19  417 

1  940 

25  290 

5-16-inch  continuous  plates  and  angles. 

Width  of  plates,  12  in.,  1  in.  and  7.35  in. 
7-16-inch  continuous  plates  and  angles. 

26.8 

16.168 

1,765 

28,020 

Plates  12  in.  wide  

26  8 

20  954 

2,242 

25,770 

8-inch  channels,  latticed  

13.3 

7.628 

679 

33,910 

8  '                "                      

20  0 

7  621 

924 

34,120 

8  *                "                       

26.8 

7.673 

1,255 

29,870 

8-ir  ch  channels,  latticed,  swelled  sides.  . 

13  4 

7.624 

684 

33,530 

8      '          •    "                                **            "     .. 

20  0 

7.517 

921 

33,390 

g   >                          4,                                                        •        ii                       U        _ 

26.8 

7.702 

1,280 

30,770 

10    '              "                       

16  8 

11  944 

1  470 

33  740 

10  "              "                       

25  0 

12  175 

1,926 

32,440 

10-inch  channels,  latticed,  swelled  sides. 

16.7 

12.366 

1,549 

31,130 

"            "              "              "           " 

25.0 

11.932 

1,962 

32,740 

*  10-inch  channels,  latticed  one  side;  con- 

tinuous plate  one  side  

25.0 

17.622 

1,848 

26,190 

1  10  inch  channels,  latticed  one  side;  con- 

tinuous plate  one  side  

25.0 

17.721 

1,827 

17,270 

*  Pins  in  centre  of  gravity  of  channel  bars  and  continuous  plate,  1.63 
inches  from  centre  line  of  channel  bars, 
•f  Pins  placed  in  centre  of  gravity  of  channel  bars. 

EFFECT  OF  COLD-DRAWING  ON   STEEL. 

Three  tensile  bars  and  two  compression  bars,  cut  from  the  same  bar  of 
hot-rolled  steel,  from  the  Norway  Steel  and  Iron  Company: 

Tensile  Elonga- 

strength  per  tion. 

sq.  in.,  Ibs.  per  cent. 

1.  Piece  of  the  original  hot-rolled  bar,  length 

66  inches,  diameter  2.03  inches.    Gauged 

length  30  inches 55,400  23.9 

2.  Diameter  reduced  in  compressing  dies  (one 

pass),  .094  inch.  Gauged  length  20  inches.        70,420.  2.7 

3.  Diameter  reduced  in  compression  dies  (one 

pass),  .222  inch.  Gauged  length  20  inches. 


81,890  0.075 

Compress.  Amount  Corn- 
Stress,  Ibs.  of  Com-  press, 
per  sq.  in.  press.,  in.  set,  in. 

4.  Compression  test  of  cold-drawn  bar  (same 

as  No.  3).      Length  4  inches,  diameter 

1.808  inches  75,000  .0562             .0395 

5.  Do.,  same  as  No.  4 75,000  .0578             .0400 

Pieces  4  and  5  both  had  diameters  increased  in  the  middle  to  1.821  inches, 
and  at  the  ends  to  1.813  inches. 


300 


STRENGTH   OF   MATERIALS. 


TESTS  OF  AMERICAN  WOODS.    (See  also  page  300.) 
In  all  cases  a  large  number  of  tests  were  made  of  each  wood.     Minimum 
and  maximum  results  only  are  given.    All  of  the  test  specimens  had  a  sec- 
tional area  of  1.575  X  1.575  inches.    The  transverse  test  specimens  were  39.3? 
inches  between  supports,  and  the  compressive  test  specimens  were  12.60 

o     t>; 

inches  long.    Modulus  of  rupture  calculated  from  formula-/?  =  xv-^;  P  = 
load  in  pounds  at  the  middle,  I  =  length  in  inches,  b  —  breadth,  d  —  depth: 


Name  of  Wood. 

Transverse  Tests. 
Modulus  of 
Rupture. 

Compression 
Parallel  to 
Grain,  pounds 
per  square  inch. 

Min. 

Max. 

Min. 

Max. 

Cucumber  tree  (Magnolia  acuminata)  .  . 
Yellow   poplar  white    wood  (Lirioden- 
dron  tulipiferd)                  .  .            

7,440 
6,560 
6,720 

9,680 
8,610 
12,200 
8,310 
7,470 
10,190 
9,830 
10,290 
5,950 
5,180 
10,220 
8,250 

6,720 

4,700 
8,400 
14,870 
11.560 
7,010 
9  760 

12,050 
11,756 
11,530 

20,130 
13,450 
21,730 
16,800 
11,130 
14.560 
14.300 
18,500 
15,800 
10,150 
13,952 
15,070 

11,360 

11,740 
16,320 
20,710 
19,430 

18,360 
18,370 
18,420 

12,870 
18,840 

17,610 
13,430 
9,530 
15,100 
10,030 
11,530 
10,980 

21,060 
11,650 
14,680 

17,920 
16,770 

4,560 
4,150 
3,810 

7,460 
6,010 
8,330 
5,830 
5,630 
6,250 
6,240 
6,650 
4,520 
4,050 
6,980 
4,960 

4,960 

5,480 
6,940 
7,650 
7,460 
5,810 
4,960 
4,540 
3,680 
5,770 

5,770 
3,790 
2,660 
4,400 
5,060 
3,750 
2,580 

4,010 
4,150 
4,500 

4,880 
6,810 

7,410 
5,790 
6,480 

9.940 

7,500 
11,940 
9,120 

7,620 
9,400 
7,480 
8,080 
8,830 
5,970 
8,790 
8,040 

7,340 

6,810 
8,850 
10,280 
8,470 
9,070 
8,970 
8,550 
6,650 
7,840 

8,590 
6,510 
5,810 
7,040 
7,140 
5,600 
4,680 

10,600 
5,300 
7,420 

9,800 
10,700 

White    wood,   Bass  wood  (Tilia  Ameri- 
cana) 

Sugar-maple,    Rock-maple   (Acer   sac- 
charinum           

Red  maple  (Acer  rubrum)  .  
Locust  (Robinia  pseudacacia) 

AVild  cherry  (Prunus  serotina) 

Sweet  gum  (Liquidambar  styraciflua)  .  . 
Dogwood  (Cornus  florida)  

Sour  gum,  Pepperidge  (Nyssa  sylvatica). 
Persimmon  (Diospyros  Virginiana).  .  .  . 
White  ash  (Fraxunis  Americana) 

Sassafras  (Sassafras  ojfficinale). 

Slippery  elm  (  Ulmus  fulva)  

\Vhite  elm  (Ulmus  Americana) 

Sycamore;  Buttonwood  (Pla  tanus  occi- 
dentalis)    .  .  .  

Butternut;    white  walnut   (Juglans  ci- 
nerea)  

Black  walnut  (Juglan?  nigra) 

Shellbark  hickory  (Carya  alba)  

Pignut  (Carya  porcina)      

V^hite  oak  (Onercus  alba)               .     . 

Black  oak  (Quercus  tinctoria)  

7,900 
5,950 
13,850 

11,710 
8,390 
6,310 
5,640 
9,530 
5,610 
3,780 

9,220 
9,900 
7,590 

8,220 
10,080 

Chestnut  (Castanea  vutg<tris) 

Beech  (Faous  ferruojineti)          ,  

Canoe-birch,  paper-birch  (Betula  papy- 

Cottonwood  (Populus  moniliferct)  

White  cedar  (Thuja  occidentalis)  
Red  cedar  (Juniperus  Virginiana)  .   ... 
Cypress  (Saxodium  Distichum)  

\Vhite  pine  (Pinus  strobus) 

Spruce  pine  (Pinus  glabra)  

Long-leaved  pine,  S'outhern  pine  (Pinus 
pdlustris) 

White  spruce  (Picea  alba''  

Hemlock  (Tsuga  Canadensis) 

Red  fir,  yellow  fir  (Pseudotsuga  Doug- 
lasii)     

Tamarack  (Larix  Americana)  

SHEARING  STRENGTH  OF  IRON  AND  STEEL. 

H.  V.  Loss  in  American  Engineer  and  Railroad  Journal,  March  and  April, 
2893,  describes  an  extensive  series  of  experiments  on  the  shearing  of  iron 
and  steel  bars  in  shearing  machines.  Some  of  his  results  are  : 


CHAINS. 


307 


Depth  of  penetration  at  point  of  maximum  resistance  for  soft  steel  bars 
is  independent* of  the  width,  but  varies  with  the  thickness.  If  d  =  depth  of 
penetration  and  t  =  thickness,  d  =  M  for  a  flat  knife,  d  =  .25  t  for  a  4°  bevel 
knife,  and  d  =  .16  |/f3  for  an  8°  bevel  knife.  The  ultimate  pressure  per  inch 
of  width  in  flat  steel  bars  is  approximately  50,000  Ibs.  X  t.  The  energy  con- 
sumed in  foot  pounds  per  inch  width  of  steel  bars  is,  approximately:  1" 
thick,  1300  ft.-lbs.;  W,  2500;  1%",  3700;  1%",  4500;  the  energy  increasing 
at  a  slower  rate  than  the  thickness.  Iron  angles  require  more  energy 
than  steel  angles  of  the  same  size;  steel  breaks  while  iron  has  to  be 
cut  off.  For  hot-rolled  steel  the  resistance  per  square  inch  for  rectan- 
gular sections  varies  from  4400  Ibs.  to  20,500  Ibs.,  depending  partly  upon  its 
hardness  and  partly  upon  the  size  of  its  cross-area,  which  latter  element 
indirectly  but  greatly  indicates  the  temperature,  as  the  smaller  dimensions 
require  a  considerably  longer  time  to  reduce  them  down  to  size,  which  time 
again  means  loss  of  heat. 

It  is  not  probable  that  the  resistance  in  practice  can  be  brought  very 
much  below  the  lowest  figures  here  given— viz.,  4400  Ibs.  per  square  inch- 
as  a  decrease  of  1000  Ibs.  will  henceforth  mean  a  considerable  increase  in 
cross-section  and  temperature. 

HOLDING-POWER  OF  BOIL.ER-TUBES  EXPANDED 
INTO  TUBE-SHEETS. 

Experiments  by  Chief  Engineer  W.  H.  Shock,  U.  S.  N.,  on  brass  tubes,  2^ 
inches  diameter,  expanded  into  plates  %-inch  thick,  gave  results  ranging 
from  5850  to  46.000  Ibs.  Out  of  48  tests  5  gave  figures  under  10,000  Ibs.,  12 
between  10,000  and  20,000  Ibs.,  18  between  20,000  and  30,000  Ibs.,  10  between 
30,000  and  40,000  Ibs.,  and  3  over  40,000  Ibs. 

Experiments  by  Yarrow  &  Co.,  on  steel  tubes,  2  to  2^4  inches  diameter, 
gave  results  similarly  varying,  ranging  from  7900  to  41,715  Ibs.,  the  majority 
ranging  from  20,000  to  30,000  Ibs.  In  15  experiments  on  4  and  5  inch  tubes 
the  strain  ranged  from  20,720  to  68,040  Ibs.  Beading  the  tube  does  not  neces- 
sarily give  increased  resistance,  as  some  of  the  lower  figures  were  obtained 
with  beaded  tubes.  (See  paper  on  Rules  Governing  the  Construction  of 
Steam  Boilers,  Trans.  Engineering  Congress,  Section  Gr,  Chicago,  1893.) 

CHAINS. 

Weight  per  Foot,  Proof  Test  and  Breaking  Weignt. 

(Pennsylvania  Railroad  Specifications.) 


Nominal 
Diameter 
of  Wire, 
inches. 

Description. 

Specifications. 

Weight  per 
foot,  Ibs. 

Proof  Test, 
Ibs. 

Breaking 
Weight, 
IbS. 

5/32 
3/16 

y* 

5/16 

7/16 
7/16 

| 

9 

m 
m 
m 

Lock-chain   

0.20 

Fire-door  chain  

0  35 

Crossing-gate  chain  

0.70 
.10 
.50 
.50 
.90 
.90 
2.50 
2.50 
4.00 
4.00 
5.50 
5.50 
7.40 
9.50 
12.00 
15.00 
21.00 

1500 
3000 
3500 
4000 
5000 
5500 
7000 
7500 
11,000 
11,000 
16,000 
16,000 
22,000 
30,000 
40,000 
50,000 
70,000 

3000 
5500 
7000 
7500 
9500 
10,000 
12,500 
13,000 
20,000 
20,000 
29,000 
29,000 
40,000 
55,000 
66,000 
82,000 
116,000 

Sprocket-wheel  chain 

Brake-chain    

Crane-chain 

Drop-bottom  branch  chain. 
Crane-chain  

Drop-bottom  main  chain..  .  . 
Crane-chain  

Safety    " 

Crane     "             

Log        "     

Crane     "            

<t         ti 

u             it 

.4                  t( 

11                   it 

Elongation  of  all  sizes,  10  per  cent.    All  chain  must  stand  the  prescribed 
proof  test  without  deformation. 


308 


STRENGTH   OF   MATERIALS. 


British  Admiralty  Proving  Tests  of  Chain  Cables.— Stud 
links.     Minimum  size  in  inches  and  16ths.    Proving  test  in  tons  of  2240  Ibs. 

Mi«.  Size:  H  f§  ft  it  ii  1  1&  ^  1&  !•&  l&  l&  1TV 
Test,  tons:  8£g  10&  11£§  13£g  15£§  18  205%  22£§  25^  28?%  31  34  37235. 
Min.  Size:  I8  I9  I10  I11  I12  I13  I14  I16  2  21  22  23. 
Test,  tons:  40£g  43$-§  47^g  51  ^  552%  595%  6V<5  6~M  72  76££  81 5%  912%. 

Wrought-iron  Chain  Cables.— The  strength  of  a  chain  link  is 
less  than  twice  that  of  a  straight  bar  of  a  sectional  area  equal  to  that  of  one 
side  of  the  link.  A  weld  exists  at  one  end  and  a  bend  at  the  other,  each  re- 
quiring at  least  one  heat,  which  produces  a  decrease  in  the  strength.  The 
report  of  the  committee  of  the  U.  S.  Testing  Board,  on  tests  of  wrought-iron 
and  chain  cables  contains  the  following  conclusions.  That  beyond  doubt, 
when  made  of  American  bar  iron,  with  cast-iron  studs,  the  studded  link  is 
inferior  in  strength  to  the  unstudded  one. 

"That  when  proper  care  is  exercised  in  the  selection  of  material,  a  varia- 
tion of  5  to  17  per  cent  of  the  strongest  may  be  expected  in  the  resistance 
of  cables.  Without  this  care,  the  variation  may  rise  to  25  per  cent. 

"  That  with  proper  material  and  construction  the  ultimate  resistance  of 
the  chain  may  be  expected  to  vary  from  155  to  170  per  cent  of  that  of  the 
bar  used  in  making  the  links,  and  show  an  average  of  about  163  per  cent. 

"  That  the  proof  test  of  a  chain  cable  should  be  about  50  per  cent  of  the 
ultimate  resistance  of  the  weakest  link.'1 

The  decrease  of  the  resistance  of  the  studded  below  the  unstudded  cable 
is  probably  due  to  the  fact  that  in  the  former  the  sides  of  the  link  do  not 
remain  parallel  to  each  other  up  to  failure,  as  they  do  in  the  latter.  The  re- 
sult is  an  increase  of  stress  in  the  studded  link  over  the  unstudded  in  the 
proportion  of  unity,  to  the  secant  of  half  the  inclination  of  the  sides  of  the 
former  to  each  other. 

From  a  great  number  of  tests  of  bars  and  unfinished  cables,  the  commit- 
tee considered  that  the  average  ultimate  resistance,  and  proof  tests  of  chain 
cables  made  of  the  bars,  whose  diameters  are  given,  should  be  such  as  are 
shown  in  the  accompanying  table. 

ULTIMATE  RESISTANCE  AND   PROOF  TESTS   OF  CHAIN  CABLES. 


Diani. 
of 
Bar. 

Average  resist. 
=  163#  of  Bar. 

Proof  Test. 

Diam. 
of 
Bar. 

Average  resist. 
=  163^  of  Bar. 

Proof  Test. 

Inches. 

Pounds. 

Pounds. 

Inches. 

Pounds. 

Pounds. 

1  1/16 

71,172 

33,840 

1  9/16 

162,283 

77,159 

1  1/16 

79,544 

37,820 

1% 

174,475 

82,956 

^ 

88,445 

42,053 

1  11/16 

187,075 

88,947 

1  3/16 

97,731 

46,468 

IK 

200,074 

95,128 

1% 

107,440 

51,084 

1  13/16 

213,475 

101,499 

1  5/16 

117,577 

55,903 

m 

227,271 

108,058 

1% 

128,129 

60,920 

1  15/16 

241,463 

114,806 

1  7/16 

139,103 

66,138 

2 

256,040 

121,737 

IK 

150,485 

71,550 

STRENGTH  OF   GLASS. 

(Fairbairn's  "Useful  Information  for  Engineers,"  Second  Series.) 

Best          Common    Extra  White 
Flint  Glass.  Green  Glass.  Crown  Glass. 

Mean  specific  gravity  3.078  2.528  2.450 

Mean  tensile  strength,  Ibs.  per  sq.  in.,  bars..       2,413  2,896  2,540 

do.  thin  plates.       4,200  4,800  6,000 

Mean  crush's  strength,  Ibs.  p.  sq.  in.,  cyl'drs.     27,582          39,876          31,003 
do.  cubes.     13,130          20,206          21,867 

The  bars  in  tensile  tests  were  about  ^  inch  diameter.  The  crushing  tests 
were  made  on  cylinders  about  %  inch  diameter  and  from  1  to  2  inches  high, 
and  on  cubes  approximately  1  inch  on  a  side.  The  mean  transverse  strength 
of  glass,  as  calculated  by  Fairbairn  from  a  mean  tensile  strength  of  25(50 
Ibs.  and  a  mean  compressive  strength  of  30,150  Ibs.  per  sq.  in.,  is,  for  a  bar 
supported  at  the  ends  and  loaded  in  the  middle, 

w  =  3140*f , 


STRENGTH    OF   TIMBER. 


309 


in  vyhich  w  =  breaking  weight  in  Ibs.,  b  =  breadth,  d  —  depth,  and  I  —  length, 
in  inches.  Actual  tests  will  probably  show  wide  variations  in  both  direc- 
tions from  the  mean  calculated  strength. 

STRENGTH  OF  COPPER  AT  HIGH  TEMPERATURES. 

The  British  Admiralty  conducted  some  experiments  at  Portsmouth  Dock- 
yard in  1877,  on  the  effect  of  increase  of  temperature  on  the  tensile  strength 
of  copper  and  various  bronzes.  The  copper  experimented  upon  was  in  rods 
.72-in.  diameter,  having  a  tensile  strength  of  about  25  tons  per  square  inch. 

The  following  table  shows  some  of  the  results: 


Temperature 
Fahr. 

Tensile  Strength 
in  Ibs.  per  sq.  in. 

Temperature 
Fahr. 

Tensile  Strength 
in  Ibs.  per  sq.  in. 

Atmospheric. 
100° 
200° 
300° 

23,115 
23,366 
22,110 
21,607 

Atmospheric. 
400° 
500° 

21,105 
19,597 

Up  to  a  temperature  of  400°  F.  the  loss  of  strength  was  only  about  10  per 
cent,  and  at  500°  F.  the  loss  was  16  per  cent.  The  temperature  of  steam  at 
200  Ibs.  pressure  is  382°  F.,  so  that  according  to  these  experiments  the  loss 
of  strength  at  this  point  would  not  be  a  serious  matter.  Above  a  tempera- 
ture of  500°  the  strength  is  seriously  affected. 

STRENGTH    OF    TIMBER. 

Strength  of  Long-leaf  Pine  (Yellow  Pine,  Pinus  Palustris)  from 
Alabama  (Bulletin  No.  8,  Forestry  Div.,  Dept.  of  Agriculture,  1893.  Tests 
by  Prof.  J.  B.  Johnson.) 

The  following  is  a  condensed  table  of  the  range  of  results  of  mechanical 
tests  of  over  2000  specimens,  from  26  trees  from  four  different  sites  in 
Alabama  ;  reduced  to  15  per  cent  moisture  : 


Butt  Logs. 

Middle  Logs. 

Top  Logs. 

Av'g  of 
all  Butt 
Logs. 

Specific  gravity 

0.449  to  1.039 
4,762  to  16,200 

4,930  to  13,110 
1,119  to    3,117 

0.23  to  4.69 
4,781  to    9,850 

675  to    2,094 
8,600  to  3  1,890 

464  to    1,299 

0.575  to  0.859 
7,640  t(>  17,128 

5,540  to  11,790 
1,136  to    2,982 

1.34  to  4.21 
5,030  to    9,300 

656  to    1,445 
6,330  to  29,500 

539  to    1,230 

0.484  to  0.907 
4,268  to  15,554 

2.553  to  11,950 
842  to    2,697 

^-09  to  4.  65 
4,587  to  9,100 

584  to  1,766 
4,170  to  23,280 

484  to    1156 

0.767 
12,614 

9,460 
1,926 

2.98 
7,452 

1,598 
17,359 

866 

3WL 

Trans  verse  strength,-  —  — 

do       do.  atelast.  limit. 
Mod.  of  elast.,  thous.  Ibs. 
Relative  elast.  resilience, 
inch-pounds  per  cub.  in. 
Crushing  endwise,  str.  per 
sq.  in  -Ibs    

Crushing    across    grain, 
strength  per  sq.  in.,  Ibs. 
Tensile  strength  per  sq.  in. 
Shearing  strength    (with 
grain),  mean  per  sq.  in  . 

Some  of  the  deductions  from  the  tests  were  as  follows  : 

1.  With  the  exception  of  tensile  strength  a  reduction  of  moisture  is  ac- 
companied by  an  increase  in  strength,  stiffness,  and  toughness. 

2.  Variation  in  strength  goes  generally  hand-in-hand  with  specific  gravity. 

3.  In  the  first  20  or  30  feet  in  height  the  values  remain  constant  ;  then 
occurs  a  decrease  of  strength  which  amounts  at  70  feet  to  20  to  40  per  cent 
of  that  of  the  butt-log. 

4.  In  shearing  parallel  with  the  grain  and  crushing  across  and  parallel 
with  the  grain,  practically  no  difference  was  found. 

5.  Large  beams  appear  10  to  20  per  cent  weaker  than  small  pieces. 

6.  Compression  tests  endwise  seem  to  furnish  the  best  average  statement 
of  the  value  of  wood,  and  if  one  test  only  can  be  made,  this  is  the  safest,  as 
was  also  recognized  by  Bauschinger. 

7.  Bled  timber  is  in  no  respect  inferior  to  unbled  timber, 


310 


STRENGTH    OF   MATERIALS. 


The  figures  for  crushing  across  the  grain  represent  the  load  required  to 
cause  a  compression  of  15  per  cent.  The  relative  elastic  resilience,  in  inch- 
pounds  per  cubic  inch  of  the  material,  is  obtained  by  measuring  the  area 
of  the  plotted-strain  diagram  of  the  transverse  test  from  the  origin  to  the 
point  in  the  curve  at  which  the  rate  of  deflection  is  50  per  cent  greater  than 
the  rate  in  the  earlier  part  of  the  test  where  the  diagram  is  a  straight  line. 
This  point  is  arbitrarilj7  chosen  since  there  is  no  definite  "elastic  limit  "  in 
timber  as  there  is  in  iron.  The  "strength  at  the  elastic  limit"  is  the 
strength  taken  at  this  same  point.  Timber  is  not  perfectly  elastic  for  any 
load  if  left  on  any  great  length  of  time. 

The  long-leaf  pine  is  found  in  all  the  Southern  coast  states  from  North 
Carolina  to  Texas.  Prof.  Johnson  says  it  is  probably  the  strongest  timber 
in  large  sizes  to  be  had  in  the  United  "States.  In  small  selected  specimens, 
other  species,  as  oak  and  hickory,  may  exceed  it  in  strength  and  tough- 
ness. The  other  Southern  yellow  pines,  viz.,  the  Cuban,  short-leaf  and 
the  loblolly  pines  are  inferior  to  the  long-leaf  about  in  the  ratios  of  their 
specific  gravities  ;  the  long-leaf  being  the  heaviest  of  all  the  pines.  It 
averages  (kiln-dried)  48  pounds  per  cubic  foot,  the  Cuban  47,  the  short-leaf 
40,  and  the  loblolly  34  pounds. 

Strength  of  Spruce  Timber.— The  modulus  of  rupture  of  spruce 
is  given  as  follows  by  different  authors  :  Hatfield,  9900  Ibs.  per  square  inch  ; 
Rankine,  11,100 ;  Laslett,  9045  ;  Trautwine,  8100  ;  Rodman,  6168.  Traut- 
wine  advises  for  use  to  deduct  one-third  in  the  case  of  knotty  and  poor 
timber. 

Prof.  Lanza,  in  25  tests  of  large  spruce  beams,  found  a  modulus  of 
rupture  from  2995  to  5666  Ibs.;  the  average  being  4613  Ibs.  These  were 
average  beams,  ordered  from  dealers  of  good  repute.  Two  beams  of 
selected  stock,  seasoned  four  years,  gave  7562  and  8748  Ibs.  The  modulus 
of  elasticity  ranged  from  897,000  to  1,588,000,  averaging  1,294,000. 

Time  tests  show  much  smaller  values  for  both  modulus  of  rupture  and 
modulus  of  elasticity.  A  beam  tested  to  5800  Ibs.  in  a  screw  machine  was 
left  over  night,  and  the  resistance  was  found  next  morning  to  have  dropped 
to  about  3000,  and  it  broke  at  3500. 

Prof.  Lanza  remarks  that  while  it  was  necessary  to  use  larger  factors  of 
safety,  when  the  moduli  of  rupture  were  determined  from  tests  with  smaller 
pieces,  it  will  be  sufficient  for  most  timber  constructions,  except  in  factories, 
to  use  a  factor  of  four.  For  breaking  strains  of  beams,  he  states  that  it  is 
better  engineering  to  determine  as  the  safe  load  of  a  timber  beam  the  load 
that  will  not  deflect  it  more  than  a  certain  fraction  of  its  span,  say  about 
1/300  to  1/400  of  its  length. 

Properties  of  Timber. 

(N.  J.  Steel  &  Iron  Co.'s  Book.) 


Description. 

Weight 
per 
cubic 
foot,  in 
Ibs. 

Tensile 
Strength 
per  sq.  inch, 
in  Ibs. 

Crushing 
Strength  per 
sq.  inch, 
in  Ibs. 

Relative 
Strength 
for    Cross 
Breaking. 
White 
Pine-  100. 

Shearing 
Strength 
with  the 
Grain, 
Ibs.  per 
sq.  inch 

Ash  ... 

43  to  55.8 
43  to  53.4 
50  to  56.8 

11,  000  to  17,207 
11,500  to  18,000 
10,300  to  11,400 

4,400  to   9,363 
5,800  to   9,363 
5,600  to   6,000 

130  to  180 
100  to  144 
55  to  63 
130 
96  to  123 
96 
88  to  95 
150  to  210 
132  to  227 
122  to  220 
130  to  177 
155  to  189 
100 
98  to  170 
86  to  110 

458  to  700 

Beech 

Cedar 

Cherry  

Chestnut 

33 
34  to  36.7 

10,500 
13,400  to  13,489 
8,700 
12,800  to  18,000 
20,500  to  24,800 
10,500  to  10.584 
10,253  to  19,500 

5,350  to  5,600 
6,831  to  10,331 
5,700 
8,925 
9,113  to  11,700 
8,150 
4,664  to  9,509 
6,850 
5,000  to  6.650 
5,400  to   9,500 
5,050  to  7,850 
7,500 

Elm  

Hemlock 

Hickory. 

Locust 

44 

49 
45  to  54.5 
70 

367  to  647 
752  to  966 

225  to  423 

286  to  415 
253  to  374 

Maple  
Oak,  White  
Oak,  Live  

Pine,  White.... 
Pi  rie,  Yellow... 
Spruce  
Walnut,  Black. 

30 

28.  8  to  33 

42 

16.606  to  12.666 

12,600  to  19,200 
10,000  to  19,500 
9,286  to  1(5,000 

STRENGTH    OF   TIMBER. 


311 


The  above  table  should  be  taken  with  caution.  The  range  of  variation  in 
the  species  is  apt  to  be  much  greater  than  the  figures  indicate.  See  Johnson's 
tests  on  long-leaf  pine,  and  Lanza's  on  spruce,  above.  The  weight  of  yellow 
pine  in  the  table  is  much  less  than  that  given  by  Johnson.  (W.  K.) 

Compressive  Strengths  of  American  Wood*,  when  slowly 
and  carefully  seasoned.— Approximate  averages,  deduced  from  many  exper- 
iments made  with  the  U.  S.  Government  testing-machine  at  Watertown, 
Mass.,  by  Mr.  S.  P.  Sharpless,  for  the  Census  of  1880.  Seasoned  woods  resist 
crushing  much  better  than  green  ones;  in  many  cases,  twice  as  well.  Differ- 
ent specimens  of  the  same  wood  vary  greatly.  The  strengths  may  readily 
vary  as  much  as  one-third  part  more  or  less  from  the  average. 


End- 
wise,* 
Ibs.  per 
sq.  in. 

Side- 
wise,'!' 
Ibs.  per 
sq.  in. 

End- 
wise,* 
Ibs.  per 
sq.  in. 

Side- 
wise,  t 
Ibs.   per 
sq.  in. 

.01 

1300 
800 
1100 
1300 
600 
700 

1300 
700 

500 
700 
1700 
900 
13(50 
500 
1300 
1300 
600 
2000 
1600 
500 

1900 
1600 
1700 

1400 

.1 

.01 

.1 

4300 
2900 

4000 
4200 
4500 
3000 

1200 
1400 

2000 
2600 
1100 
2100 
1300 
1200 

2600 

2600 
1600 
1400 

Ash,  red  and  white 
Aspen                , 

6800 
4400 
7000 
8000 
4400 
5400 

COOO 
6000 

4400 

5000 
8000 
5300 
5200 
6000 
6800 
7700 
5300 
8000 
10000 
5000 

9800 
7000 
9000 

5300 

3000 
1400 
1900 
2600 
1400 
1600 

2600 
1000 

900 
1300 
2600 
1600 
2600 
1200 
2600 
2600 
1100 
4000 
13000 
900 

4400 
2600 
5300 

2600 

Maple: 
sugar  and  black., 
white  and  red  — 
Oak  : 
white,    post     (or 
iron),  swamp 
white,  red,  and 
black  
scrub  and  basket, 
chestnut  and  live 
pin 

8000 
6800 

7000 
6000 
7500 
6500 

5400 
6300 

5000 
8500 
5000 
5000 
5700 
4500 

6000 

8000 
5400 
4400 

1900 
1300 

1600 
1700 
1600 
1300 

fGOO 
600 

1000 
1300 
600 
1300 
700 
600 

1300 

1300 
700 
700 

Beech    

Birch  
Buckeye 

Butternut 

Buttomvood 
(sycamore) 
Cedar,  red  

Cedar,  white  (arbor- 
vitae)  
Catalpa  (Ind.bean) 
Cherry,  wild  
Chestnut..  ,  
Coffee-tree,  Ky  
Cypress,  bald  
Elm,  Am.  or  white 
"     red 

Pine  : 
white  ... 

red  or  Norway.... 
pitch  and  Jersey 
scrub 

Georgia  
Poplar.  ,  

Hemlock  

Sassafras.  .  .   

Spruce,  black  
"        white  
Sycamore    (button- 
wood)  

Lignum-vitce  
Linden,  American. 
Locust: 
black  and  yellow, 
honey  
Mahogany  — 
Maple: 
broad-leafed,  Ore. 

Walnut  : 
black.   
white  (butternut). 
Willow        

*  Specimens  1.57  ins.  square  X  12.6  ins.  long. 

t  Specimens  1.57  ins.  square  X  6.3  ins.  long.  Pressure  applied  at  mid-length 
by  a  punch  covering  one-fourth  of  the  length.  The  first  column  gives  the 
loads  producing  an  indentation  of  .01  inch,  the  second  those  producing  an 
indentation  of  .1  inch,  (See  also  page  306). 

Expansion  of  Timber  Due  to  the  Absorption  of  Water. 

(De  Volson  Wood,  A.  S.  M.  E.,  vol.  x.) 

Pieces  36  X  5  in.,  of  pine,  oak,  and  chestnut,  were  dried  thoroughly,  and 
then  immersed  in  water  for  37  days. 
The  mean  per  cent  of  elongation  and  lateral  expansion  were: 

Pine.  Oak.  Chestnut. 

Elongation,  per  cent 0.065  0.085  0165 

Lateral  expansion,  percent 2.6  3.5  3.65 

Expansion  of  Wood  by  Heat.— Traut wine  gives  for  the  expansion 
of  white  pine  for  1  degree  Fahr.  1  part  in  440.530,  or  for  180  degrees  1  part  in 
2447,  or  about  one-third  of  the  expansion  of  iron, 


312 


STREKGTH   OF  MATERIALS. 


Shearing  Strength  of  American  Woods,  adapted  for 
Pins  or  Treenails. 

J.  C.  Trautwine  (Jour.  Franklin  Inst.).    (Shearing  across  the  grain.) 


per  sq.  in. 

Ash ..  6280 

Beech 5223 

Birch 5595 

Cedar  (white) 1372 

"      1519 

Cedar  (Central  American) 3410 

Cherry 2945 

Chestnut 1536 

Dogwood 6510 

Ebony 7750 

Gum 5890 

Hemlock 2750 

Locust  7176 


per  sq.  in. 

Hickory 6045 

7285 

Maple 6355 

Oak 4425 

Oak  (live). 8480 

Pine  (white) 2480 

Pine  (Northern  yellow 4340 

Pine  (Southern  yellow) 5735 

Pine  (very  resinous  yellow) 5053 

Poplar 4418 

Spruce 3255 

Walnut  (black) 4728 

Walnut  (common) 2830 


THE   STRENGTH  OF   BRICK,   STONE,  ETC. 

A  great  advance  has  recently  been  made  in  the  manufacture  of  brick,  in 
the  direction  of  increasing  their  strength.  Chas.  P.  Chase,  in  Engineering 
News,  says:  "  Taking  the  tests  as  given  in  standard  engineering  books  eight 
or  ten  years  ago,  we  find  in  Trautwine  the  strength  of  brick  given  as  500  to 
4200  Ibs.  per  sq.  in.  Now,  taking  recent  tests  in  experiments  made  at 
Watertown  Arsenal,  the  strength  ran  from  5000  to  22,000  Ibs.  per  sq.  in.  In 
the  tests  on  Illinois  paving-brick,  by  Prof.  I.  O.  Baker,  we  find  an  average 
strength  in  hard  paving  brick  of  over  5000  Ibs.  per  square  inch.  The  average 
crushing  strength  of  ten  varieties  of  paving-brick  much  used  in  the  West,  I 
find  to  be  7150  Ibs.  to  the  square  inch." 

A  recent  test  of  brick  made  by  the  dry-clay  process  at  Watertown  Arsenal, 
according  to  Paving,  showed  an  average  compressive  strength  of  3972  Ibs. 


Ibs.  per  sq.  in.     This  indicates  almost  as  great  compressive  strength  as 
granite  paving-blocks,  which  is  from  12,000  to  20,000  Ibs.  per  sq.  in. 

The  following  notes  on  bricks  are  from  Trautwine's  Engineer's  Pocket' 
book : 

Strength  of  Brick.— 40  to  300  tons  per  sq.  ft.,  622  to  4668  Ibs.  per  sq.  in. 
A  soft  brick  will  crush  under  450  to  600  Ibs.  per  sq.  in.,  or  30  to  40  tons  per 
square  foot,  but  a  first-rate  machine-pressed  brick  will  stand  200  to  400  tons 
per  sq.  ft.  (3112  to  6224  Ibs.  per  sq.  in.). 

Weight  of  Bricks.— Per  cubic  foot,  best  pressed  brick,  150  Ibs.;  good 
pressed  brick,  131  Ibs.;  common  hard  brick,  125  Ibs.;  good  common  brick, 
118  Ibs. ;  soft  inferior  brick,  100  Ibs. 

Absorption  of  "Water.— A  brick  will  in  a  few  minutes  absorb  ^  to 
%.  Ib.  of  water,  the  last  being  1/7  of  the  weight  of  a  hand-moulded  one,  or  ^ 
of  its  bulk. 

Tests  of  Bricks,  full  size,  on  flat  side.  (Tests  made  at  Water- 
town  Arsenal  in  1883.) — The  bricks  were  tested  between  flat  steel  buttresses. 
Compressed  surfaces  (the  largest  surface)  ground  approximately  flat.  The 
bricks  were  all  about  2  to  2.1  inches  thick,  7.5  to  8.1  inches  long,  and  3.5  to 
3.76  inches  wide.  Crushing  strength  per  square  inch:  One  lot  ranged  from 
11,056  to  16,734  Ibs.;  a  second,  12,995  to  22,351;  a  third,  10,390  to  12,709.  Other 
tests  gave  results  from  5960  to  10,250  Ibs.  per  sq.  in. 

Crushing  Strength  of  Masonry  Materials.  (From  Howe's 
*'  Retaining- Walls.") 

tons  per  sq.  ft.  tons  per  sq.  ft. 

Brick,  best  pressed..     40  to   300        Limestones  and  marbles.  250  to  1000 

Chalk 20to      30        Sandstone 150  to    550 

Granite 300  to  1200       Soapstone 400  to   800 

Strength  of  Granite. — The  crushing  strength  of  granite  is  commonly 
rated  at  12,000  to  15,000  Ibs.  per  sq.  in.  when  tested  in  two-inch  cubes,  and 
only  the  hardest  and  toughest  of  the  commonly  used  varieties  reach  a 
strength  above  20,000  Ibs.  Samples  of  granite  from  a  quarry  on  the  Con- 


STRENGTH   OF  LIME   AND   CEMENT  MORTAR.        313 


hecticut  River,  tested  at  the  Watertown  Arsenal,  have  shown  a  strength  of 
35,965  Ibs.  per  sq.  in.  (Engineering  News,  Jan.  12,  1893). 

Strength  of  Avondale,  Pa..  Limestone— (Engineering  News, 
Feb.  9,  1893).— Crushing  strength  of  2  in.  cubes:  light  stone  12,112,  gray  stone 
18,040.  Ibs.  per  sq.  in.  , 

Transverse  test  of  lintels,  tool-dressed,  42  in.  between  knife-edge  bear- 
ings, load  with  knife-edge  brought  upon  the  middle  between  bearings: 
Gray  stone,  section  6  in.  wide  X  10  in.  high,  broke  under  a  load  of  20,950  Ibs. 

Modulus  of  rupture 2,200 

Light  stone,  section  8J4  in.  wide  X  10  in.  high,  broke  under 14,720    " 

Modulus  of  rupture 1,170 

Absorption.— Gray  stone 051  of  \% 

Light  stone 052  of  \% 

Transverse  Strength  of  Flagging. 

(N.  J.  Steel  &  Iron  Co.'s  Book.) 

EXPERIMENTS  MADE  BY  R.  G.  HATFIELD  AND  OTHERS. 
b  =  width  of  the  stone  in  inches;  d  =  its  thickness  in  inches;  I  —  distance 
between  bearings  in  inches. 

The  breaking  loads  in  tons  of  2000  Ibs.,  for  a  weight  placed  at  the  centre 
oi  the  space,  will  be  as  follows: 

5£x  ^x 


Dorchester  freestone 264 

Aubigny  freestone 216 

Caen  freestone 144 

Glass 1.000 

Slate 1 .2  to  2.7 


Bluestone  flagging 744 

Quincy  granite 624 

Little  Falls  freestone 576 

Belleville,  N.  J.,  freestone 480 

Granite  (another  quarry) 432 

Connecticut  freestone 312 

Thus  a  block  of  Quincy  granite  80  inches  wide  and  6  inches  thick,  resting 
on  beams  36  inches  in  the  clear,  would  be  broken  by  a  load  resting  midway 

80  V  86 

between  the  beams  =  —     —  X  .624  =  49.92  tons, 
oo 

STRENOTH  OF   LIME  AN»  CEMENT   MORTAR. 

(Engineering,  October  2,  1891.) 

Tests  made  at  the  University  of  Illinois  on  the  effects  of  adding  cement  to 
lime  mortar.  In  all  the  tests  a  good  quality  of  ordinary  fat  lime  was  used, 
slaked  for  two  days  in  an  earthenware  jar,  adding  two  parts  by  weight  of 
water  to  one  of  lime,  the  loss  by  evaporation  being  made  up  by  fresh  addi- 
tions of  water.  The  cements  used  were  a  German  Portland,  Black  Diamond 
(Louisville),  and  Rosendale.  As  regards  fineness  of  grinding,  85  per  cent  of 
the  Portland  passed  through  a  No.  100  sieve,  as  did  72  per  cent  of  the  Rosen- 
dale.  A  fairly  sharp  sand,  thoroughly  washed  and  dried,  passing  through  a 
No.  18  sieve  and  caught  on  a  No.  30,  was  used.  The  mortar  in  all  cases  con- 
sisted of  two  volumes  of  sand  to  one  of  lime  paste.  The  following  results 
were  obtained  on  adding  various  percentages  of  cement  to  the  mortar: 

Tensile  Strength,  pounds  per  square  inch. 


Age  \ 

4 
Days. 

7 
Days. 

14 
Days. 

21 
Days. 

28 
Days. 

50 
Days. 

84 
Days. 

Lime  mortar    

4 

8 

10 

13 

18 

21 

26 

20  per  cent  Rosendale.. 

5 

Wi 

12 

17 

17 

18 

20     l             Portland.... 

5 

gix> 

14 

20 

25 

24 

26 

30                  Rosendale.. 

7 

11 

13 

18% 

21 

22J4 

23 

30                  Portland.... 

8 

16 

18 

22 

25 

28 

27 

40                  Rosendale.  . 

10 

12 

16^6 

21* 

22^ 

24 

36 

40                   Portland..  . 

27 

39 

38 

43 

47 

59 

57 

60                   Rosendale.  . 

9 

13 

20 

16 

22 

22^ 

23 

60                  Portland.... 

45 

58 

55 

68 

67 

102 

78 

80                  Rosendale.  . 

12 

18J4 

22^ 

27 

29 

31J* 

33 

80                  Portland.... 

87 

91 

103 

124 

94 

210 

145 

100                  Rosendale.  . 

18 

33 

26 

31 

34 

46 

48 

100                  Portland.... 

90 

120 

146 

152 

181 

205 

202 

314  STRENGTH  OF  MATERIALS. 

MODULI  OF  ELASTICITY;  OF  VARIOUS  MATERIALS. 

The  modulus  of  elasticity  determined  from  a,  tensile  test  of  a  bar  of  any 
material  is  the  quotient  obtained  by  dividing  the  tensile  stress  in  pounds  per 
square  inch  at  any  point  of  the  test  by  the  elongation  per  inch  of  length 
produced  by  that  stress  ;  or  if  P  =  pounds  of  stress  applied,  K  =  the  sec- 
tional area,  I  =  length  of  the  portion  of  the  bar  in  which  the  measure- 
ment is  made,  and  A  =  the  elongation  in  that  length,  the  modulus  of 

elasticity  1?  —  —  -j-  -  =  — • .    The  modulus  is  generally  measured  within  the 

K.        I         K.\ 

elastic  limit  only,  in  materials  that  have  a  well-defined  elastic  limit,  such  as 
iron  and  steel,  and  when  not  otherwise  stated  the  modulus  is  understood  to 
be  the  modulus  within  the  elastic  limit.  Within  this  limit,  for  such  materials 
the  modulus  is  practically  constant  for  any  given  bar,  the  elongation  being 
directly  proportional  to  the  stress.  In  other  materials,  such  as  cast  iron, 
which  have  no  well-defined  elastic  limit,  the  elongations  from  the  beginning 
of  a  test  increase  in  a  greater  ratio  than  the  stresses,  and  the  modulus  is 
therefore  at  its  maximum  near  the  beginning  of  the  test,  and  continually 
decreases.  The  moduli  of  elasticity  of  various  materials  have  already  been 
given  above  in  treating  of  these  materials,  but  the  following  table  gives 
some  additional  values  selected  from  different  sources  : 

Brass,  cast 9,170,000 

"      wire 14,230,000 

Copper 15,000,000  to  18,000,000. 

Lead 1,000,000 

Tin,  cast 4,600,000 

Iron,  cast 12,000,000  to  27,000,000  (?) 

Iron,  wrought 22,000,000  to  29,000,000 

Steel 26,000,000  to  32,000,000 

Marble 25,000,000 

Slate 14,500,000 

Glass 8,000,000 

Ash 1,600,000 

Beech 1,300,000 

Birch 1,250,000  to    1,500,000 

Fir 869,000  to    2,191,000 

Oak  974,000  to    2,283.000 

Teak 2,414,000 

Walnut 306.000 

Pine,  long-leaf  (butt-logs). . .      1,1 19,000  to    3,117,000       Avge.  1,926,000 
The  maximum    figures  given  by  many  writers  for  iron  and  steel,  viz., 
40,000,000  and  42,000,000,  are  undoubtedly  erroneous;. 

Prof.  J.  B.  Johnson,  in  his  report  on  Long-leaf  Pine,  1893,  says :  "  The 
modulus  of  elasticity  is  the  most  constant  and  reliable  property  of  all 
engineering  materials.  The  wide  range  of  value  of  the  modulus  of  elasticity 
of  the  various  metals  found  in  public  records  mast  be  explained  by  erro- 
neous methods  of  testing." 

In  a  tensile  test  of  cast  iron  by  the  author  (VaG  Nf'fTtrand1s  Science  Series, 
No.  41,  page  45),  in  which  the  ultimate  strength  was  23,285  Ibs.  per  sq.  in., 
the  measurements  of  elongation  were  madcr+o  .0001  inch,  and  the  modulus 
of  elasticity  was  found  to  decrease  from  the  beginning  of  the  test,  as 
follows:  At  1000  Ibs.  per  sq.  in,,  25,000,000  ;  at  2000  Ibs.,  16,666,000  ;  at  4000 
Ibs.,  15,384,000  ;  at  6000  Ibs.,  13,636,000;  at  8000  ibs.,  12,500,000  :  at  12,000  Ibs., 
11,250,000  ;  at  15,000  Ibs.,  10,000,000  ;  at  20,000  Ibs.,  8,000.000  ;  at  23,000  Ibs., 
6,140,000.  The  modulus  of  elasticity  of  steel  (within  the  elastic  limit)  is 
remarkably  constant,  notwithstanding  great  variations  in  chemical  a.naiysis, 
temper,  etc.  It  rarely  is  found  below  28,000,000  or  above  31,000,000.  It  is 
generally  taken  at  30,000,000  in  engineering  calculations. 

FACTORS  OF   SAFETY. 

A  factor  of  safety  is  the  ratio  in  which  the  load  that  is  just  sufficient  to 
overcome  instantly  the  strength  of  a  piece  of  material  is  greater  than  the 
greatest  safe  ordinary  working  load.  (Rankine.) 

Rankine  gives  the  following  "examples  of  the  values  of  those  factors 
which  occur  in  machines  ": 

r^flrt  r  nflH       Live  Load,         Live  Load, 
Dead  Load.        Greatestt  Mean. 

Iron  and  steel  3  6  from  6  to  40 

Timber 4  to  5  8  to  10  .... 

Masonry 4  8  .... 


FACTORS   OF   SAFETY.  315 

The  great  factor  of  safety,  40,  is  for  shafts  in  millwork  which  transmit 
very  variable  efforts. 

Unwin  gives  the  following  "  factors  of  safety  which  have  been  adopted  in 
certain  cases  for  different  materials."  They  "  include  an  allowance  for 
ordinary  contingencies." 


In  Temporary  In  Permanent    In  Structures 
j^oau.       Structures.      Structures,     subi.  to  Shocks. 

Wrought  iron  and  steel. 

3 

4 

4  to  5 

10 

3 

4 

5 

10 

Timber 

4 

10 

Brickwork.  .           ... 

6 

Masonry.  .  . 

20 

20  to  30 

exp 

says:    "In  rega 

margin  that  should  be  left  for  safety,  much  depends  upon  the  character  of 
the  loading.  If  the  load  is  simply  a  dead  weight,  the  margin  may  be  com- 
paratively small;  but  if  the  structure  is  to  be  subjected  to  percussive  forces 
or  shocks,  the  margin  should  be  comparatively  large  on  account  of  the 
indeterminate  effect  produced  by  the  force.  In  machines  which  are  sub- 
jected to  a  constant  jar  while  in  use,  it  is  very  difficult  to  determine  the 
proper  margin  which  is  consistent  with  economy  and  safety.  Indeed,  in 
such  cases,  economy  as  well  as  safetjr  generally  consists  in  making  them 
excessively  strong,  as  a  single  breakage  may  cost  much  more  than  the  extra 
material  necessary  to  fully  insure  safety." 

For  discussion  of  the  resistance  of  materials  to  repeated  stresses  and 
shocks,  see  pages  238  to  240. 

Instead  of  using  factors  of  safety  it  is  becoming  customary  in  designing 
to  fix  a  certain  number  of  pounds  per  square  inch  as  the  maximum  stress 
.vliicli  will  be  allowed  on  a  piece.  Thus,  in  designing  a  boiler,  instead  of 
naming  a  factor  of  safety  of  6  for  the  plates  and  10  for  the  stay-bolts,  the 
ultimate  tecsile  strength  of  the  steel  being  from  50,000  to  60,0001bs.  persq.  in., 
an  allowable  working  stress  of  10,000  Ibs.  per  sq.  in.  on  the  plates  and  6000 
Ibs.  per  sq.  in.  on  the  stay-bolts  may  be  specified  instead.  So  also  in 
Merriman's  formula  for  columns  (see  page  260)  the  dimensions  of  a  column 
are  calculated  after  assuming  a  maximum  allowable  compressive  stress  per 
square  inch  on  the  concave  side  of  the  column. 

The  factors  for  masonry  under  dead  load  as  given  by  Rankine  and  by  Unwin, 
viz. ,  4  and  20,  show  a  remarkable  difference,  which  may  possibly  be  explained 
as  follows  :  If  the  actual  crushing  strength  of  a  pier  of  masonry  is  known 
from  direct  experiment,  then  a  factor  of  safety  of  4  is  sufficient  for  a  pier  of 
the  same  size  and  quality  under  a  steady  load:  but  if  the  crushing  strength 
is  merely  assumed  from  figures  given  by  the  authorities  (such  as  the  crush- 
ing strength  of  pressed  brick,  quoted  above  from  Howe's  Retaining  Walls,  40 
to  300  tons  per  square  foot,  average  170  tons),  then  a  factor  of  safety  of  20 
may  be  none  too  great.  In  this  case  the  factor  cf  safety  is  really  a  "'factor 
of  ignorance." 

The  selection  of  the  proper  factor  of  safety  or  the  proper  maximum  unit 
stress  for  any  given  case  is  a  matter  to  be  largely  determined  by  the  judg- 
ment of  the  engineer  and  by  experience.  No  definite  rules  can  be  given. 
The  customary  or  advisable  factors  in  many  particular  cases  will  be  found 
where  these  cases  are  considered  throughout  this  book.  In  general  the 
following  circumstances  are  to  be  taken  into  account  in  the  selection  of 
a  factor  : 

1.  When  the  ultimate  strength  of  the  material  is  known  within  narrow 
limits,  as  in  the  case  of  structural  steel  when  tests  of  samples  have  been 
made,  when  the  load  is  entirely  a  steady  one  of  a  known  amount,  and  there 
is  no  reason  to  fear  the  deterioration  of  the  metal  by  corrosion,  the  lowest 
factor  that  should  be  adopted  is  3. 

2.  When  the  circumstances  of  1  are  modified  by  a  portion  of  the  load  being 
variable,  as  in  floors  of  warehouses,  the  factor  should  be  not  less  than  4. 

3.  When  the  whole  load,  or  nearly  the  whole,  is  apt  to  be  alternately  put 
on  and  taken  off,  as  in  suspension  rods  of  floors  of  bridges,  the  factor  should 
be  5  or  6. 

4.  When  the  stresses  are  reversed  in  direction  from  tension  to  compres- 
sion, as  in  some  bridge  diagonals  and  parts  of  machines,  the  factor  should 
be  not  less  than  6. 


316  STRENGTH   OF   MATERIALS. 

5.  When  the  piece  is  subjected  to  repeated  shocks,  the  factor  should  be 
not  less  than  10. 

6.  When  the  piece  is  subject  to  deterioration  from  corrosion  the  section 
should  be  sufficiently  increased  to  allow  for  a  definite  amount  of  corrosion 
before  the  piece  be  so  far  weakened  by  it  as  to  require  removal. 

7.  When  the  strength  of  the  material,  or  the  amount  of  the  load,  or  both 
are  uncertain,  the  factor  should  be  increased  by  an  allowance  sufficient  to 
cover  the  amount  of  the  uncertainty. 

8.  When  the  strains  are  of  a  complex  character  and  of  uncertain  amount, 
such  as  those  in  the  crank-shaft  of  a  reversing  engine,  a  very  high  factor  is 
necessary,  possibly  even  as  high  as  40,  the  figure  given  by  Rankine  for  shafts 
in  millwork. 

THE  MECHANICAL,  PROPERTIES  OF  CORK. 

Cork  possesses  qualities  which  distinguish  it  from  all  other  solid  or  liquid 
bodies,  namely,  its  power  of  altering  its  vulume  in  a  very  marked  degree  in 
consequence  of  change  of  pressure.  It  consists,  practically,  of  an  aggrega- 
tion of  minute  air-vessels,  having  thin,  water-tight,  and  very  strong  walls, 
and  hence,  if  compressed,  the  resistance  to  compression  rises  in  a  manner 
more  like  the  resistance  of  gases  than  the  resistance  of  an  elastic  solid  such 
as  a  spring.  In  a  spring  the  pressure  increases  in  proportion  to  the  dis- 
tance to  which  the  spring  is  compressed,  but  with  gases  the  pressure  in- 
creases in  a  much  more  rapid  manner;  that  is,  inversely  as  the  volume 
which  the  gas  is  made  to  occupy.  But  from  the  permeability  of  cork  to 
air,  it  is  evident  that,  if  subjected  to  pressure  in  one  direction  only,  it  will 
gradually  part  with  its  occluded  air  by  effusion,  that  is,  by  its  passage 
through  the  porous  walls  of  the  cells  in  which  it  is  contained.  The  gaseous 
part  of  cork  constitutes  53g  of  its  bulk.  Its  elasticity  has  not  only  a  very 
considerable  range,  but  it  is  very  persistent.  Thus  in  the  better  kind  of  corks 
used  in  bottling  the  corks  expand  the  instant  they  escape  from  the  bottles. 
This  expansion  may  amount  to  an  increase  of  volume  of  75$,  even  after  the 
corks  have  been  kept  in  a  state  of  compression  in  the  bottles  for  ten  years. 
If  the  cork  be  steeped  in  hot  water,  the  volume  continues  to  increase  till 
it  attains  nearly  three  times  that  which  it  occupied  in  the  neck  of  the  bottle. 

When  cork  is  subjected  to  pressure  a  certain  amount  of  permanent  defor- 
mation or  "permanent  set"  takes  place  very  quickly.  This  property  is 
common  to  all  solid  elastic  substances  when  strained  beyond  their  elastic 
limits,  but  with  cork  the  limits  are  comparatively  low.  Besides  the  perma- 
nent set,  there  is  a  certain  amount  of  sluggish  elasticity— that  is,  cork  on 
being  released  from  pressure  springs  back  a  certain  amount  at  once,  but 
the  complete  recovery  takes  an  appreciable  time. 

Cork  which  had  been  compressed  and  released  in  water  many  thousand 
times  had  not  changed  its  molecular  structure  in  the  least,  and  had  contin- 
ued perfectly  serviceable.  Cork  which  has  been  kept  under  a  pressure  of 
three  atmospheres  for  many  weeks  appears  to  have  shrunk  to  from  80fe  to 
85#  of  its  original  volume.  — Van  Nostrand's  Eng'g  Mag.  1886,  xxxv.  307. 
TESTS  OF  VULCANIZED  INDIA-RUBBER. 

Lieutenant  L.  Vladomiroff,  a  Russian  naval  officer,  has  recently  carried 
out  a  series  of  tests  at  the  St.  Petersburg  Technical  Institute  with  a  view  to 
establishing  rules  for  estimating  the  quality  of  vulcanized  india-rubber. 
The  following,  in  brief,  are  the  conclusions  arrived  at,  recourse  being  had 
to  physical  properties,  since  chemical  analysis  did  not  give  any  reliable  re- 
sult: 1.  India-rubber  should  not  give  the  least  sign  of  superficial  cracking 
when  bent  to  an  angle  of  180  degrees  after  five  hours  of  exposure  in  a  closed 
air-bath  to  a  temperature  of  125°  C.  The  test-pieces  should  be  2.4  inches 
thick.  2.  Rubber  that  does  not  contain  more  than  half  its  weight  of  metal- 
lic oxides  should  stretch  to  five  times  its  length  without  breaking.  3.  Rub- 
ber free  from  all  foreign  matter,  except  the  sulphur  used  in  vulcanizing  it, 
should  stretch  to  at  least  seven  times  its  length  without  rupture.  4.  The 
extension  measured  immediately  after  rupture  should  not  exceed  12#  of  the 
original  length,  with  given  dimensions.  5.  Suppleness  may  be  determined 
by  measuring  the  percentage  of  ash  formed  in  incineration.  This  may  form 
the  basis  for  deciding  between  different  grades  of  rubber  for  certain  pur- 
poses. 6.  Vulcanized  rubber  should  not  harden  under  cold.  These  rules 
have  been  adopted  for  the  Russian  navy.—  Iron  Age,  June  15,  1893. 

XYL.OMTH,  OR  WOO»STONE 

is  a  material  invented  in  1883,  but  only  lately  introduced  to  the  trade  by 
Otto  Serrig  &  Co.,  of  Pottschappel,  near  Dresden.    It  is  made  of  magneSte 


ALUMINUM — ITS   PROPERTIES  AND    USES.  317 

cement,  or  calcined  magnesite,  mixed  with  sawdust  and  natural ed  with  a 
solution  of  chloride  of  calcium.  This  pasty  mass  is  spread  out  into  sheets 
and  submitted  to  a  pressure  of  about  1000  ibs.  to  the  square  inch,  and  then 
simply  dried  in  the  air.  Specific  gravity  1.553.  The  fractured  surface  shows 
a  uniform  close  grain  of  a  yellow  color.  It  has  a  tensional  resistance  when 
dry  of  100  Ibs.  per  square  inch,  and  when  wet  about  66  Ibs.  When  immersed 
in  water  for  12  hours  it  takes  up  2.1%  of  its  weight,  and  3.8$  when  immersed 
216  hours. 

When  treated  for  several  days  with  hydrochloric  acid  it  loses  2.3#  in 
weight,  and  shows  no  loss  of  weight  under  boiling  in  water,  brine,  soda-lye, 
and  solution  of  sulphates  of  iron,  of  copper,  and  of  ammonium.  In  hardness 
the  material  stands  between  feldspar  and  quartz,  and  as  a  non-conductor  of 
heat  it  ranks  between  asbestos  and  cork. 

It  stands  fire  well,  and  at  a  red  heat  it  is  rendered  brittle  and  crumbles  at 
the  edges,  but  retains  its  general  form  and  cohesion.  This  xylolith  is  sup- 
plied in  sheets  from  14  in.  to  iy^  in.  thick,  and  up  to  one  metre  square.  It 
is  extensively  used  in  Germany  for  floors  in  railway  stations,  hospitals,  etc., 
and  for  deck's  of  vessels.  It  can  be  sawed,  bored,  and  shaped  with  ordinary 
woodworking  tools.  Putty  in  the  joints  and  a  good  coat  of  paint  make  it 
entirely  water-proof,  It  is  sold  in  Germany  for  flooring  at  about  7  cents  per 
square  foot,  and  the  cost  of  laying  adds  about  4  cents  more.—Eng'lg  News, 
July  28,  1892,  and  July  27,  1893. 

AL.UMINUM— ITS    PROPERTIES    AND    USES. 
(By  Alfred  E.  Hunt,  Pres't  of  the  Pittsburgh  Reduction  Co.) 

The  specific  gravity  of  pure  aluminum  in  a  cast  state  is  2.58  ;  in  rolled 
bars  of  large  section  it  is  2  6  ;  in  very  thin  sheets  subjected  to  high  com- 
pression under  chilled  rolls,  it  is  as  much  as  2.7.  Taking  the  weight  of  a 
given  bulk  of  cast  aluminum  as  1,  wrought  iron  is  2.90  times  heavier  ;  struc- 
tural steel,  2.95  times  ;  copper,  3.60  ;  ordinary  high  brass,  3.45.  Most  wood 
suitable  for  use  in  structures  has  about  one  third  the  weight  of  aluminum, 
which  weighs  0.092  Ib.  to  the  cubic  inch. 

Pure  aluminum  is  practically  not  acted  upon  by  boiling  water  or  steam. 
Carbonic  oxide  or  hydrogen  sulphide  does  not  act  upon  it  at  any  tempera- 
ture under  600°  F.  It  is  not  acted  upon  by  most  organic  secretions. 

Hydrochloric  acid  is  the  best  solvent  for  aluminum,  and  strong  solutions 
of  caustic  alkalies  readily  dissolve  it.  Ammonia  has  a  slight  solvent  action, 
and  concentrated  sulphuric  acid  dissolves  aluminum  upon  heating,  with 
evolution  of  sulphurous  acid  gas.  Dilute  sulphuric  acid  acts  but  slowly  on 
the  metal,  though  the  presence  of  any  chlorides  in  the  solution  allow  rapid 
decomposition.  Nitric  acid,  either  concentrated  or  dilute,  has  very  little 
action  upon  the  metal,  and  sulphur  has  no  action  unless  the  metal  is  at  a  red 
heat.  Sea-water  has  very  little  effect  on  aluminum.  Strips  of  the  metal 
placed  on  the  sides  of  a  wooden  ship  corroded  less  than  1/1000  inch  after  six 
months'  exposure  to  sea-water,  corroding  less  than  copper  sheets  similarly 
placed. 

In  malleability  pure  aluminum  is  only  exceeded  by  gold  and  silver.  In 
ductility  it  stands  seventh  in  the  series,  being  exceeded  by  gold,  silver, 
platinum,  iron,  very  soft  steel,  and  copper.  Sheets  of  aluminum  have  been 
rolled  down  to  a  thickness  of  0.0005  inch,  and  beaten  into  leaf  nearly  as 
thin  as  gold  leaf.  The  metal  is  most  malleable  at  a  temperature  of  between 
400°  and  600°  F.,  and  at  this  temperature  it  can  be  drawn  down  between 
rolls  with  nearly  as  much  draught  upon  it  as  with  heated  steel.  It  has  also 
been  drawn  down  into  the  very  finest  wire.  By  the  Mannesmann  process 
aluminum  tubes  have  been  made  in  Germany. 

Aluminum  stands  very  high  in  the  series  as  an  electro-positive  metal,  and 
contact  with  other  metals  should  be  avoided,  as  it  would  establish  a  galvanic 
couple. 

The  electrical  conductivity  of  aluminum  is  only  surpassed  by  pure  copper, 
silver,  and  gold.  With  silver  taken  at  100  the  electrical  conductivity  of 
aluminum  is  54,20  ;  that  of  gold  on  the  same  scale  is  78;  zinc  is  29.90;  iron  is 
only  16,  and  platinum  10.60.  Pure  aluminum  has  no  polarity,  and  the 
metal  in  the  market  is  absolutely  non-magnetic. 

Sound  castings  can  be  made  of  aluminum  in  either  dry  or  "  green  "  sand 
moulds,  or  in  metal  "chills.11  It  must  not  be  heated'  much  beyond"  its 
melting-point,  and  must  be  poured  with  care,  owing  to  the  ready  absorption 
of  occluded  gases  and  air.  The  shrinkage  in  cooling  is  17/64  inch  per  foot, 
or  a  little  more  than  ordinary  brass.  It  should  be  melted  in  plumbago 
crucibles,  and  the  metal  becomes  molten  at  a  temperature  of  1120°  F.  ac- 
cording to  Professor  Roberts- Austen,  or  at  1300°  F.  according  to  Richards. 


318  STRENGTH    OF   31ATERIALS. 

The  coefficient  of  linear  expansion,  as  tested  on  %-inch  round  aluminum 
rods,  is  0.00002295  per  degree  centigrade  between  the  freezing  and  boiling 
point  of  water.  The  mean  specific  heat  of  aluminum  is  higher  than  that  of 
any  other  metal,  excepting  only  magnesium  and  the  alkali  metals.  From 
zero  to  the  melting-point  it  is  0.2185;.  water  being  taken  as  1,  and  the  latent 
heat  of  fusion  at  28.5  heat  units.  The  coefficient  of  thermal  conductivity  of 
unannealed  aluminum  is  37.96;  of  annealed  aluminum,  38.37.  As  a  conductor 
of  heat  aluminum  ranks  fourth,  being  exceeded  only  by  silver,  copper,  and 
gold. 

Aluminum,  under  tension,  and  section  for  section,  is  about  as  strong  as 
cast  iron.  The  tensile  strength  of  aluminum  is  increased  by  cold  rolling  or 
cold  forging,  and  there  are  alloys  which  add  considerably  to  the  tensile 
strength  without  increasing  the  specific  gravity  to  over  3  or  3.25. 

The  strength  of  commercial  aluminum  is  given  in  the  following  table  as 
the  result  of  many  tests  : 

Elastic  Limit         Ultimate  Strength     Percentage 
per  sq.  in.  in  per  sq.  in.  in  of  Reduct'n 

Form.  Tension,  Tension,  of  Area  in 

Ibs.  Ibs.  Tension. 

Castings 6,500  15,000  15 

Sheet 12,000  24,000  35 

Wire 16,000-30,000  30,000-65,000  60 

Bars 14,000  28,000  40  - 

The  elastic  limit  per  square  inch  under  compression  in  cylinders,  with 
length  twice  the  diameter,  is  3500.  The  ultimate  strength  per  square  inch 
under  compression  in  cylinders  of  same  form  is  12,000.  The  modulus  of 
elasticity  of  cast  aluminum  is  about  11,000,000.  It  is  rather  an  open  metal  in 
its  texture,  and  for  cylinders  to  stand  pressure  an  increase  in  thickness  must 
be  given  to  allow  for  this  porosity.  Its  maximum  shearing  stress  in  castings 
is  about  12,000,  and  in  forgings  about  16,000,  or  about  that  of  pure  copper. 

Pure  aluminum  is  too  soft  and  lacking  in  tensile  strength  and  rigidity  for 
many  purposes.  Valuable  alloys  are  now  being  made  which  seem  to  give 
great  promise  for  the  future.  They  are  alloys  containing  from  2$  to  7%  or  8$ 
of  copper,  manganese,  iron,  and  nickel.  As  nickel  is  one  of  the  principal 
constituents,  these  alloys  have  the  trade  name  of  "  Nickel-aluminum.'" 

Plates  and  bars  of  this  nickel  alloy  have  a  tensile  strength  of  from  40,000  to 
50,000  pounds  per  square  inch,  an  elastic  limit  of  55$  to  60$  of  the  ultimate  ten- 
sile strength,  an  elongation  of  20$  in  2  inches,  and  a  reduction  of  area  of  25$. 

This  metal  is  especially  capable  of  withstanding  the  punishment,  and 
distortion  to  which  structural  material  is  ordinarily  subjected.  Nickel- 
aluminum  alloys  have  as  much  resilience  and  spring  as  the  very  hardest  of 
hard-drawn  brass. 

Their  specific  gravity  is  about  2.80  to  2.85,  where  pure  aluminum  has  a 
specific  gravity  of  2.72. 

In  castings,  more  of  the  hardening  elements  are  necessary  in  order  to  give 
the  maximum  stiffness  and  rigidity,  together  with  the  strength  and  ductility 
of  the  metal;  the  favorite  alloy  material  being  zinc,  iron,  manganese,  and 
copper.  Tin  added  to  the  alloy  reduces  the  shrinkage,  and  alloys  of  alumi- 
num and  tin  can  be  made  which  have  less  shrinkage  than  cast  iron. 

The  tensile  strength  of  hardened  aluminum-alloy  castings  is  from  20,000 
to  25,000  pounds  per  square  inch. 

Alloys  of  aluminum  and  copper  form  two  series,  both  valuable.  The 
first  is  aluminum-bronze,  containing  from  5$  to  11^$  of  aluminum;  and  the 
second  is  copper-hardened  aluminum,  containing  from  2$  to  15$  of  copper. 
Aluminum-bronze  is  a  very  dense,  fine-grained,  and  strong  alloy,  having  good 
ductility  as  compared  with  tensile  strength.  The  10$  bronze  in  forged  bars 
will  give  100,000  Ibs.  tensile  strength  per  square  inch,  with  60,000  Ibs.  elastic 
limit  per  square  inch,  and  10$  elongation  in  8  inches.  The  5$  to  7J^$  bronze 
has  a  specific  gravity  of  8  to  8.30,  as  compared  with  7.50  for  the  10$  to  11^4$ 
bronze,  a  tensile  strength  of  70,000  to  80,000  Ibs.,  an  elastic  limit  of  40,000 
Ibs.  per  square  inch,  and  an  elongation  of  30$  in  8  inches. 

Aluminum  is  used  by  steel  manufacturers  to  prevent  the  retention  of  the 
occluded  gases  in  the  steel,  and  thereby  produce  a  solid  ingot.  The  propor- 
tions of  the  dose  ransre  from  ^  Ib.  to  several  pounds  of  aluminum  per  ton  of 
steel.  Aluminum  is  also  used  in  giving  extra  fluidity  to  steel  used  in  castings, 
making  them  sharper  and  sounder.  Added  to  cast  iron,  aluminum  causes 
the  iron  to  be  softer,  free  from  shrinkage,  and  lessens  the  tendency  to ''chill.1' 

With  the  exception  of  lead  and  mercury,  aluminum  unites  with  all  metals, 


ALLOYS. 


319 


though  it  unites  with  antimony  with  great  difficulty.  A  small  percentage 
of  silver  whitens  and  hardens  the  metal,  and  gives  it  added  strength;  and 
this  alloy  is  especially  applicable  to  the  manufacture  of  fine  instruments 
and  apparatus.  The  following  alloys  have  been  found  recently  to  be  useful 
in  the  aits:  Nickel-aluminum,  composed  of  20  parts  nickel  to  80  of  aluminum; 
rosine,  made  of  40  parts  nickel,  10  parts  silver,  30  parts  aluminum,  and  20 
parts  tin,  for  jewellers1  work;  mettaline,  made  of  35  parts  cobalt,  25  parts 
aluminum,  10  parts  iron,  and  30  parts  copper.  The  aluminum-bourbounz 


12.94$;  silicon,  1.32$;  iron,  none. 


apidly 

ciently.  A  German  solder  said  to  give  good  results  is  made  of  80$  tin  to  20$ 
zinc,  using  a  flux  composed  of  80  parts  stearic  acid,  10  parts  chloride  of 
zinc,  and  10  parts  of  chloride  of  tin.  Pure  tin,  fusing  at  250°  C.,  has  also 
been  used  as  a  solder.  The  use  of  chloride  of  silver  as  a  flux  has  been 
patented,  and  used  with  ordinary  soft  solder  has  given  some  success.  A 
pure  nickel  soldering-bit  should  be  used,  as  it  does  not  discolor  aluminum 
as  copper  bits  do. 

ALLOYS. 


OF    COPPER    AND    TIN. 

(Extract  from  Report  of  U.  S.  Test  Board.*) 


1 

3 

l 
la 
o 

3 
4 
5 
6 

8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 

00 

23 
24 

25 
26 

Mean  Com- 
position by 
Analysis. 

Tensile  Strength, 
Ibs.  per  sq.  in. 

Elastic  Limit. 
Ibs.  per  sq.  in. 

Elongation, 
per  cent  in  5 
inches. 

Transverse  Test, 
Modulus  of 
Rupture. 

Deflection,  V  sq. 
Bar  22  in.  long, 
inches. 

Crushing 
Strength, 
Ibs.  per  sq.  in. 

Torsion 
Tests. 

Maxinmm 
Tor.  Mom- 
ent, ft.-lbs. 

Angle  of 
Torsion, 
degrees. 

O'p- 
par. 

Tin. 

100. 
100. 
97.89 
96.06 
94.11 
92.11 
90.27 
88.41 
87.15 
82.70 
80.95 
77.56 
76.63 
72.89 
69.84 
68.58 
67.87 
65.34 
56.70 
44.52 
34.22 
23.35 
15.08 
11.49 
8.57 
3.72 
0. 

27,800 
12,760 
24,580 
32,000 

14.000 
11.000 
10,000 
16,000 

6.47 
0.47 
13.33 
14.29 

29,848 
21  ,251 

bent. 
2.31 

42.000 
39,000 
34,000 
42,048 

143 
65 
150 
157 

153 
40 
317 
247 

1.90 
3.76 
5  43 

33,232 
38,659 
43,731 
49,400 
60,403 
34,531 
67,930 
56,715 
29,926 
32.210 
9,512 

bent. 

4.00 
0.63 
0.49 
0.16 
0.19 
0.05 

7.80 
9.58 
11  59 

28,540 
26,860 

19,000 
15,750 

5.53 
3.66 

42,000 
38,000 

160 
175 

126 
114 

12.73 
17.34 

18.84 
22.25 
23.24 
26.85 
29.88 
31.26 
32.10 
34.47 
43.17 
55.28 
65.80 
76.29 
84.62 
88.47 
91.39 
96.31 
100. 

29,430 

20,000 

3.33 

53,666 

182 

100 

32.980 
22,010 

22,010  ' 

0.04 
0. 
0. 
0. 

78,000 

190 

16 

114,000 

122 

3.4 

5,585 

5,585 

0. 
0. 
0. 
0. 
0. 
0. 
0. 
0. 

4.16" 

6.87 
12.32 
35.51 

12,076 
9,152 
9,477 
4,776 
2,126 
4,776 
5,384 
12,408 
9,063 
10,706 
5.305 
6,925 
3.740 

0.06 
0.04 
0.05 
0.02 
0.02 
0.03 
0.04 
0.27 
0.86 
5.85 
bent. 

147,000 

18 

1.5 

"2,261 
1.455 
3.010 
3,371 
6,775 

"6,380 
6,450 
4,780 
3,505 

2,201 
1,455 
3,010 
3,371 
6,775 

'  "3,500  ' 
3.500 
2,750 

84,7'00 

16 

1 

35.800 
19,600 

23 
17 

1 
2 

6.500     2  '. 
10,100;     23 
9,800     23 
9,800     23 
6,400      12 

25 
62 
132 
220 

557 

*  The  tests  of  the  alloys  of  copper  and  tin  and  of  copper  and  zinc,  the  re- 
sults of  which  are  published  in  the  Report  of  the  U.  S.  Board  appointed  to 
test  Iron,  Steel,  and  other  Metals,  Vols.  I  and  II,  1879  and  1881.  were  made 
by  the  author  under  direction  of  Prof.  R.  H.  Thurston,  chairman  of  the 
Committee  on  Alloys.    See  preface  to  the  report  of  the  Committee,  in  Vol.  I. 

320  ALLOYS. 

Nos.  la  and  2  were  full  of  blow-holes. 

Tests  Nos.  1  and  la  show  the  variation  in  cast  copper  due  to  varying  COEK 
ditions  of  casting.  In  the  crushing  tests  Nos.  12  to  20,  inclusive,  crushed  and 
broke  under  the  strain,  but  all  the  others  bulged  and  flattened  out.  In  these 
cases  the  crushing  strength  is  taken  to  be  that  which  caused  a  decrease  of 
10$  in  the  length.  The  test-pieces  were  2  in.  long  and  %  in.  diameter.  The 
torsional  tests  were  made  in  Thurston's  torsion-machine,  on  pieces  %  in. 
diameter  and  1  in.  long  between  heads. 

Specific  Gravity  of  tlie  Copper-tin  Alloys.— The  specific 
gravity  of  copper,  as  found  in  these  tests,  is  8.874  (tested  in  turnings  from 
the  ingot,  and  reduced  to  39.1°  F.).  The  alloy  of  maximum  sp.  gr.  8.956 
contained  62.42  copper,  37.48  tin,  and  all  the  alloys  containing  less  than  37$ 
tin  varied  irregularly  in  sp.  gr.  between  8.65  and  8.93,  the  density  depending 
not  on  the  composition,  but  on  the  porosity  of  the  casting.  It  is  probable 
that  the  actual  sp.  gr.  of  all  these  alloys  containing  less  than  37$  tin  is  about 
8.95,  and  any  smaller  figure  indicates  porosity  in  the  specimen. 

From  37$  to  100$  tin,  the  sp.  gr.  decreases  regularly  from  the  maximum  of 
8.956  to  that  of  pure  tin,  7.293. 

Note  on  the  Strength  of  the  Copper-tin  Alloys. 

The  bars  containing  from  2$  to  24$  tin,  inclusive,  have  considerable 
strength,  and  all  the  rest  are  practically  worthless  for  purposes  in  which 
strength  is  required.  The  dividing  line  between  the  strong  and  brittle  alloys 
is  precisely  that  at  which  the  color  changes  from  golden  yellow  to  silver- 
white,  viz.,  at  a  composition  containing  between  24$  and  30$  of  tin. 

It  appears  that  the  tensile  and  compressive  strengths  of  these  alloys  are 
in  no  way  related  to  each  other,  that  the  torsional  strength  is  closely  pro- 
portional to  the  tensile  strength,  and  that  the  transverse  strength  may  de- 
pend in  some  degree  upon  the  compressive  strength,  but  it  is  much  more 
nearly  related  to  the  tensile  strength.  The  modulus  of  rupture,  as  obtained 
by  the  transverse  tests,  is,  in  general,  a  figure  between  those  of  tensile  and 
compressive  strengths  per  square  inch,  but  there  are  a  few  exceptions  in 
which  it  is  larger  than  either. 

The  strengths  of  the  alloys  at  the  copper  end  of  the  series  increase  rapidly 
with  the  addition  of  tin  'till  about  4$  of  tin  is  reached.  The  transverse 
strength  continues  regularly  to  increase  to  the  maximum,  till  the  alloy  con- 
taining about  17J/£$  of  tin  is  reached,  while  the  tensile  and  torsional 
strengths  also  increase,  but  irregularly,  to  the  same  point.  Tliis  irregularity 
is  probably  due  to  porosity  of  the  metal,  and  might  possibly  be  removed  by 
any  means  which  would  make  the  castings  more  compact.  The  maximum 
is  reached  at  the  alloy  containing  82.70  copper,  17.34  tin,  the  transverse 
strength,  however,  being  very  much  greater  at  this  point  than  the  tensile 
or  torsional  strength.  From  the  point  of  maximum  strength  the  figures 
drop  rapidly  to  the  alloys  containing  about  27.5$  of  tin,  and  then  more  slowly 
to  37.5$,  at  which  point  the  minimum  (or  nearly  the  minimum)  strength,  by 
all  three  methods  of  test,  is  reached.  The  alloys  of  minimum  strength  are 
found  from  37.5$  tin  to  52.5$  tin.  The  absolute  minimum  is  probably  about 
45$  of  tin. 

From  52.5$  of  tin  to  about  77.5$  tin  there  is  a  rather  slow  and  irregular  in- 
crease in  strength.  From  77.5$  tin  to  the  end  of  the  series,  or  all  tin,  the 
strengths  slowly  and  somewhat  irregularly  decrease. 

The  results  of  these  tests  do  not  seem  to  corroborate  the  theory  given  by 
some  writers,  that  peculiar  properties  are  possessed  by  the  alloys  which 
are  compounded  of  simple  multiples  of  their  atomic  weights  or  chemical 
equivalents,  and  that  these  properties  are  lost  as  the  compositions  vary 
more  or  less  from  this  definite  constitution.  It  does  appear  that  a  certain 
percentage  composition  gives  a  maximum  strength  and  another  certain 
percentage  a  minimum,  but  neither  of  these  compositions  is  represented  by 
simple  multiples  of  the  atomic  weights. 

There  appears  to  be  a  regular  law  of  decrease  from  the  maximum  to  the 
minimum  strength  which  does  not  seem  to  have  any  relation  to  the  atomic 
proportions,  but  only  to  the  percentage  compositions. 

Hardness. — The  pieces  containing  less  than  24$  of  tin  were  turned  in 
the  lathe  without  difficulty,  a  gradually  increasing  hardness  being  noticed, 
the  last  named  giving  a  very  short  chip,  and  requiring  frequent  sharpening 
of  the  tool. 

With  the  most  brittle  alloys  it  was  found  impossible  to  turn  the  test-pieces 
in  the  lathe  to  a  smooth  surface.  No.  13  to  No.  17  (26.85  to  34.47  tin)  could 
not  be  cut  with  a  tool  at  all.  Chips  would  fly  off  in  advance  of  the  tool  and 


ALLOYS   OF   COPPER  AND   ZISTC. 


321 


beneath  it,  leaving  a  rough  surface ;  or  the  tool  would  sometimes,  apparently, 
crush  off  portions  of  the  metal,  grinding  it  to  powder.  Beyond  40#  tin  the 
hardness  decreased  so  that  the  bars  could  be  easily  turned. 

ALLOYS  OF    COPPER  AND  ZINC.    (U.  S.  Test  Board). 


No. 

Mean  Com- 
position by 
Analysis. 

Tensile 
Strength, 
Ibs.  per 
sq,  in. 

Elastic 
Limit 
$of 
Break- 

TinS, 
Load, 

Ibs.  per 
sq.  in. 

1  Elongation  % 
in  5  inches. 

Trans- 
verse 
Test 
Modu- 
lus of 
Rup- 
ture. 

cl    . 

.2  t-.2 

I** 

§?! 

Crush- 
ing 
Str'gth 
per  sq. 
in.,  Ibs. 

Torsional 

Tests. 

Ill 

H    04J 

!gCM 

«»-i  a 
°o 
<£'w    . 

p 

Cop- 
per. 

Zinc. 

1 

3 
4 

5 
6 
7 
8 
9 
10 

:i 
:3 

14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

97.83 
82.93 
81.91 
77.39 
76.65 
73.20 
71.20 
69.74 
66.27 
63.44 
60.94 
58.49 
55.15 
54.86 
49.66 
48.99 
47.56 
43.36 
41.30 
32.94 
29.^0 
20.81 
12.12 
4.35 
Cast 

1.88 
16.98 
17.99 
22.45 
23.08 
26.47 
28.54 
30.06 
33.50 
36.36 
38.65 
41.10 
44.44 
44.78 
50.14 
50.82 
52.28 
56.22 
58.12 
66.23 
70.17 
77.63 
86.67 
94.59 
Zinc. 

27,240 
32,600 
32.670 
35,630 
30,520 
31,580 
30,510 
28,120 
37,800 
48,300 
41,065 
50,450 
44,280 
46,400 
30,990 
26,050 
24,150 
9,170 
3,727 
1,774 
6,414 
9,000 
12,413 
18,065 
5.400 

130 
155 
166 
169 
165 
168 
164 
143 
176 
202 
194 
227 
209 
223 
172 
176 
155 
88 
18 
29 
40 
65 
82 
81 
37 

357 
329 
345 
311 
267 
293 
269 
202 
257 
230 
202 
93 
109 
72 
38 
16 
13 
2 
2 
1 
2 
1 
3 
22 
142 

26.1 
30.6 
20.0 
24.6 
23.7 
29.5 
28.7 
25.1 
32.8 
40.1 
54.4 
44.0 
53.9 
54.5 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
100. 
75. 

26.7 
31.4 
35.5 
35.8 
38.5 
29.2 
20.7 
37.7 
C1.7 
20.7 
10.1 
15.3 
8.0 
5.0 
0.8 
0.8 

'0.2 
0.4 
0.5 
0.7 

23,197 
21,193 
25,374 
22,325 
25,894 
24,468 
26,930 
28,459 
43,216' 
38,968 
63,C04 
42,463 
47,955 
33,467 
40,189 
48,471 
17,691 
7,761 
8,296 
16,579 
22,972 
35,026 
26,162 
7.539 

Bent 

t 

« 

1.26 
0.61 
1.17 
0.10 
0.04 
0.04 
0.04 
0.13 
0.31 
0.46 
0.12 

42,000 



'  75,000 
"  78,000 

117,400 

121,000 
*  52,152 

22,000 

Variation  in  Strength  of  Gun-bronze,  and  Means  of 
Improving  the  Strength.—  The  figures  obtained  for  alloys  of  from 
7.8$  to  12.7$  tin,  viz.,  from  26,860  to  29,430  pounds,  are  much  less  than  are 
usually  given  as  the  strength  of  gun-metal.  Bronze  guns  are  usually  cast 
under  the  pressure  of  a  head  of  metal,  which  tends  to  increase  the  strength 
and  density.  The  strength  of  the  upper  part  of  a  gun  casting,  or  sinking 
head,  is  not  greater  than  that  of  the  small  bars  which  have  been  tested  in 
these  experiments.  The  following  is  an  extract  from  the  report  of  Major 
Wade  concerning  the  strength  and  density  of  gun-bronze  (1850): — Extreme 
variation  of  six  samples  from  different  parts  of  the  same  gun  (a  32- pounder 
howitzer):  Specific  gravity,  8.487  to  8.835;  tenacity,  26,4'28  to  52,192.  Extreme 
variation  of  all  the  samples  tested:  Specific  gravity,  8.308  to  8.850;  tenacity, 
23,108  to  54,531.  Extreme  variation  of  all  the  samples  from  the  gun  heads: 
Specific  gravity,  8.308  to  8.756;  tenacity,  23,529  to  35,484. 

Major  Wade  says:  The  general  results  on  the  quality  of  bronze  as  it  is 
found  in  guns  are  mostly  of  a  negative  character.  They  expose  defects  in 
density  and  strength,  develop  the  heterogeneous  texture  of  the  metal  in  dif- 
ferent parts  of  the  same  gun,  and  show  the  irregularity  and  uncertainty  of 
quality  which  attend  the  casting  of  all  guns,  although  made  from  s  milar 
materials,  treated  in  like  manner. 

Navy  ordnance  bronze  containing  9  parts  copper  and  1  part  tin,  tested  at 
Washington,  D.  C.,  in  1875-6,  showed  a  variation  in  tensile  strength  from 
29,800  to  51,400  Ibs.  per  square  inch,  in  elongation  frcm  3$  to  58$,  and  in  spe- 
cific gravity  from  8.39  to  8.88. 

That  a  great  improvement  may  be  made  in  the  density  and  tenacity  of 
gun-bronze  by  compression  has  been  shown  by  the  experiments  of  Mr.  S.  B. 
Dean  in  Boston,  Mass.,  in  1869,  and  by  those  of  General  Uchatius  in  Austria 
in  1873.  The  former  increased  the  density  of  the  metal  next  the  bore  of  the 
gun  from  8.321  to  8.875,  and  the  tenacity  from  27,^38  to  41,471  pounds  per 


322 


ALLOYS. 


square  inch.   The  latter,  by  a  similar  process,  obtained  the  following  figures 

for  tenacity: 

Pounds  per  sq.  in. 

Bronze  with  10#  tin 72,053 

Bronze  with  8^  tin 73,958 

Bronze  with  6$  tin 77,656 

OF   COPPER,   TIN,  AND  ZINC. 

(Report  of  U.  S.  Test  Board,  Vol.  II,  1881.) 


No. 

Analysis, 
Original  Mixture. 

Transverse 
Strength. 

Tensile 
Strength  per 
square  inch. 

Elongation 
per  cent  in 
5  inches. 

in 
Report. 

Modulus 

Deflec- 

Cu. 

Sn. 

Zn. 

of 

tion, 

A. 

B. 

A. 

B. 

Rupture 

ins. 

72 

90 

5 

5 

41,334 

2.63 

23,660 

30,740 

2.34 

9.68 

5 

88.14 

1.86 

10 

31,986 

3  67 

3-3,000 

33,000 

17.6 

19.5 

70 

85 

5 

10 

44,457 

2.85 

28,840 

28,560 

6.80 

5.28 

71 

85 

10 

5 

62,470 

2.56 

35,680 

36,000 

2.51 

2.25 

89 

85 

12.5 

2.5 

62,405 

2.83 

34,500 

32,800 

1.29 

2.79 

88 

82.5 

12.5 

5 

60,960 

1.61 

36,000 

34,000 

.86 

.92 

77 

82.5 

15 

2.5 

69,045 

1.09 

33,600 

33.800 

.68 

67 

80 

5 

15 

42,618 

3.88 

37,560 

32,300 

"iiie"' 

3.59 

68 

80 

10 

10 

67,117 

2.45 

32.830 

31,950 

1  .57 

1.67 

69 

80 

15 

5 

54,476 

.44 

32,350 

30,760 

.55 

.44 

86 

77.5 

10 

12.5 

63,849 

1.19 

35,500 

36,000 

1.00 

1.00 

87 

77.5 

12.5 

10 

01,705 

.71 

36,000 

32,500 

72 

.59 

63 

75 

5 

20 

55,355 

2.91 

33,140 

34,960 

2^50 

3.19 

85 

75 

7.5 

17.5 

62,607 

1.39 

33,700 

39,300 

1.56 

1.33 

64 

75 

10 

15 

58,345 

.73 

35,320 

34,000 

1.13 

1.25 

65 

75 

15 

10 

51.109 

.31 

35,440 

28.000 

.59 

.54 

66 

75 

20 

5 

40;235 

21 

23  140 

27  660 

43 

83 

72.5 

7.5 

20 

51,839 

2.86 

32,700 

34,800 

3^73 

3.78 

84 

72.5 

10 

17.5 

53,230 

.74 

30,000 

30,000 

.48 

.49 

59 

70 

5 

25 

57,349 

1.37 

38,000 

32,940 

2.06 

.99 

82 

70 

7.5 

22.5 

48,836 

.36 

38,000 

32,400 

.84 

.40 

60 

70 

10 

20 

36,520 

.18 

33,140 

26.300 

.31 



61 

70 

15 

15 

37,924 

.20 

33,440 

27.800 

.25 

62 

70 

20 

10 

15,126 

.08 

17,000 

12,900 

03 

81 

67.5 

2.5 

30 

58,34C 

2.91 

34,720 

45.850 

7.27 

3.09 

74 

67.5 

5 

27.5 

55,976 

.49 

34.000 

34,460 

1.06 

.43 

75 

67.5 

7.5 

25 

46,875 

.32 

29,500 

C0,000 

.36 

.26 

80 

65 

2.5 

32.5 

56,949 

2.36 

41,350 

38,300 

3.26 

3.02 

55 

65 

5 

30 

51  ,369 

.56 

37,140 

36,000 

1.21 

.61 

56 

65 

10 

25 

27,075 

.14 

25,720 

22,500 

.15 

.19 

57 

65 

15 

20 

13,591 

.07 

6,820 

7,231 

58 

65 

20 

15 

11,932 

.05 

3,765 

2,665 

79 

62.5 

2.5 

35 

69,255 

2.34 

44,400 

45,000 

2.15 

2.19 

78 

60 

2.5 

37.5 

69,508 

1.46 

57,400 

52,900 

4.87 

3.02 

52 

60 

5 

35 

46,076 

.28 

41,160 

38,330 

.39 

.40 

53 

60 

10 

30 

24,699 

.13 

21,780 

21,240 

.15 

54 

60 

15 

25 

18,248 

.09 

18,020 

12,400 

12 

58.22 

2.30 

39.48 

95,623 

1.99 

66,500 

67,600 

3.13 

3.15 

3 

58.75 

8.75 

32.5 

35,752 

.18 

Broke 

before  t 

est;  ver 

y  brittle 

4 

57.5 

21.25 

21.25 

2,752 

.02 

725 

1,300 

73 

55 

0.5 

44.5 

72,308 

3.05 

68,900 

68,900 

9.43 

"h'.ss" 

50 

55 

5 

40 

38,174 

.22 

27,400 

30,500 

.46 

.43 

51 

55 

10 

35 

28,258 

.14 

25,460 

18,500 

.29 

.10 

49 

50 

5 

45 

20,814 

.11 

23,000 

31,300 

.66 

.45 

The  transverse  tests  were  made  in  bars  1  in.  square,  22  in.  between  sup- 
ports. The  tensile  tests  were  made  on  bars  0.798  in.  diarn.  turned  from  the 
two  halves  of  the  transverse-test  bar,  one  half  being  marked  A  and  the 
other  J5. 


ALLOYS   OF   COPPER,,   TIX,  AND   ZINC.  323 

Ancient  Bronzes.— The  usual  composition  of  ancient  bronze  was  the 
same  as  that  of  modern  gun-metal — 90  copper,  10  tin;  but  the  proportion  of 
tin  varies  from  5$  to  15#,  and  in  some  cases  lead  has  been  found.  Some  an- 
cient Egyptian  tools  contained  88  copper,  12  tin. 

Strength  of  the  Copper-zinc  Alloys.— The  alloys  containing  less 
than  15 fa  of  zinc  by  original  mixture  were  generally  defective.  The  bars 
were  full  of  blow-holes,  and  the  metal  showed  signs  of  oxidation.  To  insure 
good  castings  it  appears  that  copper-zinc  alloys  should  contain  more  than 
15#  of  zinc. 

From  No.  2  to  No.  8  inclusive,  16.98  to  80.06g  zinc  the  bars  show  a  remark- 
able similarity  in  all  their  properties.  They  have  all  nearly  the  same 
strength  and  ductility,  the  latter  decreasing  slightly  as  zinc  increases,  and 
are  nearly  alike  in  color  and  appearance.  Between  Nos.  8  and  10,  30.06  and 
3G.36g  zinc,  the  strength  by  all  methods  of  test  rapidly  increases.  Between 
No.  10  and  No.  15,  36.36  and  50.14$  zinc,  there  is  another  group,  distinguished 
by  high  strength  and  diminished  ductility.  The  alloy  of  maximum  tensile, 
transverse  and  torsioual  strength  contains  about  41%  of  zinc. 

The  alloys  containing  less  than  55#  of  zinc  are  all  yellow  metals.  Beyond 
55$  the  color  changes  to  white,  and  the  alloy  becomes  weak  and  brittle.  Be- 
tween 70$  and  pure  zinc  the  color  is  bluish  gray,  the  brittle  ness  decreases 
and  the  strength  increases,  but  not  to  such  a  degree  as  to  make  them  useful 
for  Constructive  purposes. 

Difference  between  Composition  fey  Mixture  and  by 
Analysis. — There  is  in  every  case  a  smaller  percentage  of  zinc  in  the 
average  analysis  than  in  the  original  mixture,  an  1  a  larger  percentage  of 
copper.  The  loss  of  zinc  is  variable,  but  in  general  averages  from  1  to  2$. 

Liquation  or  Separation  of  the  Metals.— In  several  of  the 
bars  a  considerable  amount  of  liquation  took  place,  analysis  showing  a 
difference  in  composition  of  the  two  ends  of  the  bar.  In  such  cases  the 
change  in  composition  was  gradual  from  one  end  of  the  bar  to  the  other, 
the  upper  end  in  general  containing  the  higher  percentage  of  copper.  A 
notable  instance  was  bar  No.  13,  in  the  above  table,  turnings  from  the  upper 
end  containing  40.36$  of  zinc,  and  from  the  lower  end  48.52$. 

Specific  Gravity. — The  specific  gravity  follows  a  definite  law.  varying 
with  the  composition,  and  decreasing  with  the  addition  of  zinc.  From  the 
plotted  curve  of  specific  gravities  the  following  mean  values  are  taken: 

Per  cent  zinc 0       10      20      30      40      50      60      70      80      90     100. 

Specific  gravity 8.80  8.72  8.60  8.40  8.36  8.20  8.00  7.72  7.40  7.20  7.14. 

Graphic  Representation  of  the  Law  of  Variation  of 
Strength  of  Copper-Tin-Ziiic  Alloys.— In  an  equilateral  triangle 
the  sum  of  the  perpendicular  distances  from  any  point  within  it  to  the  three 
sides  is  equal  to  the  altitude.  Such  a  triangle  can  therefore  be  used  to 
show  graphically  the  percentage  composition  of  any  compound  of  three 
parts,  such  as  a  triple  alloy.  Let  one  side  represent  0  copper,  a  second 
0  tin,  and  the  third  0  zinc,  the  vertex  opposite  each  of  these  sides  repre- 
senting 100  of  each  element  respectively.  On  points  in  a  triangle  of  wood 
representing  different  alloys  tested,  wires  were  erected  of  lengths  propor- 
tional to  the  tensile  strengths,  arid  the  triangle  then  built  up  with  plaster  to 
the  height  of  the  wires.  The  surface  thus  formed  has  a  characteristic 
topography  representing  the  variations  of  strength  with  variations  of 
composition.  The  cut  shows  the  surface  thus  made.  Tie  vertical  section 
to  the  left  represents  the  law  of  tensile  strength  of  the  copper-tin  alloys, 
the  one  to  the  right  that  of  tin-zinc  alloys,  and  the  one  at  the  rear  that  of 
the  copper- zinc  alloys.  The  high  point  represents  the  strongest  possible 
alloys  of  the  three  metals.  Its  composition  is  copper  55,  zinc  43,  tin  2,  and  its 
strength  about  70,000  Ibs.  The  high  ridge  from  this  point  to  the  point  of 
maximum  height  of  the  section  on  the  left  is  the  line  of  the  strongest  alloys, 
represented  by  the  formula  zinc  +  (3  X  tin)  =  55. 

All  alloys  lying  to  the  rear  of  the  ridge,  containing  more  copper  and  less 
tin  or  zinc  are  alloys  of  greater  ductility  than  those  on  the  line  of  maximum 
strength,  and  are  the  valuable  commercial  alloys;  those  in  front  on  the  decliv- 
ity toward  the  central  valley  are  brittle,  and  those  in  the  valley  are  both  brit- 
tle and  weak.  Passing  from  the  valley  toward  the  section  at  the  right  the 
alloys  lose  their  brittleness  and  become  soft,  the  maximum  softness  being 
at  tin  =  100,  but  they  remain  weak,  as  is  shown  by  the  low  elevation  of  the 
surface.  This  model  was  planned  and  constructed  by  Prof.  Thurston  in 
1877.  (See  Trans.  A.  S,  C.  E.  1881,  Report  of  theU.  S.  Board  appointed  to 


324 


ALLOYS. 


test  Iron,  Steel,  etc.,  vol.  ii.,  Washington,  1881,  and  Thurston's  Materials 
of  Engineering,  vol.  iii.) 

The  best  alloy  obtained  in  Thurston's  research  for  the  U.  S.  Testing  Board 
has  the  composition,  Copper  55,  Tin  0.5,  Zinc  44.5.  The  tensile  strength  in  a 
cast  bar  was  68,900  Ibs.  per  sq.  in.,  two  specimens  giving  the  same  result;  the 
elongation  was  47  to  51  per  cent  in  5  inches.  Thurston's  formula  for  copper- 
tin-zinc  alloys  of  maximum  strength  (Trans.  A.  S.  C.  EM  1881)  is  «-J-  3£  =  55, 


FIG.  77. 

in  which  z  is  the  percentage  of  zinc  arid  t  that  of  tin.  Alloys  proportioned 
according  to  this  formula  should  have  a  strength  of  about  40,000  Ibs. 
per  sq.  in.  -f-500z.  The  formula  fails  with  alloys  containing  less  than  1  per 
cent  of  tin. 

The  following  would  be  the  percentage  composition  of  a  number  of  alloys 
made  according  to  this  formula,  and  their  corresponding  tensile  strength  in 
castings : 


Tin.       Zinc.     Copper. 


52 
49 
46 
43 
40 
37 
34 


47 
49 
51 
53 
55 
57 
59 


Tensile 
Strength, 

Ibs.  per 
sq.  in. 
66,000 
64,500 
63,000 
61,500 
60,000 
58,500 
57,000 


Tin.      Zinc.     Copper. 


10 
18 
14 
16 

18 


31 
28 
25 
19 
13 


61 

63 
65 
69 
73 

81 


Tensile 


sq.  in. 

55,500 
54,000 
52,500 
49,500 
46,500 
43,500 
40,500 


These  alloys,  while  possessing  maximum  tensile  strength,  would  in  general 
be  too  hard  for  easy  working  by  machine  tools.  Another  series  made  on 
the  formulas  -f  4  t'=  50  would  have  greater  ductility,  together  with  cc"- 
siderable  strength,  as  follows,  the  strength  being  calculated  *s  ItefciS^ 
tensile  strengh  iu  Ibs.  per  sq.  in.  =  40,000  +  500,?. 


ALLOYS   OF   COPPER,  TIK,  AKD   ZIKC. 


325 


Tin.      Zinc.     Copper. 


46 
42 


34 


53 
56 
59 
62 
65 
68 


Tensile 
Strength, 

Ibs.  per 
sq.  in. 
63,000 
61,000 
59,000 
57,000 
55,000 
53,000 


Tin.      Zinc.     Copper. 


7 
8 
9 
10 
11 
12 


22 
18 
14 
10 


71 

74 

77 


sq.  in. 

51,000 
49,000 
47,000 
45,000 
43,000 
41,000 


Composition    of  Alloys   in   Everyday   Use   in    Brass 
Foundries.     (American  Machinist.) 


Cop 
per. 

Zinc. 

Tin. 

Lead. 

Admiralty  metal 
Bell  metal 

Ibs. 

87 

16 

Ibs. 
5 

Ibs. 
8 

4 

Ibs. 

For  parts  of  engines  on  board 
naval  vessels. 
Bells  for  ships  and  factories. 
For  plumbers,  ship  and  house 
brass  work. 
For  bearing  bnshesf  or  shafting. 
For  pumps  and  other  hydraulic 
purposes. 
Castings    subjected   to   steam 
pressure. 
For  heavy  bearings. 
Metal  from  which  bolts  and  nuts 
are  forged,valve  spindles,  etc. 
For  valves,  pumps  and  general 
work. 
For   cog    and    worm    wheels, 
bushes,  axle  bearings,  slide 
valves,  etc. 
Flanges  for  copper  pipes. 
Solder  for  the  above  flanges. 

Brass  (yellow)  . 
Bush  metal  .  . 

16 

64 
32 

20 

16 
60 

90 

16 
50 

8 

8 
1 

1 

"46" 

3 

50 

4 
3 

4 
1 

Gun  metal  
Steam  metal 

Hard  gun  metal.  .  . 
Muntz  metal  

Phosphor  bronze., 
tt             «t 

Brazing  metal  
"      solder  

8  ph< 
10     " 

3S.  tin 

Gurley's  Bronze.— 16  parts  copper,  1  tin,  1  zinc,  y>  lead,  used  by 
W.  &  JL.  E.  Gurley  of  Troy  for  the  framework  of  their  engineer's  transits. 
Tensile  strength  41,114  Ibs.  per  sq.  in.,  elongation  '21%  in  1  inch,  sp.  gr.  8.696. 
(W.  J.  Keep,  Trans.  A.  I.  M.  E.  18'JO.) 

Useful  Alloys  of  Copper,  Tin,  and  Zinc. 

(Selected  from  numerous  sources.) 

Copper.    Tin.        Zinc. 
U.  S.  Navy  Dept.  journal  boxes  I  _  j    6 

and  guide-gibs )       I  82.8 

Tobin  bronze 58.22 

Naval  brass 62 

Com  position,  U.  S.  Navy 88 

Brass  bearings  (J.  Rose) j  87  7 

Gun  metal 92.5 

"        »'      ,                                     9! 

"     ,                87.75 

"        "      85 

»«        "      ,                                   83 

i  13 

Tough  brass  for  engines "i  76  5 

Bronze  for  rod-boxes  (Lnf ond) 82 

"       "    pieces  subject  to  shock.. 

Red  brass  parts 

lt     per  cent 

Bronze  for  pump  casings  (Lafond)... 
"    eccentric  straps.        " 

"    shrill  whistles »u 

"       "   low-toned  whistles 81 


1 
13.8 

2.30 

1 
10 

8 
11.0 

5 

7 

9.75 

5 

2 
11.8 


83 
20 


88 
84 


15 
1 
4.4 

10 
14 
18 
17 


parts. 
3?4    per  cent. 
39.48    "       " 
37         ||       |* 

1  parts. 
1.3   percent. 
2.5      "       " 

2  "       " 
2.5     "       " 

10        "       " 
15         "       " 

2  parts. 

11.7  percent. 

2  slightly  malleable. 

1.50  0.50  lead. 

1  1 

4.3  4.3       " 


2.0  antimony. 

2.0        " 


326 


ALLOYS. 


Art  bronze,  dull  red  fracture  

Copper. 

Tin.        Zinc. 
2             1 

Gold  bronze  

89.5 

2.1          5.6 

2.8  lead. 

Bearing  metal  

...       89 

8            3 

"             

.  .  .  .      89 

2^         8^ 

*'           "                                .   .. 

.  .  .  .      86 

14 

"           "      

....      8BU 

12%         2 

"           " 

80 

18            2 

**           *« 

....      79 

18            2>£ 

y,  lead. 

"           «* 

....       74 

9^         9i/£ 

7  lead. 

English  brass  of  A.D.  1504  

.  .  .  .       64 

3           29J4 

3*4  lead. 

Co  pper-Nickel 

Alloys,  German  Silver. 

Copper. 

Nickel. 

Tin. 

Zinc, 

German  silver  

51.6 

25.8 

22.6 

50.2 

14.8 

3.1 

31.9 

**           "              

51.1 

13.8 

3.2 

31.9 

*'           »' 

.  .     52  to  55 

18  to  25 

20  to? 

Nickel         u     . 

75  to  66 

25  to  33 

A  refined  copper-nickel  alloy  containing  50$  copper  and  49$  nickel,  with 
very  small  amounts  of  iron,  silicon  and  carbon,  is  produced  direct  from 
Bessemer  matte  in  the  Sudbury  (Canada)  Nickel  Works.  German  silver 
manufacturers  purchase  a  ready-made  alloy,  which  melts  at  a  low  heat  and 
requires  simple  addition  of  zinc,  instead  of  buying  the  nickel  and  copper 
separately.  This  alloy,  "50-50"  as  it  is  caller],  is  almost  indistinguishable 
from  pure  nickel.  Its  cost  is  less  than  nickel,  its  melting  point  much  lower, 
it  can  be  cast  solid  in  any  form  desired,  and  furnishes  a  casting  which  works 
easily  in  the  lathe  or  planer,  yielding  a  silvery  white  surface  unchanged  by 
air  or  moisture.  For  bullet  casings  now  used  in  various  British  and  conti- 
nental rifles,  a  special  alloy  of  80$  copper  and  20$  nickel  is  made. 

Special  Alloys.    (Engineer,  March  24, 1893.) 
JAPANESE  ALLOYS  for  art  work  : 


Copper. 

Silver. 

Gold. 

Lead. 

Zinc. 

Iron. 

Shaku-do  
Shibu-icbi  

94.50 
67.31 

1.55 
32.07 

3.73 
traces. 

0.11 
.52 

trace. 

trace. 

GILBERT'S  ALLOY  for  cera-perduta  process,  for  casting  in  plaster-of-paris  • 
Copper  91.4  Tin  5.7  Lead  2.9       Very  fusible. 


COPPER-Z1NOIRON 

(F.  L.  Garrison,  Jour.  Frank.  Inst.,  June  and  July,  1891.) 
]>elta  Metal.—  This  alloy,  which  was  formerly  known  as  sterro-metal, 
is  composed  of  about  60  copper,  from  34  to  44  zinc,  2  to  4  iron,  and  1  to  2  tin. 
The  peculiarity  of  all  these  alloys  is  the  content  of  iron,  which  appears  to 
have  the  property  of  increasing  their  strength  to  an  unusual  degree.     In 
making  delta  metal  the  iron  is  previously  alloyed  with  zinc  in  known  and 
definite    proportions.      When  ordinary   wrought-iron    is    introduced    into 
molten  zinc,  the  latter  readily  dissolves  or  absorbs  the  former,  and  will  take 
it  up  to  the  extent  of  about  5$  or  more.     By  adding  the  zinc-iron  alloy  thus 
obtained  to  the  requisite  amount  of  copper,  it  is  possible  to  introduce  an\ 
definite  quantity  of  iron  up  to  5$  into  the  copper  alloy.    Garrison  gives  tin- 
foil owing  as  the  range  of  composition  of  copper-zinc-iron,  and  copper-zinc- 
tin-iron  alloys  : 

I.  II. 

Percent.  Percent. 

Iron  ...................  0.1  to5  Iron  .................  ....  0.1  to  5 

Copper  ................    50to65  Tin  .....................  0.1  to  10 

Zinc  ..............   ...  49.9  to  30  Zinc.  ....................  1.8  to  45 

Copper  ..................    98  to  40 

The  advantages  claimed  for  delta  metal  are  great  strength  and  toughness. 
It  produces  sound  castings  of  close  grain.    It  can  be  rolled  and  forged  hot 
and  can  stand  a  certain  amount  of  drawing  and  hammering  when  cold.     It 
takes  a  high  polish,  and  when  exposed  to  the  atmosphere  tarnishes  less  than 
brass. 


PHOSPHOR-BRONZE  AND  OTHER  SPECIAL  BRONZES.   327 

When  cast  in  sand  delta  metal  has  a  tensile  strength  of  about  45,000  pounds 
per  square  inch,  and  about  10$  elongation  ;  when  rolled,  tensile  strength  of 
60,000  to  75, 000  pounds  per  square  inch,  elongation  from  9^  to  \t%  on  bars  1.128 
inch  in  diameter  and  1  inch  area. 

Wallace  gives  the  ultimate  tensile  strength  33,600  to  51,520  pounds  per 
square  inch,  with  from  \§%  to  20$  elongation. 

Delta  metal  can  be  forged,  stamped  and  rolled  hot.  It  must  be  forged  at 
a  dark  cherry-red  heat,  and  care  taken  to  avoid  striking  when  at  a  black 
heat. 

According  to  Lloyd's  Proving  House  tests,  made  at  Cardiff,  December  20, 
18S7,  a  half-inch  delta  metal-rolled  bar  gave  a  tensile  strength  of  88,400 
pounds  per  square  inch,  with  an  elongation  of  30$  in  three  inches. 

ToMu  Bronze.— This  alloy  is  practically  a  sterro  or  delta  metal  with 
the  addition  of  a  small  amount  of  lead,  which  tends  to  render  copper  softer 
and  more  ductile. 

The  following  analyses  of  Tobin  bronze  were  made  by  Dr.  Chas.  B.  Dudley: 

Pig  Metal,        Test  Bar  (Rolled), 
per  cent.  per  cent. 

Copper 59.00  61.20 

Zinc..  , 38.40  37.14 

Tin     2.16  0.90 

Iron  0.11  0.18 

Lead 0.31  0.35 

Dr.  Dudley  writes,  "  We  tested  the  test  bars  and  found  78,500  tensile 
strength  with  15$  elongation  in  two  inches,  and  40^$  in  eight  inches.  This 
high  tensile  strength  can  only  be  obtained  when  the  metal  is  manipulated. 
Such  high  results  could  hardly  be  expected  with  cast  metal." 

The  original  Tobin  bronze  in  1875,  as  described  by  Thurston,  Trans. 
A.  S.  C.  E  1881,  had,  composition  of  copper  58.22,  tin  2.30,  zinc  39.48.  As 
cast  it  had  a  tenacity  of  66,000  Ibs.  per  sq.  in.,  and  as  rolled  79,000  Ibs. ;  cold 
rolled  it  gave  104,000  Ibs. 

A  circular  of  Ansonia  Brass  &  Copper  Co.  gives  the  following  :— The  tensile 
strength  of  six  Tobin  bronze  one-inch  round  rolled  rods,  turned  down  to  a 
diameter  of  %  of  an  inch,  tested  by  Fairbanks,  averaged  79,600  Ibs.  per  sq. 
in.,  and  the  elastic  limit  obtained  on  three  specimens  averaged  54,257  Ibs.  per 
sq. in. 

At  a  cherry-red  heat  Tobin  bronze  can  be  forged  and  stamped  as  readily 
as  steel.  Bolts  and  nuts  can  be  forged  from  it,  either  by  hand  or  by  ma- 
chinery, with  a  marked  degree  of  economy.  Its  great  tensile  strength,  and 
resistance  to  the  corrosive  a,ction  of  sea-water,  render  it  a  most  suitable 
metal  for  condenser  plates,  steam-launch  shafting,  ship  sheathing  and 
fastenings,  nails,  hull  plates  for  steam  yachts,  torpedo  and  life  boats,  and 
ship  deck  fittings. 

The  Navy  Department  has  specified  its  use  for  certain  purposes  in  the 
machinery  of  the  new  cruisers.  Its  specific  gravity  is  8.071.  The  weight  of 
a  cubic  inch  is  .291  Ib. 

PHOSPHOR-BRONZE:  AND  OTHER  SPECIAL 
BRONZES. 

Phosphor-bronze.— In  the  year  1868,  Montefiore  &  Kunzel  of  Liege, 
Belgium,  found  by  adding  small  proportions  of  phosphorus  or  "phosphoret 
of  tin  or  copper''  to  copper  that  the  oxides  of  that  metal,  nearly  always 
present  as  an  impurity,  more  or  less,  were  deoxidized  and  the  copper  much 
improved  in  strength  and  ductility,  the  grain  of  the  fracture  became  finer, 
the  color  brighter,  and  a  greater  fluidity  was  attained. 

Three  samples  of  phosphor-bronze  tested  by  Kirkaldy  gave  : 

Elastic  limit,  Ibs.  per  sq.  in  23,800       24,700       16,100 

Tensile  strength,  Ibs.  per  sq.  in.  ...     52,625       46,100       44.448 
Elongation,  per  cent 8.40  1 .50  33.40 

The  strength  of  phosphor-bronze  varies  like  that  of  ordinary  bronze 
according  to  th^  percentages  of  copper,  tin,  zinc,  lead,  etc.,  in  the  alloy. 

Deoxidized  Bronze.— This  alloy  resembles  phosphor  bronze  some- 
what in  composition  and  also  delta  metal,  in  containing  zinc  and  iron.  The 
following  analysis  gives  its  average  composition: 


Copper  8267 

Tin 12.40 

Zinc  3.23 

Lead 2.14 


Iron 0.10 

Silver  0.07 

Phosphorus 0.005 

100.615 


328 


ALLOYS. 


Comparison  of  Copper,  Silicon-bronze,  and  Phosphor- 
bronze  Wires. 

(Engineering,  Nov.  23,  1883.) 


Description  of  Wire. 

Tensile  Strength  per 
square  inch  in 

Relative 
Conductivity. 

Tons. 

Lbs. 

Pure  copper  

17.78 
18.27 
48.25 
45.71 

39,827 
41,690 
108,080 
102,390 

100  per  cent. 
96 
34 
26 

Silicon  bronze  (telegraph).  
"           "        (telephone) 

Phosphor  Bronze  (telephone)  ...  

(Aluminum  Bronze.  Cowles  Electric  Smelting  and  Al.  Co. 's  circular.) 

The  standard  A  No.  2  grade  of  aluminum  bronze,  containing  H$  of  alumi- 
num and  9( •%  of  copper,  has  many  remarkable  characteristics  which  dis- 
tinguish it  from  all  other  metals. 

The  tenacity  of  castings  of  A  No.  2  grade  metal  varies  between  75,000 
and  90,000  Ibs.  to  the  square  inch,  with  from  4%  to  14$  elongation. 

Increasing  the  proportion  of  aluminum  in  bronze  beyond  110  producer  a 
brittle  alloy;  therefore  nothing  higher  than  the  A  No.  1,  which  contains  11$, 
is  >i  ade. 

The  B,  C,  D,  and  E  grades,  containing  7^$,  5$,  2J$£,  and  \y^%  of  aluminum, 
respectively,  decrease  in  tenacity  in  the  order  named,  that  of  the  former 
being  about  65,000  pounds,  while  the  latter  is  25,000  pounds.  While  there  is 
also  a  proportionate  decrease  in  transverse  and  torsional  strengths,  elastic 
limit,  and  resistance  to  compression  as  the  percentage  of  aluminum  is  low- 
ered and  that  of  copper  raised,  the  ductility  on  the  other  hand  increases  in 
the  same  proportion.  The  specific  gravity  of  the  A  No.  1  grade  is  7.56. 

Bell  Bros.,  Newcastle,  gave  the  specific  gravity  of  the  aluminum  bronzes 
as  below: 

3$  aluminum 8.691 

4$          "          8.621 

5$          "          8.369 

10$          "  7.689 

Casting. — The  melting  point  of  aluminum  bronze  varies  slightly  with 
the  amount  of  aluminum  contained,  the  higher  grades  melting  at  a  some- 
what lower  temperature  than  the  lower  grades.  The  A  No.  1  grades  melt 
at  about  1700°  F.,  a  little  higher  than  ordinary  bronze  or  brass. 

Aluminum  bronze  shrinks  more  than  ordinary  brass.  As  the  metal  solidi- 
fies rapidly  it  is  necessary  to  pour  it  quickly  and  to  make  the  feeders  amply 
large,  so  that  there  will  be  no  '"freezing"  in  them  before  the  casting  is 
properly  fed.  Baked-sand  moulds  are  preferable  to  green  sand,  except  for 
small  castings,  and  when  fine  skin  color-  are  desired  in  the  castings.  (See 
paper  by  Thos.  D.  West,  Trans.  A.  S.  M.  E.  1886,  vol.  viii.) 

All  grades  of  aluminum  bronze  can  be  rolled,  s wedged,  spun,  or  drawn 
cold  except  A  1  and  A  2.  They  can  all  be  worked  at  a  bright  red  heat. 

In  rolling,  swedging,  or  spinning  cold,  it  should  be  annealed  very  often,  and 
at  a  brighter  red  heat  than  is  used  foi:  annealing  brass. 

Brazing. — Aluminum  bronze  will  braze  as  well  as  any  other  metal, 
using  one  quarter  brass  solder  (zinc  500,  copper  500  (and 'three  quarters 
borax,  or,  better,  three  quarters  cryolite. 

Soldering.— To  solder  aluminum  bronze  with  ordinary  soft  (pewter) 
solder:  Cleanse  well  the  parts  to  be  joined  free  from  grease  and  dirt.  Then 
place  the  parts  to  be  soldered  in  a  strong  solution  of  sulphate  of  copper  and 
place  in  the  bath  a  rod  of  soft  iron  touching  the  parts  to  be  joined.  After 
a  while  a  coppery-like  surface  will  be  seen  on  the  metal.  Remove  from 
bath,  rinse  quite  clean,  and  brighten  the  surfaces.  These  surfaces  can  then 
be  tinned  by  using  a  fluid  consisting  of  zinc  dissolved  in  hydrochloric  acid,  in 
the  ordinary  way,  with  common  soft  solder. 

Mierzinski  recommends  ordinary  hard  solder,  and  says  that  Hulot  uses 
an  alloy  of  the  usual  half-and-half  lead-tin  solder,  with  12.5$,  25$  or  50$  ot 
zinc  amalgam. 


ALUMINUM   BROHZE. 


329 


Tests  of  Aluminum  Bronzes. 

(By  John  H.  J.  Dagger,  in  a  paper  read  before  the  British  Association,  1889.) 


Per  cent 
of 
Aluminum. 

Tensile  Strength. 

Elonga- 
tion, 
per  cent. 

Specific 
Gravity. 

Tons  per 
square  inch. 

Pounds  per 
square  inch. 

11...           

40  to  45 
33  "  40 
25  "  30 
15  "  18 
13  "  15 
11  "  13 

89,600  to  100,800 
73,920  "    89,600 
56.000  "    67.200 
33,600  "    40,320 
29,120  "    33,600 
24,640  "    29,120 

8 
14 
40 
40 
50 
55 

7.23 
7.69 
8.00 
8.37 
8.69 

10  

71^  

5  5V*j 

1J4  

Both  physical  and  chemical  tests  made  of  samples  cut  from  various  sec- 
tions of  2\4fo,  5#,  7^,  or  10$  alumiuized  copper  castings  tend  to  prove  that 
the  aluminum  unites  itself  with  each  particle  of  copper  with  uniform  pro- 
portion in  each  case,  so  that  we  have  a  product  that  is  free  from  liquation 
and  highly  homogeneous.  (R.  C.  Cole,  Iron  Age,  Jan.  16,  1890.) 

Aluminum-Brass  (E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  vol.  xviii.)— 
Cowles  altttnmum-brass  is  made  by  fusing  together  equal  weights  of  A  1 
aluminum-bronze,  copper,  and  zinc.  The  copper  and  bronze  are  first  thor- 
oughly melted  and  mixed,  and  the  zinc  is  finally  added.  The  material  is  left 
in  the  furnace  until  small  test-bars  are  taken  from  it  and  broken.  When 
these  bars  show  a  tensile  strength  of  80,000  pounds  or  over,  with  2  or  3  per 
cent  ductility,  the  metal  is  ready  to  be  poured.  Tests  of  this  brass,  on  small 
bars,  have  at  times  shown  as  high  as  100,000  pounds  tensile  strength. 

The  screw  of  the  United  States  gunboat  Petrel  is  cast  from  this  brass, 
mixed  with  a  trifle  less  zinc  in  order  to  increase  its  ductility. 
Tests  of  Aluminum-Brass. 
(Cowles  E.  S.  &  Al.  Co.) 


Specimen  (Castings.) 

Diameter 
of  Piece, 
Inch. 

Area, 
sq.  in. 

Tensile 
Strength; 

Ibs.  per 
sq.  in. 

Elastic 
Limit, 
Ibs.  per 
sq.  in. 

Elonga- 
tion, 
per  ct. 

Remarks. 

15#  A  grade  Bronze.  ) 
Yi%  Zinc             > 

.465 

.1698 

41,225 

17,668 

41H 

%to 
£  §  * 

68$  Copper         .         j 

!-S» 

1  part  A  Bronze  ) 
1  part  Zinc                  /- 

465 

1698 

78,327 

214 

«»§.§ 

1  part  Copper  j 
1  part  A  Bronze  —  | 
1  part  Zinc                  /• 

.460 

1661 

72,246 

2^ 

i^s 
III-s 

1  part  Copper  ( 

B* 

The  first  bra.ss  on  the  above  list  is  an  extremely  tough  metal  with  low 
elastic  limit,  made  purposely  so  as  to  "  upset  "  easily.  The  other,  which  is 
called  Aluminum-brass  No  2,  is  very  hard. 

We  have  not  in  this  country  or  in  England  any  official  standard  by  which 
to  judge  of  the  physical  characteristics  of  cast  metals.  There  are  two  con- 
ditions that  are  absolutely  necessary  to  be  known  before  we  can  make  a 
fair  comparison  of  different  materials:  namely,  whether  the  casting  was 
made  in  dry  or  green  sand  or  in  a  chill,  and  whether  it  was  attached  to  a 
larger  casting  or  cast  by  itself.  It  has  also  been  found  that  chill  castings 
give  higher  results  than  sand-castings,  and  that  bars  cast  by  themselves 
purposely  for  testing  almost. invariably  run  higher  than  test-bars  attached 
to  castings.  It  is  also  a  fact  that  bars  cut  out  from  castings  are  generally 
weaker  than  bars  cnst  alone.  (E.  H.  Cowles.) 

Caution  as  to  Reported  Strength  of  Alloys.— The  same 
variation  in  strength  which  has  been  found  in  tests  of  gun-metal  (copper 
and  tin)  noted  above,  must  be  expected  in  tests  of  aluminum  bronze  and  in 
fact  of  all  alloys.  They  are  exceedingly  subject  to  variation  in  density  and 
in  grain,  caused  by  differences  in  method  of  molding  and  casting,  tempera- 
ture of  pouring,  size  and  shape  of  casting,  depth  of  "sinking  head,'1  etc. 


330 


ALLOYS. 


A  hi  min  ii m   Hardened  by  Addition  of  Copper   Rolled 


Sheets  .04  Inch   Thick. 


Al. 

Per  cent. 
100 

98 

96 

94 


Cu. 
Per  cent. 


Sp.  Gr. 
Calculated. 

2. "78 
2.90 
3.02 
3.14 


(The  Engineer,  Jan  2, 1891.) 

Tensile  Strength 


Sp.  Gr. 

Determined. 

2.67 

2.71 

2.77 
2.82 
2.85 


in  pounds  per 
square  inch. 
26,535 
43,563 
44,130 
54,773 
50,374 


Tests  of  Aluminum  Alloys. 

(Engineer  Harris,  U.  S.  N.,  Trans.  A.  I.  M.  E.,  vol.  xviii.) 


Composition. 

Tensile 
Strength, 
per  sq.  in. 
Ibs. 

Elastic 
Limit. 
Ibs.  per 
sq.  in. 

Elonga- 
tion, 
per  ct. 

Reduc- 
tion of 
Area, 
per  ct. 

Cop- 
per. 

Alumi- 
num. 

Silicon. 

Zinc. 

Iron. 

91.50* 

88.50 
91.50 
90.00 
63.00 
63.00 
91.50 
93.00 
88.50 
92.00 

6.50$ 
9.33 
6.50 
9.00 
3.33 
3.33 
6.50 
6.50 
9.33 
6.50 

1.75* 
1.66 
1.75 
1.00 
0.33 
0.33 
1.75 
0.50 
1.66 
0.50 

0.25$ 
0.50 
0.25 

60,700 
66,000 
67,600 
72,830 
82,200 
70,400 
59,100 
53,000 
69,930 
46.530 

18,000 
27,000 
24,000 
33.000 
60,000 
55,000 
1  9,000 
19,000 
33,000 
17.000 

23.2 
3.8 
13. 
2.40 
2.33 
0.4 
15.1 
6.2 
1.33 
7.8 

30.7 
7.8 
21.62 
5.78 
9.88 
4.33 
23  59 
15.5 
3.30 
19.19 

33.33* 
33.33 

0.25 

0.50 

For  comparison  with  the  above  6  tests  of  "  Navy  Yard  Bronze,"  Cu  88, 
Sn  10,  Zn  2,  are  given  in  which  the  T.  S.  ranges  from  18,000  to  24,590,  E.  L. 
from  10,000  to  33,000,  El.  2.5  to  5.8$,  Red.  4.7  to  10.89. 

Alloys  of  Aluminum,  Silicon  and  Iron. 

M.  and  E.  Bernard  have  succeeded  in  obtaining  through  electrolysis,  by 
treating  directly  and  without  previous  purification,  the  aluminum  earths 
(red  and  white  bauxites)  the  following  : 

Alloys  such  asferro-aluminum,  ferro-silicon-aluminum  and  silicon-alumi- 
num, where  the  proportion  of  silicon  may  exceed  10$  which  are  employed 
in  the  metallurgy  of  iron  for  refining  steel  and  cast-iron. 

Also  silicon-aluminum,  where  the  proportion  of  silicon  does  not  exceed 
10$,  which  may  be  employed  in  mechanical  constructions  in  a  rolled  or 
hammered  condition,  in  place  of  steel,  on  account  of  their  great  resistance, 
especially  where  the  lightness  of  the  piece  in  construction  constitutes  one 
of  the  main  conditions  of  success. 

The  following  analyses  are  given: 

1.  Alloys  applied  to  the  metallurgy  of  iron,  the  refining  of  steel  and  cast 
iron: 


Types. 
No  1      .      

Aluminum. 

No.  2  . 

70 

No  3                           ...   . 

70 

No  4  .  ...     

70 

No  5 

70 

No.  6  

70 

2.  Mechanical  alloys: 
Types. 
No  1 

No  2      

No.  3... 

Iron. 

25$ 
20 
15 
10 
10 
trace 


Silicon.       Manganese. 


10 
15 
20 
10 
20 


Aluminum. 


90 
90 


Silicon. 

6.75$ 

9.25 
10.00 


0 

0 

0 
10 
10 

Iron. 
1.25$ 
0.75 

trace. 


Up  to  this  time  it  has  been  thought  that  silicon  was  rather  injurious  when 
alloyed  with  aluminum.  From  numerous  experiences  it  has  been  demon- 
strated that  it  gives  to  aluminum  some  remarkable  properties  of  resistance; 
the  best  results  were  with  alloys  where  the  proportion  of  iron  was  very  low, 
and  the  proportion  of  silicon  in  the  neighborhood  of  10$.  Above  that  pro- 


ALLOYS   OF   MA^GAKESE   AND   COPPER.  331 

portion  the  alloy  becomes  crystalline  and  can  no  longer  be  employed.  The 
density  of  the  alloys  of  silicon  is  approximately  the  same  as  that  of  alumi- 
num.— La  Metallurqie,  189*2. 

Tungsten  and.  Aluminum. — Mr.  Leinhardt  Mannesmann  says  that 
the  addition  of  a.  little  tungsten  to  pure  aluminum  or  its  alloys  communi- 
cates a  remarkable  resistance  to  the  action  of  cold  and  hot  water,  salt  water 
and  other  re-agents.  When  the  proportion  of  tungsten  is  sufficient  the 
alloys  offer  great  resistance  to  tensile  strains. 

Aluminum  and  Tin.— M.  Bourbouze  has  compounded  an  alloy  of 
aluminum  and  tin,  by  fusing  together  JOO  parts  of  the  former  with  10  parts 
of  the  latter.  This  alloy  is  paler  than  aluminum,  and  has  a  specific  gravity 
of  2.85.  The  alloy  is  not  as  easily  attacked  by  several  reagents  as  alumi- 
num is,  and  it  can  also  be  worked  more  readily.  Another  advantage  is  that 
it  can  be  soldered  as  easily  as  bronze,  without  further  preliminaiy  prepara- 
tions. 

Aluminum-Antimony  Alloys.— Dr.  C.  R.  Alder  Wright  describes 
some  aluminum-antimony  alloys  in  a  communication  read  before  the  Society 
of  Chemical  Industry.  The  results  of  his  researches  do  not  disclose  the 
existence  of  a  commercially  useful  alloy  of  these  two  metals,  and  have 
greater  scientific  than  practical  interest.  A  remarkable  point  is  that  the 
alloy  with  the  chemical  composition  Al  Sb  has  a  higher  melting  point  than 
either  aluminum  or  antimony  alone,  and  that  when  aluminum  is  added  to 
pure  antimony  the  melting-point  goes  up  from  that  of  antimony  (450°  C.) 
to  a  certain  temperature  rather  above  that  of  silver  (1000°  C.). 

AI^OYS  OF  MANGANESE  AND  COPPER. 

Various  Manganese  Alloys.— E.  H.  Cowles,  in  Trans.  A.  I.  M.  E., 

vol.  xviii,  p.  495,  states  that  as  the  result  of  numerous  experiments  on 
mixtures  of  the  several  metals,  copper,  zinc,  tin,  lead,  aluminum,  iron,  and 
manganese,  and  the  metalloid  silicon,  and  experiments  upon  the  same  in 
ascertaining  tensile  strength,  ductility,  color,  etc.,  the  most  important 
determinations  appear  to  be  about  as  follows  : 

1.  That  pure  metallic  manganese  exerts  a  bleaching  effect  upon  copper 
more  radical  in  its  action  even  than  nickel.    In  other  words,  it  was  found 
that  18*^$  of  manganese  present  in  copper  produces  as  white  a  color  in  the 
resulting  alloy  as  25$  of   nickel  would  do,  this  being  the  amount  of  each 
required  to  remove  the  last  trace  of  red. 

2.  That  upwards  of  20$  or  25$  of  manganese  may  be  added  to  copper  with- 
out reducing  its  ductility,  although  doubling  its  tensile  strength  and  chang- 
ing its  color. 

3.  That  manganese,  copper,  and  zinc  when  melted  together  and  poured 
into  moulds  behave  very  much   like  the  most  "  j-easty  "  German  silver, 
producing  an  ingot  which  is  a  mass  of  blow-holes,  and  which  swells  up 
above  the  mould  before  cooling. 

4.  That  the  alloy  of  manganese  and  copper  by  itself  is  very   easily 
oxidized. 

5.  That  the  addition  of  1.25$  of  aluminum  to  a  manganese-copper  alloy 
converts  it  from  one  of  the  most  refractory  of  metals  in  the  casting  process 
into  a  metal  of  superior  casting  qualities,  and  the  non  corrodibility  of  which 
is  in  many  instances  greater  than  that  of  either  German  or  nickel  silver. 

A  "silver-bronze  "  alloy  especially  designed  for  rods,  sheets,  and  wire 
has  the  following  composition  :  Manganese,  18;  aluminum,  1.20;  silicon,  0.5; 
zinc,  13;  and  copper,  67.5$.  It  has  a  tensile  strength  of  about  57,000  pounds 
on  small  bars,  and  ^'0$  elongation.  It  has  been  rolled  into  thin  plate  and 
drawn  into  wire  .008  inch  in  diameter.  A  test  of  the  electrical  conductivity 
of  this  wire  (of  size  No.  32)  shows  its  resistance  to  be  41.44  times  that  of  pure 
copper.  This  is  far  lower  conductivity  than  that  of  German  silver. 

Manganese  Bronze.  (F.  L.  Garrison,  Jour.  F.  I.,  1891.)— This  alloy 
has  been  used  extensively  for  casting  propeller-blades.  Tests  of  some  made 
by  B.  H.  Cramp  &  Co.,  of  Philadelphia,  gave  an  average  elastic  limit  of 
30,000  pounds  per  square  inch,  tensile  strength  of  about  60,000  pounds  per 
square  inch,  with  an  elongation  of  8$  to  10$  in  sand  castings.  When  rolled, 
the  elastic  limit  is  about  80,000  pounds  per  square  inch,  tensile  strength 
95,000  to  106,000  pounds  per  square  inch,  with  an  elongation  of  12$  to  15$. 

Compression  tests  made  at  United  States  Navy  Department  from  the 
metal  in  the  pouring-gate  of  propeller-hub  of  U.  S.  S.  Maine  gave  in  two  tests 
a  crushing  stress  of  126,450  and  135.750  Ibs.  per  sq.  in.  The  specimens  were 
1  inch  high  by  0.7  X  0.7  inch  in  cross-section  =  0.49  square  inch.  Both  speci- 


332  ALLOYS. 

mens  gave  way  by  shearing,  on  a  plane  making  an  angle  of  nearly  45°  with 
the  direction  of  stress. 

A  test  on  a  specimen  IXlXl  inch  was  made  from  a  piece  of  the  same 
pouring-gate.  Under  stress  of  150,000  pounds  it  was  flattened  to  0.72  inch 
high  by  about  1*4  X  1J4  inches,  but  without  rupture  or  any  sign  of  distress. 

One  of  the  great  objections  to  the  use  of  manganese  bronze,  or  in  fact 
any  alloy  except  iron  or  steel,  for  the  propellers  of  iron  ships  is  on  account 
of  the  galvanic  action  set  up  between  the  propeller  and  the  stern-posts. 
This  difficulty  has  in  great  measure  been  overcome  by  putting  strips  of 
rolled  zinc  around  the  propeller  apertures  in  the  stern-frames. 

The  following  analysis  of  Parsons'  manganese  bronze  No.  2  was  made 
from  a  chip  from  the  propeller  of  Mr.  W.  K.  Vanderbilt's  yacht  Alva. 

Copper... 88.644 

Zinc  1  570 

Tin 8.700 

Iron 0.720 

Lead 0.295 

Phosphorus trace 


It  will  be  observed  there  is  no  manganese  present  and  the  amount  of  zinc 
is  very  small. 

E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  vol.  xviii,  says  :  Manganese  bronze,  so 
called,  is  in  reality  a  manganese  brass,  for  zinc  instead  of  tin  is  the  chief 
element  added  to  the  copper.  Mr.  P.  M.  Parsons,  the  proprietor  of  this 
brand  of  metal,  has  claimed  for  it  a  tensile  strength  of  from  24  to  28  tons  on 
small  bars  when  cast  in  sand.  Mr.  W.  C.  Wallace  states  that  brass-founders 
of  high  repute  in  England  will  not  admit  that  manganese  bronze  has  more 
thnn  from  12  to  17  tons  tensile  strength.  Mr.  Horace  See  found  tensile 
strength  of  45,000  pounds,  and  from  $%  to  12V£$  elongation. 

GERMAN-SILVER  AND  OTHER  NICKEL  ALLOYS. 

Copper.  Nickel.  Zinc. 

Chinese  packfong 40.4  31.6  6.5         parts. 

tutenag 8  3  6.5 

German  silver 2  1  1 

1     (cheaper) 8  2  3.5 

"      (closely  resembles  sil).    8  3  3.5  " 

For  analyses  of  some  German-silvers  see  page  326. 

German  Silver. — The  composition  of  German  silver  is  a  very  uncertain 
thing  and  depends  largely  on  the  honesty  of  the  manufacturer  and  the 
price  the  purchaser  is  willing  to  pay.  It  is  composed  of  copper,  zinc,  and 
nickel  in  varying  proportions.  The  best  varieties  contain  from  18$  to  25$  of 
nickel  and  from  30£to30£or  zinc,  the  remainder  being  copper.  The  more 
expensive  nickel  silver  contains  from  25$  to  38$  of  nickel  and  from  75$  to  66$ 
of  copper.  The  nickel  is  used  as  a  whitening  element;  it  also  strengthens 
the  alloy  and  renders  it  harder  and  more  non-corrodible  than  the  brass 
made  without  it,  of  copper  and  zinc.  Of  all  troublesome  alloys  to  handle  in 
the  foundry  or  rolling-mill,  German  silver  is  the  worst.  It  is  unmanageable 
and  refractory  at  every  step  in  its  transition  from  the  crude  elements  into 
rods,  sheets,  or  wire.  (E.  H.  Cowles,  Trans.  A.  I.  M.  E.,  vol.  xviii.  p.  494.) 

ALLOYS  OF  BISMUTH. 

By  adding  a  small  amount  of  bismuth  to  lead  that  metal  may  be  hard- 
ened and  toughened.  An  alloy  consisting  of  three  parts  of  lead  and  two  of 
bismuth  has  ten  times  the  hardness  and  twenty  times  the  tenacity  of  lead. 
The  alloys  of  bismuth  with  both  tin  and  lead  are  extremely  fusible,  and 
take  fine  impressions  of  casts  and  moulds.  An  alloy  of  one  part  bismuth, 
two  parts  tin,  and  one  part  lead  is  used  by  pewter-workers  as  a  soft  solder, 
and  by  soap-makers  for  moulds.  An  alloy  of  five  parts  bismuth,  two  parts 
tin,  and  three  parts  lead  melts  at  199°  F  ,  and  is  somewhat  used  for  ster- 
eotyping, and  for  metallic  writing-pencils.  Thorpe  gives  the  following 
proportions  for  the  better-known  fusible  metals; 


BEARING-METAL  ALLOTS. 


333 


Name  of  Alloy. 

Bismuth. 

Lead. 

Tin. 

Cad- 
mium 

Mer- 
cury. 

Melting- 
point. 

Newton's      

50 

31.25 

18.75 

202°    F 

Rose's               ... 

50 

28.10 

24.10 

203° 

D'Arcet's      

50 

25.00 

25.00 

201° 

D'Arcet's  with  mercury. 
Wood's        .        

50 
50 

25.00 
25.00 

25.00 
12  50 

12.50 

250.0 

113° 
149° 

Lipowitz's                 .  . 

50 

26  90 

12  78 

10  40 

149° 

Guthrie's  "Entectic"... 

50 

20.55 

21  10 

14  03 

"  Very  low  " 

The  action  of  heat  upon  some  of  these  alloys  is  remarkable.  Thus,  Lipo- 
witz's  alloy,  which  solidifies  at  149°  Fah.,  contracts  very  rapidly  at  first,  as 
it  cools  from  this  point.  As  the  cooling  goes  on  the  contraction  becomes 
slower  and  slower,  until  the  temperature  falls  to  101.3°  Fah.  From  this 
point  the  alloy  expands  as  it  cools,  until  the  temperature  falls  to  about  77° 
Fah.,  after  which  it  again  contracts,  so  that  at  32°  F.  a  bar  of  the  alloy  has 
the  same  length  as  at  115°  F. 

Alloys  of  bismuth  have  been  used  for  making  fusible  plugs  for  boilers,  but 
it  is  found  that  they  are  altered  by  the  continued  action  of  heat,  so  that  one 
cannot  rely  upon  them  to  melt  at  the  proper  temperature.  Pure  Banca  tin 
is  used  by  the  U.  S.  Government  for  fusible  plugs. 

FUSIBLE  ALL.OYS.    (From  various  sources.) 

Sir  Isaac  Newton's,  bismuth  5,  lead  3,  tin  2,  melts  at 212°  F. 

Rose's,  bismuth  2,  lead  1,  tin  1,  melts  at 200 

Wood's,  cadmium  1,  bismuth  4,  lead  2.  tin  1,  melts  at 165 

Guthrie's,  cadmium  13.29,  bismuth  47.38,  lead  19.36,  tin  19.97,  melts  at.  160 

Lead  3,  tin  5,  bismuth  8,  melts  at 208 

Lead  1,  tin  3,  bismuth  5,  melts  at 212 

Lead  1,  tin  4,  bismuth  5,  melts  at 240 

Tin  1,  bismuth  1,  melts  at 286 

Lead  2,  tin  3,  melts  at 334 

Tin  2,  bismuth  1,  melts  at 336 

Lead  1,  tin  2,  melts  at 360 

Tin  8,  bismuth  1,  melts  at 392 

Lead  2,  tin  1,  melts  at , 475 

Lead  1,  tin  1,  melts  at 466 

Lead  1.  tin  3,  melts  at 334 

Tin  3,  bisrnutli  1,  melts  at 392 

Lead  1,  bismuth  1,  melts  at 257 

Lead  1,  Tin  1,  bismuth  4,  melts  at „ 201 

Lead  5,  tin  3,  bismuth  8,  melts  at 202 

Tin  3,  bismuth  5,  melts  at , 202 

BEARING-METAL,  AL.LOYS. 

(C,  B.  Dudley,  Jour.  F.  /.,  Feb.  and  March,  1892.) 

Alloys  are  used  as  bearings  in  place  of  wrought  iron,  cast  iron,  or  steel, 
partly  because  wear  and  friction  are  believed  to  be  more  rapid  when  two 
metals  of  the  same  kind  work  together,  partly  because  the  soft  metals  are 
more  easily  worked  and  got  into  proper  shape,  and  partly  because  it  is  de- 
sirable to  use  a  soft  metal  which  will  take  the  wear  rather  than  a  hard 
metal,  which  will  wear  the  journal  more  rapidly. 

A  good  bearing-metal  must  have  five  characteristics:  (1)  It  must  be  strong 
enough  to  carry  the  load  without  distortion.  Pressures  on  car-journals  are 
frequently  as  high  as  350  to  400  Ibs.  per  square  inch. 

(2)  A  good  bearing-metal  should  not  heat  readily.    The  old  copper-tin 
bearing,  made  of  seven  parts  copper  to  one  part  tin,  is  more  apt  to  heat 
than  some  other  alloys.    In  general,  research  seems  to  show  that  the  harder 
tne  bearing-metal,  the  more  likely  it  is  to  hear. 

(3)  Good  bearing-metal  should  work  well  in  the  foundry.   Oxidation  while 
melting  causes  spongy  castings.    It  can  be  prevented  by  a  liberal  use  of 
powdered  charcoal  while  melting.    The  addition  of  \%  to  2%  of  zinc  or  a 
small  amount  of  phosphorus  greatly  aids  in  the  production  of  sound  cast- 
ings.   This  is  a  principal  element  of  value  in  phosphor-bronze. 


334 


ALLOYS. 


(4)  Good  bearing-metals  should  show  small  friction.  It  is  true  that  friction 
is  almost  wholly  a  question  of  the  lubricant  used;  but  the  metal  of  the  bear- 
ing has  certainly  some  influence. 

(5)  Other  things  being  equal,  the  best  bearing-metal  is  that  which  wears 
slowest. 

The  principal  constituents  of  bearing-metal  alloys  are  copper,  tin,  lead, 
zinc,  antimony,  iron,  and  aluminum.  The  following  table  gives  the  constitu- 
ents of  most  of  the  prominent  bearing-metals  as  analyzed  at  the  Pennsyl^ 
vania  Railroad  laboratory  at  Altoona. 

Analyses  of  Bearing-metal  Alloys. 


Metal. 

Cop- 
per. 

Tin. 

Lead. 

Zinc. 

Anti- 

Iron. 

70.20 

4.25 

14.75 

10  20 

0.55 
trace 

Anti-friction  metal  
White  metal  

1.60 

98.13 

87.92 

"i2'08' 

Car-brass  lining  
Salgee  anti-friction  

-4M 

trace 
9  91 

14.38 

84.87 
1.15 
67.73 

85  ".57 

15.10 

Graphite  bearing-metal        .   ... 

16.73 

18.83 

?   (1) 
"  (2) 

Antirnonial  lead  

75!47 

9.72 

80.69 
14.57 

Cornish  bronze  

77.83 
92.39 
trace 

9.60 
2.37 

12.40 
5.10 
83.55 
78.44 
0.31 
15.06 
12.52 

trace 

trace 

0.98 
38.40 

trace(3) 
0.07 
trace(4) 
0.65 
0.11 

Delta  metal  
*Magnolia  metal     

"ie.'45 

19.60 

American  anti-friction  metal 

Tobin  bronze 

59.00 
75.80 
76.41 
90.52 

2.16 
9.20 
10.60 
9.58 

Graney  bronze  ..        

Damascus  bronze  
Manganese  bronze  



'•  (5) 

Ajax  metal               

81.24 
55.73 

10.98 
"O.Q7 

7  27 
88!32 

'84.33 
94.40 
9.61 
15.00 

(6) 

Anti-friction  metal  
Harrington  bronze  

'42.67 
trace 

11.93 

e!o3 

'oies'" 

0.61 

Hard  lead  

Phosphor-bronze  —  
Ex.  B.  metal  

79.17 
76.80 

10.22 
8.00 



(7) 
(8) 

Other  constituents: 

(1)  No  graphite. 

(2)  Possible  trace  of  carbon. 

(3)  Trace  of  phosphorus. 

(4)  Possible  trace  of  bismuth. 


(5)  No  manganese. 

(6)  Phosphorus  or  arsenic,  0.37. 

(7)  Phosphorus,  0.94. 

(8)  Phosphorus,  0.20. 

*  Dr.  H.  C.  Torrey  says  this  analysis  is  erroneous  and  that  Magnolia 
metal  always  contains  tin. 

As  an  example  of  the  influence  of  minute  changes  in  an  alloy,  the  Har- 
rington bronze,  which  consists  of  a  minute  proportion  of  iron  in  a  copper- 
zinc  alloy,  showed  after  rolling  a  tensile  strength  of  75,000  Ibs.  and  20$  elon- 
gation in  2  inches. 

In  experimenting  on  this  subject  on  the  Pennsylvania  Railroad,  a  certain 
number  of  the  bearings  were  made  of  a  standard  bearing-metal,  and  the 
same  number  were  made  of  the  metal  to  be  tested.  These  bearings  were 
placed  on  opposite  ends  of  the  same  axle,  one  side  of  the  car  having  the 
standard  bearings,  the  other  the  experimental.  Before  going  into  service 
the  bearings  were  carefully  weighed,  and  after  a  sufficient  time  they  were 
again  weighed. 

The  standard  bearing-metal  used  is  the  "  S  bearing-metal  "  of  the  Phos- 
phor-bronze Smelting  Co.  It  contains  about  7'9.70^  copper,  9.50$  lead.  10$ 
tin,  and  0.80#  phosphorus.  A  large  number  of  experiments  have  shown  that 
the  loss  of  weight  of  a  bearing  of  this  metal  is  1  Ib.  to  each  18,000  to  25,000 
miles  travelled.  Besides  the  measurement  of  wear,  observations  were  made 
on  the  frequency  of  "  hot  boxes  "  with  the  different  metals. 

The  results  of  the  tests  for  wear,  so  far  as  given,  are  condensed  into  the 
following  table: 


BEARIKG-METAL  ALLOYS.  335 

Composition.  Rate 

Metal.  , v      of 

Copper.         Tin.  Lead.       Phos.       Arsenic.  Wear. 

Standard 79.70  10.00  9.50          0.80  100 

Copper-tin 87.50  12.50  148 

Copper- tin,  second  experiment,  same  metal 153 

Copper- tin,  third  experiment,  same  metal 147 

Arsenic-bronze  89.20  10.00  ....  ....  0.80         142 

Arsenic-bronze 79.20  10.00  7.00  ....  0.80         115 

Arsenic-bronze 79.70  10.00  9.50  0.80          101 

"K"brorize 77.00  10.50  12.50  ....  ....  92 

"  K  "  bronze,  second  experiment,  same  metal  92.7 

Alloy  "B" 77.00  8.00  15.00  ....          86.5 

The  old  copper-tin  alloy  of  7  to  1  has  repeatedly  proved  its  inferiority  to  the 
phosphor-bronze  metal.  Many  more  of  the  copper-tin  bearings  heated 
than  of  the  phosphor-bronze.  The  showing  of  these  tests  was  so  satisfac- 
tory that  phosphor-bronze  was  adopted  as  the  standard  bearing-metal  of 
the  Pennsylvania  R.R.,  and  was  used  for  a  long  time. 

The  experiments,  however,  were  continued.  It  was  found  that  arsenic 
practically  takes  the  place  of  phosphorus  in  a  copper-tin  alloy,  and  three 
tests  were  made  with  arsenic-  bronzes  as  noted  above.  As  the  proportion 
to  lead  is  increased  to  correspond  with  the  standard,  the  durability  increases 
as  well.  In  view  of  these  results  the  "  K  "  bronze  was  tried,  in  which  neither 
phosphorus  nor  arsenic  were  used,  and  in  which  the  lead  was  increased 
above  the  proportion  in  the  standard  phosphor-bronze.  The  result  was  that 
the  metal  wore  7.30$  slower  than  the  phosphor-bronze.  No  trouble  from 
heating  was  experienced  with  the  "  K  "  bronze  more  than  with  the  standard. 
Dr.  Dudley  continues: 

At  about  this  time  we  began  to  find  evidences  that  wear  of  bearing-metal 
alloys  varied  in  accordance  with  the  following  law:  "  That  alloy  which  has 
the  greatest  power  of  distortion  without  rupture  (resilience),  will  best  resist 
wear."  It  was  now  attempted  to  design  an  alloy  in  accordance  with  this 
law,  taking  first  the  proportions  of  copper  and  tin,  9^  parts  copper  to  1  of 
tin  was  settled  on  by  experiment  as  the  standard,  although  some  evidence 
since  that  time  tends  to  show  that  12  or  possibly  15  parts  copper  to  1  of  tin 
might  have  been  better.  The  influence  of  lead  on  this  copper-tin  alloy  seems 
to  be  much  the  same  as  a  still  further  diminution  of  tin.  However,  the 
tendency  of  the  metal  to  yield  under  pressure  increases  as  the  amount  of 
tin  is  diminished,  and  the  amount  of  the  lead  increased,  so  a  limit  is  set  to 
the  use  of  lead.  A  certain  amount  of  tin  is  also  necessary  to  keep  the  lead 
alloyed  with  the  copper. 

Bearings  were  cast  of  the  metal  noted  in  the  table  as  alloy  "  B,11  and  it 
wore  13.5$  slower  than  the  standard  phosphor-bronze.  This  metal  is  now 
the  standard  bearing-metal  of  the  Pennsylvania  Railroad,  being  slightly 
changed  in  composition  to  allow  the  use  of  phosphor-bronze  scrap.  The 
formula  adopted  is:  Copper,  105  Ibs.;  phosphor-bronze,  60  Ibs. ;  tin,  9%  Ibs. ; 
lead,  25J4  Ibs.  By  using  ordinary  care  in  the  foundry,  keeping  the  metal 
well  covered  with  charcoal  during  the  melting,  no  trouble  is  found  in  casting 
good  bearings  with  this  metal.  The  copper  and  the  phosphor-bronze  can  be 
put  in  the  pot  before  putting  it  in  the  melting-hole.  The  tin  and  lead  should 
be  added  after  the  pot  is  taken  from  the  fire. 

It  is  not  known  whether  the  use  of  a  little  zinc,  or  possibly  some  other 
combination,  might  not  give  still  better  results.  For  the  present,  however, 
this  alloy  is  considered  to  fulfil  the  various  conditions  required  for  good 
bearing-metal  better  than  any  other  alloy.  The  phosphor-bronze  had  an 
ultimate  tensile  strength  of  30,000  Ibs.,  with  6#  elongation,  whereas  the  alloy 
"  B  "  had  24,000  Ibs.  tensile  strength  and  \\%  elongation. 

(For  other  bearing-metals,  see  Alloys  containing  antimony,  on  next  page, 


336 


ALLOYS. 


ALLOTS  CONTAINING  ANTIMONY. 

VARIOUS  ANALYSES  OF  BABBITT  METAL,  AND  OTHER  ALLOYS  CONTAINING 
ANTIMONY. 


Tin. 

Copper 

Antimony. 

Zinc. 

Lead. 

Bismuth. 

Babbitt  metal    1     50 
for  light  duty  j  I"  =89.  3 
Harder  Babbitt  I      96 
for  bearings*  [=88.9 
Britannia  85.7 

1 
1.8 
4 
3.7 
1.0 

5  parts 
8.9perct. 
8  parts 
7.4perct. 
10.1 
16.2 
16. 
25.5 
62. 
13. 
7.1 
10. 

2.9 
1.9 
1. 

81.9 

"         81.0 

2 
4 
10 
1.5 

I* 

"         70.5 

22 

6. 

"Babbitt1'  ....        45.5 
Plate  pewter..        89.3 
White  metal...        85 

40.0 

1.8 
comotives. 

Bearings  on  Ger.  lo 

*  It  is  mixed  as  follows:  Twelve  parts  of  copper  are  first  melted  and  then 
36  parts  of  tin  are  added;  24  parts  of  antimony  are  put  in,  and  then  36  parts 
of  tin,  the  temperature  being  lowered  as  soon  as  the  copper  is  melted  in 
order  not  to  oxidize  the  tin  and  antimony,  the  surface  of  the  bath  being 
protected  from  contact  with  the  air.  The  alloy  thus  made  is  subsequently 
remeltpd  in  the  proportion  of  50  parts  of  alloy  to  100  tin.  (Joshua  Rose.) 

White-metal  Alloys.— The  folio  wing  alloys  are  used  as  lining  metals 
by  the  Eastern  Railroad  of  France  (1890): 


Number. 

1 

2 


Lead. 
..   65 
..     0 
..70 
..  80 


Antimony. 
25 

11.12 
20 
8 


Tin. 
0 

83.? 
10 
12 


Copper. 
10 

5.55 
0 
0 


No.  1  is  used  for  lining  cross-head  slides,  rod-brasses  and  axle-bearings: 
No.  2  for  lining  axle-bearings  and  connecting-rod  brasses  of  heavy  engines; 
No.  3  for  lining  eccentric  straps  and  for  bronze  slide-valves;  and  No.  4  for 
metallic  rod-packing. 

Some  of  the  best-known  white-metal  alloys  are  the  following  (Circular 
of  Hoveler  &  Dieckhaus,  London,  1893): 

Tin.       Antimony.    Lead. 
86 


1.  Parsons' , 

2.  Richards' 

3.  Babbitt's 

4.  Fentons' 

5.  French  Navy. 

6.  German  Navy 


70 

55 

16 

7 

85 


1 

15 
18 
0 
0 


2 


Copper. 
2 


Zinc. 
27 

0 

0 
79 
87« 


"There  are  engineers  who  object  to  white  metal  containing  lead  or  zinc. 
This  is,  however,  a  prejudice  quite  unfounded,  inasmuch  as  lead  and  zinc 
often  have  properties  of  great  use  in  white  alloys." 

It  is  a  further  fact  that  an  "easy  liquid"  alloy  must  not  contain  more 
than  18$  of  antimony,  which  is  an  invaluable  ingredient  of  white  metal  for 
improving  its  hardness;  but  in  no  case  must  it  exceed  that  margin,  as  this 
would  reduce  the  plasticity  of  the  compound  and  make  it  brittle. 

Hardest  alloy  of  tin  and  lead:  6  tin,  4  lead.  Hardest  of  all  tin  alloys  (?):  74 
tin,  18  antimony,  8  copper. 

Alloy  for  thin  open-work,  ornamental  castings:  Lead  2,  antimony  1. 
White  metal  for  patterns:  Lead  10,  bismuth  6,  antimony  2,  common  brass  8, 
tin  10. 

Type-metal  is  made  of  various  proportions  of  lead  and  antimony,  from 
17$  to  20$  antimony  according  to  the  hardness  desired. 

Babbitt  Metals.    (C.  R.  Tompkins,  Mechanical  News,  Jan.  1891.) 
The  practice  of  lining  journal-boxes  with  a  metal  that  is  sufficiently  fusi- 
ble to  be  melted  in  a  common  ladle  is  not  always  so  much  for  the  purpose 
of  securing  anti-friction  properties  as  for  the  convenience  and  cheapness  of 
forming  a  perfect  bearing  in  line  with  the  shaft  without  the  necessity  of 


ALLOYS   CONTAINING  ANTIMONY.  337 

boring  them.    Boxes  that  are  bored,  no  matter  how  accurate,  require  great 
care  in  fitting  and  attaching  them  to  the  frame  or  other  parts  of  a  machine. 

It  is  not  good  practice,  however,  to  use  the  shaft  for  the  purpose  of  cast- 
ing the  bearings,  especially  if  the  shaft  be  steel,  for  the  reason  that  the  hot 
metal  is  apt  to  spring  it;  the  better  plan  is  to  use  a  mandrel  of  the  same 
size  or  a  trifle  larger  for  this  purpose.  For  slow-running  journals,  where 
the  load  is  moderate,  almost  any  metal  that  may  be  conveniently  melted 
and  will  run  free  will  answer  the  purpose.  For  wearing  properties,  with  a 
moderate  speed,  there  is  probably  nothing  superior  to  pure  zinc,  but  when 
not  combined  with  some  other  metal  it  shrinks  so  much  in  cooling  that  it 
cannot  be  held  firmly  in  the  recess,  and  soon  works  loose;  and  it  lacks  those 
anti-friction  properties  which  are  necessary  in  order  to  stand  high  speed. 

For  line-shafting,  and  all  work  where  the  speed  is  not  over  300  or  400  r.  p. 
w.,  an  alloy  of  8  parts  zinc  and  2  parts  block-tin  will  not  only  wear  longer 
than  any  composition  of  this  class,  but  will  successfully  resist  the  force  of 
a  heavy  load.  The  tin  counteracts  the  shrinkage,  so  that  the  metal,  if  not 
overheated,  will  firmly  adhere  to  the  box  until  it  is  worn  out.  But  this 
mixture  does  not  possess  sufficient  anti-friction  properties  to  warrant  its  use 
in  fast-running  journals. 

Among  all  the  soft  metals  in  use  there  are  none  that  possess  greater  anti- 
friction properties  than  pure  lead;  but  lead  alone  is  impracticable,  for  it  is  so 
soft  that  it  cannot  be  retained  in  the  recess.  But  when  by  any  process  lead 
can  be  sufficiently  hardened  to  be  retained  in  the  boxes  without  materially 
injuring  its  anti-friction  properties,  there  is  no  metal  that  will  wear  longer 
in  ligrht  fast-running  journals.  With  most  of  the  best  and  most  popular 
anti-friction  metals  in  use  and  sold  under  the  name  of  the  Babbitt  metal, 
the  basis  is  lead. 

Lead  and  antimony  have  the  property  of  combining  with  each  other  in 
all  proportions  without  impairing  the  anti-friction  properties  of  either.  The 
antimony  hardens  the  lead,  and  when  mixed  in  the  proportion  of  80  parts 
lead  by  weight  with  20  parts  antimony,  no  other  known  composition  of 
metals  possesses  greater  anti-friction  or  wearing  properties,  or  will  stand  a 
higher  speed  without  heat  or  abrasion.  It  runs  f  ree  in  its  melted  state,  has 
no  shrinkage,  and  is  better  adapted  to  light  high-speeded  machinery  than 
any  other  known  metal.  Care,  however,  should  be  manifested  in  using  it, 
and  it  should  never  be  heated  beyond  a  temperature  that  will  scorch  a  dry 
pine  stick. 

Many  different  compositions  are  sold  under  the  name  of  Babbitt  metal. 
Some  are  good,  but  more  are  worthless;  while  but  very  little  genuine  Babbitt 
metal  is  sold  that  is  made  strictly  according  to  the  original  formula.  Most 
of  the  metals  sold  under  that  name  are  the  refuse  of  type-foundries  and 
other  smelting-works,  melted  and  cast  into  fancy  ingots  with  special  brands, 
and  sold  under  the  name  of  Babbitt  metal. 

It  is  difficult  at  the  present  time  to  determine  the  exact  formulas  used  by 
the  original  Babbitt,  the  inventor  of  the  recessed  box,  as  a  number  of  differ, 
ent  formulas  are  given  for  that  composition.  Tin,  copper,  and  antimony 
were  the  ingredients,  and  from  the  best  sources  of  information  the  original 
proportions  were  as  follows  : 

Another  writer  gives: 

50partstin  =  89. 3#  83. 3# 

2  parts  copper =    3.6^  8.3# 

4  parts  antimony =    1.1%  8.3# 

The  copper  was  first  melted,  and  the  antimony  added  first  and  then  about 
ten  or  fifteen  pounds  of  tin,  the  whole  kept  at  a  dull-red  heat  and  constantly 
stirred  until  the  metals  were  thoroughly  incorporated,  after  which  the 
balance  of  the  tin  was  added,  and  after  being  thoroughly  stirred  again  it 
was  then  cast  into  ingots.  When  the  copper  is  thoroughly  melted,  and 
before  the  antimony  is  added,  a  handful  of  powdered  charcoal  should  be 
thrown  into  the  crucible  to  form  a  flux,  in  order  to  exclude  the  air  and  pre- 
vent the  antimony  from  vaporizing;  otherwise  much  of  it  will  escape  in  the 
form  of  a  vapor  and  consequently  be  wasted.  This  metal,  when  carefully 
prepared,  is  probably  one  of  the  best  metals  in  use  for  lining  boxes  that  are 
subjected  to  a  heavy  weight  and  wear;  but  for  light  fast-running  journals 
the  copper  renders  it  more  susceptible  to  friction,  and  it  is  more  liable  to 
heat  than  the  metal  composed  of  lead  and  antimony  in  the  proportions  just 
given. 


338 


STKEKGTH   OF  MATERIALS. 


SOLDERS. 

Common  solders,  equal  parts  tin  and  lead;  fine  solder,  2  tin  to  1  lead;  cheap 
solder,  2  lead,  1  tin. 
Fusing-point  of  tin- lead  alloys: 


Tin  1  to  lead  25 


Tin  \y^  to  lead  1 . 


.  .334°  F. 
...340 
..  356 
...365 
...378 
...381 


Gold  solder  for  I4-carat 
1^.    Another:  Silver  145 


558°  F. 

"  1  "     "     10 541 

44  1  "     "       5 511  "  3 

44   1  44     "       3. .....482  44  4 

44  1  "     "       2 441  *4  5 

44  1  "     44       1 370  "  6 

Common  pewter  contains  4  lead  to  1  tin. 
Gold  solder:  14  parts  gold,   6  silver,  4  copper, 
gold:  25  parts  gold,  25  silver,  12^  brass,  1  zinc. 

Silver  solder:  Yellow  brass  70  parts,  zinc  7,  tin 
parts,  brass  (3  copper,  1  zinc)  73,  zinc  4. 
German-silver  solder:  Copper  38,  zinc  54,  nickel  8. 
Novel's  solders  for  aluminum: 

Tin  100  parts,  lead  5;  melts  at  536°  to  572°  F. 

44    100      "      zinc  5;  "        536   to  612 

41 1000      "      copper  10  to  15;         "        662  to  842 
44  1000      44      nickel   10  to  15;        "        662  to  842 

Novel's  solder  for  aluminum  bronze:  Tin  900  parts,  copper  100,  bismuth  2 
to  3.  It  is  claimed  that  this  solder  is  also  suitable  for  joining  aluminum  to 
copper,  brass,  zinc,  iron,  or  nickel. 

ROPES  AND  CABLES. 

STRENGTH  OF  ROPES. 

(A  S.  Newell  &  Co.,  Birkenhead.    Klein's  Translation  of  Weisbach,  vol.  iii, 
part  1,  sec.  2.) 


Hemp. 

Iron. 

Steel. 

Girth. 

Weight 
per 
Fathom. 

Girth. 

Weight 
per 
Fathom. 

Girth. 

Weight 
per 
Fathom. 

Tensile 
Strength. 

Inches. 

Pounds. 

Inches. 

Pounds. 

Inches. 

Pounds. 

Gross  tons. 

2% 

2 

1 

1 

2 

1^ 

\\^ 

1 

1 

3 

3% 

4 

1% 

2 

4 

m 

2^ 

1/^2 

l^ij 

5 

4^2 

5 

3 

6 

2  8 

31^ 

1% 

2 

7 

gi/ 

7 

21X 

4 

1M 

2^ 

8 

2/4 

4V£ 

9 

6 

9 

2% 

5  ~ 

]7/ 

3 

10 

2/^ 

5^ 

11 

gi/ 

10 

osz 

6 

2 

31^ 

12 

2% 

6V£ 

2i/j 

4 

13 

7 

12 

2% 

7 

2J4 

41^2 

14 

3 

71^ 

15 

7Lj£ 

14 

31^1 

8 

2% 

5 

16 

3/4 

gi^ 

17 

8 

16 

87! 

9 

2V^> 

5V^ 

18 

3i^j 

10 

2% 

6 

20 

8}x> 

18 

3% 

11 

294 

giz 

22 

3% 

12 

24 

91^ 

22 

3% 

13 

3M 

8 

26 

10 

26 

4 

14 

28 

11 

30 

15 

3% 

9 

30 

4% 

16 

32 

4/^ 

18 

31^ 

10 

36 

12 

34 

4% 

20 

3% 

12 

40 

STRENGTH    OF   ROPES. 
Flat  Ropes. 


339 


Hemp. 

Iron. 

Steel. 

Girth. 

Weight 
per 
Fathom  . 

Girth. 

Weight, 
per 
Fathom  . 

Girth. 

Weight 
per 
Fathom  . 

Tensile 
Strength. 

Inches. 

Pounds. 

Inches. 

Pounds. 

Inches. 

Pounds. 

Gross  tons. 

4x1^ 

20 

2^x1^ 

11 

20 

5      x  1J4 

24 

13 

23 

5V6  x  If! 

26 

2%  x  •% 

15 

27 

5%  x  iy2 

28 

3     x% 

16 

2     x^4 

10 

28 

6      x  li^ 

30 

3J4  x% 

18 

52/4  x  ^ 

11 

32 

7x1% 

36 

3J4  x% 

20 

2J4xJ4 

12 

36 

8^  x  21/6 

40 

3^x11/16 

22 

2^xU 

13 

40 

8^  x  2i/4 

45 

4     x  11/16 

25 

2%x3j 

15 

45 

9      x  2y% 

50 

4^x34 

28 

3     x% 

16 

50 

$ya  x  2% 

55 

4^x% 

32 

3^x?| 

18 

56 

10      x  2^ 

60 

4%x% 

34 

3^x% 

20 

60 

j  u       x  xy^          ou  <*^  x  %  a*  oy2  x  y%  zu  o' 

Working    Load,    Diameter,    and   Weight   of   Ropes 
Chains.    (Klein's  Weisbach,  vol.  iii,  part  1,  sec.  2,  p.  561.) 

Hemp  ropes:  d  =  diam.  of  rope.  Wire  rope:  d  =  diam.  of  wire,  n  — 
number  of  wires,  G  =  weight  per  running  foot,  k  =  permissible  load  in 
pounds  per  square  inch  of  section,  P=  permissible  load  on  rope  or  chain. 

Oval  chains:  d  =  diam  of  iron  used  ;  inside  dimensions  of  oval  1.5dand 
2.6d.  Each  link  is  a  piece  of  chain  2.6cZ  long.  G0  =  weight  of  a  single  link  = 
2.10c£3  Ibs. ;  G  =  weight  per  running  foot  =  9.73d2  Ibs. 


and 


Hempen  Rope. 

Wire  Rope. 

Dry  and  Un  tarred. 

Wet  or  Tarred. 

1420 

1160 

17000 

d  (ins.)  = 

P(lbs.)  = 
G  (Ibs  )  = 

0.03  VP 
1.28d8  =  0.00035P 

0.033  VP 
1.54d2  =  O.ON005P 

0.0087  Y  — 

13350nd»  =r  45906? 
2.91nd2=o.000218P 

fc  (Ibs.)  = 
d  (ins.)  = 
P  (Ibs  )  = 
G  (Ibs  )  = 

Open-link  Chain. 

Stud-link  Chain. 

8500 

0.0087  VP 
13350(^2  -  13606? 
9.73(22  =  0.000737P 

11400 

0.0076  VP 
17800^2  -  16606? 
10.65cZ2  =  0.0006P 

StU'l  Chains  4/3  times  as  strong  as  open-link  variety.  [This  is  contrary  to 
the  statements  of  Capt.  Beardslee,  U.  S.  N.,  in  the  report  of  the  U.  S.  test 
Board.  He  holds  that  the  open  link  is  stronger  than  the  studded  link.  See 
p.  308  ante]. 


340 


STREHGTH   OF   MATERIALS. 


STRENGTH   AND  WEIGHT   OF  WIRE   ROPE,   HEMPEN    ROPE,  AND 
CHAIN  CABLES.    (Klein's  Weisbach.) 


Breaking  Load 
in  tons  of 
2240  Ibs. 

Kind  of  Cable. 

Girth  of  Wi  re  Rope 
and  of  Hemp  Rope 
Diameter  of  Iron 
of  Chain,  inches. 

Weight  of  One 
Foot  In  length. 
Pounds. 

ITon  
8  Tons  

(  Wire  Rope 
•<  Hemp  Rope 
(  Chain 
(  Wire  Ropo 
•<  Hemp  Rope 

1.0 

2.0 

& 

5  0 

0.125 
0.177 
0.500 
0.438 
0  978 

12  Tons  

(  Chain 
j  Wire  Rope 
-\  Hemp  Rope 

^ 

7.0 

2.667 
0.753 
2  036 

16  Tons  

(Chain 
(  Wire  Rope 
K  Hemp  Rope 

11/16 
3.0 
8.0 

4.502 
1.136 
2  365 

20  Tons  .  .   .. 

/  Chain 
(  Wire  Rope 
•s  Hemp  Rope 

13/16 
3.5 
9  0 

6.169 
1.546 
3  225 

24  Tons  
30  Tons  
36  Tons  
44  Tons  

(  Chain 
Wire  Rope 
4  Hemp  Rope 
(  Chain 
(  Wire  Rope 
•<  Hemp  Rope 
(  Chain 
(Wire  Rope 
•<  Heinp  Rope 
1  Chain 
I  Wire  Rope 
•s  Hemp  Rope 

29/32 
4.0 
10.0 
31/32 
4.5 
11.0 
1.1/16 
5.0 
12.5 
1.3/16 
5.5 
14.0 

7.674 
2.043 
4.166 
8.836 
2.725 
5.000 
10.335 
3.723 
5.940 
13.01 
4.50 
6.94 

54  Tons  

(  Chain 
j  Wire  Rope 
•<  Hemp  Rope 
(  Chain 

1.5/16 
6.0 
5.0 
1.7/16 

16.00 
5.67 
7.92 
19.16 

Length  sufficient  to  provide  the  maximum  working  stress  : 

Hempen  rope,  dry  and  untarred 2855  feet. 

*'     wet  or  tarred 1975     ** 

Wire  rope 4590     " 

Open -link  chain 1360     *' 

Studchain 1660     " 

Sometimes,  when  the  depths  are  very  great,  ropes  are  given  approximately 
the  form  of  a  body  of  uniform  strength,  by  making  them  of  separate  pieces, 
whose  diameters  diminish  towards  the  lower  end.  It  is  evident  that  by  this 
means  the  tensions  in  the  fibres  caused  by  the  rope's  own  weight  can  be 
considerably  diminished. 

Rope  for  Hoisting  or  Transmission.  Manila  Rope 
(C.  W.  Hunt  Company,  New  York  J — Rope  used  for  hoisting  or  for  trans- 
mission of  power  is  subjected  to  a  very  severe  test.  Ordinary  rope  chafes 
and  grinds  to  powder  in  the  centre,  while  the  exterior  may  look  as  though 
it  was  little  worn. 

In  bending  a  rope  over  a  sheave,  the  strands  and  the  yarns  of  these  strands 
slide  a  small  distance  upon  each  other,  causing  friction,  and  wear  the  rope 
internally. 

The  "  Stevedore  "  rope  used  by  the  C.  W.  Hunt  Co.  is  made  by  lubricating 
the,  fibres  with  plumbago,  mixed  with  sufficient  tallow  to  hold  it  in  position. 
This  lubricates  the  yarns  of  the  rope,  and  prevents  internal  chafing  and 
wear.  After  running  a  short  time  the  exterior  of  the  rope  gets  compressed 
and  coated  with  the  lubricant. 

In  manufacturing  rope,  the  fibres  are  first  spun  into  a  yarn,  this  yarn 
being  twisted  in  a  direction  called  "right  hand."  From  20  to  80  of  these 
yarns,  depending  on  the  size  of  the  rope,  are  then  put  together  and  twisted 
in  the  opposite  direction,  or  "left  hand,"  into  a  strand.  Three  of  these 


STRENGTH  OF   ROPES.  341 

strands,  for  a  3-strand,  or  four  for  a  4-strand  rope,  are  then  twisted 
together,  the  twist  being  again  in  the  "right  hand  "  direction.  When  the 
strand  is  twisted,  it  untwists  each  of  the  threads,  and  when  the  three 
strands  are  twisted  together  into  rope,  it  untwists  the  strands,  but  again 
twists  up  the  threads.  It  is  this  opposite  twist  that  keeps  the  rope  in  its 
proper  form.  When  a  weight  is  hung  on  the  end  of  a  rope,  the  tendency  is 
for  the  rope  to  untwist,  and  become  longer.  In  untwisting  the  rope,  it 
would  twist  the  threads  up,  and  the  weight  will  revolve  umil  the  strain  of 
the  untwisting  strands  just  equals  the  strain  of  the  threads  being  twisted 
tighter.  In  making  a  rope  it  is  impossible  to  make  these  strains  exactly 
balance  each  other.  It  is  this  fact  that  makes  it  necessary  to  take  out  the 
"turns"  in  a  new  rope,  that  is,  untwist  it  when  it  is  put  at  work.  The 
proper  twist  that  should  be  put  in  the  threads  has  been  ascertained  approx- 
imately by  experience. 

The  amount  of  work  that  the  rope  will  do  varies  greatly.  It  depends  not 
only  on  the  quality  of  the  fibre  and  the  method  of  laying  up  the  rope,  but 
also  on  the  kind  of  weather  when  the  rope  is  used,  the  blocks  or  sheaves 
over  which  it  is  run,  and  the  strain  in  proportion  to  the  strain  put  upon  the 
rope.  The  principal  wear  comes  in  practice  from  defective  or  badly  set 
sheaves,  from  excess  of  load  and  exposure  to  storms. 

The  loads  put  upon  the  rope  should  not  exceed  those  given  in  the  tables, 
for  the  most  economical  wear.  The  indications  of  excessive  load  will  be  the 
twist  coming  out  of  the  rope,  or  one  of  the  strands  slipping  out  of  its  proper 
position.  A  certain  amount  of  twist  comes  out  in  using  ir  the  first  day  or 
two,  but  after  that  the  rope  should  remain  substantially  the  same.  If  it 
does  not,  the  load  is  too  great  for  the  durability  of  the  rope.  If  the  rope 
wears  on  the  outside,  and  is  good  on  the  inside,  it  shows  that  it  has  been 
chafed  in  running  over  the  pulleys  or  sheaves.  If  the  blocks  are  very  small, 
it  will  increase  the  sliding  of  the  strands  and  threads,  and  result  in  a  more 
rapid  internal  wear.  Rope  made  for  hoisting  and  for  rope  transmission  is 
usually  made  with  four  strands,  as  experience  has  shown  this  to  be  the  most 
serviceable. 

The  strength  and  weight  of  "  stevedore  "  rope  is  estimated  as  follows: 

Breaking  strength  in  pounds  =   720  (circumference  in  inches)2; 
Weight  in  pounds  per  foot      —  .032  (circumference  in  inches)2. 

The  Technical  Words  relating  to  Cordage  most  frequently 
heard  are: 

YARN. — Fibres  twisted  together. 

THREAD.— Two  or  more  small  yarns  twisted  together. 

STRING.— The  same  as  a  thread  but  a  little  larger  yarns. 

STRAND. — Two  or  more  large  yarns  twisted  together. 

CORD.— Several  threads  twisted  together. 

ROPE. — Several  strands  twisted  together. 

HAWSER.— A  rope  of  three  strands. 

SHROUD-LAID. — A  rope  of  four  strands. 

CABLE.— Three  hawsers  twisted  together. 

YARNS  are  laid  up  left-handed  into  strands. 

STRANDS  are  laid  up  right-handed  into  rope. 

HAWSERS  are  laid  up  left-handed  into  a  cable. 
A  rope  is  : 

LAID  by  twisting  strands  together  in  making  the  rope. 

SPLICED  by  joining  to  another  rope  by  interweaving  the  strands. 

WHIPPED.— By  winding  a  string  around  the  end  to  prevent  untwisting. 

SERVED. — When  covered  by  winding  a  yarn  continuously  and  tightly 
around  it. 

PARCELED. — By  wrapping  with  canvas. 

SEIZED.— When  two  parts  are  bound  together  by  a  yarn,  thread  or  string. 

PAYED.— When  painted,  tarred  or  greased  to  resist  wet. 

HAUL. — To  pull  on  a  rope. 

TAUT — Drawn  tight  or  strained. 

Splicing  of  Ropes. — The  splice  in  a  transmission  rope  is  not  only  the 
weakest  part  of  the  rope  but  is  the  first  part  to  fail  when  the  rope  is  worn 
out.  If  the  rope  is  larger  at  the  splice,  the  projecting  part  will  wear  on  the 
pulleys  and  the  rope  fail  from  the  cutting  off  of  the  strands.  The  following 
directions  are  given  for  splicing  a  4-strand  rope. 

The  engravings  show  each  successive  operation  in  splicing  a  1%  inch 
manila  rope.  Each  engraving  was  made  from  a  full-size  speqimeq, 


342 


STEEKGTH  OF   MATEBIALS. 


FIG.  81. 
SPLICING  OF  ROPES. 


SPLICING   OF   ROPES. 


343 


Tie  a  piece  of  twine,  9  and  10,  around  the  rope  to  be  spliced,  about  6  feet 
from  each  end.  Then  unlay  the  strands  of  each  end -back  to  the  twine. 

Butt  the  ropes  together  and  twist  each  corresponding  pair  of  strands 
loosely,  to  keep  them  from  being  tangled,  as  shown  in  Fig.  78. 

The  twine  10  is  now  cut,  and  the  strand  8  unlaid  and  strand  7  carefully  laid 
in  its  place  for  a  distance  of  four  and  a  half  feet  from  the  junction. 

The  strand  0  is  next  unlaid  about  one  and  a  half  feet  and  strand  5  laid  in 
its  place. 

The  ends  of  the  cores  are  now  cut  off  so  they  just  meet. 

Unlay  strand  1  four  and  a  half  feet,  laying  strand  2  in  its  place. 

Unlay  strand  3  one  and  a  half  feet,  laying  in  strand  4. 

Cut  all  the  strands  off  to  a  length  of  about  twenty  inches,  for  convenience 
in  manipulation. 

The  rope  now  assumes  the  form  shown  in  Fig.  79  with  the  meeting  points 
of  the  strands  three  feet  apart. 

Each  pair  of  strands  is  successively  subjected  to  the  following  operation: 

From  the  point  of  meeting  of  the  strands  8  and  7,  unlay  each  one  three 
turns;  split  both  the  strand  8  and  the  strand  7  in  halves  as  far  back  as  they 
are  now  unlaid  and  "  whip  "  the  end  of  each  half  strand  with  a  small 
piece  of  twine. 

The  half  of  the  strand  7  is  now  laid  in  three  turns  and  the  half  of  8  also 
laid  in  three  turns.  The  half  strands  now  meet  and  are  tied  in  a  simple 
knot,  11,  Fig.  80,  making  the  rope  at  this  point  its  original  size. 

The  rope  is  now  opened  with  a  marlin  spike  and  the  half  strand  of  7 
worked  around  the  half  strand  of  8  by  passing  the  end  of  the  half  strand  7 
through  the  rope,  as  shown  in  the  engraving,  drawn  taut  and  again  worked 
around  this  half  strand  until  it  reaches  the  half  strand  13  that  was  not  laid 
in.  This  half  strand  13  is  now  split,  and  the  half  strand  7  drawn  through 
the  opening  thus  made,  and  then  tucked  under  the  two  adjacent  strands,  as 
shown  in  Fig.  81.  The  other  half  of  the  strand  8  is  now  wound  around  the 
other  half  strand  7  in  the  same  manner.  After  each  pair  of  strands  has 
been  treated  in  this  manner,  the  ends  are  cut  off  at  12,  leaving  them  about 
four  inches  long.  After  a  few  days'  wear  they  will  draw  imo  (he  body  of  the 
rope  or  wear  off.  so  that  the  locality  of  the  splice  can  scarcely  be  detected. 

Coal  Hoisting.  (0.  W.  Hunt  Co.).— The  amount  of  coal  that  can  be 
hoisted  with  a  rope  varies  greatly.  Under  the  ordinary  conditions  of  use 
a  rope  hoists  from  5000  to  8000  tons.  Where  the  circumstances  are  more 
favorable,  the  amounts  run  up  frequently  to  12,000  or  15,000  tons,  occasion- 
ally to  20,000  and  in  one  case  32,400  tons  to  a  single  fall. 

When  a  hoisting  rope  is  first  put  in  use,  it  is  likely  from  the  strain  put  upon 
it  to  twist  up  when  the  block  is  loosened  from  the  tub.  This  occurs  in  the 
first  day  or  two  only.  The  rope  should  then  be  taken  down  and  the 
"  turns  "  taken  out  of  the  rope.  When  put  up  again  the  rope  should  give 
no  further  trouble  until  worn  out. 

It  is  necessary  that  the  rope  should  be  much  larger  than  is  needed  to  bear 
the  strain  from  the  load. 

Practical  experience  for  many  years  has  substantially  settled  the  most 
economical  size  of  rope  to  be  used  which  is  given  in  the  table  below. 

Hoisting  ropes  are  not  spliced,  as  it  is  difficult  to  make  a  splice  that  will 
not  pull  out  while  running  over  the  sheaves,  and  the  increased  wear  to  be 
obtained  in  this  way  is  very  small. 

Coal  is  usually  hoisted  with  what  is  commonly  called  a  "  double  whip;  " 
that  is,  with  a  running  block  that  is  attached  to  the  tub  which  reduces  the 
strain  on  the  rope  to  approximately  one  half  the  weight  of  the  load  hoisted. 
The  following  table  gives  the  usual  sizes  of  hoisting  rope  and  the  proper 
working  strain: 

Stevedore  Hoisting-rope. 
C.  W.  Hunt  Co. 


Circumference  of 
the  rope  in  ins. 

Proper  Working 
Strain  on  the  Rope 
in  Ibs. 

Nominal  size  of 
Coal  tubs.    Double 
whip. 

Approximate 
Weight  of  a  Coil, 
in  Ibs. 

3 

sya 

g 

350 
500 
650 
800 
1000 

1/6  to  1/5  tons. 

1/5  "  2    « 

360 

480 
650 
830 
960 

rope  is  ordered  by  circumference,  transmission  rope  by  diameter, 


344 


STRENGTH   OF   MATERIALS. 


Weight  and  Strength  of  Manila  Cordage. 

Dodge  Manufacturing  Co. 


C 

S 

1    | 

0& 

fe 

1     | 

c& 

Ss 

4-1    ffi  "~H 

O  g  S 

§«. 

I 
1 

is 

*o  £.2 

a 

11 

fig 

11! 

.2a 

"1 

f|| 

a  ft 

|fl 

*»&4  § 

S  >»o 

"S 

*'a 

•  '53  fe  § 

2  >»o 

"S 

33  '" 

£   S 

55  -°  A 

fc 

S'" 

^   a 

OQ'0'2' 

£ 

3/16 

12 

540 

50' 

5/16 

310 

16,000 

'  ii' 

M 

18 

780 

33'   4" 

% 

346 

18,062 

:      8 

5/16 

24 

1,000 

25 

V*> 

390 

20,250 

6 

% 

30 

1,280 

20 

9/16 

435 

22,500 

5 

7/16 

37 

1,562 

17    8 

480 

25,000 

3 

/^s 

46 

2,250 

13 

1% 

581 

30,250 

9/16 

65 

3,062 

9    3 

2 

678 

36,000 

10% 

ftk 

80 

4,000 

7    6 

2^ 

797 

42,250 

9 

M 

98 

5,000 

6 

2% 

920 

49,000 

13/16 

120 

6,250 

5 

$9 

1,106 

56,250 

?£ 

% 

142 

7,500 

4    3 

2% 

1,265 

64,000 

5^ 

j 

170 

9,000 

3    6 

%% 

1,420 

72,250 

5 

1  1/16 

200 

10,500 

3 

3 

1,572 

81,000 

4^ 

l/^ 

230 

12,250 

2    7 

3/4j 

1,760 

90,250 

4 

1M 

271 

14,000 

2    3 

3% 

1,951 

100,000 

3H 

Diam. 
in. 

Circum- 
ference, 
in. 

Ultimate 
Strength. 
Ibs. 

Coeffi- 
cient. 

Diam. 
in. 

Circum- 
ference. 
in. 

Ultimate 
Strength. 
Ibs. 

Coeffi- 
cient. 

1 

m 

I 

3  4 

3^ 

2,000 
3,250 
4,000 
6,000 
7,000 
9,350 

900 
845 
820 
790 
780 
765 

2  8 

334 

4k 

f 
F 

10,000 
13,000 
15,000 
18,200 
21,750 
25,000 

760 
745 
735 
725 
712 
700 

For  rope-driving  Mr.  Hunt  recommends  that  the  working  strain  should 
not  exceed  1/20  of  the  ultimate  breaking  strain.  For  further  data  on  ropes 
see  "  Rope-driving." 

Knots.— A  great  number  of  knots  have  been  devised  of  which  a  few 
only  are  illustrated,  but  those  selected  are  the  most  frequently  used.  In 
the  cuts.  Fig.  82,  they  are  shown  open,  or  before  being  drawn  taut,  in  order 
to  show  the  position  of  the  parts.  The  names  usually  given  to  them  are: 

A.  Bight  of  a  rope. 

B.  Simple  or  Overhand  knot. 
Figure  8  knot. 

Double  knot. 
Boat  knot. 
Bowline,  first  step. 
Bowline,  second  step. 
Bowline  completed. 
Square  or  reef  knot. 


C. 

D. 

E. 

F. 

G. 

H. 

I.  . 

J.     Sheet  bend  or  weaver's  knot. 

K.    Sheet  bend  with  a  toggle. 

L.     Carrick  bend. 

M.    Stevedore  knot  completed. 

N.    Stevedore  knot  commenced. 

Q.     Slip  knot. 


T. 
U. 
V. 


P.    Flemish  loop. 
Q.    Chain  knot  with  toggle. 
R.    Half-hitch. 
S.     Timber-hitch. 
Clove  hitch. 
Rolling-hitch. 

Timber-hitch  and  half-hitch. 
W.   Blackwall-hitch. 
X.    Fisherman's  bend. 
Y.    Round  turn  and  half-hitch. 
Z.     Wall  knot  commenced. 
A  A.        "        "•    completed. 
B  B.    Wall  knot  crown  commenced. 
C  C.  completed. 


KHOTS. 


345 


The  principle  of  a  knot  is  that  no  two  parts,  which  would  move  in  the 
same  direction  if  the  rope  were  to  slip,  should  lay  along  side  of  and  touch- 
ing each  other. 

The  bowline  is  one  of  the  most  useful  knots,  it  will  not  slip,  and  after 
being  strained  is  easily  untied.  Commence  by  making  a  bight  in  the  rope, 
then  put  the  end  through  the  bight  and  under  the  standing  part  as  shown  in 
G,  then  pass  the  end  again  through  the  bight,  and  haul  tight. 

The  square  or  reef  knot  must  not  be  mistaken  for  the  "  granny  "  knot 
that  slips  under  a  strain.  Knots  H,  K  and  M  are  easily  untied  after  being 
under  strain.  The  knot  M  is  useful  when  the  rope  passes  through  an  eye 
and  is  held  by  the  knot,  as  it  will  not  slip  and  is  easily  untied  after  being 
strained. 

ABC  0  E 


FIG.  82.— KNOTS. 

The  timber  hitch  S  looks  as  though  it  would  give  way,  but  it  will  not;  the 
greater  the  strain  the  tighter  it  will  hold.  The  wall  knot  looks  complicated, 
but  is  easily  made  by  proceeding  as  follows:  Form  a  bight  with  strand  1 
and  pass  the  strand  2  around  the  end  of  it,  and  the  strand  3  round  the  end 
of  2  and  then  through  the  bight  of  1  as  shown  in  the  cut  Z.  Haul  the  ends 
taut  when  the  appearance  is  as  shown  in  AA.  The  end  of  the  strand  1  is 
now  laid  over  the  centre  of  the  knot,  strand  2  laid  over  1  and  3  over  2,  when 
the  end  of  3  is  passed  through  the  bight  of  1  as  shown  in  BB.  Haul  all  the 
strands  taut  as  shown  in  CC. 


346 


STRENGTH   OF   MATERIALS. 


To  Splice  a  "Wire  Rope.— The  tools  required  will  be  a  small  marline 
spike,  nipping  cutters,  and  either  clamps  or  a  small  hernp-rope  sling  with 
which  to  wrap  around  and  untwist  the  rope.  If  a  bench-vise  is  accessible 
it  will  be  found  convenient. 

In  splicing  rope,  a  certain  length  is  used  up  in  making  the  splice.  An 
allowance  of  not  less  than  16  feet  for  J^  inch  rope,  and  proportionately 
longer  for  larger  sizes,  must  be  added  to  the  length  of  an  endless  rope  in 
ordering. 

Having  measured,  carefully,  the  length  the  rope  should  be  after  splic- 
ing, and  marked  the  points  M  and  M',  Fig.  83,  unlay  the  strands  from  each 
end  E  and  E'  to  M  and  M'  and  cut  off  the  centre  at  M  and  M',  and  then: 

(1).  Interlock  the  six  unlaid  strands  of  each  end  alternately  and  draw 
them  together  so  that  the  points  M  and  M'  meet,  as  in  Fig.  84. 

(2).  Unlay  a  strand  from  one  end,  and  following  the  unlay  closely,  lay  into 
the  seam  or  groove  it  opens,  the  strand  opposite  it  belonging  tb  the  other 
end  of  the  rope,  until  within  a  length  equal  to  three  or  four  times  the  length 
of  one  lay  of  the  rope,  and  cut  the  other  strand  to  about  the  same  length 
from  the  point  of  meeting  as  at  A,  Fig.  85. 

(3).  Unlay  the  adjacent  strand  in  the  opposite  direction,  and  following  the 
unlay  closely,  lay  in  its  place  the  corresponding  opposite  strand,  cutting  the 
ends  as  described  before  at  B,  Fig.  85. 

There  are  now  four  strands  laid  in  place  terminating  at  A  and  B,  with  the 
eight  remaining  at  MM',  as  in  Fig.  85. 

It  will  be  well  after  laying  each  pair  of  strands  to  tie  them  temporarily  at 
the  points  A  and  B. 

Pursue  the  same  course  with  the  remaining  four  pairs  of  opposite  strands, 


FIG.  83. 


FIG.  86. 

SPLICING  WIRE  ROPE. 
stopping  each  pair  about  eight  or  ten  turns  of  the  rope  short  of  the  preced- 


ing  pair,  and  cutting  the  ends  as  before. 
We  now 


. 

have  all  the  strands  laid  in  their  proper  places  with  their  respect- 
ive ends  passing  each  other,  as  in  Fig.  86. 

All  methods  of  rope-splicing  are  identical  to  this  point:  their  variety  con- 
sists in  the  method  of  tucking  the  ends.  The  one  given  below  is  the  one 
most  generally  practiced. 

Clamp  the  rope  either  in  a  vise  at  a  point  to  the  left  of  A,  Fig.  86,  and  by  a 
hand-clamp  applied  near  A,  open  up  the  rope  by  untwisting  sufficiently  to 
cut  the  core  at  A,  and  seizing  it  with  the  nippers,  let  an  assistant  draw  it 
put  slowly,  you  following  it  closely,  crowding  the  strand  in  its  place  until  it 
is  all  laid  in.  Cut  the  core  where  the  strand  ends,  and  push  the  end  back 
into  its  place.  Remove  the  clamps  and  let  the  rope  close  together  around  it. 
Draw  out  the  core  in  the  opposite  direction  and  lay  the  other  strand  in  the 
centre  of  the  rope,  in  the  same  manner.  Repeat  the  operation  at  the  five 
remaining  points,  and  hammer  the  rope  lightly  at  the  points  where  the  ends 
pass  each  other  at  A,  A,  B,  B,  etc.,  with  small  wooden  mallets,  and  the 
splice  is  complete,  as  shown  in  Fig.  87. 

If  a  clamp  and  vise  are  not  obtainable,  two  rope  slings  and  short  wooden 
levers  may  be  used  to  untwist  and  open  up  the  rope. 

A  rope  spliced  as  above  will  be  nearly  as  strong  as  the  original  rope  and 
smooth  everywhere.  After  running  a  few  days,  the  splice,  if  well  made, 
cannot  be  found  except  by  close  examination. 

The  above  instructions  have  been  adopted  by  the  leading  rope  manufac- 
turers of  America. 


HELICAL   STEEL   SPRINGS.  347 

SPRING-S. 

Definitions.  -A  spiral  spring  is  one  which  is  wound  around  a  fixed 
point  or  centre,  and  continually  receding  from  it  like  a  watch  spring.  A 
helical  spring  is  one  which  is  wound  around  an  arbor,  and  at  the  same  time 
advancing  like  the  thread  of  a  screw.  An  elliptical  or  laminated  spring  is 
made  of  flat  bars,  plates,  or  "leaves,"  of  regularly  varying  lengths,  super- 
posed one  upon  the  other. 

Laminated  Steel  Springs.— Clark  (Rules,  Tables  and  Data)  gives 
the  following  from  his  work  on  Railway  Machinery,  1855: 

_  1.66L3  .  bt*n .  _1.66L3. 

:     bt*n  '  ~  '  ~~ 


A  =  elasticity,  or  deflection,  in  sixteenths  of  an  inch  per  ton  of  load, 
s  =  working  strength,  or  load,  in  tons  (2240  Ibs.), 
L  =  span,  when  loaded,  in  inches, 
6  =  breadth  of  plates,  in  inches,  taken  as  uniform, 
£  =  thickness  of  plates,  in  sixteenths  of  an  inch, 
n  =  number  of  plates. 

NOTE.— The  span  and  the  elasticity  are  those  due  to  the  spring  when 
weighted. 

2.  When  extra  thick  back  and  short  plates  are  used,  they  must  be  replaced 
by  an  equivalent  number  of  plates  of  the  ruling  thickness,  prior  to  the  em- 
ployment of  the  first  two  formulae.     This  is  found  by  multiplying  the  num- 
ber of  extra  thick  plates  by  the  cube  of  their  thickness,  and  dividing  by  the 
cube  of  the  ruling  thickness.    Conversely,  the  number  of  plates  of  the  ruling 
thickness  given  by  the  third  formula,  required  to  be  deducted  and  replaced 
by  a  given  number  of  extra  thick  plates,  are  found  by  the  same  calculation. 

3.  It  is  assumed  that  the  plates  are  similarly  and'  regularly  formed,  and 
that  they  are  of  uniform  breadth,  and  but  slightly  taper  at  the  ends. 

Reuleaux's  Constructor  gives  for  semi-elliptic  springs: 

Snbh*  6P/3 

=  — fiT~         a          f  =  F~7)T3 ' 

S  =  max.  direct  fibre-strain  in  plate;         b  =  width  of  plates; 
n  =  number  of  plates  in  spring;  h  =  thickness  of  plates; 

/  —  one  half  length  of  spring;  /  =  deflection  of  end  of  spring; 

P  =  load  on  one  end  of  spring;  E  =  modulus  of  direct  elasticity. 

The  above  formula  for  deflection  can  be  relied  upon  where  all  the  plates 
of  the  spring  are  regularly  shortened;  but  in  semi-elliptic  springs,  as  used, 
there  are  generally  several  plates  extending  the  full  length  of  the  spring, 
and  the  proportion  of  these  long  plates  to  the  whole  number  is  usually  about 

one  fourth.    In  such  cases/  =  "','  . ,  Q.    (G.  R.  Henderson,  Trans.  A.  S.  M.  E., 

Enbh3 
vol.  xvi.) 

In  order  to  compare  the  formulae  of  Reuleaux  and  Clark  we  may  make 
the  following  substitutions  in  the  latter:  s  in  tons  =  Pin  Ibs.  -5-  1120;  AS  — 
!(»/;  L  =  2l;  t  —  16/i ;  then 

-Ifif-      1.66X8Z3XP*  ,  PI3 

f  ~  4096  X  1120  X  nbW  *  ~  5,527,133' 

which  corresponds  with  Reuleaux's  formula  for  deflection  if  in  the  latter  we 
take  E  =  33,162,800. 


P  256iiM2  I2.687nfe/i2 

Also        s  =  im^ii^l>r    whence     p=     —i ' 

which  corresponds  with  Reuleaux's  formula  for  working  load  when  Sin  the 
latter  is  taken  at  76,120. 

The  value  of  E  is  usually  taken  at  30,000,000  and  S  at  80,000,  in  which  case 
Reuleaux's  formulae  become 

13.333n&/i2  P/3 

— 


Helical  Steel  Springs.— Clark  quotes  the  following  from  the  report 
on  Safety  Valves  (Trans.  Inst.  Erigrs.  and  Shipbuilders  in  Scotland,  1874-5); 


348  SPRINGS. 

E  —  compression  or  extension  of  one  coil  in  inches, 

d  =  diameter  from  centre  to  centre  of  steel  bar  constituting  the  spring, 

in  inches, 

w  =  weight  applied,  in  pounds, 
D  =  diameter,  or  side  of  the  square,  of  the  steel  bar,  in  sixteenths  of  an 

inch, 
C  =  a  constant,  which  may  be  taken  as  22  for  round  steel  and  30  for 

square  steel. 

NOTE.—  The  deflection  .EJfor  one  coil  is  to  be  multiplied  by  the  number  of 
free  coils,  to  obtain  the  total  deflection  for  a  given  spring. 

The  relation  between  the  safe  load,  size  of  steel,  and  diameter  of  coil,  may 
be  taken  for  practical  purposes  as  follows: 

—,  for  round  steel; 


Rankine's  Machinery  and  Mill  work,  p.  390,  gives  the  following: 
JT   _    cd*  w   =  .196/d».  v    =  18.566n/r», 

v    ~~  Q4nrs  *  r-  cd 

—^  =  greatest  safe  sudden  load. 

In  which  d  is  the  diameter  of  wire  in  inches;  c  a  co-efficient  of  transverse 
elasticity  of  wire,  say  10,500,000  to  12,000,000  for  charcoal  iron  wire  and  steel; 
r  radius  to  centre  of  wire  in  coil;  n  effective  number  of  coils;  /  greatest  safe 
shearing  stress,  say  30,000;  W  any  load  not  exceeding  greatest  safe  load; 
v  corresponding  extension  or  compression;  Wj  greatest  safe  load;  and  vt 
greatest  safe  steady  extension  or  compression. 

If  the  wire  is  square,  of  the  dimensions  d  x  d,  the  load  for  a  given  deflec- 
tion is  greater  than  for  a  round  wire  of  the  diameter  d  in  the  ratio  of  2.81  to 
1.96  or  of  1  .43  to  1,  or  of  10  to  7,  nearly. 

Wilson  Hartnell  (Proc.  Inst.  M.  E.,  1882,  p.  426),  says:  The  size  of  a  spiral 
spring  may  be  calculated  from  the  formula  on  page  304  of  "  Rankine's  Use- 
ful Rules  and  Tables";  but  the  experience  with  gaiter's  springs  has  shown 
that  the  safe  limit  of  stress  is  more  than  twice  as  great  as  there  given, 
namely  60,000  to  70,000  Ibs.  per  square  inch  of  section  with  %  inch  wire,  and 
about  50,000  with  ^  inch  wire.  Hence  the  work  that  can  be  done  by 
springs  of  wire  is  four  or  five  times  as  great  as  Rankine  allows. 

For  %  inch  wire  and  under, 

12,000  X  (diam.  of  wire)3 
Maximum  load  m  Ibs.  =    Mean  raditls  of  springs  ; 

Weight  in  Ibs.  to  deflect  spring  1  in.  *  N  J^  cVifsT(rad.)3- 

The  work  in  foot-pounds  that  can  be  stored  up  in  a  spiral  spring  would 
lift  it  above  50  ft. 

In  a  few  rough  experiments  made  with  Salter's  springs  the  coefficient  of 
rigiditv  was  noticed  to  be  12,600,000  to  13,700,000  with  y±  inch  wire;  11,000,000 
for  11/3-3  inch  :  and  10,600,000  to  10,900,000  for  %  inch  wire. 

Helical  Springs.—  J.  Begtrup,  in  the  American  Machinist  of  Aug. 
18,  1892,  gives  formulas  for  the  deflection  and  carrying  capacity  of  helical 
springs  of  round  and  square  steel,  as  follow: 


p(p 
• 


V  for  round  steel. 


V  for  square  steel. 


HELICAL   SPRINGS. 


349 


W  =  carrying  capacity  in  pounds, 

<S  =  greatest  tensile  stress  per  square  inch  of  material, 
d  =  diameter  of  steel, 
D  =  outside  diameter  of  coil, 
F  =  deflection  of  one  coil, 
E  =  torsional  modulus  of  elasticity, 
P  =  load  in  pounds. 

From  these  formulas  the  following  table  has  been  calculated  by  Mr.  Beg- 
trup.  A  spring  being  made  of  an  elastic  material,  and  of  such  shape  as  to 
allow  a  great  amount  of  deflection,  will  not  be  affected  by  sudden  shocks  or 
blows  to  the  same  extent  as  a  rigid  body,  and  a  factor  of  safety  very  much 
less  than  for  rigid  constructions  may  be  used. 

HOW  TO  USE  THE  TABLE. 

When  designing  a  spring  for  continuous  work,  as  a  car  spring,  use  a 
greater  factor  of  safety  than  in  the  table;  for  intermittent  working,  as  in 
a  steam-engine  governor  or  safety  valve,  use  figures  given  in  table;  for 
square  steel  multiply  line  Wby  1.2  and  line  jPby  .59. 

Example  1. — How  much  will  a  spring  of  %"  round  steel  and  3"  outside 
diameter  carry  with  safety  ?  In  the  line  headed  D  we  find  3,  and  right  un- 
derneath 473,  which  is  the  weight  it  will  carry  with  safety.  How  many  coils 
must  this  spring,  have  so  as  to  deflect  3"  with  a  load  of  400  pounds  ?  Assum- 
ing a  modulus  of  elasticity  of  12  millions  we  find  in  the  centre  line  headed 
F  the  figure  .0610;  this  is  deflection  of  one  coil  for  a  load  of  100  pounds; 
therefore  .061  X  4  =  .244"  is  deflection  of  one  coil  for  400  pounds  load,  and  3 
-i-  .244  =  12J/2  is  the  number  of  coils  wanted.  This  spring  will  therefore  be 
4'W  long  when  closed,  counting  working  coils  only,  and  stretch  to  7%". 

Example  2. — A  spring  3*4"  outside  diameter  of  7/16"  steel  is  wound  close; 
how  much  can  it  be  extended  without  exceeding  the  limit  of  safety  ?  We 
find  maximum  safe  load  for  this  spring  to  be  702  pounds,  and  deflection  of 
one  coil  for  100  pounds  load  .0405  inches;  therefore  7.02  x  .0405  =  .284"  is  the 
greatest  admissible  opening  between  coils.  We  may  thus,  without  know- 
ing the  load,  ascertain  whether  a  spring  is  overloaded  or  not. 

Carrying  Capacity  and  Deflection  of  Helical  Springs  of 
Round  Steel. 

d  =  diameter  of  steel.  D  =  outside  diameter  of  coil.  W  =  safe  working 
load  in  pounds— tensile  stress  not  exceeding  60,000  pounds  per  square  inch. 
F  —  deflection  by  a  load  of  100  pounds  of  one  coil,  and  a  modulus  of  elasti- 
city of  10,  12  and  14  millions  respectively.  The  ultimate  carrying  capacity 
will  be  about  twice  the  safe  load. 


is 
ni 

'S 

D 
W 

-\ 

.25 
35 
.0276 
.0236 
.0197 

.50 
15 
.3588 
.3075 
.2562 

.75 
9 
1.433 

1.228 
1.023 

1.00 

3!  562 
3.053 
2.544 

1.25 
5 

7.250 
6.214 
5.178 

1.50 
4.5 

12.88 
11.04 
9.200 

1.75 

3.8 

20.85 
17.87 
14.89 

2.00 
3.3 
31.57 
27.06 

22.55 





Is 

1 

D 
W 

*\ 

.50 
107 
.0206 
.0176 
.0147 

.75 
65 
.0937 
.0804 
.0670 

1.00 
46 
.2556 
.2191 
.182 

1.25 
36 
.5412 
.4639 
.3866 

1.50 
29 

.9856 
.8448 
.7040 

1.75 
25 
1  .624 
1.392 
1.160 

2  00 
22 

2.492 
2.136 
1.780 

2.25 
19 
3.625 
3.107 

2.589 

2.50 
17 
5.056 
4.334 
3.612 

it. 

nl 

ts 

3J 

11 
S3 

D 
W 

'1 

D 
W 

-1 

75 

241 
.0137 
.0118 
.0098 

1.00 
167 
.0408 
.0350 
.0292 

1.25 
128 
.0907 

.0778 
.0648 

1.50 
104 
.1703 
.1460 
.1217 

1.75 
88 
.2866 
.2457 
.2048 

2.00 
75 
.4466 

.3828 
.3190 

2.25 
66 
.6571 
.5632 
.4693 

2.50 
59 
.9249 
.7928 
.6607 

2.75 
53 
1.256 
1.077 
.8975 

3.00 
49 
1.660 
1.423 

1.186 



1.25 
368 
'.0199 
.0171 
.0142 

1.50 
294 
.0389 
.0333 
.0278 

1.75 
r  245 
r  .0672 
.0576 
.0480 

2.00 
210 
.1067 
.0914 
.0762 

2.25 
184 
.1593 
.1365 
.1137 

2.50 
164 
•  .2270 
.1944 
.1610 

2.75 

147 
.3109 
.2665 
.2221 

3.00 
134 
.4139 
.3548 
.2957 

3.25 
123 

.5375 
.4607 
.3839 

3.50 
113 
.6835 

.5859 
.4883 

350 


SPKIKGS. 


Carrying  Capacity  and  Reflection  of  Helical  Springs  of 
Round  Steel.— (Continued). 


fb 

s 

II 
•£ 

D 
W 

•\ 

1.50 
605 
.0136 
.0117 

1.75 
500 
.0242 
0207 

2.00 
426 
.0392 
.0336 

2.25 
371 
.0593 

.0508 

2.50 
329 
.0854 
.0732 

2.75 

295 
.1187 
.1012 

3.00 
267 
.1583 

.1357 

3.25 
245 

.2066 
1771 

3.50 
226 
.2640 
.2:263 

3.75 

209 
.3312 
2839 

4.00 
195 
.4089 
.3505 

.0097 

.0173 

.0280 

.0424 

.0610 

.0853 

.1131 

.1476 

.1886 

.2366 

.2921 

is 

II 
•d 

D 
W 

-] 

2.00 
765 
.0169 
.0145 
.0120 

2.25 
663 
.0259 
.0222 
.0185 

2.50 
589 
.0377 
.0323 
.0269 

2.75 
523 
.0528 
.0452 
.0376 

3.00 
473 

.0711 
.0610 
.0508 

3.25 
433 

.0935 
.0801 
.0668 

3.50 
398 
.1200 
.1029 
.0858 

3.75 

368 
.1513 
.1297 
.1081 

4.00 
343 
.1874 
.1606 
.1338 

4.25 
321 
.2290 
.1963 
.1635 

4.50 
301 
.2761 
.2367 
.1972 

eb 
5 
|| 

"8 

^ 
II 
*8 

cb 

§ 
II 
"8 

D 
W 

:i 

D 
W 

d 

D 
W 

-\ 

2.00 
1263 

.0081 
.0069 
.0058 

2.25 
1089 
.0126 
.0108 
.0090 

2.50 
957 
.0186 
.0160 
.0133 

2.75 

853 
.0-262 
.0225 

.0187 

3.00 
770 
.0357 
.0306 
.0255 

3.25 

702 
.0472 
.0405 
.0337 

3.50 
644 
.0617 
.0529 
.0441 

3.50 

982 
.0336 
.0288 
.0240 

3.75 
596 
.0772 
.0661 
.0551 

4.00 
544 
.0960 
.0823 
.0686 

4.50 
486 
.1423 
.1220 
.1017 

4.50 
736 
.0796 
.0683 
.0569 

5.00 
945 
.0679 
.0582 
.0485 

5.00 
432 
.2016 
.1728 
.1440 

5.00 
654 
.1134 

.0972 
.0810 

2.00 
1963 
.0042 
.0036 
.0030 

2.50 
2163 
.0056 
.0048 
.0040 

2.25 
1683 
.0067 
.0057 
.0048 

2.50 
1472 
.0099 
.0085 
.0071 

2.75 
1309 
.0141 
.0121 
.0101 

3.00 
1178 
.0194 
.0167 
.0139 

3  25 
1071 
.0259 
.0222 
.0185 

3.75 
906 
.0427 
.0366 
.0305 

4.00 
8*1 

.0534 
.0457 
.0381 

2.75 
1916 
.0081 
.0070 
.0058 

3.00 
1720 
.0112 
.0096 
.0080 

3.25 
1560 
.0151 
.0129 
.0108 

3.50 
14-27 
.0197 
.0169 
.0141 

3.75 
1315 
.0252 
.0216 
.0180 

4.00 
1220 
.0316 
.0271 
.0225 

4.25 
1137 
.0390 
.0334 
.0278 

4.50 
1065 
.0474 
.0406 
.0339 

5.50 
849 
.0935 
.0801 
.0668 

& 

II 

'B 

III 
-B> 

It 
II 
•8 

k 
II 
"8 

^ 

II 

TS 

D 
W 

H 

2.50 
3068 
.0034 
.0029 
.0024 

2.75 
2707 
.0049 
.0042 
.0035 

3.00 
2422 

.0068 
.0058 
.0049 

3.25 

2191 
.0092 
.0079 
.0066 

3.50 
2001 
.01-21 
.0104 

.0086 

3.75 
1841 
.0155 
.0133 
.0111 

4.00 
1704 
.0196 
.0168 
.0140 

4.25 
1587 
.0243 
.0208 
.0173 

4.50 
1484 
.0297 
.0254 
.0212 

5.00 
1315 
.0427 
.0366 
.0305 

5.50 
1180 
.0591 
.0506 
.0422 

D 
W 

H 

D 
W 

'A 

D 

W 

rA 

D 
W 

'\ 

3.00 
3311 
.0043 
.0037 
.0030 

3.25 

2988 
.0058 
.0050 
.0042 

3.50 
2723 
.0077 
.0066 
.0055 

3.75 

2500 
.0100 
.0086 
.0071 

4.00 
2311 
.0127 
.0108 
.0090 

4.25 
2151 
.0157 
.0135 
.0112 

4.50 
2009 
.0193 
.0165 
.0138 

4.75 

1885 
.0233 
.0:200 
.0167 

5.00 
1776 
.0279 
.0239 
.0199 

5.00 
2339 
.0189 
.0162 
.0135 

5.50 
3413 
.0115 
.0098 
.0082 

5.50 
1591 
.0388 
.0333 
0277 

5.50 
2093 
.0264 
.0226 
.0188 

6.00 
1441 
.0522 
.0447 
.0373 

6.00 
1893 
.0356 
.0305 
.0254 

3.00 
4418 
.0028 
.0024 
.0020 

3.25 
3976 
.0038 
0033 
.0027 

3.50 
3615 
.0051 
.0044 
.0036 

3.75 
3313 
.0066 
.0057 
.0047 

4.00 
3058 
.0084 
.0072 
.0060 

4.25 

2810 
.0105 
.0090 
.0075 

4.50 
2651 
.0129 
.0111 
.0093 

4  75 
2485 
.0157 
.0135 
.0113 

5.25 
3607 
.0097 
.0083 
.0009 

5.25 
5544 
.0059 
.0051 
.0043 

3.50 
6013 
.0021 
.0018 
.0015 

3.75 
5490 
.0027 
.0024 
.0020 

4.00 
5051 
.0035 
.0030 
.0025 

4.25 
4676 
.0045 
.0038 
.0032 

4.50 
4354 
.0055 
.0047 
.0039 

4.75 
407'3 
.0067 
.0058 
.0048 

4.75 
6283 
.0041 
.0035 
.0029 

5.00 
3826 
.0081 
.0070 
.0058 

5.00 
5890 
.0049 
.0043 
.0035 

6.00 
3080 
.0156 
.0134 
.0112 

6.50 
2806 
.0207 
.0177 
.0148 

6.50 
4284 
.0129 
.0111 
.0092 

3.50 
9425 
.0012 
.0010 
.0008 

3.75 

8568 
.0016 
.0014 
.0011 

4.00 
7854 
.0021 
.0018 
.0015 

4.25 

7250 
.0026 
.0023 
.0019 

4.50 
6732 
.0033 
.0028 
.  0023 

5.501,  6.00 
5236  4712 
.0071  .0097 
.0061:.  0083 
.0051  .0069 

The  formulae  for  deflection  or  compression  given  by  Clark,  Hartnell,  and 
Begtrup.  although  very  different  in  form,  show  a  substantial  agreement 
when  reduced  to  the  same  form.  Let  d  =  diameter  of  wire  in  inches,  D^  = 
mean  diameter  of  coil,  n  the  number  of  coils,  w  the  applied  weight  ID 
pounds,  and  C  a  coefficient,  then 


HELICAL   SPRINGS.  351 

Compression  or  extension  of  one  coil  =  ^^J-; 

(7d4 
Weight  in  pounds  to  cause  comp.  or  ext.  of  1  in.  =  y^y 

The  coefficient  C  reduced  from  Hartnell's  formula  is  8  X  180,000  =1,440,000; 
according  to  Clark,  164  X  22  =  1,441.792,  and  according  to  Begtrup  (using 
12,000,000  for  the  torsional  modulus  of  elasticity)  =  12,000,000  -=-  8  =  1,500,000. 

Rankine's  formula  for  greatest  safe  extension,  v\  = ^~  rnav  take 

the  form  v±  =  ''      ™ *  -  if  we  use  30,000  and  12,000,000  as  the  values  for  / 

and  c  respectively. 

The  several  formulae  for  safe  load  given  above  may  be  thus  compared, 
letting  d  =  diameter  of  wire,  and  D1  =  mean  diameter  of  coil,  Rankine, 


w  =  :  Cla,.k,  W  =  ;  Begtrup,   W  =  ;    Hartnell. 

7  JJ-l  LJ-L 

W  =   -^— ; — .    Substituting  for  /  the  value  30,000  given  by  Rankine,  and  for 

S,  60,000  as  given  by  Begtrup,  we  have  W  =  11,760  ~  Rankine;  12,288  — 

J-J\  .Z/i 

Clark;  23,562-^  Begtrup;  24,000  ^-  Hartnell. 

x/i  z/i 

Taking  from  the  Pennsylvania  Railroad  specifications  the  capacity  when 
closed  of  the  following  springs,  in  which  d  =  diameter  of  wire,  D  diameter 
outside  of  coil,  D:  =  D  —  d,  c  capacity,  H  height  when  free,  and  h  height 
when  closed,  all  in  inches. 

No.  T.  d  =  y±  D  =  1H  DI  =  1H  c  =  400  H  =    9    h  =  6 

8.  %  3  214  1,900  8             5 

K.  %  5%  5  2,100  7             414 

D.  1  5  4  8,100  10U         8 

7.  \Y±  8  6%  10,000  9             5% 

C.  1J6  4%  3%  16,000  4%          3% 

and  substituting  the  values  of  c  in  the  formula  c  =  W  =  x  —  we  find  x,  the 

L/i 

coefficient  of  j?  to  be  respectively  32,000;  38,000;  32,400;  24,888;  34,560; 
42,140,  average  34,000. 

Taking  12,000  as  the  coefficient  of  —  according  to  Rankine  and  Clark  for 

Ui 

safe  load,  and  24,000  as  the  coefficient  according  to  Begtrup  and  Hartnell, 
we  have  for  the  safe  load  on  these  springs,  as  we  take  one  or  the  other  co- 
efficient, 

rp  o  17"  7)  7"  ri 

Rankine  and  Clark...  .     150         600     1,012     3,000     3,750     5,400'lbs. 

Hartnell 300       1,200     2,024     6,000     7,500    10,800    " 

Capacity  when  closed,  as  above    400       1,900     2,100     8,100    10,000    16,000    " 

J.  W.  Cloud  (Trans.  A.  S.  M.  E.,  v.  173)  gives  the  following: 

Snd* 

P=^R         and      ' 
P  =  load  on  spring; 

S  =  maximum  shearing  fibre-strain  in  bar; 
d  =  diameter  of  steel  of  which  spring  is  made; 
R  —  radius  of  centre  of  coil ; 
I  =  length  of  bar  before  coiling; 
G  =  modulus  of  shearing  elasticity; 
/  =  deflection  of  spring  under  load. 

Mr.  Cloud  takes  S  =  80,000  and  G  =  12,600,000. 

The  stress  in  a  helical  spring  is  almost  wholly  one  of  torsion.  For  method 
of  deriving  the  formulae  for  springs  from  torsional  formula  see  Mr.  Cloud's 
paper,  above  quoted, 


352 


SPRINGS. 


ELLIPTICAL    SPRINGS,    SIZES,    AND    PROOF    TESTS. 
Pennsylvania  Railroad  Specifications,  1889. 


p 

_r 

'S 

CD 

Tests. 

4J  •* 

rn  82 

rC 

O  73"  as 

Class. 

3| 

>_£ 

o-g 

I 

5l| 

ft 

5.5 

2 

«T 

•0 

I 

|sl 

To  stand  ins.  High. 

With  Load 
of  Ibs. 

A,  Triple  

40 

nr 

3     x% 

3 

(  3%  between  bands. 
•<3            "              " 

4800 
5500 

4 

(2 

A.  p.  t.* 

3%        " 

6650 

C,  Quadruple.. 

40 

15J^ 

3     x% 

3 

h 

8000 

D  Triple  

36 

11% 

3     x% 

3 

(2 
4 

1  3           " 

A.  p.  t.* 

6000 
8000 

(  5  bet.  centre  of  eye 

E,  Single  

40 

sin. 

3     x  % 

3x11/32 

•<     and  top  of  leaf. 

When  free 

J3 

2350 

F  Triple  

36 

11% 

3     x  «^i 

3x11/32 

2^  between  bands. 

11.800 

<?,  Double  

32 

*7S 

3      x»^ 

3 

1  3  4      |;         ;; 

When  free 

8000 

H,  Double  

36 

9^ 

3     x% 

4 

5400 
6000 

^  j  Double,    { 
•«•  I   6  plates  I 

22 

10% 

3^x% 

4^x11/32 

13/16    li             4i 

13,800 

r    \  Double,    I 
1/1  1    7  plates  f 

22 

10% 

3^x% 

4^x11/32 

13/16    "             " 

15,600 

(4 

8000 

Jlf,  Quadruple.. 

40 

3     x% 

3 

J   O                     «'                         " 

•Jo 

10,000 

1  2           u 

A.  p.  t.* 

*  A.  p.  t.,  auxiliary  plates  touching. 

PHOSPHOR-RRONZE  SPRINGS. 

Wilfred  Lewis  (Engineers'  Club,  Philadelphia,  1887)  made  some  tests  with 
phosphor-bronze  wire,  .12  in.  diameter,  coiled  in  the  form  of  a  spiral  spring, 
1^4  in.  diameter  from  centre  to  centre,  making  52  coils. 

This  spring  was  loaded  gradually  up  to  a  tension  of  30  Ibs.,  but  as  the  load 
was  removed  it  became  evident  that  a  permanent  set  had  taken  place. 
Such  a  spring  of  steel,  according  to  the  practice  of  the  P.  R.  R.,  might  be 
used  for  40  Ibs.  A  weight  of  21  Ibs.  was  then  suspended  so  as  to  allow  a 
small  amount  of  vibration,  and  the  length  measured  f  rom  day  to  day.  In  30 
hours  the  spring  lengthened  from  20%  inches  to  21^  inches,  and  in  200  hours 
to  21J4  inches.  It  was  concluded  that  21  Ibs.  was  too  great  for  durability,  and 
that  probably  10  Ibs.  was  as  much  as  could  be  depended  upon  with  safety. 

For  a  given  load  the  extension  of  the  bronze  spring  was  just  double  the 
extension  of  a  similar  steel  spring,  that  is,  for  the  same  extension  the  steel 
spring  is  twice  as  strong. 

SPRINGS    TO    RESIST    TORSION  A  L    FORCE. 

(Reuleaux's  Constructor.) 

Flat  spiral  or  helical  spring. . .  P  =  f  ~  ; 

o  R 

Round  helical  spring P  = ; 

32    R 

Round  bar,  in  torsion P  =  —t  —• 

16    A 

Flat  bar,  in  torsion ...  . .  P  =  £-  — ^ 

3R   A/ifi 


=  »= 


G        baha 


P  —  force  applied  at  end  of  radius  or  lever-arm  R ;  #  =  angular  motion  at 
end  of  radius  R;  8  =  permissible  maximum  stress,  =  4/5  of  permissible 
stress  in  flexure;  E  =  modulus  of  elasticity  in  tension:  G  =  torsional  modu- 
lus, =  2/5  E\  I  —  developed  length  of  spiral,  or  length  of  bar;  d  =  diameter 
of  wire;  b  =  breadth  of  flat  bar;  h  =  thickness. 


HELICAL  SPRINGS  FOR  CARS  AND  LOCOMOTIVES.     353 


IN 
i 

I 

0 


.0 


t 


SI 

03 

PS 
5! 

SB 

I 


- 

^ 

w 

H 
s 


vflO  XjO       N 

rt         T^\  tffl\        ~ 

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00 

i" 

s| 

s 

2 


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«  cats 


•T-n-COTP        ^     CO 


00       00       <D 


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^  W  O  «0  O  10  00  O  W  00  CO  c     00  So 


'H  *H  ' 


o     '^'-'' 

2       »W\i— < 


cfe" 


354  RIVETED   JOINTS. 


RIVETED   JOINTS. 

Fairfoairn's  Experiments.    (From  Report  of  Committee  on 

Riveted  Joints,  Proc.  hist.  M.  E.,  April,  1881.) 

The  earliest  published  experiments  on  riveted  joints  are  contained  in  the 
memoir  by  Sir  W.  Fairbairn  in  the  Transactions  of  the  Royal  Society.  Mak- 
ing certain  empirical  allowances,  he  adopted  the  following  ratios  as  ex- 
pressing the  relative  strength  of  riveted  joints: 

Solid  plate 100 

Double-riveted  joint 70 

Single-riveted  joint ...  56 

These  well-known  ratios  are  quoted  in  most  treatises  on  riveting,  and  are 
still  sometimes  referred  to  as  having  a  considerable  authority.  It  is  singular, 
however,  that  Sir  W.  Fairbairn  does  not  appear  to  have  been  aware  that  the 
proportion  of  metal  punched  out  in  the  line  of  fracture  ought  to  be  different 
in  properly  designed  double  and  single  riveted  joints.  These  celebrated 
ratios  would  therefore  appear  to  rest  on  a  very  unsatisfactory  analysis  of 
the  experiments  on  which  they  were  based. 

Loss  of  Strength  in  Punched  Plates.— A  report  by  Mr.  W. 
Parker  and  Mr.  John,  made  in  1878  to  Lloyd's  Committee,  on  the  effect  of 
punching  and  drilling,  showed  that  thin  steel  plates  lost  comparatively  little 
from  punching,  but  that  in  thick  plates  the  loss  was  very  considerable. 
The  following  table  gives  the  results  for  plates  punched  and  not  annealed 
or  reamed: 

Thickness  of  Material  of  Loss  of  Tenacity, 

Plates.  Plates.  per  cent. 

}4  Steel  8 

%  18 

^  "  26 

%  "  33 

%  Iron  18  to  23 

The  effect  of  increasing  the  size  of  the  hole  in  the  die-block  is  shown  in 
the  following  table: 

Total  Taper  of  Hole  Material  of           Loss  of  Tenacity  due  to 

in  Plate,  inches.  Plates.                  Punching,  per  cent. 

1-16  Steel                                  17.8 

^  12.3 

Y±  (Hole  ragged)  24.5 

The  plates  were  from  0.675  to  0.712  inch  thick.  When  %-in.  punched  holes 
were  reamed  out  to  1%  in.  diameter,  the  loss  of  tenacity  disappeared,  and 
the  plates  carried  as  high  a  stress  as  drilled  plates.  Annealing  also  restores 
to  punched  plates  their  original  tenacity. 

Strength  of  Perforated  Plates. 

(P.  D.  Bennett,  Eng'g,  Feb.  12,  1886,  p.  155.) 

Tests  were  made  to  determine  the  relative  effect  produced  upon  tensile 
strength  of  a  flat  bar  of  iron  or  steel:  1.  By  a  %-inch  hole  drilled  to  the  re- 
quired size;  2,  by  a  hole  punched  ^  inch  smaller  and  then  drilled  to  the 
size  of  the  first  hole;  and,  3,  by  a  hole  punched  in  the  bar  to  the  size  of  the 
drilled  bar.  The  relative  results  in  strength  per  square  inch  of  original  area 
were  as  follows: 

1.  2.  8.  4. 

Iron.        Iron.       Steel.       Steel. 

Unperforated  bar 1.000        1.000        1.000        1.000 

Perforated  by  drilling 1.029        1.012        1.068        1.103 

"    punching  and  drilling.  1.030        1.008        1.059        1.110 
"    punching  only 0.795       0.894        0.935       0.927 

In  tests  2  and  4  the  holes  were  filled  with  rivets  driven  by  hydraulic  pres- 
sure. The  increase  of  strength  per  square  inch  caused  by  drilling  is  a  phe- 
nomenon of  similar  nature  to  that  of  the  increased  strength  of  a  grooved  bar 
over  that  of  a  straight  bar  of  sectional  area  equal  to  the  smallest  section  of 
the  grooved  bar.  Mr.  Bennett's  tests  on  an  iron  bar  0.84  in.  diameter,  10  in. 


EFFICIENCY  OF  1UVETIXG  BY  DIFFERENT  METHODS.    355 


long,  and  a  similar  bar  turned  to  0.84  in.  diameter  at  one  point  only,  showed 
that  the  relative  strength  of  the  latter  to  the  former  was  1.323  to  i.OOO. 

Riveted  Joints.— Drilling  versus  Punching  of  Holes. 

The  Report  of  the  Research  Committee  of  the  Institution  of  Mechanical 
Engineers,  on  Riveted  Joints  (1881),  and  records  of  investigations  by  Prof . 
A.  B.  W.  Kennedy  (1881,  1882,  and  1885),  summarize  the  existing  information 
regarding  the  comparative  effects  of  punching  and  drilling  upon  iron  and 
steel  plates.  From  an  examination  of  the  voluminous"  tables  given  in  Pro- 
fessor Unwin's  Report,  the  results  of  the  greatest  number  of  the  experi- 
ments made  on  iron  and  steel  plates  lead  to  the  general  conclusion  that, 
while  thin  plates,  even  of  steel,  do  not  suffer  very  much  from  punching,  yet 
in  those  of  ^-iuch  thickness  and  upwards  the  loss  of  tenacity  due  to  punch- 
ing ranges  from  10$  to  23$  in  iron  plates,  and  from  11$  to  33$  in  the  case  of 
mild  steel.  In  drilled  plates  there  is  no  appreciable  loss  of  strength.  It  is 
possible  to  remove  the  bad  effects  of  punching  by  subsequent  reaming  or 
annealing;  but  the  speed  at  which  work  is  turned  out  in  these  days  is  not 
favorable  to  multiplied  operations,  and  such  additional  treatment  is  seldom 
practised.  The  introduction  of  a  practicable  method  of  drilling  the  plating 
of  ships  and  other  structures,  after  it  has  been  bent  and  shaped,  is  a  matter 
of  great  importance.  If  even  a  portion  of  the  deterioration  of  tenacity  can 
be  prevented,  a  much  stronger  structure  results  from  the  same  material  and 
the  same  scantling.  This  has  been  fully  recognized  in  the  modern  English 
practice  (1887)  of  the  construction  of  steam-boilers  with  steel  plates;  punch- 
ing in  such  cases  being  almost  entirely  abolished,  and  all  rivet-holes  being 
drilled  after  the  plates  have  been  bent  to  the  desired  form. 

Comparative  Efficiency  of  Riveting  done  by  Different 
Methods. 

The  Reports  of  Professors  Unwin  and  Kennedy  to  the  Institution  of  Me- 
chanical Engineers  (Proc.  1881,  1882,  and  1885)  tend  to  establish  the  four  fol- 
lowing points: 

1.  That  the  shearing  resistance  of  rivets  is  not  highest  in  joints  riveted  by 
means  of  the  greatest  pressure; 

2.  That  the  ultimate  strength  of  joints  is  not  affected  to  an  appreciable 
extent  by  the  mode  of  riveting;  and,  therefore, 

3.  That  very  great  pressure  upon  the  rivets  in  riveting  is  not  the  indispen- 
sable requirement  that  it  has  been  sometimes  supposed  to  be; 

4.  That  the  most  serious  defect  of  hand-riveted  as  compared  with  machine- 
riveted  work  consists  in  the  fact  that  in  hand -riveted  joints  visible  slip 
commences  at  a  comparatively  small  load,  thus  giving  such  joints  a  low 
value  as  regards  tightness,  and  possibly  also  rendering  them  liable  to  failure 
under  sudden  strains  after  slip  has  once  commenced. 

The  following  figures  of  mean  results,  taken  from  Prof.  Kennedy's  tables 
(Proceedings  1885,  pp.  218-225),  give  a  comparative  view  of  hand  and  hy- 
draulic riveting,  as  regards  their  ultimate  strengths  in  joints,  and  the  periods 
at  which  in  both  cases  visible  slip  commenced. 


Total  Breaking  Load. 

Load  at  which  Visible  Slip  began. 

Hand-riveting. 

Hydraulic  Rivet- 
ing. 

Hand  -riveting. 

Hydraulic  Rivet- 
ing. 

Tons. 
86.01 

aue 

U9.2 
193.6' 

Tons. 
85.75 
77.00 
82.70 
78.58 
145.5 
140.2 
183.1 
183.7 

Tons. 
21.7 

25i6 

31.7 

25.0 

Tons. 
47.5 
35.0 
53.7 
54.0 
49.7 
46.7 
56.0 

In  these  figures  hand-riveting  appears  to  be  r  <ther  better  than  hydraulic 
riveting,  as  far  as  regards  ultimate  strength  of  joint;  but  is  very  much  in- 
ferior to  hydraulic  work,  in  view  of  the  small  proportion  of  load  borne  by 
it  before  visible  slip  commenced. 


356 


RIVETED    JOIXTS. 


Some  of  the  Conclusions  of  the  Committee  of  Research 
on  Riveted  Joints. 

(Proc.  Inst.  M.  E.,  Apl.  1885.) 

The  conclusions  all  refer  to  joints  made  in  soft  steel  plate  with  steel 
rivets,  the  holes  ail  drilled,  and  the  plates  in  their  natural  state  (unannealed). 
In  every  case  the  rivet  or  shearing  area  has  been  assumed  to  be  that  of  the 
holes,  not  the  nominal  (or  real)  area  of  the  rivets  themselves.  Also,  the 
strength  of  the  metal  in  the  joint  has  been  compared  with  that  of  strips 
cut  from  the  same  plates,  and  not  merely  with  nominally  similar  material. 

The  metal  between  the  rivet-holes  has  a  considerably  greater  tensile  re- 
sistance per  square  inch  than  the  unperforated  metal.  This  excess  tenacity 
amounted  to  more  than  20$,  both  in  %-inch  and  %-inch  plates,  when  the 
pitch  of  the  rivet  was  about  1.9  diameters.  In  other  cases  %-inch  plate  gave 
an  excess  of  15$  at  fracture  with  a  pitch  of  2  diameters,  of  10%  with  a  pitch 
of  3.6  diameters,  and  of  6.6$,  with  a  pitch  of  3.9  diameters;  and  %-inch  plate 
gave  7.8$  excess  with  a  pitch  of  2.8  diameters. 

In  single-riveted  joints  it  may  be  taken  that  about  22  tons  per  square  inch 
is  the  shearing  resistance  of  rivet  steel,  when  the  pressure  on  the  rivets  does 
not  exceed  about  40  tons  per  square  inch.  In  double-riveted  joints,  with 
rivets  of  about  %  inch  diameter,  most,  of  the  experiments  gave  about  24  tons 
per  square  inch  as  the  shearing  resistance,  but  the  joints  in  one  series  went 
at  22  tons. 

The  ratio  of  shearing  resistance  to  tenacity  is  not  constant,  but  diminishes 
very  markedly  and  not  very  irregularly  as  the  tenacity  increases. 

The  size  of  the  rivet  heads  and  ends  plays  a  most  important  part  in  the 
strength  of  the  joints— at  any  rate  in  the  case  of  single-riveted  joints.  An 
increase  of  about  one  third  in  the  weight  of  the  rivets  (all  this  increase,  of 
course,  going  to  the  heads  and  ends)  was  found  to  add  about  8J^$  to  the 
resistance  of  the  joint,  the  plates  remaining  unbroken  at  the  full  shearing 
resistance  of  22  tons  per  square  inch,  instead  of  tearing  at  a  shearing  stress 
of  only  a  little  over  20  tons.  The  additional  strength  is  probably  due  to  the 
prevention  of  the  distortion  of  the  plates  by  the  great  tensile  stress  in  the 
rivets. 

The  intensity  of  bearing  pressure  on  the  rivet  exercises,  with  joints  propor- 
tioned in  the  ordinary  way,  a  very  important  influence  on  their  strength. 
So  long  as  it  does  not  exceed  40  tons  per  square  inch  (measured  on  the  pro- 
jected area  of  the  rivets),  it  does  not  seem  to  affect  their  strength  ;  but  pres- 
sures of  50  to  55  tons  per  square  inch  seem  to  cause  the  rivets  to  shear  in 
most  cases  at  stresses  varying  from  16  to  18  tons  per  square  inch.  For  or- 
dinary joints,  which  are  to  be  made  equally  strong  in  plate  arid  in  rivets, 
the  bearing  pressure  should  therefore  probably  not  exceed  42  or  43  tons  per 
square  inch.  For  double-riveted  butt-joints  perhaps,  as  will  be  noted  later, 
a  higher  pressure  may  be  allowed,  as  the  shearing  stress  may  probably  not 
be  more  than  10  or  18  tons  per  square  inch  when  the  plate  tears. 

A  margin  (or  net  distance  from  outside  of  holes  to  edge  of  plate)  equal  to  the 
diameter  of  the  drilled  hole  has  been  found  sufficient  in  all  cases  hitherto  tried. 

To  attain  the  maximum  strength  of  a  joint,  the  breadth  of  lap  must  be 
such  as  to  prevent  it  from  breaking  zigzag.  It  has  been  found  that  the  net 
metal  measured  zigzag  should  be  from  30$  to  35$  in  excess  of  that  measured 
straight  across,  in  order  to  insure  a  straight  fracture.  This  corresponds  to 
a  diagonal  pitch  of  2/3  p  -f  rf/3,  if  p  be  the  straight  pitch  and  d  the  diam- 
eter of  the  rivet-hole. 

Visible  slip  or  "give"  occurs  always  in  a  riveted  joint  at  a  point  very 
much  below  its  breaking  load,  and  by'  no  means  proportional  to  that  load. 
A  collation  of  the  results  obtained  in  measuring  the  slip  indicates  that  it  de- 
pends upon  the  number  and  size  of  the  rivets  in  the  joint,  rather  than  upon 
anything  else  ;  and  that  it  is  tolerably  constant  for  a  given  size  of  rivet  in  a 
given  type  of  joint.  The  loads  per  rivet  at  which  a  joint  will  commence  to 
slip  visibly  are  approximately  as  follows  : 


Diameter  of  Rivet. 

Type  of  Joint. 

Riveting. 

Slipping  Load  per 
Rivet. 

%  inch 

llnch 
1     " 
1     " 

Single-riveted 
Double-riveted 
Double-riveted 
Single-riveted 
Double-riveted 
Double-riveted 

Hand 
Hand 
Machine 
Hand 
Hand 
Machine 

2.5  tons 
3.0  to  3.5  tons 
7  tons 
3.2  tons 
4.3  tons 
8  to  10  tons 

DOUBLE-RIVETED   LAP-JOINTS. 


35? 


To  find  the  probable  load  at  which  a  joint  of  any  breadth  will  commence 
to  slip,  multiply  the  number  of  rivets  in  the  given  breadth  by  the  proper 
figure  taken  from  the  last  column  of  the  table  above.  It  will  be  understood 
that  the  above  figures  are  not  given  as  exact;  but  they  represent  very  well 
the  results  of  the  experiments. 

The  experiments  point  to  simple  rules  for  the  proportioning  of  joints  of 
maximum  strength.  Assuming  that  a  bearing  pressure  of  43  tons  per  square 
inch  may  be  allowed  on  the  rivet,  and  that  the  excess  tenacity  of  the  plate 
is  10$  of  its  original  strength,  the  following  table  gives  the  values  of  the  ratios 
of  diameter  d  of  hole  to  thickness  t  of  plate  (d  -4-  /),  and  of  pitch  p  to  diam- 
eter of  hole  (p  -r-  d)  in  joints  of  maximum  strength  in  %-inch  plate. 

For  Single-riveted  Plates. 


Original  Tenacity  of 
Plate. 

Shearing  Resistance  of 
Rivets. 

Ratio. 
d+t 

Ratio. 
p  -*-d 

Ratio. 
Plate  Area 

Tons  per 
sq.  in. 

Lbs.  per 
sq.  in. 

Tons  per 
sq.  in. 

Lbs.  per 
sq.  in. 

Rivet  Area 

30 

28 
30 
28 

67,200 
62,720 
67,200 
62,720 

22 

22 
24 
24 

49,200 
49,200 
53,760 
53,760 

2.48 
2.48 
2.28 
2.28 

2.30 
2.40 
2.27 
2.36 

0.667 
0.785 
0.713 
0.690 

This  table  shows  that  the  diameter  of  the  hole  (not  the  diameter  of  the 
rivet)  should  be  2^  times  the  thickness  of  the  plate,  and  the  pitch  of  the 
rivets  2%  times  the  diameter  of  the  hole.  Also,  it  makes  the  mean  plate  area 
71  #  of  the  rivet  area. 

If  a  smaller  rivet  be  used  than  that  here  specified,  the  joint  will  not  be  of 
uniform,  and  therefore  not  of  maximum,  strength;  but  with  any  other  size 
of  rivet  the  best  result  will  be  got  by  use  of  the  pitch  obtained  from  the 
simple  formula 

P  =  a  -j-  +  d, 

where,  as  before,  d  is  the  diameter  of  the  hole. 
The  value  of  the  constant  a  in  this  equation  is  as  follows: 

For  30-ton  plate  and  22- ton  rivets,  «=  0.524 
"    28  "  22          "  "    0.558 

"    30  "  24          "  "    0.570 

44    28  "  24         "  "    0.606 

Or,  in  the  mean,  the  pitch  p  =  0.56  -T-  -f-  d. 

It  should  be  noticed  that  with  too  small  rivets  this  gives  pitches  often  con- 
siderably smaller  in  proportion  than  2%  times  the  diameter. 

For  double-riveted,  lap-joints  a  similar  calculation  to  that  given 
above,  but  with  a  somewhat  smaller  allowance  for  excess  tenacity,  on 
account  of  the  large  distance  between  the  rivet-holes,  shows  that  for  joints 
of  maximum  strength  the  ratio  of  diameter  to  thickness  should  remain  pre- 


cisely as  in  single-riveted  joints;  while  the  ratio  of  pitch  to  diameter  of  hole 
ould  be  3.64  for  30-ton  plates  and  22  or  24  ton  rivets,  and  3.82  for  $ 


•  28-ton 


shou 

plates  with  the  same  r  ivets. 

Here,  still  more  than  in  the  former  case,  it  is  likely  that  the  prescribed 
size  of  rivet  may  often  be  inconveniently  large.  In  this  case  t&e  diameter 
of  rivet  should  be  taken  as  large  as  possible;  and  the  strongest  joint  for  a 
given  thickness  of  plate  and  diameter  of  hole  can  then  be  obtained  by  using 
the  pitch  given  by  the  equation 

•p  =  a  --  -f  d, 

Nvhere  the  values  of  the  constant  a  for  different  strengths  of  plates  and 
rivets  may  be  taken  as  follows: 


358 


RIVETED   JOINTS. 


Table  of  Proportions  of  Double-riveted  Iiap-joints9 

d2 


in  which  p  =  a  —  -  +  d. 


Thickness  of 
Plate. 


Original  tenacity 
of  Plate,     ' 

Shearing  Resist-     Value  of  Con- 
ance  of  Rivets.               stant. 

Tons  per  sq.  in. 

Tons  per  sq.  in.                   a 

30 

24                            1.15 

28 

24 

.22 

30 

22 

.05 

28 

22 

.12 

30 

24 

.17 

28 

24 

.25 

30 

22 

.07 

28 

22 

.14 

Practically,  having  assumed  the  rivet  diameter  as  large  as  possible,  we 
can  fix  the  pitch  as  follows,  for  any  thickness  of  plate  from  %  to  %  inch: 


For  30-ton  plate  and  24-ton  rivets  j 


_\ 


30 

28 


(1 

it          «     ga     „ 

«<        «    24    « 

p  -  1.06  -  - 

P  =  I.*£- 


In  double-riveted  butt-joints  it  is  impossible  to  develop  the  full 
shearing  resistance  of  the  joint  without  getting  excessive  bearing  pressure, 
because  the  shearing  area  is  doubled  without  increasing  the  area  on  which 
the  pressure  acts  Considering  only  the  plate  resistance  and  the  bearing 
pressure,  and  taking  this  latter  as  45  tons  per  square  inch,  the  best  pitch 
would  be  about  4  times  the  diameter  of  the  hole.  We  may  probably  say 
with  some  certainty  that  a  pressure  of  from  45  to  50  tons  per  square  inch  on 
the  rivets  will  cause  shearing  to  take  place  at  from  16  to  18  tons  per  square 
inch.  Working  out  the  equations  as  before,  but  allowing  excess  strength  of 
only  5f0  on  account  of  the  large  pitch,  we  find  that  the  proportions  of  double- 
riveted  butt-joints  of  maximum  strength,  under  given  conditions,  are  those 
of  the  following  table: 

Double-riveted  Butt-joints. 

Ratio  Ratio 

d,  p 

t  d 

1.80  3.85 

1.80  4.06 

1.70  4.03 

1.70  4.27 

2.00  4.20 

2.00  4.42 

Practically,  therefore,  it  may  be  said  that  we  get  a  double-riveted  butt-joint 
of  maximum  strength  by  making  the  diameter  of  hole  about  1.8  times  the 
thickness  of  the  plate,  and  making  the  pitch  4.1  times  the  diameter  of  the 
hole. 

The  proportions  just  given  belong  to  joints  of  maximum  strength.  But  in 
a  boiler  the  one  part  of  the  joint,  the  plate,  is  much  more  affected  by  time 
than  the  other  part,  the  rivets.  It  is  therefore  not  unreasonable  to  estimate 
the  percentage  by  which  the  plates  might  be  weakened  by  corrosion,  etc., 
before  the  boiler  would  be  unfit  for  use  at  its  proper  steam-pressure,  and  to 
add  correspondingly  to  the  plate  area.  Probably  the  best  thing  to  do  in  this 
case  is  to  proportion  the  joint,  not  for  the  actual  thickness  of  plate,  but  for 
a  nominal  thickness  less  than  the  actual  by  the  assumed  percentage.  In 
this  case  the  joint  will  be  approximately  one  of  uniform  strength  by  the 
time  it  has  reached  its  final  workable  condition ;  up  to  which  time  the  joint 
as  a  whole  will  not  really  have  been  weakened,  the  corrosion  only  gradually 
bringing  the  strength  of  the  plates  down  to  that  of  rivets. 


Original  Ten- 

Shearing Re- 

Bearing 

acity 

sistance 

Pres- 

of Plate, 

of  Rivets, 

sure, 

Tons  per 

Tons  per 

Tons  per 

sq.  in. 

sq.  in. 

sq.  in. 

30 

16 

45 

28 

16 

45 

30 

18 

48 

28 

18 

48 

30 

16 

50 

28 

16 

50 

JOINTS. 


350 


Efficiencies  of  Joints, 

The  average  results  of  experiments  by  r,he  committee  gave:  For  double- 
riveted  lap-joints  in  %-inch  plates,  efficiencies  ranging  from  67.1$  to  81.2$. 
For  double-riveted  butt-joints  (in  double  shear)  61.4$  to  71.3$.  These  low  re- 
sults were  probably  due  to  the  use  of  very  soft  steel  in  the  rivets.  For  single- 
riveted  lap-joints  of  various  dimensions  the  efficiencies  varied  from  54.8$  to 
60.8$. 

The  experiments  showed  that  the  shearing  resistance  of  steel  did  not  in- 
crease nearly  so  fast  as  its  tensile  resistance.  With  very  soft  steel,  for 
instance,  of  only  26  tons  tenacity,  the  shearing  resistance  was  about  80$  of 
the  tensile  resistance,  whereas  with  very  hard  steel  of  52  tons  tenacity  the 
shearing  resistance  was  only  somewhere  about  65$  of  the  tensile  resistance. 

Proportions  of  Pitch  and  Overlap  of  Plates  to   Diameter 
of  Rivet-Hole  and  Thickness  of  Plate. 

(Prof.  A.  B.  W.  Kennedy,  Proc.  Inst.  M.  E.,  April,  1885.) 
t  =  thickness  of  plate; 

d  =  diameter  of  rivet  (actual)  in  parallel  hole; 
p  =  pitch  of  rivets,  centre  to  centre; 
s  =  space  between  lines  of  rivets; 
(I  =  overlap  of  plate. 

The  pitch  is  as  wide  as  is  allowable  without  imparing  the  tightness  of  the 
joint  under  steam. 

For  single-riveted  lap-joints  in  the  circular  seams  of  boilers  which  have 
double-riveted  longitudinal  lap  joints, 
d  =  t  x  2.25; 

p  =  d  x  2.25  =  t  x  5  (nearly); 
I  =  t  x  6. 
For  double-riveted  lap-joints: 

d  =  2.25* ; 
p  =  8t; 
s  -  4.5t ; 
I  =  10.5*. 


Single-riveted  Joints. 


Double  -riveted  Joints. 


t 


I 


3-16 

5-te 

7-16 


7-16 
9-16 
11-16 
13-16 


15-16 


23-16 
2  123-16 


3-16 


nie 

9-16 


7-16 
9-16 
11-16 
13-16 


13-16 

m 


With  these  proportions  and  good  workmanship  there  need  be  no  fear  of 
leakage  of  steam  through  the  riveted  joint. 

The  net  diagonal  area,  or  area  of  plate,  along  a  zigzag  line  of  fracture 
should  not  be  less  than  30$  in  excess  of  the  net  area  straight  across  the 
joint,  and  35$  is  better. 

Mr.  Theodore  Cooper  (R.  R.  Gazette,  Aug.  22,  1890)  referring  to  Prof.  Ken- 
nedy's statement  quoted  above,  gives  as  a  sufficiently  approximate  rule  for 
the  proper  pitch  between  the  rows  in  staggered  riveting,  one  half  of  the 
pitch  of  the  rivets  in  a  row  plus  one  quarter  the  diameter  of  a  rivet-hole. 

Apparent  Excess  in  Strength   of  Perforated  over  Un per- 
forated Plates.    (Proc.  Inst.  M.  E.,  October,  1888.) 
The  metal  between  the  rivet-holes  has  a  considerably  greater  tensile  re- 
sistance per  square  inch  than  the  unperf  orated  metal.    This  excess  tenacity 
amounted  to  more  than  20$,  both  in  %-inch  and  ^-inch  plates,  when  the 
pitch  of  the  rivets  was  about  1.9  diameters.     In  other  cases  %-inch  plate 
gave  an  excess  of  15$  at  fracture  with  a  pitch  of  2  diameters,  of  10$  with  a 
pitch  of  3.6  diameters,  and  of  6.6$  with  a  pitch  of  3.9  diameters;  and  ^-inch 
plate  gave  7.8$  excess  with  a  pitch  of  2.8  diameters. 


360 


RIVETED   JOINTS. 


(1)  The   "excess  strength  due  to  perforation  "  is  increased  by  anything 
which  tends  to  make  the  stress  in  the  plate  uniform,  and  to  diminish  the 
effect  of  the  narrow  strip  of  metal  at  the  edge  of  the  specimen. 

(2)  It  is  diminished  by  increase  in  the  ratio  of  p/d,  of  pitch  to  diameter  of 
hole,  so  that  in  this  respect  it  becomes  less  as  the  efficiency  of  the  joint 
increases. 

(3)  It  is  diminished  by  any  increase  in  hardness  of  the  plate. 

(4)  For  a  given  ratio  p/d,  of  pitch  to  diameter  of  hole,  it  is  also  apparently 
diminished  as  the  thickness  of  the  plate  is  increased.    The  ratio  of  pitch  to 
thickness  of  plate  does  not  seem  to  affect  this  matter  directly,  at  least 
within  the  limits  of  the  experiments. 

Test  of  Double»riveted  Lap  and  Butt  Joints. 

(Proc.  Inst.  M.  E.,  October,  1888.) 

Steel  plates  of  25  to  26  tons  per  square  inch  T.  S.,  steel  rivets  of  24.6  tons 
shearing-strength  per  square  inch. 

Thickness  of     Diameter  of    Ratio  of  Pitch     SSSeS^Of 


Plate 


Rivet-holes,      to  Diameter. 


Lap 
Butt 
Lap 

Butt'.' 

" 
Lap 

Butt".' 


0.8" 

0-7 

1.1 

1.6 

1.1 

1.6 

1.3 

1.75 

1.3 


3.62 
3.93 
2.82 
3.41 
4.00 
3.94 
2.42 
3.00 
3.92 


75.2 
76.5 
68.0 
73.6 
72.4 
76.1 
63.0 
70.2 
76.1 


Some  Rules  which  have  been  Proposed  for  the  Diameter 
of  the  Rivet  in  Single  Shear.    (Iron,  June  18,  1880.) 

Browne d  =  2t  (\\ith  double  covers  1J40  (1) 

Fairbairn d  =  2t  for  plates  less  than  %  in.  (2) 

"        d  =  \\^t  for  plates  greater  than  %  in.  (3) 

Lemaitre d  —  1.52  -f  0.16  (4) 

Antoine d  =  1.1  \/1  (5) 

Pohlig d  =  2t  for  boiler  riveting  (6) 

"          d  =  3t  for  extra  strong  riveting  (?) 

Redtenbacher rf  =  1.5£to2£  (8) 

Unwin d  —  Y^t  -}-  5/16  to  %t  -f  %  (9) 

"     d  =  1.2  \'1  (10) 

The  following  table  contains  some  data  of   the  sizes  of   rivets  used  in 
practice,  and  the  corresponding  sizes  given  by  some  of  these  rules. 
Diameter  of  Rivets  for  Different  Thicknesses  of  Plates. 


Thick- 
ness of 
plate. 
Inches. 


5/16 
7/16 

9/16 
11/16 

_~_ 
13/16 

15/16 
1 


Diameter  of  Rivets,  in  inches. 


13/16 


13/16 


15/16  1 


1 
ll/16  1 


is/ie 


1 

f  1/16 


r-r-i 


irbai 
and 


21/32 


27/32 

4       15/16 
1  1/32 

m 


% 


1  7/32 


. 


23/32 
13/16 
15/16 

1 

1  3/16 


11/16 


13/16 


15/16 
15/16 


1 
1 

1  1/16 


11/16 
13/16 


15/16 
1 
1  1/16 


if/16 


1  3/32 

1  3/16 


RIVETED   JOINTS. 


361 


Strength   of  Double -riveted   Seams,   Calculated.  —  W.  6. 

Ruggles,  Jr.,  in  Pon.er  for  June,  1890,  gives  tables  of  relative  strength  of 
rivets  and  parts  of  sheet  between  rivets  in  double-riveted  seams,  compared 
with  strength  of  shell,  based  on  the  assumption  that  the  shearing  strength 
of  rivets  and  the  tensile  strength  of  steel  are  equal.  The  following  figures 
show  the  sizes  in  his  tables  which  show  the  nearest  approximation  to  equal- 
ity of  strength  of  rivets  and  parts  of  plates  between  the  rivets,  together 
with  the  percentage  of  each  relative  to  the  strength  of  the  solid  plate. 


esss  of  | 
nches. 

Pitch 
of 

Size  of 
Rivet- 

Percentage  of 
Strength  of 
Plate. 

«t-  03 

o  £ 

11 

Pitch 
of 

Size  of 
Rivet- 

Percentage  of 
Strength  of 
Plate. 

c  ™ 
•*  <o 

Rivets, 

holes, 

a 
-*  <D 

Rivets, 

holes, 

O.J3 

It 

inches. 

inches. 

Rivets. 

Plate. 

w  -iS 

23 

EH  PL, 

inches. 

inches. 

Rivets. 

Plate. 

H 

2^6 

^ 

.739 

.765 

7/16 

2% 

% 

.734 

.728 

24 

»>i^ 

9/16 

.795 

.775 

7/16 

3;Nj 

13/16 

.758 

.740 

M 

31^ 

y 

.785 

.800 

7/16 

3% 

% 

.758 

.759 

y± 

3% 

11/16 

.819 

.810 

7/16 

41^ 

15/16 

.765 

.773 

5/16 

£i^ 

9/16 

.749 

.735 

V& 

2L< 

% 

.707 

.700 

5/16 

2% 

% 

.748 

.762 

^ 

2% 

13/16 

.721 

.718 

5/16 

31^ 

11/16 

.761 

.780 

/^ 

g 

.740 

.731 

5/16 

3% 

% 

.780 

.793 

/^ 

3^4 

15/16 

.736 

.750 

% 

2^4 

% 

.727 

.722 

\^ 

4/^j 

1 

.761 

.758 

% 

2% 

11/16 

.755 

.738 

9/16 

2% 

13/16 

.701 

.690 

% 

31^ 

M 

.754 

.760 

9/16 

3 

% 

.714 

.708 

% 

3% 

13/16 

.762 

.776 

9/16 

3% 

15/16 

.727 

.722 

% 

41^ 

% 

.777 

.788 

9/16 

3% 

1 

.745 

.733 

7/16 

2% 

11/16 

.714 

.711 

9/16 

4J4 

1  1/16 

.742 

.750 

H.  De  B.  Parsons  (Am.  Engr.  &  E.  R.  Jour.,  1893)  holds  that  it  is  an  error  to 
assume  that  the  shearing  strength  of  the  rivet  is  equal  to  the  tensile  strength. 
Also,  referring  to  the  apparent  excess  in  strength  of  perforated  over  unper- 
f orated  plates,  he  claims  that  on  account  of  the  difficulty  in  properly  match- 
ing the  holes,  and  of  the  stress  caused  by  forcing,  as  is  too  often  the  case 
in  practice,  this  additional  strength  cannot  be  trusted  much  more  than 
that  of  friction. 

Adopting  the  sizes  of  iron  rivets  as  generally  used  in  American  practice 
for  steel  plates  from  14  to  1  inch  thick:  the  tensile  strength  of  the  plates  as 
60,000  Ibs. ;  the  shearing  strength  of  the  rivets  as  40,000  for  single-shear  and 
35,500  for  double  -  shear,  Mr.  Parsons  calculates  the  following  table  of 
pitches,  so  that  the  strength  of  the  rivets  against  shearing  will  be  approxi- 
mately equal  to  that  of  the  plate  to  tear  between  rivet-holes.  The  diameter 
of  the  rivets  has  in  all  cases  been  taken  at  1/16  in.  larger  than  the  nominal 
size,  as  the  rivet  is  assumed  to  fill  the  hole  under  the  power  riveter. 

Riveted  Joints. 

LAP  OR  BUTT  WITH  SINGLE  WELT— STEEL  PLATES  AND  IRON  RIVETS. 


Thickness 

Diameter 

Pitch. 

Efficiency. 

of 
Plates. 

of 
Rivets. 

Single. 

Double. 

Single. 

Double. 

in. 

in. 

in. 

in. 

1  3/16 

1% 

55.7* 

70.  0£ 

% 

94 

1  11/16 

2  11/16 

52.7 

68.6 

Via 

% 

1% 

2% 

49.0 

65.9 

% 

% 

1  11/16 

2  7/16 

43.6 

60.4 

M 

1 

itt 

2% 

42.0 

59.5 

% 

1 

1  1/8 

\% 

23/16 

2  7/16 
2% 

38.6 
38.1 

55.4 
54.9 

362 


RIYETED   JOINTS. 


Calculated   Efficiencies— Steel  Plates  and  Steel  Rivets.— 

The  differences  between  the  calculated  efficiencies  given  in  the  two  tables 
above  are  notable.  Those  given  by  Mr.  Ruggles  are  probably  too  high,  since 
he  assumes  the  shearing  strength  of  the  rivets  equal  to  the  tensile  strength 
of  the  plates.  Those  given  by  Mr.  Parsons  are  probably  lower  than  will  be 
obtained  in  practice,  since  the  figure  he  adopts  for  shearing  strength  is 
rather  low,  and  he  makes  no  allowance  for  excess  of  strength  of  the  perfo- 
rated over  the  unperforated  plate.  The  following  table  has  been  calculated 
by  th  author  on  the  assumptions  that  the  excess  strength  of  the  perforated 
plate  is  10#,  and  that  the  shearing  strength  of  the  rivets  per  square  inch  is 
four  fifths  of  the  tensile  strength  of  the  plate.  If  t  =  thickness  of  plate, 
d  —  diameter  of  rivet-hole,  p  =  pitch,  and  T  —  tensile  strength  per  square 
inch,  then  for  single-riveted  plates 

(p  -  d)t  X  1.1021  =  ^--d*  X  \  T,    whence  p  =  .571^  +  d. 

4  O  t 

For  double-riveted  plates,  p  =  1.142-j  +  d. 

The  coefficients  .571  and  1.142  agree  closely  with  the  averages  of  those 
given  in  the  report  of  the  committee  of  the  institution  of  Mechanical  En- 
gineers, quoted  on  pages  357  and  358,  ante. 


Pitch. 

Efficiency. 

Pitch. 

Efficiency. 

1 
1 

Diam. 
of 
Rivet- 
hole. 

fl 

•§£ 
I* 

if 

^ 

i* 

p 

rW 

^O 

Diam. 
of 
Rivet- 
hole. 

^S1 

U« 

C  i> 

ii 
•§•§ 

°% 

bi'£ 
s  o> 

l£ 

•S'-s 
5  ^ 

H 

^S 

o  >. 
fitf 

*J 

Ic 
H 

«l 

o  > 

fis 

5 

Sg 

in. 

in. 

in. 

in. 

% 

* 

in. 

in. 

in. 

in. 

^ 

% 

3/16 

7/16 

1.020 

1.603 

57.1 

72.7 

y> 

H 

1.392 

2.035 

46.1 

63.1 

" 

^ 

1.261 

2.023 

60.5 

75.3 

% 

1.749 

2.624 

50.0 

66.6 

H 

/^ 

1.071 

1.642 

53.3 

69.6 

*' 

i 

2.142!  3.284 

53.3 

70.0 

9/16 

1.285 

2.008 

56.2 

72.0 

" 

2.570 

4.016 

56.2 

72.0 

5/16 

9/16 

1.137 

1.712 

50.5 

67.1 

9/16 

% 

1.321 

1.892 

43.2 

60.3 

M 

% 

1.339 

2.053 

53.3 

69.5 

% 

1.652 

2.429 

47.0 

64.0 

" 

11/16 

.551 

2.415 

55.7 

71.5 

«* 

i 

2.015 

3.030 

50.4 

67.0 

% 

^ 

.218 

1.810 

48.7 

65.5 

" 

2.410 

3.694 

53.3 

69.5 

'• 

M 

.607 

2.463 

53.3 

69.5 

" 

1J4 

2.836 

4.422 

55.9 

71.5 

** 

% 

.041 

3.206 

57.1 

72.7 

% 

^4 

1.264 

1.778 

40.7 

57.8 

7/16 

% 

.136 

1.647 

45.0 

62.0 

"• 

% 

1.575 

2.274 

44.4 

61.5 

u 

M 

.484 

2.218 

49.5 

66.2 

'« 

1 

1.914 

2.827 

47.7 

64.6 

*« 

% 

1.869 

2.864 

53.2 

69.4 

" 

Jl/ 

2.281 

3.438 

50.7 

67.3 

1 

2.305 

3.610 

56.6 

72.3 

" 

5 

2.678 

4.105 

53.3 

69.5 

Riveting  Pressure  Required  for  Bridge  and  Boiler 
Work. 

(Wilfred  Lewis,  Engineers'  Club  of  Philadelphia,  Nov.,  1893.) 

A  number  of  %-inch  rivets  were  subjected  to  pressures  between  10,000  and 
60.000  Ibs.  At  10,000  Ibs.  the  rivet  swelled  and  filled  the  hole  without  forming 
a  head.  At  20,000  Ibs.  the  head  was  formed  and  the  plates  were  slightly 
pinched.  At  30.000  Ibs.  the  rivet  was  well  set.  At  40,000  Ibs.  the  metal  in  the 
plate  surrounding  the  rivet  began  to  stretch,  and  the  stretching  became 
more  and  more  apparent  as  the  pressure  was  increased  to  50,000  and  60,000 
Ibs.  From  these  experiments  the  conclusion  might  be  drawn  that  the  pres- 
sure required  for  cold  riveting  was  about  300,000  Ibs.  per  square  inch  of  rivet 
section.  In  hot  riveting,  until  recently  there  was  never  any  call  for  a  pres- 
sure exceeding  60,000  Ibs.,  but  now  pressures  as  high  as  150,000  Ibs.  are  not 
Uncommon,  and  even  300,000  Ibs.  have  been  contemplated  as  desirable. 


SHEARING  RESISTANCE  OF  RIVET  IRON  AND  STEEL.   363 


Apparent  Shearing  Resistance  of  Rivet  Iron  and  Steel. 

(Proc.  Inst.  M.  E.,  1879,  Engineering,  Feb.  20,  1880.) 

The  true  shearing  resistance  of  the  rivets  cannot  be  ascertained  from 
experiments  on  riveted  joints  (1),  because  the  uniform  distribution  of  the 
load  to  all  the  rivets  cannot  be  insured;  (2)  because  of  the  friction  of  the 
plates,  which  has  the  effect  of  increasing  the  apparent  resistance  to  shear- 
ing in  an  element  uncertain  in  amount.  Probably  in  the  case  of  single- 
riveted  joints  the  shearing  resistance  is  not  much  affected  by  the  friction; 


Iron,  single  shear  (12  bars). . 
"     double  shear  (8  bars). . 


Ultimate  Shearing  Stress 
Tons  per  sq  in.    Lbs.  per  sq.  in. 


24.15 
22.10 
22.62 
22.30 


54.096  i 
49.504  i 
50.669 
49.952 


Clarke. 

Barnaby. 
Rankine. 


44     %-in.  rivets 23.05  to  25.57  51.632  to  57.277  ) 

"     %-in.  rivets 24.32  to  27.94  54.477  to  62.362  VRiley. 

"      mean  value : 25.0  56. 000  ) 

41     %-in.  rivets 19.01  42.582  Greig and  Eyth. 

Steel 17  to  26  38.080  to  58.240  Parker. 

Landore  steel,  %-in.  rivets..  31.67  to  33.69  70.941  to  75.466  ) 

"  "      pl-in.  rivets...  30. 45  to  35. 73  68.208  to  80.035  VRiley. 

"  "      mean  value..  33.3  74.592) 

Brown's  steel 22 . 18  49 . 683  Greig  and  Eyth. 

Fail-bairn's  experiments  show  that  a  rivet  is  6^  weaker  in  a  drilled  than 
in  a  punched  hole.  By  rounding  the  edge  of  the  rivet-hole  the  apparent 
shearing  resistance  is  increased  12#.  Mr.  Maynard  found  the  rivets  4% 
weaker  in  drilled  holes  than  in  punched  holes.  But  these  results  were 
obtained  with  riveted  joints,  and  not  by  direct  experiments  on  shearing. 
There  is  a  good  deal  of  difficulty  in  determining  the  true  diameter  of  a 
punched  hole,  and  it  is  doubtful  whether  in  these  experiments  the  diameter 
was  very  accurately  ascertained.  Messrs.  Greig  and  Eyth's  experiments 
also  indicate  a  greater  resistance  of  the  rivets  in  punched  holes  than  in 
drilled  holes. 

If,  as  appears  above,  the  apparent  shearing  resistance  is  less  for  double 
than  for  single  shear,  it  is  probably  due  to  unequal  distribution  of  the  stress 
on  the  two  rivet  sections. 

The  shearing  resistance  of  a  bar,  when  sheared  in  circumstances  which 
prevent  friction,  is  usually  less  than  the  tenacity  of  the  bar.  The  following 
results  show  the  decrease  : 


Tenacity  of 
Bar. 

Shearing 
Resistance. 

Ratio. 

Harkort  iron    

26  4 

16.5 

0  62 

La  valley,  iron  

25.4 

20.2 

0.79 

•  j 

Greig  and  Eyth,  iron.  .  . 
44                 "     steel.. 

22.2 

28.8 

19.0 
22.1 

0.85 
0.77 

In  Wohler's  researches  (in  1870)  the  shearing  strength  of  iron  was  found 
to  be  four-fifths  of  the  tenacity.  Later  researches  of  Bauschinger  confirm 
this  result  generally,  but  they  show  that  for  iron  the  ratio  of  the  shearing 
resistance  and  tenacity  depends  on  the  direction  of  the  stress  relatively  to 
the  direction  of  rolling.  The  above  ratio  is  valid  only  if  the  shear  is  in  a 
plane  perpendicular  to  the  direction  of  rolling,  and  if  the  tension  is  applied 
parallel  to  the  direction  of  rolling.  The  shearing  resistance  in  a  plane 
parallel  to  the  direction  of  rolling  is  different  from  that  in  a  plane  perpen- 
dicular to  that  direction,  and  agmn  differs  according  as  the  plane  of  shear  is 
perpendicular  or  parallel  to  the  breadth  of  the  bar.  In  the  former  case  the 
resistance  is  18  to  20$  greater  than  in  a  plane  perpendicular  to  the  fibres,  or 
is  equal  to  the  tenacity.  In  the  latter  case  it  is  only  half  as  great  as  in  a 
plane  perpendicular  to  the  fibres, 


364 


STP:EL. 


IRON  AND   STEEL. 


CLASSIFICATION  OF  IRON  ANI>  STEEL,. 


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CAST  IROK.  365 

CAST  IRON. 

Grading  of  Pig  Iron.— Pig  iron  is  commonly  graded  according  to  its 
fracture,  the  number  of  grades  varying  in  different  districts.  In  Eastern 
Pennsylvania  the  principal  grades  recognized  are  known  as  No.  1  and  2 
foundry,  gray  forge  or  No.  3,  mottled  or  No.  4,  and  white  or  No.  5.  Inter- 
mediate grades  are  sometimes  made,  as  No.  2  X,  between  No.  1  and  No.  2, 
and  special  names  are  given  to  irons  more  highly  silicized  than  No.  1,  as 
No.  1  X,  silver-gray,  and  soft.  Charcoal  foundry  pig  iron  is  graded  by  num- 
bers 1  to  5,  but  the  quality  is  very  different  from  the  corresponding  num- 
bers in  anthracite  and  coke  pig.  Southern  coke  pig  iron  is  graded  into  ten 
or  more  grades.  Grading  by  fracture  is  a  fairly  satisfactory  method  of 
grading  irons  made  from  uniform  ore  mixtures  and  fuel,  but  is  unreliable  as 
a  means  of  determining  quality  of  irons  produced  in  different  sections  or 
from  different  ores.  Grading  by  chemical  analysis,  in  the  latter  case,  is  the 
only  satisfactory  method.  The  following  analyses  of  the  five  standard 
grades  of  northern  foundry  and  mill  pig  irons  are  given  by  J.  M.  Hartman 
(Bull.  L  <&S.A.,  Feb.,  1892): 

No.  1.  No.  2.  No.  3.  No.  4.  No.  4  B.  No.  5. 

Iron 92.37  92.31  94.66  94.48  94.08  94.68 

Graphitic  carbon  ..      3.52  2.99  2.50  2.02  2.02        

Combined  carbon..        .13  .37  1.52  1.98  1.43  3.83 

Silicon 2.44  2.52  .72  .56  .92  .41 

Phosphorus 1.25  1.08  .26  .19  .04  .04 

Sulphur 02  .02  trace  .08  .04  .02 

Manganese 28  .72  .34  .67  2.02  .98 

CHARACTERISTICS  OP  THESE  IRONS. 

No.  1.  Gray. — A  large,  dark,  open-grain  iron,  softest  of  all  the  numbers 
and  used  exclusively  in  the  foundry.  Tensile  strength  low.  Elastic  limit 
low.  Fracture  rough.  Turns  soft  and  tough. 

No.  2.  Gray. —A  mixed  large  and  small  dark  grain,  harder  than  No.  1  iron, 
and  used  exclusively  in  the  foundry.  Tensile  strength  and  elastic  limit 
higher  than  No.  1.  Fracture  less  rough  than  No.  1.  Turns  harder,  less 
tough,  and  more  brittle  than  No.  1. 

No.  3.  Gray. — Small,  gray,  close  grain,  harder  than  No.  2  iron,  used  either 
in  the  rolling-mill  or  foundry.  Tensile  strength  and  elastic  limit  higher  than 
No.  2.  Turns  hard,  less  tough,  and  more  brittle  than  No.  2. 

No.  4.  Mottled. — White  background,  dotted  closely  with  small  black  spots 
of  graphitic  carbon ;  little  or  no  grain.  Used  exclusively  in  the  rolling-mill. 
Tensile  strength  and  elastic  limit  lower  than  No.  3.  Turns  with  difficulty; 
less  tough  and  more  brittle  than  No.  3.  The  manganese  in  the  B  pig  iron 
replaces  part  of  the  combined  carbon,  making  the  iron  harder  and  closing 
the  grain,  notwithstanding  the  lower  combined  carbon. 

No.  5.  White.—  Smooth,  white  fracture,  no  grain,  used  exclusively  in  the 
rolling  mill.  Tensile  strength  and  elastic  limit  much  lower  than  No.  4.  Too 
hard  to  turn  and  more  brittle  than  No.  4. 

Southern  pig  irons  are  graded  as  follows,  beginning  with  the  highest  in 
silicon:  Nos.  1  and  2  silvery,  Nos.  1  and  2  soft,  all  containing  over  3$  of 
silicon;  Nos.  1,  2,  arid  3 foundry,  respectively  about  2.75$,  2.5$  and  2%  silicon; 
No.  1  mill,  or  "foundry  forge;"  No.  2  mill,  or  gray  forge;  mottled;  white. 

Good  charcoal  chilling  iron  for  car  wheels  contains,  as  a  rule,  0.56  to  0.95 
silicon.  0.08  to  0.90  manganese,  0.05  to  0.75  phosphorus.  The  following  is  an 
analysis  of  a  remarkably  strong  car  wheel:  Si,  0.734;  Mn,  0.438:  P.  0.428, 
S,  0.08;  Graphitic  C,  3.083;  Combined  C,  1.247;  Copper,  0.029.  The  chill  was 


per  f,q.  in 

Influence  of  Silicon,  Pliospborus,  Sulphur,  and  Man- 
ganese upon  Cast  Iron.— W.  J.  Keep,  of  Detroit,  in  several  papers 
(Trans  A  I.  M.  E.,  1889  to  1893),  discusses  the  influence  of  various  chemical 
elements  on  thn  quality  of  cast  iron.  From  these  the  following  notes  have 
been  condensed: 

SILICON.— Pig  iron  contains  all  the  carbon  that  it  could  absorb  during  its 
reduction  in  the  blast-furnace.  Carbon  exists  in  cast  iron  in  two  distinct 
forms.  In  chemical  union,  as  "  combined"  carbon,  it  cannot  be  discerned, 
except  as  it  may  increase  the  whiteness  of  the  fracture,  in  so-called  white 


366  IKOtf  AND   STEEL. 

iron.  Carbon  mechanically  mixed  with  the  iron  as  graphite  is  visible,  vary- 
ing in  color  from  gray  to  black,  while  the  fracture  of  the  iron  ranges  from  a 
light  to  a  very  dark  gray. 

Silicon  will  expel  carbon,  if  the  iron,  when  melted,  contains  all  the  car- 
bon that  it  can  hold  and  a  portion  of  silicon  be  added. 

Prof.  Turner  concludes  from  his  tests  that  the  amount  of  silicon  producing 
the  maximum  strength  is  about  1.80$.  But  this  is  only  true  when  a  white 
base  is  used.  If  an  iron  is  used  as  a  base  which  will  produce  a  sound  casting 
to  begin  with,  each  addition  of  silicon  will  decrease  strength.  Silicon  itself  is 
a  weakening  agent.  Variations  in  the  percentage  of  silicon  added  to  a  pig 
iron  will  not  insure  a  given  strength  or  physical  structure,  but  these  results 
will  depend  upon  the  physical  properties  of  the  original  iron. 

After  enough  silicon  has  been  added  to  cause  solid  castings,  any  further 
addition  and  consequent  increase  of  graphite  weakens  the  casting.  The 
softness  and  strength  given  to  castings  by  a  suitable  addition  of  silicdn 
is,  by  a  further  increase  of  silicon,  changed  to  stiffness,  brittleness,  and 
weakness. 

As  strength  decreases  from  increase  of  graphite  and  decrease  of  combined 
carbon,  deflection  increases;  or,  in  other  words,  bending  is  increased  by 
graphite.  When  no  more  graphite  can  form  and  silicon  still  increases,  de- 
flection diminishes,  showing  that  high  silicon  not  only  weakens  iron,  but 
makes  it  stiff.  This  stiffness  is  not  the  same  strength-stiffness  which  is 
caused  by  compact  iron  and  combined  carbon.  It  is  a  brittle-stiffness. 

In  pig  irons  which  received  their  silicon  while  in  the  blast-furnace  the 
graphite  more  easily  separates,  and  the  shrinkage  is  less  than  in  any  mix- 
ture. As  silicon  increases,  shrinkage  also  increases.  Silicon  of  itself  in- 
creases shrinkage,  though  by  reason  of  its  action  upon  the  carbon  in  ordi- 
nary practice  it  is  truly  said  that  silicon  "takes  the  shrinkage  out  of  cast- 
iron."  The  slower  a  casting  crystallizes,  the  greater  will  be  the  quantity 
of  graphite  formed  within  it. 

Silicon  of  itself,  however  small  the  quantity  present,  hardens  cast-iron; 
but  the  decrease  of  hardness  from  the  change  of  the  combined  carbon  to 
graphite,  caused  by  the  silicon,  is  so  much  more  rapid  than  the  hardening 
produced  by  the  increase  of  silicon,  that  the  total  effect  is  to  decrease  hard- 
ness, until  the  silicon  reaches  from  3  to  b%. 

As  practical  foundry- work  does  not  call  for  more  than  3$  of  silicon,  the 
ordinary  use  of  silicon  does  reduce  the  hardness  of  castings;  but  this  is  pro- 
duced through  its  influence  on  the  carbon,  and  not  its  direct  influence  on  the 
iron. 

When  the  change  from  combined  to  graphite  carbon  has  ceased  to  dimin- 
ish hardness,  say  at  from  2j/  to  5$  of  silicon,  the  hardening  by  the  silicon 
itself  becomes  more  and  more  apparent  as  the  silicon  increases. 

Shrinkage  and  hardness  are  almost  exactly  proportional.  When  silicon 
varies,  and  other  elements  do  not  vary  materially,  castings  with  low  shrink- 
age are  soft;  as  shrinkage  increases,  the  castings  grow  hard  in  almost,  if 
not  exactly,  the  same  proportion.  For  ordinary  foundry-practice  the  scale 
of  shrinkage  may  be  made  also  the  scale  of  hardness,  provided  variations  in 
sulphur,  and  phosphorus  especially,  are  not  present  to  complicate  the  re- 
sult. 

The  term  "  chilling  "  irons  is  generally  applied  to  such  as,  cooled  slowly, 
would  be  gray,  but  cooled  suddenly,  become  white  either  to  a  depth  suffi- 
cient for  practical  utilization  (e.g.,  in  car-wheels)  or  so  far  as  to  be  detrimen- 
tal. Many  irons  chill  more  or  less  in  contact  with  the  cold  surface  of  the 
mould  in  which  they  are  cast,  especially  if  they  are  thin.  Sometimes  this 
is  a  valuable  quality,  but  for  general  foundry  purposes  it  is  desirable  to 
have  all  parts  of  a  casting  an  even  gray. 

Silicon  exerts  a  powerful  influence  upon  this  property  of  irons,  partially 
or  entirely  removing  their  capacity  of  chilling. 

When  silicon  is  mixed  with  irons  previously  low  in  silicon  the  fluidity  is 
increased. 

It  is  not  the  percentage  of  silicon,  but  the  state  of  the  carbon  and  the 
action  of  silicon  through  other  elements,  which  causes  the  iron  to  be  huid. 

Silicon  irons  have  always  had  the  reputation  of  imparting  fluidity  to  other 
irons.  This  conies,  no  doubt,  from  the  fact  that  up  to  3$  or  4f,  they  increase 
the  quantity  of  graphite  in  the  resulting  casting. 

From  the  statement  of  Prof.  Turner,  that  the  maximum  strength  occurs 
with  just  such  a  percentage  of  silicon,  and  his  statement  that  a  founder  can, 
with  silicon,  produce  just  the  quality  of  iron  that  he  may  need,  and  from 
his  naming  the  composition  of  what  he  calls  a  typical  foundry-iron,  some 


INFLUENCE  OF  SILICON,  ETC.,  UPOtf  CAST  IROX.     36? 

founders  have  inferred  that  if  they  knew  the  percentages  of  silicon  in  their 
irons  and  in  their  ferro-silicon,  they  need  only  mix  so  as  to  get  2%  of  silicon 
in  order  to  obtain,  always  and  with  certainty,  the  maximum  strength.  The 
solution  of  the  problem  is  not  so  simple.  Each  of  the  irons  which  the  foun- 
der uses  will  have  peculiar  tendencies,  given  them  in  the  blast-furnace, 
which  will  exert  their  influence  in  the  most  unexpected  ways.  However,  a 
white  iron  which  will  invariably  give  porous  and  brittle  castings  can  be 
made  solid  and  strong  by  the  addition  of  silicon;  a  further  addition  of  sili- 
con will  turn  the  iron  gray;  and  as  the  grayness  increases  the  iron  will  grow 
weaker.  Excessive  silicon  will  again  lighten  the  grain  and  cause  a  hard  and 
brittle  as  well  as  a  very  weak  iron.  The  only  softening  and  shrinkage-les- 
sening influence  of  silicon  is  exerted  during  the  time  when  graphite  is  being 
produced,  and  silicon  of  itself  is  not  a  softener  or  a  lessener  of  shrinkage; 
but  through  its  influence  on  carbon,  and  only  during  a  certain  stage,  does  it 
produce  these  effects. 

PHOSPHORUS.— While  phosphorus  of  itself,  in  whatever  quantity  present, 
weakens  cast-iron,  yet  in  quantities  less  than  1.5$  its  influence  is  n  -t  suffi- 
ciently great  to  overbalance  other  beneficial  effects,  which  are  exerted 
before  the  percentage  reaches  \%.  Probably  no  element  of  itself  weakens 
cast  iron  as  much  as  phosphorus,  especially  when  present  in  large  quantities. 

Shrinkage  is  decreased  when  phosphorus  is  increased.  All  high-phosphorus 
pig  irons  have  low  shrinkage.  Phosphorus  does  not  ordinarily  harden  cast 
iron,  probably  for  the  reason  that  it  does  not  increase  combined  carbon. 

The  fluidity  of  the  metal  is  slightly  increased  by  phosphorus,  but  not  to 
any  such  great  extent  as  has  been  ascribed  to  it. 

The  property  of  remaining  long  in  the  fluid  state  must  not  be  confounded 
with  fluidity,  for  it  is  not  the  measure  of  its  ability  to  make  sharp  castings, 
or  to  run  into  the  very  thin  parts  of  a  mould.  Generally  speaking,  the  state- 
ment is  justified  that,  to  some  extent,  phosphorus  prolongs  the  fluidity  of 
the  iron  while  it  is  filling  the  mould. 

The  old  Scotch  irons  contained  about  \%  of  phosphorus.  The  foundry -irons 
which  are  most  sought  for  for  small  and  thin  castings  in  the  Eastern  States 
contain,  as  a  general  thing,  over  \%  of  phosphorus. 

Certain  irons  which  contain  from  4%  to  7$  silicon  have  been  so  much  used 
on  account  of  their  ability  to  soften  other  irons  that  they  have  come  to  be 
known  as  "  softeners  "  and  as  leseeners  of  shrinkage.  These  irons  are  valu- 
able as  carriers  of  silicon  ;  but  the  irons  which  are  sold  most  as  softeners 
and  shrinkage- lessen ers  are  those  containing  from  \%  to  2%  of  phosphorus. 
We  must  therefore  ascribe  the  reputation  of  some  of  them  largely  to  the 
phosphorus  and  not  wholly  to  the  silicon  which  they  contain. 

From  %%  to  \%  of  phosphorus  will  do  all  that  can  be  done  in  a  beneficial 
way,  and  all  above  that  amount  weakens  the  iron,  without  corresponding 
benefit.  It  is  not  necessary  to  search  for  phosphorus-irons.  Most  irons 
contain  more  than  is  needed,  and  the  care  should  be  to  keep  it  within  limits. 

SULPHUR.— Only  a  small  percentage  of  sulphur  can  be  made  to  remain 
in  carbonized  iron,  and  it  is  difficult  to  introduce  sulphur  into  gray  cast  iron 
or  into  any  carbonized  iron,  although  gray  cast  iron  often  takes  from  the 
fuel  as  much  more  sulphur  as  the  iron  originally  contained.  Percentages 
of  sulphur  that  could  be  retained  by  gray  cast  iron  cannot  materially  injure 
the  iron  except  through  an  increase  of  shrinkage.  The  higher  the  carbon, 
or  the  higher  the  silicon,  the  smaller  will  be  the  influence  exerted  by 

The  influence  of  sulphur  on  all  ca«t  iron  is  to  drive  out  carbon  and 
silicon  and  to  increase  chill,  to  increase  shrinkage,  and,  as  a  general  thing,  to 
decrease  strength  ;  but  if  in  practice  sulphur  will  not  enter  such  iron,  we 
shall  not  have  any  cause  to  fear  this  tendency.  In  every-day  work,  however, 
it  is  found  at  times  that  iron  which  was  gray  when  put  into  the  cupola  comes 
out  white,  with  increased  shrinkage  and  chill,  and  often  with  decreased 
strength.  This  is  caused  by  decreased  silicon,  and  can  be  remedied  by  an 
increase  of  silicon. 

Mr  Keep's  opinion  concerning  the  influence  of  sulphur,  quoted  above,  is 
disagreed  with  by  J.  B.  Nau  (Iron  Aye,  March  29,  1894).  He  says  :  m 

"Sulphur  in  whatever  shape  it  may  be  present,  has  a  deleterious  influence 


OUlpIlur    111  WJMHttSVtJi    SUctpC  ll>  incvy   Lie  p*v?crcuu,  a.   >KJ  iv  •L»^+^~~*  -~...^ «- 

on  the  iron.  It  has  the  tendency  to  render  the  iron  white  by  the  influence 
it  exercises  on  the  combination  between  carbon  and  iron.  Pig  iron  contain- 
ing a  certain  percentage  of  it  becomes  porous  and  full  of  holes,  and  castings 
made  from  sulphurous  iron  are  of  inferior  quality.  This  happens  especially 
when  the  element  is  present  in  notable  quantities.  With  foundry-iron  con- 
taining as  high  as  0.1$  of  sulphur,  castings  of  greater  strength  may  be  ob- 


368  IRON"   AHD   STEEL. 

tained  than  when  no  sulphur  is  present.  Thus,  in  some  tests  on  this  element 
quoted  by  R.  Akerman,  it  is  stated  that  in  the  foundry-iron  from  Finspong, 
used  in  the  manufacture  of  cannons,  a  percentage  of  0.1$  to  0.14$  of  sulphur 
in  the  iron  increased  its  strength  to  a  considerable  extent.  The  percentage 
of  sulphur  found  originally  in  the  irou  put  in  the  cupola  is  liable  to  be 
further  increased  by  part  of  the  sulphur  that  is  invariably  found  in  the  coke 
used.  It  is  seldom  that  a  coke  with  a  small  percentage  of  sulphur  is  found, 
whereas  coke  containing  \%  of  it  and  over  is  very  common.  With  such  a 
fuel  in  the  cupola,  if  no  special  precautions  are  resorted  to,  the  percentage 
of  sulphur  in  the  metal  will  in  most  cases  be  increased." 

That  the  sulphur  contents  of  pig  iron  may  be  increased  by  the  sulphur 
contained  in  the  coke  used,  is  shown  by  some  experiments  in  the  cupola, 
reported  by  Mr.  Nau.  Seven  consecutive  heats  were  made. 

The  sulphur  content  of  the  coke  was  1$,  and  11.7$  of  fuel  was  added  to  the 
charge. 

Before  melting,  the  silicon  ranged  from  0.320  to  0.830  in  the  seven  heats  ; 
after  melting,  it  was  from  0.110  to  0.534,  the  loss  in  melting  being  from  .100 
to  .375.  The  sulphur  before  melting  was  from  .076  to  .090,  and  after  melting 
from  .132  to  .174,  a  gain  from  .044  to  .098. 

From  the  results  the  following  conclusions  were  drawn  : 

1.  Iii  all  the  charges,  without  exception,  sulphur  increased  in  the  pig  iron 
after  its  passage  through  the  cupola.     In  some  cases  this  increase  more 
than  doubled  the  original  amount  of  sulphur  found  in  the  pig  iron. 

2.  The  increase  of  the  sulphur  contents  in  the  iron  follows  the  elimination 
of  a  greater  amount  of  silicon  from  that  same  iron.    A  larger  amount  of 
limestone  added  to  these  charges  would  have  produced  a  more  basic  cinder, 
and  undoubtedly  less  sulphur  would  have  been  incorporated  in  the  iron. 

3.  This  coke  contained  1$  of  sulphur,  and  if  all  its  sulphur  had  passed  into 
the  iron  there  would  have  been  an  average  increase  of  0.12  of  sulphur  for 
the  seven  charges,  while  the  real  increase  in  the  pig  iron  amounted  to  only 
0.081.     This  shows  that  two  thirds  of  the  sulphur  of  the  coke  was  taken  up 
by  the  iron  in  its  passage  through  the  cupola. 

'MANGANESE.— Manganese  is  a  nearly  white  metal,  having  about  the  same 
appearance  when  fractured  as  white  cast  iron.  Its  specific  gravity  is 
about  8,  while  that  of  white  cast  iron,  reasonably  free  from  impurities,  is 
but  a  little  above  7.5.  As  produced  commercially,  it  is  combined  with  iron, 
and  with  small  percentages  of  silicon,  phosphorus,  and  sulphur. 

It  is  generally  produced  in  the  blast-furnace.  If  the  manganese  is  under 
40$,  with  the  remainder  mostly  iron,  and  silicon  not  over  0.50$,  the  alloy  is 
called  spiegeleisen,  and  the  fracture  will  show  flat  reflecting  surfaces,  from 
which  it  takes  its  name. 

With  manganese  above  50$,  the  iron  alloy  is  called  ferro-manganese. 

As  manganese  increases  beyond  50$,  the  mass  cracks  in  cooling,  and  when 
it  approaches  98$  the  mass  crumbles  or  falls  in  small  pieces. 

Manganese  combines  with  iron  in  almost  any  proportion,  but  if  an  iron 
containing  manganese  is  remelted,  more  or  less  of  the  manganese  will  escape 
by  volatilization,  and  by  oxidation  with  other  elements  present  in  the  iron. 
If  sulphur  be  present,  some  of  the  manganese  will  be  likely  to  unite  with  it 
and  escape,  thus  reducing  the  amount  of  both  elements  in  the  casting. 

Cast  iron,  when  free  from  manganese,  cannot  hold  more  than  4.50$  of  car- 
bon, and  3.50$  is  as  much  as  is  generally  present ;  but  as  manganese  increases, 
carbon  also  increases,  until  we  often  find  it  in  spiegel  as  high  as  5$,  and  in 
ferro-manganese  as  high  as  6$.  This  effect  on  capacity  to  hold  carbon  is 
oeculiar  to  manganese. 

Manganese  renders  cast  iron  less  plastic  and  more  brittle. 

Manganese  increases  the  shrinkage  of  cast  iron.  An  increase  of  1$  raised 
the  shrinkage  26$.  Judging  from  some  test  records,  manganese  does  not 
influence  chill  at  ail;  but  other  tests  show  that  with  a  given  percentage  of 
silicon  the  carbon  may  be  a  little  more  inclined  to  remain  in  the  combined 
form,  and  therefore  the  chill  may  be  a  little  deeper.  Hence,  to  cause  the 
chill  to  be  the  same,  it  would  seem  that  the  percentage  of  silicon  should  be 
a  little  higher  with  manganese  than  without  it. 

An  increase  of  1$  of  manganese  increased  the  hardness  40$.  If  a  hard 
chill  is  required,  manganese  gives  it  by  adding  hardness  to  the  whole  casting. 

J.  B.  Nau  (Iron  Age^  March  29,  1894),  discussing  the  influence  of  manga- 
nese on  cast  iron,  says: 

Manganese  favors  the  combination  between  carbon  and  iron.  Its  influ- 
ence, when  present  in  sufficiently  large  quantities,  is  even  great  enough  not 
only  to  keep  the  carbon  which  would  be  naturally  found  in  pig  iron  com- 


TESTS  OF  CAST  IROK.  369 

bined,  but  it  increases  the  capacity  of  iron  to  retain  larger  amounts  of  car- 
bon and  to  retain  it  all  in  the  combined  state. 

Manganese  iron  is  often  used  for  foundry  purposes  when  some  chill  and 
hardness  of  surface  is  required  in  the  casting.  For  the  rolls  of  steel-rail 
mills  we  always  put  into  the  mixture  a  large  amount  of  mauganiferous  iron, 
and  the  rolls  so  obtained  always  presented  the  desired  hardness  of  surface 
and  in  general  a  mottled  structure  on  the  outside.  The  inside,  which  al- 
ways cooled  much  slower,  was  gray  iron.  One  of  the  standard  mixtures  that 
invariably  gave  good  results  was  the  following: 

50$  of  foundry  iron  with  1.3$  silicon  and  1.5$  manganese; 
35$  of  foundry  iron  with  \%  silicon  and  1.5$  manganese; 
15$  steel  (rail  ends)  with  about  0.35$  to  0.40$  carbon. 

The  roll  resulting  from  this  mixture  contained  about  1$  of  silicon  and  1$ 
of  manganese. 

Another  mixture,  which  differed  but  little  from  the  preceding,  was  as 
follows: 

45$  foundry  iron  with  about  1.3$  silicon  and  1.5$  manganese; 

30$  foundry  iron  with  about  1$  silicon  and  1.5$  manganese; 

10$  white  or  mottled  iron  with  about  0.5$  to  0.6$  Si.  and  1.2$  Mn. 

15$  Bessemer  steel-rail  ends  with  about  0.35$  to  0.40$  C.  and  0.6$  to  1$  Mn. 

The  pig  iron  used  in  the  preceding  mixtures  contained  also  invariably 
from  1.5$  to  1.8$  of  phosphorus,  so  that  the  rolls  obtained  therefrom  carried 
about  1.3$  to  1.4$  of  that  element.  The  last  mixture  used  produced  rolls 
containing  on  the  average  0.8$  to  1$  of  silicon  and  1$  of  manganese.  When- 
ever we  tried  to  make  those  rolls  from  a  mixture  containing  but  0.2$  to  0.3$ 
manganese  our  rolls  were  invariably  of  inferior  quality,  grayer,  and  con- 
sequently softer.  Manganese  iron  cannot  be  used  indiscriminately  for 
foundry  purposes.  When  greater  softness  is  required  in  the  castings  man- 
ganese has  to  be  avoided,  but  when  hardness  to  a  certain  extent  has  to  be 
obtained  manganese  iron  can  be  used  with  advantage. 

Manganese  decreases  the  magnetism  of  the  iron.  This  characteristic  in- 
creases with  the  percentage  of  manganese  that  enters  into  the  composition 
of  the  iron.  The  iron  loses  all  its  magnetism  when  manganese  reaches  25$ 
of  its  composition.  This  peculiarity  has  been  made  use  of  by  French 
metallurgists  to  draw  a  clear  line  between  spiegel  and  ferro-  manganese. 
When  the  pig  contains  less  than  25$  of  manganese  it  is  classified  as  spiegel, 
and  when  it  contains  more  than  25  it$  is  classified  as  ferro-manganese.  For 
this  reason  manganese  iron  has  to  be  avoided  in  castings  of  dynamo  fields 
and  other  pieces  belonging  to  electric  machinery,  where  magnetic  con  due  - 
tibility  is  one  of  the  first  considerations. 

Irregular  Distribution  of  Silicon  in  Pig  Iron.-J.  W. 
Thomas  (Iron  Aye,  Nov.  12,  1891)  finds  in  analyzing  samples  taken  from  every 
other  bed  of  a  cast  of  pig  iron  that  the  silicon  varies  considerably,  the  iron 
coining  first  from  the  furnace  having  generally  the  highest  percentage.  In 
one  series  of  tests  the  silicon  decreased  from  2.040  to  1.713  from  the  first  bed 
to  the  eleventh.  In  another  case  the  third  bed  had  1.260  Si.,  the  seventh  1.718, 
and  the  eleventh  1.101.  He  also  finds  that  the  silicon  varies  in  each  pig,  be- 
ing higher  at  the  point  than  at  the  butt.  Some  of  his  figures  are:  point  of 
pig  2.328  Si.,  butt  of  same  2.157;  point  of  pig  1.834,  butt  of  same  1.787. 

Some  Tests  of  Cast  Iron.    (G.  Lanza,  Trans.  A.  S.  M.  E.,  x.,  187.)— 
The  chemical  analyses  were  as  follows: 

Gun  Iron,        Common  Iron, 
per  cent.  per  cent. 

Total  carbon  ....................  3.51  ..... 

Graphite..  .....................  2.80  ..... 

Sulphur  ...........  .  .............  0.133  0.173 

Phosphorus  ....................    0.155  0.413 

Silicon  ..........................  1.140  1.89 

The  test  specimens  were  26  inches  long  and  square  in  section;  those  tested 
with  the  skin  on  being  very  nearly  one  inch  square,  and  those  tested  with 
the  skin  removed  being  cast  nearly  one  and  one  quarter  inches  square,  and 
afterwards  planed  down  to  one  inch  square. 


Tensile  Elastic  n 

Strength.  Limit.  ticjt 

Unplaned  common  .  20.200  to  23.000  T.  S.  Av.  =  22,066         6,500  13,194,233 

Planed  common  ...  20,800  to  20,800    ki      "      =20,520         5,833  11,943.953 

Unplaned  gun  .....     27,000  to  28,775    "      "      =28,175  11,000  16,130,300 

Planed  gun  ______    ..  29.500  to  31,000    "      "      =30,500         8,500  15,932,880 


370  IROK   AKD   STEEL. 

The  elastic  limit  is  not  clearly  defined  in  cast  iron,  the  elongations  increas 
\ux  faster  than  the  increase  of  the  loads  from  the  beginning  of  the  test 
The  modulus  of  elasticity  is  therefore  variable,  decreasing  as  the  loads  in- 
crease. For  example,  the  following  results  of  a  test  of  common  cast  iron 
reported  by  Prof.  Lanza: 

T  b«$  ner  «*n   in   Elongation  in         Sets,  Modulus  of 

Lbs.  per  sq.  in.      13  4  incheg  in  Elasticity. 

1000  .0004  18,217,400 

2000  .0013  16,777,700 

3000  .0024  14,085,400 

4000  .0036  13,101,200 

5000  .0048  12,809,200 

6000  .0061  .0000  12,319,300 

8000  .0088  .0001  11,600,800 

10000  .0119  .0001  10,930500 

12000  .0162  .0007  9,714,200 

CHEMISTRY  OF  FOUNDRY  IRONS. 

(C.  A.  Meissner,  Columbia  College  Q?ly,  1890;  Iron  Age,  1890.) 

Silicon  is  a  very  important  element  in  foundry  irons.  Its  tendency  when 
not  above  2^  is' to  cause  the  carbon  to  separate  out  as  graphite,  giving  the 
casting  the  desired  benefits  of  graphitic  iron.  Between  2^  and  3$$£  silicon 
is  best  adapted  for  iron  carrying  a  fair  proportion  of  low  silicon  scrap  and 
close  iron,  for  ordinarily  no  mixture  should  run  below  1J$6  silicon  to  get  good 
castings. 

From  3$  to  5%  silicon,  as  occurs  in  silvery  iron,  will  carry  heavy  amounts  of 
scrap.  Castings  are  liable  to  be  brittle,  however,  if  not  handled  carefully 
as  regards  proportion  of  scrap  used. 

From  l^j  $to  2%  silicon  is  best  adapted  for  machine  work;  will  give  strong 
clean  castings  if  nor,  much  scrap  is  used  with  it. 

Below  \%  silicon  seems  suited  for  drills  and  castings  that  have  to  stand 
great  variations  in  temperature. 

Silicon  has  the  effect  of  making  castings  fluid,  strong,  and  open-grained  ; 
also  sound,  by  its  tendency  to  separate  the  graphite  from  the  total  carbon, 
and  consequent  slight  expansion  of  the  iron  on  cooling,  causing  it  to  fill  out 
thoroughly.  Phosphorus,  when  high,  has  a  tendency  to  make  iron  fluid, 
retain  its  heat  longer,  thereby  helping  to  fill  out  all  small  spaces  in  casting. 
It  makes  iron  brittle,  however,  when  above  %%  in  castings.  It  is  excellent 
when  high  to  use  in  a  mixture  of  low-phosphorus  irons,  up  to  ty$>  giving 
good  results,  but,  as  said  before,  the  casting  should  be  below  %#.  It  has  a 
strong  tendency  when  above  \%  in  pig  to  make  the  iron  less  graphitic,  pre- 
venting the  separation  of  graphite. 

Sulphur  in  open  iron  seldom  bothers  the  founder,  as  it  is  seldom  present 
to  any  extent.  The  conditions  causing  open  iron  in  the  furnace  cause  low 
sulphur.  A  little  manganese  is  an  excellent  antidote  against  sulphur  in  the 
furnace.  Irons  above  \%  manganese  seldom  have  any  sulphur  of  any  con- 
sequence. 

Graphite  is  the  all-important  factor  in  foundry  irons;  unless  this  is  present 
in  sufficient  amount  in  the  casting,  the  latter  will  be  liable  to  be  poor. 
Graphite  causes  iron  to  slightly  expand  on  cooling,  makes  it  soft,  tough  and 
fluid.  (The  statement  as  to  expansion  on  cooling  is  denied  by  VV.  J.  Keep.) 

Relation  of  the  Appearance  of  Fracture  to  the  Chemical 
Composition.  —  S.  H.  Chauvenet  says  when  run  [from  the  blast-fur- 
nace] the  lower  bed  is  almost  always  close-grain,  but  shows  practically  the 
same  analysis  as  the  large  grain  in  the  rest  of  the  cast.  If  the  iron  runs 
rapidly,  the  lower  bed  may  have  as  large  grain  as  any  in  the  cast.  If  the 
iron  runs  rapidly  for,  say,'  six  beds  and  some  obstruction  in  the  tap-hole 
causes  the  seventh  bed  to  fill  up  slowly  and  sluggishly,  this  bed  may  be 
close-grain,  although  the  eighth  bed,  if  the  obstruction  is  removed,  will  be 
open-grain.  Neither  the  graphitic  carbon  nor  the  silicon  seems  to  have  any 
influence  on  the  fracture  in  these  cases,  since  by  analysis  the  graphite  and 
silicon  is  the  same  in  each.  The  question  naturally  arises  whether  it  would 
not  be  better  to  be  guided  by  the  analysis  than  by  the  fracture.  The  frac- 
ture is  a  guide,  but  it  is  not  an  infallible  guide.  Should  not  the  open-  and 
the  close-grain  iron  from  the  same  cast  be  numbered  under  the  same  grade 
when  they  have  the  same  analysis  ? 

Mr.  Meissner  had  many  analyses  made  for  the  comparison  of  fracture 


CHEMISTRY    OP   FOUNDRY    IRONS. 


371 


with  analysis,  and  unless  the  condition  of  furnace,  whether  the  iron  ran 


fast  or  slow,  and  from  what  part  of  pig  bed  the  sample  is  taken,  are  known, 
the  fracture  is  often  very  misleading.    Take  the  following  analyses: 

Silicon  

A. 

B. 

C. 

D. 

E. 

F. 

4.315 
0.008 
3.010 

4.818 
0.008 
2.757 

4.270 
0.007 
2.680 

3.328 
0.033 
2.243 

3.869 
0.006 
3.070 
0.108 

3.861 
0.006 
3.100 
0.096 

Sulphur  
Graphitic  car.. 
Comb,  carbon.. 

A.  Very  close-grain  iron,  dark  color,  by  fracture,  gray  forge. 

B.  Open-grain,  dark  color,  by  fracture.  No.  1. 

C.  Very  close-grain,  by  fracture,  gray  forge. 

D.  Medium-grain,  by  fracture,  No.  2,  but  much  brighter  and  more  open 
than  A,  C,  or  F. 

E.  Very  large,  open-grain,  dark  color,  by  fracture,  No.  1. 

F.  Very  close-grain,  by  fracture,  gray  forge. 

By  comparing  analyses  A  and  B,  or  E  and  F,  it  appears  that  the  close- 
grain  iron  is  in  each  case  the  highest  in  graphitic  carbon.  Comparing  A 
and  E,  the  graphite  is  about  the  same,  but  the  close-grain  is  highest  in 
silicon. 


Analyses  of  Foundry  Irons, 

SCOTCH  IRONS. 


(C.  A.  Meissner.) 


Name. 

Grade. 

Silicon. 

Phos- 
phorus. 

Manga- 
nese. 

Sul- 
phur. 

Graph- 
ite. 

Comb. 
Carbois 

Summerlee        •  • 

1 

2  70 

0  545 

1  80 

0  01 

3  09 

0  25 

1 
1 

2 

2.47 
3.44 
2  70 

0.760 
1.000 
0.810 

2.51 
1.70 
2  90 

0.015 
0.015 
0  02 

2  00 

0  80 

Eglinton  

1 

2.15 

0  618 

2.80 

0  025 

3.76 

0  21 

Coltness 

1 

2  59 

0  840 

1  70 

0  010 

3  75 

3  75 

Carnbroe        .  .. 

1 

1.70 

1  100 

1.83 

0  008 

3  50 

0.40 

Glengarnock  
Glengarnock  said 
to  carry  %  scrap 

1 

2 

3.03 
4.00 

1.200 
0.900 

2.85 
3.41 

0.010 

1.78 

0.90 

AMERICAN  SCOTCH  IRONS. 


No. 
Sample 

Silicon. 

Phos- 
phorus. 

Manganese 

Sulphur. 

No. 
Grade. 

1 

6  00 

0  430 

1  00 

1 

2 

1  67 

1  920 

1  90 

casting 

3 

2  40 

1  000 

1  70 

2 

4 

1.28 

0  690 

1.40 

2 

5a 

3  50 

0  613 

2  51 

1 

56 

2  90 

0  733 

1  40 

casting 

6a 

3  44 

1  000 

1  70 

0  015 

1 

6b 

3  35 

1  300 

1  50 

0  912 

1 

7 

3  68 

0  503 

2  96 

1 

DESCRIPTION  OF  SAMPLES. — No.  1.  Well  known  Ohio  Scotch  iron,  almost 
silvery,  but  carries  two-thirds  scrap;  made  from  part  black-band  ore.  Very 
successful  brand.  The  high  silicon  gives  it  its  scrap-carrying  capacity. 

No.  2.  Brier  Hill  Scotch  castings,  made  at  scale  works;  castings  demand- 
ing more  fluidity  than  strength. 


372 


IROK   AND   STEEL. 


No.  3.  Formerly  a  famous  Ohio  Scotch  brand,  not  now  in  the  market 
Made  mainly  from  black-band  ore. 

No.  4.  A  good  Ohio  Scotch,  very  soft  and  fluid;  made  from  black-band 
ore-mixture. 

Nos.  5a  and  56.  Brier  Hill  Scotch  iron  and  casting;  made  for  stove  pur- 
poses; 350  Ibs.  of  iron  used  to  150  Ibs.  scrap  gave  very  soft  fluid  iron;  worked 
well. 

No.  6a.  Shows  comparison  between  Summerlee  (Scotch)  (6a)  and  Brier  Hill 
Scotch  (66).  Drillings  came  from  a  Cleveland  foundry,  which  found  both 
irons  closely  alike  in  physical  and  working  quality. 

No.  7.  One  of  the  best  southern  brands,  very  hard  to  compete  with,  owing 
to  its  general  qualities  and  great  regularity  of  grade  and  general  working. 

MACHINE  IRONS. 


Sample 
No. 

Silicon. 

Phos- 
phorus. 

Manga- 
nese. 

Sulphur. 

Graphite. 

Comb. 
Carbon. 

Grade 
No. 

8 

2.80 

0  492 

0  61 

0.015 

1 

9 

1  30 

0.262 

0.70 

0  030 

3 

10a 

2  66 

0  770 

1.20 

0.020 

2.51 

2 

106 

3  63 

0  411 

1  25 

0  014 

3.05 

1 

11 

2  10 

0.415 

0.60 

0  050 

2 

12 
13 

1.37 
3  10 

0.294 
0  124 

1.51 
trace 

0.080 
0  021 

2.31 

0.78 

2 

2 

14 

2  12 

0.610 

0.80 

15 

1  70 

0  632 

1  60 

I6a 

1  45 

0  470 

1  25 

0  009 

2 

166 

1  40 

0  316 

1  37 

0  008 

17 

3  26 

0  426 

0  25 

1 

18 

0.80 

0.164 

0.90 

0.015 

1 

DESCRIPTION  OF  SAMPLES. — No.  8.  A  famous  Southern  brand  noted  for  fine 
machine  castings. 

No.  9.  Also  a  Southern  brand,  a  very  good  machine  iron. 

Nos.  ll)a  and  106.  Formerly  one  of  the  best  known  Ohio  brands.  Does  not 
shrink;  is  very  fluid  and  strong.  Foundries  having  used  this  have  reported 
very  favorably  on  it. 

No.  11.  Iron  from  Brier  Hill  Co.,  made  to  imitate  No.  3  ;  was  stronger 
than  No.  3;  did  not  pull  castings;  was  fluid  and  soft. 

No.  12.  Copy  of  a  very  strong  English  machine  iron. 

No.  13.  A  Pennsylvania  iron,  very  tough  and  soft.  This  is  partially  Besse- 
mer iron,  which  accounts  for  strength,  while  high  silicon  makes  it  soft. 

No.  14.  Castings  made  from  Brier  Hill  Co. 's  machine  brand  for  scale  works, 
very  satisfactory,  strong,  soft  and  fluid. 

No.  15.  Castings  made  from  Brier  Hill  Co.'s  one  half  machine  brand,  one 
half  Scotch  brand,  for  scale  works,  castings  desired  to  be  of  fair  strength, 
but  very  fluid  and  soft. 

No.  16a.  Brier  Hill  machine  brand  made  to  compete  with  No.  3. 

No.  166.  Castings  (clothes-hooks)  from  same,  said  to  have  worked  badly, 
castings  being  white  and  irregular.  Analysis  proved  that  some  other  iron 
too  high  in  manganese  had  been  used,  and  probably  not  well  mixed. 

No.  17.  A  Pennsylvania  iron,  no  shrinkage,  excellent  machine  iron,  soft 
and  strong. 

No.  18.  A  very  good  quality  Northern  charcoal  iron. 

"Standard    Grades"    of  the    Brier   Hill   Iron   and   Coal 
Company. 

Brier  Hill  Scotch  Iron.— Standard  Analysis,  Grade  Nos.  1  and  2. 

Silicon 2. 00  to  3. 00 

Phosphorus 0.50  to  0.75 

Manganese 2.00  to  2. 50 

Used  successfully  for  scales,  mowing-machines,  agricultural  implements, 
novelty  hardware,  sounding-boards,  stoves,  and  heavy  work  requiring  no 
special  strength. 


CHEMISTRY    OF   FOUNDRY    IRONS. 


372 


Brier  Hill  Silvery  Iron.— Standard  Analysis,  Grade  No.  1. 

Silicon 3. 50  to  5. 50 

Phosphorus 1 .00  to  1 .50 

Manganese 2.00  to  2.25 

Used  successfully  for  hollow-ware,  car-wheels,  etc.,  stoves,  bumpers,  and 
similar  work,  with  heavy  amounts  of  scrap  in  all  cases.  Should  be  mainly 
used  where  fluidity  and  no  great  strength  is  required,  especially  for  heavy 
work.  When  used  with  scrap  or  close  pig  low  in  phosphorus,  castings  of 
considerable  strength  and  great  fluidity  can  be  made 

Fairly  Heavy  Machine  Iron.— Standard  Analysis,  Grade  No.  1. 

Silicon 1 .75  to  2.50 

Phosphorus 0.50to0.60 

Manganese 1.20  to  1.40 

The  best  iron  for  machinery,  wagon-boxes,  agricultural  implements, 
pump-w'orks,  hardware  specialties,  lathes,  stoves,  etc.,  where  no  large 
amounts  of  scrap  are  to  be  carried,  and  where  strength,  combined  with 
great  fluidity  and  softness,  are  desired.  Should  not  have  much  scrap  with 
it. 

Regular  Machine  Iron. — Standard  Analysis,  Grade  Nos.  1  and  2. 

Silicon 1.50  to  2.00 

Phosphorus 0.30  to  0.50 

Manganese 0.80  to  1.00 

Used  for  hardware,  lawn-mowers,  mower  and  reaper  works,  oil-well 
machinery,  drills,  fine  machinery,  stoves,  etc.  Excellent  for  all  small  fine 
castings  requiring  fair  fluidity,  softness,  and  mainly  strength.  Cannot  be 
well  used  alone  for  large  castings,  but  gives  good  results  on  same  when  used 
with  above  mentioned  heavy  machine  grade;  also  when  used  with  the 
Scotch  in  right  proportion.  Will  carry  but  little  scrap,  and  should  be  used 
alone  for  good  strong  castings. 

For  Axles  and  Materials  Requiring  Great  Strength,  Grade  No.  2. 

Silicon 1 . 50 

Phosphorus 0.200  and  less. 

Manganese 0.80 

This  gave  excellent  results. 

A  good  neutral  iron  for  guns,  etc.,  will  run  about  as  follows  : 

Silicon 1 . 00 

Phosphorus 0.25 

Sulphur 0.20 

Manganese none. 

It  should  be  open  No.  1  iron. 

This  gives  a  very  tough,  elastic  metal.  More  sulphur  would  make  tough 
but  decrease  elasticity. 

For  fine  castings  demanding  elegance  of  design   but  no  strength,  phos- 
phorus to  3.00$  is  good.    Can  also  stand  1.50$  to  2. 00$  manganese.    For  work 
of  a  hard,  abrasive  character  manganese  can  run  2.00$  in  casting. 
Analyses  of  Castings. 


Sample 
No. 

Silicon. 

Phos- 
phorus. 

Manganese 

Sulphur. 

Graphite. 

Comb. 
Carbon. 

31 

2  50 

1  400 

2.20 

3-2 

0  85 

0.351 

0.92 

0  030 

33 
34tt 

1.53 
1.84 

0.327 
0.577 

1.08 
1.04 

0.040 

3.10 

0.58 

346 

2  20 

0  742 

1  10 

34c 

2  50 

1  208 

1  16 

35« 

2.80 

0.418 

0.54 

356 

3  10 

1  280 

1.14 

35c 

3.30 

0.879 

0.80 

35tf 

2.88 

0.408 

1.10 

35e 

4  50 

0.660 

0.78 

36 

3.43 

1.439 

0.90 

0.025  . 

37a 

2  68 

0.900 

1.30 

876 

1.90 

0.980 

1.20 

374  IRCW   AND   STEEL. 

No.  31.  Sewing-machine  casting,  said  to  be  very  fluid  and  good  casting. 
This  is  an  odd  analysis.  I  should  say  it  would  have  been  too  hard  and  brit- 
tle, yet  no  complaint  was  made. 

No.  32.  Very  good  machine  casting,  strong,  soft,  no  shrinkage. 

No.  33.  Drillings  from  ati  annealer-box  that  stood  the  heat  very  well. 

No.  34a.  Drillings  from  door-hinge,  very  strong  and  soft. 

No.  346.  Drillings  from  clothes-hooks,  tough  and  soft,  stood  severe  ham- 
mering. 

No.  34c.  Drillings  from  window-blind  hinge,  broke  off  suddenly  at  light 
strain.  Too  high  phosphorus. 

No.  35«.  Casting  for  heavy  ladle  support,  very  strong. 

Nos  356  and  35c.  Broke  after  short  usage.  Phosphorus  too  high.  Car- 
bumpers. 

No.  35d.  Elbow  for  steam  heater,  very  tough  and  strong. 

No.  36.  Cog-wheels,  very  good,  shows  absolutely  no  shrinkage. 

No.  37.  Heater  top  network,  requiring  fluidity  but  no  strength.     * 

No.  37a.  Gray  part  of  above. 

No.  376.  White,  honeycombed  part  of  above.  Probably  bad  mixing  and 
got  chilled  suddenly. 

STRENGTH    OF    CAST    IRON. 

Rankine  gives  the  following  figures: 

Various  qualities,  T.  S 13,400  to        29,000,  average        16,500 

Compressive  strength 82,000  to       145,000,        4*  112,000 

Modulus  of  elasticity 14,000,000  to  22,900,000,        "         17,000,000 

Specific  Gravity  and  Strength,    (Major  Wade,  1856.) 

Third-class  guns:  Sp.  Gr.  7.087,  T.  S.  20,148.  Another  lot:  least  Sp.  Gr.  7.163, 
T.  S.  22,402. 

Second-class  guns:  Sp.  Gr.  7.154,  T.  S.  24,767.  Another  lot :  mean  Sp.  Gr. 
7.302,  T.  S.  27,232. 

First  class  guns:  Sp.  Gr.  7.204,  T.  S.  28,805.  Another  lot:  greatest  Sp.  Gr 
7.402,  T.  S.  31,027. 

Strength  of  Charcoal  Pig  Iron. -Pig  iron  made  from  Salisbury 
ores,  in  furnaces  at  Wassaic  and  Millerton,  N.  Y.,  has  shown  over  40,000  Ibs. 
T.  S.  per  square  inch,  one  sample  giving  42,281  Ibs.  Muirkirk,  Md.,  iron 
tested  at  the  Washington  Navy  Yard  showed:  average  for  No.  2  iron  "21,601 
Ibs. ;  No.  3,  23,959  Ibs. ;  No.  4,  41,329  Ibs. ;  average  density  of  No.  4,  7.336  (J.  C. 
I.  W.,  v.  p.  44.) 

Nos.  3  and  4  charcoal  pig  iron  from  Chapinville,  Conn.,  showed  a  tensile 
strength  per  square  inch  of  from  34,761  Ibs.  to  41,882  Ibs.  Charcoal  pig  iron 
from  Shelby,  Ala.  (tests  made  in  August,  1891),  showed  a  strength  of 
34,800  Ibs.  for  No.  3;  No.  4,  39,675  Ibs. ;  No.  5,  46,450  Ibs. ;  and  a  mixture  of 
equal  parts  of  Nos.  2,  3,  4.  and  5,  41.470  ibs.  (Bull.  I.  &  S.  A.) 

Variation  of  Density  and  Tenacity  of  Gun-irons,— An  in- 
crease of  density  invariably  follows  the  rapid  cooling  of  cast  iron,  and  as  a 
general  rule  the  tenacity  is  increased  by  the  same  means.  The  tenacity 
generally  increases  quite  uniformly  with  the  density,  until  the  latter  ascends 
to  some 'given  point;  after  which  an  increased  density  is  accompanied  by  a 
diminished  tenacity. 

The  turning-point  of  density  at  which  the  best  qualities  of  gun-iron  attain 
their  maximum  tenacity  appears  to  be  about  7.30.  At  this  point  of  density, 
or  near  it,  whether  in  proof-bars  or  gun-heads,  the  tenacity  is  greatest. 

As  the  density  of  iron  is  increased  its  liquidity  when  melted  is  diminished. 
This  causes  it  to  congeal  quickly,  and  to  form  cavities  in  the  interior  of  the 
casting.  (Pamphlet  of  Builders1  Iron  Foundry,  1893.) 

Specifications  for  Cast  Iron  for  the  World's  Fair  Rulld- 
ings9  1892,— Except  where  chilled  iron  is  specified,  all  castings  shall  be 
of  tough  gray  iron,  free  from  injurious  cold-shuts  or  blow-holes,  true  to 
pattern,  and  of  a  workmanlike  finish.  Sample  pieces  1  in.  square,  cast  from 
the  same  heat  of  metal  in  sand  moulds,  shall  be  capable  of  sustaining  on  a 
clear  span  of  4  feet  6  inches  a  central  load  of  500  Ibs.  when  tested  in  the 
rough  bar. 

Specifications  for  Tests  of  Cast  Iron  in  12"  B,  L.  Mortars, 
(Pamphlet  of  Builders  Iron  Foundry,  1893.) — Charcoal  Gun  Iron.— The  tensile 
strength  of  the  metal  must  average  at  each  end  at  least  30,000  Ibs.  per 
square  inch  ;  no  specimen  to  be  over  37,000  Ibs.  per  square  inch  ;  but  one 
specimen  from  each  end  may  be  as  low  as  28,000  Ibs.  per  square  inch.  The 


MALLEABLE   CAST   IROtf.  375 

long  extension  specimens  will  not  be  considered  in  making  up  these  aver- 
ages, but  must  show  a  good  elongation  and  an  ultimate  strength,  for  each 
specimen,  of  not  less  than  24,000  Ibs.  The  density  of  the  metal  must  be  such 
as  to  indicate  that  the  metal  has  been  sufficiently  refined,  but  not  carried  so 
high  as  to  impair  the  other  qualities. 

Specifications  for  Grading  Pig?  Iron  for  Car  Wheels  by 
Chill  Tests  made  at  the  Furnace.  (Penna.  R.  R.  Specification.-, 
1883  )— The  chill  cup  is  to  be  filled,  evtnifuli,  at  about  the  middle  of  every 
cast  from  the  furnace.  The  test-piece  so  made  will  be  7J^  inches  long,  3J^ 
inches  wide,  and  1%  inches  thick,  and  is  to  be  broken  across  the  centre  when 
entirely  cold.  The  depth  of  chill  will  be  shown  on  the  bottom  of  the  test- 
piece,  and  is  to  be  measured  by  the  clean  white  portion  to  the  point  where 
gray  specks  begin  to  show  in  the  white.  The  grades  are  to  be  by  eighths  of 
an  inch,  viz.,  ^,  J4,  %,  14,  % .%,  %,  etc.,  until  the  iron  is  mottled;  the  lowest 
grade  being  ^  of  an  inch  in  depth  of  chill.  The  pigs  of  each  cast  are  to  b 
marked  with  the  depth  of  chill  shown  by  its  test-piece,  and  each  grade 
is  to  be  kept  by  itself  at  the  furnace  and  in  forwarding. 

Mixture  of  Cast  Iron  with  Steel.— Car  wheels  are  sometimes 
made  from  a  mixture  of  charcoal  iron,  anthracite  iron,  and  Bessemer 
steel.  The  following  shows  the  tensile  strength  of  a  number  of  tests  of 
wheel  mixtures,  the  average  tensile  strength  of  the  charcoal  iron  used  being 
22,000  Ibs.: 

Ibs.  per  sq.  in. 

Charcoal  iron  with  2*4$  steel ....   22,467 

"         *    3%#steel ' 26,733 

"         '    &W"  steel  an  d  6*4#  anthracite.... 24,400 

'    7i<«$  steel  and  iy>%  anthracite 28,150 

"         *    2M&  steH,  2^  wro't  iron,  and  &/&  anth. ..  25,550 

__^  "         '    5    %  steel,  5$  wro't  iron,  and  10  %  anth 26,500 

(Jour.  C.  L  W.,  iii.  p.  184.) 

Cast  Iron  Partially  Bessemerized.— Car  wheels  made  of  par- 
tially Bessemerized  iron  (blown  in  a  Bessemer  converter  for  3^  minutes), 
chilled  in  a  chill-test  mould  over  an  inch  deep,  just  as  a  test  of  cold-blast 
charcoal  iron  for  car  wheels  would  chill.  Car  wheels  made  of  this  blown 
iron  have  run  250,000  miles.  (Jour.  C.  L  W.^  vi.  p.  77.) 

Bad  Cast  Iron.— On  October  15,  1891,  the  cast-iron  fly-wheel  of  a  large 
pair  of  Corliss  engines  belonging  to  the  Amoskeag  Mfg.  Co.,  of  Manchester, 
N.  H.,  exploded  from  centrifugal  force.  The  fly-wheel  was  30  feet  diam- 
eter and  110  inches  face,  with  one  set  of  12  arms,  and  weighed  116,000  Ibs. 
After  the  accident,  the  rim  castings,  as  well  as  the  ends  of  the  arms,  were 
found  to  be  full  of  flaws,  caused  chiefly  by  the  drawing  and  shrinking  of  the 
metal.  Specimens  of  the  metal  were  tested  for  tensile  strength,  and  varied 
from  15,000  Ibs.  per  square  inch  in  sound  pieces  to  1000  Ibs.  in  spongy  ones. 
None  of  these  flaws  showed  on  the  surface,  and  a  rigid  examination  of  the 
parts  before  they  were  erected  failed  to  give  any  cause  to  suspect  their  true 
nature.  Experiments  were  carried  on  for  some  time  after  the  accident  in 
the  Amoskeag  Company's  foundry  in  attempting  to  duplicate  the  flaws,  but 
with  no  success  in  approaching  the  badness  of  these  castings. 

MALLEABLE   CAST   IRON. 

Malleableized  cast  iron,  or  malleable  iron  castings,  are  castings  made 
jf  ordinary  cast  iron  which  have  been  subjected  to  a  process  of  decarboni- 
zation,  which  results  in  the  production  of  a  crude  wrought  iron.  Handles, 
latches,  and  other  similar  articles,  cheap  harness  mountings,  plowshares, 
iron  handles  for  tools,  wheels,  and  pinions,  and  many  small  parts  of  ma- 
chinery, are  made  of  malleable  cast  iron.  For  such  pieces  charcoal  cast  iron 
of  the  best  quality  (or  other  iron  of  similar  chemical  composition),  should 
be  selected.  Coke  irons  low  in  silicon  and  sulphur  have  been  used  in  place 
of  charcoal  irons.  The  castings  are  made  in  the  usual  way,  and  are  then 
imbedded  in  oxide  of  iron,  in  the  form,  usually,  of  hematite  ore,  or  in  per- 
oxide of  manganese,  and  exposed  to  a  full  red-heat  for  a  sufficient  length  of 
tims,  to  insure  the  nearly  complete  removal  of  the  carbon.  This  decarboniza- 
tiorr  is  conducted  in  cast-iron  boxes,  in  which  the  articles,  if  small,  are 
packed  in  alternate  layers  with  the  decarbonizing  material.  The  largest 
pieces  require  the  longest  time.  The  fire  is  quickly  raised  to  the  maximum 
temperature,  but  at  the  close  of  the  process  the  furnace  is  cooled  very 
slowly.  The  operation  requires  from  three  to  five  days  with  ordinary  small 
castings,  and  may  take  two  weeks  for  large  pieces. 


376 


IRON   AHD   STEEL. 


Rules  for  Use  of  Malleable  Castings,  by  Committee  of  Master 
Carbuilders1  Ass'n,  1890. 

1.  Never  run  abruptly  from  a  heavy  to  a  light  section. 

2.  As  the  strength  of  malleable  cast  iron  lies  in  the  skin,  expose  as  much 
surface  as  possible.     A  star-shaped  section  is  the  strongest  possible  from 
which  a  casting  can  be  made.  For  brackets  use  a  number  of  thin  ribs  instead 
of  one  thick  one. 

3.  Avoid  all  round  sections;  practice  has  demonstrated  this   to  be  the 
weakest  form.    Avoid  sharp  angles. 

4.  Shrinkage  generally  in  castings  will  be  3/16  in.  per  foot. 
Strength  of  Malleable  Cast  Iron.— Experiments  on  the  strength 

of  malleable  cast  iron,  made  in  1891  by  a  committee  of  the  Master  Car- 
builders'  Association.  The  strength  of  this  metal  varies  with  the  thickness, 
as  the  following  results  on  specimens  from  14  in.  to  1^$  in.  in  thickness  show: 


Dimensions. 

Tensile  Strength. 

Elongation. 

Elastic  Limit. 

in.           in. 
1.52  by     .25 

Ib.  per  sq.  in. 
34,700 

percent  in  4  in. 

i 

Ib.  per  sq.  in. 
21,100 

1.52           .39 

33,700 

2 

15,200 

1.53           .5 

32,800 

2 

17,000 

1.53           .64 

32,100 

2 

19,400 

2.               .78 

25,100 

jl^ 

15,400 

1.54           .88 

33,600 

l/^ 

19,300 

1.06         1.02 

30,600 

1 

17,600 

1.28        1.3 

27,400 

1 

1.52         1.54 

28,200 

m 

The  low  ductility  of  the  metal  is  worthy  of  notice.  Tl 
the  following  table  of  the  comparative  tensile  resistan 
malleable  cast  iron,  as  compared  with  other  materials: 


The  committee  gives 
~~       and  ductility  of 


Ultimate 
Strength, 
Ib.  per  sq.  in 

Comparative 
Strength  ; 
Cast  Iron 

Elongation 
Per  Cent 
in  4  in. 

Comparative 
Ductility; 
Malleable 
Cast  Iron 
-  1. 

Cast  iron 

20  000 

1 

0  35 

0  17 

Malleable  cast  iron. 
Wrought  iron  
Steel  castings  

32,000 
50,000 
60,000 

1.6 
2.5 
3 

2.00 
20.00 
10.00 

1 
10 
5 

Another  series  of  tests,  reported  to  the  Association  in 
following: 


'2,  gave  the 


Thick- 
ness. 

Width. 

Area. 

Elastic 
Limit. 

Ultimate 
Strength. 

Elongation 
in  8  in. 

in. 

.271 

in. 

2.81 

sq.  in. 
.7615 

Ib.  per  sq. 
23.520 

Ib.  per  sq.  in. 
32,620 

percent. 
1.5 

.293 

2.78 

.8145 

22,650 

28,160 

.6 

.39 

2.82 

1.698 

20,595 

32,060 

1.5 

.41 

2.79 

1.144 

20,230 

28,850 

1.0 

.529 

2.76 

1.46 

19,520 

27,875 

1.1 

.661 

2.81 

1.857 

18,840 

25,700 

.7 

.-8 

2.76 

2.208 

18.390 

25,120 

1.1 

1.025 

2.82 

2.890 

18,220 

28,720 

1.5  • 

1.117 

2.81 

3.138 

17,050 

25,510 

1.3 

.1.021 

2.82 

2.879 

18,410 

26,950 

1.8 

WKOUGHT   IROl 


WROUGHT  IRON. 

Influence  of  Chemical  Composition  on  the  Properties 
of  Wrought  Iron,  (Beardslee  on  Wrought  Iron  and  Chain  Cables. 
Abridgement  by  VV.  Kent.  Wiley  &  Sous,  1879.)— A  series  of  2000  tests  of 
specimens  from  14  brands  of  wrought  iron,  most  of  them  of  high  repute, 
was  made  in  1877  by  Capt.  L.  A.  Beardslee,  U.S.N.,  of  the  United  States 
Testing  Board.  Forty-two  chemical  analyses  were  made  of  these  irons, 
\\ith  a  view  to  determine  what  influence  the  chemical  composition  had 
upon  the  strength,  ductility,  and  welding  power.  From  the  report  of  these 
tests  by  A.  L.  Holley  the  following  figures  are  taken  : 


Average 

Chemical  Composition. 

Brand. 

Tensile 

Strength. 

S. 

P. 

Si. 

C. 

Mn. 

Slag. 

L 

66,598 

trace 

(0.065 
"JO.  084 

0.080 
0.105 

0.212 
0.512 

0.005 
0.029 

0.192 
0.452 

P 

54,363 

(0.009 
(0.001 

0.250 
0.095 

0.182 
0.028 

0.033 
0.066 

0.033 
0.009 

0.84S 
1.214 

B 

52,764 

0.008 

0.231 

0.156 

0.015 

0.017 

J 

51,754 

JO.  003 
1  0.005 

0.140 
0.291 

0.182 
0.321 

0.027 
0.051 

trace 
0.053 

0.678 
1.724 

O 

51,134 

JO.  004 
"(0.005 

0.067 
0.078 

0.065 
0.073 

0.045 
0.042 

0.007 
0.005 

1.168 
0.974 

C 

50,765 

0.007 

0.169 

0.154 

0.042 

0.021 

Tensile 
Strength. 

Reduction 
of  Area. 

Elongation. 

Welding  Power. 

1 

18 

19 

most  imperfect. 

6 

6 

3 

badly. 

12 

16 

15 

best. 

16 

19 

18 

rather  badly. 

18 

1 

4 

very  good. 

19 

12 

16 



Where  two  analyses  are  given  they  are  the  extremes  of  two  or  more  ana- 
lyses of  the  brand.  Where  one  is  given  it  is  the  only  analysis.  Brand  L 
should  be  classed  as  a  puddled  steel. 

ORDER  OP  QUALITIES  GRADED  FROM  No.  1  TO  No.  19. 
Brand. 

L 
P 
B 
J 
O 
C 

The  reduction  of  area  varied  from  54.2  to.  25.9  per  cent,  and  the  elonga- 
tion from  29.9  to  8.3  per  cent. 

Brand  O,  the  purest  iron  of  the  series,  ranked  No.  18  in  tensile  strength, 
but  was  one  of  the  most  ductile;  brand  B.  fquite  impure,  was  below  the 
average  both  in  strength  and  ductility,  but  was  the  best  in  welding  power; 
P,  also  quite  impure,  was  one  of  the  best  in  every  respect  except  welding, 
while  L,  the  highest  in  strength,  was  not  the  most  pure,  it  had  the  least 
ductility,  and  its  welding  power  was  most  imperfect.  The  evidence  of  the 
influence  of  chemical  composition  upon  quality,  therefore,  is  quite  contra- 
dictory and  confusing.  The  irons  differing  remarkably  in  their  mechanical 
properties,  it  was  found  that  a  much  more  marked  influence  upon  their 
qualities  was  caused  by  different  treatment  in  rolling  than  by  differences  in 
composition. 

In  regard  to  slag  Mr.  Holley  says  :  "  It  appears  that  the  smallest  and 
most  worked  iron  often  has  the  most  slag.  It  is  hence  reasonable  to  con- 
clude that  an  iron  may  be  dirty  and  yet  thoroughly  condensed." 

In  his  summary  of  "  What  is  learned  from  chemical  analysis,'1  he  says  : 
"  So  far,  it  may  appear  that  little  of  use  to  the  makers  or  users  of  wrought 
iron  has  been  learned.  .  .  .  The  character  of  steel  can  be  surely  pred- 
icated on  the  analyses  of  the  materials;  that  of  wrought  iron  is  altered  by 
subtle  and  unobserved  causes  " 

Influence  of  Reduction  in  Rolling  from  Pile  to  Bar  on 
the  Strength  of  Wrought  Iron.— The  tensile  strength  of  the  irons 
used  in  Beardslee's  tests  ranged  from  46,000  to  62,700  Ibs.  per  sq.  in.,  brand 
L,  which  was  really  a  steel,  not  being  considered.  Some  specimens  of  L 
gave  figures  as  high  as  70,000  Ibs.  The  amount  of  reduction  of  sectional 


3f*/o 
78 


AKD   STEEL. 


area  in  rolling  the  bars  has  a  notable  influence  on  the  strength  and  elastic 
limit;  the  greater  the  reduction  from  pile  to  bar  the  higher  the  strength. 
The  following  are  a  few  figures  from  tests  of  one  of  the  brands  : 

Size  of  bar,  in.  diam.:  432  1  ^             y± 

Area  of  pile,  sq.  in.:  80              80              72  25  9               3 

Bar  per  cent  of  pile  :  15.7           8.83           4.36  3.14  2.17           1.6 

Tensile  strength,  lb.:  46,322        47,761        48,280  51,128  52,275  59,585 

Elast ic  limit,  lb.:  23,430       26,400        31,892  36,467  39,126  

Specifications  for  Wrought  Iron  (F.  H.  Lewis,  Engineers'  Club 
of  Philadelphia,  1891).—!.  All  wrought  iron  must  be  tough,  ductile,  fibrous, 
and  of  uniform  quality  for  each  class,  straight,  smooth,  free  from  cinder- 
pockets,  flaws,  buckles,  blisters,  and  injurious  cracks  along  the  edges,  and 
must  have  a  workmanlike  finish.  No  specific  process  or  provision  of 
manufacture  will  be  demanded,  provided  the  material  fulfils  the  require- 
ments of  these  specifications. 

2.  The  tensile  strength,  limit  of  elasticity,  and  ductility  shall  be  deter- 
mined from  a  standard  test-piece  not  less  than  14  inch  thick,  cut  from  the 
full-sized  bar,  and  planed  or  turned  parallel.    The  area  of  cross-section  shall 
not  be  less  than  %  square  inch.    The  elongation  shall  be  measured  after 
breaking  on  an  origin jl  length  of  8  inches. 

3.  The  tests  shall  show  not  less  than  the  following  results: 


Ultimate 
Strength, 
Ibs  per  sq. 
inch. 

Limit  of 
Elasticity, 
Ibs.  per  sq. 
inch. 

Elongation  in 
8  inches, 
per  cent. 

For  bar  iron  in  tension  

50000 

26000 

18 

For  shape  iron 

48000 

26  000 

15 

For  plates  under  36  in.  wide  
For  plates  over  36  in.  wide  

48,000 
46,000 

26,000 
25,000 

12 
10 

4.  When   full-sized  tension  members  are  tested  to  prove  the  strength  of 
their  connections,  a  reduction  in  their  ultimate  strength  of  (500  x  width  of 
bar)  pounds  per  square  inch  will  be  allowed. 

5.  All  iron  shall  bend,  cold,  180  degrees  around  a  curve  whose  diameter 
is  twice  the  thickness  of  piece  for  bar  iron,  and  three  times  the  thickness 
for  plates  and  shapes. 

6.  Iron  which  is  to  be  worked  hot  in  the  manufacture  must  be  capable 
of  bending  sharply  to  a  riglit  angle  at  a  working  heat  without  sign  of 
fracture. 

7.  Specimens  of  tensile  iron  upon  being  nicked  on  one  side  and  bent  shall 
show  a  fracture  nearly  all  fibrous. 

8.  All  rivet  iron  must  be  tough  and  soft,  and  be  capable  of  bending  cold 
until  the  sides  are  in  close  contact  without  sign  of  fracture  on  the  convex 
sidp  of  the  curve. 

Pennsylvania  Railroad  Specifications  for  Merchant  Bar 
Iron  or  Steel,— Miscellaneous  merchant  bar  iron  or  steel  tor  which  no 
special  specifications  defining  shapes  and  uses  are  issued,  should  have  a 
tensile  strength  of  50,000  to  55,000  Ibs.  per  square  inch  and  an  elongation  of 
20%  in  a  section  originally  2  inches  long. 

No  iron  or  steel  will  be  accepted  under  this  specification  if  tensile  strength 
falls  below  48,000  Ibs  or  goes  above  60,000  Ibs.  per  square  inch,  nor  if  elon- 
gation is  less  than  15$  in  2  inches,  nor  if  it  shows  a  granular  fracture  cover- 
ins:  more  than  50$  of  the  fractured  surface,  nor  if  it  shows  any  difficulty  in 
welding. 

In  preparing  test-pieces  from  round  or  rectangular  bars,  they  will  be 
turned  or  shaped  so  that  the  tested  sections  may  be  the  central  portion  of 
the  bar,  in  all  sizes  up  to  1%  inches  in  any  diametrical  or  side  measurement. 
In  larger  sizes  test-pieces  will  be  made  to  fall  about  half-way  from  centre  to 
circumference. 

Bars  of  iron  ^  in.  thick  or  less,  or  tortured  forms  of  iron,  such  as  angle,  tee 
or  channel  bars,  will  be  accepted  if  tensile  strength  is  above  45,000  Ibs.  and 
elongation  above  12$;  but  the  testing  of  such  sizes  and  sections  is  optional. 


FORMULA  FOR  UNIT  STRAINS  FOR  IKON  AND  STEKL.  3? 9 


Specifications  for  Wrought  Iron  for  the  World's  Fair 
Buildings.  (Eng'g  News,  March  26,  189^.)  All  iron  to  be  used  in  the 
tensile  members  of  open  trusses,  laterals,  pins  and  bolts,  except  plate  iron 
over  8  inches  wide,  and  shaped  iron,  must  show  by  the  standard  test-pieces 
a  tensile  strength  in  Ibs.  per  square  inch  of  : 

7,000  X  area  of  original  bar  in  sq.  in. 
circumference  of  original  bar  in  inches ' 

with  an  elastic  limit  not  less  than  half  the  strength  given  by  this  formula, 
and  an  elongation  of  20$  in  8  in. 

Plate  iron  24  inches  wide  and  under,  and  more  than  8  inches  wide,  must 
show  by  the  standard  test-pieces  a  tensile  strength  of  48,000  Ibs.  per  sq.  in. 
with  an  elastic  limit  not  less  than  26,000  Ibs.  per  square  inch,  and  an  elon- 
gation of  not  less  than  12$.  All  plates  over  24  inches  in  width  must  have  a 
tensile  strength  not  less  than  46,000  Ibs.,  with  an  elastic  limit  not  less  than 
26,000  Ibs.  per  square  inch.  Plates  from  24  inches  to  36  inches  in  width  must 
have  an  elongation  of  not  less  than  10$;  those  from  38  inches  to  48  inches  in 
width,  8$;  over  48  inches  in  width,  5$. 

All  shaped  iron,  flanges  of  beams  and  channels,  and  other  iron  not  herein- 
before specified,  must  show  by  the  standard  test-pieces  a  tensile  strength  in 
Ibs.  per  square  inch  of  : 

7,000  X  area  of  original  bar 
circumference  of  original  bar' 

with  an  elastic  limit  of  not  less  than  half  the  strength  given  by  this  formula, 
and  an  elongation  of  15$  for  bars  %  inch  and  less  in  thickness,  and  of  12$  for 
bars  of  greater  thickness.  For  webs  of  beams  and  channels,  specifications 
for  plates  will  apply. 

All  rivet  iron  must  be  tough  and  soft,  and  pieces  of  the  full  diameter  of 
the  rivet  must  be  capable  of  bending  cold,  until  the  sides  are  in  close  contact, 
without  sign  of  fracture  on  the  convex  side  of  the  curve. 

Stay-bolt  Iron.— Mr.  Vauclain,  of  the  Baldwin  Locomotive  Works, 
at  a  meeting  of  the  American  Railway  Master  Mechanics'  Association,  in 
1892,  says:  Many  advocate  the  softest  iron  in  the  market  as  the  best  for 
stay-bolts.  He  believed  in  an  iron  as  hard  as  was  consistent  with  heading 
the  bolt  nicely.  The  higher  the  tensile  strength  of  the  iron,  the  more  vibra- 
tions it  will  stand,  for  it  is  not  so  easily  strained  beyond  the  yield-point. 
The  Baldwin  specifications  for  stay-bolt  iron  call  for  a  tensile  strength  of 
50,000  to  52,000  Ibs.  per  square  inch,  the  upper  figure  being  preferred,  and 
the  lower  being  insisted  upon  as  the  minimum. 

FORMUI^  FOR  UNIT  STRAINS  FOR  IRON  AND 

STEEL  IN  STRUCTURES. 
(F.  H.  Lewis,  Engineers'  Club  of  Philadelphia,  1891.) 

The  following  formulas  for  unit  strains  per  square  inch  of  net  sectional 
area  shall  be  used  in  determining  the  allowable  working  stress  in  each  mem- 
ber of  the  structure.  (For  definitions  of  soft  and  medium  steel  see  Specifi- 
cations for  Steel.) 

Tension  Members. 


Wrought  Iron. 

Soft  Steel. 

Medium  Steel. 

Floor-beam  hangers  or 
suspenders,     forged 
bars        ...        ... 

Will  not  be  used 

Will  not  be  used 

7000 

Counter-ties 

6000 

7000 

Suspenders,      hangers 
and  counters,  riveted 
members,    net    sec- 
tion      

5000 

5500 

7000 

Solid  rolled  beams  
Riveted  truss  members 
and    tension   flanges 
of  girders,  net    sec- 
tion 

8000 

7000(1  1  mhM 

8000 

8$  greater  than 
iron 

Will  not  be  used 
90006  1  min>) 

Forged  eyebars  

Lateral    or    cross-sec- 
tion rods  ,  

V        max./ 
Will  not  be  used 

15,000 

Will  not  be  used 
16,000 

V        max./ 

9000(1  +  -^) 
>         max./ 
/For    eyebars\ 
V  only,  17,000   / 

380 


IROK   AND   STEEL. 


Shearing. 


Wrought  Iron. 

Soft  Steel. 

Medium  Steel. 

On  pinsand  shop  rivets 
On  field  rivets  

6000 
4800 

6600 
5200 

7200 
Will  not  be  used 

In  webs  of  girders  

Will  not  be  used 

5000 

6000 

JBearing. 


Wrought  Iron. 

Soft  Steel. 

Medium  Steel. 

On     projected     semi- 
intrados  of  main-pin 
holes  

12000 

13  200 

14  500 

On  projected  semi-in- 
trados  of  rivet-holes* 
On  lateral  pins  
Of  bed  -plates  on  ma- 
sonry   

12,000 
15,000 

250  Ibs.  per  sq.  in. 

13,200 
16,500 

14,500 
18,000 

*  Excepting  that  in  pin-connected  members  taking  alternate  stresses,  the 
bearing  stress  must  not  exceed  9000  Ibs.  for  iron  or  steel. 
Bending. 

On  extreme  fibres  of  pins  when  centres  of  bearings  are  considered  as 
points  of  application  of  strains: 

Wrought  Iron,  15,000.        Soft  Steel,  16,000.       Medium  Steel,  17,000. 
Compression  Members. 


Wrought  Iron. 

Soft  Steel. 

Medium 
Steel. 

Chord  sections  : 
Flat  ends        

,000  0  +  ^-)-  3»- 

One  flat  and  one  pin  end.. 

Chords  with  pin  ends  and 
all  end-posts 

7000  (14-^^)-  40- 

10</ 

Ofl<£ 

All  trestle-posts.  .          .... 

7000  (l  I    miD")      35  l 

greater 
than 

greater 
than 

Intermediate  posts  

7500  -  40  - 

iron 

iron 

Lateral  struts,  and    com- 
pression  in   collision 
struts,    stiff    suspenders 
and  stiff  chords         .   ... 

10,500  -  50  - 

r 

J 

In  which  formulae  I  —  length  of  compression  member  in  inches,  and  r  - 
least  radius  of  gyration  of  member  in  inches.    No  compression  member 
shall  have  a  length  exceeding  45  times  its  least  width,  and  no  post  should  be 
used  in  which  l-*-r  exceeds  125. 
Members  Subject  to  Alternate  Tension  and  Compression. 


Wrought  Iron. 

Soft  Steel. 

Medium 
Steel. 

For  compression  only.  .  . 
For  the  greatest  stress  .  . 

Use  the  formulae  above 
"Good         nmx>  leSSer    ^ 

$%  greater 
than  iron 

20$  greater 
than  iron 

|WWV*      2  max.  greater-/ 

Use  the  formula  giving  the  greatest  area  of  section. 

The  compression  flanges  of  beams  and  plate  girders  shall  ha.ve  the  same 
cross -section  as  the  tension  flanges. 


FORMULA  FOR  UNIT  STRAINS  FOR  IRON  AND  STEEL.   381 

W.  If.  Burr,  discussing  the  formulae  proposed  by  Mr.  Lewis,  says:  "  Taking 
the  results  of  experiments  as  a  whole,  I  am  constrained  to  believe  that  they 
indicate  at  least  15$  increase  of  resistance  for  soft-steel  columns  over  those 
of  wrought  iron,  with  from  20$  to  25$  for  medium  steel,  rather  than  10$  and 
20$  respectively. 

"The  high  capacity  of  soft  steel  for  enduring  torture  fits  it  eminently  for 
alternate  and  combined  stresses,  and  for  that  reason  I  would  give  it  15$ 
increase  over  iron,  with  about  22$  for  medium  steel. 

"Shearing  tests  on  steel  seem  to  show  that  15$  and  22$  increases,  for  the 
two  grades  respectively,  are  amply  justified. 

44 1  should  not  hesitate  to  assign  15$  and  22$  increases  over  values  for  iron 
for  bearing  and  bending  of  soft  and  medium  steel  as  being  within  the  safe 
limits  of  experience.  Provision  should  also  be  made  for  increasing  pin- 
shearing,  bending  and  bearing  stresses  for  increasing  ratios  of  fixed  to  mov- 
ing loads  " 

Maximum  Permissible  Stresses  in  Structural  Materials 
used  in  Buildings.  (Building  Ordinances  of  the  City  of  Chicago,  189,3.) 
Cast  iron,  crushing  stress:  For  plates,  15,000  Ibs.  per  square  inch;  for  lintels, 
brackets,  or  corbels,  compression  13,500  Ibs."  per  square  inch,  and  tension 
3000  Ibs.  per  square  inch.  For  girders,  beams,  corbels,  brackets,  and  trusses, 
10,000  Ibs.  per  square  inch  for  steel  and  12,000  Ibs.  for  iron. 

For  plate  girders  : 

maximum  bending  moment  in  ft.-lbs. 
Flange  area  =  — ~j^ — 

D  —  distance  between  centre  of  gravity  of  flanges  in  feet. 
n  -  j  13,500  for  steel. 
~  1  10,000  for  iron. 

maximum  shear  (  10,000  for  steel, 

Web  area  -         — - —      — .    C  =  -j    6,000  for  iron. 

For  rivets  in  single  shear  per  square  inch  of  rivet  area  : 

Steel.  Iron. 

If  shop-driven 9000  Ibs.         7500  Ibs. 

If  field-driven  7500    '4  6000    4k 

For  timber  girders  : 

b  =  breadth  of  beam  in  inches. 
d  =  depth  of  beam  in  inches. 
cbd*  I  =  length  of  beam  in  feet. 

6  =  ~~T '  ( 160  for  long-leaf  yellow  pine, 

c  =  •<  120  for  oak, 

(  100  for  white  or  Norway  pine. 

Proportioning  of  Materials  in  the  Memphis  Bridge  (Geo. 
S.  Morison,  Trails.  A.  S.  C.  E.,  1893). — The  entire  superstructure  of  the  Mem- 
phis bridge  is  of  steel  and  it  was  all  worked  as  steel,  the  rivet-holes  being 
drilled  in  all  principal  members  and  punched  and  reamed  in  the  lighter 
members. 

The  tension  members  were  proportioned  on  the  basis  of  allowing  the  dead 
load  to  produce  a  strain  of  20,000  Ibs.  per  square  inch,  and  the  live  load  a 
strain  of  10,000  Ibs.  per  square  inch.  In  the  case  of  the  central  span,  where 
the  dead  load  was  twice  the  live  load,  this  corresponded  to  15,000  Ibs.  total 
strain  per  square  inch,  this  being  the  greatest  tensile  strain. 

The  compression  members  were  proportioned  on  a  somewhat  arbitrary 
basis.  No  distinction  was  made  between  live  and  dead  loads.  A  maximum 
strain  of  14,000  Ibs.  per  square  inch  was  allowed  on  the  chords  and  other 
large  compression  members  where  the  length  did  not  exceed  16  times  the 
least  transverse  dimension,  this  strain  being  reduced  750  Ibs.  for  each  addi- 
tional unit  of  length.  In  long  compression  members  the  maximum  length 
was  limited  to  30  times  the  least  transverse  dimension,  and  the  strains 
limited  to  6,000  Ibs.  per  square  inch,  this  amount  being  increased  by  200  Ibs. 
for  each  unit  by  which  the  length  is  decreased. 

Wherever  reversals  of  strains  occur  the  member  was  proportioned  to  re- 
sist the  sum  of  compression  and  tension  on  whichever  basis  (tension  or 
compression)  there  would  be  the  greatest  strain  per  square  inch  ;  and,  in 
addition,  the  net  section  was  proportioned  to  resist  the  maximum  tension, 
and  the  gross  section  to  resist  the  maximum  compression. 

The  floor  beams  and  girders  were  calculated  on  the  strain  being  limited  to 
10,000  Ibs.  per  square  inch  in  extreme  fibres.  Rivet-holes  in  cover-plates  and 
flanges  were  deducted. 


382 


IROK   AKD    STEEL. 


The  rivets  of  steel  in  drilled  or  reamed  holes  were  proportioned  on  the 
basis  of  a  bearing  strain  of  15,000  Ibs.  per  square  inch  and  a  shearing  strain 
of  7500  Ibs.  per  square  inch,  and  special  pains  were  taken  to  get  the  double 
shear  in  as  many  rivets  as  possible.  This  was  the  requirement  for  shop 
rivets.  In  the  case  of  field  rivets,  the  number  was  increased  one-half. 

The  pins  were  proportioned  on  the  basis  of  a  bearing  strain  of  18,000  Ibs. 
per  square  inch  and  a  bending  strain  of  20,000  Ibs.  per  square  inch  in  ex- 
treme fibre,  the  diameters  of  the  pins  being  never  made  more  than  one  inch 
less  than  the  width  of  the  largest  eye-bar  attaching  to  them. 

The  weight  on  the  rollers  of  the  expansion  joint  on  Pier  II  is  40,000  l^s. 
per  linear  foot  of  roller,  or  3,333  Ibs.  per  linear  inch,  the  rollers  being  15  ins. 
in  diameter. 

As  the  sections  of  the  superstructure  were  unusually  heavy,  and  the  strains 
from  dead  load  greatly  in  excess  of  those  from  moving  load,  it  was  thought 
best  to  use  a  slightly  higher  steel  than  is  now  generally  used  for  lighter 
structures,  and  to  work  this  steel  without  punching,  all  holes  being  drilled. 
A  somewhat  softer  steel  was  used  in  the  floor-system  and  other  lighter 
parts. 

The  principal  requirements  "which  were  to  be  obtained  as  the  results  of 
tests  on  samples  cut  from  finished  material  were  as  follows: 


Max. 
Ultimate 
Strength, 
Ibs.  per 
sq.  inch. 

Min. 
Ultimate 
Strength, 
Ibs.  per 
sq.  inch. 

Min.  Elastic 
Limit,  Ibs, 
per  sq.  in  . 

Min.  per- 
centage of 
Elongation 
in  8  inches. 

Min.  Per- 
centage of 
Reduction 
at  Fracture 

High-grade  steel. 
Eye-bar  steel  

78,500 
75,000 

69,000 
66,000 

40,000 
38,000 

18 
20 

38 
40 

Medium  steel  — 

72,500 

64,000 

37,000 

22 

44 

Soft  steel 

63000 

55  000 

30000 

28 

50 

TENACITY  OF  METAL.S  AT  VARIOUS 
TEMPERATURES. 

The  British  Admiralty  made  a  series  of  experiments  to  ascertain  what  loss 
of  strength  and  ductility  takes  place  in  gun-metal  compositions  when  raised 
to  high  temperatures.  It  was  found  that  all  the  varieties  of  gun-metal 
suffer  a  gradual  but  not  serious  loss  of  strength  and  ductility  up  to  a  certain 
temperature,  at  which,  within  a  few  degrees,  a  great  change  takes  place, 
the  strength  falls  to  about  one  half  the  original,  and  the  ductility  is  wholly 
gone.  At  temperatures  above  this  point,  up  to  500,  there  is  little,  if  any, 
further  loss  of  strength  ;  the  temperature  at  which  this  great  change  and 
loss  of  strength  takes  place,  although  uniform  in  the  specimens  cast  from 
the  same  pot,  varies  about  100°  in  the  same  composition  cast  at  different 
temperatures,  or  with  some  varying  conditions  in  the  foundry  process. 
The  temperature  at  which  the  change  took  place  in  No.  1  series  was  ascer- 
tained to  be  about  370°.  and  in  that  of  No.  2,  at  a  little  over  250°.  Whatever 
may  be  the  cause  of  this  important  difference  in  the  same  composition,  the 
fact  stated  may  be  taken  as  certain.  Rolled  Muntz  metal  and  copper  are 
satisfactory  up  to  500°,  and  may  be  used  as  securing-bolts  with  safety. 
Wrought  iron,  Yorkshire  and  remanufactured,  increase  in  strength  up  to 
500°,  but  lose  slightly  in  ductility  up  to  300°,  where  an  increase  begins  arid 
continues  up  to  500°,  where  it  is  still  less  than  at  the  ordinary  temperature 
of  the  atmosphere.  The  strength  of  Landore  steel  is  not  affected  by  temper- 
ature up  to  500°,  but  its  ductility  is  reduced  more  than  one  half.  (Iron,  Oct. 
6,  1877.) 

Tensile  Strength  of  Iron  and  Steel  at  High  Tempera- 
tures.—James  E.  Howard's  tests  (Iron  Age,  April  10,  1890),  shows  that  the 
tensile  strength  of  steel  diminishes  as  the  temperature  increases  from  0° 
until  a  minimum  is  reached  between  200°  and  300°  F.,  the  total  decrease 
being  about  4000  Ibs.  per  square  inch  in  the  softer  steels,  and  from  6000  to 
8000  Ibs.  in  steels  of  over  80,000  Ibs.  tensile  strength.  From  this  minimum  point 
the  strength  increases  up  to  a  temperature  of  400°  to  650°  F.,  the  maximum 
being  reached  earlier  in  the  harder  steels,  the  increase  amounting  to  from 
10,000  to  20,000  Ibs.  per  square  inch  above  the  minimum  strength  at  from  200o 


TENACITY  OF  METALS  AT  VARIOUS  TEMPERATURES.    383 

to  300°.  From  this  maximum,  the  strength  of  all  the  steel  decreases  steadily 
at  a  rate  approximating  10,000  Ibs.  decrease  per  100°  increase  of  tempera- 
ture. A  strength  of  20,000  Ibs.  per  square  inch  is  still  shown  by  .10  C.  steel 
at  about  1000°  F.,  and  by  .60  to  1.00  C.  steel  at  about  1600°  F. 

The  strength  of  wrought  iron  increases  with  temperature  from  0°  up  to  a 
maximum  at  from  400  to  600°  F.,  the  increase  being  from  8000  to  10,000  Ibs. 
per  square  inch,  and  then  decreases  steadily  till  a  strength  of  only  6000  Ibs. 
per  square  inch  is  shown  at  1500°  F. 

Cast  iron  appears  to  maintain  its  strength,  with  a  tendency  to  increase, 
until  900°  is  reached,  beyond  which  temperature  the  strength  gradually 
diminishes.  Under  the  highest  temperatures,  1500°  to  1600°  F.,  numerous 
cracks  on  the  cylindrical  surface  of  the  specimen  were  developed  prior  to 
rupture.  It  is  remarkable  that  cast  iron,  so  much  inferior  in  strength  to  the 
steels  at  atmospheric  temperature,  under  the  highest  temperatures  has 
nearly  the  same  strength  the  high-temper  steels  then  have. 

Strength  of  Iron  and  Steel  Boiler-plate  at  High  Tem- 
peratures. (Chas.  Huston,  Jour.  F.  /.,  1877.) 

AVERAGE  OP  THREE  TESTS  OP  EACH. 

Temperature  F.  68°  575°  925° 

Charcoal  iron  plate,  tensile  strength,  Ibs 55.366       63,080       65,343 

"      contr.  of  area  % 26  23  21 

Soft  open-hearth  steel,  tensile  strength,  ibs 54,600       66,083       64,350 

"  "       contr.  % ...   47  38  33 

"    Crucible  steel,  tensile  strength,  Ibs 64,000       69,266       68,600 

"      contr.  % 36  30  21 

Strength  of  Wrought  Iron  and  Steel  at  High  Temper- 
atures. (Jour.  F1.  7.,  cxii.,  1881,  p.  241.)  Kollmann's  experiments  at  Ober- 
hausen  included  tests  of  the  tensile  strength  of  iron  and  steel  at  tempera- 
tures ranging  between  70°  and  2000°  F.  Three  kinds  of  metal  were  tested, 
viz.,  fibrous  iron  having  an  ultimate  tensile  strength  of  52,464  Ibs.,  an  elastic 
strength  of  38,280  Ibs.,  and  an  elongation  of  17.5$;  fine-grained  iron  having 
for  the  same  elements  values  of  56,892  Ibs.,  39,113  Ibs.,  and  20$;  and  Bes- 
semer steel  having  values  of  84,826  Ibs.,  55,029  Ibs..  and  14.5$.  The  mean 
ultimate  tensile  strength  of  each  material  expressed  in  per  cent  of  that  at 
ordinary  atmospheric  temperature  is  given  in  the  following  table,  the  fifth 
column  of  which  exhibits,  for  purposes  of  comparison,  the  results  of  experi- 
ments carried  on  by  a  committee  of  the  Franklin  Institute  in  the  years 
1832-36. 

Fibrous         Fine-grained     Bessemer        Franklin 

Temperature      Wrought  Iron,  Steel,  Institute, 

Degrees  F.       Iron,  p.  c.          per  cent.  per  cent.        per  cent. 

0  100.0  100.0  100.0  96.0 

100  100.0  100.0  100.0  102.0 

200  100.0  100.0  100.0  105.0 

300  97.0  100.0  100.0  106.0 

400  95.5  100.0  100.0  106.0 

500  92.5  98.5  98.5  104.0 

600  88.5  95.5  92.0  99  5 

700  81.5  90.0  68.0  92.5 

800  67.5  77.5  44.0  75.5 

900  44.5  51.5  36.5  53.5 

1000  26.0  36.0  31.0  36.0 

1100  20.0  30.5  26.5 

1200  18.0  28.0  22.0 

1300  16.5  23.0-  18.0 

1400  13.5  19.0  15.0 

1500  10.0  15.5  12.0 

1600  7.0  12.5  10.0 

1700  5.5  10.5  8.5 

1800  4.5  8.5  7.5 

1900  3.5  7.0  6.5 

2000  3.5  5.0  5.0 

The  Effect  of  Cold  on  the  Strength  of  Iron  and  Steel.— 

The  following  conclusions  were  arrived  at  by  Mr.  Styffe  in  1865  : 

(1)  That  the  absolute  strength  of  iron  and  steel  is  not  diminished  by 
cold,  but  that  even  at  the  lowest  temperature  which  ever  occurs  in  Sweden 
it  is  at  least  as  great  as  at  the  ordinary  temperature  (about  60°  F.). 


384  IRON    AND    STEEL. 

(2)  That  neither  in  steel  nor  in  iron  is  the  extensibility  less  in  severe  cold 
than  at  the  ordinary  temperature. 

(3)  That  the  limit  of  elasticity  in  both  steel  and  iron  lies  higher  in  severe 
cold. 

(4)  That  the  modulus  of  elasticity  in  both  steel  and  iron  is  increased  on 
reduction  of  temperature,  and  diminished  on  elevation  of  temperature  ;  but 
that  these  variations  never  exceed  0.05  %  for  a  change  of  temperature  of  1.8° 
F.,  and  therefore  such  variations,  at  least  for  ordinary  purposes,  are  of  no 
special  importance. 

Mr.  C.  P.  Sandberg  made  in  1867  a  number  of  tests  of  iron  rails  at  various 
temperatures  by  means  of  a  falling  weight,  since  he  was  of  opinion  that, 
although  Mr.  Styffe's  conclusions  were  perfectly  correct  as  regards  tensile 
strength,  they  might  not  apply  to  the  resistance  of  iron  to  impact  at  low 
temperatures.  Mr.  Sandberg  convinced  himself  that  "  the  breaking  strain  " 
of  iron,  such  as  was  usually  employed  for  rails,  "  as  tested  by  sudden  blows 
or  shocks,  is  considerably  influenced  by  cold  ;  such  iron  exhibiting  at  10°  F. 
only  from  one  third  to  one  fourth  of  the  strength  which  it  possesses  at 
84°  F."  Mr.  J.  J.  Webster  (Irist.  C.  E.,  1880)  gives  reasons  for  doubting 
the  accuracy  of  Mr.  Sandberg's  deductions,  since  the  tests  at  the  lower 
temperature  were  nearly  all  made  with  21  -ft.  lengths  of  rail,  while  those  at 
the  higher  temperatures  were  made  with  short  lengths,  the  supports  in 
every  case  being  the  same  distance  apart. 

W.  H.  Barlow  (Proc.  Inst.  C.  E.)  made  experiments  on  bars  of  wrought 
iron,  cast  iron,  malleable  cast  iron,  Bessemer  steel,  and  tool  steel.  The  bars 
were  tested  with  tensile  and  transverse  strains,  and  also  by  impact ;  one 
half  of  them  at  a  temperature  of  50°  F.,  and  the  other  half  at  5°  F.  The 
lower  temperature  was  obtained  by  placing  the  bars  in  a  freezing  mixture, 
care  being  taken  to  keep  the  bars  covered  with  it  during  the  whole  time  of 
the  experiments. 

The  results  of  the  experiments  were  summarized  as  follows  : 

1.  When  bars  of  wrought  iron  or  steel  were  submitted  to  a  tensile  strain 
and  broken,  their  strength  was  not  affected  by  severe  cold  (5°  F.),  but  their 
ductility  was  increased  about  \%  in  iron  and  3$  in  steel. 

2.  When  bars  of  cast  iron  were  submitted  to  a  transverse  strain  at  a  low 
temperature,  their  strength  was  diminished  about  3$  and  their  flexibility 
about  16$. 

3.  When  bars  of  wrought  iron,  malleable  cast    iron,  steel,  and  ordinary 
cast  iron  were  subjected  to  impact  at  a  temperature  of  5°  F.,  the  force  re- 
quired to  break  them,  and  the  extent  of  their  flexibility,  were  reduced  as 
follows,  viz.: 

Reduction  of  Force  Reduction  of  Flexi- 

of  Impact,  per  cent.  bility,  per  cent. 

Wrought  iron,  about 3  18 

Steel  (best  cast  tool),  about 3^ 

Malleable  cast  iron,  about •  •  %  15 

Cast  iron,  about 21  not  taken 

The  experience  of  railways  in  Russia,  Canada,  and  other  countries  where 
the  winter  is  severe  is  that,  the  breakages  of  rails  and  tires  are  far  more 
numerous  in  the  cold  weather  than  in  the  summer.  On  this  account  a 
softer  class  of  steel  is  employed  in  Russia  for  rails  than  is  usual  in  more 
temperate  climates. 

The  evidence  extant  in  relation  to  this  matter  leaves  no  doubt  that  the 
capability  of  wrought  iron  or  steel  to  resist  impact  is  reduced  by  cold.  On 
the  other  hand,  its  static  strength  is  not  impaired  by  low  temperatures. 

Effect  of  l,ow  Temperatures  011  Strength  of  Railroad 
Axles.  (Thos.  Andrews,  Proc.  Inst.  C.  E.,  1891.)— Axles  6  ft.  6  in.  long 
between  centres  of  journals,  total  length  7  ft.  3V£  in.,  diameter  at  middle  4^ 
in.,  at  wheel-sets  5^  in.,  journals  3^  X  7  in.  were  tested  by  impact  at  temper- 
atures of  0°  and  100°  F.  Between  the  blows  each  axle  was  half  turned  over, 
and  was  also  replaced  for  15  minutes  in  the  water-bath. 

The  mean  force  of  concussion  resulting  from  each  impact  was  ascertained 
as  follows  : 

Let  h  =  height  of  free  fall  in  feet,  w  =  weight  of  test  ball,  hw  -  W  = 
"energy,"  or  work  in  foot-tons,  x  =  extent  of  deflections  between  bearings, 

W       hw 
then  F  (mean  force)  =  —  =  — . 


DURABILITY   OF   IRO^,  CORROSION,  ETC. 


385 


The  results  of  these  experiments  show  that  whereas  at  a  temperature  of 
0°  F.  a  total  average  mean  force  of  179  tons  was  sufficient  to  cause  the 
breaking  of  the  axles,  at  a  temperature  of  100°  F.  a  total  average  mean 
force  of  428  tons  was  requisite  to  produce  fracture.  In  other  words,  the  re- 
sistance to  concussion  of  the  axles  at  a  temperature  of  0°  F.  was  only  about 
42#  of  what  it  was  at  a  temperature  of  100°  F. 

The  average  total  deflection  at  a  temperature  of  0°  F.  was  6.48  in.,  as 
against  15.06  in.  with  the  axles  at  100°  F.  under  the  conditions  stated;  this 
represents  an  ultimate  reduction  of  flexibility,  under  the  test  of  impact,  of 
about  57%  for  the  cold  axles  at  0°  F.,  compared  with  the  warm  axles  at 
100°  F. 

EXPANSION  OF  IRON  AND  STEEL    BY  HEAT. 

James  E.  Howard,  engineer  in  charge  of  the  U.  S.  testing-machine  at  Wa- 
tertown,  Mass.,  gives  the  following  results  of  tests  made  on  bars  35  inches 
long  (Iron  Age,  April  10,  1890): 


Metal. 

Marks. 

Chemical  composition. 

Coefficient  of 
Expansion. 

C. 

Mn. 

Si. 

Feby 
difference. 

Per  degree 
F.  per  unit 
of  length. 

Wrought  iron  

.0000067302 
.0000067561 
.0000066259 
.0000065149 
.0000066597 
.0000066202 
.0000063891 
.0000064716 
.0000063167 
.0000062335 
.0000061700 
.0000059261 
.0000091286 

Steel 

la 
2a 
3a 
4a 
5a 
6a 
7a 
8a 
9a 
IGa 

.09 
.20 
.31 
.37 
.51 
.57 
.71 
.81 
.89 
.97 

.11 
.45 
.57 
.70 
.58 
.93 
.58 
.56 
.57 
.80 

99.80 
99.35 
99.12 
98.93 
98.89 
98.43 
98.63 
98.46 
98.35 
97.95 

.02 
.07 
.08 
.17 
.19 
.28 

N 

Cast  (gun)  iron 

Drawn  copper  

DURABILITY  OF  IRON,  CORROSION,  ETC. 

Durability  of  Cast  Iron.— Frederick  Graff,  in  an  article  on  the 
Philadelphia  water-supply,  says  that  the  first  cast-iron  pipe  used  there  was 
laid  in  1820.  These  pipes  were  made  of  charcoal  iron,  and  were  in  constant 
use  for  53  years.  They  were  uncoated,  and  the  inside  was  well  filled  with 
tubercles.  In  salt  water  good  cast  iron,  even  uncoated,  will  last  for  a  cen- 
tury at  least;  but  it  often  becomes  soft  enough  to  be  cut  by  a  knife,  as  is 
shown  in  iron  cannon  taken  up  from  the  bottom  of  harbors  after  long  sub- 
mersion. Close-grained,  hard  white  metal  lasts  the  longest  in  sea  water. — 
Eng^g  News,  April  23.  1887,  and  March  2(5. 189-2. 

Tests  of  Iron  after  Forty  Years'  Service.— A  square  link  12 
inches  broad,  1  inch  thick  and  about  12  feet  long  was  taken  from  the  Kieff 
bridge,  then  40  years  old,  and  tested  in  comparison  with  a  similar  link  which 
had  been  preserved  in  the  stock-house  since  the  bridge  was  built.  The  fol- 
lowing is  the  record  of  a  mean  of  four  longitudinal  test-pieces,  1  X  \Y%  X  8 
inches,  taken  from  each  link  (Stahl  und  Eisen,  1890): 

Old  Link  taken  New  Link  from 

from  Bridge.  Store-house. 

Tensile  strength  per  square  inch,  tons 21 .8  22.2 

Elastic  limit                                   "         11.1  11.9 

Elongation,  per  cent 14.05  13.42 

Contraction,  per  cent 17.35  18.75 

Durability  of  Iron  in  Bridges.  (G.  Lindenthal,  Eng'g,  May  2, 
1884,  p.  139.)— The  Old  Monongahela  suspension  bridge  in  Pittsburgh,  built 
in  1845,  was  taken  down  in  1882.  The  wires  of  the  cables  were  frequently 
Btrainedto  half  of  their  ultimate  strength,  yet  on  testing  them  after  37  years' 


386  IROtf  AND   STEEL. 

use  they  showed  a  tensile  strength  of  from  72,700  to  100,000  Ibs.  per  square 
inch.  The  elastic  limit  was  from  67,100  to  78,600  Ibs.  per  square  inch.  Re- 
duction at  point  of  fracture,  35$  to  75$.  Their  diameter  was  0.13  inch. 

A  new  ordinary  telegraph  wire  of  same  gauge  tested  for  comparison 
showed:  T.  S.,  of  100,000  Ibs.;  E.  L.,  81,550  Ibs.;  reduction,  57$.  Iron  rods 
used  as  stays  or  suspenders  showed:  T.  S.,  43,770  10  49,720  Ibs.  per  square 
inch;  E.  L.,  26,380  to  29,200.  Mr.  Lindenthal  draws  these  conclusions  from 
his  tests: 

"  The  above  tests  indicate  that  iron  highly  strained  for  a  long  number  of 
years,  but  still  within  the  elastic  limit,  and  exposed  to  slight  vibration,  will 
not  deteriorate  in  quality. 

"That  if  subjected  to  only  one  kind  of  strain  it  will  not  change  its  texture, 
even  if  strained  beyond  its  elastic  limit,  for  many  yer\rs.  It  will  stretch  and 
behave  much  as  in  a  testing-machine  during  a  long  test. 

"That  iron  will  change  its  texture  only  when  exposed  to  alternate  severe 
straining,  as  in  bending  in  different  directions.  If  the  bending  is  slight  but 
very  rapid,  as  in  violent  vibrations,  the  effect  is  the  same." 

Corrosion  of  Iron  Bolts.— On  bridges  over  the  Thames  in  London, 
bolts  exposed  to  the  action  of  the  atmosphere  and  rain-water  \\  ere  eaten 
away  in  25  years  from  a  diameter  of  %  in.  to  y%  in.,  and  from  %  in.  diameter 
to  5/16  inch. 

Wire  ropes  exposed  to  drip  in  colliery  shafts  are  very  liable  to  corrosion. 

Corrosion  of  Iron  and  Steel.— Experiments  made  at  the  Riverside 
Iron  Works,  Wheeling,  VV.  Va.,  on  the  comparative  liability  to  rust  of  iron 
and  soft  Bessemer  steel:  A  piece  of  iron  plate  and  a  similar  piece  of  steel, 
both  clean  and  bright,  were  placed  in  a  mixture  of  yellow  loam  and  sand, 
with  which  had  been  thoroughly  incorporated  some  carbonate  of  soda,  nitrate 
of  soda,  ammonium  chloride,  and  chloride  of  magnesium.  The  earth  as 
prepared  was  kept  moist.  At  the  end  of  33  days  the  pieces  of  metal  were 
taken  out,  cleaned,  and  weighed,  when  the  iron  was  found  to  have  lost  0.84$ 
of  its  weight  and  the  steel  0.72$.  The  pieces  were  replaced  and  after  28  days 
weighed  again,  when  the  iron  was  found  to  have  lost  2.06$  of  its  original 
weight  and  the  steel  1.79$.  (Eng'g,  June  26,  1891.) 

Corrosive  Agents  in  tlie  Atmosphere.— The  experiments  of  F. 
Grace  Calvert  (Chemical  News,  March  3,  1871)  show  that  carbonic  acid,  in 
the  presence  of  moisture,  is  the  agent  which  determines  the  oxidation  of 
iron  in  the  atmosphere.  He  subjected  perfectly  cleaned  blades  of  iron  and 
steel  to  the  action  of  different  gases  for  a  period  of  four  months,  with 
results  as  follows : 

Dry  oxygen,  dry  carbonic  acid,  a  mixture  of  both  gases,  dry  and  damp 
oxygen  and  ammonia:  no  oxidation.  Damp  oxygen:  in  three  experiments 
one  blade  only  was  slightly  oxidized. 

Damp  carbonic  acid:  slight  appearance  of  a  white  precipitate  upon  the 
iron,  found  to  be  carbonate  of  iron.  Damp  carbonic  acid  and  oxygen: 
oxidation  very  rapid.  Iron  immersed  in  water  containing  carbonic  acid 
oxidized  rapidly. 

Iron  immersed  in  distilled  water  deprived  of  its  gases  by  boiling  rusted 
the  iron  in  spots  that  were  found  to  contain  impurities. 

Galvanic  action  is  a  most  active  agent  of  corrosion.  It  takes  place 
when  two  metals,  one  electro-negative  to  the  other,  are  placed  in  contact 
and  exuosed  to  dampness. 

Sulphurous  acid  (the  product  of  the  combustion  of  the  sulphur  in  coal)  is 
an  exceedingly  active  corrosive  agent,  especially  when  the  exposed  iron  is 
coated  with  soot.  This  accounts  for  the  rapid  corrosion  of  iron  in  railway 
bridges  exposed  to  the  smoke  from  locomotives.  (See  account  of  experi- 
ments by  the  author  on  action  of  sulphurous  acid  in  Jour.  Frank.  List.,  June, 
1875,  p.  437.)  An  analysis  of  sooty  iron  rust  from  a  railway  bridge  showed 
the  presence  of  sulphurous,  sulphuric,  and  carbonic  acids,  chlorine,  and 
ammonia.  Bloxam  states  that  ammonia  is  formed  from  the  nitrogen  of  the 
air  during  the  process  of  rusting. 

Rustless  Coatings  for  Iron  and  Steel.— Tinning,  enamelling,  lac- 
quering, galvanizing,  electro-chemical  painting,  and  other  preservative 
methods  are  discussed  in  two  important  papers  by  M.  P.  Wood,  in  Trans. 
A.  S.  M.  E.,  vols.  xv  and  xvi. 

A  Method  of  Producing  an  luoxidizable  Surface  on 
iron  and  steel  by  means  of  electricity  has  Leen  developed  by  M.  A.  de  Meri- 
tens  (Engine »ring.)  The  article  to  be  protected  is  placed  in  a  bath  of  ordi- 
nary or  distilled  water,  at  a  temperature  of  from  158°  to  176°  F.,  and  an 
electric  current  is  sent  through,  The  water  is  decomposed  into  its  elements, 


DURABILITY   OF   IRON,  CORROSION,  ETC.  387 

oxygen  and  hydrogen,  and  the  oxygen  is  deposited  on  the  metal,  while  the 
hydrogen  appears  at  the  other  pole,  which  may  either  be  the  tank  in  which 
the  operation  is  conducted  or  a  plate  of  carbon  or  metal.  The  current  has 
only  sufficient  electromotive  force  to  overcome  the  resistance  of  the  circuit 
and  to  decompose  the  water;  for  if  it  be  stronger  than  this,  the  oxygen  com- 
bines with  the  iron  to  produce  a  pulverulent  oxide,  which  has  no  adherence. 
If  the  conditions  are  as  they  should  be,  it  is  only  a  few  minutes  after  the 
oxygen  appears  at  the  metal  before  the  darkening  of  the  surface  shows 
that  the  gas  has  united  with  the  iron  to  form  the  magnetic  oxide  Fe3O4, 
which  it  is  well  known  will  resist  the  action  of  the  air  and  protect  the  metal 
beneath  it.  After  the  action  has  continued  an  hour  or  two  the  coating  is 
sufficiently  solid  to  resist  the  scratch-brush,  and  it  will  then  take  a  brilliant 
polish. 

If  a  piece  of  thickly  rusted  iron  be  placed  in  the  bath,  its  sesquioxide 
(Fe2O3)  is  rapidly  transformed  into  the  magnetic  oxide.  This  outer  layer 
has  no  adhesion,  but  beneath  it  there  will  be  found  a  coating  which  is 
actually  a  part  of  the  metal  itself. 

In  the  early  experiments  M.  de  Meritens  employed  pieces  of  steel  only, 
but  in  wrought  and  cast  iron  he  was  not  successful,'  for  the  coating  came  off 
with  the  slightest  friction.  He  then  placed  the  iron  at  the  negative  pol  of 
the  apparatus,  after  it  had  been  already  applied  to  the  positive  pole.  Here 
the  oxide  w*as  reduced,  and  hydrogen  was  accumulated  in  the  pores  of  the 
metal.  The  specimens  were  then  returned  to  the  anode,  when  it  was  found 
that  the  oxide  appeared  quite  readily  and  was  very  solid.  But  the  result 
was  not  quite  perfect,  and  it  was  not  until  the  bath  was  filled  with  distilled 
water,  in  place  of  that  from  the  public  supply,  that  a  perfectly  satisfactory 
result  was  attained. 

Manganese  Plating  of  Iron  as  a  Protection  front  Rust. 
— According  to  the  Italian  Pro.gre.sso,  articles  of  iron  can  be  protected 
against  rust  by  sinking  them  near  the  negative  pole  of  an  electric  bath  com- 
posed of  10  litres  of  water,  50  grammes  of  chloride  of  manganese,  and  200 
grammes  of  nitrate  of  ammonium.  Under  the  influence  of  the  current  the 
bath  deposits  on  the  articles  a  film  of  metallic  manganese  which  prevents 
them  from  rusting. 

A  Non-oxidizing  Process  of  Annealing  is  described  by  H. 
P.  Jones,  in  Eng'g  News,  Jan.  2,  1892.  The  ordinary  process  of  annealing, 
by  means  of  which  hard  and  brittle  iron  or  steel  is  rendered  soft  and  tough, 
consists  in  heating  the  metal  to  a  good  red-l*eat  and  then  allowing  it  to  cool 
gradually.  While  the  metal  is  in  a  heated  condition  the  surface  becomes 
oxidized;  and  although  for  many  classes  of  work  this  scale  of  oxide  is  of 
practical  importance,  yet  in  some  cases  it  is  very  undesirable  and  even 
necessitates  considerable  expense  in  its  removal. 

The  new  process  uses  a  uon -oxidizing  gas,  and  is  the  invention  of  Mr. 
Horace  K.  Jones,  of  Hartford,  Conn.  The  principal  feature  of  this  process 
consists  in  keeping  the  annealing-retort  in  communication  with  the  gas 
holder  or  gas  main  during  the  entire  process  of  heating  and  cooling,  the  ^as 
thus  being  allowed  to  expand  back  into  the  main,  and  being,  therefore, 
kept  at  a  practically  constant  pressure. 

The  retorts  used  are  made  from  wrought-iron  tubes.  The  gas  used  is 
taken  directly  from  the  mains  supplying  the  city  with  illuminating  gas.  It 
was  noticed  that  if  metal  which  had  been  blued  or  slightly  oxidized  nras  sub- 
jected to  the  annealing  process  it  came  out  bright,  the  oxide  being  reduced 
by  the  action  of  the  gas.  Practical  use  has  been  made  of  this  fact  in  deoxi- 
diziug  metal. 

Comparative  tests  were  made  of  specimens  of  metal  annealed  in  illlumi- 
nating  gas  and  of  specimens  annealed  in  nitrogen.  The  results  of  these  tests 
were  compared  with  the  results  of  tests  of  specimens  annealed  in  an  open 
fire  and  cooled  in  ashes,  and  of  specimens  of  the  unannealed  metal,  and 
thus  the  relative  efficiency  of  the  gas  process  was  determined. 

The  specimens  were  made  from  steel  wire  .188  in.  in  diameter  and  were 
turned  down  to  diameters  of  .156  and  .150  in.  Different  lots  of  wire  were 
tested  in  order  to  secure  average  results.  The  elongations  were  in  each 
case  referred  to  an  original  length  of  1.15  ins. 

The  difference  in  total  per  cent  of  elongation  and  in  breaking  load  between 
the  specimens  annealed  in  nitrogen  and  those  annealed  in  illuminating  gas 
is  very  slight.  The  average  results  were  as  follows: 


388 


IKON   AND    STEEL, 


Lot. 

Gas  used. 

No. 
Test 
Pieces. 

Breaking 
Load, 
Ibs.  persq.  in. 

Elongation. 

Total  p.  c. 

p.  c.  gained. 

A 

Nitrogen 
Illuminating 
Nitrogen 
Illuminating 
Nitrogen 
Illuminating 
Open  fire 
Unannealed 
Unaunealed 

4 
4 
4 
4 
5 
5 
8 
5 
5 

62,140 
63,140 
60.000 
60,400 
57,880 
57.070 
63,090 
97,120 
80,790 

29.12 

28.08 
28.00 
27.20 
30.88 
29.60 
26.76 
7.12 
8.80 

22.00 
20.86 
19.20 
18.40 
23.76 
22.48 
19.64 

B  
C 

D  
E  

F  
G     

H 

I 

Painting  Wood  and  Iron  Structures.  (E.  H.  Brown,  Eng'rs 
Club  of  Phila.,  Engineering  Neivs,  April  20,  1893.) — A  paint  consists  of  two 
portions — the  pigment  and  the  vehicle  or  binder.  The  pigment  is  a  solid 
substance  which  is  more  or  less  finely  ground,  so  as  to  be  capable  (when 
mixed  with  tbe  vehicle)  of  being  spread  out  in  a  thin  layer  or  coating  over 
the  surface  to  be  painted.  The  vehicle  or  binder  is  the  liquid  in  which  the 
pigment  is  mixed  or  ground,  which  serves  to  spread  the  pigment  over  the 
surface  to  be  painted,  and  which  also  holds  it  to  that  surface.  For  ordinary 
painting  the  most  generally  used  vehicle  is  linseed  oil. 

Linseed  oil  possesses  the  peculiar  property  of  drying  by  uniting  with  the 
oxygen  of  the  air  to  form  a  tough,  leather-like  compound  called  linoxin. 

For  painting  on  wood,  zinc  white  has  valuable  pigment  properties,  but 
these  seem  to  be  most  fully  developed  when  this  pigment  is  used  in  con- 
junction with  white  lead,  and  then  to  the  best  advantage  when  the  mixture 
is  used  as  a  final  coat  over  an  elastic  undercoating  of  white  lead.  So  far  no 
other  white  base  has  been  discovered  which  possesses  at  the  same  time  the 
other  properties  which  render  white  lead  valuable,  namely,  covering  and 
spreading  capacity. 

Of  the  inert  pigments,  lampblack  is  probably  the  most  valuable.  Being 
almost  pure  carbon,  it  is  practically  unchangeable  except  by  fire.  It  has  the 
peculiar  property  of  absorbing  great  quantities  of  linseed  oil,  and  hence  of 
spreading  over  a  large  surface.  French  ochre,  an  earth  pigment  containing 
more  or  less  of  the  hydrated  oxide  of  iron,  possesses  the  property  of  absorb- 
ing a  large  quantity  of  oil,  and  hence  has  considerable  spreading  capacity, 
and  also  holds  very  firmly  to  any  wooden  surface  to  which  it  may  be  applied. 

The  various  mineral  and  metallic  paints  are  almost  all  natural  or  artificial 
iron  oxides.  While  these  are  cheap  and  useful  for  painting  rough  wooden 
structures  they  are  sometimes  really  quite  dangerous  for  application  to  iron 
work,  because,  instead  of  preventing  oxidation,  they  are  apt  to  further  it. 

Coal  tar  is  much  used  as  a  paint  for  the  roughest  class  of  work,  both  wood 
and  iron;  in  the  latter  case  especially  for  cast-iron  pipes,  smoke-stacks,  and 
work  to  be  buried  underground.  It  has  the  nature  both  of  a  resin  and  an  oil. 
It  has  the  disadvantage  of  becoming  exceedingly  brittle  by  the  action  of  cold, 
and  softening  at  115°  F.  Asphalt  permits  of  somewhat  wider  range  of  temper- 
ature, but  otherwise  exhibits  the  same  peculiarities.  These  substances,  while 
they  last,  are  probably  the  most  valuable  of  paints,  especially  under  water; 
but  they  are  unfortunate  in  their  tendency  to  flow  or  crawl  on  the  surface 
to  which  they  are  applied,  finally  leaving  the  upper  portions  almost  or  quite 
bare.  This  is  the  case  even  under  ground. 

Red  lead  has  long  been  regarded  as  the  best  possible  preservative  for  clean 
dry  iron.  But  in  order  to  be  most  effective,  the  iron  must  be  perfectly  clean 
and  free  from  any  suspicions  of  rust,  and  absolutely  dry.  Red  lead  should 
be  perfectly  pure  and  of  the  best  and  most  careful  preparation.  That  from 
any  well  known  corroding  house  may  be  depended  upon  for  purity,  but  not 
always  for  quality.  It  is  simply  a  red  oxide  of  lead.  The  best  type  is  orange 
mineral,  which  is  made  by  roasting  white  lead.  On  account  of  its  expense 
this  is  not  so  frequently  used  as  it  would  deserve.  Red  lead  proper  is  made 
directly  from  the  metal,  which  is  first  oxidized  to  the  yellow  litharge,  and 
then  to  the  red  oxide.  This,  however,  does  not  give  as  good  a  paint  as  thar, 
made  from  the  scrap,  settlings,  and  tailings  of  the  white  lead  works.  As  red 
lead  saponifies  very  quickly  with  linseed  oil,  it  must  be  used  within  a  few 
days  after  being  ground,  and,  moreover,  it  is  rather  difficult  to  work 


CHEMICAL  COMPOSITION  AND  PHYSICAL  CHARACTER.    389 

Hence  there  is  great  temptation  to  add  some  substance,  such  as  whiting,  to 
it  in  order  to  make  it  work  freer,  as  well  as  to  cost  less  money  for  material. 

Before  painting  iron  work  it  is  essential  that  the  iron  itself  should  be  ab- 
solutely free  from  rust.  Rust  has  the  peculiar  property  of  spreading  and 
extending  from  a  centre,  if  there  be  the  slightest  chance  to  do  so.  Hence,  a 
small  amount  of  rust  on  the  iron  may  grow  under  the  surface  of  the  paint, 
especially  if  it  be  true,  as  Dr.  Dudley  asserts,  that  linseed  oil  is  permeable 
by  air  and  moisture,  and  in  time  the  paint  will  be  flaked  off  by  the  rust  un- 
derneath, thus  gradually  exposing  the  bare  surface  of  the  iron  to  the  action 
of  its  destroying  agent,  oxygen  in  the  presence  of  water.  It  is  necessary 
to  remove  all  the  scale  possible  from  wrought  iron  by  means  of  stiff  wire 
brushes,  and  then  to  remove  the  rust  by  a  pickle  of  very  dilute  acid,  which 
must  afterward  be  thoroughly  washed  off  before  the  paint  is  applied.  The 
surface  of  the  iron  should  be  dry  and  at  least  moderately  warmed  before  it 
is  primed.  The  best  method  of  painting  a  tin  roof  is  to  carefully  remove 
all  traces  of  oil  or  grease  from  the  surface  of  the  tin  while  it  is  yet  bright 
wilh  benzine;  then  to  apply  a  coat  of  red  lead  and  linseed  oil,  or  the  best 
quality  of  metallic  paint,  and  to  follow  this  with  one  or  two  coats  of  graphite 
paint.  The  graphite  is  almost  unchangeable  by  atmospheric  action,  and  is 
remarkably  waterproof  as  well. 

Red  Lead  as  a  Preservative  of  Iron.— A.  J.  Whitney  writes  to 
Engineering  News,  August,  1891,  that  in  30  years'  experience  he  has  found 
red  lead  to  be  th^  best  material  for  preserving  iron  under  all  circumstances. 

Quantity  of  Paint  Required  for  a  Given  Surface.  (M.  P. 
Wood.)— Sq.  ft,  of  surface  -i-  200  =  gallons  of  liquid  paint  for  two  coats;  sq. 
ft.  of  surface  -s-  18  =  Ibs.  of  pure  white  lead  for  three  coats. 

Qualities  of  Paints.— The  Railroad  and  Engineering  Journal,  vols. 
liv  and  Iv,  1890  and  1891,  has  a  series  of  articles.on  paint  as  applied  to  ivooden 
structures,  its  chemical  nature,  application,  adulteration,  etc.,  by  Dr.  C.  B. 
Dudley,  chemist,  and  F.  N.  Pease,  assistant  chemist,  of  the  Penna.  R.  R. 
They  give  the  results  of  a  long  series  of  experiments  on  paint  as  applied  to 
railway  purposes. 

Graphite  Paint.  (M.  P.  Wood.)— Graphite,  mixed  with  pure  boiled 
linseed  oil  in  which  a  small  percentage  of  litharge,  red  lead,  manganese,  or 
other  metallic  salt  has  been  added  at  the  time  of  boiliug  to  aid  in  the  oxida- 
tion of  the  oil,  forms  a  most  effective  paint  for  metallic  surfaces,  as  well  as 
for  wood  and  fibrous  substances.  Wood  surfaces  protected  by  this  paint, 
and  exposed  to  the  action  of  sea- water  for  a  number  of  years,  are  foand  in 
a  perfect  state  of  preservation. 

STEEL. 

RELATION     BETWEEN    THE     CHEMICAL    COMPOSI- 
TION AND  PHYSICAL  CHARACTER  OF  STEEL,. 

W.  R.  Webster  (see  Trans.  A.  I.  M.  E.,  vols.  xxi  and  xxii,  1893-4)  gives  re- 
sults of  several  hundred  analyses  and  tensile  tests  of  basic  Bessemer  steel 
plates,  and  from  a  study  of  them  draws  conclusions  as  to  the  relation  of 
chemical  composition  to  strength,  the  chief  of  which  are  condensed  as 
follows  : 

The  indications  are  that  a  pure  iron,  without  carbon,  phosphorus,  man- 
ganese, silicon,  or  sulphur,  if  it  could  be  obtained,  would  have  a  tensile 
strength  of  31,750  Ibs.  per  square  inch,  if  tested  in  a  %-inch  plate.  With 
this  as  a  base,  a  table  is  constructed  by  adding  the  following  hardening 
effects,  as  shown  by  increase  of  tensile  strength,  for  the  several  elements 
named. 

Carbon,  a  constant  effect  of  800  Ibs.  for  each  0.01$. 

Sulphur,         "  500        "        "       0.01*. 

Phosphorus,  the  effect  is  higher  in  high-carbon  than  in  low-carbon  steels. 

With  carbon  hundreths  % 9      10      11      12      13      H      15      16      17 

Each  . 01#  P  has  an  effect  of  Ibs.  900  1000  1100  1200  1300  1400  1500  1500  150(7 

Manganese,  the  effect  decreases  as  the  per  CQnt  of  manganese  increases. 

.20  .25  .30  .35  .40  .45  .50  .55 
to  to  to  to  to  to  to 
.30  .35  .40  .45  .50  .55  .65 

Str'gth  increases  for  .Olg  240   240   220    200    180    160    140    120     100     100  Ibs. 

Total  incr.  from  0  Mn. ..  3600  4800  5900  6900  7800  8600  9300  9900  10,400  11,400 


(    .00    .15    .20    .25 

Mn  being  per  cent •<     to     to     to     to 

j    .15    .20    .25    .30 


390 


STEEL. 


Silicon  is  so  low  in  this  steel  that  its  hardening  effect  has  not  been  con- 
sidered. 

With  the  above  additions  for  carbon  and  phosphorus  the  following  table 
has  been  constructed  (abridged  from  the  original  by  Mr.  Webster).  To  the 
figures  given  the  additions  for  sulphur  and  manganese  should  be  made  as 
above. 

Estimated    Ultimate    Strengths  of  Basic  Bessemer   Steel 
Plates, 

For  Carbon,  .06  to  .24;  Phosphorus,  .00  to  .10;  Manganese  and  Sulphur,  .00  in 
all  cases. 


Carbon. 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

.22 

.24 

Phos.  .005 

39,950 

41,550 

43,250 

44,950 

46,650 

48,300 

49,900 

51,500 

53,100 

54,700 

.01 

40,350 

41,950 

43,750 

45,550 

17,350 

49,050  50,650 

52,250 

53,850 

55,450 

"       .02 

41,150 

42,750 

44,750 

46,750 

48,750 

50,550 

52,150 

53,750 

55.350 

56,950 

44       .03 

41,950 

43,550 

45,750 

47,950 

50,150 

52,050 

53,650 

55,250 

5(5,850 

58,450 

4       .04 

42.750 

41,350 

46,750 

49,150 

51,550 

53,550 

55,150 

56,750 

58,350 

59,950 

'       .05 

43,550 

45,150 

47,750 

50,350 

52,950 

55.050 

56.650 

58,250 

59,850 

61.450 

4       .06 

44,350 

45,950 

48,750 

51,550 

54,350 

56,550  58,150 

59.750 

61  350 

62,950 

'       .0? 

45,150  46,750 

49,750 

52,750 

55,750 

58,050 

59,650 

61.250 

6v\850 

64,450 

4       .08 

45,950 

47,550 

50,750 

53.951 

57,150 

59,550  61,150 

62,750 

64,350 

65.950 

4       .09 

46,750 

48,350 

51,750 

55,15( 

58,550 

61,050  62,650 

64.250 

65,850 

67,450 

4       .10 

47,550 

49,150 

52,750 

56,35( 

59,950 

62.550 

64.150 

65.750 

67.850 

68,950 

.001  Phos  = 

HOlbs. 

801bs. 

100  Ib 

120  11 

140  Ib  150  Ib  150  Ib 

150  Ib 

150  Ib 

150  Ib 

Iii  all  rolled  steel  the  quality  depends  on  the  size  of  the  bloom  or  ingot 
from. which  it  is  rolled,  the  work  put  on  it,  and  the  temperature  at  which  if 
is  finished,  as  well  as  the  chemical  composition. 

The  above  table  is  based  on  tests  of  plates  %  inch  thick  and  under  7i 
inches  wide;  for  other  plates  Mr.  Webster  gives  the  following  corrections 
for  thickness  and  width.  They  are  made  necessary  only  by  the  effect  of 
thickness  and  width  on  the  finishing  temperature  in  ordinary  practice. 
Steel  is  frequently  spoiled  by  being  finished  at  too  high  a  temperature. 
Corrections  for  Size  of  Plates. 

Plates.  Up  to  70  ins.  wide.  Over  70  ins.  wide. 

Inches  thick.  Lbs.  Lbs. 

%    andover. -2000  —1000 

11/16          44         —1750  —   750 

%  "         —1500  —500 

9/16  4         —1250  —   250 

—1000  —       0 

—   500  ±500 

0  +  1000 

-f  3000  +  5000 

Comparing  the  actual  result  of  tests  of  408  plates  with  the  calculated 
results,  Mr.  Webster  found  the  variation  to  range  as  in  the  table  below. 
Summary  of  the  Differences  Between  Calculated  and 

Actual  Results  in  4O8  Tests  of  Plate  Steel. 
In  the  first  three  columns  the  effects  of  sulphur  were  not  considered;  in 
the  last  three  columns  the  effect  of  sulphur  was  estimated  at  500  Ibs.  for 
each  .Olfc  of  S. 


. 

JJ 

_ 

jOO 

rffil 

'~  —i 
0/^2 

| 

g 

<vrz 

£ 

& 

S3«5 

js3 

S 

a 

I 

43 

-C  0>  C  --^ 

a 

& 

o 
H 

£ 

g 

i 

«!!* 

Per  cent  within  1000  Ibs.. 

23!  4 

32.1 

28.4 

24.6 

27.0 

26.0 

28.4 

44        4'       2000    "  .. 
44        '4        "       3000    "  .. 

40.9 
62.5 

48  9 
71.3 

45.6 
67.6 

67.8 

73.0 

70.8 

74.7 

"       4000    "  .. 

75.5 

81.0 

78.7 

82.5 

85.2 

84.1 

89.9 

44       5000    "  .. 

89.5 

91.1 

90.4 

93.0 

92.8 

92.9 

94.9 

STRENGTH  OF  BESSEMER  AtfD  OPEN-HEARTH  STEELS.   391 


The  last  figure  in  the  table  would  indicate  that  if  specifications  were  drawn 
calling  for  steel  plates  not  to  vary  more  than  5000  Ibs.  T.  S.  from  a  specified 
figure  (equal  to  a  total  range  of  10,000  Ibs.),  there  would  be  a  probability  of 
the  rejection  of  5$  of  the  blooms  rolled,  even  if  the  whole  lot  was  made 
from  steel  of  identical  chemical  analysis.  In  1000  heats  only  2%  of  the  heats 
failed  to  meet  the  requirements  of  the  orders  on  which  they  were  graded; 
the  loss  of  plates  was  much  less  than  1$,  as  one  plate  was  rolled  from  each 
heat  and  tested  before  rolling  the  remainder  of  the  heat. 

R.  A.  Hadfield  (Jour.  Iron  &  Steel  Inst.,  No.  1,  1894)  gives  the  strength  of 
very  pure  Swedish  iron,  remelted  and  tested  as  cast,  20.1  tons  (45,024  Ibs.) 
per  sq.  in.;  remelted  and  forged,  21  tons  (47.040  Ibs  ).  The  analysis  of  the 
cast  bar  was  :  C,  0.08;  Si,  0.04;  S,  0.02  ;  P,  0.02;  Mn,  0.01 ;  Fe.  99.82. 

Effect  of  Oxygen  upon  Strength  of  Steel.— A.  Lantz,  of  the 
Peine  works,  Germany,  in  a  letter  to  Mr.  Webster,  says  :  "  We  have  found 
during  the  current  year  (1893)  that  oxygen  plays  an  important  role,  till  now 
little  observed— such,  indeed,  that  given  a  like  content  of  carbon,  phospho- 
rus, and  manganese  in  the  blows,  a  blow  with  greater  oxygen  content  gives 
a  greater  hardness  and  less  ductility  than  a  blow  with  less  oxygen  content.1' 
The  method  used  for  determining  oxygen  is  that  of  Prof.  Ledebur,  given  in 
Staid  und  Eisen,  May,  1892,  p.  193.  The  variation  in  oxygen  content  may 
make  a  difference  in  strength  of  nearly  one -half  ton  per  square  inch. 
(Jour.  Iron  &  Steel  Inst.,  No.  1,  1894.) 

RANGE  OF  VARIATION  IN  STRENGTH  OF  BESSEMER 
ANO  OPEN-HEARTH   STEELS. 

The  Carnegie  Steel  Co.  in  1888  published  a  list  of  1057  tests  of  Bessemer 
and  open-hearth  steel,  from  which  the  following  figures  are  selected  : 


Kind  of  Steel. 

No.  of  Tests. 

Elastic  Limit. 

Ultimate 
Strength. 

Elongation 
per  cent 
in  8  inches. 

High't. 

Lowest 

High't. 

Lowest 

High't. 

Lowest 

(a)  Bess,  structural.  .  . 
(b)  "  "  ... 
(c)  Bess,  angles  
(d)  O  H.  fire-box.  ... 

100 

170 
72 
95 

46,570 
47,690 
41,890 

39,230 
39,970 
32,630 

71,300 
73,540 
63,450 
62,790 
66,062 
69.9-10 

61,450 
65,200 
56,130 
50,350 
59.440 
63,970 

33.00 
30.25 
34.30 
36.00 
27.50 
30.00 

23.75 
23.15 
26.25 

25.62 
19.25 
22  75 

(e)  Tank 

19 

(  f)  0.  H.  bridge  

90 

REQUIREMENTS  OF  SPECIFICATIONS. 
(a)  Elastic  limit,  35,000  ;  tensile  strength,  62,000  to  70,000  ;  elong.  22$  in  8  in. 
(6)  Elastic  limit,  40,000  ;    tensile  strength,  67,000  to  75,000. 

(c)  Elastic  limit,  30,000  ;    tensile  strength,  56,000  to  64,000  ;  elong.  20$  in  8  in. 

(d)  Tensile  strength,  50,000  to  62,000  ;   elong.  26$  in  4  in. 

(e)  Tensile  strength,  60,000  to  65,000  ;   elong.  18$  in  8  in. 
(/)  Tensile  strength.  64,000  to  70,000  ;   elong.  20$  in  8  in. 

Strength  of  Open-hearth  Structural  Steel.  (Pencoyd  Iron 
Works.)— As  a  general  rule,  the  percentage  of  carbon  in  steel  determines  its 
hardness  and  strength.  The  higher  the  carbon  the  harder  the  steel,  the 
higher  the  tenacity,  and  the  lower  the  ductility  will  be.  The  following  list 
exhibits  the  average  physical  properties  of  good  open-hearth  steel  : 


Percentage 
of  Carbon. 

Ultimate 
Tenacity, 
Ibs.  per  sq.  in. 

Elastic 
Limit, 
Ibs.  per  sq.  in. 

Stretch  in 
8  inches. 

Reduction  of 
Area,  %. 

.10 
.15 
.20 
.25 
.30 
.35 
.40 

57,000 
62,000 
67,000 
72,000 
77,000 
82,000 
87,000 

34,000 
37,000 
40,000 
43,000 
46,000 
49,000 
52.000 

28  per  cent. 
26        " 
24 
22        " 
20 
18 
16        " 

55  per  cent. 
50 
45 
40 
35 
30 
25 

The  coefficient  of  elasticity  is  practically  uniform  for  all  grades,  and  is 
the  same  as  for  iron,  viz.,  29,000,000  Ibs.  These  figures  form  the  average  of 
a  numerous  series  of  tests  from  rolled  bars,  and  can  only  serve  as  an  ap- 


392 


STEEL. 


proximation  in  single  instances,  when  the  variation  from  the  average  may 
be  considerable.  Steel  below  .10  carbon  should  be  capable  of  doubling  flat 
without  fracture,  after  being  chilled  from  a  red  heat  in  cold  water.  Steel 
of  .15  carbon  will  occasionally  submit  to  the  same  treatment,  but  will 
usually  bend  around  a  curve  whose  radius  is  equal  to  the  thickness  of 
the  specimen  ;  about  90$  of  specimens  stand  the  latter  bending  test  without 
fracture.  As  the  steel  becomes  harder  its  ability  to  endure  this  bending 
test  becomes  more  exceptional,  and  when  the  carbon  ratio  becomes  .20, 
little  over  25$  of  specimens  will  stand  the  last-described  bending  test.  Steel 
having  about  .40$  carbon  will  usually  harden  sufficiently  to  cut  soft  iron 
and  maintain  an  edge. 
Mehrtens  gives  the  following  tables  in  Stahl  und  Eisen  (Iron  Age,  April  20, 


Basic  Bessemer  Steel. 
68 O  Charges. 

Elastic  Limit,  Charges  within 

pounds  per  Range,  per  cent 

sq.  in,.  of  total  number. 

35.500  to  38,400 15.0 

38,400  to  39,800 31 .6 

39,800  to  41 ,200  27.5 

41,200  to  42,700 16.0 

42,700  to  46,400 9.9 

Tensile  Strength,       Charges  within 

pounds  per  Range,  per  cent 

sq.  in.  of  total  number. 

55,600  to  56,900. 18.67 

56.900  to  58,300 38.67 

58,300  to  59,700 23.53 

59,700  to  61,200 15.60 

61,200  to  62,300  ...   3.53 

STRUCTURAL  STEEL. 

Charges  within 

Elongation.  Range,  per  cent 

per  cent.  of  total  number. 

21  to  25    2.65 

25to26 8.53 

26  to  27 17.35 

27  to  28 26 . 76 

28  to  29. .,. 23.68 

29  to  30 14.41 

30  to  32. 5 6.62 


Basic  Open-hearth  Struc- 
tural Steel. 
489  Charges. 

Elastic  Limit,  Charges  within 

pounds  per  Range,  per  cent 

sq.  in.  of  total  charges 

34,400  to  37.000 12.3 

37,000  to  38,400 15.6 

38,400  to  39,800 20.3 

39,800  to  41, '-200 17.4 

41, 200  to  42, 700 12.8 

42,700  to  44,100 11.4 

44,100  to  48,400 8.5 

Tensile  Strength. 

55,800  to  56,900 8.0 

56,900  to  58,300 26 . 4 

58,300  to  59,700 25.4 

59,700  to  61,200 19.6 

6 1,200  to  62, 600 11.2 

62,600  to  65,100 9.04 

Elongation, 
per  cent. 

20  to  25... 21.7 

25  to  26 7.7 

28  to  27 10.0 

27  to  28    11.0 

28  to  29 12.0 

29  to  30 13  3 

30  to  37.1 24.3 

RIVET  STEEL,  19  CHARGES. 
Tensile  Strength. 

51,800 5.3 

51,900  to  53,300 .  ..  26.3 

53,300  to  54,900 21 .0 

54,900  to  56,300 21.0 


RIVET  STEEL. 
25.2  to  26 20.0 

26  to27 15.0 

27  to  28 25.0 

28  to  29 25.0        56; 300  to  56,900 26.4 

29  to  29.8 15.0  Elongation  all  above  25  percent. 

In  the  basic  Bessemer  steel  over  90$  was  below  0.08  phosphorus,  and  all 

were  below  0.10;  manganese  was  below  0.6  in  over  90$,  and  below  0.9  in  all  ; 
sulphur  was  below  0.05  in  84$,  the  maximum  being  0.071;  carbon  was  below 
0.10,  and  silicon  below  0.01  in  all.  In  the  basic  open-hearth  steel  phosphorus 
was  below  0.06  in  96$,  the  maximum  being  0.08;  manganese  below 0.50  in  97$; 
sulphur  below  0.07  in  88$,  the  maximum  being  0.12.  The  carbon  ranged 
from  0.09  to  0.14. 

Low  Tensile  Strength  of  Very  Pure  Steel.— Swedish  nail-rod 
open-hearth  steel,  tested  by  the  author  in  1881,  showed  a  tensile  strength  of 
only  42,591  Ibs.  per  sq.  in.  A  piece  of  American  nail-rod  steel  showed  45,021 
Ibs.  per  sq.  in.  Both  steels  contained  about  .10  carbon  and  .015  phosphorus, 
and  were  very  low  in  sulphur,  manganese,  and  silicon.  The  pieces  tested 
were  bars  about  2  X  %  in.  section. 

Low  Strength  Due  to  Insufficient  Work.  (A.  E.  Hunt, 
Trans.  A.  I.  M.  E.,  1886.)— Soft  steel  ingots,  made  in  the  ordinary  way  for 
boiler  plates,  have  only  from  10,000  to  20,000  Ibs.  tensile  strength  per  sq.  in., 
an  elongation  of  only  about  10$  in  8  in.,  and  a  reduction  of  area  of  less  than 
20$.  Such  ingots,  properly  heated  and  rolled  down  from  10  in.  to  y%  in. 


STRENGTH  OF  BESSEMER  AND  OPEN-HEARTH  STEELS.   393 


Elongation    Reduction 


in  8  in. 

Per  cent. 

27 

25 

22 


of  Area. 
Per  cent. 

62 

50 

48 

49 


thickness,  will  give  from  55,000  to  65,000  Ibs.  tensile  strength,  an  elongation 
in  8  in.  of  from  23$  to  33$,  and  a  reduction  of  area  of  from  55$  to  70$.  Any 
work  stopping  short  of  the  above  reduction  in  thickness  ordinarily  yields  in- 
termediate results  in  its  tensile  tests. 

Hardening  of  Soft  Steel.— A.  E.  Hunt  (Trans.  A.  I.  M.  E.,  1883,  vol. 
xii),  says  that  soft  steel,  no  matter  how  low  in  carbon,  will  harden  to- a  cer- 
tain extent  upon  being  heated  red-hot  and  plunged  into  water,  and  that  it 
hardens  more  when  plunged  into  brine  and  less  when  quenched  in  oil. 

An  illustration  was  a  heat  of  open-hearth  steel  of  0.15$  carbon  and  0.29$  of 
manganese,  which  gave  the  following  results  upon  test-pieces  from  the  same 
Y±  in.  thick  plate. 

Maximum 

Load. 
Ibs.  per  sq.  in. 

Unhardened 55,000 

Hardened  in  water 74,000 

Hardened  in  brine 84,000 

Hardened  in  oil 67,700 

While  the  ductility  of  such  hardened  steel  does  not  decrease  to  the  extent 
that  the  increased  tenacity  would  indicate,  and  is  much  superior  to  that  of 
normal  steel  of  the  high  tenacity,  still  the  greatly  increased  tenacity  after 
hardening  indicates  that  there  must  be  a  considerable  molecular  change  in 
the  steel  thus  hardened,  and  that  if  such  a  hardening  should  be  created 
locally  in  a  steel  plate,  there  must  be  very  dangerous  internal  strains  caused 
thereby. 

Effect  of  €old  Rolling.— Cold  rolling  of  iron  and  steel  increases  the 
elastic  limit  and  the  ultimate  strength,  and  decreases  the  ductility.  Major 
Wade's  experiments  on  bars  rolled  and  polished  cold  by  Lauth's  process 
showed  an  average  increase  of  load  required  to  give  a  slight  permanent  set 
as  follows  :  Transverse,  162$;  torsion,  130$;  compression,  161$  on  short 
columns  1^4  in.  long,  arid  64$  on  columns  8  in.  long;  tension,  95$.  The  hard- 
ness, as  measured  by  the  weight  required  to  produce  equal  indentations, 
was  increased  50$;  and  it  was  found  that  the  hardness  was  as  great  in  the 
centre  of  the  bars  as  elsewhere.  Sir  W.  Fairbairn's  experiments  showed  an 
increase  in  ultimate  tensile  strength  of  50$,  and  a  reduction  in  the  elongation 
in  10  in.  of  from  2  in.  or  20$,  to  0.79  in.  or  7.9$. 

Comparison  of  Tests  of  Full-size    Eye-bars  and  Sample 

Test-pieces  of  Same  Steel  Used  in  the  Memphis  Bridge. 

(Geo.  S.  Morison,  Trans.  A.  S.  C.  E.,  1893.) 


Full-Sized  Eyebars,     . 
Sections  10"  wide  X  1  to  2  3/16"  thick. 


Reduc- 

Elongation. 

Elastic 

Max. 

Reduc- 

Elon- 

Elastic 

Max. 

tion  of 

Limit, 

Load, 

tion, 

gation, 

Limit, 

Load, 

Area, 

p.c. 

Inches. 

p.c. 

Ibs.  per 

sq.  in. 

p.c. 

p.c. 

Ibs.  per 

sq.  in. 

39.6 

20.2 

16.8 

35,100 

67,490 

47.5 

27.5 

41,580 

73,050 

39.7 

26.6 

8.2 

37,680 

70,160 

52.6 

24.4 

42,650 

75,620 

44  A 

36.8 

11.8 

39,700 

65,500 

47.9 

28.8 

40,280 

70,280 

38.5 

38.5 

17.3 

33,140 

65,060 

47.5 

27.5 

41,580 

73,050 

40.0 

32.5 

13.5 

32,860 

65,600 

44.5 

20.0 

43,750 

75,000 

39.4 

36.8 

15.3 

31,110 

61,060 

42.7 

28.8 

42,210 

69,730 

34.6 

32.9 

13.7 

33,990 

63,220 

52.2 

28.1 

40,^30 

69,720 

32.6 

13.0 

13.5 

29,330 

63,100 

48.3 

28.8 

38,090 

71,300 

7.3 

20  8 

6.9 

28,080 

55,160 

43.2 

24.2 

38,320 

70,220 

38.1 

28.9 

14.1 

29,670 

62,140 

59.6 

26.3 

40,200 

71,080 

31.8 

24.0 

11.8 

32.700 

65,400 

40.3 

25.0 

39,360 

69,360 

48.6 

39.4 

19.3 

30,500 

58,870 

40.3 

25.0 

40,910 

70,360 

10.3 

11.8 

12.3 

33,360 

73,550 

51.5 

25.5 

40,410 

69,900 

44.6 

32.0 

15.7 

32,520 

60,710 

43.6 

27.0 

40,400 

70,490 

46.0 

35.8 

14.9 

28,000 

58,720 

44.4 

29.5 

40,000 

66,800 

41.8 

23.5 

13.1 

32,290 

62,270 

42.8 

21.3 

40,530 

72,240 

41  2 

47.1 

15.1 

29,970 

58,680 

45.7 

27.0 

40,610 

70,480 

Sample  Bars  from  Same  Melts, 
about  1  in.  area. 


The  average  strength  of  the  full-sized  eye-bars  was  about  8000  Ibs. 
in.,  or  about  12$,  less  than  that  of  the  sample  test-pieces. 


per  sq:. 


394  STEEL. 

TREATMENT    OF    STRUCTURAL    STEEL. 

(James  Christie,  Trans.  A.  S.  C.  E.,  1893.) 

Effect  of  Punching  and  Shearing.— There  is  no  doubt  that  steel 
of  higher  tensile  strength  than  is  now  accepted  for  structural  purposes 
should  not  be  punched  or  sheared,  or  that  the  softer  material  may  contain 
elements  prejudicial  to  its  use  however  treated,  but  especially  if  punched. 
But  extensive  evidence  is  on  record  indicating  that  steel  of  good  quality,  in 
bars  of  moderate  thickness  and  below  or  not  much  exceeding  80,000  Ibs. 
tensile  strength,  is  not  a,ny  more,  and  frequently  not  as  much,  injured  as 
wrought  iron  by  the  process  of  punching  or  shearing. 

The  physical  effects  of  punching  and  shearing  as  denoted  by  tensile  test 
are  for  iron  or  steel: 

Reduction  of  ductility;  elevation  of  tensile  strength  at  elastic  limit;  reduc- 
tion of  ultimate  tensile  strength. 

In  very  thin  material  the  superficial  disturbance  described  is  less  than  in 
thick;  in  fact,  a  degree  of  thinness  is  reached  where  this  disturbance  prac- 
tically ceases.  On  the  contrary,  as  thickness  is  increased  the  injury 
becomes  more  evident. 

The  effects  described  do  not  invariably  ensue;  for  unknown  reasons  there 
are  sometimes  marked  deviations  from  what  seems  to  be  a  general  result. 

By  thoroughly  annealing  sheared  or  punched  steels  the  ductility  is  to  a 
large  extent  restored  and  the  exaggerated  elastic  limit  reduced,  the  change 
being  modified  by  the  temperature  of  reheating  and  the  method  of  cooling. 

It  is  probable  that  the  be.vt  results  combined  with  least  expenditure  can 
be  obtained  by  punching  all  holes  where  vital  strains  are  not  transferred  by 
the  rivets;  and  by  reaming  for  important  joints  where  strains  on  riveted 
joints  are  vital,  or  wherever  perforation  may  reduce  sections  to  a  minimum. 
The  reaming  should  be  sufficient  to  thoroughly  remove  the  material  dis- 
turbed by  punching;  to  accomplish  this  it  is  best  to  enlarge  punched  holes 
at  least  ^  in  diameter  \\ith  the  reamer. 

Riveting.— It  is  the  current  practice  to  perforate  holes  1/16  in.  larger 
than  the  rivet  diameter.  For  work  to  be  reamed  it  is  also  a  usual  require- 
ment to  punch  the  holes  from  y&  to  3/10  in.  less  than  the  finished  diameter, 
the  holes  being  reamed  to  the  proper  size  after  the  various  parts  are 
assembled. 

It  is  also  excellent  practice  to  remove  the  sharp  corner  at  both  ends  of 
the  reamed  holes,  so  that  a  fillet  will  be  formed  at  the  junction  of  the  body 
and  head  of  the  finished  rivets. 

The  rivets  of  either  iron  or  mild  steel  should  be  heated  to  a  bright  red  or 
yellow  heat  and  subjected  to  a  pressure  of  not  less  than  50  tons  per  square 
inch  of  sectional  area. 

For  rivets  of  ordinary  length  this  pressure  has  been  found  sufficient  to 
completely  fill  the  hole.  If,  however,  tie  holes  and  the  rivets  are  excep- 
tionally long,  a  greater  pressure  and  a  slower  movement  of  the  closing  tool 
than  is  used  for  shorter  rivets  has  been  found  advantageous  in  compelling 
the  more  sluggish  flow  of  the  metal  throughout  the  longer  hole. 

Welding.— No  welding  should  be  allowed  on  any  steel  that  enters  into 
structures. 

Upsetting. —Enlarged  ends  on  tension  bars  for  screw-threads,  eyebars, 
etc.,  are  formed  by  upsetting  the  material.  With  proper  treatment  and  a 
sufficient  increment  of  enlarged  sectional  area  over  the  body  of  the  bar  the 
result  is  entirely  satisfactory.  The  upsetting  process  should  be  performed 
so  that  the  properly  heated  metal  is  compelled  to  flow  without  folding  or 
lapping. 

Annealing. — The  object  of  annealing  structural  steel  is  for  the  purpose 
of  securing  homogeneity  of  structure  that  is  supposed  to  be  impaired  by  un- 
equal heating,  or  by  the  manipulation  necessarily  attendant  on  certain  pro- 
cesses. The  objects  to  be  annealed  should  be  heated  throughout  to  a 
uniform  temperature  and  uniformly  cooled. 

The  physical  effects  of  annealing,  as  indicated  by  tensile  tests,  depend  on 
the  grade  of  steel,  or  the  amount  of  hardening  elements  associated  with  it; 
also  on  the  temperature  to  which  the  steel  is  raised,  and  the  method  or  rate 
of  cooling  the  heated  material. 

The  physical  effects  of  annealing  medium-grade  steel,  as  indicated  by  ten- 
sile test,  are  reported  very  differently  by  different  observers,  some  claiming 
directly  opposite  results  from  others.  It  is  evident,  when  all  the  attendant 
conditions  are  considered,  that  the  obtained  results  must  vary  both  in  kind 
ancl  degree, 


TREATMENT   OF   STRUCTURAL   STEEL.  395 

The  temperatures  employer!  will  vary  from  1000°  to  1500°  F.:  possibly  even 
a  wider  range  is  used.  In  some  cases  the  heated  steel  is  withdrawn  at  full 
temperature  from  the  furnace  and  allowed  to  cool  in  the  atmosphere;  in 
others  the  mass  is  removed  from  the  furnace,  but  covered  under  a  muffle, 
to  lessen  the  free  radiation;  or.  again,  the  charge  is  retained  in  the  furnace, 
and  the  whole  mass  cooled  with  the  furnace,  and  more  slowly  than  by  either 
of  the  other  methods. 

The  best  general  results  from  annealing  will  probably  be  obtained  by  in- 
troducing the  material  into  a  uniformly-heated  oven  in  which  the  tempera- 
ture is  not  so  high  as  to  cause  a  possibility  of  cracking  by  sudden  and 
unequal  changing  of  temperature,  then  gradually  raising  the  temperature 
L>f  the  material  until  it  is  uniformly  about  1200°  F.,  then  withdrawing  the 
material  after  the  temperature  is  somewhat  reduced  and  cooling  under 
shelter  of  a  muffle,  sufficiently  to  prevent  too  free  and  unequal  cooling  on 
the  one  hand  or  excessively  slow  cooling  on  the  other. 

G.  G.  Men  rt  en  a,  Trans.  A.  S.  C.  E.  1F93,  says:  "  A  good  mild  steel  can  be 
worked  as  readily  as  wrought  iron  in  the  shop  or  the  field,  and  even  bear 
still  harder  treatment.  It  was,  however,  of  ten  thought  necessary  to  require 
preliminary  annealing  to  remove  the  initial  strains  due  to  rolling.  The  an- 
nealing is  undoubtedly  of  great  advantage  to  all  steel  above  64,000  Ibs. 
strength  per  square  inch,  but  it  is  questionable  whether  it  is  necessary  in 
softer  steels.  The  distortions  due  to  heating  cause  trouble  in  subsequent 
straightening,  especially  of  thin  plates.  It  cannot  be  denied,  however,  that 
annealing  produces  greater  toughness. 

"  In  a  general  way  all  unannealed  mild  steel  for  a  strength  of  56,000  to 
64,000  Ibs.  may  be  worked  in  the  same  way  as  wrought  iron.  Rough  treat- 
ment or  working  at  a  blue  heat  must,  however,  be  prohibited.  Such  treat 
inent  cannot  be  borne  by  wrought  iron,  although  it  does  not  suffer  so  much 
as  soft  steel.  Shearing  is  to  be  avoided,  except  to  prepare  rough  plates, 
which  should  afterwards  be  smoothed  by  machine  tools  or  files  before  using. 
Drifting  is  also  to  be  avoided,  because  the  edges  of  holes  are  thereby 
strained  beyond  the  yield  point.  Reaming  drilled  holes  is  not  necessary, 
particularly  when  sharp  drills  are  used  and  neat  work  is  done.  A  slight- 
countersinking  of  the  edges  of  drilled  holes  is  all  that  is  necessary.  Work- 
ing the  material  while  heated  should  be  avoided  as  far  as  possible,  and  the 
engineer  should  bear  this  in  mind  when  designing  structures.  Upsetting, 
cranking,  and  bending  ought  to  be  avoided,  but  when  necessary  the  material 
should  be  annealed  after  completion. 

"  The  riveting  of  a  mild-steel  rivet  should  be  finished  as  quickly  as  possible, 
before  it  cools  to  the  dangerous  heat.  For  this  reason  machine  work  is  the 
best.  There  is  a  special  advantage  in  machine  work  from  the  fact  that  the 
pressure  can  be  retained  upon  the  rivet  until  it  has  cooled  sufficiently  to 
prevent  elongation  and  the  consequent  loosening  of  the  rivet.1' 

Punching  and  Drilling-  of  Steel  Plates.  (Proc.  Inst.  M.  E., 
Aug.  1887,  p.  3,'G.) — In  Prof.  Unwin's  report  the  results  of  the  greater  num- 
ber of  the  experiments  made  on  iron  and  steel  plates  lead  to  the  general 
conclusion  that,  while  thin  plates,  even  of  steel,  do  not  suffer  very  much 
from  punching,  yet  in  those  of  ^  in.  thickness  and  upwards  the  loss  of  te- 
nacity due  to  punching  ranges  from  10#  to  23#  in  iron  plates  and  from  \\%  to 
&3$  in  the  case  of  mild  steel.  Mr.  Parker  found  the  loss  of  tenacity  in  steel 
plates  to  be  as  high  as  fully  one  third  of  the  original  strength  of  the  plate. 
In  drilled  plates,  on  the  contrary,  there  is  no  appreciable  loss  of  strength. 
It  is  even  possible  to  remove  the  bad  effects  of  punching  by  subsequent 
reaming  or  annea'ing. 

Working  Steel  at  a  Blue  Heat,— Not  only  are  wrought  iron  and 
steel  much  more  brittle  at  a  blue  heat  (i.e.,  the  heat  that  would  produce  an  ox- 
ide coating  ranging  from  light  straw  to  blue  on  bright  steel,  430°  to  600°  F.), 
but  while  they  are  probably  not  seriously  affected  by  simple  exposure  to  blue- 
ness,  even  if  prolonged,  yet  if  they  be  worked  in  this  range  of  temperature 
they  remain  extremely  brittle  after  cooling,  and  may  indeed  be  more  brittle 
than  when  at  blueness;  this  last  point,  however,  is  not  certain.  (Howe, 
"  Metallurgy  of  Steel,"  p.  534.) 

Tests  by  Prof.  Krohn,  for  the  German  State  Railways,  show  that  working 
at  blue  heat  has  a  decided  influence  on  all  materials  tested,  the  injury  done 
being  greater  on  wrought  iron  and  harder  steel  than  on  the  softer  steel. 
The  fact  that  wrought  iron  is  injured  by  working  at  a  blue  heat  was  reported 
by  Stromeyer.  (Engineering  News,  Jan.  9,  1892.) 

A  practice  among  boiler-makers  for  guarding  against  failures  due  to  work- 
ing at  a  blue  heat  consists  in  the  cessation  of  work  as  §0011  a,§  a  plate  whicU 


396 


STEEL. 


had  been  red-hot  becomes  so  cool  that  the  mark  produced  by  rubbing  a 
hammer-handle  or  other  piece  of  wood  will  not  glow.  A  plate  which  is  not 
hot  enough  to  produce  this  effect,  yet  too  hot  to  be  touched  by  the  hand,  is 
most  probably  blue-hot,  and  should  under  no  circumstances  be  hammered 
or  bent.  (C.  E.  Stromeyer,  Proc.  Inst  C.  E.  1886.) 

Welding  of  Steel.— A.  E.  Hunt  (A.  I.  M.  E.,  1892)  says:  I  have  never 
seen  so-called  "  welded  "  pieces  of  steel  pulled  apart  in  a  testing-machine  OP 
otherwise  broken  at  the  joint  which  have  not  shown  a  smooth  cleavage^ 
plane,  as  it  were,  such  as  in  iron  would  be  condemned  as  an  imperfect 
weld.  My  experience  in  this  matter  leads  me  to  agree  with  the  position 
t?iken  by  Mr.  William  MetcalE  in  his  paper  upon  Steel  in  the  Trans.  A.  S. 
C.  E.,  vol.  xvi.,  p.  301.  Mr.  Metcalf  says,  "I  do  not  believe  steel  can  be 
welded." 

INFLUENCE    OF  ANNEALING    UPON    MAGNETIC 
CAPACITY. 

Prof.  D.  E.  Hughes  (Eng'g,  Feb.  8,  1884,  p.  130)  has  invented  a  "  Magnetic 
Balance,'1  for  testing  the  condition  of  iron  and  steel,  which  consists  chiefly  of 
a  delicate  magnetic  needle  suspended  over  a  graduated  circular  index,  and 
a  magnet  coil  for  magnetizing  the  bar  to  be  tested.  He  finds  that  the  fol- 
lowing laws  hold  with  every  variety  of  iron  and  steel : 

1 .  The  magnetic  capacity  is  directly  proportional  to  the  softness,  or  mo- 
lecular freedom. 

2.  The  resistance  to  a  feeble  external  magnetizing  force  is  directly  as  the 
hardness,  or  molecular  rigidity. 

The  magnetic  balance  shows  that  annealing  not  only  produces  softness  in 
iron,  and  consequent  molecular  freedom,  but  it  entirely  frees  it  from  all 
strains  previously  introduced  by  drawing  or  hammering.  Thus  a  bar  of 
iron  drawn  or  hammered  has  a  peculiar  structure,  say  a  fibrous  one,  which 
gives  a  greater  mechanical  strength  in  one  direction  than  another.  This 
bar,  if  thoroughly  annealed  at  high  temperatures,  becomes  homogeneous  in 
all  directions,  and  has  no  longer  even  traces  of  its  previous  strains,  provided 
that  there  has  been  no  actual  mechanical  separation  into  a  distinct  series  of 
fibres. 

Effect  of  Annealing  upon  tlie  Magnetic  Capacity  of 
Different  Wires;  Tests  by  tlie  Magnetic  Balance. 


Description. 

Magnetic  Capacity. 

Bright  as  sent. 

Annealed. 

Best  Swedish  charcoal  iron, 

Swedish  Siemens-Martin  ire 
Puddled  iron  best  best 

first  variety, 
second    " 
third       " 
>n             .... 

deg.  on  scale. 
230 
236 
275 
165 
212     ' 
150 
115 
50 

deg.  on  scale. 
525 
510 
503 
430 
340 
291 
172 
84 

Bessemer  steel  soft  

"             "      hard 

Crucible  fine  cast  steel  

Crucible  Fine  Steel,  Tempered. 

Magnetic 
Capacity. 

Bright-yellow  heat  cooled  completely  in  cold  water.  .   . 

28 

Yellow-red  heat  cooled  completely  in  cold  water 

Bright  yellow,  let  down  in  cold  water  to  straw  color  
"      .,.**        "           "          "           blue 

33 
43 

"           "        cooled  completely  in  oil       

51 

"            "        let  down  in  water  to  white 

58 

Reheat  cooled  completely  in  water 

66 

"             "               "            "  oil           

72 

Annealed,    "              "            "oil  

84 

SPECIFICATIONS   FOR  STEEL.  397 

SPECIFICATIONS    FOR    STEEI,. 

Structural  Steel.— There  has  been  a  change  during  the  ten  years  from 
1880  to  1890,  in  the  opinions  of  engineers,  as  to  the  requirements  in  specifica- 
tions for  structural  steel,  in  the  direction  of  a  preference  for  metal  of  low 
tensile  strength  and  great  ductility.  The  following  specifications  of  differ- 
ent dates  are  given  by  A.  E.  Hunt  and  G,  H.  Clapp,  Trans.  A.  I.  M.  E.  18'JO, 
xix,  926: 

TENSION  MEMBERS.         1879.         1881.        1882.     1885.        1887.  1888. 

Elastic  limit...  ..  50,000  40@45,000  40.000  40,000      40,000          38.000 

Tensile  strength 80,000  70@80,000  70.000  70,000  67@~5,000  63@70.000 

Elongation  in  8  in 12*  18*  18*        18*  20*  22* 

Reduction  area 20*  30*  45*       42*  42*  45* 

Kind  of  steel O.H.  O.H.  or  B.  O.H.     Not    O.H.  or  B.  O.H.or  B. 

spec. 

COMPRESSION  MEMBERS  •. 

Elastic  limit  .. Same  50@55,000  50,000  50,000      Same  as  tension 

Tensile  strength as  80@90,000  80,000  80,000           members. 

Elongation  in  8  in ten-  12*            15*        15* 

Reduction  area  sion.  20*           35*        35* 

F.  H.  Lewis  (Iron  Age,  Nov.  3,  1892)  says:  Regarding  steel  to  be  used  under 
the  same  conditions  as  wrought  iron,  that  is,  to  be  punched  without  ream- 
ing, there  seems  to  be  a  decided  opinion  (and  a  growing  one)  among  engi- 
neers, that  it  is  not  safe  to  use  steel  in  this  way,  when  the  ultimate  tensile 
strength  is  above  65,000  Ibs.  ^Fhe  reason  for  this  is,  not  so  much  because 
there  is  any  marked  change  in  the  material  of  this  grade,  but  because  all 
steel,  especially  Bessemer  steel,  has  a  tendency  to  segregations  of  carbon 
and  phosphorus:,  producing  places  in  the  metal  which  are  harder  than  they 
normally  should  be.  As  long  as  the  percentages  of  carbon  and  phosphorus 
are  kept  low.  the  effect  of  these  segregations  is  inconsiderable;  but  when 
these  percentages  are  increased,  the  existence  of  these  hard  spots  in  the 
metal  becomes  more  marked,  and  it  is  therefore  less  adapted  to  the  treat- 
ment to  which  wrought  iron  is  subjected. 

There  is  a  wide  consensus  of  opinion  that  at  an  ultimate  of  64,000  to  65,000 
Ibs.  the  percentages  of  carbon  and  phosphorus  (which  are  the  two  harden- 
ing elements)  reach  a  point  where  the  steel  has  a  tendency  to  become  tender, 
and  to  crack  when  subjected  to  rough  treatment. 

A  grade  of  steel,  therefore,  running  in  ultimate  strength  from  54,000  to 
62,000  Ibs.,  or  in  some  cases  to  64,000  Ibs.,  is  now  generally  considered  a 
proper  material  for  this  class  of  work. 

Millard  Hunsicker,  engineer  of  tests  of  Carnegie,  Phipps  &  Co,,  writes  as 
follows  concerning  grades  of  structural  steel  (Eng'g  News,  June  2,  1892): 

Grade  of  Steel.—  Steel  shall  be  of  three  grades— soft,  medium,  high. 

Soft  Steel. — Specimens  from  finished  material  for  test,  cut  to  size  speci- 
fied above,  shall  have  an  ultimate  strength  of  from  54,000  to  62,000  Ibs.  per 
sq.  in.;  elastic  limit  one  half  the  ultimate  strength;  minimum  elongation  of 
26*  in  8  in,;  minimum  reduction  of  area  at  fracture  50*.  This  grade  of 
steel  to  bend  cold  180°  flat  on  itself,  without  sign  of  fracture  on  the  outside 
of  the  bent  portion. 

Medium,  Steel. — Specimens  from  finished  material  for  test,  cut  to  size 
specified  above,  shall  have  an  ultimate  strength  of  60,000  to  68,000  Ibs.  per 
sq.  in.;  elastic  limit  one  half  the  ultimate  strength;  minimum  elongation  20* 
in  8  in.;  minimum  reduction  of  area  at  fracture,  40*.  This  grade  of  steel 
to  bend  cold  180°  to  a  diameter  equal  to  the  thickness  of  the  piece  tested, 
without  crack  or  flaw  on  the  outside  of  the  bent  portion. 

High  Steel. — Specimens  from  finished  material  for  test,  cut  to  size  speci- 
fied above,  shall  have  an  ultimate  strength  of  66  000  to  74,000  Ibs.  per  sq.  in. ; 
elastic  limit  one  halt'  the  ultimate  strength;  minimum  elongation.  18*  in  8 
in. ;  minimum  reduction  of  area  at  fracture,  35*.  This  grade  of  steel  to  bend 
cold  180°  to  a  diameter  equal  to  three  times  the  thickness  of  the  test-piece, 
without  crack  or  flaw  on  the  outside  of  the  bent  portion. 

P.  H.  Lewis,  Engineers'  Club  of  Phila.,  1891,  gives  specifications  for  struc- 
tural steel  as  follows:  The  phosphorus  in  acid  open-hearth  steel  must  be 
less  than  0.10*.  and  in  all  Bessemer  or  basic  steel  must  be  less  than  0.08*. 

The  material  will  be  tested  in  specimens  of  at  least  one  half  square  inch 
section,  cut  from  the  finished  material.  Each  melt  of  steel  will  be  tested 
and  each  section  rolled,  and  also  widely  differing  gauges  of  the  same  section. 


398  STEEL* 

Requirements.  Soft  Steel.  Medium  Steel. 

Elastic  limit,  Ibs.  per  sq.  in. ,  at  least 32,000  35,000 

Ultimate  strength,  Ibs.  per  sq.  in 54,000  to  62,000  60,000  to  70,000 

Elongation  in  8  in.,  at  least 25$  20$ 

Reduction  of  area,  per  cent,  at  least 45$  40$ 

In  soft  steel  for  web-plates  over  36  in.  wide  the  elongation  will  be  reduced 
to  20$  and  the  reduction  of  area  to  40$. 

It  must  bend  cold  180  degrees  and  close  down  on  itself  without  cracking 
on  the  outside. 

%-inch  holes  pitched  %  inch  from  a  roll-finished  or  machined  edge  and  2 
inches  between  centres  must  not  crack  the  metal;  and  %-inch  holes  pitched 
1^  inches  between  centres  and  1^  inches  from  the  edge  must  not  split  the 
metal  between  the  holes. 

Medium  steel  must  bend  180  degrees  on  itself  around  a  l^>-inch  round  bar. 

Full-sized  eye-bars,  when  tested  to  destruction,  must  show  an  ultimate 
strength  of  at  least  56,000  Ibs.,  and  stretch  at  least  10$  in  a  length  of  10  feet. 

A.  E.  Hunt,  in  discussing  Mr.  Lewis's  specifications,  advises  a  requirement 
as  to  the  character  of  the  fracture  of  tensile  tests  being  entirely  silky  in 
sections  of  less  than  7  square  inches,  and  in  larger  sections  the  test  specimen 
not  to  contain  over  25$  crystalline  or  granular  fracture.  He  also  advises 
the  drifting  test  as  a  requirement  of  both  soft  and  medium  steel;  the  require- 
ment being  worded  about  as  follows:  "  Steel  to  be  capable  of  having  a  hole, 


diameter  in  the  case  of  medium  steel,  without  fracture."  This  drifting  test 
is  an  excellent  requirement,  not  only  as  a  matter  of  record,  but  as  a  meas- 
ure of  the  ductility  of  the  steel. 

H.  H.  Campbell^  Trans.  A.  I.  M.  E.  1893,  says:  In  adhering  to  the  safest 
course,  engineers  are  continually  calling  for  a  metal  with  lower  phosphorus 
The  limit  has  been  0.10$;  it  is  now  0.08$:  soon  it  will  be  0.06$;  it  should  be 
0.04$. 

A.  E.  Hunt,  Trans.  A.  I.  M.  E.  1892,  says:  Why  should  the  tests  for  steel 
be  so  much  more  rigid  than  for  iron  destined  for  the  same  purpose  ?  Some 
of  the  reasons  are  as  follows:  Experience  shows  that  the  acceptable  quali- 
ties of  one  melt  of  steel  offer  no  absolute  guarantee  that  the  next  melt  to  it, 
even  though  made  of  the  same  stock,  will  be  equally  satisfactory. 

Again,  good  wrought  iron,  in  plates  and  angles,  has  a  narrow  range  (from 
25,000  to  27,000  Ibs.)  in  elastic  limit  per  square  inch,  and  a  tensile  strength  of 
from  46,000  to  52,000  Ibs.  per  square  inch;  whereas  for  steel  the  range  in 
elastic  limit  is  from  27,000  to  80,000  Ibs.,  and  in  tensile  strength  from  48,000  to 
120,000  Ibs.  per  square  inch,  with  corresponding  variations  in  ductility, 
Moreover,  steel  is  much  more  susceptible  than  wrought  iron  to  widely  vary- 
ing effects  of  treatment,  by  hardening,  cold  rolling,  or  overheating. 


It  is  now  almost  universally  recognized  that  soft  steel,  if  properly  made 
and  of  good  quality,  is  for  many  purposes  a  safe  and  satisfactory  substitute 
for  wrought  iron,  being  capable  of  standing  the  same  shop-treatment  as 
wrought  iron.  But  the  conviction  is  equally  general,  that  poor  steel,  or  an 
unsuitable  grade  of  steel,  is  a  very  dangerous  substitute  for  wrought  iron 
even  under  the  same  unit  strains. 

For  this  reason  it  is  advisable  to  make  more  rigid  requirements  in  select- 
ing material  which  may  range  between  the  brittleness  of  glass  and  a  clmc- 
tility  greater  than  that  of  wrought  iron. 

Specifications  for  Steel  for  the  World's  Fair  Buildings, 
Chicago,  1892.  —  No  steel  shall  contain  more  than  .08$  of  phosphorus. 
From  three  separate  ingots  of  each  cast  a  round  sample  bar,  not  Jess  than 
94  in.  in  diameter,  and  having  a  length  not  less  than  twelve  diameters  be- 
tween jaws  of  testing  machine,  shall  be  furnished  and  tested  by  the  manu- 
facturer. From  these  test-pieces  alone  the  quality  of  the  material  in  the 
steel  works  shall  be  determined  as  follows: 

All  the  test-bars  must  have  a  tensile  strength  of  from  60.000  to  68,000  Ibs.  per 
square  inch,  an  elastic  limit  of  not  less  than  half  the  tensile  strength  of  the 
test-bar,  an  elongation  of  not  less  than  24$,  and  a  reduction  of  area  of  not 
.less  than  40$  at  the  point  of  fracture.  In  determining  the  ductility,  the  elon- 
gation shall  be  measured  after  breaking  on  an  original  length  of  ten  times 
the  shortest  dimension  of  the  test-piece, 

Rivet  steel  shall  have  a  tensile  strength  of  from  52,000  to  58,000  Ibs.  per 
square  inch,  and  an  elastic  limit,  elongation,  and  reduction  of  area  at  the 


SPECIFICATIONS   FOR   STEEL. 


399 


point  of  fracture  as  stated  above  for  test-bars,  and  be  capable  of  bending 
double  flat,  without  sign  of  fracture  on  the  convex  surface  of  the  bend. 

Boiler.  Ship,  and  Tank  Plates.  W.  F.  Mattes  (Iron  Age,  July 
9,  1893)  recommends  that  the  different  qualities  of  steel  plates  be  classified 
as  follows  : 


Tank. 

Ship. 

Shell. 

Fire-box. 

Tensile  test,  longitudinal 
coupon 

j    Limit, 
(     75  000 

j     55,000 
1  to  65  000 

J     55,000 
{   to  65  000 

j     55,000 
(  to  60,000 

Elongation  in  8-in.  longitu- 
dinal coupon,  per  cent  

20 

22^£ 

25 

Bending    test,  longitudinal 
coupon  

Flat. 

Flat 

Flat. 

Bending  test,  transverse 

f  

j  Over  1  in. 

j  Overfill. 

j-    Flat. 

Phosphorus  limit  

0  15 

0.10 

0.06 

0  045 

Sulphur  limit  

(  

0.065 

0.05 

Surface  inspection.     .  . 

Easy 

i  Careful 

Close. 

Rigid. 

A  steel-manufacturing  firm  in  Pittsburgh  advertises  six  different  grades 
of  steel  as  follows  : 
Extra  fire-box.        Fire-box.        Extra  flange.        Flange.        Shell.        Tank. 

The  probable  average  phosphorus  content  in  these  grades  is,  respectively: 
.02  .03  .04  0.6  0.8  .10. 

Different  specifications  for  steel  plates  are  the  following  (1889) : 

United  States  Navy.— Shell :  Tensile  strength,  58,000  to  67,000  Ibs.  per  sq. 
in. ;  elongation,  22$  in  8-in.  transverse  section,  25$  in  8-in.  longitudinalsection. 

Flange  :  Tensile  strength,  50,000  to  58,000  Ibs.;  elongation.  26$  in  8  inches. 

Chemical  requirements  :  P.  not  over  .035$  ;  S.  not  over  .040$. 

Cold-bending  test :  Specimen  to  stand  being  bent  flat  on  itself. 

Quenching  test :  Steel  heated  to  cherry-red,  plunged  in  water  82°  F.,  and 
to  be  bent  around  curve  1^  times  thickness  of  the  plate. 

British  Admiralty. —Tensile  strength,  58,240  to  67,200  Ibs.;  elongation  in 
8  in.,  20$  ;  same  cold-bending  and  quenching  tests  as  U.  S.  Navy. 

American  Boiler-makers'  Association.— Tensile  strength,  55,000  to  65,000 
Ibs. ;  elongation  in  8  in.,  20$  for  plates  %  in.  thick  and  under  ;  22$  for  plates 
%  in.  to  %  in.  ;  25$  for  plates  %  in.  and  over. 

Cold-bending  test :  For  plates  ^  in.  thick  and  under,  specimen  must  bend 
back  on  itself  without  fracture  ;  for  plates  over  }£  in.  thick,  specimen  must 
withstand  bending  180°  around  a  mandril,  1^  times  the  thickness  of  the 
plate. 

Chemical  requirements  :  P.  not  over  .040$  ;  S.  not  over  .030$. 

American  Shipmasters'  Association. — Tensile  strength,  62,000  to  72,000 
Ibs.:  elongation,  16$  on  pieces  9  in.  long. 

Strips  cut  from  plates,  heated  to  a  low  red  and  cooled  in  water  the  tem- 
perature of  which  is  82°  F.,  to  undergo  without  crack  or  fracture  being 
doubled  over  a  curve  the  diameter  of  which  does  not  exceed  three  times 
the  thickness  of  the  piece  tested. 

Boiler  Shell-plates,  Front  Tube-plate,  and  Butt-strips. 
(Pemia.  R.  R.,  1892.)— The  metal  desired  is  a  homogeneous  steel  having  a 
tensile  strength  of  60,000  Ibs.  per  sq.  in.,  and  an  elongation  of  25$  in  a 
section  originally  8  in.  long.  These  plates  will  not  be  accepted  if  the  test- 
piece  shows— 

1.  A  tensile  strength  of  less  than  55,000  Ibs.  per  sq.  in.  ;  2.  An  elongation 
in  section  originally  8  in.  long  less  than  20$ ;  3.  A  tensile  strength  over 
65,000  Ibs.  per  sq.  in.  ;  should,  however,  the  elongation  be  27$  or  over,  plates 
will  not  be  reacted  for  high  strength. 

Inside    Fire-box:    Plates,    including   Back    Tube-plate. 
(Penna.  R.  R.,  1892.)— The  metal  should  show  a  tensile  strength  of  60,000  Ibs. 
persq.  in.,  and  an  elongation  of  28$  in  a  test  section  originally  8  in.  long. 
Chemical  Composition.  Desired.  Will  be  Rejected. 

Carbon 0. 18  per  cent.        over  0.25,  below  0.15 

Phosphorus,  not  above 0.03        '*  over  0.04 

Manganese,  not  above 0.40        **  over  0.55 

Silicon,  not  above 0.02        "  over  0.04 

Sulphur,  not  above 0.02        "  over  0.05 

Copper,  not  above 0.03       "  over  0.05 


400  STEEL. 

These  plates  will  not  be  accepted  if  the  test-piece  shows:  1.  A  tensile 
strength  of  less  than  55,000  Ibs.  per  sq.  in. ;  2.  An  elongation  in  section 
originally  8  in.  long,  less  than  22%  (20%  in  plates  %  inch  thick)  ;  3.  A  tensile 
strength  over  65,000  Ibs.  per  sq.  in.  (68,000  for  plates  J4  in.  thick);  should, 
however,  the  elongation  be  30%  or  over,  plates  will  not  be  rejected  for  high 
strength  ;  4.  Any  single  seam  or  cavity  more  than  14  in.  long  in  either  of  the 
three  fractures  obtained  on  test  for  homogeneity,  as  described  below. 

Homogeneity  test :  A  portion  of  the  test-piece  is  nicked  with  a  chisel,  or 
grooved  on  a  machine,  transversely  about  a  sixteenth  of  an  inch  deep,  in 
three  places  about  1J4  in-  apart.  The  first  groove  should  be  made  on  one 
side,  1J4  in.  from  the  square  end  of  the  piece;  the  second,  1J4  in.  from 
it  on  the  opposite  side;  and  the  third,  1*4  m-  from  the  last,  and  on  the 
opposite  side  from  it.  The  test-piece  is  then  put  in  a  vise,  with  the  first 
groove  about  *4  m-  above  the  jaw,  care  being  taken  to  hold  it  firmly. 
The  projecting  end  of  the  test-piece  is  then  broken  off  by  means  of  a  ham- 
mer, a  number  of  light  blows  being  used,  and  the  bending  being  away 
from  the  groove.  The  piece  is  broken  at  the  other  two  grooves  in  the  same 
way.  The  object  of  this  treatment  is  to  open  and  render  visible  to  the  eye 
any  seams  due  to  failure  to  weld  up,  or  to  foreign  interposed  matter,  or 
cavities  due  to  gas  bubbles  in  the  ingot.  After  rupture,  one  side  of  each 
fracture  is  examined,  a  pocket  lens  being  used  if  necessary,  and  the  length 
of  the  seams  and  cavities  is  determined.  The  length  of  the  longest  seam  or 
cavity  determines  the  acceptance  or  rejection  of  the  plate. 

Dr.  0.  B.  Dudley,  chemist  of  the  Penna.  R.  R.  (Trans.  A.  I.  M.  E.  1892,  vol. 
xx.  p.  709),  gives  as  an  example  of  the  progressive  improvement  in  specifi- 
cations the  following  :  In  the  early  days  of  steel  boilers  the  specification  in 
force  called  for  steel  of  not  less  than  50,000  Ibs.  tensile  strength  and  not  less 
than  25%  elongation.  Some  metal  was  received  having  75,000  Ibs.  tensile 
strength,  and  as  the  elongation  was  all  right  it  was  accepted ;  but  when  those 
plates  were  being  flanged  in  the  boiler-shop  they  cracked  and  went  to 
pieces.  As  a  result,  an  upper  limit  of  65,000  Ibs.  tensile  strength  was 
established. 

Am.  Ry.  Master  Mechanics'  Assn.,  1894.— Same  as  Penna.  R.  R.  Specifica- 
tions of  1892,  including  homogeneity  test. 

Plate,  Tank,  and  Sheet  Steel,  (Penna.  R.  R.,  1888.*)— A  test  strip 
taken  lengthwise  of  each  plate,  YB  in.  thick  and  over,  without  annealing, 
should  have  a  tensile  strength  of  60,000  Ibs.  per  sq.  in.,  and  an  elongation  of 
25%  in  a  section  originally  2  in.  long. 

Sheets  will  not  be  accepted  if  the  tests  show  the  tensile  strength  less  than 
55,000  Ibs.  or  greater  than  70,000  Ibs.  per  sq.  in.,  nor  if  the  elongation  falls 
below  20^. 

Steel  Billets  for  Main  and  Parallel  Rods.  (Penna.  R.  R.,  1884.) 
— One  billei  from  each  lot  of  25  billets  or  smaller  shipment  of  steel  for  main 
or  parallel  rods  for  locomotives  will  have  a  piece  drawn  from  it  under  the 
hammer  and  a  test-section  will  be  turned  down  on  this  piece  to  %  in.  in 
diameter  and  2  in.  long.  Such  test-piece  should  show  a  tensile  strength  of 
85,000  Ibs.  and  an  elongation  of  15$. 

No  lot  will  be  acceptable  if  the  test  shows  less  than  80,000  Ibs.  tensile 
strength  or  12%  elongation  in  2  in. 

Locomotive  Spring  Steelo  (Penna.  R.  R.,  1887.)— Bars  which  vary 
more  than  0.01  in.  in  thickness,  or  more  than  0.02  in.  in  width,  from  the  size 
ordered,  or  which  break  where  they  are  not  nicked,  or  which,  when  properly 
nicked  and  held,  fail  to  break  square  across  where  they  are  nicked,  will  be 
returned.  The  metal  desired  has  the  following  composition:  Carbon,  1.00$; 
manganese,  0.25$;  phosphorus,  not  over  0.03$;  silicon,  not  over  0.15$;  sul- 
phur, not  over  0.03$;  copper,  not  over  0.03$. 

Shipments  will  not  be  accepted  which  show  on  analysis  less  than  0.90$  or 
over  1.10$  of  carbon,  or  over  0.50$  of  manganese,  0.05$  of  phosphorus,  0.25$ 
of  silicon,  0.05$  of  sulphur,  and  0.05$  of  copper. 

Steel  for  Locomotive  Driving-axles.  (Penna.  R.  R.,  1883.)— 
Steel  for  driving-axles  should  have  a  tensile  strength  of  85,000  Ibs.  per  sq.  in. 
and  an  elongation  of  15$  in  section  originally  2  in.  long  and  %  in.  diameter, 
taken  midway  between  centre  and  circumference  of  the  axle. 

Axles  will  not  be  accepted  if  tensile  strength  is  less  than  80,000  Ibs.,  nor  if 
elongation  is  below  12$. 

Steel  for  Crank-pins.     (Penna.  R.  R.,  1886.) — Steel  ingots  for  crank* 

*  The  Penna.  R.  R.  specifications  of  the  several  dates  given  are  still  in  force, 
July,  m± 


SPECIFICATIONS   FOR  STEEL.  401 

pins  must  be  swaged  as  per  drawings.  For  each  lot  of  50  ingots  ordered,  51 
must  be  f urnisbed,  from  wbicb  one  will  be  taken  at  random,  and  two  pieces, 
with  test  sections  %  in.  diameter  and  2  in.  long,  will  be  cut  from  any  part  of 
it,  provided  that  centre  line  of  test-pieces  falls  1^  m-  from  centre  line  of  in- 
&ot.  Such  test-pieces  should  have  a  tensile  strength  of  85,000  Ibs.  per  sq.  in. 
and  an  elongation  of  15$.  Ingots  will  not  be  accepted  if  the  tensile  strength 
is  less  than  80,000  Ibs.  nor  if  the  elongation  is  below  12$. 

Dr.  Chas.  B.  Dudley,  Chemist  of  the  P.  R.  R.  (Trans.  A.  I.  M.  E.  1892),  re- 
ferring to  this  specification,  says  :  In  testing  a  recent  shipment,  the  piece 
from  one  side  of  the  pin  showed  88,000  Ibs.  strength  and  22%  elongation,  and 
the  piece  from  the  opposite  side  showed  106,000  Ibs.  strength  and  14$  elonga- 
tion. Each  piece  was  above  the  specified  strength  and  ductility,  but  the 
lack  of  uniformity  between  the  two  sides  of  the  pin  was  so  marked  that  it 
was  finally  determined  not  to  put  the  lot  of  50  pins  in  use.  To  guard  against 
trouble  of  this  sort  in  future,  the  specifications  are  to  be  amended  to  require 
that  the  difference  in  ultimate  strength  of  the  two  specimens  shall  not  be 
more  than  3000  Ibs. 

Steel  Car-axles.  (Penna.  R.  R.,  1891.)— For  each  100  axles  ordered  101 
must  be  furnished,  from  which  one  will  be  taken  at  random,  and  subjected 
to  tests  prescribed. 

Axles  for  passenger  cars  and  passenger  locomotive  and  tender  trucks 
must  be  made  of  steel  and  be  rough  turned  throughout.  Two  test-pieces 
will  be  cut  from  an  axle,  and  the  test  sections  of  %  in.  diameter  by  2  in.  long 
may  fall  at  any  part  of  the  axle  provided  that  the  centre  line  of  the  test- 
section  is  1  in.  from  the  centre  line  of  the  axle.  Such  test-pieces  should  have 
a  tensile  strength  of  80,000  Ibs.  per  sq.  in.  and  an  elongation  of  20$.  Axles 
will  not  be  accepted  if  the  tensile  strength  is  less  than  75,000  Ibs.  or  the 
elongation  below  15$,  nor  if  the  fractures  arc  irregular. 

Axles  for  freight  cars  and  freight-locomotive  tender  trucks  must  be  made 
of  steel,  and  will  be  subjected  to  the  following  test,  which  they  must  stand 
without  fracture  : 

AXLES  4  IN.  DIAMETER  AT  CENTRE  —  Five  blows  at  20  ft.  of  a  1640-lb.  weight, 
striking  midway  between  supports  3  ft.  apart;  axle  to  be  turned  over  after 
each  blow. 

AXLES  4%  IN.  DIAMETER  AT  CENTRE— Five  blows  at  25  ft.  of  a  1640-lb.  weight, 
striking  midway  between  supports  3  ft.  apart:  axles  to  be  turned  over  after 
each  blow. 

Steel  for  Rails.— P.  H.  Dudley  (Trans.  A.  S.  C.  E.  1893)  recommends 
the  following  chemical  composition  for  rails  of  the  weights  specified  : 

Weights  per  yard 60,  65,  and  70  Ibs.       75  and  80  Ibs.     100  Ibs. 

Carbon 45  to  .55$  .50  to  .60$          .65  to  .75$ 

For  all  weights:  Manganese,  .80$  to  1.00$;  silicon,  .10$  to  .15$;  phos- 
phorus, not  over  .06$;  sulphur,  not  over  .07$. 

Carbon  by  itself  up  to  or  over  1$  increases  the  hardness  and  tensile  strength 
of  the  iron  rapidly,  and  at  the  same  time  decreases  the  elongation.  The 
amount  of  carbon  in  the  early  rails  ranged  from  0.25  to  0.5  of  1%.  while  in 
recent  rails  and  very  heavy  sections  it  has  been  increased  to  0.5,  0.6,  and  0.75 
of  1$.  With  good  irons  and  suitable  sections  it  can  run  from  0.55  to  0.75  of 
1$.  according  to  the  section,  and  obtain  fine-grain  tough  rails  with  low 
phosphorus. 

Manganese  is  a  necessary  ingredient  in  the  first  place  to  take  up  the  oxide 
of  iron  formed  in  the  bath  of  molten  metal  during  the  blow.  It  also  is  of  great 
assistance  to  check  red  shortness  of  the  ingots  during  the  first  passes  in 
the  blooming  train.  In  the  early  rails  0.4  to  0.5  of  1$  was  sufficient  when 
the  ingots  were  hammered  or  the  reductions  in  the  passes  in  the  trains  were 
very  much  lighter  than  to  day.  With  the  more  rapid  rolling  of  recent  years 
the  manganese  is  very  often  'increased  to  1.25$  to  1.5$.  It  makes  the  rails 
hard  with  a  coarse  crystallization  and  with  a  decided  tendency  to  brittleness. 
Rails  high  in  manganese  seem  to  flow  quite  easily,  especially  under  severe 
service  or  the  use  of  sand,  and  oxidize  rapidly  in  tunnels.  From  0.80  to  1.00$ 
seems  to  be  all  that  is  necessary  for  good  rolling  at  the  present  time. 

Steel  Rivets.  (H.  C.  Torranoe,  Amer.  Boiler  Mfrs.  Assn.,  1890.)— The 
Government  requirements  for  the  rivets  used  in  boilers  of  the  cruisers  built 
in  1890  are:  For  longitudinal  seams,  58,000  to  67,000  Ibs.  tensile  strength; 
elongation,  not  less  than  26$  in  8  in.,  and  all  others  a  tensile  strength  of 
50,000  to  58,000  Ibs.,  with  an  elongation  of  not  less  than  30$.  They  shall  be 
capable  of  being  flattened  out  cold  under  the  hammer  to  a  thickness  of  one 
half  the  diameter,  and  of  being  flattened  out  hot  to  a  thickness  of  one  third 


402  STEEL. 

the  diameter  without  showing  cracks  or  flaws.    The  steel  must  not  contain 
more  than  .035  of  l#of  phosphorus,  nor  more  than  .04  of  \%  of  sulphur. 

A  lot  of  20  succesiye  tests  of  rivet  steel  of  the  low  tensile  strength  quality 
and  12  tests  of  the  higher  tensile  strength  gave  the  following  results: 

Low  Steel.  Higher. 

Tensile  strength,  Ibs.  per  sq.  in ...    51,230  to  54,100       59,100  to  61,850 

Elastic  limit,  Ibs.  per  sq.  in 31,050  to  33,190       32,080  to  33,070 

Elongation  in  8  in.,  per  cent 30.5  to  35  25  28.5  to  31.75 

Carbon,  per  cent 11  to  .14  .16  to  .18 

Phosphorus 027  to  .029  .03 

Sulphur 033  to  .035  .033  to  .035 

The  safest  steel  rivets  are  those  of  the  lowest  tensile  strength,  since  they 
are  the  least  liable  to  become  hardened  and  fracture  by  hammering,  or  to 
break  from  repeated  coucussive  and  vibratory  strains  to  which  they  are 
subjected  in  practice.  For  calculations  of  the  strength  of  riveted  joints  the 
tensile  strength  may  be  taken  as  the  average  of  the  figures  above  given,  or 
52,665  Ibs.,  and  the  shearing  strength  at  45,000  Ibs.  per  sq.  in. 

MISCELLANEOUS  NOTES  ON  STEEL. 

May  Carbon  be  Burned  Out  of  Steel  ?— Experiments  made  at 
the  Laboratory  of  the  Penna.  Railroad  Co.  (Specifications  for  Springs,  1888) 
with  the  steel  of  spiral  springs,  show  that  the  place  from  which  the  borings 
are  taken  for  analysis  has  a  very  important  influence  on  the  amount  of  car- 
bon found.  If  the  sample  is  a  piece  of  the  round  bar,  and  the  borings  are 
taken  from  the  end  of  this  piece,  the  carbon  is  always  higher  than  if  the 
borings  are  taken  from  the  side  of  the  piece.  It  is  common  to  find  a  differ- 
ence of  0.10$  between  the  centre  and  side  of  the  bar,  and  in  some  cases  the 
difference  is  as  high  as  0.23$.  Furthermore,  experiments  made  with  samples 
taken  from  the  drawn  out  end  of  the  bar  show,  usually,  less  carbon  thai 
samples  taken  from  the  round  part  of  the  bar,  even  though  the  borings  may 
be  taken  out  of  the  side  in  both  cases. 

Apparently  during  the  process  of  reducing  the  metal  from  the  ingots  to  thti 
round  bar,  with  successive  heatings,  the  carbon  in  the  outside  of  the  bar  is* 
burned  out. 

66  Recalescence  "  of  Steel.— If  we  heat  a  bar  of  copper  by  a  flame 
of  constant  strength,  and  note  carefully  the  interval  of  time  occupied  ia 
passing  from  each  degree  to  the  next  higher  degree,  we  find  that  these  in- 
tervals increase  regularly,  i.e.,  that  the  bar  heats  more  and  more  slowly,  as 
its  temperature  approaches  that  of  the  flame.  If  we  substitute  a  bar  of 
steel  for  one  of  copper,  we  find  that  these  intervals  increase  regularly  up  to 
a  certain  point,  when  the  rise  of  temperature  is  suddenly  and  in  most  cases 
greatly  retarded  or  even  completely  arrested.  After  this  the  regular  rise  of 
temperature  is  resumed,  though  other  like  retardations  may  recur  as  the 
temperature  rises  farther.  So  if  we  cool  a  bar  of  steel  slowly  the  fall  o/' 
temperature  is  greatly  retarded  when  it  reaches  a  certain  point  in  dull  red 
ness.  If  the  steel  contains  much  carbon,  and  if  certain  favoring  conditions 
be  maintained,  the  temperature,  after  descending  regularly,  suddenly  rises 
spontaneously  very  abruptly,  remains  stationary  a  while,  and  then  ^de- 
scends. This  spontaneous  reheating  is  known  as  "  recalescence." 

These  retardations  indicate  that  some  change  which  absorbs  or  evolves 
heat  occurs  within  the  metal.  A  retardation  while  the  temperature  is  rising 
points  to  a  change  which  absorbs  heat;  a  retardation  during  cooling  points 
to  some  change  which  evolves  heat.  (Henry  M.  Howe,  on  "  Heat  Treatment 
of  Steel,'1  Trans.  A.  I.  M.  E.,  vol.  xxii.) 

Effect  of  Nicking  a  Steel  Bar.— The  statement  is  sometimes  made 
that,  owing  to  the  homogeneity  of  steel,  a  bar  with  a  surface  crack  or  nick 
in  one  of  its  edges  is  liable  to  fail  by  the  gradual  spreading  of  the  nick,  and 
thus  break  under  a  very  much  smaller  load  than  a  sound  bar.  With  iron  it 
is  contended  this  does  not  occur,  as  this  metal  has  a  fibrous  structure.  Sir 
Benjamin  Baker  has,  however,  shown  that  this  theory,  at  least  so  far  as 
statical  stress  is  concerned,  is  opposed  to  the  facts,  as  he  purposely  made 
nicks  in  specimens  of  the  mild  steel  used  at  the  Forth  Bridge,  but  found 
that  the  tensile  strength  of  the  whole  was  thus  reduced  by  only  about  one 
ton  per  square  inch  of  section.  In  an  experiment  by  the  Union  Bridge  Com- 
pany a  full-sized  steel  counter -bar,  with  a  screw-turned  buckle  connection, 
was  tested  under  a  heavy  statical  stress,  and  at  the  same  time  a  weight 
weighing  1040  Ibs.  was  allowed  to  drop  on  it  from  various  heights.  The  bar 
was  first  broken  by  ordinary  statical  strain,  and  showed  a  breaking  stress  of 


MISCELLANEOUS  NOTES  Otf   STEEL. 


403 


68,800  Ibs.  per  square  inch.  The  longer  of  the  broken  parts  was  then  placed 
in.  the  machine  and  put  under  the  following  loads,  whilst  a  weight,  as  already 
mentioned,  was  dropped  on  it  from  various  heights  at  a  distance  of  five 
feet  from  the  sleeve-nut  of  the  turn-buckle,  as  shown  below: 

Stress  in  pounds  per  sq.  in 50,000       55,000       60,000       63,000       65,000 

ft.  in.       ft.  in.       ft.  in.       ft.  in.       ft.  in. 

Height  of  fall 21  26  30  40  50 

The  weight  was  then  shifted  so  as  to  fall  dirctly  on  the  sleeve-nut,  and  the 
test  proceeded  as  follows: 

Stress  on  specimen  in  Ibs.  per  square  inch  65,350         65,350         68,800 

ft.  ft.  ft. 

Height  of  fall 366 

It  will  be  seen  that  under  this  trial  the  bar  carried  more  than  when  origi- 
nally tested  statically,  showing  that  the  nicking  of  the  bar  by  screwing  had 
not  appreciably  weakened  its  power  of  resisting  shocks. —  Eiufg  News. 

Electric  Conductivity  of  Steel.— Louis  Campredon  reports  in  Le 
Genie  Civil  the  results  of  a  series  of  experiments  made  to  ascertain  the  rela- 
tions between  electric  resistance  and  chemical  compositions  of  steel.  The 
wires  were  No.  17,  3  mm.  diameter.  The  results  are  given  in  the  table  below: 


Car- 
bon. 

Silicon. 

Sulphur. 

Phos- 
phorus. 

Manga- 
nese. 

Total. 

Electric 
Resist- 
ance, 
Ohms. 

1 

0.090 

•0.020 

0.050 

0.030 

0.210 

0.410 

127.7 

2  
3  
4  

0.100 
0.100 
0.100 

0.020 
0.020 
0.020 

0.050 
0.060 
0.050 

0.040 
0.040 
0.050 

0.240 
0.260 
0.310 

0.450 
0.480 
0.530 

133.0 
137.5 
140.3 

5  
6  
7  
8  
9  
10  

0.120 
0.110 
0.100 
0.120 
0.110 
0.140 

0.030 
0.030 
0.020 
0.020 
0.030 
0.030 

0.070 
0.060 
0.070 
0.070 
0.060 
0.060 

0.050 
0.060 
0.040 
0.070 
0.060 
0.080 

0.330 
0.350 
0.400 
0.400 
0.490 
0.540 

0.600 
0.610 
0.630 
0.680 
0.750 
0.850 

142.7 
144.5 
149.0 
150.3 
156.0 
173.0 

An  examination  of  these  series  of  figures  shows  that  the  purer  and  softer 
steel  the  better  is  its  electric  conductivity,  and,  furthermore,  that  manga- 
nese is  the  element  which  most  influences  the  conductivity. 

Specific  Gravity  of  Soft  Steel.  (W.  Kent,  Trans.  A.  I.  M.  E.,  xiv. 
585.)— Five  specimens  of  boiler-plate  of  C.  0.14,  P.  0.03  gave  an  average  sp. 
gr.  of  7.932,  maximum  variation  0.008.  The  pieces  were  first  planed  to  re- 
move all  possible  scale  indentations,  then  filed  smooth,  then  cleaned  in 
dilute  sulphuric  acid,  and  then  boiled  in  distilled  water,  to  remove  all  traces 
of  air  from  the  surface. 

The  figures  of  specific  gravity  thus  obtained  by  careful  experiment  on 
bright,  smooth  pieces  of  steel  are,  however,  too  high  for  use  in  determining 
the  weights  of  rolled  plates  for  commercial  purposes.  The  actual  average 
thickness  of  these  plates  is  always  a  little  less  than  is  shown  by  the  calipers, 
on  account  of  the  oxide  of  iron  on  the  surface,  and  because  the  surface  is 
not  perfectly  smooth  and  regular.  A  number  of  experiments  on  commercial 
plates,  and  comparison  of  other  authorities,  led  to  the  figure  7.854  as  the 
average  specific  gravity  of  open-hearth  boiler-plate  steel.  This  figure  is 
easily  remembered  as  being  the  same  figure  with  change  of  position  of  the 
decimal  point  (.7854)  which  expresses  the  relation  of  the  area  of  a  circle  to 
that  of  its  circumscribed  square.  Taking  the  weight  of  a  cubic  foot  of  water 
at  02°  F.  as  62.36  Ibs.  (average  of  several  authorities),  this  figure  gives  489.775 
Ibs.  as  the  weight  of  a  cubic  foot  of  steel,  or  the  even  figure,  490  Ibs.,  may  be 
taken  as  a  convenient  figure,  and  accurate  within  the  limits  of  the  error  of 
observation. 

A  common  method  of  approximating  the  weight  of  iron  plates  is  to  con- 
sider them  to  weigh  40  Ibs.  per  square  foot  one  inch  thick.  Taking  this 
weight  and  adding  2%  gives  almost  exactly  the  weight  of  steel  boiler-plate 
given  above  (40  X  12  X  1.02  =  489.6  Ibs.  per  cubic  foot). 

Occasional  Failures  of  Bessemer  Steel.— G.  H.  Clapp  and  A. 
E.  Hunt,  in  their  paper  on  "  The  Inspection  of  Materials  of  Construction  in 


404  STEEL. 

the  United  States  "  (Trans.  A.  I.  M.  E.,  vol.  xix),  say:  Numerous  instances 
could  be  cited  to  show  the  unreliability  of  Bessemer  steel  for  structural  pur- 
poses. One  of  the  most  marked,  however,  was  the  following:  A  12-in.  I-beam 
weighing  30  Ibs.  to  the  foot,  20  feet  long,  on  being  unloaded  from  a  car 
broke  in  two  about  6  feet  from  one  end. 

The  analyses  and  tensile  tests  made  do  not  show  any  cause  for  the  failure. 

The  cold  and  quench  bending  tests  of  botli  the  original  %-in.  round  test- 
pieces,,and  of  pieces  cut  from  the  finished  material,  gave  satisfactory  re- 
sults; the  cold-bending  tests  closing  down  on  themselves  without  sign  of 
fracture. 

Numerous  other  cases  of  angles  and  plates  that  were  so  hard  in  places  as 
to  break  off  short  in  punching,  or,  what  was  worse,  to  break  the  punches, 
have  come  under  pur  observation,  and  although  makers  of  Bessemer  steel 
claim  that  this  is  just  as  likely  to  occur  in  open-hearth  as  in  Bessemer  steel, 
we  have  as  yet  never  seen  an  instance  of  failure  of  this  kind  in  open-hearth 
steel  having  a  composition  such  as  C  0.25$,  Mn  0.70$,  P  0.80$.  - 

J.  W.  Wailes.  in  a  paper  read  before  the  Chemical  Section  of  the  British 
Association  for  the  Advancement  of  Science,  in  speaking  of  mysterious 
failures  of  steel,  states  that  investigation  shows  that  "  these  failures  occur 
in  steel  of  one  class,  viz.,  soft  steel  made  by  the  Bessemer  process.11 

Segregation  in  Steel  Ingots.  (A.  Pourcel,  Trans.  A.  I.  M.  E.  1893.) 
— H.  M.  Howe,  in  his  "  Metallurgy  of  Steel,'1  gives  a  resume  of  observations, 
with  the  results  of  numerous  analyses,  bearing  upon  the  phenomena  of  seg- 
regation. 

In  1881  Mr.  Stubbs.  of  Manchester,  showed  the  heterogeneous  results  of 
analyses  made  upon  different  parts  of  an  ingot  of  large  section. 

A  test-piece  taken  24  inches  from  the  head  of  the  ingot  7.5  feet  in  length 
gave  by  analysis  very  different  results  from  those  of  a  test-piece  taken  30 
inches  from  the  bottom. 

C.  Mn.  Si.  S.  P. 

Top     0.92  0.535  0.043  0.161  0.261 

Bottom 037  0.498  0.006  0.025  0.096 

Windsor  Richards  says  he  had  often  observed  in  test-pieces  taken  from 
different  points  of  one  plate  variations  of  0.05$  of  carbon.  Segregation  is 
specially  pronounced  in  an  ingot  in  its  central  portion,  and  around  the 
space  of  the  piping. 

It  is  most  observable  in  large  ingots,  but  in  blocks  of  smaller  weight  and 
limited  dimensions,  subjected  to  the  influence  of  solidification  as  rapid  as 
casting  within  thick  walls  will  permit,  it  may  still  be  observed  distinctly. 
An  ingot  of  Martin  steel,  weighing  about  1000  Ibs.,  and  having  a  height  of 
1 .10  feet  and  a  section  of  10.24  inches  square,  gave  the  following: 

1.  Upper  section:  C.  S.  P.  Mn. 

Border 0.330  0.040  0.033  0.420 

Centre 0.530  0.077  0.057  0.430 

2.  Lower  section:  C.  S.  P.  Mn. 

Border 0.280  0.029  0.016  0.390 

Centre 0.290  0.030  0.038  0.390 

3.  Middle  section:  C.  S.  P.  Mn. 

Border 0.320  0.025  0.025  0400 

Centre 0.320  0.048  0.048  0.40^ 

Segregation  is  less  marked  in  ingots  of  extra-soft  metal  cast  in  cast-iron 
moulds  of  considerable  thickness.  It  is,  however,  still  important  and  ex- 
plains the  difference  often  shown  by  the  results  of  tests  on  pieces  taken 
from  different  portions  of  a  plate.  Two  samples,  taken  from  the  sound  part 
of  a  flat  ingot,  one  on  the  outside  and  the  other  in  the  centre,  7.9  inches  from 
the  upper  edge,  gave: 

C.  S.  P.  Mn. 

Centre 0.14  0.053  0.072  0.576 

Exterior 0.11  0.036  0.027  0.610 

Manganese  is  the  element  most  uniformly  disseminated  in  hard  or  soft 
steel. 

For  cannon  of  large  calibre,  if  we  reject,  in  addition  to  the  part  cast  in 
sand  and  called  the  masselotte  (sinking-head),  one  third  of  the  upper  part 
of  the  ingot,  we  can  obtain  a  tube  practically  homogeneous  in  composition, 
because  the  central  part  is  naturally  removed  by  the  boring  of  the  tube. 
With  extra-soft  steels,  destined  for  ship-  or  boiler-plates,  the  solution  for 
practically  perfect  homogeneity  lies  in  the  obtaining  of  a  metal  more  closely 
deserving  its  name  of  extra  soft  metal 


STEEL   CASTINGS.  405 

The  injurious  consequences  of  segregation  must  be  suppressed  by  reduc- 
ing, as  far  as  possible,  the  elements  subject  to  liquation. 
Earliest    Uses   of  Steel   for   Structural    Purposes.    (G.  G. 

Mehrtens,  Trans.  A.  S.  C.  E.  1893).— The  Pennsylvania  Railroad  Company 
first  introduced  Bessemer  steel  in  America  in  locomotive  boilers  in  the  year 
1863,  but  the  steel  was  too  hard  and  brittle  for  such  use.  The  first  plates 
made  for  steel  boilers  had  a  tenacity  of  85,000  to  92,OCO  Ibs.  and  an  elongation 
of  but  7%  to  10$.  The  results  were  not  favorable,  and  the  steel  works  were 
soon  forced  to  offer  a  material  of  less  tenacity  and  more  ductility.  The  re- 
quirements were  therefore  reduced  to  a  tenacity  of  78,000  Ibs.  or  less,  and 
the  elongation  was  increased  to  15$  or  more.  Even  with  this,  between  the 
years  1870  aud  1880,  many  explosions  occurred  and  many  careful  examina- 
tions were  made  to  determine  their  cause.  It  was  found  on  examining  the 
rivet-holes  that  there  were  incipient  changes  in  the  metal,  many  cracks 
around  them,  and  points  near  them  were  corroded  with  rust,  all  caused  by 
the  shock  of  tools  in  manufacturing.  It  was  evident  that  the  material 
was  unsuitable,  and  that  the  treatment  must  be  changed.  In  the  beginning 
of  1878,  Mr.  Parker,  chief  engineer  of  the  Lloyds,  stated  that  there  was  then 
but  one  English  steamer  in  possession  of  a  steel  boiler;  a  year  later  there 
were  120.  In  1878  there  were  but  five  large  English  steamers  built  of  steel, 
while  in  1883  there  were  116  building.  The  use  of  Bessemer  steel  in  bridge- 
building  was  tried  first  on  the  Dutch  State  railways  in  1863-64,  then  in  Eng. 
land  and  Austria.  In  1874  a  bridge  was  built  of  Bessemer  steel  in  Austria. 
The  first  use  of  cast  steel  for  bridges  was  in  America,  for  the  St.  Louis  Arch 
Bridge  and  for  the  wire  of  the  East  River  Bridge.  These  gave  an  impetus 
to  the  use  of  ingot  metal,  and  before  1880  the  Glasgow  and  Plattsmouth 
Bridges  over  the  Missouri  River  were  also  built  of  ingot  metal.  Steel  eye- 
bars  were  applied  for  the  first  time  in  the  Glasgow  Bridge.  Since  1880  the 
introduction  of  mild  steel  in  all  kinds  of  engineering  structures  has  steadily 
increased. 

STEEL  CASTINGS. 

(E.  S.  Cramp,  Engineering  Congress,  Dept.  of  Marine  Eng'g,  Chicago,  1893.) 

In  1891  American  steel-founders  had  successfully  produced  a  considerable 
variety  of  heavy  and  difficult  castings,  of  which  the  following  are  the  most 
noteworthy  specimens: 

Bed-plates  up  to  24,000  Ibs.;  stern-posts  up  to  54,000  Ibs.;  stems  up  to 
21,000  Ibs. ;  hydraulic  cylinders  up  to  11,000  Ibs. ;  shaft-struts  up  to  32,000  Ibs. ; 
hawse-pipes  up  to  7500'lbs. ;  stern-pipes  up  to  8000  Ibs.' 

The  percentage  of  success  in  these  classes  of  castings  since  1890  has  ranged 
from  65$  in  the  more  difficult  forms  to  90$  in  the  simpler  ones;  the  tensile 
strength  has  been  from  62,000  to  78,000  Ibs.,  elongation  from  15$  to  25$.  The 
best  performance  recorded  is  that  of  a  guide,  cast  in  January,  1893,  which 
developed  84,000  Ibs.  tensile  strength  and  15.6$  elongation. 

The  first  steel  castings  of  which  anything  is  generally  known  were 
crossing-frogs  made  for  the  Philadelphia  &  Reading  R.  R.  in  July,  1867,  by 
the  William  Butcher  Steel  Works,  now  the  Midvale  Steel  Co.  The  moulds 
were  made  of  a  mixture  of  ground  fire-brick,  black-lead  crucible-pots 
ground  fine,  and  fire-clay,  and  washed  with  a  black-lead  wash.  The  steel 
was  melted  in  crucibles,  and  was  about  as  hard  as  tool  steel.  The  surface 
of  these  castings  was  very  smooth,  but  the  interior  was  very  much  honey- 
combed. This  was  before  the  days  when  the  use  of  silicon  was  known  for 
solidifying  steel.  The  sponginess,  which  was  almost  universal,  was  a  great 
obstacle  to  their  general  adoption. 

The  next  step  was  to  leave  the  ground  pots  out  of  the  moulding  mixture 
and  to  wash  the  mould  with  finely  ground  fire-brick.  This  was  a  great  im- 
provement, especially  in  very  heavy  castings;  but  this  mixture  still  clung  so 
strongly  to  the  casting  that  only  comparatively  simple  shapes  could  be  made 
with  certainty.  A  mould  made  of  such  a  mixture  became  almost  as  hard  as 
fire-brick,  and  was  such  an  obstacle  to  the  proper  shrinkage  of  castings, 
that,  when  at  all  complicated  in  shape,  they  had  so  great  a  tendency  to 
crack  as  to  make  their  successful  manufacture  almost  impossible.  By  this 
time  the  use  of  silicon  had  been  discovered,  and  the  only  obstacle  in  the  way 
of  making  good  castings  was  a  suitable  moulding  mixture.  This  was  ulti- 
mately found  in  mixtures  having  the  various  kinds  of  silica  sand  as  the 
principal  constituent. 

One  of  the  most  fertile  sources  of  defects  in  castings  is  a  bad  design. 
Very  intricate  shapes  can  be  cast  successfully  if  they  are  so  designed  as  to 


406 


STEEL. 


cool  uniformly.  Mr.  Cramp  says  while  he  is  not  yet  prepared  to  state  that 
anything  that  can  be  cast  successfully  in  iron  can  be  cast  in  steel,  indica- 
tions seem  to  point  that  way  in  all  cases  where  it  is  possible  to  put  on  suit- 
able sinking-heads  for  feeding  the  casting. 

H.  L.  Gantt  (Trans.  A.  S.  M.  E.,  xii.  710)  says:  Steel  castings  not  only 
shrink  much  more  than  iron  ones,  but  with  less  regularity.  The  amount  of 
shrinkage  varies  with  the  composition  and  the  heat  of  the  metal;  the  hotter 
the  metal  the  greater  the  shrinkage;  and,  as  we  get  smoother  castings  from 
hot  metal,  it  is  better  to  make  allowance  for  large  shrinkage  and  pour  the 
metal  as  hot  as  possible.  Allow  3/16  or  y\  in.  per  ft.  in  length 
for  shrinkage,  and  y±  in.  for  finish  on  machined  surfaces,  except  such  as  are 
cast  4%up."  Cope  surfaces  which  are  to  be  machined  should,  in  large  or 
hard  castings,  have  an  allowance  of  from  %  to  ^  in.  for  finish,  as  a  large 
mass  of. metal  slowly  rising  in  a  mould  is  apt  to  become  crusty  on  the  sur- 
face, and  such  a  crust  is  sure  to  be  full  of  imperfections.  On  small,  soft 
castings  ^  in.  on  drag  side  and  y±  in.  on  cope  side  will  be  sufficient.  No  core 
should  have  less  than  y±  in-  finish  on  a  side  and  very  large  ones  should  have 
as  much  as  y%  in.  on  a  side.  Blow-holes  can  be  entirely  prevented  in  cast- 
ings by  the  addition  of  manganese  and  silicon  in  sufficient  quantities;  but 
both  of  these  cause  brittleness,  and  it  is  the  object  of  the  conscientious  steel- 
maker to  put  no  more  manganese  and  silicon  in  his  steel  than  is  just  suffi- 
cient to  make  it  solid.  The  best  results  are  arrived  at  when  all  portions  of 
the  castings  are  of  a  uniform  thickness,  or  very  nearly  so. 

The  following  table  will  illustrate  the  effect  of  annealing  on  tensile 
strength  and  elongation  of  steel  castings  : 


Carbon. 

Unannealed. 

Annealed. 

Tensile  Strength. 

Elongation. 

Tensile  Strength. 

Elongation. 

.23$ 
.37 
.53 

68,738 
85,540 
90,121 

22.40$ 
8.20 
2.35 

67.210 
82,228 
106.415 

31.  40$ 
21.80 
9.80 

The  proper  annealing  of  large  castings  takes  nearly  a  week. 

The  proper  steel  for,  roll  pinions,  hammer  dies,  etc.,  seems  to  be  that  con- 
taining about  .60#  of  carbon.  Such  castings,  properly  annealed,  have  worn 
well  and  seldom  broken.  Miscellaneous  gearing  should  contain  carbon  .40$ 
to  60$,  gears  larger  in  diameter  being  softest.  General  machinery  castings 
should,  as  a  rule,  contain  less  than  .40$  of  carbon,  those  exposed  to  great 
shocks  containing  as  low  at  .20$  of  carbon.  Such  castings  will  give  a  tensile 
strength  of  from  60,000  to  80,000  Ibs.  per  sq.  in.  and  at  least  15$  extension  in 
a  2  in.  long  specimen.  Machinery  and  hull  castings  for  war-vessels  for  the 
United  States  Navy,  as  well  as  carriages  for  naval  guns,  contain  from  .20$  to 
30$  of  carbon. 

The  following  is  a  partial  list  of  castings  in  which  steel  seems  to  be 
rapidly  taking  the  place  of  iron:  Hydraulic  cylinders,  crossheads  and  pistons 
for  large  engines,  roughing  rolls,  rolling-mill  spindles,  coupling-boxes,  roll 
pinions,  gearing,  hammer-heads  and  dies,  riveter  stakes,  castings  for  ships, 
car  couplers,  etc. 

For  description  of  methods  of  manufacture  of  steel  castings  by  the  Besse- 
mer, open-hearth,  and  crucible  processes,  see  paper  by  P.  G.  Salom,  Trans. 
A.  I.  M.  E.  xiv,  118. 

Specifications  for  steel  castings  issued  by  the  U.  S.  Navy  Department,  1889 
(abridged) :  Steel  for  castings  must  be  made  by  either  the  open-hearth  or 
the  crucible  process,  and  must  not  show  more  than  .06$  of  phosphorus.  All 
castings  must  be  annealed,  unless  otherwise  directed.  The  tensile  strength 
of  steel  castings  shall  be  at  least  60,000  Ibs.,  with  an  elongation  of  at  least 
15$  in  8  in .  for  all  castings  for  moving  parts  of  the  machinery,  and  at  least 
10$  in  8  in.  for  other  castings.  Bars  1  in.  sq.  shall  be  capable  of  bending 
cold,  without  fracture,  through  an  angle  of  90°,  over  a  radius  not  greater 
than  \y%  in.  All  castings  must  be  sound,  free  from  injurious  roughness, 
sponginess,  pitting,  shrinkage,  or  other  cracks,  cavities,  etc. 

Pennsylvania  Railroad  specifications,  1888:  Steel  castings  should  have  a 
tensile  strength  of  70,000  Ibs.  per  sq.  in.  and  an  elongation  of  15$  in  section 
originally  2  in.  long.  Steel  castings  \\ill  not  be  accepted  if  tensile  strength 


MANGANESE,  NICKEL,  AND  OTHER  "  ALLOY"  STEELS.  407 

falls  below  60,000  Ibs.,  nor  if  the  elongation  is  less  than  12$,  nor  if  cast- 
ings have  blow-holes  and  shrinkage  cracks.  Castings  weighing  80  Ibs.  or 
more  must  have  cast  with  them  a  strip  to  be  used  as  a  test-piece.  The  di- 
mensions of  this  strip  must  be  %  in.  sq.  by  12  in.  long. 

MANGANESE,   NICKEI^  AND  OTHER   "AI.L.OY" 

STEELS. 

Manganese  Steel.  (H.  M.  Howe,  Trans.  A.  S.  M.  E.,  vol.  xii.)— Man- 
ganese steel  is  an  alloy  of  iron  and  manganese,  incidentally,  and  probably 
unavoidably,  containing  a  considerable  proportion  of  carbon. 

The  effect  of  small  proportions  of  manganese  on  the  hardness,  strength, 
and  ductility  of  iron  is  probably  slight.  The  point  at  which  manganese 
begins  to  have  a  predominant  effect  is  not  known  :  it  may  be  somewhere 
about  2.5$.  As  the  proportion  of  manganese  rises  above  2.5$  the  strength 
and  ductility  diminish,  while  the  hardness  increases.  This  effect  reaches  a 
maximum  with  somewhere  about  6$  of  manganese.  When  the  proportion 
of  this  element  rises  beyond  6$  the  strength  and  ductility  both  increase, 
while  the  hardness  diminishes  slightly,  the  maximum  of  both  strength  and 
ductility  being  reached  with  about  14$  of  manganese.  With  this  proportion 
the  metal  is  still  so  hard  that  it  is  very  difficult  to  cut  it  with  steel  tools.  As 
the  proportion  of  manganese  rises  above  15$  the  ductility  falls  off  abruptly, 
the  strength  remaining  nearly  constant  till  the  manganese  passes  18$,  when 
it  in  turn  diminishes  suddenly. 

Steel  containing  from  4$  to  6.5$  of  manganese,  even  if  it  have  but  0.37$  of 
carbon,  is  reported  to  be  so  extremely  brittle  that  it  can  be  powdered  under 
a  hand-hammer  when  cold  ;  }Tet  it  is  ductile  when  hot. 

Manganese  steel  is  very  free  from  blow-holes  ;  it  welds  with  great  diffi- 
culty ;  its  toughness  is  increased  by  quenching  from  a  yellow  heat  ;  its  elec- 
tric resistance  is  enormous,  and  very  constant  with  changing  temperature  ; 
it  is  low  in  thermal  conductivity.  Its  remarkable  combination  of  great  hard 
A^ess,  which  cannot  be  materially  lessened  by  annealing,  and  great  tensile 
strength,  with  astonishing  toughness  and  ductility,  at  once  creates  and 
limits  its  usefulness.  The  fact  that  manganese  steel  cannot  be  softened, 
(hat  it  ever  remains  so  hard  that  it  can  be  machined  only  with  great  diffi- 
culty, sets  up  a  barrier  to  its  usefulness. 

The  following  comparative  results  of  abrasion  tests  of  manganese  and 
tfther  steel  were  reported  by  T.  T.  Morrell : 

ABRASION  BY  PRESSURE  AGAINST  A  REVOLVING  HARDENED-STEEL  SHAFT. 

Loss  of  weight  of  manganese  steel 1.0 

blue-tempered  hard  tool  steel 0.4 

annealed  hard  tool  steel 7.5 

hardened  Otis  boiler-plate  steel 7.0 

annealed      "  "    14.0 

ABRASION  BY  AN  EMERY-WHEEL. 

Loss  of  weight  of  hard  manganese-steel  wheels 1 .00 

softer  "      1.19 

hardest  carbon-steel  wheels 1 .23 

soft  "     2.85 

The  hardness  of  manganese  steel  seems  to  be  of  an  anomalous  kind.  The 
alloy  is  hard,  but  under  some  conditions  not  rigid.  It  is  very  hard  in  its 
resistance  to  abrasion  ;  it  is  not  always  hard  in  its  resistance  to  impact. 

Manganese  steel  forges  readily  at  a  yellow  heat,  though  at  a  bright  white 
heat  it  crumbles  under  the  hammer.  But  it  offers  greater  resistance  to 
deformation,  i.e.,  it  is  harder  when  hot,  than  carbon  steel. 

The  most  important  single  use  for  manganese-steel  is  for  the  pins  which 
hold  the  buckets  of  elevated  dredgers.  Here  abrasion  chiefly  is  to  be 
resisted. 

Another  important  use  is  for  the  links  of  common  chain-elevators. 
As  a  material  for  stamp-shoes,  for  horse-shoes,  for  the  knuckles  of  an 
automatic  car-coupler,  manganese  steel  has  not  met  expectations. 

Manganese  steel  has  been  regularly  adopted  for  the  blades  of  the  Cyclone 
pulverizer.  Some  manganese-steel  wheels  are  reported  to  have  run  over 
300.000  miles  each  without  turning,  on  a  New  England  railroad. 

Nickel  Steel.— The  remarkable  tensile  strength  and  ductility  of  nickel 
steel,  as  shown  by  the  test-bars  and  the  behavior  of  nickel-steel  armor- 
plate  under  shot  tests,  are  witness  of  the  valuable  qualities  conferred  upon 
steel  by  the  addition  of  a  few  per  cent  of  nickel. 


408 


STEEL. 


The  following  tests  were  made  on  nickel  steels  by  Mr.  Maunsel  White  of 
the  Bethlehem  Iron  Company  (Eng.  &  M.  Jour.,  Sept.  16,  1893.) : 


Specimen 
from  — 

is 

5 

Is 

3 

Tensile 
Str'gth, 
Ibs.  per 
sq.  in. 

Elastic 
Limit, 
Ibs.  per 
sq.  in. 

p.  c. 
ex. 

p.  c. 
cont. 

:f 

Forged 

i  .625 

4 

276,800 
246,595 

2.75 
4  25 

"Yof 

Special 
treatment. 

1 

bars.  * 

1    ^ 

" 

105,300 

19.25 

55.0 

Annealed. 

03 

f  .564 

4 

142,800 

'  74.000 

13.0 

28.2 

'a; 

" 

" 

143.200 

74,000 

12.32 

27.6 

"o  "{ 

• 

" 

u 

117,600 

64,000 

17.0 

46.0 

'c 

1/4  -in. 

1    t< 

" 

119,200 

65,000 

16.66 

42.1 

round 
rolled  bar.t 

;: 

M 

91,600 
91,200 

51,000 
51,000 

22.25 
21.62 

53.2 
53.4 

co 

" 

M 

85,200 

53,000 

21.82 

49.5 

I 

" 

" 

86,000 

48,000 

21.25 

47.4 

-3  f 

(  .798 

8 

115,464 

51,820 

36.25 

66.23 

1  1 

l*4-in.  sq. 

J    " 

" 

112,600 

60.000 

37.87 

62.82 

" 

bar,  rolled,  t 

" 

" 

102,010 

39,180 

41.37 

69.59 

Annealed. 

•si 

I   " 

" 

102,510 

40,200 

44.00 

68.34 

M 

1" 

r  .500 

2 

114,590 

56,020 

47.25 

68.4 

1-in.  round 

J  M 

*' 

115,610 

59,080 

45.25 

62.3 

bar,  rolled.  § 

s  " 

i 

" 

105,240 

45,170 

49.65 

72.8 

Annealed. 

&  I 

I  " 

" 

106,780 

45,170 

55.50 

63.6 

*  Forged  from  6-in.  ingot  to  %  in.  diam.,  with  conical  heads  for  holding. 

t  Showing  the  effect  of  varying  carbon. 

j  Rolled  clown  from  14-in.  ingot  to  lJ4-in.  square  billet,  and  turned  to  size. 

§  Rolled  down  from  14-in.  ingot  to  1-in.  round,  and  turned  to  size. 

Nickel  steel  has  shown  itself  to  be  possessed  of  some  exceedingly  valuable 
properties;  these  are,  resistance  to  cracking,  high  elastic  limit,  and  homo- 
geneity. Resistance  to  cracking,  a  property  to  which  the  name  of  non  flssi- 
bility  has  been  given,  is  shown  more  remarkably  as  the  percentage  of  nickel 
increases.  Bars  of  27$  nickel  illustrate  this  property.  A  1^4-in.  square  bar 
was  nicked  *4  U1-  deep  and  bent  double  on  itself  without  further  fracture 
than  the  splintering  off,  as  it  were,  of  the  nicked  portion.  Sudden  failure  or 
rupture  of  this  steel  would  be  impossible  ;  it  seems  to  possess  the  toughness 
of  rawhide  with  the  strength  of  steel.  With  this  percentage  of  nickel  the 
steel  is  practically  non  corrodible  and  non-magnetic.  The  resistance  to 
cracking  shown  by  the  lower  percentages  of  nickel  is  best  illustrated  in  the 
many  trials  of  nickel-steel  armor. 

The  elastic  limit  rises  in  a  very  marked  degree  with  the  addition  of  about 
3$  of  nickel,  the  other  physical  properties  of  the  steel  remaining  unchanged 
or  perhaps  slightly  increased. 

In  such  places  (shafts,  axles,  etc.)  where  failure  is  the  result  of  the  fatigue 
of  the  metal  this  higher  elastic  limit  of  nickel  steel  will  tend  to  prolong  in- 
definitely the  life  of  the  piece,  and  at  the  same  time,  through  its  superior 
toughness,  offer  greater  resistance  to  the  sudden  strains  of  shock. 

Howe  states  that  the  hardness  of  nickel  steel  depends  on  the  proportion 
of  nickel  and  carbon  jointly,  nickel  up  to  a  certain  percentage  increasing 
the  hardness,  beyond  this  lessening  it.  Thus  while  steel  with  2$  of  nickel 
and  0.90$  of  carbon  cannot  be  machined,  with  less  than  5$  nickel  it  can  be 
worked  cold  readily,  provided  the  proportion  of  carbon  be  low.  As  the 
proportion  of  nickel  rises  higher,  cold-working  becomes  less  easy.  It  forges 
easily  whether  it  contain  much  or  little  nickel. 

The  presence  of  manganese  in  nickel  steel  is  most  important,  as  it  appears 
that  without  the  aid  of  manganese  in  proper  proportions,  the  conditions  of 
treatment  would  not  be  successful. 

Tests  of  Nickel  Steel.— Two  heats  of  open-hearth  steel  were  made  by 
the  Cleveland  Rolling  Mill  Co.,  one  ordinary  steel  made  with  9000  Ibs.  each 
scrap  and  pig,  and  165  Ibs.  ferro-manganese,  the  other  the  same  with  the 
addition  of  3$,  or  540  Ibs.  of  nickel.  Tests  of  six  plates  rolled  from  each 
heat.,  0.24  to  0.3  in.  thick,  gave  results  as  follows  : 

Ordinary  steel,  T.  S.  52,500  to  56,500  ;  E.  L.  32,800  to  37,900  ;  elong.  26     to  32$. 
NtakAl  frtAAl.          "     63,370  to  67,100  ;     c>     47,100  to  48,200;       4i       aai/*  «•«  ww 


MANGANESE,  NICKEL,  AND  OTHER  "  ALLOY"  STEELS.  409 

The  nickel  steel  averages  31$  higher  in  elastic  limit,  20$  higher  in  ultimate 
tensile  strength,  with  but  slight  reduction  in  ductility.  (Eng.  &  M.  Jour., 
Feb.  25,  1893.) 

Aluminum  Steel.— R.  A.  Hadfield  (Trans.  A.  I.  M.  E.  1890)  says  : 
Aluminum  appears  to  be  of  service  as  an  addition  to  baths  of  molten  iron  or 
steel  unduly  saturated  with  oxides,  and  this  in  properly  regulated  steel 
manufacture  should  not  often  occur.  Speaking  generally,  its  role  appears 
to  be  similar  to  that  of  silicon,  though  acting  more  powerfully.  The  state- 
ment that  aluminum  lowers  the  melting-point  of  iron  seems  to  have  no 
foundation  in  fact.  If  any  increase  of  heat  or  fluidity  takes  place  by  the 
addition  of  small  amounts  of  aluminum,  it  may  be  due  to  evolution  of  heat, 
owing  to  oxidation  of  the  aluminum,  as  the  calorific  value  of  this  metal  is 
very  high— in  fact,  higher  than  silicon.  According  to  Berthollet,  the  con- 
version of  aluminum  to  A12O3  equals  7900  cal. ;  silicon  to  SiO2  is  stated  as  7800. 

The  action  of  aluminum  may  be  classed  along  with  that  of  silicon,  sulphur, 
phosphorus,  arsenic,  and  copper,  as  giving  no  increase  of  hardness  to  iron, 
in  contradistinction  to  carbon,  manganese,  chromium,  tungsten,  and  nickel. 
Therefore,  whilst  for  some  special  purposes  aluminum  may  be  employed  in 
the  manufacture  of  iron,  at  any  rate  with  our  present  knowledge  of  its 
properties,  this  use  cannot  be  large,  especially  when  taking  into  considera- 
tion the  fact  of  its  comparatively  high  price.  Its  special  advantage  seems  to 
be  that  it  combines  in  itself  the  advantages  of  both  silicon  and  manganese; 
but  so  long  as  alloys  containing  these  metals  are  so  cheap  and  aluminum 
dear,  its  extensive  use  seems  hardly  probable. 

J.  E.  Stead,  in  discussion  of  Mr.  Hadfield's  paper,  said:  Every  one  of  our 
trials  has  indicated  that  aluminum  can  kill  the  most  fiery  steel,  providing, 
of  course,  that  it  is  added  in  sufficient  quantity  to  combine  with  all  the  oxy- 
gen which  the  steel  contains.  The  metal  will  then  be  absolutely  dead,  and 
will  pour  like  dead-melted  silicon  steel.  If  the  aluminum  is  added  as  metal- 
lic aluminum,  and  not  as  a  compound,  and  if  the  addition  is  made  just  be- 
fore the  steel  is  cast,  1/10$  is  ample  to  obtain  perfect  solidity  in  the  steel. 

Clirome  Steel.  (F.  L.  Garrison,  Jour.  F.  /.,  Sept.  1891.)— Chromium 
Increases  the  hardness  of  iron,  perhaps  also  the  tensile  strength  and  elastic 
limit,  but  it  lessens  its  weldibility. 

Ferro  chrome,  according  to  Berthier,  is  made  by  strongly  heating  the 
mixed  oxides  of  iron  and  chromium  in  brasqued  crucibles,  adding  powdered 
charcoal  if  the  oxide  of  chromium  is  in  excess,  and  fluxes  to  scorify  the 
earthy  matter  and  prevent  oxidation.  Chromium  does  not  appear  to  give 
steel  the  power  of  becoming  harder  when  quenched  or  chilled.  Howe  states 
that  chrome  steels  forge  more  readily  than  tungsten  steels,  and  when  not 
containing  over  0.5  of  chromium  nearly  as  well  as  ordinary  carbon  steels  of 
like  percentage  of  carbon.  On  the  whole  the  status  of  chrome  steel  is  not 
satisfactory.  There  are  other  steel  alloys  coming  into  use,  which  are  so 
much  better,  that  it  would  seem  to  be  only  a  question  of  time  when  it  will 
drop  entirely  out  of  the  race.  Howe  states  that  many  experienced  chemists 
have  found  no  chromium,  or  but  the  merest  traces,  in  chrome  steel  sold  in 
the  markets. 

J.  W.  Langley  (Trans.  A.  S.  C.  E.  1892)  says:  Chromium,  like  manganese, 
is  a  true  hardener  of  iron  even  in  the  absence  of  carbon.  The  addition  of  1% 
or  2$  of  chromium  to  a  carbon  steel  will  make  a  metal  which  gets  exces- 
sively hard.  Hitherto  its  principal  employment  has  been  in  the  production 
of  chilled  shot  and  shell.  Powerful  molecular  stresses  result  during  cooling, 
and  the  shells  frequently  break  spontaneously  months  after  they  are  made. 

Tungsten  Steel— Musliet  Steel.  (J.  B.  Nau,  Iron  Age,  Feb.  11, 1892.) 
—By  incorporating  simultaneously  carbon  and  tungsten  in  iron,  it  is  possi- 
ble to  obtain  a  much  harder  steel  than  with  carbon  alone,  without  danger  of 
an  extraordinary  brittleness  in  the  cold  metal  or  an  increased  difficulty  in 
the  working  of  the  heated  metal. 

When  a  special  grade  of  hardness  is  required,  it  is  frequently  the  custom 
to  use  a  high  tungsten  steel,  known  in  England  as  special  steel.  A  specimen 
from  Sheffield,  used  for  chisels,  contained  9.3$  of  tungsten,  0.7$  of  silver, 
and  0.6$  of  carbon.  This  steel,  though  used  with  advantage  in  its  untem- 
pered  state  to  turn  chilled  rolls,  was  not  brittle;  nevertheless  it  was  hard 
enough  to  scratch  glass. 

A  sample  of  Mushet's  special  steel  contained  8.3$  of  tungsten  and  1 .73$  of 
manganese.  The  hardness  of  tungsten  steel  cannot  be  increased  by  the  or- 
dinary process  of  hardening. 

The  only  operation  that  it  can  bo  submitted  to  when  cold  is  grinding.  It 
has  to  be  given  its  final  shape  through  hammering  at  a  red  heat,  and  even 


410  STEEL. 

then,  when  the  percentage  of  tungsten  is  high,  it  has  to  be  treated  very 
carefully;  and  in  order  to  avoid  breaking  it,  not  only  is  it  necessary  to  reheat 
it  several  times  while  it  is  being  hammered,  but  when  the  tool  lias  acquired 
the  desired  shape  hammering  must  still  be  continued  gently  and  with  nu- 
merous bluws  until  it  becomes  nearly  cold.  Then  only  can  it  be  cooled  en- 
tirely. 

Tungsten  is  not  only  employed  to  produce  steel  of  an  extraordinary  hard- 
ness, but  more  especially  to  obtain  a  steel  which,  with  a  moderate  hardness, 
allies  great  toughness,  resistance,  and  ductility.  Steel  from  Assailly,  used 
for  this  purpose,  contained  carbon,  0.5i»$;  silicon,  0.04$;  tungsten,  0.3$; 
phosphorus,  0.04$;  sulphur,  0.005$. 

Mechanical  tests  made  by  Styffe  gave  the  following  results  : 

Breaking  load  per  square  inch  of  original  area,  pounds. .    172,424 

Reduction  of  area,  per  cent  0.54 

Average  elongation  after  fracture,  per  cent  13 

According  to  analyses  made  by  the  Duo  de  Luynes  of  ten  specimens  of  the 
celebrated  Oriental  damasked  steel,  eight  contained  tungsten,  two  of  them 
in  notable  quantities  (0.518$  to  1$),  while  in  all  of  the  samples  analyzed 
nickel  was  discovered  ranging  from  traces  to  nearly  4$. 

Stein  &  Schwartz  of  Philadelphia,  in  a  circular  say  :  It  is  stated  that 
tungsten  steel  is  suitable  for  the  manufacture  of  steel  magnets,  since  it  re- 
tains its  magnetism  longer  than  ordinary  steel.  Mr.  Kniesche  has  made 
tungsten  up  to  98$  fine  a  specialty.  Dr.  Heppe,  of  Leipsig,  has  written  a 
number  of  articles  in  German  publications  on  the  subject.  The  following 
instructions  are  given  concerning  the  use  of  tungsten:  In  order  to  produce 
cast  iron  possessing  great  hardness  an  addition  of  one  half  to  one  and  one 
half  of  tungsten  is  all  that  is  needed.  For  bar  iron  it  must  be  carried  up  to 
1$  to  2$,  but  should  not  exceed  2^$.  For  puddled  steel  the  range  is  larger, 
but  an  addition  beyond  3V£$  only  increases  the  hardness,  so  that  it  is  brought 
up  to  1*4$  only  for  special  tools,  coinage  dies,  drills,  etc.  For  tires  2J^$  to  5$ 
have  proved  best,  and  for  axles  ^  to  1^$.  Cast  steel  to  which  tungsten  has 
been  added  needs  a  higher  temperature  for  tempering  than  ordinary  steel, 
and  stiouid  be  hardened  only  between  yellow,  red,  and  white.  Chisels  made 
of  tungsten  steel  should  be  drawn  between  cherry-red  and  blue,  and  stand 
well  on  iron  and  steel.  Tempering  is  best  done  in  a  mixture  of  5  parts  of 
yellow  rosin,  3  parts  of  tar,  and  2  parts  of  tallow,  and  then  the  article  is 
once  more  heated  and  then  tempered  as  usual  in  water  of  about  15°  C. 

Wnitwortli.  Compressed  Steel.  (Proc.  Inst.  M.  E.,  May,  1887,  p. 
167.)— In  this  system  a  gradually  increasing  pressure  up  to  6  or  8  tons  per 
square  inch  is  applied  to  the  fluid  ingot,  and  within  half  an  hour  or  less 
after  the  application  of  the  pressure  the  column  of  fluid  steel  is  shortened 
\Y%  inch  per  foot  or  one  eighth  of  its  length;  the  pressure  is  then  kept  on  fo; 
several  hours,  the  result  being  that  the  metal  is  compressed  into  a  perfectly 
solid  and  homogeneous  material,  free  from  blow-holes. 

lu  large  gun-ring  ingots  during  cooling  the  carbon  is  driven  to  the  centre, 
the  centre  containing  0.8  carbon  and  the  outer  ring  0.3.  The  centre  is  bored 
out  until  a  test  shows  that  the  inside  of  the  ring  contains  the  same  percent- 
age of  carbon  as  the  outside. 

Compressed  steel  is  made  by  the  Bethlehem  Iron  Co.  and  the  Carnegie 
Steel  Co.  for  armor-plate  and  for  gun  and  other  heavy  forgings. 

CRUCIBLE  STEEL. 

Selection  of  Grades  by  the  Eye,  and  Effect  of  Heat  Treat- 
ment. (J.  W.  Langley,  Aruer.  Chemist,  November,  1876.)— In  1874,  Miller, 
Metcalf  &  Parkin,  of  Pittsburgh,  selected  eight  samples  of  steel  which  were 
believed  to  form  a  set  of  graded  specimens,  the  order  being  based  on  the 
quantity  of  carbon  which  they  were  supposed  to  contain.  They  were  num- 
bered from  one  to  eight.  On  analysis,  the  quantity  of  carbon  was  found  to 
follow  the  order  of  the  numbers,  while  the  other  elements  present— silicon, 
phosphorus,  and  sulphur — did  not  do  so.  The  method  of  selection  is 
described  as  follows  : 

The  steel  is  melted  in  black-lead  crucibles  capable  of  holding  about  eighty 
pounds;  when  thoroughly  fluid  it  is  poured  into  cast-iron  moulds,  and  when 
cold  the  top  of  the  ingot  is  broken  off,  exposing  a  freshly-fractured  surface. 
The  appearance  presented  is  that  of  confused  groups  of  crystals,  all  appear- 
ing to  have  started  from  the  outside  and  to  have  met  in  the  centre;  this 
general  form  is  common  to  all  ingots  of  whatever  composition,  but  to  the 
trained  eye,  and  only  to  one  long  and  critically  exercised,  a  minute  but  in- 


CRUCIBLE   STEEL. 


411 


deseribable  difference  is  perceived  between  varying  samples  of  steel,  and 
this  difference  is  now  known  to  be  owing  almost  wholly  to  variations  in  the 
amount  of  combined  carbon,  as  the  following  table  will  show.  Twelve  sam- 
ples selected  by  the  eye  alone,  and  analyses  of  drillings  taken  direct  from 
the  ingot  before  it  had  been  heated  or  hammered,  gave  results  as  below: 


Ingot 

Nos. 

Iron  by 
Diff. 

Carbon. 

Diff.  of 
Carbon. 

Silicon. 

Phos. 

Sulph. 

1 

99  614 

302 

.019 

.047 

.018 

2 

99.455 

.490 

.188 

.034 

.005 

.016 

3 

99.363 

.529 

.039 

.043 

.047 

.018 

4 

99.270 

.649 

.120 

.039 

.030 

.012 

5 

99.119 

.801 

.152 

.029 

.035 

.016 

6 

99.086 

.841 

.040 

.039 

.024 

.010 

7 

99.044 

.867 

.026 

.057 

.014 

.018 

8 

99.040 

.871 

.004 

.053 

.024 

.012 

9 

98.900 

.955 

.084 

.059 

.070 

.016 

10 

98  861 

1.005 

.050 

.088 

.034 

.012 

11 

98.752 

1.058 

.053 

.120 

.064 

.006 

12 

98.834 

1.079 

.021 

.039 

.044 

.004 

Here  the  carbon  is  seen  to  increase  in  quantity  in  the  order  of  the  num- 
bers, while  the  other  elements,  with  the  exception  of  total  iron,  bear  no  rela- 
tion to  the  numbers  on  the  samples.  The  mean  difference  of  carbon  is  .071. 

In  mild  steels  the  discrimination  is  less  perfect. 

The  appearance  of  the  fracture  by  which  the  above  twelve  selections 
were  made  can  only  be  seen  in  the  cold  ingot  before  any  operation,  except 
the  original  one  of  casting,  has  been  performed  upon  it.  As  soon  as  it  is 
hammered,  the  structure  changes  in  a  remarkable  manner,  so  that  all  trace 
of  the  primitive  condition  appears  to  be  lost. 

Another  method  of  rendering  visible  to  the  eye  the  molecular  and  chemi- 
cal changes  which  go  on  in  steel  is  by  the  process  of  hardening  or  temper- 
ing. When  the  metal  is  heated  and  plunged  into  water  it  acquires  an 
increase  of  hardness,  but  a  loss  of  ductility.  If  the  heat  to  which  the  steel 
has  been  raised  just  before  plunging  is  too  high,  the  metal  acquires  intense 
hardness,  but  it  is  so  brittle  as  to  be  worthless;  the  fracture  is  of  a  bright, 
granular,  or  sandy  character.  In  this  state  it  is  said  to  be  burned,  and  it 
cannot  again  be  restored  to  its  former  strength  and  ductility  by  annealing; 
it  is  ruined  for  all  practical  purposes,  but  in  just  this  state  it  again  shows 
differences  of  structure  corresponding  with  its  content  in  carbon.  The 
nature  of  these  changes  can  be  illustrated  by  plunging  a  bar  highly  heated 
at  one  end  and  cold  at  the  other  into  water,  and  then  breaking  it  off  in 
pieces  of  equal  length,  when  the  fractures  will  be  found  to  show  appear- 
ances characteristic  of  the  temperature  to  which  the  sample  was  raised. 

The  specific  gravity  of  steel  is  influenced  not  only  by  its  chemical  analy- 
sis, but  by  the  heat  to  which  it  is  subjected,  as  is  shown  by  the  following 
table  (densities  referred  to  60°  F.): 

Specific  gravities  of  twelve  samples  of  steel  from  the  ingot;  also  of  six 
hammered  bars,  each  bar  being  overheated  at  one  end  and  cold  at  the 
other,  in  this  state  plunged  into  ivater,  and  then  broken  into  pieces  of 
equal  length. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

Ingot  

7.855 

7.836 

7.841 

7.829 

7.838 

7.824 

7.819 

7.818 

7.813 

7.807 

7.803 

7.805 

Bar: 

*Burned  1... 

7.818 

".791 

7.789 

7.752 

7.744 

7.690 

2.   . 

7.814 

".811 

7.784 

7.755 

7.749 

7.741 

3... 

7  823 

~830 

7.780 

7.758 

7.755 

7.769 

4... 

7,826 

".849 

7.808 

7.773 

7.789 

7.798 

5... 

7831 

"806 

7.812 

7.790 

7.812 

7.811 

Cold  6... 



7.844 

".824 

7.829 

7.825 

7.826 

7.825 

*  Order  of  samples  from  bar. 


412 


STEEL. 


Effect  of  Heat  on  the  Grain  of  Steel.  (W.  Metcalf,— Jeans  on 
Steel,  p.  642.) — A  simple  experiment  will  show  the  alteration  produced  in  a 
high-carbon  steel  by  different  methods  of  hardening..  If  a  bar  of  such  steel 
be  nicked  at  about  9  or  10  places,  and  about  half  an  inch  apart,  a  suitable 
specimen  is  obtained  for  the  experiment.  Place  one  end  of  the  bar  in  a 
good  fire,  so  that  the  first  nicked  piece  is  heated  to  whiteness,  while  the  rest 
of  the  bar,  being  out  of  the  fire,  is  heated  up  less  and  less  as  we  approach 
the  other  end.  As  soon  as  the  first  piece  is  at  a  good  white  heat,  which  of 
course  burns  a  high  carbon  steel,  and  the  temperature  of  the  rest  of  the  bar 
gradually  passes  down  to  a  very  dull  red,  the  metal  should  be  taken  out  of 
the  fire  and  suddenly  plunged  in  cold  water,  in  which  it  should  be  left  till 
quite  cold.  It  should  then  be  taken  out  and  carefully  dried.  An  examina- 
tion with  a  file  will  show  that  the  first  piece  has  the  greatest  hardness, 
while  the  last  piece  is  the  softest,  the  intermediate  pieces  gradually  passing 
from  one  condition  to  the  other.  On  now  breaking  off  the  pieces  at  each 
nick  it  will  be  seen  that  very  considerable  and  characteristic  changes  have 
been  produced  in  the  appearance  of  the  metal.  The  first  burnt  piece  is  very 
open  or  crystalline  in  fracture;  the  succeeding  pieces  become  closer  and 
closer  in  the  grain  until  one  piece  is  found  to  possess  that  perfectly- 
even  grain  and  velvet-like  appearance  which  is  so  much  prized  by  experi- 
enced steel  users.  The  first  pieces  also,  which  have  been  too  much  hard- 
ened, will  probably  be  cracked;  those  at  the  other  end  will  not  be  hardened 
through.  Hence  if  it  be  desired  to  make  the  steel  hard  and  strong,  the 
temperature  used  must  be  high  enough  to  harden  the  metal  through,  but 
not  sufficient  to  open  the  grain. 

Changes  in  Ultimate  Strength  and  Elasticity  due  to 
Hammering,  Annealing,  and  Tempering.  (J.  W.  Langley, 
Trans.  A.  S.  C.  E.  1892.)— The  following  table  gives  the  result  of  tests  made 
on  some  round  steel  bars,  all  from  the  same  ingot,  which  were  tested  by 
tensile  stresses,  and  also  by  bending  till  fracture  took  place: 


05 

Carbon  . 

.2  ' 

«3  £-§ 

CG 

Is 

C  2 

O  -<-J 

£4* 

o> 

.0 

Treatment. 

^ 

.il 

0> 

1  §  5 

cS  o 

a 

ti 

1 

I& 

i 

ssi 

C  ^ 

o  ^ 

{§» 

^ 

Jtf 

s 

JH 

1 

Cold-hammered  bar 

153 

1.25 

.47 

.575 

92,420 

141,500 

2.00 

2.42 

2 

Bar  drawn  black.... 

75 

1.25 

.47 

.577 

114,700 

138,400 

6.00 

12.45 

3 

Bar  annealed  

175 

1.31 

.70 

.580 

68,110 

98,410 

10.00 

11.69 

4 

Bar    hardened   and 

drawn  black  

30 

1.09 

.36 

.578 

152,800 

248,700 

8.33 

17.9 

The  total  carbon  given  in  the  table  was  found  by  the  color  test,  which  is 
affected,  not  only  by  the  total  carbon,  but  by  the  condition  of  the  carbon. 
The  analysis  of  the  steel  was: 

Manganese 24 

Carbon    (true    total   carbon,    by 
combustion) 1.31 


Silicon   242 

Phosphorus 02 

Sulphur 009 


Heating  Tool  Steel.  (Miller,  Metcalf  &  Parkin,  1877.)— There  are 
three  distinct  stages  or  times  of  heating:  First,  for  forging;  second,  for 
hardening;  third,  for  tempering. 

The  first  requisite  for  a  good  heat  for  forging  is  a  clean  fire  and  plenty  of 
fuel,  so  that  jets  of  hot  air  will  not  strike  the  corners  of  the  piece;  next,  the 
fire  should  be  regular,  and  give  a  good  uniform  heat  to  the  whole  part  to  be 
forged.  It  should  be  keen  enough  to  heat  the  piece  as  rapidly  as  may  be, 
and  Callow  it  to  be  thoroughly  heated  through,  without  being  so  fierce  as  to 
overheat  the  corners. 

Steel  should  not  be  left  in  the  fire  any  longer  than  is  necessary  to  heat  it 
clear  through,  as  "  soaking  "  in  fire  is  very  injurious;  and,  on  the  other  hand, 
it  is  necessary  that  it  should  be  hot  through,  to  prevent  surface  cracks. 

By  observing  these  precautions  a  piece  of  steel  may  always  be  heated 
safely,  up  to  even  a  bright  yellow  heat,  when  there  is  much  forging  to  be 
done  on  it. 


CKUCIBLE   STEEL.  413 

The  best  and  most  economical  of  welding  fluxes  is  clean,  crude  borax, 
which  should  be  first  thoroughly  melted  and  then  ground  to  fine  powder. 

After  the  steel  is  properly  heated,  it  should  be  forged  to  shape  as  quickly 
as  possible;  and  just  as  the  red  heat  is  leaving  the  parts  intended  for  cutting 
edges,  these  parts  should  be  refined  by  rapid,  light  blows,  continued  until 
the  red  disappears. 

For  the  second  stage  of  heating,  for  hardening,  great  care  should  be  used: 
first,  to  protect  the  cutting  edges  and  working  parts  from  heating  more 
rapidly  than  the  body  of  the  piece;  next,  that  the  whole  part  to  be  hardened 
be  heated  uniformly  through,  without  any  part  becoming  visibly  hotter 
than  the  other.  A  uniform  heat,  as  low  as  will  give  the  required  hardness, 
is  the  best  for  hardening. 

For  every  variation  of  heat,  which  is  great  enough  to  be  seen,  thei'e  will 
result  a  variation  in  grain,  which  may  be  seen  by  breaking  the  piece:  and 
for  every  such  variation  in  temperature,  there  is  a  very  good  chance  for  a 
crack  to  be  seen.  Many  a  costly  tool  is  ruined  by  inattention  to  this  point. 

The  effect  of  too  high  heat  is  to  open  the  grain;  to  make  the  steel  coarse. 
The  effect  of  an  irregular  heat  is  to  cause  irregular  grain,  irregular  strains, 
and  cracks. 

As  soon  as  the  piece  is  properly  heated  for  hardening,  it  should  be 
promptly  and  thoroughly  quenched  in  plenty  of  the  cooling  medium,  water, 
brine,  or  oil,  as  the  case  may  be. 

An  abundance  of  the  cooling  bath,  to  do  the  work  quickly  and  uniformly 
all  over,  is  very  necessary  to  good  and  safe  work. 

To  harden  a  large  piece  safely  a  running  stream  should  be  used. 

Much  uneven  hardening  is  caused  by  the  use  of  too  small  baths. 

For  the  third  stage  of  heating,  to  temper,  the  first  important  requisite  is 
again  uniformity.  The  next  is  time;  the  more  slowly  a  piece  is  brought 
down  to  its  temper,  the  better  and  safer  is  the  operation. 

When  expensive  tools  are  to  be  made  it  is  a  wise  precaution  to  try  small 
pieces  of  the  steel  at  different  temperatures,  so  as  to  find  out  how  low  a  heat 
will  erive  the  necessary  hardness.  The  lowest  heat  is  the  best  for  any  steel. 

Heating  to  Forge.— The  trouble  in  the  forge  fire  is  usually  uneven 
heat,  and  not  too  high  heat.  Suppose  the  piece  to  be  forged  has  been  put 
into  a  very  hot  fire,  and  forced  as  quickly  as  possible  to  a  high  yellow  heat, 
so  that  it  is  almost  up  to  the  scintillating  point.  If  this  be  done,  in  a  few 
minutes  the  outside  will  be  quite  soft  and  in  a  nice  condition  for  forging, 
while  the  middle  parts  will  not  be  more  than  red-hot.  Now  let  the  piece  be 
placed  under  the  hammer  and  forged,  and  the  soft  outside  will  yield  so 
much  more  readily  than  the  hard  inside,  that  the  outer  particles  will  be  torn 
asunder,  while  the  inside  will  remain  sound. 

Suppose  the  case  to  be  reversed  and  the  inside  to  be  much  hotter  than  the 
outside;  that  is,  that  the  inside  shall  be  in  a  state  of  semi-fusion,  while  the 
outside  is  hard  and  firm.  Now  let  the  piece  be  forged,  and  the  outside  will 
be  all  sound  and  the  whole  piece  will  appear  perfectly  good  until  it  is 
cropped,  and  then  it  is  found  to  be  hollow  inside. 

In  either  case,  if  the  piece  had  been  heated  soft  all  through,  or  if  it  had  been 
only  red-hot  all  through,  ir,  would  have  forged  perfectly  sound. 

In  some  cases  a  high  heat  is  more  desirable  to  save  heavy  labor  but  in 
every  case  where  a  fine  steel  is  to  be  used  for  cutting  purposes  it  must  be 
borne  in  mind  that  very  heavy  forging  refines  the  bars  as  they  slowly  cool, 
and  if  the  smith  heats'  such  refined  bars  until  they  are  soft,  he  raises  the 
grain,  makes  them  coarse,  and  he  cannot  get  them  fine  again  unless  he  has 
a  very  heavy  steam-hammer  at  command  and  knows  how  to  use  it  well. 

Annealing.  (Miller,  Metcalf  &  Parkin.)— Annealing  or  softening  is 
accomplished  by  heating  steel  to  a  red  heat  and  then  cooling  it  very  slowly, 
to  prevent  it  from  getting  hard  again. 

The  higher  the  degree  of  heat,  the  more  will  steel  be  softened,  until  the 
limit  of  softness  is  reached,  when  the  steel  is  melted. 

It  does  not  follow  that  the  higher  a  piece  of  steel  is  heated  the  softer  it 
will  be  when  cooled,  no  matter  how  slowly  it  may  be  cooled;  this  is  proved 
by  the  fact  that  an  ingot  is  always  harder  than  a  rolled  or  hammered  bar 
made  from  it. 

Therefore  there  is  nothing  gained  by  heating  a  piece  of  steel  hotter  than 
a  good,  bright,  cherry-red:  on  the  contrary,  a  higher  heat  has  several  dis- 
advantages: First.  If  carried  too  far,  it  may  leave  the  steel  actually  harder 
than  a  good  red  heat  would  leave  it.  Second.  If  a  scale  is  raised  on  the 
steel,  this  scale  will  be  harsh,  granular  oxide  of  iron,  and  will  spoil  the  tools 
used  to  cut  it.  Third.  A  high  scaling  heat  continued  for  a  little  time 


414  STEEL. 

changes  the  structure  of  the  steel,  makes  it  brittle,  liable  to  crack  in  hard- 
ening, and  impossible  to  refine. 

To  anneal  any  piece  of  steel,  heat  it  red-hot;  heat  it  uniformly  and  heat  it 
through,  taking  care  not  to  let  the  ends  and  corners  get  too  hot. 

As  soon  as  it  is  hot,  take  it  out  of  the  fire,  the  sooner  the  better,  and  cool 
it  as  slowly  as  possible.  A  good  rule  for  heating  is  to  heat  it  at  so  low  a  red 
that  when  the  piece  is  cold  it  will  still  show  the  blue  gloss  of  the  oxide  that 
was  put  there  by  the  hammer  or  the  rolls. 

Steel  annealed  in  this  way  will  cut  very  soft;  it  will  harden  very  hard, 
without  cracking;  and  when  tempered  it  will  be  very  strong,  nicely  refined, 
and  will  hold  a  keen,  strong  edge. 

tempering. — Tempering  steel  is  the  act  of  giving  it,  after  it  has  been 
shaped,  the  hardness  necessary  for  the  work  it  has  to  do.  This  is  done  by 
first  hardening  the  piece,  generally  a  good  deal  harder  than  is  necessary, 
and  then  toughening  it  by  slow  heating  and  gradual  softening  until  it  is  just 
right  for  work. 

A  piece  of  steel  properly  tempered  should  always  be  finer  in  grain  than 
the  bar  from  which  it  is  made.  If  it  is  necessary,  in  order  to  make  the  piece 
as  hard  as  is  required,  to  heat  it.  so  hot  that  after  being  hardened  the  grain 
will  be  as  coarse  as  or  coarser  than  the  grain  in  the  original  bar,  then  the  steel 
itself  is  of  too  low  carbon  for  the  desired  work. 

If  a  great  degree  of  hardness  is  not  desired,  as  in  the  case  of  taps,  and 
most  tools  of  complicated  form,  and  it  is  found  that  at  a  moderate  heat  the 
tools  are  too  hard  and  are  liable  to  crack,  the  smith  should  first  use  a  lower 
heat  in  order  to  save  the  tools  already  made,  and  then  notify  the  steelmaker 
that  his  steel  is  too  high,  so  as  to  prevent  a  recurrence  of  the  trouble. 

For  descriptions  of  various  methods  of  tempering  steel,  see  "Tempering 
of  Metals,"  by  Joshua  Rose,  in  App.  Cyc.  Mech.,  vol.  ii.  p.  863;  also, 
"  Wrinkles  and  Recipes,"  from  the  Scientific  American.  In  both  of  these 
works  Mr.  Rose  gives  a  "color  scale,"  lithographed  in  colors,  by  which  the 
color  to  which  the  temper  is  to  he  drawn  for  different  tools  is  shown.  The 
following  is  a  list  of  the  tools  in  their  order  on  the  color  scale,  together  with 
the  approximate  color  and  the  temperature  at  which  the  color  appears  on 
brightened  steel  when  heated  in  the  air  : 

Scrapers  for  brass;  very  pale  yel-       Hand -plane  irons. 

low,  430°  F.  Twist-drills. 

Steel-engraving  tools.  Flat  drills  for  brass. 

Slight  turning  tools.  Wood-boring  cutters. 

Hammer  faces.  Drifts. 

Planer  tools  for  steel.  Coopers1  tools. 

Ivory-cutting  tools.  Edging  cutters;  light  purple,  530°  F. 

Planer  tools  for  iron.  Augers. 

Paper-cutters.  Dental  and  surgical  instruments. 

Wood-engraving  tools.  Cold  chisels  for  steel. 

Bone  cutting  tools.  Axes;  dark  purple,  550°  F. 
Milling-cutters;  straw  yellow,  46Q°  F.        Gimlets. 

Wire-drawing  dies.  Cold  chisels  for  cast  iron. 

Boring-cutters.  Saws  for  bone  and  ivory. 

Leather-cutting  dies.  Needles. 

Screw-cutting  dies.  Firmer-chisels. 

Inserted  saw-teeth.  Hack-saws. 

Taps.  Framing-chisels. 

Rock-drills.  Cold  chisels  for  wrought  iron. 

Chasers.  Moulding  and  planing  cutters  to  b.i 
Punches  and  dies.  filed. 

Penknives.  Circular  saws  for  metal. 

Reamers.  Screw-drivers. 

Haif-round  bits.  Springs. 

Planing  and  moulding  cutters.  Saws  for  wood. 
Stone-cutting   tools;  brown  yellow^  Dark  blue,  570°  F. 

500°  F.  Pale  blue,  610°. 

Gouges,  Blue  tinged  with  green,  630°* 


FORCE,  STATICAL  MOMEKT,  EQUILIBRIUM,  ETC.    415 
MECHANICS. 

FORCE,  STATICAL  MOMENT,  EQtIH,IHRIUM5  ETC. 

MECHANICS  is  the  science  that  treats  of  the  action  of  force  upon  bodies. 

A  Force  is  anything  that  tends  to  change  the  state  of  a  body  with  respect 
to  rest  or  motion.  If  a  body  is  at.rest,  anything  that  tends  to  put  it  in  mo- 
tion is  a  force;  if  a  body  is  in  motion,  anything  that  tends  to  change  either 
its  direction  or  its  rate  of  motion  is  a  force. 

A  force  should  always  mean  the  pull,  pressure,  rub,  attraction  (or  repul- 
sion) of  one  body  upon  another,  and  always  implies  the  existence  of  a  simul- 
taneous equal  and  opposite  force  exerted  by  that  other  body  on  the  first  body, 
i.e.,  the  reaction.  In  no  case  should  we  call  anything  a  force  unless  we  can 
conceive  of  it  as  capable  of  measurement  by  a  spring-balance,  and  are  able 
to  say  from  what  other  body  it  comes.  (I.  P.  Church.) 

Forces  may  be  divided  into  two  classes,  extraneous  and  molecular:  extra- 
neous forces  act  on  bodies  from  without;  molecular  forces  are  exerted  be- 
tween the  neighboring  particles  of  bodies. 

Extraneous  forces  are  of  two  kinds,  pressures  and  moving  forces:  pres- 
sures simply  tend  to  produce  motion;  moving  forces  actually  produce 
motion.  Thus,  if  gravity  act  on  a  fixed  body,  it  creates  pressure;  if  on  a  free 
body,  it  produces  motion. 

Molecular  forces  are  of  two  kinds,  attractive  and  repellent:  attractive 
forces  tend  to  bind  the  particles  of  a  body  together;  repellent  forces  tend 
to  thrust  them  asunder.  Both  kinds  of  molecular  forces  are  continually 
exerted  between  the  molecules  of  bodies,  and  on  the  predominance  of  one 
or  the  other  depends  the  physical  state  of  a  body,  as  solid,  liquid,  or  gaseous. 

The  Unit  of  Force  used  in  engineering,  by  English  writers,  is  the 
pound  avoirdupois.  (For  some  scientific  purposes,  as  in  electro-dynamics, 
forces  are  sometimes  expressed  in  "  absolute  units.11  The  absolute  unit  of 
force  is  that  force  which  acting  on  a  unit  of  mass  during  a  unit  of  time  pro- 
duces a  unit  of  velocit}^;  in  English  measures,  that  force  which  acting  on 
the  mass  whose  weight  is  one  pound  in  London  will  in  one  second  produce  a 
velocity  of  one  foot  per  second  =  1  -=-  32.187  of  the  weight  of  the  standard 
pound  avoirdupois  at  London.  In  the  French  C.  G.  S.  or  centimetre-gramme 
second  system  it  is  the  force  which  acting  on  the  mass  whose  weight  is  one 
gramme  at  Paris  will  produce  in  one  second  a  velocity  of  one  centimetre  per 
second.  This  unit  is  called  a  *"  dyne  "  =  1/981  gramme  at  Paris.) 

Inertia  is  that  property  of  a  body  by  virtue  of  which  it  tends  to  continue 
in  the  state  of  rest  or  motion  in  which  it  may  be  placed,  until  acted  on  by 
some  force. 

Newton9*  Laws  of  Motion,— 1st  Law.  If  a  body  be  at  rest,  it  will 
remain  at  rest;  or  if  in  motion,  it  will  move  uniformly  in  a  straight  line  till 
acted  on  by  some  force. 

2d  Law.  If  a  body  be  acted  on  by  several  forces,  it  will  obey  each  as 
ohough  the  others  did  not  exist,  and  this  whether  the  body  be  at  rest  or  in 
motion. 

3d  Law.  If  a  force  act  to  change  the  state  of  a  body  with  respect  to  rest 
or  motion,  the  body  will  offer  a  resistance  equal  and  directly  opposed  to  the 
force.  Or,  to  every  action  there  is  opposed  an  equal  and  opposite  reaction. 

Graphic  Representation  of  a  Force.-— Forces  may  be  repre- 
sented geometrically  by  straight  lines,  proportional  to  the  forces.  A  force 
is  given  when  we  know  its  intensity,  its  point  of  application,  and  the  direc- 
tion in  which  it  acts.  When  a  force  is  represented  by  a  line,  the  length  of  the 
line  represents  its  intensity;  one  extremity  represents  the  point  of  applica- 
tion; and  an  arrow-head  at  the  other  extremity  shows  the  direction  of  the 
force. 

Composition  of  Forces  is  the  operation  of  finding  a  single  force 
whose  effect  is  the  same  as  that  of  two  or  more  given  forces.  The  required 
force  is  called  the  resultant  of  the  given  forces. 

Resolution  of  Forces  is  the  operation  of  finding  two  or  more  forces 
whose  combined  effect  is  equivalent  to  that  of  a  given  force.  The  required 
forces  are  called  components  of  the  given  force. 

The  resultant  of  two  forces  applied  at  a  point,  and  acting  in  the  same  di- 
rection, is  equal  to  the  sum  of  the  forces.  If  two  forces  act  in  opposite 
directions,  their  resultant  is  equal  to  their  difference,  and  it  acts  in  the 
direction  of  the  greater. 


416 


MECHANICS. 


If  any  number  of  forces  be  applied  at  a  point,  some  in  one  direction  and 
others  in  a  contrary  direction,  their  resultant  is  equal  to  the  sum  of  those 
that  act  in  one  direction,  diminished  by  the  sum  of  those  that  act  in  the  op- 
posite direction;  or,  the  resultant  is  equal  to  the  algebraic  sum  of  the  com- 
ponents. 

Parallelogram  of  Forces.— If  two  forces  acting  on  a  point  be  rep- 
resented in  direction  and  intensity  by  adjacent  sides  of  a  parallelogram, 
their  resultant  will  be  represented  by  that  diagonal  of  the  parallelogram 
which  passes  through  the  point.  Thus  OR,  Fig. 
88,  is  the  resultant  of  O$and  OP. 

Polygon  of  Forces.— If  several  forces  are 
applied  at  a  point  and  act  in  a  single  plane,  their 
resultant  is  found  as  follows: 

Through  the  point  draw  a  line  representing  the 
first  force  ;  through  the  extremity  of  this  draw 
a  line  representing  the  second  force;  and  so  on, 
throughout  the  system;  finally,  draw  a  line  from 
the  starting-point  to  the  extremity  of  the  last  line 
drawn,  and  this  will  be  the  resultant  required. 

Suppose  the  body  A,  Fig.  89,  to  be  urged  in  the  directions  Al,  A2,  A3,  A4, 
and  A5  by  forces  which  are  to  each  other  as  the  lengths  of  those  lines. 
Suppose  these  forces  to  act  successively  and  the  body  to  first  move  from  A 
to  1 ;  the  second  force  A2  then  acts  and  finding  the  body  at  1  would  take  it 
to  2';  the  third  force  would  then  carry  it  to  3',  the  fourth  to  4',  and  the  fifth 
to  5'.  The  line  A5'  represents  in  magnitude  and  direction  the  resultant  of 
all  the  forces  considered.  If  there  had 
been  an  additional  force,  Ax,  in  the  group, 
the  body  would  be  returned  by  that  force 
to  its  original  position,  supposing  the 
forces  to  act  successively,  but  if  they  had 
acted  simultaneously  the  body  would  never  2 
have  moved  at  all;  the  tendencies  to  mo- 
tion balancing  each  other. 

It  follows,  therefore,  that  if  the  several 
forces  which  tend  to  move  a  body  can  be 
represented  in  magnitude  and  direction 
by  the  sides  of  a  closed  polygon  taken  in 
order,  the  body  will  remain  at  rest;  but  if 
the  forces  are  represented  by  the  sides  of 
an  open  polygon,  the  body  will  move  and  the  direction  will  be  represented 
by  the  straight  line  which  closes  the  polygon. 

Twisted  Polygon.— The  rule  of  the  polygon  of  forces  holds  true  even 
when  the  forces  are  not  in  one  plane.  In  this  case  the  lines  .41,  1-2',  2'-3', 
etc.,  form  a  twisted  polygon,  that  is,  one  whose  sides  are  not  in  one  plane. 

Parallelopipedon  of  Forces.— If  three  forces  acting  on  a  point  be 
represented  by  three  edges  of  a  parallelepiped  on  which  meet  in  a  common 
point,  their  resultant  will  be  represented  by  the  diagonal  of  the  parallel 
pipedon  that  passes  through  their  common  point. 

Thus  OR,  Fig.  90,  is  the  resultant  of  OQ,  OS,  and  OP.  OM  is  the  result- 
ant of  OF  and  OQ,  and  OR  is  the  resultant  of  OMand  OS. 

Moment  of  a  Force.— The  mo- 
ment of  a  force  (sometimes  called  stat- 
ical moment),  with  respect  to  a  point, 
is  the  product  of  the  force  by  the  per- 
pendicular distance  from  the  point  to 
the  direction  of  the  force.  The  fixed 
point  is  called  the  centre  of  mo- 
S 


FIG.  90, 


FIG.  91. 


FORCE,  STATICAL   MOMENT,   EQUILIBRIUM,  ETC.    417 

ments  ;  the  perpendicular  distance  is  the  lever-arm  of  the  force;  and  the 
moment  itself  measures  the  tendency  of  the  force  to  produce  rotation  about 
the  centre  of  moments. 

If  the  force  is  expressed  in  pounds  and  the  distance  in  feet,  the  moment 
is  expressed  in  foot-pounds.  It  is  necessary  to  observe  the  distinction  be- 
tween foot-pounds  of  statical  moment  and  foot-pounds  of  work  or  energy. 
(See  Work.) 

In  the  bent  lever,  Fig.  91  (from  Trautwine),  if  the  weights  n  and  m  repre- 
sent forces,  their  moments  about  the  point  /  are  respectively  n  X  af  and 
m  X  fc.  If  instead  of  the  weight  in  a  pulling  force  to  balance  the  weight 
n  is  applied  in  the  direction  bs,  or  by  or  bd,  s,  y,  and  d  being  the  amounts  of 
these  forces,  their  respective  moments  are  s  x  ft,  y  X  fb,  d  X  fh. 

If  the  forces  acting  on  the  lever  are  in  equilibrium  it  remains  at  rest,  and 
the  moments  on  each  side  of  /  are  equal,  that  is,  n  X  af  =  m  X  /c,  or  s  X  ft, 
or  y  X  fb,  or  d  X  hf. 

The  moment  of  the  resultant  of  any  number  of  forces  acting  together  in 
the  same  plane  is  equal  to  the  algebraic  sum  of  the  moments  of  the  forces 
taken  separately. 

Statical  Moment.  Stability.— The  statical  moment  of  a  body  is 
the  product  of  its  weight  by  the  distance  of  its  line  of  gravity  from  some 
assumed  line  of  rotation.  The  line  of  gravity  is  a  vertical  line  drawn  from 
its  centre  of  gravity  through  the  body.  The  stability  of  a  body  is  that  re- 
sistance which  its  weight  alone  enables  it  to  oppose  against  forces  tending 
to  overturn  it  or  to  slide  it  along  its  foundation. 

To  be  safe  against  turning  on  an  edge  the  moment  of  the  forces  tending  to 
overturn  it,  taken  with  reference  to  that  edge,  must  be  less  than  the  stati- 
cal moment.  When  a  body  rests  on  an  inclined  plane,  the  line  of  gravity 
being  vertical,  falls  toward  the  lower  edge  of  the  body,  and  the  condition  of 
its  not  being  overturned  by  its  own  weight  is  that  the  line  of  gravity  must 
fall  within  this  edge.  In  the  case  of  an  inclined  tower  resting  on  a  plane 
the  same  condition  holds — the  line  of  gravity  must  fall  within  the  base.  The 
condition  of  stability  against  sliding  along  a  horizontal  plane  is  that  the  hor- 
izontal component  of  the  force  exerted  tending  to  cause  it  to  slide  shall  be 
less  than  the  product  of  the  weight  of  the  body  into  the  coefficient  of  fric- 
tion between  the  base  of  the  body  and  its  supporting  plane.  This  coefficient 
of  friction  is  the  tangent  of  the  angle  of  repose,  or  the  maximum  angle  at 
which  the  supporting  plane  might  be  raised  from  the  horizontal  before  the 
body  would  begin  to  slide.  (See  Friction.) 

The  Stability  of  a  J>aiii  against  overturning  about  its  lower  edge 
is  calculated  by  comparing  its  statical  moment  referred  to  that  edge  with 
the  resultant  pressure  of  the  water  against  its  upper  side.  The  horizontal 
pressure  on  a  square  foot  at  the  bottom  of  the  dam  is  equal  to  the  weight  of 
a  column  of  water  of  one  square  foot  in  section,  and  of  a  height  equal  to  the 
distance  of  the  bottom  below  water-level ;  or,  if  H  is  the  height,  the  pressure 
at  the  bottom  per  square  foot  =  62.4  X  H Ibs.  At  the  water-level  the  pres- 
sure is  zero,  and  it  increases  uniformly  to  the  bottom,  so  that  the  sum  of  the 
pressures  on  a  vertical  strip  one  foot  in  breadth  may  be  represented  by  the 
area  of  a  triangle  whose  base  is  62.4  X  H  and  whose  altitude  is  H,  or  62.4J?2-*-2. 
The  centre  of  gravity  of  a  triangle  being  %  of  its  altitude,  the  resultant  of 
all  the  horizontal  pressures  may  be  taken  as  equivalent  to  the  sum  of  the 
pressures  acting  at  %H,  and  the  moment  of  the  sum  of  the  pressures  is 
therefore  62.4  X  H3  -f-  6. 

Parallel  Forces. — If  two  forces  are  parallel  and  act  in  the  same  direc- 
tion, their  resultant  is  parallel  to  both,  and  lies  between  them,  and  the  inten- 
sity of  the  resultant  is  equal  to  the  sum  of  the  intensities  of  the  two  forces. 
Thus  in  Fig.  91  the  resultant  of  the  forces  n  and  m  acts  vertically  down- 
ward at/,  and  is  equal  to  n  -j-  m. 

If  two  parallel  forces  act  at  the  extremities  of  a  straight  line  and  in  the 
same  direction,  the  resultant  divides  the  line  joining  the  points  of  application 
of  the  components,  inversely  as  the  components.  Thus  in  Fig.  91,  m  :  n  :: 
af :  fc ;  and  in  Fig.  92,  P :  Q : :  SN  :  SM.  N 

The  resultant  of  two  parallel  forces  V] 

acting  in  opposite  directions  is  parallel  /     ' 

to  both,  lies  without  both,  on  the  side  Spx 


and  in  the  direction  of  the  greater,  / 

and  its  ' 
ence   c 
forces. 


and  its  intensity  is  equal  to  the  differ-      Mi^L 
ence   of   the   intensities   of   the   two 


418  MECHANICS. 

Thus  the  resultant  of  the  two  forces  Q  and  P,  Fig.  93,  is  equal  to  Q  -  P- 

R.    Of  any  two  parallel  forces  and  their 

N  resultant  each  is  proportional  to  the  dis- 

Q-< -p  tance  between  the  other  two;  thus  in  both 

/  Figs.  92  and  93,  P  :  Q  :  R  :  :  SN :  SM :  MN. 

Mr} — vp          Couples.— If  P  and  Q  be  equal  and  act 

/  in  opposite  directions,  R  =  0;  that  is,  they 

/  have  no  resultant.    Two  such  forces  cou- 

_  <£ I >.R  stitute  what  is  called  a  couple. 

C  The  tendency  of  a  couple  is  to  produce 

FIG.  93.  rotation;   the  measure  of  this  tendency, 

called  the  moment  of  the  couple,  is  the 
product  of  one  of  the  forces  by  the  distance  between  the  two. 

Since  a  couple  has  no  single  resultant,  no  single  force  can  balance  a 
couple.  To  prevent  the  rotation  of  a  body  acted  on  by  a  couple  the  applica- 
tion of  two  other  forces  is  required,  forming  a  second  couple.  Thus  in  Fig. 
94,  P  and  Q  forming  a  couple,  may  be  balanced 
by  a  second  couple  formed  by  R  and  S.  The  -J.R 

point  of  application  of  either  R  or  S  may  be  a 
fixed  pivot  or  axis.  i  P 

Moment  of  the  couple  PQ  =  P(c  +  b  +  a)  = 
moment  of  RS  -  Rb.  Also,  P  -f  R  =  Q  -f  8. 

The  forces  R  and  8  need  not  be  parallel  to  P        c 

and  Q,  but  if  not,  then  their  components  parallel 
to  PQ  are  to  be  taken  instead  of  the  forces 
themselves. 

Equilibrium  of  Forces.— A  system  of 
forces  applied  at  points  of  a  solid  body  will  be 
in  equilibrium  when  they  have  no  tendency  to  7  S 

8 reduce  motion,  either  of  translation  or  of  rota-  FIG.  94. 

on. 

The  conditions  of  equilibrium  are  :  1.  The  algebraic  sum  of  the  compo- 
nents of  the  forces  in  the  direction  of  any  three  rectangular  axes  must  be 
separately  equal  to  0. 

y.  The  algebraic  sum  of  the  moments  of  the  forces,  with  respect  to  any 
three  rectangular  axes,  must  be  separately  equal  to  0. 

If  the  forces  lie  in  a  plane  :  1.  The  algebraic  sum  of  the  components  of  the 
forces,  in  the  direction  of  any  two  rectangular  axes,  must  be  separately 
equal  to  0. 

2.  The  algebraic  sum  of  the  moments  of  the  forces,  with  respect  to  any 
point  in  the  plane,  must  be  equal  to  0. 

If  a  body  is  restrained  by  a  fixed  axis,  as  in  case  of  a  pulley,  or  wheel  and 
axle,  the  forces  will  be  in  a  equilibrium  when  the  algebraic  sum  of  the  mo- 
ments of  the  forces  with  respect  to  the  axis  is  equal  to  0. 


CENTRE   OF    GRAVITY. 


iry  par 

vavif.v  i«  t.h*»  r«Ant.rp>  nf  matriitiiflA 

re  be 
the 

wnoie  ngure  irorri  any  given  piaue  is  me  metiij  ut  me  uistcinues  ui  me  centres 
of  magnitude  of  the  several  equal  parts  from  that  plane.) 

If  a  body  be  suspended  at  its  centre  of  gravity,  it  will  be  in  equilibrium  in 
all  positions.  If  it  be  suspended  at  a  point  out  of  its  centre  of  gravity,  it 
will  swing  into  a  position  such  that  its  centre  of  gravity  is  vertically  beneath 
its  point  of  suspension. 

T<>  find  the  centre  of  gravity  of  any  plane  figure  mechanically,  suspend 
the  figure  by  any  point  near  its  edge,  and  mark  on  it  the  direction  of  a 
plumb-line  hung  from  that  point ;  then  suspend  it  from  some  other  point, 
and  again  mark  the  direction  of  the  plumb-line  in  like  manner.  Then  the 
centre  of  gravity  of  the  surface  will  be  at  the  point  of  intersection  of  the 
two  marks  of  the  plumb-line. 

The  Centre  of  Gravity  of  Regular  Figures,  whether  plane  or 
solid,  is  the  same  as  their  geometrical  centre  ;  for  instance,  a  straight  line, 


MOMENT  OF   INERTIA.  419 

parallelogram,    regular   polygon,    circle,    circular   ring,    prism,  cylinder, 
sphere,  spheroid,  middle  frustums  of  spheroid,  etc. 

Of  a  triangle :  On  a  line  drawn  from  any  angle  to  the  middle  of  the  op- 
posite side,  at  a  distance  of  one  third  of  the  line  from  the  side;  or  at  the 
intersection  of  such  lines  drawn  from  any  two  angles. 

Of  a  trapezium  or  trapezoid :  Draw  a  diagonal,  dividing  it  into  two  tri- 
angles. Draw  a  line  joining  their  centres  of  gravity.  Draw  the  other 
diagonal,  making  two  other  triangles,  and  a  line  joining  their  centres.  The 
intersection  of  the  two  lines  is  the  centre  of  gravity  required. 

Of  a  sector  of  a  circle  :  On  the  radius  which  bisects  the  arc,  2cr  -s-  3/  from 
the  centre,  c  being  the  chord,  r  the  radius,  and  I  the  arc. 

Of  a  semicircle :  On  the  middle  radius,  .4244r  from  the  centre. 

Of  a  quadrant :  On  the  middle  radius,  .6002r  from  the  centre. 

Of  a  segment  of  a  circle  ;  c3  -*-  12a  from  the  centre,    c  =  chord,  a  =  area. 

Of  a  parabolic  surface  :  In  the  axis,  3/5  of  its  length  from  the  vertex. 

Of  a  semi-parabola  (surface) ;  3/5  length  of  the  axis  from  the  vertex,  and 
%  of  the  semi-base  from  the  axis. 

Of  a  cone  or  pyramid  ;  In  the  axis,  J4  °f  its  length  from  the  base. 

Of  a  paraboloid  :  In  the  axis,  %  of  its  length  from  the  vertex. 

Of  a  cylinder,  or  regular  prism  ;  In  the  middle  point  of  the  axis. 

Of  a  frustum  of  a  cone  or  pyramid  :  Let  a  —  length  of  a  line  drawn  from 
the  vertex  of  the  cone  when  complete  to  the  centre  of  gravity  of  the  base,  and 
a'  that  portion  of  it  between  the  vertex  and  the  top  of  the  frustum;  then 
distance  of  centre  of  gravity  of  the  frustum  from  centre  of  gravity  of  its 

_  a      3ct/3 

~~  4  ~~  4(a24-aa'  +  a/2)* 

For  two  bodies,  fixed  one  at  each  end  of  a  straight  bar,  the  common 
centre  of  gravity  is  in  the  bar,  at  that  point  which  divides  the  distance 
between  their  respective  centres  of  gravity  in  the  inverse  ratio  of  the 
weights.  In  this  solution  the  weight  of  the  bar  is  neglected.  But  it  may 
be  taken  as  a  third  body,  and  allowed  for  as  in  the  following  directions  : 

For  more  than  two  bodies  connected  in  one  system:  Find  the  common 
centre  of  gravity  of  two  of  them  ;  and  find  the  common  centre  of  these  two 
jointly  with  a  third  body,  and  so  on  to  the  last  body  of  the  group. 

Another  method,  by  the  principle  of  moments :  To  find  the  centre  of 
gravity  of  a  system  of  bodies,  or  a  body  consisting  of  several  parts,  whose 
several  centres  are  known.  If  the  bodies  are  in  a  plane,  refer  their  several 
centres  to  two  rectangular  co-ordinate  axes.  Multiply  each  weight  by  its 
distance  from  one  of  the  axes,  add  the  products,  and  divide  the  sum  by  the 
sum  of  the  weights:  the  result  is  the  distance  of  the  centre  of  gravity  from 
that  axis.  ,  Do  the  same  with  regard  to  the  other  axis.  If  the  bodies  are 
not  in  a  plane,  refer  them  to  three  planes  at  right  angles  to  each  other,  and 
determine  the  mean  distance  of  the  sum  of  the  weights  from  each  of  the 
three  planes. 

MOMENT  OF  INERTIA. 

The  moment  of  inertia  of  the  weight  of  a  body  with  respect  to  an  axis  is 
the  algebraic  sum  of  the  products  obtained  by  multiplying  the  weight  of 
each  elementary  particle  by  the  square  of  its  distance  from  the  axis.  If  the 
moment  of  inertia  with  respect  to  any  axis  =  /,  the  weight  of  any  element 
of  the  body  =  iv,  and  its  distance  from  the  axis  •=  ?•,  we  have  /  =  2(w;r2). 

The  moment  of  inertia  varies,  in  the  same  body,  according  to  the  position 
of  the  axis.  It  is  the  least  possible  when  the  axis  passes  through  the  centre 
of  gravity.  To  find  the  moment  of  inertia  of  a  body,  referred  to  a  given 
axis,  divide  the  body  into  small  parts  of  regular  figure.  Multiply  the  weight 
of  each  part  by  the  square  of  the  distance  of  its  centre  of  gravity  from  the 
axis.  The  sum  of  the  products  is  the  moment  of  inertia.  The  value  of  the 
moment  of  inertia  thus  obtained  will  be  more  nearly  exact,  the  smaller  and 
more  numerous  the  parts  into  which  the  body  is  divided. 

MOMENTS  OF  INERTIA  OF  REGULAR  SOLIDS. — Rod,  or  bar,  of  uniform  thick- 
ness, with  respect  to  an  axis  perpendicular  to  the  length  of  the  rod, 

1=  ^(f+rf2) (1) 

W  —  weight  of  rod,  21  =  length,  d  —  distance  of  centre  of  gravity  from  axis. 
Thin  circular  plate,  axis  in  its)    T       _,_  /ra    .     ,0\ 
own  plane,  $  1=  W  (-^ +d*)\ (2) 

r  =  radius  of  plate. 


420  MECHANICS. 

Circular  plate,axis  perpendicular  >   _       rTr/>'2   ,     J0\ 
to  the  plate,  lI~W\J+<*)  ........    (3^ 

Circular  ring,  axis  perpendicular  I  /r2-f-?'/2    ,    ™\  ,,,, 

to  its  own  plane,  w  \  -  3  —        a  /'      •    •    •    •    (4J 

r  and  r'  are  the  exterior  and  interior  radii  of  the  ring. 
Cylinder,  axis   perpendicular  to  )   ,       nrfr*   ,    I*    ,     -,n\ 

the  axis  of  the  cylinder,  ^VT^T^^V'      '    *    '    *    (5) 

r  —  radius  of  base,  21  —  length  of  the  cylinder. 

By  making  d  =  0  in  any  of  the  above  formulae  we  find  the  moment  of 
inertia  for  a  parallel  axis  through  the  centre  of  gravity. 

The  moment  of  inertia.  2tor2,  numerically  equals  the  weight  of  a  body 
which,  if  concentrated  at  the  distance  unity  from  the  axis  of  rotation,  would 
require  the  same  work  to  produce  a  given  increase  of  angular  velocity  that  the 
actual  body  requires.  It  bears  the  same  relation  to  angular  acceleration 
which  weight  does  to  linear  acceleration  (Rankine).  The  term  moment  of 
inertia  is  also  used  in  regard  to  areas,  as  the  cross-sections  of  beams  under 
strain.  In  this  case  I  =  2ar2,  in  which  a  is  any  elementary  area,  and  r  its 
distance  from  the  centre.  (See  Moment  of  Inertia,  under  Strength  of  Ma- 
terials, p.  247.) 

CENTRE  AND  RADIUS  OF  GYRATION. 

The  centre  of  gyration,  with  reference  to  an  axis,  is  a  point  at  which,  if 
the  entire  weight  of  a  body  be  concentrated,  its  moment  of  inertia  will  re- 
main unchanged;  or,  in  a  revolving  body,  the  point  in  which  the  whole 
weight  of  the  body  may  be  conceived  to  be  concentrated,  as  if  a  pound  of 
platinum  were  substituted  for  a  pound  of  revolving  feathers,  the  angular 
velocity  and  the  accumulated  work  remaining  the  same.  The  distance  of 
this  point  from  the  axis  is  the  radius  of  gyration.  If  W  —  the  weight  of  a 
body,  I  —  Swr2  =  its  moment  of  inertia,  and  k  =  its  radius  of  gyration, 


The  moment  of  inertia  —  the  weight  x  the  square  of  the  radius  of  gyration. 

To  find  the  radius  of  gyration  divide  the  body  into  a  considerable  number 
of  equal  small  parts  —  the  more  numerous  the  more  nearly  exact  is  the  re- 
sult,— then  take  the  mean  of  all  the  squares  of  the  distances  of  the  parts 
from  the  axis  of  revolution,  and  find  the  square  root  of  the  mean  square. 
Or,  if  the  moment  of  inertia  is  known,  divide  it  by  the  weight  and  extract 
the  square  root.  For  radius  of  gyration  of  an  area,  as  a  cross-section  of  a 
beam,  divide  the  moment  of  inertia  of  the  area  by  the  area  and  extract  the 
square  root. 

The  radius  of  gyration  is  the  least  possible  when  the  axis  passes  through 
the  centre  of  gravity.  This  minimum  radius  is  called  the  principal  radius 
of  gyration.  If  we  denote  it  by  k  and  any  other  radius  of  gyration  by  &', 
we  have  for  the  five  cases  given  under  the  head  of  moment  of  inertia  above 
the  following  values  : 

(l)ieRod,  axis  perpen.to  J  fc  = 


(2)  Circular  plate,  axis  )   r,  _  -.    *./  _  .  /»'a 
in  its  plane,  \  K  ~  y  "4 

(3)  Circular  plate,  axis  )  T  __ 
perpen.  to  plane,        } 

(4)  Circular  ring,  axis  )   fc  __ 
perpen.  to  plane,       j" 

^ra^8  peri  '-|/f+?;  *  YT+| 


CENTRES   OF   OSCILLATION   AND   OF   PEKCUSSIOK*    421 


Principal  Radii  of  Gyration  and  Squares  of  Radii  of 
Gyration. 

(For  radii  of  gyration  of  sections  of  columns,  see  page  249.) 


Surface  or  Solid. 

Rad.  of  Gyration. 

Square  of  R. 
of  Gyration. 

^Parallelogram  •  1  axis  at  its  base 

.5773/1 
.2886ft 

.5773Z 

.2886Z 

.577  y7>2  +  c2 

^/l2 

1/12/i2 

^2 
1/12/2 

(6«  4-  c2)  -f-  3 
4Z2  +  62 

height  h          J     "    mid-height  

Straight  rod  :           )  axis  at  end  ... 

length  I,  or  thm  V,.u  JrJ  length 
rectang.  plate      i                   lengtn.. 
Rectangular  prism: 
axes  2a,  26,  2c,  referred  to  axis  2a.  .  . 
Parallelepiped:  length  I,  base  6,  axis  | 

.289  VW  +  62 

.289  |//i2  4-  /i'2 
.408/1 

Hollow  square  lube: 
out.  side  h,  inn'r  h',  axis  mid-length  .  . 
very  thin,  side  =  /t,  "              ** 

Thin  rectangular  tube:  sides  6,  7i,  } 
axis  mid-length                         .         C 

12 

(/I2  +  7l'2)  -5-  12 
/I2  -5-6 

7i2    /i  +  3fc 
12'  /t  +  6 
J4r»  =  fca-s-16 

(/i2  +  'i/2)  -5-  16 
^2      ra 

12  +  4 
W* 

(R^  +  r^+2 
l*  A,  R*  +  r2 

12  +    rr 

i»          #2 

12+   2 

r2 
r2 

y^ 

2/5r2 
2/5?-2 

J|r« 

b2  +  c2 

•*V£? 

yQr 

Thin  circ.  plate:  rad.r,diam./<,ax.  diam. 
Flat  circ.  ring:  diams.  h,  h',  axis  diam. 
Solid    circular   cylinder:     length   I,  \ 
axis  diameter  at  mid-length  f 
Circular  plate:    solid  wheel  of  uni-  j 
form  thickness,  or  cylinder  of  any  >• 
length,  referred  to  axis  of  cyl  ) 
Hollow  circ.  cylinder,  or  flat  ringrl 
Z,   length;    R,  r,  outer  and  inner! 
radii.    Axis,  1,  longitudinal  axis;  [ 
2,  diam.  at  mid-length  J 

M  v^2+/t/a 

.289  VI*  +  3r* 
.7071r 

.7071  VR*  -H-2 

.289  V/2+3(^2-f  r2) 

Same:  very  thin,  axis  its  diameter  
"      radius  r;  axis,  longitud'l  axis.  . 
Circumf  .  of  circle,  axis  its  centre  
"         "       "         "      "   diam 

.289  4/i2  -f  6#« 
r 

.7071r 
.6325r 

.6325r 
.5773r 

.4472  Vb*  -f  c2 
/jR5  -  r5 

Sphere*  radius  r  axis  its  diam  

Spheroid  :    equatorial  radius  ?*,   re-  \ 
volving  polar  axis  a  f 

Paraboloid  :    r  =  rad.  of  base,  rev.  I 
on  axis            .                    .                    f 

Ellipsoid:  semi-axes  a,  6,  c;  revolv-  (_ 
in01  on  axis  *Za             .                          ( 

5 
2  #e  -  r5 

Spherical  shell:  radii  R,  r,  revolving  ( 
on  its  d  iam  j 

.632u|/  K~  __  7.3 

.8165r 
.5477r 

5  #3  -  r3 
%,* 

0.37-2 

Same*  very  thin  radius  r  

Solid  cone:  r  =  rad.  of  base,  rev.  on  1 
axis      f 

CENTRES  OF  OSCH.I.ATION  ANB  OF   PERCUSSION. 

Centre  of  Oscillation,— If  a  body  oscillate  about  a  fixed  horizontal 
axis,  not  passing  through  its  centre  of  gravity,  there  is  a  point  in  the  line 
drawn  from  the  centre  of  gravity  perpendicular  to  the  axis  whose  motion 
is  the  same  as  it  would  be  if  the  whole  mass  were  collected  at  that  point 
and  allowed  to  vibrate  as  a  pendulum  about  the  fixed  axis.  This  point  is 
called  the  centre  of  oscillation. 

Tlie  Radius  of  Oscillation,  or  distance  of  the  centre  of  oscillation 
from  the  point  of  suspension  =  the  square  of  the  radius  of  gyration  -f-  dis- 
tance of  the  centre  of  gravity  from  the  point  of  suspension  or  axis.  The 
centres  of  oscillation  and  suspension  are  convertible. 

If  a  straight  line,  or  uniform  thin  bar  or  cylinder,  be  suspended  at  one  end, 
oscillating  about  it  as  an  axis,  the  centre  of  oscillation  is  at  %  the  length  of 


422  MECHANICS. 

the  rod  from  the  axis.  If  the  point  of  suspension  is  at  ^  the  length  from 
the  end,  the  centre  of  oscillation  is  also  at  %  the  length  from  the  axis,  that 
is,  it  is  at  the  other  end.  In  both  cases  the  oscillation  will  be  performed  in 
the  same  time.  If  the  point  of  suspension  is  at  the  centre  of  gravity,  the 
length  of  the  equivalent  simple  pendulum  is  infinite,  and  therefore  the  time 
of  vibration  is  infinite. 

For  a  sphere  suspended  by  a  cord,  r=  radius,  h  =  distance  of  axis  of 
motion  from  the  centre  of  the  sphere,  h'  —  distance  of  centre  of  oscillation 

2  ra 

from  centre  of  the  sphere,  I  =  radius  of  oscillation  =  h  -f  h'  =  h  4-  -  —• 

5  h 

If  the  sphere  vibrate  about  an  axis  tangent  to  its  surface,  h  =  r,  and  I  =  r 

•f  2/5r.    If  h  =  lOr,  I  =  lOr  -f  ^- 

Lengths  of  the  radius  of  oscillation  of  a  few  regular  plane  figures  or  thin 
plates,  suspended  by  the  vertex  or  uppermost  point. 

1st.  When  the  vibrations  are  flatwise,  or  perpendicular  to  the  plane  of  the 
figure: 

In  an  isosceles  triangle  the  radius  of  oscillation  is  equal  to  %  of  the  height 
of  the  triangle. 

In  a  circle,  %  of  the  diameter. 

In  a  parabola,  5/7  of  the  height. 

2d.  When  the  vibrations  are  edgewise,  or  in  the  plane  of  the  figure: 

In  a  circle  the  radius  of  oscillation  is  %  of  the  diameter. 

In  a  rectangle  suspended  by  one  angle,  %  of  the  diagonal. 

In  a  parabola,  suspended  by  the  vertex,  5/7  of  the  height,  plus  J^  of  the 
parameter. 

In  a  parabola,  suspended  by  the  middle  of  the  base,  4/7  of  the  height  plus 
}/j3  the  parameter. 

Centre  of  Percussion.— The  centre  of  percussion  of  a  body  oscillat- 
ing about  a  fixed  axis  is  the  point  at  which,  if  a  blow  is  struck  by  the  body, 
the  percussive  action  is  the  same  as  if  the  whole  mass  of  the  body  were  con- 
centrated at  the  point.  This  point  is  identical  with  the  centre  of  oscillation. 

THE  PENOIIL.UM. 

A  body  of  any  form  suspended  from  a  fixed  axis  about  which  it  oscillates 
by  the  force  of  gravity  is  called  a  compound  pendulum.  The  ideal  mbdy 
concentrated  at  the  centre  of  oscillation,  suspended  from  the  centre  of  sus- 
pension by  a  string  without  weight,  is  called  a  simple  pendulum.  This  equi- 
valent simple  pendulum  has  the  same  weight  as  the  given  body,  and  also 
the  same  moment  of  inertia,  referred  to  an  axis  passing  through  the  point 
of  suspension,  and  it  oscillates  in  the  same  time. 

The  ordinary  pendulum  of  a  given  length  vibrates  in  equal  times  when  the 
angle  of  the  vibrations  does  not  exceed  4  or  5  degrees,  that  is,  -2°  or  2Vi>°  each 
side  of  the  vertical.  This  property  of  a  pendulum  is  called  its  isochronism. 

The  time  of  vibration  of  a  pendulum  varies  directly  as  the  square  root  of 
the  length,  and  inversely  as  the  square  root  of  the  acceleration  due  to  grav- 
ity at  the  given  latitude  and  elevation  above  the  earth's  surface. 

If  T  =  the  time  of  vibration,  I  =  length  of  the  simple  pendulum,  g  =  accel- 

/T  vT 

eration  =  32.16,  T=  IT  A/  -;  since  TT  is  constant,  2Toc  J— .    At  a  given  loca- 

r    9  Vg 

tion  g  is  constant  and  Tec  Vl.    If  I  be  constant,  then  for  any  location 

yoc  _!_.   if  The  constant,  gT*  =  w2/;    I  cc  g-   g  =  ^—.    From  this  equation 

VQ 

the  force  of  gravity  at  any  place  may  be  determined  if  the  length  of  the 
simple  pendulum,  vibrating  seconds,  at  that  place  is  known.  At  New  York 
this  length  is  39.1017  inches  =  3.2585  ft.,  whence  g  -  32.16  ft.  At  London  the 
length  is  39.1393  inches.  At  the  equator  39.0152  or  39.0168  inches,  according 
to  different  authorities. 
Time  of  vibration  of  a  pendulum  of  a  given  length  at  New  York 

=  t  : 

t  being  in  seconds  and  I  in  inches.  Length  of  a  pendulum  having  a  given 
time  of  vibration,  I  =  *«  X  39.1017  inches. 


VELOCITY,  ACCELERATION,  FALLING  BODIES.     423 

The  time  of  vibration  of  a  pendulum  may  be  varied  by  the  addition  of  a 
weight  at  a  point  above  the  centre  of  suspension,  which  counteracts  the 
lower  weight,  and  lengthens  the  period  of  vibration.  By  varying  the  height 
of  the  upper  weight  the  time  is  varied. 


or  cue  upper  weigiit  tne  nine  is  varieu. 

To  find  the  weight  of  the  upper  bob  of  a  compound  pendulum,  vi 
seconds,  when  the  weight  of  the  lower  bob,  and  the  distances  of  the  i 
from  the  point  of  suspension  are  given: 


and  the  distances  of  the  weights 


(89.1+P)-D" 

'V 


W  —  the  weight  of  the  lower  bob,  w  =  the  weight  of  the  upper  bob;  D  — 
the  distance  of  the  lower  bob  and  d  =  the  distance  of  the  upper  bob  from 
the  point  of  suspension,  in  inches. 

Thus,  by  means  of  a  second  bob,  short  pendulums  may  be  constructed  to 
vibrate  as  slowly  as  longer  pendulums. 

By  increasing  w  or  d  until  the  lower  weight  is  entirely  counterbalanced, 
the  time  of  vibration  may  be  made  infinite. 

Conical  Pendulum.—  A  weight  suspended  by  a  cord  and  revolving 
at  a  uniform  speed  in  the  circumference  of  a  circular  horizontal  plane 
whose  radius  is  ?-,  the  distance  of  the  plane  below  the  point  of  suspension  be- 
ing h,  is  held  in  equilibrium  by  three  forces  —  the  tension  in  the  cord,  the  cen- 
trifugal force,  which  tends  to  increase  the  radius  r,  and  the  force  of  gravity 
acting  downward.  If  v  =  the  velocity  in  feet  per  second,  the  centre  of 
gravity  of  the  weight,  as  it  describes  the  circumference,  g  =  32.16,  and  r 
and  h  are  taken  in  feet,  the  time  in  seconds  of  performing  one  revolution  is 


If  t  -  1  second,  h  =  .8146  foot  =  9.775  inches. 

The  principle  of  the  conical  pendulum  is  used  in  the  ordinary  fly-ball 
governor  for  steam-engines.  (See  Governors.) 

CENTRIFUGAL  FORCE. 

Aybody  revolving  in  a  curved  path  of  radius  =  R  in  feet  exerts  a  force, 
called  centrifugal  force,  F,  upon  the  arm  or  cord  which  restrains  it  from 
moving  in  a  straight  line,  or  "flying  off  at  a  tangent.'1  If  W  -  weight  of 
the  body  in  pounds,  N  —  number  of  revolutions  per  minute,  v  =  linear 
velocity  of  the  centre  of  gravity  of  the  body,  in  feet  per  second,  g  =  32.16, 
then 

_2nRN  Wv*         Wv*    _  W4ir*RN*  _  WRN* 

~60~;  0B~~""32.16B~       36000        =     2933     = 

If  n  =  number  of  revolutions  per  second,  F  =  1.2276PFBn2. 

(For  centrifugal  force  in  fly-wheels,  see  Fly-wheels.) 

VELOCITY,  ACCELERATION,  FALLING  BODIES. 

Velocity  is  the  rate  of  motion,  or  the  distance  passed  over  by  a  body  in 
a  given  time. 

If  s  =  space  in  feet  passed  over  in  t  seconds,  and  v  =  velocity  in  feet  per 
second,  if  the  velocity  is  uniform, 

~~  v 

If  the  velocity  varies  uniformly,  the  mean  velocity  VQ  =  V*  ^  *\  in  which 
v1  is  the  velocity  at  the  beginning  and  v?  the  velocity  at  the  end  of  the  time  t. 


Acceleration  is  the  change  in  velocity  which  takes  place  in  a  unit  of 
time.  Unit  of  acceleration  =  a  =  \  foot  per  second  in  one  second.  For 
uniformly  varying  velocity,  the  acceleration  is  a  constant  quantity,  and 

V»    —   Vi  Va    -    V, 

'    v^^v^-  at\    t-—  --  r.    .    .    .(2) 


424  MECHAKICS* 

If  the  body  start  from  rest,  v±  =  0;  then 

v0  =  ~;     Vt  =  2v0;    a  =  -£-  ;    va  =  at  ;    v2  -  ctJ  s  0;     t  -  ^. 

Combining  (1)  and  (2),  we  have 

t,  2  _  v  a  a£2  a£2 


If  Vl  =  0,  s  =  ^p-f  . 

Retarded  Motion.—  If  the  body  start  with  a  velocity  vt  and  come  to 

i'i 
rest,  i>2  —  0;  then  s  =  —t. 

In  any  case,  if  the  change  in  velocity  is  v, 

V 


For  a  body  starting  from  or  ending  at  rest,  we  have  the  equations 

v 
-t 


v  a£2 

v  —  at  ;    s  =  -t',    s  =  —  rj-  ;    -u2  =  2as. 


Falling  Bodies.-  In  the  case  of  falling  bodies  the  acceleration  due 
to  gravity  is  32.16  feet  per  second  in  one  second,  =  g.  Then  if  v  =  velocity 
acquired  at  the  end  of  t  seconds,  or  final  velocity,  and  h  —  height  or  space 
in  feet  passed  over  in  the  same  time, 

V  -  gt    =  32.16Z    =    ^2gh  =  8.02  |//I  =-£-'» 

I  Q  1£   f»Q^2  ^  ^ 

A  =  -=16.0St'=-^    =  —        =-; 

.__v  v  /Wi  _  \'h          _2^. 

~  g      =  32~T6    =  Y   ~g~  =  4. "61  ~~  ~v  ? 

w  =  space  fallen  through  in  the  Tth  second  =  g(T  —  }£). 
Value  of  g.— The  value  of  g  increases  with  the  latitude,  and  decreases 
with  the  elevation.    At  the  latitude  of  Philadelphia,  40°,  its  value  is  32. 1 6.    At 
the  sea-level,  Everett  gives  g  =  32.173  —  .082  cos  2  lat.  -.000003  height  in 
feet.     At  Parisjat.  48°  50'  N.,  g  =  OS0.87  cm.  =  32.181  ft. 

Values  of  V&7,  calculated  by  an  equation  given  by  C.  S.  Pierce,  are  given 
in  a  table  in  Smith's  Hydraulics,  from  which  we  take  the  following  : 
Latitude  .._._..        0°  10°  20°  30°  40°  50°  60° 

Value  of  tf2g..    8.0112      8.0118      8.0137      8.0165      8.0199      8.0235      8.0269 

The  value  of  V2p  decreases  about  .0004  for  every  1000  feet  increase  in  ele- 
vation above  the  sea-level. 

For  all  ordinary  calculations  for  the  United  States,  g  is  generally  taken  at 
32.16,  and  tf2g  at  8.02.  In  England  g  —  32.2,  \/2g  -  8.025.  Practical  limit- 
ing values  of  g  for  the  United  States,  according  to  Pierce,  are  : 

Latitude  49°  at  sea-level  g  =  32.186 

"        25°  10,000  feet  above  the  sea g  =  32.089 

From  the  above  formula  for  falling  bodies  we  obtain  the  following : 
Daring  the  first  second  the  body  starting  from  a  state  of  rest  (resistance 
of  the  air  neglected)  falls  g  -z-  2  =  16.08  feet  ;  the  acquired  velocity  is  g  = 

32.16  ft.  per  sec. ;  the  distance  fallen  in  two  seconds  is  h  =  -~   =  16  08  X  4  = 

64.32  ft. ;  and  the  acquired  velocity  is  v  =  gt  =  64.32  ft.  The  acceleration,  or 
increase  of  velocity  in  each  second,  is  constant,  and  is  32.16  ft.  per  sec.  Solv- 
ing the  equations  for  diflerent  times,  we  find  for 

Seconds,  t 1        2       3       4       5        G. 

Acceleration,  pr 32.16      X     1        1        1        1        1         1 

Velocity  acquired  at  end  of  time,  v. ...  32.16     x    1       '2       3       4       5        6 

Height  of  fall  in  each  second,  u — '—     X    1       3       5       7       9       U 

Total  height  of  fall,  h ^?     X    I       4       9      16     25      3G 


VELOCITY,  ACCELERATION,    FALLING    BODIES.      425 


Fig.  95  represents  graphically  the  velocity,  space,  etc.,  of  a  body  falling  for 


six  seconds.    The  vertical  line  at  the  left  is     h      u     v     t 
;the  time  in  seconds,  the  horizontal  lines 
represent  one  half  the  acquired  velocities 
at  the  end  of  each  second.     The  area  of 
the  small  triangle  at  the  top  represents 
the  height   fallen   through    in    the    first 
second  =  yzg  =  16.08  feet,  and  each  of  the 
other  triangles  is  an  equai  space.    The 
number  of  triangles  between  each  pair  of 
horizontal  lines  represents  the  height  of     9 
fall  in  each  second,  and  the  number  of 
triangles  between  any  horizontal  line  and 
the  top  is  the  total  height  fallen  during  16 
the  time.     The  figures  under  /t,  u,  and  v 
adjoining  the  cut  are  to  be  multiplied  by 
16.08  to  obtain  the  actual  velocities  and  25 
heights  for  the  given  times. 

Angular  and  Linear  Velocity 
of  a  Turning  Body.  —  Let  r  —  radius  of  a  36 
turning  body  in  feet,  n  =  number  of  revo- 
lutions per  minute,  v  =  linear  velocity  of 


1      2    1" 


434    2" 


5      6    3" 


7     8    4" 


9    10    5" 


11    12    6" 


\ 
\\ 


\\\ 


FIG.  95. 


a  point  on  the  circumference  in  feet  per  second,  and  60v  =  velocity  in  feet 
per  minute. 


Angular  velocity  is  a  term  used  to  denote  the  angle  through  which  any 
radius  of  a  body  turns  in  a  second,  or  the  rate  at  which  any  point  in  it 
having  a  radius  equal  to  unity  is  moving,  expressed  in  feet  per  second.  The 
unit  of  angular  velocity  is  the  angle  which  at  a  distance  =  radius  from  the 

180 
centre  is  subtended  by  an  arc  equal  to  the  radius.    This  unit  angle  =  — 

degrees  =  57.3°.    2?r  X  57.3°  =  360°,  or  the  circumference.    If  A  =  angular 
v     2irn 


velocity,  v  =  Ar,  A  =  -  = 


(50 


Height  Corresponding  to  a  Given  Acquired  Velocity. 


K 

• 

>> 

>> 

>> 

>^ 

& 

1 

% 

8 

I 

| 

A 

b£ 

1 

§ 

| 

§ 

8 

§ 

IB 

v 

'o> 

£ 

ID 

"S 

*o3 

'S 

*cB 

<D 

•5 

0) 

g 

W 

w 

n 

> 

W 

>. 

w 

> 

a 

'feet 

jp.sec. 

feet. 

feet 
p.  sec. 

feet. 

feet 
)  sec. 

feet. 

feet 
p.  sec. 

feet. 

feet 
p.  sec. 

feet. 

feet 
p.  sec. 

feet. 

.35 

.0010 

13 

2.62 

34 

17.9 

55 

47.0 

76 

89.8 

97 

146 

,50 

.0039 

14 

3.04 

35 

19.0 

56 

48.8 

77 

92.2 

98 

149 

.75 

.0087 

15 

3.49 

36 

20.1 

57 

50.5 

78 

94.6 

99 

152 

1.00 

.016 

16 

3.98 

37 

21.3 

58 

52.3 

79 

97.0 

100 

155 

1.25 

.024 

17 

4.49 

38 

22.4 

59 

54.1 

80 

99.5 

105 

171 

1.50 

.035 

18 

5.03 

39 

23.6 

60 

56.0 

81 

102.0 

110 

188 

1.75 

.048 

19 

5.61 

40 

24.9 

61 

57.9 

82 

104.5 

115 

205 

2 

.062 

20 

6.22 

41 

26.1 

62 

59.8 

83 

107.1 

120 

224 

2.5 

.097 

21 

6.85 

42 

27.4 

63 

61.7 

84 

109.7 

130 

263 

3 

.140 

22 

7.52 

43 

28.7 

64 

63.7 

85 

112.3 

140 

304 

3.5 

.190 

23 

8.21 

44 

30.1 

65 

65.7 

86 

115.0 

150 

350 

4 

.248 

24 

8.94 

45 

31.4 

66 

67.7 

87 

117.7 

175 

476 

4.5 

.314 

25 

9.71 

46 

32.9 

67 

69.8 

88 

120.4 

200 

622 

5 

.388 

26 

10.5 

47 

34.3 

68 

71.9 

89 

128.2 

300 

1399 

6 

.559 

27 

11.3 

48 

35.8 

69 

74.0 

90 

125.9 

400 

2488 

7 

.761 

28 

12.2 

49 

37.3 

70 

76.2 

91 

128.7 

500 

3887 

8 

.994 

29 

13.1 

50 

38.9 

71 

78.4 

92 

131.6 

600 

5597 

9 

1.26 

30 

14.0 

51 

40.4 

72 

80.6 

93 

134.5 

700 

7618 

10 

1.55 

81 

14.9 

52 

42.0 

73 

82.9 

94 

137.4 

800 

9952 

11 

1.88 

32 

15.9 

53 

43.7 

74 

85.1 

95 

140.3 

900 

12593 

12 

2.24 

33 

16.9 

54 

45.3 

75 

87.5 

96 

143.3 

1000 

155^7 

426 


MECHANICS. 


Falling  Bodies :  Velocity  Acquired  by  a  Body  Falling  a 
Given  Height. 


«j 

•  A 
bD 

"1 

Velocity. 

4_j 

1 

1 

Velocity. 

1 

s 

Velocity. 

-M 

& 
& 
® 
B 

Velocity. 

4 

55 
W 

Velocity. 

A 

bfl 

1 

Velocity. 

feet. 

feet 
p.  sec. 

feet. 

feet 
p.sec. 

feet. 

feet 
p.sec. 

fppt   feet 
teefc'  p.sec. 

feet. 

feet 
).sec. 

feet. 

feet 
p.sec. 

.005 

.57 

.39 

5.01 

1.20 

8.79 

5. 

17.9 

23. 

38.5 

72 

68.1 

.010 

.80 

.40 

5.07 

1.22 

8.87 

.2 

18.3 

.5 

38.9 

73 

68.5 

.015 

.98 

.41 

5.14 

1.24 

8.94 

.4 

18.7 

24. 

39.3 

74 

69.0 

.020 

1.13 

.42 

5.20 

1.26 

9.01 

.6 

19.0 

.5 

39.7 

75 

69.5 

.025 

1.27 

.43 

5.26 

1.28 

9.08 

.8 

19.3 

25 

40.1 

76 

69.9 

.030 

1.39 

.44 

5.32 

1.30 

9.15 

6. 

19.7 

26 

40.9 

77 

70.4 

.035 

1.50 

.45 

5.38 

1.32 

9.21 

.2 

20.0 

27 

41.7 

78 

70.9 

.040 

1.60 

.46 

5.44 

1.34 

9.29 

.4 

20.3 

28 

42.5 

79 

71.3 

.045 

1.70 

.47 

5.50 

1.36 

9.36 

.6 

20.6 

29 

43.2 

80 

71.8 

.050 

1.79 

.48 

5.56 

1.38 

9.43 

.8 

20.9 

30 

43.9 

81 

72.2 

.055 

1.88 

.49 

5.61 

1.40 

9.49 

7. 

21.2 

31 

44.7 

82 

72.6 

.060 

1.97 

.50 

5.67 

1.42 

9.57 

.2 

21.5 

32 

45.4 

83 

73.1 

.065 

2.04 

.51 

5.73 

1.44 

9.62 

.4 

21.8 

33 

46.1 

84 

73.5 

.070 

2.12 

.52 

5.78 

1.46 

9.70 

.6 

22.1 

34 

46.8 

85 

74.0 

.075 

2.20 

.53 

5.84 

1.48 

9.77 

.8 

22.4 

35 

47.4 

86 

74.4 

.080 

2.27 

.54 

5.90 

1.50 

9.82 

8. 

22.7 

36 

48.1 

87 

74.8 

.085 

2.34 

.55 

5.95 

1.52 

9.90 

.2 

23.0 

37 

48.8 

88 

75.3 

.090 

2.41 

.56 

6.00 

1.54 

9.96 

.4 

23.3 

38 

49.4 

89 

75.7 

.095 

2.47 

.57 

6.06 

1.56 

10.0 

.6 

23.5 

39 

50.1 

90 

76.1 

.100 

2.54 

.58 

6.11 

1.58 

10.1 

.8 

23.8 

40 

50.7 

91 

76.5 

.105 

2.60 

.59 

6.16 

1.60 

10.2 

9. 

24.1 

41 

51.4 

92 

76.9 

.110 

2.66 

.60 

6.21 

1.65 

10.3 

<2 

24.3 

42 

52.0 

93 

77.4 

.115 

2.72 

.62 

6.32 

1.70 

10.5 

'A 

24.6 

43 

52.6 

94 

77.8 

.120 

2.78 

.64 

6.42 

1.75 

10.6 

.6 

24.8 

44 

53.2 

95 

78.2 

.125 

2.84 

.66 

6.52 

1.80 

10.8 

.8 

25.1 

45 

53.8 

96 

78.6 

.130 

2.89 

.68 

6.61 

1.90 

11.1 

10. 

25.4 

46 

54.4 

97 

79.0 

.14 

3.00 

.70 

6.71 

2. 

11.4 

.5 

26.0 

47 

55.0 

98 

79.4 

.15 

3.11 

.72 

6.81 

2.1 

11.7 

11. 

26.6 

48 

55.6 

99 

79.8 

.16 

3.21 

.74 

6.90 

2.2 

11.9 

.5 

27.2 

49 

56.1 

100 

80.2 

.17 

3.31 

.76 

6.99 

2.3 

12.2 

12. 

27.8 

50 

56.7 

125 

89.7 

.18 

3.40 

.78 

7.09 

2.4 

12.4 

•  .5 

28.4 

51 

57.3 

150 

98.3 

.19 

3.50 

.30 

7.18 

2.5 

12.6 

13. 

28.9 

52 

57.8 

175 

106 

.20 

3.59 

.82 

7.26 

2.6 

12.9 

.5 

29  5 

53 

58.4 

200 

114 

.21 

3.68 

.84 

7.35 

2.7 

13.2 

14. 

30.0 

54 

59.0 

225 

120 

.22 

3.76 

.86 

7.44 

2.8 

13.4 

.5 

30.  5 

55 

59.5 

250 

126 

.23 

3.85 

.88 

7.53 

2.9 

13.7 

15. 

31.1 

56 

60.0 

275 

133 

.24 

3.93 

.90 

7.61 

3. 

13.9 

.5 

31.6 

57 

60.6 

300 

139 

.25 

4.01 

.92 

7.69 

3.1 

14.1 

16. 

32.1 

58 

61.1 

350 

150 

.26 

4.09 

.94 

7.78 

3-2 

14.3 

.5 

32.6 

59 

61.6 

400 

160 

.27 

4.17 

.96 

7.86 

3-3 

14.5 

17. 

88.1 

60 

62.1 

450 

170 

.28 

4,25 

.98 

7.94 

3.4 

14.8 

.5 

33.6 

61 

62.7 

500 

179 

.29 

4.32 

1.00 

8.02 

3.5 

15.0 

18. 

34.0 

<52 

63.2 

550 

188 

.30 

4.39 

1.02 

8.10 

3.6 

15.2 

.5 

34.5 

63 

63.7 

600 

197 

.31 

4.47 

1.04 

8.18 

3-7 

15.4 

19. 

35.0 

64 

64.2 

700 

212 

.32 

4.54 

1.06 

8.26 

3.8 

15.6 

.5 

35.4 

65 

64.7 

800 

227 

.33 

4.61 

1.08 

8.34 

3-9 

15.8 

20. 

35.9 

66 

65.2 

900 

241 

.34 

4.68 

1.10 

8.41 

4- 

16.0 

.5 

36.3 

67 

65.7 

1000 

254 

.35 

4.74 

1.12 

8.49 

.2 

16.4 

21. 

36.8 

68 

66.1 

2000 

359 

.36 

4.81 

1.14 

8.57 

.4 

16.8 

.5 

37.2 

69 

66.6 

3000 

439 

.37 

4.88 

1.16 

8.64 

,6 

17.2 

22. 

37.6 

70 

67.1 

4000 

507 

.38 

4.94 

1.18 

8.72 

.3 

17.6 

.5 

38.1 

71 

67.6 

5000 

567 

Parallelogram  of  Velocities.— The  principle  of  the  composition 
and  resolution  of  forces  may  also  be  applied  to  velocities  or  to  distances 
moved  in  given  intervals  of  time.  Referring  to  Fig.  88,  page  416,  if  a  body 
at  O  has  a  force  applied  to  it  which  acting  alone  would  give  it  a  velocity 
represented  by  OQ  per  second,  and  at  the  same  time  it  is  acted  on  l>7 


VELOCITY,   ACCELERATION^   FALLIKG   BODIES.      427 

another  force  which  acting  alone  would  give  it  a  velocity  OP  per  second, 
the  result  of  the  two  forces  acting  together  for  one  second  will  carry  it  to 
R,  OR  being  the  diagonal  of  the  parallelogram  of  OQ  and  OP,  and  the 
resultant  velocity.  If  the  two  component  velocities  are  uniform,  the  result- 
ant will  be  uniform  and  the  line  OR  will  be  a  straight  line;  but  if  either 
velocity  is  a  varying  one,  the  line  will  be  a  curve.  Fig.  96  shows  the 
resultant  velocities,  also  the  path  traversed 

by  a  body  acted  on  by  two  forces,  one  of      A         j        o        38 
which  would  carry  it  at  a  uniform  velocity  — J~ 

over  the  intervals  1,  2,  3,  B,  and  the  other  of 
which  would  carry  it  by  an  accelerated  mo- 
tion over  the  intervals  a,  6,  c,  D  in  the  same 
times.  At  the  end  of  the  respective  inter- 
vals the  body  will  be  found  at  C,,  <?,,,•  C3,  (7, 
and  the  mean  velocity  during  each  interval 
is  represented  by  the  distances  between 
these*  points.  Such  a  curved  path  is  trav- 
ersed by  a  shot,  the  impelling  force  from 
the  gun  giving  it  a  uniform  velocity  in  the 
direction  the  gun  is  aimed,  and  gravity  giv- 
ing it  an  accelerated  velocity  downward.  FIG.  96. 
The  path  of  a  projectile  is  a  parabola.  The 

distance  it  will  travel  is  greatest  when  its  initial  direction  is  at  an  angle  45° 
above  the  horizontal. 

Mass— Force  of  Acceleration.— The  mass  of  a  body,  or  the  quantity 
of  matter  it  contains,  is  a  constant  quantity,  while  the  weight  varies  according 
to  the  variation  in  the  force  of  gravity  at  different  places.  If  fir  =  the  acceler- 
ation due  to  gravity,  and  w  =  weight,  then  the  mass  m  =  — ,  iv  —  mg.  Weight 

here  means  the  resultant  of  the  force  of  gravity  on  the  particles  of  a  body, 
such  as  may  be  measured  by  a  spring-balance,  or  by  the  extension  or 
deflection  of  a  rod  of  metal  loaded  with  the  given  weight. 

Force  has  been  defined  as  that  which  causes,  or  tends  to  cause,  or  to 
destroy,  motion.  It  may  also  be  defined  (Kennedy's  Mechanics  of  Ma- 
chinery) as  the  cause  of  acceleration;  and  the  unit  of  force  as  the  force 
required  to  produce  unit  acceleration  in  a  unit  of  free  mass. 

Force  equals  the  product  of  the  mass  by  the  acceleration,  or  f  =  ma. 

Also,  if  v  =  the  velocity  acquired  in  the  time  t,  ft  =  mv;  /  =  mv  -f- 1;  the 
acceleration  being  uniform. 

The  force  required  to  produce  an  acceleration  of  g  (that  is,  32.16  ft.  per 

sec.)  in  one  second  is  /  =  mg  =  —  g  —  w,  or  the  weight  of  the  body.  Also, 

/  =  ma  =  mV<*  ~Vl>  in  which  va  is  the  velocity  at  the  end,  and  vt  the 
t 

velocity  at  the  beginning  of  the  time  t,  and/=  mg  = '— — -=  —a; 

~  =  -;  or,  the  force  required  to  give  any  acceleration  to  a  body  is  to  the 

weight  of  the  body  as  that  acceleration  is  to  the  acceleration  produced  by 
gravity.  (The  weight  w  is  the  weight  where  g  is  measured.) 

EXAMPLE.— Tension  in  a  cord  lifting  a  weight.  A  weight  of  100  Ibs.  is 
lifted  vertically  by  a  cord  a  distance  of  80  feet  in  4  seconds,  the  velocity 
uniformly  increasing  from  0  to  the  end  of  the  time.  What  tension  must  be 
maintained  in  the  cord?  Mean  velocity  =  v0  =  20  ft.  per  sec.;  final  velocity 

=vz  —  2vQ—  40;  accele-ation  a  =  -~  =  —  =  10.    Force  /  =  ma  —  —  —  g^gX 

10  =  31.1  Ibs.  This  is  the  force  required  to  produce  the  acceleration  only; 
to  it  must  be  added  the  force  required  to  lift  the  weight  without  accelera- 
tion, or  100  Ibs.,  making  a  total  of  131.1  Ibs. 

The  Resistance  to  Acceleration  is  the  same  as  the  force  required  to  pro- 
duce the  acceleration  =  —    -^-r— -. 
(.1        t 

Formulae  for  Accelerated  Motion.— For  cases  of  uniformly 
accelerated  motion  other  than  those  of  falling  bodies,  we  have  the  formulae 

already  given,  /  —  —  a,  = — -.— ->    If  the  body  starts  from  rest,  Vi  =  0,  va 


428  MECHANICS. 

=  v,  and/  = ,  fgt  —.  wv.     We  also  have  s  =  •--.    Transforming  and  sub- 
stituting for  g  its  value  32.16,  we  obtain 

wv*  wv  tvs  _   32.16/J  _S4.32/.s 

*  ~  ~    32.16*  ""  16708^ '    *  v  ~~w"a~~  ' 


'ivv  .iw.vu/i--  v\,  ^      /J^ 32 . 1  G/ 1 

•b^W^^w"    =  ~2~; 


wv_          1         /«» 

B  aa.ie/  ~  4.01  y    / 


t'- 

ajj.io/         4.ui   p      ./ 

For  any  change  in  velocity  /  =-  w(^-  a6472  '  /• 

(See  also  Work  of  Acceleration,  under  Work.) 

Motion  on  Inclined  Planes.— The  velocity  acquired  by  a  body 
descending  an  inclined  plane  by  the  force  of  gravity  (friction  neglected)  is 
equal  to  that  acquired  by  a  body  falling  freely  from  the  height  of  the  plane. 

The  times  of  descent  do*vn  different  inclined  planes  of  the  same  height 
irary  as  the  length  of  the  planes. 

The  rules  for  uniformly  accelerated  motion  apply  to  inclined  planes.  If  a 
Is  the  angle  of  the  plane  with  the  horizontal,  sin  a  =  the  ratio  of  the  height 

to  the  length  =  -- ,  and  the  constant  accelerating  force  is  g  sin  a.    The  final 

velocity  at  the  end  of  t  seconds  is  v  =  gt  sin  a.    The  distance  passed  over  in 
t  seconds  is  I  =  J4  Qt*  sin  a.    The  time  of  descent  is 


\    g  sin  a         4  01  yh 

MOMENTUM,  VIS-VIVA. 

Momentum,  or  quantity  of  motion  in  a  body,  is  the  product  of  the  mass 
by  the  velocity  at  any  instant  —  mv  =  —  v. 

Since  the  moving  force  =  product  of  mass  by  acceleration,  /  =  ma;  and  if 
the  velocity  acquired  in  t  seconds  =  v,  or  a  =-,/=—-;  ft  —  mv\  that  is, 

the  product  of  a  constant  force  into  the  time  in  which  it  acts  equals  numer 
ically  the  momentum. 

Since  ft  =  mv,  if  t  —  1  second  mv  —  /,  whence  momentum  might  be  de- 
fined as  numerically  equivalent  to  the  number  of  pounds  of  force  that  will 
stop  a  moving  body  in  1  second,  or  the  number  of  pounds  of  force  which 
acting  during  1  second  will  give  it  the  given  velocity. 

Vis-viva,  or  living  force,  is  a  term  used  by  early  writers  on  Mechanics 
to  denote  the  energy  stored  in  a  moving  body.  Some  defined  it  as  the  pro- 
duct of  the  mass  into  the  square  of  the  velocity,  rm;2,  —  —  v2  others  as  one 

half  of  this  quantity  or  ^wv2,  or  the  same  as  what  is  now  known  as  energy. 
The  term  is  now  practically  obsolete,  its  place  being  taken  by  the  word 
energy. 

WORK,    ENERGY,    POWER. 

Work:  is  the  overcoming  of  resistance  through  a  certain  distance.  It  is 
measured  by  the  product  of  the  resistance  into  the  space  through  which  it 
is  overcome.  It  is  also  measured  by  the  product  of  the  moving  force  into 
the  distance  through  which  the  force  acts  in  overcoming  the  resistance. 
Thus  in  lifting  a  body  from  the  earth  against  the  attraction  of  gravity,  the 
resistance  is  the  weight  of  the  body,  and  the  product  of  this  weight  into  the 
height  the  body  is  lifted  is  the  work  done. 

The  Unit  of  "Work,  in  British  measures,  is  the  foot-pound,  or  the 
amount  of  work  done  in  overcoming  a  pressure  or  weight  equal  to  one 
pound  through  one  foot  of  space. 


WORK,   ENERGY,   POWER.  429 

The  work  performed  by  a  piston  in  driving  a  fluid  before  it,  or  by  a  fluid 
In  driving  a  piston  before  it,  may  be  expressed  in  either  of  the  following 
ways: 

Resistance  X  distance  traversed 

=  intensity  of  pressure  X  area  X  distance  traversed  ; 
=•  intensity  of  pressure  X  volume  traversed. 

The  work  performed  in  lifting  a  body  is  the  product  of  the  weight  of  the 
body  into  the  height  through  which  its  centre  of  gravity  is  lifted. 

If  a  machine  lifts  the  centres  of  gravity  of  several  bodies  at  once  to  heights 
either  the  same  or  different,  the  whole  quantity  of  work  performed  in  so 
doing  is  the  sum  of  the  several  products  of  the  weights  and  heights  ;  but 
that  quantity  can  also  be  computed  by  multiplying  the  sum  of  all  the 
\veights  into  the  height  through  which  their  common  centre  of  gravity  is 
lifted.  (Rankine.) 

Power  is  the  rate  at  which  work  is  done,  and  is  expressed  by  the  quo- 
tient of  the  work  divided  by  the  time  in  which  it  is  done,  or  by  units  of  work 
per  second,  per  minute,  etc.,  as  foot-pounds  per  second.  The  most  common 
unit  of  power  is  the  horse-power,  established  by  James  Watt  as  the  power  of 
a  strong  London  draught- horse  to  do  work  during  a  short  interval,  and  used 
by  him  to  measure  the  power  of  his  steam-engines.  This  unit  is  33,000  foot- 
pounds per  minute  =  550  foot-pounds  per  second  =  1,980,000  foot-pounds  per 
hour. 

Expressions  for  Force,  Work,  Power,  etc. 

The  fundamental  conceptions  in  Dynamics  are  : 

Force,  Time,  Space,  represented  by  the  letters  F,  T,  S. 

Velocity  =  space  divided  by  time,  V  =  — ,  if  Fbe  uniform. 

Work  =  product  of  force  into  space  =  FS  =  W  =  FVT.   (Funiform.) 

Power  =  rate  of  work  =  work  divided  by  time  =  — ~  =  P  =  product  of 

force  into  velocity  =  FV. 

Power  exerted  for  a  certain  time  produces  work;  PT  =  FS  =  FVT  =  W. 

Effort  is  a  name  applied  to  a  force  which  acts  on  a  body  in  the  direction 
Of  its  motion. 

Resistance  is  that  which  is  opposed  to  a  moving  force.  It  is  equal  and 
opposite  force. 

Horse-power  Hours,  an  expression   for  work  measured   as  the 

Eroduct  of  a  power  into  the  time  during  which  it  acts  =  PT.  Sometimes  it 
i  the  summation  of  a  variable  power  for  a  given  time,  or  the  average  power 
multiplied  by  the  time. 

Energy,  or  stored  work,  is  the  capacity  for  performing  work.  It  is 
measured  by  the  same  unit  as  work,  that  is,  in  foot-pounds.  It  may  be 
either  potential,  as  in  the  case  of  a  body  of  water  stored  in  a  reservoir, 
capable  of  doing  work  by  means  of  a  water-wheel,  or  actual,  sometimes 
called  kinetic,  which  is  the  energy  of  a  moving  body.  Potential  energy  is 
measured  by  the  product  of  the  weight  of  the  stored  body  into  the  distance 
through  which  it  is  capable  of  acting,  or  by  the  product  of  the  pressure  it 
exerts  into  the  distance  through  which  that  pressure  is  capable  of  acting. 
Potential  energy  may  also  exist  as  stored  heat,  or  as  stored  chemical  energy, 
as  in  fuel,  gunpowder,  etc.,  or  as  electrical  energy,  the  measure  of  these 
energies  being  the  amount  of  work  that  they  are  capable  of  performing. 
Actual  energy  of  a  moving  body  is  the  work  which  it  is  capable  of  performing 
against  a  retarding  resistance  before  being  brought  to  rest,  and  is  equal  to 
the  work  which  must  be  done  upon  it  to  bring  it  from  a  state  of  rest  to  its 
actual  velocity. 

The  measure  of  actual  energy  is  the  product  of  the  weight  of  the  body 
into  the  height  from  which  it  must  fall  to  acquire  its  actual  velocity.  If  v  = 
the  velocity  in  feet  per  second,  according  to  the  principle  of  falling  bodies, 

<y2 

h,  the  height  due  to  the  velocity  =  — ,  and  if  w  —  the  weight,  the  energy  = 

—  =  ivh.  As  the  quantity  —  is  called  the  mass  =  m,  energy  is  equal  to  half 

the  mass  into  the  square  of  the  velocity  =  %mv*.  Since  energy  is  the  capacity 
for  performing  work,  the  units  of  work  and  energy  are  equivalent,  or  FS  » 

y^niv^  =  l-  =  wh.    Energy  exerted  =  work  done. 


430  MECHANICS. 

The  actual  energy  of  a  rotating  body  whose  angular  velocity  is  A  and 
moment  of  inertia  2?CT>3  =  I  is  -0—  ,  that  is,  the  product  of  the  moment  of 
inertia  into  the  height  due  to  the  velocity,  A,  of  a  point  whose  distance  from 
the  axis  of  rotation  is  unity  ;  or  it  is  equal  to  —  —  ,  in  which  w  is  the  weight  of 

the  body  and  v  is  the  velocity  of  the  centre  of  gyration. 

Work  of  Acceleration.  -The  work  done  in  giving  acceleration  to  a 
body  is  equal  to  the  product  of  the  force  producing  the  acceleration,  or  of 
the  resistance  to  acceleration,  into  the  distance  moved  in  a  given  time.  This 
force,  as  already  stated  equals  the  product  of  the  mass  into  the  acceleration, 

or/  =  ma  =  —  -^-J  —  -1.    If  the  distance  traversed  in  the  time  t  =  s,  then 

9        * 

.  w  v»  —  V, 

work  -fs  =  --  t~  —  ls. 

EXAMPLE.—  What  work  is  required  to  move  a  body  weighing  100  Ibs.  hori- 
zontally a  distance  of  80  ft.  in  4  seconds,  the  velocity  uniformly  increasing, 
friction  neglected  ? 

Mean  velocity  v0  =  20  ft.  per  second;  final  velocity  =  v%  =  2v0  =  40;  initial 

velocity  vl  =  0;  acceleration,  a  =  -2-r  —  -  —  —  =  10;  force  =  —a  =  —  —  -  x 

£  4  g  O^.ID 

10  =  31.1  Ibs.  ;  distance  80  ft.  ;  work  =  fs  =  31.1  X  80  =  2488  foot-pounds. 

The  energy  stored  in  the  body  moving  at  the  final  velocity  of  40  ft.  per 
second  is 


fcrov'  ?=*»:=  26  -  2488  foot-pounds, 
which  equals  the  work  of  acceleration, 

w  v<i       w  t'2  v9       1  w     , 

J  S    —    -    —S  —  -   —  •    —  ~t  —   —   •  -  Vn  •*. 

g   t       g   t  2       2  g  2 

If  a  body  of  the  weight  W  falls  from  a  height  H,  the  work  of  acceleration 
is  simply  WH,  or  the  same  as  the  work  required  to  raise  the  body  to  the 
same  height. 

Work  of  Accelerated  Rotation.—  Let  A  —  angular  velocity  of  a 
solid  body  rotating  about  an  axis,  that  is,  the  velocity  of  a  particle  whose 
radius  is  unity.  Then  the  velocity  of  a  particle  whose  radius  is  r  is  v  =  Ar. 
If  the  angular  velocity  is  accelerated  from  Aj  to^2,  the  increase  of  the 
velocity  of  the  particle  is  v2  -  vl  =  r(A-i  -  .4a),  and  the  work  of  accelerating 
it  is 

w_       v.^  —  v^  __  wr*  Ay*—  A  i9 
~9          ~2~      =  ~~g  2        ' 

in  which  iv  is  the  weight  of  the  particle. 

The  work  of  acceleration  of  the  whole  body  is 


The  term  2?or2  is  the  moment  of  inertia  of  the  body. 

"  Force  of  the  Blow  "  of  a  Steam  Hammer  or  Other  Fall- 
ing Weight.— The  question  is  often  asked:  *'  With  what  force  does  a 
tailing  hammer  strike?"  The  question  cannot  be  answered  directly,  and 
it  is  based  upon  a  misconception  or  ignorance  of  fundamental  mechanical 
laws.  The  energy,  or  capacity  of  doing  work,  of  a  body  raised  to  a  given 
height  and  let  fall  cannot  be  expressed  in  pounds,  simply,  but  only  in  foot- 
pounds, which  is  the  product  of  the  weight  into  the  height  through  which 
it  fails,  or  the  product  of  its  weight  -s-  64.32  into  the  square  of  the  velocity, 
in  feet  per  second,  which  it  acquires  after  falling  through  the  given  height. 
If  F.  =  weight  of  the  body,  M  its  mass,  g  the  acceleration  due  to  gravity, 
8  the  height  of  fall,  and  v  the  velocity  at  the  end  of  the  fall,  the  energy  in 
the  body  just  before  striking,  is  FS  =  &ftfv*  =  Wv9  -*-  2g  =  Wv9  -*-  64.32, 
which  is  the  general  equation  of  energy  of  a  moving  body.  Just  as  the 
energy  of  the  body  is  a  product  of  a  force  into  a  distance,  so  the  work  it 
does  when  it  strikes  is  not  the  manifestation  of  a  force,  which  can  be  ex- 
pressed simply  in  pounds,  but  it  is  the  overcoming  of  a  resistance  through 
a  certain  distance,  which  is  expressed  as  the  product  of  the  average  resist- 


WORK,   ENERGY,   POWER.  431 

ance  into  the  distance  through  which  it  is  exerted.  If  a  hammer  weighing 
100  Ibs.  falls  10  ft.,  its  energy  is  1000  foot-pounds.  Before  being  brought  to 
rest  it  must  do  1000  foot-pounds  of  work  against  one  or  more  resistances. 
These  are  of  various  kinds,  such  as  that  due  to  motion  imparted  to  the  body 
struck,  penetration  against  friction,  or  against  resistance  to  shearing  or 
other  deformation,  and  crushing  and  heating  of  both  the  falling  body  and  the 
body  struck.  The  distance  through  which  these  resisting  forces  act  is  gen- 
erally indeterminate,  and  therefore  the  average  of  the  resisting  forces, 
which  themselves  generally  vary  with  the  distance,  is  also  indeterminate. 
Impact  of  Bodies,—  If  two  inelastic  bodies  collide,  they  will  move  on 
together  as  one  mass,  with  a  common  velocity.  The  momentum  of  the  com- 
bined mass  is  equal  to  the  sum  of  the  momenta  of  the  two  bodies  before  im- 
pact. If  wx  and  m2  are  the  masses  of  the  two  bodies  and  Vi  and  v2  their  re- 
spective velocities  before  impact,  and  v  their  common  velocity  after  impact, 
(»»!  -f-  m^v  =  m^Vi  X  »iawa  , 


nii  -f  ma 

If  the  bodies  move  in  opposite  directions  v  =  —  —  —.  —  ?—  a,  or,  the  velocity 

m  j  -j-  ma 

of  two  inelastic  bodies  after  impact  is  equal  to  the  algebraic  sum  of  their 
momenta  before  impact,  divided  by  the  sum  of  their  masses. 

If  two  inelastic  bodies  of  equal  momenta  impinge  directly  upon  one  an- 
other from  opposite  directions  they  will  be  brought  to  rest. 

Impact  of  Inelastic  Bodies  Causes  a  JLoss  of  Energy,  and 
this  loss  is  equal  to  the  sum  of  the  energies  due  to  the  velocities  lost  and 
gained  by  the  bodies,  respectively. 


In  which  vl  —  v  is  the  velocity  lost  by  m1  and  v  —  v^  the  velocity  gained  by  wa. 
Example—  Let  wij  =  10,  w2  =  8,  vx  =  12,  v?  =  15. 

If  the  bodies  collide  they  will  come  to  rest,  for  v  =  10  X  ^  ~  f  X  *&  =  0. 

10  -f-  o 
The  energy  loss  is 


144  -f  y$  X  225  -  Y2  18  X  0  =  ^10(12  -  O)2  -f  ^8(15  -  O)2  =  1620  ft.  Ibs. 

What  becomes  of  the  energy  lost  ?  Ans.  It  is  used  doing  internal  work 
on  the  bodies  themselves,  changing  their  shape  and  heating  them. 

For  imperfectly  elastic  bodies,  let  e  —  the  elasticity,  that  is,  the  ratio 
which  the  force  of  restitution,  or  the  internal  force  tending  to  restore  the 
shape  of  a  body  after  it  has  been  compressed,  bears  to  the  force  of  compres- 
sion; and  let  wx  and  ma  be  the  masses,  v^  and  v%  their  velocities  before  im- 
pact, and  vx'i;a'  their  velocities  after  impact:  then 


v  >  - 


_ 
•}-  m2  mx  -f  w, 

v  i  -  miyi  +  m*v^    ,    m^Vi  -  v 
2 


If  the  bodies  are  perfectly  elastic,  their  relative  velocities  before  and  after 
impact  are  the  same.  That  is  :  v^'  —  v2'  =  v2  —  vlt 

In  the  impact  of  bodies,  the  sum  of  their  momenta  after  impact  is  the 
same  as  the  sum  of  their  momenta  before  impact. 

m^Vi  -f-  w2v2'  =  m-iVi  +  wi2v2. 

For  demonstration  of  these  and  other  laws  of  impact,  see  Smith's  Me- 
chanics; also,  Weisbach's  Mechanics. 

Energy  of  Recoil  of  Guns.—  (Eng^g,  Jan.  25,  1884,  p.  72.) 
Let  W  =  the  weight  of  the  gun  and  carriage; 
V  =  the  maximum  velocity  of  recoil; 
w  =  the  weight  of  the  projectile; 
v  —  the  muzzle  velocity  of  the  projectile. 

Then,  since  the  momentum  of  the  gun  and  carriage  is  equal  to  the  momen- 
tum of  the  projectile,  we  have  WV  =  wv,  or  V  =  ivv  -5-  W. 

*  The  statement  by  Prof.  W.  D.  Marks,  in  Nystrom's  Mechanics,  20th  edi- 
tion, p.  454,  that  this  formula  is  in  error  is  itself  erroneous. 


432  MECHANICS. 

Taking  the  ease  of  a  10-inch  gun  firing  a  400-lb.  projectile  with  a  muzzle 
velocity  of  1400  feet  per  second,  the  weight  of  the  gun  and  carnage  being  24 
tons  =  49,280  Ibs.,  we  find  the  velocity  of  recoil  = 

=  11  feet  per  second. 


Now  the  energy  of  a  body  in  motion  is  TFP2  -r-  2g. 

49  280  X  II2 
Therefore  the  energy  of  recoil  =  —\          -5—  =  92,593  foot-pounds. 

£   X  04.6 

400  V  14002 

The  energy  of  the  projectile  is  —         rs~  =  12,173,913  foot-pounds. 
«  X  o/&.i* 

Conservation  of  Energy.—  No  form  of  energy  can  ever  be  -pro.* 
dnced  except  by  the  expenditure  of  some  other  form,  nor  annihilated  ex- 
cept by  being  reproduced  in  another  form.  Consequently  the  sum  total  of 
energy  in  the  universe,  like  the  sum  total  of  matter,,  must  always  remain 
the  same.  (S.  Newcomb.)  Energy  can  never  be  destroyed  or  Lost;  it  can 
be  transformed,  can  be  transferred  from  one  body  to  another,  but  no 
matter  what  transformations  are  undergone,  when  the  total  effects  of  the 
exertion  of  a  given  amount  of  energy  are  summed  up  the  result  will  be 
exactly  equal  to  the  amount  originally  expended  from  the  source.  This  law 
is  called  the  Conservation  of  Energy.  (Cotterill  and  Slade.) 

A  heavy  body  sustained  at  an  elevated  position  has  potential  energy. 
When  it  falls,  just  before  it  reaches  the  earth's  surface  it  has  actual  or 
kinetic  energy,  due  to  its  velocity.  When  it  strikes  it  may  penetrate  the 
earth  a  certain  distance  or  may  be  crushed.  In  either  case  friction  results 
by  which  the  energy  is  converted  into  heat,  which  is  gradually  radiated 
into  the  earth  or  into  the  atmosphere,  or  both.  Mechanical  energy  and  heat 
are  mutually  convertible.  Electric  energy  is  also  convertible  into  heat  or 
mechanical  energy,  and  either  kind  of  energy  may  be  converted  into  the 
other. 

Sources  of  Energy,—  The  principal  sources  of  energy  on  the  earth's 
surface  are  the  muscular  energy  of  men  and  animals,  the  energy  of  the 
wind,  of  flowing  water,  and  of  fuel.  These  sources  derive  their  energy 
from  the  rays  of  the  sun.  Under  the  influence  of  the  sun's  rays  vegetation 
grows  and  wood  is  formed.  The  wood  may  be  used  as  fuel  under  a  steam 
boiler,  its  carbon  being  burned  to  carbonic  acid.  Three  tenths  of  its  heaf/ 
energy  escapes  in  the  chimney  and  by  radiation,  and  seven  tenths  appears 
as  potential  energy  in  the  steam.  In  the  steam-engine,  of  this  seven  tenth:* 
six  parts  are  dissipated  in  heating  the  condensing  water  and  are  wasted  ; 
the  remaining  one  tenth  of  the  original  heat  energy  of  the  wood  is  con- 
verted into  mechanical  work  in  the  steam-engine,  which  may  be  used  to  > 
drive  machinery.  This  work  is  finally,  by  friction  of  various  kinds,  or  pos- 
sibly after  transformation  into  electric  currents,  transformed  into  heat, 
which  is  radiated  into  the  atmosphere,  increasing  its  temperature.  Thus 
all  the  potential  heat  energy  of  the  wood  is,  after  various  transformations, 
converted  into  heat,  which,  mingling  with  the  store  of  heat  in  the  atmos- 
phere, apparently  is  lost.  But  the  carbonic  acid  generated  by  the  combus- 
tion of  the  wood  is,  again,  under  the  influence  of  the  sun's  rays,  absorbed 
by  vegetation,  and  more  wood  may  thus  be  formed  having  potential  energy 
equal  to  the  original. 

Perpetual  Motion,—  The  law  of  the  conservation  of  energy,  than 
which  no  law  of  mechanics  is  more  firmly  established,  is  an  absolute  barrier 
to  all  schemes  for  obtaining  by  mechanical  means  what  is  called  "  perpetual 
motion,"  or  a  machine  which  will  do  an  amount  of  work  greater  than  the 
equivalent  of  the  energy,  whether  of  heat,  of  chemical  combination,  of  elec- 
tricity, or  mechanical  energy,  that  is  put  into  it.  Such  a  result  would  be 
the  creation  of  an  additional  store  of  energy  in  the  universe,  which  is  not 
possible  by  any  human  agencv. 

The  Efficiency  of  a  Machine  is  a  fraction  expressing  the  ratio  of 
the  useful  work  to  the  whole  work  performed,  which  is  equal  to  the  energy 
expended.  The  limit  to  the  efficiency  of  a  machine  is  unity,  denoting  tho 
efficiency  of  a  perfect  machine  in  which  no  work  is  lost.  The  difference 
between  the  energy  expended  and  the  useful  work  done,  or  the  loss,  is 
usually  expended  either  in  overcoming  friction  or  in  doing  work  on  bodies 
surrounding  the  machine  from  which  no  useful  work  is  received.  Thus  in 
an  engine  propelling  a  vessel  part  of  the  energy  exerted  in  the  cylinder 


AKIMAL   POWER. 


433 


does  the  useful  work  of  giving?  motion  to  the  vessel,  and  the  remainder  is 
spent  in  overcoming  the  friction  of  the  machinery  and  in  making  currents 
and  eddies  in  the  surrounding  water. 

ANIJUAJL  POWER. 

Work  of  a  Man  against  Known  Resistances.    (Rankine.) 


Kind  of  Exertion. 

R, 
Ibs. 

F, 
ft.  per 

sec. 

T" 
3600 
(hours 
per 
day). 

RV, 
ft.-lbs. 
per  sec 

RVT, 

ft.  -Ibs. 
per  day.. 

1.  Raising  his   own  weight    up 
stair  or  ladder 

143 

40 
44 

143 
6 

132 

26.5 
1    12.5 
i    18.0 
(    20.0 
13.2 
15 

0.5 

0.75 
0.55 

0.13 
1.3 

0.075 

2.0 
5.0 
2.5 
14.4 
2.5 
? 

8 

6 
6 

6 
10 

10 

8 

Q 

2min. 
10 

8? 

72.5 

30 
24.2 

18.5 
7.8 

9.9 

53 
62.5 
45 

288 
33 
? 

2,088,000 

648,000 
522,720 

399,600 
280,800 

356,400 
1,526,400 

2.  Hauling  up  weights  with  rope, 
and  lowering  the  rope  un- 
loaded 

3.  Lifting  weights  by  hand  
4.  Carrying     weights    up  -stairs 
and  returning  unloaded  — 
5.  Shovelling    up     earth    to    a 
height  of  5  ft  3  in 

6.  Wheeling  earth  in  barrow  up 
slope  of  1  in  12,  J^  horiz. 
veloc.  0.9  ft.  per  sec.  and  re- 
turning unloaded 

7.  Pushing  or  pulling  horizon- 
tally (capstan  or  oar) 

8.  Turning  a  crank  or  winch  .  . 

9.  Working  pump  
10  Hammering 

1,296,000 

1,188,000 
480,000 

EXPLANATION.—!?,  resistance;  F,  effective  velocity  =  distance  through 
which  R  is  overcome  -*-  total  time  occupied,  including  the  time  of  moving 
unloaded,  if  any;  T",  time  of  working,  in  seconds  per  day;  T"  -5-  3600,  same 
time,  in  hours  per  day;  J?F,  effective  power,  in  foot-pounds  per  second' 
RVT,  daily  work. 

Performance  of  a  Man  in  Transporting  Loads 
Horizontally*    (Rankiue.) 


Kind  of  Exertion. 

Ibs. 

F, 

ft.-sec. 

T 
3600 
(hours 
pei- 
day). 

LF, 
Ibs. 
con- 
veyed 
1  foot. 

LVT, 
Ibs.  con- 
veyed 
1  foot. 

11.  Walking  unloaded,  transport- 
ing his  own  weight  
12.  Wheeling  load  L  in  2-whld. 

14C 

5 

10 

700 

25,200,000 

barrow,  return  unloaded.. 

224 

l*Ni 

10 

373 

13,428,000 

13.  Ditto  in  1-wh.  barrow,  ditto.. 

132 

ja^c 

10 

220 

7,920,000 

14.  Travelling  with  burden  

90 

2k£ 

7 

225 

5,670,000 

15.  Carrying  burden,  returning 

unloaded  

140 

1% 

6 

233 

5,032  800 

(  252 

0 

0 

16.  Carrying  burden,  for  30  sec- 

•{126 

11.7 

1474.2 

7 

1    o 

23.1 

0 



EXPLANATION.— L,  load;  F,  effective  velocity,  computed  as  before;  T', 
time  of  working,  in  seconds  per  day;  T"  -H-  3600,  same  time  in  hours  per  day; 
LV,  transport  per  second,  in  Ibs.  conveyed  one  foot;  L VT,  daily  transport. 


434 


MECHANICS. 


In  the  first  line  only  of  each  of  the  two  tables  above  is  the  weight  of  the 
man  taken  into  account  in  computing  the  work  done. 

Clark  says  that  the  average  net  daily  work  of  an  ordinary  laborer  at  a 

pump,  a  winch,  or  a  crane  may  be 
taken  at  3300  foot-pounds  per  minute, 
or  one -tenth  of  a  horse-power,  for  8 
hours  a  day;  but  for  shorter  periods 
from  four  to  five  times  this  rate  may 
be  exerted. 

Mr.  Glynn  says  that  a  man  may 
exert  a  force  of  25  Ibs.  at  the  handle 
of  a  crane  for  short  periods;  but  that 
for  continuous  work  a  force  of  15  Ibs. 
is  all  that  should  be  assumed,  moving 
through  220  feet  per  minute. 

Man-wheel.— Fig.  97  is  a  sketch 
of  a  very  efficient  man-power  hoist- 
ing-machine which  the  author  saw  in 
Berne,  Switzerland,  in  1889.  The  face 
of  the  wheel  was  wide  enough  for 
three  men  to  walk  abreast,  so  that 
FIG.  97.  nine  men  could  work  in  it  at  one  time. 

Work  of  a  Horse  against  a  Known  Resistance.    (Rankine.) 


Kind  of  Exertion. 

R. 

V. 

T. 

3600 

RV. 

RVT. 

1.  Cantering  and  trotting,  draw- 
ing a  light  railway  carriage 
(thoroughbred) 

(    min.  22^ 
•<  mean  30^| 
f   max  50 

[l4% 

4 

447^ 

6,444,000 

2.  Horse  drawing  cart  or  boat, 
walking  (draught-horse)  .... 
3.  Horse  drawing  a  gin  or  mill, 
walking 

120 
100 

3.6 
3  0 

8 

8 

432 

300 

12,441,600 
8  640  000 

4    Ditto  trotting         .  .   .  . 

66 

6  5 

4U 

429 

6  950  000 

EXPLANATION.—/?,  resistance,  in  Ibs.;  F,  velocity,  in  feet  per  second;  T 
-5-  3600,  hours  work  per  day;  RV,  work  per  second;  RVT,  work  per  day. 


assigned  by  Watt  to  the  ordinary  unit  of  the  rate  of  work  of  pr 

It  is  the  mean  of  several  results  of  experiments,  and  may  be  considered  the 

average  of  ordinary  performance  under  favorable  circumstances. 

Performance  of  a  Horse  in  Transporting  Loads 
Horizontally.    (Rankine.) 


Kind  of  Exertion. 

L. 

V. 

T. 

LV. 

LVT. 

5.  Walking   with   cart,    always 
loaded 

1500 

3  6 

10 

5400 

194  400  000 

6   Trotting  ditto      .  .          

750 

7  2 

\y% 

5400 

87,480,000 

7.  Walking  with  cart,  going  load- 
ed,    returning     empty;  F, 
mean  velocity  

1500 

2.0 

10 

3000 

108,000,000 

8.  Carrying  burden,  walking... 
9.  Ditto,  trotting  .  .  . 

270 
180 

3.6 

7.2 

10 

7 

972 

1296 

34,992,000 
32,659,200 

EXPLANATION.— I/,  load  in  Ibs.;  F,  velocity  in  feet  per  second;  IT -i- 3600, 
working  hours  per  day;  Z/F,  transport  per  second;  LVT,  transport  per  day. 

This  table  has  reference  to  conveyance  on  common  roads  only,  and  those 
evidently  in  bad  order  as  respects  the  resistance  to  traction  upon  them. 

Horse  Oin. — In  this  machine  a  horse  works  less  advantageously 
than  in  drawing  a  carriage  along  a  straight  track.  In  order  that  the  best 


ELEMEKTS   OF  MACHINES.  435 

possible  results  may  be  realized  with  a  horse-gin,  the  diameter  of  the  cir- 
cular track  in  which  the  horse  walks  should  not  be  less  than  about  forty 
feet. 

Oxen,  Mules,  Asses.— Authorities  differ  considerably  as  to  the  power 
of  tiiese  animals.  The  following  may  be  taken  as  an  approximative  com- 
parison between  them  and  draught-horses  (Rankine): 

Ox.— Load,  the  same  as  that  of  average  draught-horse;  best  velocity  and 
work,  two  thirds  of  horse. 

Mule.— Load,  one  half  of  that  of  average  draught-horse;  best  velocity, 
the  same  with  horse:  work  one  half. 

Ass.— Load,  one  quarter  that  of  average  draught-horse;  best  velocity  the 
same;  work  one  quarter. 

Reduction  of  Draught  of  Horses  by  Increase  of  Grade 
of  Roads.  (Engineering  Record,  Prize  Essays  on  Roads,  1892.) — Experi- 
ments on  English  roads  by  Gayffier  &  Parnell: 

Calling  load  that  can  be  drawn  on  a  level  100: 

On  a  rise  of 1  in  100.  1  in  50.  1  in  40.  1  in  30.  1  in  26.  1  in  20.  1  in  10. 

A  horse  can  draw  only       90.          81.         72.          64.         54.         40.  25. 

The  Resistance  of  Carriages  on  Roads  is  (according  to  Gen. 
Morin)  given  approximately  by  the  following  empirical  formula: 

R  =  ^  [a  +  b(u  -  3.28)]. 

In  this  formula  R  =  total  resistance;  r  =  radius  of  wheel  in  inches;  W  — 
gross  load ;  u  =  velocity  in  feet  per  second ;  while  a  and  b  are  constants, 
whose  values  are:  For  good  broken-stone  road,  a  =  .4  to  .55,  b  —  .024  to  .026; 
for  paved  roads,  a  —  .27,  b  —  .0684. 

Rankine  states  that  on  gravel  the  resistance  is  about  double,  and  on 
sand  five  times,  the  resistance  on  good  broken-stone  roads. 

ELEMENTS  OF  MACHINES. 

The  object  of  a  machine  is  usually  to  transform  the  work  or  mechanical 
energy  exerted  at  the  point  where  the  machine  receives  its  motion  into 
work  at  the  point  where  the  final  resistance 

is  overcome.    The  specific  end  may  be  to       A C  B 

change  the  character  or  direction  of  mo- 
tion, as  from  circular  to  rectilinear,  or  vice 
versa,  to  change  the  velocity,  or  to  overcome 
a  great  resistance  by  the  application  of  a 
moderate  force.  In  all  cases  the  total  energy 
exerted  equals  the  total  work  done,  the  latter 
including  the  overcoming  of  all  the  £ rictional  FlQ.  98. 
resistances  of  the  machine  as  well  as  the  use- 
ful work  performed.  No  increase  of  power 
can  be  obtained  from  any  machine,  since  this 
is  impossible  according  to  the  law  of  conser- 
vation of  energy.  In  a  f  rictionless  machine  the  I B 

product  of  the  force  exerted  at  the  driving- 
point  into  the  velocity  of  the  driving-point, 
or  the  distance  it  moves  in  a  given  interval 
of  time,  equals  the  product  of  the  resistance 
into  the  distance  through  which  the  resist- 
ance is  overcome  in  the  same  time.  FlQ.  99. 

The  most  simple  machines,  or  elementary 
machines,  are  reducible  to  three  classes,  viz., 
the  Lever,  the  Cord,  and  the  Inclined  Plane. 

The  first  class  includes  every  machine  con- 
sisting of  a  solid  body  capable  of  revolving  o 
on  an  axis,  as  the  Wheel  and  Axle. 

The  second  class  includes  every  machine  in 
which  force  is  transmitted  by  means  of  flexi- 
ble threads,  ropes,  etc.,  as  the  Pulley.  v  „ 

The  third  class  includes  every  machine  in  JTIG  JQO 

which  a  hard  surface  inclined  to  the  direc- 
tion of  motion  is  introduced,  as  the  Wedge  and  the  Screw. 

A  Lever  is  an  inflexible  rod  capable  of  motion  about  a  fixed  poict, 
called  a  fulcrum.  The  rod  may  be  straight  or  bent  at  any  angle,  or  curved. 

It  is  generally  regarded,  at  first,  as  without  weight,  but  its  weight  uiay  be 


D 

Ow 


ts 

Ow 


436 


MECHANICS. 


considered  as  another  force  applied  in  a  vertical  direction  at  its  centre  of 
gravity. 

The  arms  of  a  lever  are  the  portions  of  it  intercepted  bet  ween  the  force, 
P,  and  fulcrum,  (7,  and  between  the  weight,  W,  and  fulcrum. 

Levers  are  divided  into  three  kinds  or  orders,  according  to  the  relative 
positions  of  the  applied  force,  weight,  and  fulcrum. 

In  a  lever  of  the  first  order,  the  fulcrum  lies  between  the  points  at  which 
the  force  and  weight  act.  (Fig.  98.) 

In  a  lever  of  the  second  order,  the  weight  acts  at  a  point  between  the 
fulcrum  and  the  point  of  action  of  the  force.  (Fig.  99.) 

In  a  lever  of  the  third  order,  the  point  of  action  of  the  force  is  between 
that  of  the  weight  and  the  fulcrum.  (Fig.  100.) 

In  all  cases  of  levers  the  relation  between  the  force  exerted  or  the  pull, 
P,  and  the  weight  lifted,  or  resistance  overcome,  W,  is  expressed  by  the 
equation  P  X  AC  =  W  X  BC,  in  which  AC  is  the  lever-arm  of  P,  and  BC 
is  the  lever-arm  of  W,  or  moment  of  the  force  =  the  moment  of  the  resist- 
ance. (See  Moment.) 

In  cases  in  which  the  direction  of  the  force  (or  of  the  resistance)  is  not  at 
right  angles  to  the  arm  of  the  lever  on  which  it  acts,  the  "  lever-arm"  is  the 
length  of  a  perpendicular  from  the  fulcrum  to  the  line  of  direction  of  the 
force  (or  of  the  resistance).  W :  P : :  AC  :  BC,  or,  the  ratio  of  the  resistance  to 
the  applied  force  is  the  inverse  ratio  of  their  lever-arms.  Also,  if  Vw  is  the 
velocity  of  W,  and  Vp  is  the  velocity  of  P,  W :  P :  :  VP  :  Vw,  and  Px  Vp 
=  WX  Vw. 

If  Sp  is  the  distance  through  which  the  applied  force  acts,  and  Sw  is  the 
distance  the  weight  is  lifted  or  through  which  the  resistance  is  overcome, 
W :  P :  :  Sp  :  Sw,  W  X  Sw  =  PX  SP,  or  the  weight  into  the  distance  it  is  lifted 
equals  the  force  into  the  distance  through  which  it  is  exerted. 

These  equations  are  general  for  all  classes  of  machines  as  well  as  for 
levers,  it  being  understood  that  friction,  W'hich  in  actual  machines  increases 
the  resistance,  is  not  at  present  considered. 

The  Bent  Lever.— In  the  bent  lever  (see  Fig.  91,  page  416)  the  lever- 
arm  of  the  weight  w  is  cf  instead  of  bf.  The  lever  is  in  equilibrium  when 
n  x  nf  =  m  X  b/,  but  it  is  to  be  observed  that  the  action  of  a  bent  lever  may 
be  very  different  from  that  of  a  straight  lever.  In  the  latter,  so  long  as  the 
force  and  the  resistance  act  in  lines  parallel  to  each  other,  the  ratio  of  the 
lever-arms  remains  constant,  although  the  lever  itself  changes  its  inclina- 
tion with  the  horizontal.  In  the  bent  lever,  however,  this  ratio  changes: 
thus,  in  the  cut,  if  the  arm  bf  is  depressed  to  a  horizontal  direction,  the  dis- 
tance cf  lengthens  while  the  horizontal  projection  of  af  shortens,  the  latter 
becoming  zero  when  the  direction  of  af  becomes  vertical.  As  the  arm  af 
approaches  the  vertical,  the  weight  m  which  may  be  lifted  with  a  given 
force  s  is  very  great,  but  the  distance  through  which  it  may  be  lifted  is 
very  small.  In  all  cases  the  ratio  of  the  weight  m  to  the  weight  n  is  the  in- 
verse ratio  of  the  horizontal  projection  of  their  respective  lever-arms. 

The  Moving  Strut  (Fig.  101)  is  similar  to  the  bent  lever,  except  that 
,one  of  the  arms  is  missing,  and  that  the  force  and  the  resistance  to  be 

overcome  act  at  the  same  end  of  the 
single  arm.  The  resistance  in  the 
case  shown  in  the  cut  is  riot  the 
weight  W,  but  its  resistance  to 
being  moved,  R,  which  may  be  sim- 
ply that  due  to  its  friction  on  the 
horizontal  plane,  or  some  other  op- 
posing force.  When  the  angle  be- 
tween the  strut  and  the  horizontal 
plane  changes,  the  ratio  of  the 
resistance  to  the  applied  force 
changes.  When  the  angle  becomes 
very  small,  a  moderate  force  will 
overcome  a  very  great  resistance, 
which  tends  to  become  infinite  as 


FIG.  101. 


the  angle  approaches  zero.  If  a  =  the  angle,  P  X  cos  a  =  R  x  sin  a.  If 
a  =  5  degrees,  cos  a  =  .99619,  sin  a  =  .08716,  R  =  11.44  P. 

The  stone-crusher  (Fig.  102)  shows  a  practical  example  of  the  use  of  two 
moving  struts. 

Xhe  Toggle-joint  is  an  elbow  or  knee-joint  consisting  of  two  bars  sc/ 
•connected  that  they  may  be  brought  into  a  straight  line  and  made  to  pro- 
duce great  endwise  pressure  when  a  force  is  applied  to  bring  them  into  thia 


ELEMENTS   OF   MACHINES. 


437 


position.  It  is  a  case  of  two  moving  struts  placed  end  to  end,  the  moving 
force  being  applied  at  their  point  of  junction,  in  a  direction  at  right  angles 
to  the  direction  of  the  resistance,  the  other  end  of  one  of  the  struts  resting 
against  a  fixed  abutment,  and  that  of  the  other  against  the  body  to  be 
moved.  If  a  —  the  angle  each  strut  makes  with  the  straight  line  joining  the 
points  about  which  their  outer  ends  rotate,  the  ratio  of  the  resistance 
to  the  applied  force  is  R  :  P : :  cos  a  :  2  sin  a  ;  2R  sin  a  =  P  cos  a.  The 


FIG.  102. 


FIG.  103. 


W 


ratio  varies   when  the  angle  varies,   becoming  infinite  when  the  angle 
becomes  zero. 

The  toggle-joint  is  used  where  great  resistances  are  to  be  overcome 
through  very  small  distances,  as  in  stone-crushers  (Fig.  103). 

The  Inclined  Plane,  as  a  mechanical  element,  is  supposed  perfectly 
Kiard  and  smooth,  unless  friction  be  considered.  It  assists  in  sustaining  a 
heavy  body  by  its  reaction.  This  reaction,  however,  being  normal  to  the 
plane,  cannot  entirely  counteract  the  weight  of  the  body,  which  acts  verti- 
cally downward  Some  other  force  must  therefore 
be  made  to  act  upon  the  body,  in  order  that  it  may 
be  sustained. 

If  the  sustaining  force  act  parallel  to  the  plane 
(Fig.  104),  the  force  is  to  the  weight  as  the  height  of 
the  plane  is  to  its  length,  measured  on  the  incline. 

If  the  force  act  parallel  to  the  base  of  the  plane, 
the  power  is  to  the  weight  as  the  height  is  to  the 
base.  _ 

If  the  force  act  at  any  other  angle,  let  i  —  the          C  A 

angle  of  the  plane  with  the  horizon,  and  e  =  the  FlG.  104. 

angle  of  the  direction  of  the  applied  force  with  the 
angle  of  the  plane.    P :  W  ::  sin  i  :  cos  e;  P  X  cos  e  =  W  sin  i. 

Problems  of  the  inclined  plane  may  be  solved  by  the  parallelogram  of 
forces  thus : 

Let  the  weight  W  be  kept  at  rest  on  the  incline  by  the  force  P,  acting  in 
the  line  bP',  parallel  to  the  plane.  Draw  the  vertical  line  ba  to  represent 
the  weight ;  also  bb'  perpendicular  to  the  plane,  and  complete  the  parallelo- 
gram b'c.  Then  the  vertical  weight  ba  is  the  resultant  of  bbf,  the  measure  of 
support  given  by  the  plant*  to  the  weight,  and  be,  the  force  of  gravity  tend- 
ing to  draw  the  weight  down  the  plane.  The  force  required  to  maintain 
the  weight  in  equilibrium  is  represented  by  this  force  be.  Thus  the  force 
and  the  weight  are  in  the  ratio  of  be  to  ba.  Since  the  triangle  of  forces  abc 
is  similar  to  the  triangle  of  the  incline  ABC,  the  latter  may  be  substituted 
for  the  former  in  determining  the  relative  magnitude  of  the' forces,  and 

P  :  W : :  be  :  ab  : :  BC  :  AB. 

The  Wedge  is  a  pair  of  inclined  planes  united  by  their  bases.  In  the 
application  of  pressure  to  the  head  or  butt  end  of  the'wedge.  to  cause  it  to 
penetrate  a  resisting  body,  the  applied  force  is  to  the  resistance  as  the 
thickness  of  the  wedge  is  to  its  length.  Let  t  be  the  thickness,  I  the  length, 
Wthe  resistance,  and  Pthe  applied  force  or  pressure  on  the  head  of  the 

Wt  PI 

wedge.    Then,  friction  neglected,  P  :  W  :  :  t  :  I;  P  =  -p  ;       W  =  — . 

The  Screw  is  an  inclined  plane  wrapped  around  a  cylinder  in  such  a 
way  that  the  height  of  the  plane  is  parallel  to  the  axis  of  the  cylinder.  If 
the  screw  is  formed  upon  the  internal  surface  of  a  hollow  cylinder,  it  is 
usually  called  a  nut.  When  force  is  applied  to  raise  a  weight  or  overcome 
a  resistance  by  means  of  a  screw  and  nut,  either  the  screw  or  the  nut  may 


438 


MECHANICS. 


be  fixed,  the  other  being:  movable.  The  force  is  generally  applied  at  the  end 
of  a  wrench  or  lever-arm,  or  at  the  circumference  of  a  wheel.  If  r  —  radius 
of  the  wheel  or  lever  arm,  and  p  =  pitch  of  the  screw,  or  distance  between 
threads,  that  is,  the  height  of  the  inclined  plane 
for  one  revolution  of  the  screw,  P  =  the  applied 
force,  and  W—  the  resistance  overcome,  then,  neg- 
lecting resistance  due  to  friction,  2wr  X  P  =  Wp  ; 
W  —  6.283Pr  -*-  p.  The  ratio  of  P  to  W  is  thus 
independent  of  the  diameter  of  the  screw.  In 
actual  screws,  much  of  the  power  transmitted  is 
lost  through  friction. 

The  Cam  is  a  revolv- 
ing inclined  plane.  It  may 
be  either  an  inclined  plane 
wrapped  around  a  cylin- 
der in  such  a  way  that  the 
height  of  the  plane  is  ra- 
dial to  the  cylinder,  such 


FIG.  105. 


as    the    ordinary  lifting- 
p-mills 


FIG.  106. 


cam,  used  in  stamp-] 
(Fig.  105),  or  it  may  be  an  inclined  plane  curved  edgew:'se,  and  rotating  in  a 
plane  parallel  to  its  base  (Fig.  106).  The  relation  of  the  weight  to  the  applied 
force  is  calculated  in  the  same  manner  as  in  the  case  of  the  screw. 


Pulleys  or  Blocks.— P  —  force  applied,  or  pull ;  W  —  weight  lifted 
or  resistance.  In  the  simple  pulley  A  (Fig.  107)  the  point  Pon  the  pulling 
rope  descends  the  same  amount  that  the  weight  is  lifted,  therefore  P  =  W. 
In  B  and  Cthe  point  P  moves  twice  as  far  as  the  weight  is  lifted,  there- 
fore W  =  2  P.  In  B  and  C  there  is  one  movable  block,  and  two  plies  of  the 
rope  engage  with  it.  In  D  there  are  three  sheaves  in  the  movable  block, 
each  with  two  plies  engaged,  or  six  in  all.  Six  plies  of  the  rope  are  there- 
fore shortened  by  the  same  amount  that  the  weight  is  lifted,  and  the  point 
P  moves  six  times  as  far  as  the  weight,  consequently  W  =  6P.  In  general, 
the  ratio  of  W  to  P  is  equal  to  the  number  of  plies'  of  the  rope  that  are 
shortened,  and  also  is  equal  to  the  number  of  plies  that  engage  the  lower 
block.  If  the  lower  block  has  2  sheaves  and  the  upper  3,  the  end  of  the  rope 
is  fastened  to  a  hook  in  the  top  of  the  lower  block,  and  then  there  are  5 
plies  shortened  instead  of  6,  and  W  =  5  P.  If  V  —  velocity  of  W,  and  v  =••= 
velocity  of  P,  then  in  all  cases  VW  =  vP,  whatever  the  number  of  sheaves 
or  their  arrangement.  If  the  hauling  rope,  at  the  pulling  end,  passes  first 
around  a  sheave  in  the  upper  or  stationary  block,  it  makes  no  difference  in 
what  direction  the  rope  is  led  from  this  block  to  the  point  at  which  the  pull 
on  the  rope  is  applied  ;  but  if  it  first  passes  around  the  movable  block,  it  is 
necessary  that  the  pull  be  exerted  in  a  direction  parallel  to  the  line  of  action 
of  the  resistance,  or  a  line  joining  the  centres  of  the  two  blocks,  in  order  to 
obtain  the  maximum  effect.  If  the  rope  pulls  on  the  lower  block  at  an 
angle,  the  block  wrill  be  pulled  out  of  the  line  drawn  between  the  weight 
and  the  upper  block,  and  the  effective  pull  will  be  less  than  the  actual  pull 


ELEMENTS    OF   MACHINES. 


439 


D-- 


* IG-  1 


r.n  the  rope  in  the  ratio  of  the  cosine  of  the  angle  the  pulling  rope  makes 
with  the  vertical,  or  line  of  action  of  the  resistance,  to  unity. 

Differential  Pulley.  (Fig.  108.)— Two  pulleys,  Band  C,  of  different 
radii,  rotate  as  one  piece  about  a  fixed  axis,  A.  An  end- 
less chain,  BDECLKH,  passes  over  both  pulleys.  The 
rims  of  the  pulleys  are  shaped  so  as  to  hold  the  chain  and 
prevent  it  from  slipping.  One  of  the  bights  or  loops  in 
which  the  chain  hangs,  DE,  passes  under  and  supports  the 
running  block  F.  The  other  loop  or  bight,  HKL,  hangs 


freely,  and  is  called  the  hauling  part.  It  is  evident  that 
the  velocity  of  the  hauling  part  is  equal  to  that  of  the 
pitch-circle  of  the  pulley  B. 

In  order  that  the  velocity-ratio  may  be  exactly  uniform, 
the  radius  of  the  sheave  F  should  be  an  exact  mean  be- 
tween the  radii  of  B  and  C. 

Consider  that  the  point  B  of  the  cord  BD  moves  through 
an  arc  whose  length  =  AB,  during  the  same  time  the 
point  C  or  the  cord  CE  will  move  downward  a  distance  = 
AC.  The  length  of  the  bight  or  loop  BDEC  will  be 
shortened  by  AB  —  AC,  which  will  cause  the  pulley  F  to 
be  raised  half  of  this  amount.  If  P  —  the  pulling  force  on 
the  cord  HKy  and  W  the  weight  lifted  at  F,  then  P  X 

AB  =  w  x  MAB  -  AC). 

To  calculatethe  length  of  chain  required  for  a  differential 
pulley,  take  the  following  sum:  Half  the  circumference  of 
A  +  half  the  circumference  of  B  -j-  half  the  circumference 
of  F  -f-  twice  the  greatest  distance  of  F  from  A  -f-  the 
least  length  of  loop  HKL.  The  last  quantity  is  fixed 
according  to  convenience. 
The  Differential  Windlass  (Fig.  109)  is  identical  in  principle 
with  the  differential  pulley,  the  difference  in  con- 
struction being  that  in  the  differential  windlass  the 
running  block  hangs  in  the  bight  of  a  rope  whose  two 
parts  are  wound  round,  and  have  their  ends  respec- 
tively made  fast  to  two  barrels  of  different  radii, 
which  rotate  as  one  piece  about  the  axis  A.  The  dif- 
ferential windlass  is  little  used  in  practice,  because 
of  the  great  length  of  rope  which  it  requires. 

The  Differential  Screw  (Fig.  110)  is  acorn- 
pound  screw  of  different  pitches,  in  which  the 
threads  wind  the  same  way.  Nl  and  N?  are  the  two 
nuts;  SiSn  the  longer-pitched  thread;  S^S^,  the 
shorter-pitched  thread:  in  the  figure  both  these 
threads  are  left-handed.  At  each  turn  of  the  screw 
the  nut  N%  advances  relatively  to  Nz  through  a  dis- 
tance equal  to  the  difference  of  the  pitch.  The  use 
of  the  differential  screw  is  to  combine  the  slowness 
of  advance  due  to  a  fine  pitch  with  the  strength  of  thread  which  can  be 
obtained  by  means  of  a  coarse  pitch  only. 

A  Wheel  and  Axle,  or  Windlass,  resembles  two  pulleys  on  one  axis, 
having  different  diameters.  If  a  weight  be  lifted  by  means  of  a  rope  wound 
over  the  axle,  the  force  being  applied  at  the 
rim  of  the  wheel,  the  action  is  like  that  of  a 
lever  of  which  the  shorter  arm  is  equal  to 
the  radius  of  the  axle  plus  half  the  thick- 
ness of  the  rope,  and  the  longer  arm  is 
ec*ual  to  the  radius  of  the  wheel.  A  wheel 
and  axle  is  therefore  sometimes  classed 
as  a  perpetual  lever.  If  P  —  the  applied  force,  D  —  diameter  of  the  wheel, 
W  =  the  weight  lifted,  and  d  the  diameter  of  the  axle  -f-  the  diameter  of 
Uie  rope,  PD  =  Wd. 

Toothed-wheel  Gearing  is  a  combination  of  two  or  more  wheels 
and  axles  (Fig.  111).  If  a  series  of  wheels  and  pinions  gear  into  each  other, 
as  in  the  cut,  friction  neglected,  the  weight  lifted,  or  resistance  over- 
come, is  to  the  force  applied  inversely  as  the  distances  through  which 
they  act  in  a  given  time.  If  R,  Rlt  R^  be  the  radii  of  the  successive  wheels, 
measured  to  the  pitch-line  of  the  teeth,  and  r,  rlt  r2  the  radii  of  the  cor- 
responding pinions,  JPthe  applied  force,  and  W  the  weight  lifted,  Px 


Fia.  109. 


FIG.  110. 


440  MECHANICS. 

R  X  Rj  X  Ry  =  W  X  r  X  rx  X  r2,  or  the  applied  force  is  to  the  weight 
as  the  product  of  the  radii  of  the  pinions  is  to  the  product  of  the  radii  of 
the  wheels;  or,  as  the  product  of  the  numbers  expressing  the  teeth  in 
each  pinion  is  to  the  product  of  the  numbers  expressing  the  teeth  in  each 
wheel. 

Endless  Screw,  or  Worm-gear.    (Fig.  112.)— This  gear  is  com- 
4monly  used  to  convert  motion  at  high  speed  into  motion  at  very   slow 


FIG.  111. 

speed.  When  the  handle  P  describes  a  complete  circumference,  the  -pitch- 
line  of  the  cog-wheel  moves  through  a  distance  equal  to  the  pitch  of  the 
screw,  and  the  weight  TFis  lifted  a  distance  equal  to  the  pitch  of  the  screw 
multiplied  by  the  ratio  of  the  diameter  of  the  axle  to  the  diameter  of  the 
pitch-circle  of  the  wheel.  The  ratio  of  the  applied  force  to  the  weight 
lifted  is  inversely  as  their  velocities,  friction  not  being  considered ;  but  the 
friction  in  the  worm-gear  is  usually  very  great,  amounting  sometimes  to 
three  or  four  times  the  useful  work  done. 

If  v  =  the  distance  through  which  the  force  Pacts  in  a  given  time,  say  1 
second,  and  V  =  distance  the  weight  W  is  lifted  in  the  same  time,  r  = 
radius  of  the  crank  or  wheel  through  which  Pacts,  t  =  pitch  of  the  screw, 
and  also  of  the  teeth  on  the  cog-wheel,  d  =  diameter  of  the  axle, 

and  D  =  diameter  of  the  pitch-line  of  the  cog-wheel,  v  =  "~^  -- 
X  F ;  F  =  t;  X  ta  -f-  6.283rd.  Pv  =  WV -\-  friction. 

STRESSES   IN    FRAMED    STRUCTURES. 

Framed  structures  in  general  consist  of  one  or  more  triangles,  for  the 
reason  that  the  triangle  is  the  one  polygonal  form  whose  shape  cannot  be 
changed  without  distorting  one  of  its  sides.  Problems  in  stresses  of  simple 
framed  structures  may  generally  be  solved  either  by  the  application  of  the 
triangle,  paralellogram,  or  polygon  of  forces,  by  the  principle  of  the  lever, 
or  by  the  method  of  moments.  We  shall  give  a  few  examples,  referring  the 
student  to  the  works  of  Burr,  Dubois,  Johnson,  and  others  for  more  elabo- 
rate treatment  of  the  subject. 

1.  A  Simple  Crane.  (Figs.  113  and  114.)—  A  is  a  fixed  mast,  B  a  brace  or 
boom,  T  a  tie,  and  P  the  load.  Required  the  strains  in  B  and  T.  The  weight 
P,  considered  as  acting  at  the  end  of  the  boom,  is  held  in  equilibrium  by 
three  forces:  first,  gravity  acting  downwards;  second,  the  tension  in  T:  and 
third,  the  thrust  of  B.  Let  the  length  of  the  line  p  represent  the  magnitude 
of  the  downward  force  exerted  by  the  load,  and  draw  a  parallelogram  with 
sides  bt  parallel,  respectively,  to  B  and  T,  such  that  pis  the  diagonal  of  the 


Or,  more  simply,  7',  B,  and  that  portion  of  the  mast  included  between  them 
•or  A'  may  represent  a  triangle  of  forces,  and  the  forces  are  proportional  to 
the  length  of  the  sides  of  the  triangle;  that  is,  if  the  height  of  the  triangle  A' 
—  the  load  then  B  =  the  compression  in  the  brace,  and  T  —  the  tension  in  the 

T 
tie-  or  if  P  =  the  load  in  pounds,  the  tension  in  T  =  P  X  -T,,  and  th.e  com- 


STRESSES  IN  fRAilED  STRUCTURES. 


441 


pression  in  B  =  P  X  -7'.    Also,  if  a  =  the  angle  the  inclined  member  makes 

with  the  mast,  the  other  member  being  horizontal,  and  the  triangle  being 
right-angled,  then  the  length  of  the  inclined  member  =  height  of  the  tri- 
angle  X  secant  a,  and  the  strain  in  the  inclined  member  =  P  secant  a.  Also, 
the  strain  in  the  horizontal  member  =  P  tan  a. 

The  solution  by  the  triangle  or  parallelogram  of  forces,  and  the  equations 
Tension  in  T  =  P  X  T/A',  and  Compression  inB  =  P  X  B/A',  hold  true  even 
if  the  triangle  is  not  right-angled,  as  in  Fig.  115;  but  the  trigonometrical  reia- 


FIG.  113. 


Fis.  114. 


FIG.  115. 


tions  above  given  do  not  hold,  except  in  the  case  of  a  right-angled  triangTe. 
It  is  evident  that  as  A'  decreases,  the  strain  in  both  T  and  B  increases,  tend- 
ing to  become  infinite  as  A'  approaches  zero.  If  the  tie  Tis  not  attached  to 
liie  mast,  but  is  extended  to  the  ground,  as  shown  in  the  dotted  line,  the 
v.ension  in  it  remains  the  same. 

2.  A  Guyed  Crane  or  Derrick;.  (Fig.  116.)— The  strain  in  B  is,  as; 
Before,  PxB/A',  A'  being  that  portion  of  the  vertical  included  between  B  and 
T,  wherever  Tmay  be  attached  to  A.  If,  however,  the  tie  Tis  attached  to  B 
beneath  its  extremity,  there  may  be  in  addition  a  bending  strain  in  B  due  to 
a  tendency  to  turn  about  the  point  of  attachment  of  Tas  a  fulcrum. 

The  strain  in  T  may  be  calculated  by  the  principle  of  moments.  The  mo- 
ment of  P  is  PC,  that  is,  its  weight  X  its  perpendicular  distance  from  the 
point  of  rotation  of  B  on  the  mast.  The  moment  of  the  strain  on  T  is  the 
product  of  the  strain  into  the  perpendicular  distance  from  the  line  of  its 


FIG.  116. 

direction  to  the  same  point  of  rotation  of  J5,  or  Td.  The  strain  in  T  there- 
fore —  PC  H-  d.  As  d  decreases  the  strain  on  T  increases,  tending  to  infin- 
ity as  d  approaches  zero. 

The  strain  on  the  guy-rope  is  also  calculated  by  the  method  of  moments. 
The  moment  of  the  load  about  the  bottom  of  the  mast  O  is,  as  before,  PC. 
If  the  guy  is  horizontal  the  strain  in  it  is  F  and  its  moment  is  Ff,  and  F  = 
pc  _i_  f%  'if  it  is  inclined,  the  moment  is  the  strain  G  X  the  perpendicular 
distance  of  the  line  of  its  direction  from  O,  or  Gg,  and  G  =  PC  -+-  g. 

The  guy-rope  having  the  least  strain  is  the  horizontal  one  F,  and  the  strain. 


442 


in  G  —  the  strain  in  F  x  the  se- 
cant of  the  angle  between  .Fand 
6?.  As  G  is  made  more  nearly 
vertical  g  decreases,  and  the 
strain  increases,  becoming1  infi- 
nite when  g  =  0. 

3.  Shea  r-p  o  1  e  s  with 
Guys.  (Fig.  117.)—  Resultant  of 
strain  in  both  masts  =  P  X  BD 
-t-BC.  Resultant  strain  in  both 
guys=P  X  AB+BC.  The  strain 
on  each  mast  (or  guy)  will  be  half 
|jhe  above,  multiplied  by  the  se- 
cant of  half  the  angle  the  masts 
FIG.  117.  (or  guys)  make  with  each  other. 

Two  Diagonal  Braces  and  a  Tie-rod.    (Fig.  118.)— Suppose  the 
braces  are  used  to  sustain  a  single  load  P.    Compressive  stress  on  AD  = 

y2p  x  — —  ;  on  CA  =  %P  X  — B-    Tn*s  1S  true  only if  CB  and  BD  are  of  equal 

length,  in  which  case  ^  of  P  is  supported  by  each  abutment  C  and  D.    If 

they  are  unequal  in  length  (Fig.  119),  then, 

by  the  principle  of  the  lever,  find  the  re- 
actions of  the  abutments  R!  and  #a.    If  P 

is  the  load  applied  at  the  point  B  on  the 

lever  CD,  the  fulcrum  being  D,  then  RI  X 

CD  -  P  X  BD  and   #2  X  CD  =  P  X  BC\ 

Rs  =  PX  BD  -J-  CD',  RI  =  P  X  BC  H-  CD. 
The  strain  on  AC  =  RI  X  AC-i-AB,  and 

on  AD  =  R?  X  AD  -*-  AB. 
The  strain  on  the  tie  =  RI  X  CB  -s-  AB 

=  R.)  XBD  +  AB. 

.  When  CB  —  BD,  El—R^,  the  strain 

on  CB  and  BD  is  the  same,  whether 
the  braces  are  of  equal  length  or 
not,  and  is  equal  to  y%P  X  ^CD-^-AB. 
If  the  braces  support  a  uniform  load. 
as  a  pair  of  rafters,  the  strains  caused 
by  such  a  load  are  equivalent  to  that 
caused  by  one  half  of  the  load  applied 
at  the  centre.  The  horizontal  thrust 
of  the  braces  against  each  other  at  the 


FIG.  119. 


apex  equals  the  tensile  strain  in  the  tie. 

'King-post  Truss  or  Bridge.  (Fig.  120.)— If  the  load  is  distributed 
over  the  whole  length  of  the  truss,  the  effect  is  the  same  as  if  half  the  load 
were  placed  at  the  centre,  the  other  half  being  carried  by  the  abutments.  Let 
P  =  one  half  the  load  on  the  truss,  then 
tension  in  the  vertical  tie  AB  =  P.  Com- 
pression in  each  of  the  inclined  braces  = 
y%P  X  AD  H-  AB.  Tension  in  the  tie  CD 
=  y^P  X  BD  H-  AB.  Horizontal  thrust  of 
inclined  brace  AD  at  D  =  the  tension  in 
the  tie.  If  W  =  the  total  load  on  one  truss 
uniformly  distributed,  I  =  its  length  and 
d  =  its  depth,  then  the  tension  on  the  hor- 

Wl 
izontal  tie  =  -rr-r. 

on- 

Inverted  King-post  Truss.    (Fig.  121.)— If  P=  a  load  applied  al 
B,  or  one  half  of  a  uniformly  distributed  load,  then  compression  on  AB  —  P 

(the  floor-beam  CD  not  being  considered 
to  have  any  resistance  to  a  slight  bending). 
Tension  on  AC  or  AD  =  1AP  X  AD  -5-  AB. 
>     Compression  on  CD  =  V%P  X  BD  -=-  AB. 

Queen-post  Truss.  (Fig.  122.)-If 
uniformly  loaded,  and  the  queen-posts  di- 
vide the  length  into  three  equal  bays,  the 
load  may  be  considered  to  be  divided  into 
three  equal  parts,  two  parts  of  which,  Pt 
andPa,  are  concentrated  at  the  panel  joints 


FIG.  120. 


B 


A 
Fio.  121 


STRESSES   IN   FRAMED   STRUCTURES. 


443 


FIG.  isa. 


and  the  remainder  is  equally  divided  between  the  abutments  and  supported 
by  them  directly.    The  two  parts  Px  and  P2  only  are  considered  to  affect 

the  members  of  the  truss.  Strain  in 
the  vertical  ties  BE  and  CF  each 
equals  Pl  or  P2.  Strain  on  AB  and 
CD  each  =  Pr  x  CD  -*-  CF.  Strain 
on  the  tie  AE  or  EF or  ED  =  P,  X 
FD  H-  CF.  Thrust  on  BC  =  tension 
on  EF. 

For  stability  to  resist  heavy  un- 
equal loads  the  queen-post  truss 
should  have  diagonal  braces  from 
B  to  Pand  from  C  to  E. 

Inverted  Quee  n-post 
Truss.  (Fig.  123.)  —  Compression 
on  EB  and  FC  each  =  P,  or  P2. 
Compression  on  AB  or  BC  or  CD  = 
Pj  X  AB-t-EB.  Tension  on  AE  or 
FD  =  P!  x  AE-*-  EB.  Tension  on 
EF=  compression  on  BC.  For  sta- 
— -  bility  to  resist  unequal  loads,  ties 

,-,       -mo  should  be  run  from  C  to  E  and  from 

FIG.  123.  BtoF. 

Burr  Truss  of  Five  Panels.  (Fig.  124.)— Four  fifths  of  the  load  may 
be  taken  as  concentrated  at  the  points  E,  K,  L  and  Ft  the  other  fifth  being 

B  G  H  C 


supported  directly  by  the  two  abutments.  For  the  strains  in  BA  and  CD 
the  truss  may  be  considered  as  a  queen-post  truss,  with  the  loads  Px ,  Pa 
concentrated  at  E  and  the  loads  P3  ,  P4  concentrated  at  F.  Then,  compres- 
sive  strain  on  AB  =  (Pj  +  P2)  X  AB-s-BE.  The  strain  on  CD  is  the  same  if 
the  loads  and  panel  lengths  are  equal.  The  tensile  strain  on  BE  or  CF  = 
P!  +  Pa-  That  portion  of  the  truss  between  E  and  Pmay  be  considered  as 
a  smaller  queen-post  truss,  supporting  the  loads  P2 ,  P3  at  K  and  L.  The 
strain  on  EG  or  HF  —  P2  X  EG  -*-  GK.  The  diagonals  GL  and  KH  receive  no 
strain  unless  the  truss  is  unequally  loaded.  The  verticals  GK  and  HL  each 
receive  a  tensile  strain  equal  to  P2  or  P3. 

For  the  strain  in  the  horizontal  members:  BG  and  CH  receive  a  thrust 
equal  to  the  horizontal  component  of  the  thrust  in  AB  or  CD,  =  (Pl  -+-  P2) 
X  tan  angle  ABE,  or  (P,  +P2)  X  AE-r-JSE.  GH  receives  this  thrust  and 
also,  in  addition,  a  thrust  equal  to  the  horizontal  component  of  the  thrust  in 
EG  or  HF,  or,  in  all,  (Pt  +  P2  -f  P3)  X  AE-^BE. 

Ths  tension  in  AE  or  FD  equals  the  thrust  in  BG  or  flC,  and  the  tension 
in  EK.  KL,  and  LF  equals  the  thrust  in  GH. 

Pratt  or  Wliipple  Truss.  (Fig.  125.)— In  this  truss  the  diagonals  are 
ties,  and  the  verticals  are  struts  or  columns. 

Calculation  by  the  method  of  distribution  of  strains:  Consider  first  the 
load  Pi.  The  truss  having  six  bays  or  panels,  5/6  of  the  load  is  transmitted 
to  the  abutment  H,  and  1/6  to  the  abutment  O,  on  the  principle  of  the  lever. 
As  the  five  sixths  must  be  transmitted  through  JA  and  AH,  write  on  these 
members  the  figure  5.  The  one  sixth  is  transmitted  successively  through 
JC,  CK,  KD,  DL,  etc.,  passing  alternately  through  a  tie  and  a  strut.  Write 
on  these  members,  up  to  the  strut  GO  inclusive,  the  figure  1.  Then  consider 
the  load  P2  ,  of  which  4/6  goes  to  AH  and  26  to  GO.  Write  on  KB,  BJ,  JA, 
and  AH  the  figure  4,  and  on  KD,  DL,  LE.  etc.,  the  figure  2.  The  load  Pa 


444 


MECHANICS. 


transmit  3/6  in  each  direction;  write  3  on  each  of  the  members  through 
which  this  stress  passes,  and  so  on  for  all  the  loads,  when  the  figures  on  the 
several  members  will  appear  as  on  the  cut.  Adding  them  up,  we  have  the 
following  totals : 

Tension  on  diagonals  $  AJ  BH  BK  CJ  CL  DK  DM  EL  EN  FM  Fo  GN 
diagonals -j  15       o      10      1       63       3       6       1      10     0      15 


Compression  on  verticals  -{ 


DL 


EM   FN 
7        10 


GO 
15 


Each  of  the  figures  in  the  first  line  is  to  be  multiplied  by  1/6  P  X  secant  of 
angle  HAJ,  or  1/6P  X  AJ^-  AH,  to  obtain  the  tension,  and  each  figure  in  the 
lower  line  is  to  be  multiplied  by  1/6P  to  obtain  the  compression.  The  diag- 
onals HB  and  FO  receive  no  strain. 


It  is  common  to  build  this  truss  with  a  diagonal  strut  at  HB  instead  of  the 
post  HA  and  the  diagonal  AJ;  in  which  case  5/6  of  the  load  Pis  carried 
through  JB  and  the  strut  BH,  which  latter  then  receives  a  strain  =  15/tiP  x 
secant  of  HBJ. 

The  strains  in  the  upper  and  lower  horizontal  members  or  chords  increase 
from  the  ends  to  the  centre,  as  shown  in  the  case  of  the  Burr  truss.  AL 
receives  a  thrust  equal  to  the  horizontal  component  of  the  tension  in  AJ,  or 
15/6PX  tan  AJB.  BC  receives  the  same  thrust  -f  the  horizontal  component 
of  the  tension  in  BK,  and  so  on.  The  tension  in  the  lower  chord  of  each  panel 
is  the  same  as  the  thrust  in  the  upper  chord  of  the  same  panel.  (For  calcu 
lation  of  the  chord  strains  by  the  method  of  moments,  see  below.) 

The  maximum  thrust  or  tension  is  at  the  centre  of  the  chords  and  is  equa* 

to  —  -  ,  in  which  W  is  the  total  load  supported  by  the  truss,  L  is  the  length, 

oLf 

and  D  the  depth.  This  is  the  formula  for  maximum  stress  in  the  chords 
of  a  truss  of  any  form  whatever. 

The  above  calculation  is  based  on  the  assumption  that  all  the  loads  Plf  P2, 
etc.,  are  equal.  If  they  are  unequal  the  value  of  each  has  to  be  taken  into 
account  in  distributing  the  strains.  Thus  the  tension  in  AJ,  with  unequal 
loads,  instead  of  being  15  X  1/6  P  secant  0  would  be  sec  0  X  (5/6  P!  -f  4/6  P2  + 
3/6  P3  +  2/6  P4  4-  1/6  P5.)  Each  panel  load,  P1  etc.,  includes  its  fraction  of 
the  weight  of  the  truss. 

General  Formula  for  Strains  in  Diagonals  and  Verticals. 
—Let  n=  total  number  of  panels,  x  =  number  of  any  vertical  considered 
from  the  nearest  end,  counting  the  end  as  1,  r  —  rolling  load  for  each  panel, 
P  —  total  load  for  each  panel, 


Strain  on  verticals  =     " 


2n  2n 

For  a  uniformly  distributed  load,  leave  out  the  last  term, 

[r  («-!)+  (a?  -l)*J-*-2n. 

Strain   on   principal  diagonals  =  strain   on   verticals  X  secant  9,  that  is 
secant  of  the  angle  the  diagonal  makes  with  the  vertical. 

Strain  on  the  counterbraces  :  The  strain  on  the  counterbrace  in  the  first 
panel  is  0,  if  the  load  is  uniform.    On  the  2d,  3d,  4th,  etc.,  it  is  Pt^cant  & 


1+2+ 3 


,  etc.,  P  being  the  total  load  in  one  panel. 


STRESSES    IN    FRAMED    STRUCTURES. 


445 


Strain  in  the  Chords— Method  of  Moments. —Let  the  truss  be 
uniformly  loaded,  the  tot; -I  load  acting  on  it  =  W.  Weight  supported  «'it 
each  end,  or  reaction  of  the  abutment  —  W/2.  Length  of  the  truss  =  L. 
Weight  on  a  unit  of  length  —  W/L.  Horizontal  distance  from  the  nearest 
abutment  to  the  point  (say  Jfin  Fig.  125)  in  the  chord  where  the  strain  is  to 
be  determined  =  x.  Horizontal  strain  at  that  point  (tension  on  the  lower 
chord,  compression  in  the  upper)  =  H.  Depth  of  the  truss  =  D.  By  the 
method  of  moments  we  take  the  difference  of  the  moments,  about  the  point 
M,  of  the  reaction  of  the  abutment  and  of  the  load  between  and  the  abut- 
ments, and  equate  that  difference  with  the  moment  of  the  resistance,  or  of 
'the  strain  in  the  horizontal  chord,  considered  with  reference  to  a  point  in 
the  opposite  chord,  about  which  the  truss  would  turn  if  the  first  chord  were 
severed  at  M. 

The  moment  of  the  reaction  of  the  abutment  is  Wx/2.  The  moment  of 
the  load  from  the  abutment  to  M  is  W/Lx  X  the  distance  of  its  centre  of 
gravity  from  M,  which  is  x/2,  or  moment  =  Wx^  -*-  2L.  Moment  of  the  stress 

in  the  chord  =  HD  =  ^  -  ^-,  whence  H  =  ^-(x~  ^Y    If  x  =  0  or  L, 

WLL  2D^        LJ 

H  =  0.    If  x  =  L/2,  H  =  — — -,  which  is  the  horizontal  strain  at  the  middle 

oD 

of  the  chords,  as  before  given. 

The  Howe  Truss.  (Fig.  126.)— In  the  Howe  truss  the  diagonals  are 
struts,  and  the  verticals  are  ties.  The  calculation  of  strains  may  be  made 


FIG.  126. 

in  the  same  method  as  described  above  for  the  Pratt  truss. 

The  Warren  Girder.    (Fig.  127.)— In  the  Warren  girder,  or  triangular 
truss,  there  are  no  vertical  struts,  and  the  diagonals  may  transmit  either 


FIG.  127. 

tension  or  compression.  The  strains  in  the  diagonals  may  be  calculated  by 
the  method  of  distribution  of  strains  as  in  the  case  of  the  rectangular  truss. 
On  the  principle  of  the  lever,  the  load  P,  being  1/10  of  the  length  of  the 
span  from  the  line  of  the  nearest  support  a,  transmits  9/10  of  its  weight  to  a 
and  1/10  to  g.  Write  9  on  the  right  hand  of  the  strut  la.  to  represent  the 
compression,  and  1  on  the  right  hand  of  lb.  2c,  3d.  etc.,  to  represent  com- 
pression, and  on  the  left  hand  of  62,  c3.  etc.,  to  represent  tension.  The  load  P2 
transmits  7/10  of  its  weight  to  a  and  3/10  to  g.  Write  7  on  each  member  from 
2  to  o  and  3  on  each  member  from  2  to  0,  placing  the  figures  representing 
compression  on  the  right  hand  of  the  member,  and  those  representing 
tension  on  the  Jeft.  Proceed  in  the  same  manner  with  all  the  loads,  then 


446 


MECHANICS. 


sum  up  the  figures  on  each  side  of  each  diagonal,  and  write  the  difference 
of  each  sum  beneath,  and  on  the  side  of  the  greater  sum,  to  show  whether 
the  difference  represents  tension  or  compression.  The  results  are  as  follows: 
Compression,  la,  25;  2b.  15;  3c,  5;  3d,  5;  4e,  15;  5</,  25.  Tension,  1??,  15;  2c, 
5:  4d,  5;  5e,  15.  Each  of  these  figures  is  to  be  multiplied  by  1/10  of  one  of 
the  loads  as  P2 ,  and  by  the  secant  of  the  angle  the  diagonals  make  with  a 
vertical  line. 

The  strains  in  the  horizontal  chords  may  be  determined  by  the  method  of 
moments  as  in  the  case  of  rectangular  trusses. 

Roof-truss.— Solution  by  Method  of  Momenta. — The  calculation  of 
strains  in  structures  by  the  method  of  statical  moments  consists  in  taking  a 
cross-section  of  the  structure  at  a  point  where  there  are  not  more  than 
three  members  (struts,  braces,  or  chords). 

To  find  the  strain  in  either  one  of  these  members  take  the  moment  about 
the  intersection  of  the  other  two  as  an  axis  of  rotation.  The  sum  of  the 
moments  of  these  members  must  be  0  if  the  structure  is  in  equilibrium. 
But  the  moments  of  the  two  members  that  pass  through  the  point  of  refer- 
ence or  axis  are  both  0,  hence  one  equation  containing  one  unknown  quan- 
tity can  be  found  for  each  cross-section. 


FIG.  128. 


In  the  truss  shown  in  Fig.  128  take  a  cross-section  at  t?,  and  determine  the 
strain  in  the  three  members  cut  by  it,  viz.,  CE,  ED,  and  DF.  Let  X  —  force 
exerted  in  direction  CE,  Y  —  force  exerted  in  direction  DE,  Z  =  force  ex 
erted  in  direction  FD. 

For  JTtake  its  moment  about  the  intersection  of  Y"and  Z  at  D  =  Xx.  For 
Y  take  its  moment  about  the  intersection  of  JTand  Z  at  A  =  Yy.  For  Z  take 
its  moment  about  the  intersection  of  X  and  Y  at  E  —  Zz.  Let  z  =  15,  x  = 
18.6,  y  -  38.4.  AD  =  50,  CD  -  20  ft.  Let  Pj,  P2,  P3,  P4  be  equal  loads,  as 
shown,  and  3^  P  the  reaction  of  the  abutment  A. 

The  sum  of  all  the  moments  taken  about  D  or  A  or  E  will  be  0  when  the 
structure  is  at  rest.  Then  -  Xx  +  3.5P  X  50  -  P3  X  12.5  -  P2  X  25  -  P,  X 
37.5  =  0. 

The  -f-.  signs  are  for  moments  in  the  direction  of  the  hands  of  a  watch  or 
"  clockwise  "  and  —  signs  for  the  reverse  direction  or  anti-clockwise.  Since 
P  =  P,  =  P,  -  P,,  -  18.6X+  1T5P  -  75P  =  0;  -  1S.6X  =  -  100P;  X  = 

100P^-18.6  =  5.376P. 
_  Yy  +  P 3  X  37.5  +  P2  X  25  f  P,  X  12.5  =  0;  38.4F  =  75P;  Y  =  75P-=-  38.4 

=  1  953P. 

-Zz  +  3.5P  X  37.5  -  P3  X  25  -  P2  X  12.5  -  P3  X  0  =  0;   15Z  =  93.75P;   Z  - 
6.25P. 

In  the  same  manner  the  forces  exerted  in  the  other  members  have  been 
found  as  follows:  EG  =  6.73P:  GJ  =  8.07P;  JA  =  9.42P;  JH  =  1.35P;  GF  = 
1.59P;  AH  =  8.75P;  HF  =  7.50P. 

The  Fink  Roof-truss.  (Fig.  129.)—  An  analysis  by  Prof.  P.  H.  Phil- 
brick  (Van  N.  Mag..  Aug.  1H80)  gives  the  following  results: 


STRESSES   IN   FRAMED   STRUCTURES. 
C 


44? 


FIG.  129. 

W  —  total  load  on  roof; 
N  =  No.  of  panels  on  both  rafters; 
W/N  =  P  =  load  at  each  joint  6,  d,  /,  etc.; 

V  =  reaction  at  A  -  y>  W  =  y2NP  =  4P: 
AD  =  S;    AC=L;    CD  =  D; 
*i»  'a»  ^s  =  tension  on  De,  eg,  gA,  respectively; 
2,  c3,  c4  =  compression  on  Cb,  bd,  df,  and/4. 


Strains  in 

1,  or  De  =  1 1  =s  2PS  -5-  D; 

2,  "  eg  =  £2  =  3PS  -*-  D; 

3,  k'  <M  =  t3  =  7/2PS  -f-  D; 

4,  "  Af  =  c4  =  7/2PL  -j-  D; 

5,  "  fd  =  c3  =  7/2PL/D  -PD/L; 

6,  "   db  =  Cz=7/2PL/D-2PD/L', 


7,  or  bC  =  G!  =7/2  PL/D  -  3  PD/L: 

8,  "     be  or  fg  =  PS-*-  L; 

9,  "     de  =  2PS-^£; 

10,  "     erf  or  dg  =  ]^PS  -*-  D: 

11,  '*    ec  =  PS-i-D; 

12,  "     cO  =  3/2  PS  -*-  D. 


Example.— Given  a  Fink  roof -truss  of  span  64  ft.,  depth  16  ft.,  with  four 
panels  on  each  side,  as  in  the  cut;  total  load  32  tons,  or  4  tons  each  at  the 
points  /,  d,  6,  O,  etc.  (and  2  tons  each  at  A  and  B,  which  transmit  no  strain 
to  the  truss  members).  Here  W=  32  tons,  P  =  4  tons,  S  =  32  ft.,  D  =  16 
ft.,  L  =  i/S2  +  D2  =  2.236  X  D.  L  -s-  D  =  2.236,  D  +  L=  .4472,  S  -4-  D  =  2 
&  -«-  L  =  .8944.  The  strains  on  the  numbered  members  then  are  as  follows: 


1,  2X4X2         =16     tons; 

2,  3X4X2         =24        " 

3,  7/2X4X2         =  28        " 

4,  7/2  X  4  X  2.236  =  31.3    " 

5,  31.3-4  X  .447    =29.52  " 

6,  31.3- 8  X  .447    =27.72" 


7,  31.3  -  12  X  .447    =  25.94  tons, 

8,  4  X  ,8944  =    3.58    " 

9,  8  X  .8944  =    7.16    " 

10,  2X2=4 

11,  4X2=8 

12,  6  X    2       =  13 


Tlie  Economical  Angle.—  A  structure  of  tri- 
angular form,  Fiir.  129a,  is  supported  at  a  and  b.  It 
sustains  any  load  Z/,  the  elements  cc  being  in  compres- 
sion and  t  in  tension.  Required  the  angle  0  so  that 
the  total  weight  of  the  structure  shall  be  a  minimum. 
F.  R.  Honey  (Sci.  Am.  Supp.,  Jan.  17,  1895)  gives  a  solu- 

I     rri 

^ 


/f 


in  which  C  and  T  represent  (he  crushing  and  the 
sile  strength  respectively  of  the  material  employed. 


. 

It,  is  applicable  to  any  material.     For  C=  T,  tan  B  =  *  IG-  129a- 

542°.     For   C  =  0.4T  (yellow  pine),  tan  B  -  49|°.     For   C  =  0  8T  (sof  t  steel), 


tan  0  =.  534°.    For  C  =  6T(cast  iron),  tan  0  = 


448  HEAT, 


HEAT. 

THERMOMETERS. 

The  Fahrenheit  thermometer  is  generally  used  in  English-speaking  coun- 
tries, and  the  Centigrade,  or  French  thermometer,  in  countries  that  use  the 
metric  system.  In  many  scientific  treatises  in  English,  however,  the  Centi- 
grade temperatures  are  also  used,  either  with  or  without  their  Fahrenheit 
equivalents.  The  Reaumur  thermometer  is  used  in  Russia,  Sweden,  Turkey, 
and  Egypt.  (Clark.) 

In  the  Fahrenheit  thermometer  the  freezing-point  of  water  is  taken  at  32°, 
and  the  boiling-point  of  water  at  mean  atmospheric  pressure  at  the  sea- 
level,  14. Tibs,  per  sq.  in.,  is  taken  at  212°,  the  distance  between  these  two 
points  being  divided  into  180°.  In  the  Centigrade  and  Reaumur  thermometers 
the  freezing-point  is  taken  at  0°.  The  boiling-point  is  100°  in  the  Centigrade 
scale,  and  80°  in  the  Reaumur. 

1  Fahrenheit  degree          =  5/9  deg.  Centigrade    =  4/9  deg.  Reaumur. 

1  Centigrade  degree          =  9/5  deg.  Fahrenheit    =  4/5  deg.  Reaumur. 

1  Reaumur  degree  =  9/4  deg.  Fahrenheit    =  5/4  deg.  Centigrade. 

Temperature  Fahrenheit  =  9/5  X  temp.  C.  -f-  32°  =  9/4  R.  -f  32°. 

Temperature  Centigrade  =  5/9  (temp.  F.  -  32°)    =  5/4  R. 

Temperature  Reaumur     =  4/5  temp.  C.  =  4/9  (F.  —  32°). 

Mercurial  Thermometer.  (Rankine,  S.  E.,  p.  234.)— The  rate  of 
expansion  of  mercury  with  rise  of  temperature  increases  as  the  temperature 
becomes  higher  ;  from  which  it  follows,  that  if  a  thermometer  showing  the 
dilatation  of  mercury  simply  were  made  to  agree  with  an  air  thermometer 
at  32°  and  212°,  the  mercurial  thermometer  would  show  lower  temperatures 
than  the  air  thermometer  between  those  standard  points,  and  higher  tem- 
peratures beyond  them. 

For  example,  according  to  Regnault,  when  the  air  thermometer  marked 
350°  C.  (-  662°  F.),  the  mercurial  thermometer  would  mark  362.16°  C.  (= 
683.89°  F.),  the  error  of  the  latter  being  in  excess  12.16°  C.  (=  21.89°  F.). 

Actual  mercurial  thermometers  indicate  intervals  of  temperature  propor- 
tional to  the  difference  between  the  expansion  of  mercury  and  that  of  glass. 

The  inequalities  in  the  rate  of  expansion  of  the  glass  (which  are  very 
different  for  different  kinds  of  glass)  correct,  to  a  greater  or  less  extent,  the 
errors  arising  from  the  inequalities  in  the  rate  of  expansion  of  the  mercury. 

For  practical  purposes  connected  with  heat  engines,  the  mercurial  ther- 
mometer made  of  common  glass  may  be  considered  as  sensibly  coinciding 
-  with  the  air-thermometer  at  all  temperatures  not  exceeding  500°  F. 

PYROMETRY. 

Principles  Used  in  Various  Pyrometers.- Contraction  of  clay 
by  heat,  as  in  the  Wedgwood  pjTometer  used  by  potters.  Not  accurate,  as 
the  contraction  varies  with  the  quality  of  the  clay. 

Expansion  of  air,  as  in  the  air-thermometers,  Wiborgh's  pyrometer,  Ueh- 
ling  and  Steinbart's  pyrometer,  etc. 

Specific  heat  of  solids,  as  in  the  copper-ball,  platinum-ball,  and  fire-clay 
pyrometers. 

Relative  expansion  of  two  metals  or  other  substances,  as  copper  and  iron, 
as  in  Brown's  and  Bulkley's  pyrometers,  etc. 

Melting-points  of  metals,  or  other  substances,  as  in  approximate  deter- 
minations of  temperature  by  melting  pieces  of  zinc,  lead,  etc. 

Measurement  of  strength  of  a  thermo-electric  current  produced  by  heat- 
ing the  junction  of  two  metals,  as  in  Le  Chatelier's  pyrometer. 

Changes  in  electric  resistance  of  platinum,  as  in  the  Siemens  pyrometer. 

Time  required  to  heat  a  weighed  quantity  of  water  enclosed  in  a  vessel, 
as  in  the  water  pyrometer. 

Thermometer  for  Temperatures  up  to  8OO°  F.— Mercury  with 
compressed  nitrogen  in  the  tube  above  the  mercury.  Made  by  Queen  &  Co., 
Philadelphia. 


TEMPERATURES,  CENTIGRADE  AND          440 
FAHRENHEIT. 


c. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

-40 

—40. 

26 

78.8 

92 

197.6 

158 

316.4 

224 

435.2 

290 

554 

950 

1742 

-39 

-38.2 

27 

80.6 

93 

199.4 

159 

318.2 

225 

437. 

300 

572 

960 

1760 

-38 

-36.4 

28 

82.4 

94 

201.2 

1GO 

320. 

226 

438.8 

310 

590 

970 

1778 

-37 

—34.6 

29 

84.2 

95 

203. 

161 

321.8 

227 

440.6 

320 

608 

980 

1796 

-36 

-32.8 

30 

86. 

96 

204.8 

162 

323.6 

228 

442.4 

330 

626 

990 

1814 

-35 

-31. 

31 

87.8 

97 

206.6 

163 

325.4 

229 

444.2 

340 

644 

1000 

1832 

-34 

—29.2 

32 

89.6 

98 

208.4 

164 

327.2 

230 

446. 

350 

662 

1010 

1850 

-33 

—27.4 

33 

91.4 

99 

210.2 

165 

329. 

231 

447.8 

360 

680 

1020 

1868 

-32 

-25.6 

34 

93.2 

100 

212. 

166 

330.8 

449.6 

370 

698 

1030 

1886 

-31 

-23.8 

35 

95. 

101 

213.8 

167 

332.6 

233 

451.4 

380 

716 

1040 

1904 

-30 

-22. 

36 

96.8 

102 

215.6 

168 

334.4 

234 

453.2 

390 

734 

1050 

1922 

-29 

-20.2 

37 

98.6 

103 

217.4 

169 

336.2 

235 

455. 

400 

752 

1060 

1940 

-28 

-18.4 

38 

100.4 

104 

219.2 

170 

338. 

236 

456.8 

410 

770 

1070 

1958 

-2? 

-16.6 

39 

102.2 

105 

221. 

171 

339.8 

237 

458.8 

420 

788 

1080 

1976 

-26 

-14.8 

40 

104. 

106 

^22.8 

172 

341.6 

238 

460.4 

430 

806 

1090 

1994 

-25 

-13. 

41 

105.8 

107 

224.6 

173 

343.4 

239 

462  2 

440 

824 

1100 

2012 

—24 

-11.2 

42 

107.6 

108 

226.4 

174 

345.2 

240 

464. 

450 

842 

1110 

2030 

-23 

-  9.4 

43 

109.4 

109 

228.2 

175 

347. 

241 

465.8 

460 

860 

1120 

2048 

-22 

—  7.6 

44 

111.2 

110 

230. 

176 

348.8 

242 

467.6 

470 

878 

1130 

2066 

-21 

—  5.8 

45 

113. 

111 

231.8 

177 

350.6 

243 

469.4 

480 

896 

1140 

2084 

-20 

-  4. 

4(5 

114.8 

112 

233  6 

178 

352.4 

244 

471  2 

490 

914 

1150 

2102 

-19 

22 

47 

116.6 

113 

235.4 

179 

354.2 

245 

473. 

500 

932 

1160 

2120 

-18 

-  O'A 

48 

118.4 

114 

237.2 

180 

356. 

246 

474.8 

510 

950 

1170 

2138 

—17 

+  1.4 

49 

120.2 

115 

239. 

181 

357.8 

247 

476.6 

520 

968 

1180 

2156 

-16 

3.2 

50 

122. 

116 

240.8 

182 

359.6 

248 

478.4 

530 

986 

1190 

2174 

-15 

5. 

51 

123.8 

117 

242.6 

183 

361.4 

249 

480.2 

540 

1004 

1200 

2192 

-14 

6.8 

52 

125.6 

118 

244.4 

184 

363.2 

250 

482. 

550 

1022 

1210 

2210 

-13 

8.6 

53 

127.4 

119 

246.2 

185 

365. 

251 

483.8 

560 

1040 

1220 

2228 

-12 

10.4 

54 

129.2 

120 

248. 

186 

366.8 

252 

485.8 

570 

1058 

1230 

2246 

—11 

12.2 

55 

131. 

121 

249.8 

187 

368.6 

253 

487.4 

580 

1076 

1240 

2264 

-10 

14. 

56 

132.8 

122 

251.9 

188 

370.4 

254 

489.2 

590 

1094 

1250 

2282 

-  9 

15.8 

57 

134.6 

123 

253.4 

189 

372.2 

255 

491. 

600 

1112 

1260 

2300 

-  8 

17.6 

58 

136.4 

124 

255.2 

190 

374. 

256 

492.8 

610 

1130 

1270 

2318 

7 

19.4 

59 

138.2 

125 

257. 

191 

375.8 

257 

494.6 

620 

1148 

1280 

2336 

-  6 

21.2 

(50 

140. 

126 

258.8 

192 

377.6 

258 

496.4 

630 

1166 

1290 

2354 

-  5 

23. 

01 

141.8 

127 

260.6 

193 

379.4 

259 

498.2 

640 

1184 

1300 

2372 

-  4 

24.8 

02 

143.6 

128 

262.4 

194 

381.2 

260 

500. 

650 

1202 

1310 

2390 

-  3 

26.0 

(53 

145.4 

129 

264.2 

195 

383. 

261 

501.8 

660 

1220 

1320 

2408 

-  2 

28.4 

04 

147.2 

130 

266. 

196 

384.8 

262  503.6 

670 

1238 

1330 

2426 

—  1 

30.2 

65 

149. 

131 

267.8 

197 

386.6 

263 

505.4 

680 

1256 

1340 

2444 

0 

3-3. 

66 

150.8 

13-' 

269.6 

198 

388.4 

264 

507.2 

690 

1274 

1350 

2462 

4-  l 

33.8 

67 

152.6 

133 

271.4 

199 

390.2 

265 

509. 

700  j  1292 

1360 

2480 

2 

35.6 

68 

154.4 

134 

273.2 

200 

392. 

266 

510.8 

710J1310 

1370 

2498 

3 

37.4 

09 

156.2 

135 

275. 

201 

393.8 

267 

512.6 

720 

1328 

1380 

2516 

4 

39.2 

70 

158. 

136 

276.8 

202 

395.6 

268 

514.4 

730 

1346 

1390 

2534 

5 

41. 

71 

159.8 

137 

278.6 

203 

C97.4 

269 

516.2 

740 

1364 

1400 

SS52 

6 

42.8 

72 

161.6 

138 

280.4 

204 

399.2 

270 

518. 

750 

1382 

1410 

2570 

7 

44.6 

73 

163.4 

139 

282.2 

205 

401. 

271 

519.8 

700 

1400 

1420 

2588 

8 

46.4 

74 

165.2 

140 

284. 

206 

402.8 

272 

521.6 

770 

1418 

1430 

2606 

9 

48.2 

75 

167. 

141 

285.8 

207 

404.6 

273 

523.4 

780 

1436 

1440 

2624 

10 

50. 

70 

168.8 

142 

287.6 

208 

406.4 

^74 

525.2 

790 

1454 

1450 

•3642 

11 

51.8 

77 

170.6 

143 

289.4 

209 

408.2 

275 

527. 

800 

1472 

1400 

26(50 

12 

53.6 

78 

172.4 

144 

291.2 

210 

410. 

276 

528.8 

810 

1490 

1470 

2078 

13 

55.4 

79 

174.2 

145 

293. 

211 

411.8 

277 

530.6 

8-JO 

1508 

1480 

2696 

14 

57.2 

80 

176. 

146 

294.8 

212 

413.6 

278 

532.4 

830 

1526 

1490 

2714 

15 

59. 

81 

177.8 

147 

296.6 

213 

415.4 

279 

534.2 

840 

1544 

1500 

2732 

16 

60.8 

82 

179.6 

148 

298.4 

214 

417.2 

280 

536. 

850 

1562 

1510 

2750 

17 

62.6 

83 

181  4 

149 

300.2 

215 

419. 

281 

537.8 

860 

1580 

1520 

2768 

18 

64.4 

84 

183.2 

150 

302. 

216 

420.8 

282 

539.6 

870  1598 

1530 

2786 

19 

66.2 

85 

185. 

151 

303.8 

217 

422.6 

283 

541.4 

880J1616 

1540 

2804 

20 

68. 

80 

J86.8 

152 

305.6 

218 

424.4 

284 

543.2 

890  1034 

1550 

2822 

21 

69.8 

87 

188.6 

153 

307.4 

219 

426.2 

285 

545. 

900  1652 

1600 

2912 

22 

71.6 

,88 

190.4 

154 

309.2 

220 

428. 

.286 

546.8 

910 

1670 

1650 

3002 

23 

73.4 

89 

192.2 

155 

311. 

221 

429.8 

287 

548.6 

920 

1688 

1700 

3092 

24 

75.2 

90 

194. 

156 

312.8 

222 

431  .6 

288 

550.4 

930 

1706 

1750 

3182 

25 

77. 

91 

195.8 

157 

314.6 

223 

433.4 

289 

552.2 

940  1724 

1800 

3^72 

TEMPERATURES,  FAHRENHEIT  AND 
CENTIGRADE. 


F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

-40 

-40. 

26 

—  3.3 

92 

33.3 

158 

70. 

224 

106.7 

290 

143.3 

360 

182.2 

—39 

—39.4 

27 

—  2.8 

93 

33.9 

159 

70.6 

225 

107.2 

291 

143.9 

370 

187.8 

—38 

-38.9 

28 

—  2  2 

94 

34.4 

160 

71.1 

226 

107.8 

292 

144.4 

380 

193.3 

—37 

—38.3 

29 

1  i~ 

95 

35. 

161 

71.7 

227 

108.3 

293 

145. 

390 

198.9 

-36 

-37.8 

30 

—  i!i 

96 

35.6 

162 

72.2 

228 

108.9 

294 

145.6 

400 

204.4 

-35 

—37.2 

31 

-0.6 

97 

36.1 

163 

72.8 

229 

109.4 

295 

146.1 

410 

210. 

-34 

—36.7 

32 

0. 

98 

36.7 

164 

73.3 

230 

110. 

296 

146.7 

420 

215.6 

-33 

—36.1 

33 

-f  0.6 

99 

37.2 

165 

73.9 

231 

110.6 

297 

147.2 

430 

221.1 

-32 

—35.6 

34 

1.1 

100 

37.8 

166 

74.4 

232 

111.1 

298 

147.8 

440 

226.7 

-31 

—35. 

35 

1.7 

101 

38.3 

167 

75. 

233 

111.7 

299 

148.3 

450 

232.2 

—30 

—34.4 

36 

2.2 

102 

38.9 

168 

75.6 

234 

112.8 

300 

148.9 

460 

237.8 

—29 

-33.9 

37 

2.8 

103 

39.4 

169 

76.1 

235 

112.8 

301 

149.4 

470 

243.3 

—28 

-33.3 

38 

3.3 

104 

40. 

170 

76.7 

236 

113.3 

302 

150. 

480 

248.9 

—  27 

—32.8 

39 

3.9 

105 

40.6 

171 

77.2 

237 

113.9 

303 

150.6 

490 

254.4 

—26 

-32.2 

40 

4.4 

106 

41.1 

172 

77.8 

238 

114.4 

304 

151.1 

500 

260. 

—25 

-31.7 

41 

5. 

107 

41.7 

173 

78.3 

239 

115. 

305 

151.7 

510 

265.6 

—24 

-31.1 

42 

5.6 

108 

42.2 

174 

78.9 

240 

115.6 

306 

152.2 

520 

271.1 

-23 

—30.6 

43 

6.1 

109 

42.8 

175 

79.4 

241 

116.1 

307 

152.8 

530 

276.7 

-22 

—30. 

44 

6.7 

110 

43.3 

176 

80. 

242 

116.7 

308 

153.3 

540 

282.2 

-21 

-29.4 

45 

7.2 

111 

43.9 

177 

80.6 

243 

117.2 

309 

153.9 

550 

287.8 

-20 

-28.9 

46 

7.8 

112 

44.4 

178 

81.1 

244 

117.8 

310 

154.4 

560 

293.3 

-19 

—28.3 

47 

8.3 

113 

45. 

179 

81.7 

245 

118.3 

311 

155. 

570 

298.9 

-18 

-27.8 

48 

8.9 

114 

45.6 

180 

82.2 

246 

118.9 

312 

155.6 

580 

304.4 

-17 

—27.2 

49 

9.4 

115 

46.1 

181 

82.8 

247 

119.4 

313 

156.1 

590 

310. 

—  16 

—26.7 

50 

10. 

116 

46.7 

182 

83.3 

248 

120. 

314 

156.7 

600 

315.6 

—15 

—26.1 

51 

10.6 

117 

47.2 

183 

83.9 

249 

120.6 

315 

157.2 

61.0 

321.1 

—14 

—25.6 

52 

11.1 

118 

47.8 

184 

84.4 

250 

121.1 

316 

157.8 

620 

326.7 

—13 

—25. 

53 

11.7 

119 

48.3 

185 

85. 

251 

121.7 

317 

158.3 

630 

332.2 

—12 

—24  .4 

54 

12.2 

120 

48.9 

186 

85.6 

252 

122.2 

318 

158.9 

640 

337.8 

—11 

—23.9 

55 

12.8 

121 

49.4 

187 

86.1 

253 

122.8 

319 

159.4 

650 

343.3 

—10 

—23.3 

56 

13.3 

122 

50. 

188 

86.7 

254 

123.3 

320 

160. 

660 

348.9 

-  9 

—  22  8 

57 

13.9 

123 

50.6 

189 

87.2 

255 

123.9 

321 

160.6 

670 

354.4 

—  8 

—22^2 

58 

14.4 

124 

51.1 

190 

87.8 

256 

124.4 

32:. 

161.1 

680 

360. 

-  7 

—21.7 

59 

15. 

125 

51.7 

191 

88.3 

257 

125. 

323 

161.7 

690 

365.6 

—  6 

—21.1 

60 

15.6 

126 

52.2 

192 

88.9 

258 

125.6 

324 

162.2 

700 

371.1 

—  5 

—20.6 

61 

16.1 

127 

52.8 

193 

89.4 

259 

126.1 

325 

162.8 

710 

376.7 

-  4 

—20. 

62 

16.7 

128 

53.3 

194 

90. 

m 

126.7 

326 

163.3 

720 

382.2 

-  3 

—19.4 

63 

17.2 

129 

53.9 

195 

90.6 

261 

127.2 

327 

163.9 

730 

387.8 

—  2 

—18.9 

64 

17.8 

130 

54.4 

196 

91.1 

262 

127.8 

328 

164.4 

740 

393.3 

—  1 

—18  3 

65 

18.3 

131 

55. 

197 

91.7 

263 

128.3 

3-^9 

165. 

750 

398.9 

0 

-17.8 

66 

18.9 

132 

55.6 

198 

92.2 

264 

128.9 

330 

165.6 

760 

404.4 

+  1 

—17.2 

67 

19.4 

133 

56.1 

199 

92.8 

265 

129.4 

331 

166.1 

770 

410. 

2 

—16.7 

68 

20. 

134 

56.7 

200 

93.3 

266 

130. 

332 

166.7 

780 

415.6 

3 

-16.1 

69 

20.6 

135 

57.2 

201 

93.9 

267 

130.6 

333 

167.2 

790 

421.1 

4 

—15.6 

70 

21.1 

136 

57.8 

202 

94.4 

268 

131.1 

334 

167.8 

800 

426.7 

5 

—15. 

71 

21.7 

137 

58.3 

203 

95. 

26!) 

131.7 

335 

168.3 

810 

432.2 

6 

—14.4 

72 

22.2 

138 

58.9 

204 

95.6 

270 

132.2 

336 

168.9 

820 

437.8 

7 

—  13.9 

73 

22.8 

139 

59.4 

205 

96.1 

271 

132.8 

337 

169.4 

830 

443.3 

8 

—13.3 

74 

23.3 

140 

60. 

206 

96.7 

272 

133.3 

338 

170. 

840 

448.9 

9 

—12.8 

75 

23.9 

141 

60.6 

207 

97.2 

273 

133.9 

339 

170.6 

850 

454.4 

10 

—12.2 

76 

24.4 

142 

61.1 

208 

97.8 

274 

134.4 

340 

171.1 

860 

460. 

11 

—11.7 

77 

25. 

143 

61.7 

209 

98.3 

275 

135. 

341 

171.7 

870 

465.6 

12 

—11.1 

78 

25.6 

144 

62.2 

210 

98.9 

276 

135.6 

342 

172.2 

880 

471.1 

13 

—10.6 

79 

26.1 

145 

62.8 

211 

99.4 

277 

136.1 

343 

172.8 

890 

476.7 

14 

-10. 

80 

26.7 

146 

63.3 

212 

100. 

278 

136.7 

344 

173.3 

900 

482.2 

15 

—  9.4 

81 

27.2 

147 

63.9 

213 

100.6 

279 

137.2 

345 

173.9 

910 

487.8 

16 

—  8.9 

82 

27.8 

148 

64.4 

214 

101.1 

280 

137.8 

346 

174.4 

920 

493.3 

17 

—  8.3 

83 

28.3 

149 

65. 

215 

101.7 

281 

138.3 

347 

175. 

930 

498.9 

18 

-  7.8 

84 

28.9 

150 

65.6 

216 

102.2 

282 

138.9 

348 

175.6 

940 

504.4 

19 

—  7.2 

85 

29.4 

151 

66.1 

217 

102.8 

283 

139.4 

349 

176.1 

950 

510. 

20 

—  6.7 

86 

30. 

152 

66.7 

218 

103.3 

284 

140. 

350 

176.7 

960 

515.6 

21 

—  6.1 

87 

30.6 

153 

67.2 

219 

103.9 

.>85 

140.6 

351 

177.2 

970 

521.1 

22 

-  5.6 

88 

31.1 

154 

67.8 

220 

104.4 

286 

141.1 

352 

177.8 

980 

526.7 

23 

—  5. 

89 

31.7 

155 

68.3 

221 

105. 

287 

141.7 

353 

178.3 

990 

532.2 

24 

—  4.4 

90 

32.2 

156 

68.9 

222 

105.6 

288 

142.2 

354 

178.9 

000 

537.8 

25 

—  3.9 

91 

32.8 

157 

69.4 

223 

106.1 

289 

142.8 

355 

179.4 

010 

543.3 

PYROMETRY.  451 

Platinum  or  Copper  Ball  Pyrometer.— A  weighed  piece  of 
platinum,  copper,  or  iron  is  allowed  to  remain  in  the  furnace  or  heated 
chamber  till  it  has  attained  the  temperature  of  its  surroundings.  It  is  then 
suddenly  taken  out  and  dropped  into  a  vessel  containing  water  of  a  known 
weight  and  temperature.  The  water  is  stirred  rapidly  and  its  maximum 
temperature  taken.  Let  W—  weight  of  the  water,  iv  the  weight  of  the  ball, 

=  the  original  and  T  the  final  heat  of  the  water,  and  S  the  specific  heat  of 
the  metal;  then  the  temperature  of  fire  may  be  found  from  the  formula 

x=W(T-t)   {   T 

The  mean  specific  heat  of  platinum  between  32°  and  446°  F.  is  .03333  or 
1/30  that  of  water,  and  it  increases  with  the  temperature  about  .000305  for 
each  100°  F.  For  a  fuller  description,  by  J.  C.  Hoadley ,  see  Trans.  A.  S.  M.  E., 
vi.  702.  Compare  also  Henry  M.  Howe,  Trans.  A.  I.  M.  E.,  xviii.  728. 

For  accuracy  corrections  are  required  for  variations  in  the  specific  heat  of 
the  water  and  of  the  metal  at  different  temperatures,  for  loss  of  heat  by 
radiation  from  the  metal  during  the  transfer  from  the  furnace  to  the  water, 
and  from  the  apparatus  during  the  heating  of  the  water;  also  for  the  heat- 
absorbing  capacity  of  the  vessel  containing  the  water. 

Fire-clay  or  fire-brick  may  be  used  instead  of  the  metal  ball. 

Le  Cliatelier's  Tliermo-eleetric  Pyrometer,— For  a  very  full 
description  see  paper  by  Joseph  Struthers,  School  of  Mines  Quarterly,  vol. 
xii,  1891;  also,  paper  read  by  Prof.  Roberts-Austen  before  the  Iron  and  Steel 
Institute,  May  7,  1891. 

The  principle  upon  which  this  pyrometer  is  constructed  is  the  measure- 
ment of  a  current  of  electricity  produced  by  heating  a  couple  composed  of 
two  wires,  one  platinum  and  the  other  platinum  with  10%  rhodium— the  cur- 
rent produced  being  measured  by  a  galvanometer. 

The  composition  of  the  gas  which  surrounds  the  couple  has  no  influence 
on  the  indications. 

When  temperatures  above  2500°  F.  are  to  be  studied,  the  wires  must  have 
an  isolating  support  and  must  be  of  good  length,  so  that  all  parts  of  a  fur- 
nace can  be  reached. 

For  a  Siemens  furnace,  about  llt^feet  is  the  general  length.  The  wires 
are  supported  in  an  iron  tube,  ^  inch  interior  diameter  and  held-in  place  by 
a  cylinder  of  refractory  clay  having  two  holes  bored  through,  in  which  the 
wires  are  placed.  The  shortness  of  time  (five  seconds)  allows  the  tempera- 
ture to  be  taken  without  deteriorating  the  tube. 

Tests  made  by  this  pyrometer  in  measuring  furnace  temperatures  under 
a  great  variety  of  conditions  show  that  the  readings  of  the  scale  uncorreeted 
are  always  within  45°  F.  of  the  correct  temperature,  and  in  the  majority  of 
industrial  measurements  this  is  sufficiently  accurate.  Le  Chateliers  py- 
rometer Is  sold  by  Queen  &  Co.,  of  Philadelphia. 

Graduation  of  I*e  Chatelier's  Pyrometer.— W.  C.  Roberts- 
Austen  in  his  Researches  on  the  Properties  of  Alloys,  i'roc.  Inst.  M.  E.  1892, 
says  :  The  electromotive  force  produced  by  heating  the  thermo- junction 
to  any  given  temperature  is  measured  by  the  movement  of  the  spot  of  light 
on  the  scale  graduated  in  millimetres.  A  formula  for  converting  the  divi- 
sions of  the  scale  into  thermometric  degrees  is  given  by  M.  Le  Chatelier;  but 
it  is  better  to  calibrate  the  scale  by  heating  the  thermo-junction  to  temper- 
atures which  have  been  very  carefully  determined  by  the  aid  of  the  air- 
thermometer,  and  then  to  plot  the  curve  from  the  data  so  obtained.  Many 
fusion  and  boiling-points  have  been  established  by  concurrent  evidence  of 
various  kinds,  and  are  now  very  generally  accepted.  The  following  table 
contains  certain  of  these  : 


Deg.  F.  Deg.  C. 

212  100  Water  boils. 

618  326  Lead  melts. 

676  358  Mercury  boils. 

779  415  Zinc  melts. 

838  448  Sulphur  boils. 

1157  625  Aluminum  melts. 

1229  665  Selenium  boils. 


Deg.  F.  Deg.  C. 
1733  945    Silver  melts. 

1859  1015    Potassium  sul- 
phate melts. 

1913  1045    Gold  melts. 

1929  1054    Copper  melts. 

2732  1500    Palladium  melts. 

3227  1775    Platinum  melts. 


The  Temperatures  Developed  in  Industrial  Furnaces.— 

M.  Le  Chatelier  states  that  by  means  of  his  pyrometer  he  has  discovered 
that  the  temperatures  which  occur  in  melting  steel  and  in  other  industrial 
operations  have  been  hitherto  overestimated. 


452  HEAT. 

M.  Le  Chatelier  finds  the  melting  heat  of  white  cast  iron  1135°  (2075°  F.), 
and  that  of  gray  cast  iron  1220°  (22-38°  F.).  Mild  steel  melts  at  1475°  (2687° 
F.),  semi-mild  at  1455°  (2651°  F.),  and  hard  steel  at  1110°  (2570°  F.).  The 
furnace  for  hard  porcelain  at  the  end  of  the  baking  has  a  heat  of  1370° 
(2498°  F.).  The  heat  of  a  normal  incandescent  lamp  is  1800°  (3272°  F.),  but 
it  may  be  pushed  to  beyond  2100°  (3812°  F.). 

Prof.  Roberts- Austen  (Recent  Advances  in  Pyrometry,  Trans.  A.  I.  M.  E., 
Chicago  Meeting,  1S93)  gives  an  excellent  description  of  modern  forms  of 
pyrometers.  The  following  are  some  of  his  temperature  determinations. 

GOLD-MELTING,  ROYAL  MINT. 

Degrees.  Degrees. 

Centigrade.  Fahr. 

Temperature  of  standard  alloy,  pouring  into  moulds.   . . .  1180  2156 
Temperature  of  standard  alloy,  pouring  into  moulds  (on 

a  previous  occasion,  by  thermo-couple) 1147  2097 

Annealing  blanks  for  coinage,  temperature  of  chamber..    890  1634 

SILVER-MELTING,  ROYAL  MINT. 

Temperature  of  standard  alloy,  pouring  into  mould 980  1796 

TEN-TON  OPEN-HEARTH  FURNACE,  WOOLWICH  ARSENAL. 

Temperature  of  steel,  0.3$  carbon,  pouring  into  ladle 1645  2993 

Temperature  of  steel,  0.3$  carbon,  pouring  into  large 

mould 1580  2876 

Reheating  furnace,  Woolwich  Arsenal,  temperature  of 

interior 930  1706 

Cupola  furnace,  temperature  of  No.  2,  cast-iron  pouring 

into  ladle 1600  2912 

The  following  determinations  have  been  effected  by  M.  Le  Chatelier: 

BESSEMER   PROCESS. 

Six-ton    Converter. 

Degrees.        Degrees. 
Centigrade     Fahr. 

A.  Bath  of  slag 1580  2876 

B.  Metal  in  ladle 1640  2984 

C.  Metal  in  ingot  mould 1580  2876 

D.  Ingot  in  reheating  furnace... 1200  2192 

E    Ingot  under  the  hammer 1080  1976 

OPEN-HICARTH  FURNACE  (Siemens). 

Semi-Mild  Steel. 

A    Fuel  gas  near  gas  generator. 720  1328 

B.  Fuel  gas  entering  into  bottom  of  regenerator  chamber    400  752 

C.  Fuel  gas  issuing  from  regenerator  chamber. -  1200  2192 

Air  issuing  from  regenerator  cham  ber 1000  1832 

CHIMNEY  GASES. 

Furnace  in  perfect  condition  300  590 

OPEN-HEARTH  FURNACE. 

End  of  the  melting  of  pig  charge 1420  2588 

Completion  of  conversion .   1500  2732 

MOLTEN  STEEL. 
In  the  ladle— Commencement  of  casting 1580  2876 

End  of  casting 1490  2714 

In  the  moulds...     1520  2768 

For  very  mild  (soft)  steel  the  temperatures  are  higher  by  50°  C. 

SIEMENS  CRUCIBLE  OR  POT  FURNACE. 

1600°  C.,  2912°  F. 
ROTARY  PUDDLING  FURNACE. 

Degrees  C.  Degrees  F 

Furnace ...   1340-1230      2444-2246 

Puddled  ball— End  of  operation 1330  2420 


PYROMETRY.  453 

BLAST-FURNACE  (Gray -Bessemer  Pig). 

Opening  in  face  of  tuyere 1930  3506 

Molten  metal — Commencement  of  fusion 

End,  or  prior  to  tapping 1570  2858 

HOFFMAN  RED-BRICK  KILN. 
Burning  temperatures 1100  2012 

Tlie  Wiborgh  Air-pyrometer.  (E.  Trotz,  Trans.  A.  I.  M.  E. 
1892 .)_The  inventor  using  the  expansion-coefficient  of  air,  as  determined 
by  Gay-Lussae,  Dulon,  Rudberg,  and  Regnault,  bases  his  construction  on 
the  following  theory  :  If  an  air-volume,  V,  enclosed  in  a  porcelain  globe 
and  connected  through  a  capillary  pipe  with  the  outside  air,  be  heated  to 
the  temperature  T  (which  is  to  be'deterrnined)  and  thereupon  the  connection 
be  discontinued,  and  there  be  then  forced  into  the  globe  containing  V 
another  volume  of  air  V  of  known  temperature  t,  which  was  previously 
under  atmospheric  pressure  H,  the  additional  pressure  /i,  due  to  the  addi- 
tion of  the  air- volume  V  to  the  air-volume  V,  can  be  measured  by  a  ma- 
nometer. But  this  pressure  is  of  course  a  function  of  the  temperature  T. 
Hefore  the  introduction  of  V,  we  have  the  two  separate  air-volumes,  F"at 
the  temperature  2' and  V  at  the  temperature  t,  both  under  the  atmospheric 
pressure  H.  After  the  forcing  in  of  V  into  the  globe,  we  have,  on  the 
contrary,  only  the  volume  V  of  the  temperature  2',  but  under  the  pressure 
H+h. 

The  Wiborgh  Air-pyrometer  is  adapted  for  use  at  blast-furnaces,  smelting- 
works,  hardening  and  tempering  furnaces,  etc.,  where  determinations  of 
temperature  from  0°  to  2400°  F.  are  required. 

Seger's  Fire-clay  Pyrometer.  (H.  M.  Howe,  Eng.  and  Mining 
Jour.,  June  7,  1890.)— Professor  Seger  uses  a  series  of  slender  triangular 
lire-clay  pyramids,  about  3  inches  high  and  %  inch  wide  at  the  base,  and 
each  a  little  less  fusible  than  the  next :  these  he  calls  "normal  pyramids  '' 
("•  normal-kegel  ").  When  the  series  is  placed  in  a  furnace  whose  temper- 
ature is  gradually  raised,  one  after  another  will  bend  over  as  its  range  of 
plasticity  is  reached  ;  and  the  temperature  at  which  it  has  bent,  or  4k  wept," 
so  far  that  its  apex  touches  the  hearth  of  the  furnace  or  other  level  surface 
on  which  it  is  standing,  is  selected  as  a  point  on  Seger's  scale.  These  points 
may  be  accurately  determined  by  some  absolute  method,  or  they  may 
merely  serve  to  give  comparative  results.  Unfortunately,  these  pyramids 
afford  no  indications  when  the  temperature  is  stationary  'or  falling. 

Mesure  and  Nowel's  Pyrometric  Telescope.  (Ibid.)— Mesur6 
and  Nouel's  pyrometric  telescope  gives  us  an  immediate  determination  of 
the  temperature  of  incandescent  bodies,  and  is  therefore  much  better 
adapted  to  cases  where  a  great  number  of  observations  are  to  be  made,  and 
at  short  intervals,  than  Seger's.  Such  cases  arise  in  the  careful  heating  of 
steel.  The  little  telescope,  carried  in  the  pocket  or  hung  from  the  neck,  can 
be  used  by  foreman  or  heater  at  any  moment, 

It  is  based  on  the  fact  that  a  plate  of  quartz,  cut  at  right  angles  to  the 
axis,  rotates  the  plane  of  polarization  of  polarized  light  to  a  degree  nearly 
inversely  proportional  to  the  square  of  the  length  of  the  waves  ;  and, 
further,  on  the  fact  that  while  a  body  at  dull  redness  merely  emits  red 
light,  as  the  temperature  rises,  the  orange,  yellow,  green,  and  blue  waves 
successively  appear. 

If,  now,  such  a  plate  of  quartz  is  placed  between  two  Nicol  prisms  at 
right  angles,  "a  ray  of  monochromatic  light  which  passes  the  first,  or 
polarizer,  and  is  watched  through  the  second,  or  analyzer,  is  not  extin- 
guished as  it  was  before  interposing  the  quartz.  Part  of  the  light  passes 
the  analyzer,  and,  to  again  extinguish  it,  we  must  turn  one  of  the  Nicols  a 
certain  angle,"  depending  on  the  length  of  the  waves  of  light,  and  hence  on 
the  temperature  of  the  incandescent  object  which  emits  this  light.  Hence 
the  angle  through  which  we  must  turn  the  analyzer  to  extinguish  the  light 
is  a  measure  of  the  temperature  of  the  object  observed. 

The  instrument  is  made  by  Ducretet,  of  Paris,  in  two  sizes  ;  cost,  $20  and 


454 


HEAT. 


the  difference  of  temperature  between  the  inflowing  and  outflowing  air.  If 
the  inflowing  air  be  made  to  vary  with  the  temperature  to  be  measured, 
and  the  outflowing  air  be  kept  at  a  certain  constant  temperature,  then  the 
tension  in  the  space  or  chamber  between  the  two  apertures  will  be  an  exact 
measure  of  the  temperature  of  the  inflowing  air,  and  hence  of  the  tem- 
perature to  be  measured. 

In  operation  it  is  necessary  that  the  air  be  sucked  into  it  through  the  first 
minute  aperture  at  the  temperature  to  be  measured,  through  the  second 
aperture  at  a  lower  but  constant  temperature,  and  that  the  suction  be  of  a 
constant  tension.  The  first  aperture  is  therefore  located  in  the  end  of  a 
platinum  tube  in  the  bulb  of  a  porcelain  tube  over  which  the  hot  blast 
sweeps,  or  inserted  into  the  pipe  or  chamber  containing  the  gas  whose  tern 
perature  is  to  be  ascertained. 

The  second  aperture  is  located  in  a  coupling,  surrounded  by  boiling  water, 
and  the  suction  is  obtained  by  an  aspirator  and  regulated  by  a  column  of 
water  of  constant  height. 

The  tension  in  the  chamber  between  the  apertures  is  indicated  by  a 
manometer. 

The  Air-thermometer.  (Prof.  R.  C.  Carpenter,  En<fg  News,  Jan.  5, 
18U3.)— Air  is  a  perfect  thermometric  substance,  and  if  a  given  mass  of  air- 
be  considered,  the  product  of  its  pressure  and  volume  divided  by  its 
absolute  temperature  is  in  every  case  constant.  If  the  volume  of  air 
remain  constant,  the  temperature  will  vary  with  the  pressure;  if  the 
pressure  remain  constant  the  temperature  will  vary  with  the  volume.  As 
the  former  condition  is  more  easily  attained  air-thermometers  are  usually 
constructed  of  constant  volume,  in  which  case  the  absolute  temperature 
will  vary  with  the  pressure. 

If  we  denote  pressure  by  p  and  p',  the  corresponding  absolute  temper- 
atures by  Tand  T',  we  should  have 


p:p'::T:T'    and    T'=p'— . 

The  absolute  temperature  Tis  to  be  considered  in  every  case  460  high ei 
than  the  thermometer-reading  expressed  in  Fahrenheit  degrees.  From  the 
form  of  the  above  equation,  if  the  pressure  p  corresponding  to  a  known 
absolute  temperature  T  be  known,  T'  can  be  found.  The  quotient  T/p  is  a 
constant  which  may  be  used  in  all  determinations  with  the  instrument.  The 
pressure  on  the  instrument  can  be  expressed  in  inches  of  mercury,  and  is 
evidently  the  atmospheric  pressure  b  as  shown  by  a  barometer,  plus  or 
minus  an  additional  amount  h  shown  by  a  manometer  attached  to  the  air 
thermometer. 

That  is.  in  general,  p  =  b  X  ft. 

The  temperature  of  3'2°  F.  is  fixed  as  the  point  of  melting  ice,  in  which 
case  T=  460  X  32  =  492°  F.  This  temperature  can  be  produced  by  sur- 
rounding the  bulb  in  melting  ice  and  leaving  several  minutes,  so  that  the 
temperature  of  the  confined  air  shall  acquire  that  of  the  surrounding  ice. 
When  the  air  is  at  that  temperature,  note  the  reading  of  the  attached 
manometer  A,  and  that  of  a  barometer;  the  sum  will  be  the  value  of  p  cor- 
responding to  the  absolute  temperature  of  492°  F.  The  constant  of  the 
instrument,  K  =  492  —  p,  once  obtained,  can  be  used  in  all  future  determina- 
tions. 

High  Temperatures  judged  by  Color.-The  temperature  of  a 
body  can  be  approximately  judged  by  the  experienced  eye  unaided,  and 
M.  Pouillet  has  constructed  a  table,  which  has  been  generally  accepted, 
giving  the  colors  and  their  corresponding  temperature  as  below: 


] 

Incipient  red  heat.. 
Dull  red  heat  
Incipient  cherry-red 
heat  

)eg.  C. 
525 
7'00 

800 

Deg.  F. 
977 
1292 

1472 

Cherry-red  heat  
C  1  e  a  r   cherry  -  red 
heat.  .  . 

900 
1000 

1652 
183-2 

Deg.  C. 

Deep  orange  heat. . .     1 1 00 
Clear  orange  heat ..     1200 

White  heat 

Bright  white  heat. 


1800 
1400 
)  1500 

Dazzling  white  heat  V  to 
1  1600 


Deg.  F. 
2021 
2192 
2372 
2552 
2732 
to 
2912 


The  results  obtained,  however,  are  unsatisfactory,  as  much  depends  on 
the  susceptibility  of  the  retina  of  the  observer  to  light  as  well  as  the  degree 
ot  illumination  under  which  the  observation  is  made. 


QUANTITATIVE  MEASUREMENT  OF   HEAT.  455 

A  bright  bar  of  iron,  slowly  heated  in  contact  with  air,  assumes  the  fol- 
lowing tints  at  annexed  temperatures  (Claudel): 

Cent.  Fahr. 

Indigo  at 288  550 

Blueat 293  559 

Green  at 332  630 

"Oxide-gray" 400  752 


Cent.  Fahr. 

Yellow  at 225  437 

Orange  at 243  '473 

Redat 265  509 

Violet  at 277  531 


BOILING  POINTS  AT  ATMOSPHERIC  PRESSURE. 

14.7  Ibs.  per  square  inch. 

Ether,  sulphuric  .............  100°  F.       Average  sea-water  .........  213.2°  F. 

Carbon  bisulphide  .....  .....  118  Saturated  brine  ............  226 

Ammonia  ....................  140  Nitric  acid  ..................  248 

Chloroform  ..................  140  Oil  of  turpentine  ...........  315 

Bromine  ...................  145  Phosphorus  ................  554 

Woodspirit  ...............   .  150  Sulphur  ...................  570 

Alcohol  ......................  173  Sulphuric  &cid  .............  590 

Benzine  ......................  176  Linseed  oil  ................  597 

Water  .....................  212  Mercury  ...........    ........  676 

The  boiling  points  of  liquids  increase  as  the  pressure  increases.  The  boil- 
ing point  of  water  at  any  given  pressure  is  the  same  as  the  temperature  of 
saturated  steam  of  the  same  pressure.  (See  Steam.) 

MELTING-POINTS  OF  VARIOUS  SUBSTANCES. 

The  following  figures  are  given  by  Clark  (on  the  authority  of  Pouillet, 

Claudel,  and  Wilson),  except  those  marked  *,  which  are  given  by  Prof.  Rob- 

erts-Austen in  his  description  of  the  Le  Chatelier  pyrometer.    These  latter 
are  probabty  the  most  reliable  figures. 

Sulphurous  acid  ..........  -  148°  F.  Alloy,  1  tin,  1  lead.  .    370  to    466°  F. 

Carbonic  acid  .............  —  108  Tin  ...............    442  to    446 

Mercury  ...................   -     39  Cadmium  .........  .........     442 

Bromine  ..................  +      9.5  Bismuth  ............     504  to    507 

Turpentine  ...........  .  ......     14  Lead  ................    608  to    618* 

Hyponitric  acid  .............     16  Zinc    ..............     680  to    779* 

Ice  ........................  -    32  Antimony  ..........     810  to  1150 

Nitro-glycerine  ..............    45  Aluminum  .................  1157* 

Tallow  ...............  .  .  ......     92  Magnesium  .................  1200 

Phosphorus  .....  .  ...........  112  Calcium  .........  Full  red  heat. 

Acetic  acid.   ...  ............  113  Bronze  .................  1692 

Stearine  ..............  109  to  120  Silver  ..............  1733*  to  1873 

Spermaceti  ..............  „  .  .  120  Potassium  sulphate  ........  1859* 

Margaric  acid  ........  131  to  140  Gold  ..............  1913*  to  2282 

Potassium  ...........  136  to  144  Copper  ............  1929*  to  1996 

Wax  ..................  142  to  154  Cast  iron,  white.  .  .  1922    to  2075* 

Stearic  acid  ................  158  "         gray  2012  to  2786  2228* 

Sodium  ...............  194  to  208  Steel  ...............  2372   to  2532 

Alloy,  3  lead,  2  tin,  5  bismuth  199  "    hard  .....  2570*;  mild,  2687* 

Iodine  .  .  ....................  ,  225  Wrought  iron  ......  2732    to  2912 

Sulphur  .................  ....  239  Palladium  ..................  2732* 

Alloy,  \y%  tin,  1  lead  .........  334  Platinum  ..............  ...  3227* 


QUANTITATIVE  MEASUREMENT  OF  HEAT. 

Unit  of  Heat*  —  The  British  unit  of  heat,  or  British  thermal  unit 
(B.  T.  U.),  is  that  quantity  of  heat  which  is  required  to  raise  the  temperature 
of  1  Ib.  of  pure  water  1°  Fahr.,  at  or  near  39°.  1  F.,  the  temperature  of  maxi- 
mum density  of  water. 

The  French  thermal  unit,  or  calorie,  is  that  quantity  of  heat  which  is  re- 
quired to  raise  the  temperature  of  1  kilogramme  of  pure  water  1°  Cent  ,  at  or 
about  4°  C.,  which  is  equivalent  to  39°.  1  F. 

1  French  calorie  =  3.968  British  thermal  units;  1  B.  T.  U.  =  .252  calorie. 
The  "  pound  calorie  "  is  sometimes  used  by  English  writers;  it  is  the  quail- 


456 


HEAT. 


tity  of  heat  required  to  raise  the  temperature  of  1  Ib.  of  water  I6  C.  1  Ib. 
calorie  =  9/5  B.T.U.  =  0.4536  calorie.  The  heat  of  combustion  of  carbon,  to 
CO2,  is  said  to  be  8080  calories.  This  figure  is  used  either  for  French  calories  or 
tor  pound  calories,  as  it  is  the  number  of  pounds  of  water  that  can  be  raised 
1°  C.  by  the  complete  combustion  of  1  Ib..  of  carbon,  or  the  number  of 
kilogrammes  of  water  that  can  be  raised  1°  C.  by  the  combustion  of  1  kilo, 
of  carbon;  assuming  in  each  case  that  all  the  heat  generated  is  transferred 
to  the  water. 

The  Mechanical  Equivalent  of  Heat  is  the  number  of  foot- 
pounds of  mechanical  energy  equivalent  to  one  British  thermal  unit,  heat 
and  mechanical  energy  being  mutually  convertible.  Joule's  experiments, 
1843-50,  gave  the  figure  772,  which  is  known  as  Joule's  equivalent.  More  re- 
cent experiments  by  Prof.  Rowland  (Proc.  Am.  Acad.  Arts  and  Sciences^ 
1880;  see  also  Wood*s  Thermodynamics}  give  higher  figures,  and  the  most 
probable  average  is  now  considered  to  be  778. 

1  heat-unit  is  equivalent  to  778  ft.-lbs.  of  energy.  1  ft.  Ib.  =  1/778  =.0012852 
heat-units.  1  horse-power  =  33,000  ft.-lbs.  per  minute  =  2545  heat-uuits  per 
hour  =  42.416  -\-  per  minute  =  .70694  per  second.  1  Ib.  carbon  burned  to  CO., 
=  14,544  heat-units.  1  Ib.  C.  per  II. P.  per  hour  =  2545  V14544  =  in%  efficiency 
(.174986). 

Heat  of  Combustion  of  Various  Substances  in  Oxygen, 


Heat-units. 

Authority. 

Cent. 

Fahr. 

(  34.462 

62,032 

Favre  and  Silbermann. 

Hydrogen  to  liquid  water  at  0°  C  .... 

<  33,808 

60,854 

Andrews. 

|  34,342 

61,816 

Thomson. 

"           to  steam  at  100°  C  

28,732 

51,717 

Favre  and  Silbermanu. 

Carbon  (wood  charcoal)  to  carbonic 
acid,  CO2;  ordinary  temperatures. 

(    8,080 
•j    7,900 
8,137 

14,544 
14,220 
14,647 

Andrews. 
Berthelot. 

Carbon  diamond  to  COa  

7,859 

14,146 

i< 

"         black  diamond  to  CO2  

7,861 

14,150 

« 

"         graphite  to  CO2  
Carbon  to  carbonic  oxide,  CO  

7,901 
2,473 

14,222 

4,451 

Favre  and  Silbermann. 

(    2,403 

4,325 

Carbonic  oxide  to  CO2,  per  unit  of  CO 

•1    2,431 

4,376 

Andrews. 

j    2,385 

4,293 

Thomsen. 

CO  to  CO2  per  unit  of  C  =  2tg  X  2403 

5,607 

10,093 

Favre  and  Silbermann. 

Marsh-gas,  Methane,  CH4  to    water 
and  CO2 

(  13,120 
-{  13,108 
(  13,063 

23,616 
23,594 
23,513 

Thomsen. 
Andrews. 
Favre  and  Silbermann. 

Olefiant    gas,     Ethylene,    C2H4    to 
water  and  COo                                .   • 

111,858 
4  11,942 
(11,957 

21,344 
21,496 
21,523 

Andrews. 
Thomsen. 

Benzole  gas,  C8H6  to  water  and  COa 

j  10,102 
{    9,915 

18,184 
17,847 

Favre  and  Silbermann. 

In  burning  1  pound  of  hydrogen  with  8  pounds  of  oxygen  to  form  9  pounds 
of  water,  the  units  of  heat  evolved  are  62,032  (Favre  and  S.);  but  if  the 
resulting  product  is  not  cooled  to  the  initial  temperature  of  the  gases, 
part  of  the  heat  is  rendered  latent  in  the  steam.  The  total  heat  of  1  Ib. 
of  steam  at  212°  F.  is  1140.1  heat-units  above  that  of  water  at  32°,  and 
9  X  1146  1  =  10,315  heat-units,  which  deducted  from  62,032  gives  51,717  as  the 
heat  evolved  by  the  combustion  of  1  Ib.  of  hydrogen  and  8  Ibs.  of  oxygen  at 
32°  F.  to  form  steam  at  212°  F. 

By  the  decomposition  of  a  chemical  compound  as  much  heat  is  absorbed 
or  rendered  latent  as  was  evolved  when  the  compound  was  formed.  If  1  Ib. 
of  carbon  is  burned  to  CO2,  generating  14.544  B.T.U.,  and  the  COa  thus  formed 
is  immediately  reduced  to  CO  in  the  presence  of  glowing  carbon,  by  the 
reaction  CO2  +  C  =  SCO.  the  result  is  the  same  as  if  the  2  Ibs.  C  had  been 
burned  directly  to  2CO,  generating  2  X  4451  =  8902  heat-units;  consequently 
14,544  —  8902  =  5642  heat-units  have  disappeared  or  become  latent,  and  the 


SPECIFIC   HEAT. 


457 


"  unburning  "  of  COt  to  CO  is  thus  a  cooling  operation.    (For  heats  of  com- 
bustion of  various  fuels,  see  Fuel.) 

SPECIFIC  HEAT. 

Thermal  Capacity;.  —The  thermal  capacity  of  a  body  is  the  quantity 
of  heat  required  to  raise  its  temperature  one  degree.  The  ratio  of  the  heat 
required  to  raise  the  temperature  of  a  given  substance  one  degree  to  that 
required  to  raise  the  temperature  of  water  one  degree  from  the  temperature 
of  maximum  density  39.1  is  commonly  called  the  specific  heat  of  the  sub- 
stance. Some  writers  object  to  the  term  as  being  an  inaccurate  use  of  the 
words  "  specific  "  and  "  heat."  A  more  correct  name  would  be  "coefficient 
of  thermal  capacity." 

Determination  of  Specific  Heat.—  Method  by  Mixture.—  The 
body  whose  specific  beat  is  to  be  determined  is  raised  to  a  known  tempera- 
ture, and  is  then  immersed  in  a  mass  of  liquid  of  which  the  weight,  specific 
heat,  and  temperature  are  known.  When  both  the  body  and  the  liquid 
have  attained  the  same  temperature,  this  is  carefully  ascertained. 

Now  the  quantity  of  heat  lost  by  the  body  is  the  same  as  the  quantity  of 
heat  absorbed  by  the  liquid. 

Let  c,  w,  and  t  be  the  specific  heat,  weight,  and  temperature  of  the  hot 
body,  and  c',  w',  and  t'  of  the  liquid.  Let  T  be  the  temperature  the  mix- 
ture assumes. 

Then,  by  the  definition  of  specific  heat,  c  X  w  X  (t  -  T)  =  heat-units  lost 
by  the  hot  body,  and  c'  X  to'  X  (T  -  t')  =  heat-units  gained  by  the  cold 
liquid.  If  there  is  no  heat  lost  by  radiation  or  conduction,  these  must  be 
equal,  and 

cw(t  -  T)  =  c'w'(T-  t')    or    c  = 


Specific  Heats  of  Various  Substances. 

The  specific  heats  of  substances,  as  given  by  different  authorities,  show- 
considerable  lack  of  agreement,  especially  in  the  case  of  gases. 

The  following  tables  give  the  mean  specific  heats  of  the  substances  named 
according  to  Regnaulr.  (From  Rontgeu's  Thermodynamics,  p.  134.)  These 
specific  heats  are  average  values,  taken  at  temperatures  which  usually  come 
under  observation  in  technical  application.  The  actual  specific  heats  of  all 
substances,  in  the  solid  or  liquid  state,  increase  slowly  as  the  body  expands 
or  as  the  temperature  rises.  It  is  probable  that  the  specific  heat  of  a  body 
when  liquid  is  greater  than  when  solid.  For  man}'  bodies  this  has  been 
verified  by  experiment. 


SOLIDS. 


Antimony 0.0508 

Copper 0.0951 

Gold 0.03-24 

Wrought  iron 0.1138 


0.1937 


Gla 

Cast  iron 0. 1X398 

Lead 0.0314 

Platinum 0. 0324 

Silver 0.0570 

Tin  0.0562 


Steel  (soft) 0.1165 

Steel  (hard) 01175 

Zinc 0.0956 

Brass 0.0939 

Ice  ...   0.5040 


Sulphur 0.2026 

Charcoal 0.2410 

Alumina 0.1970 

Phosphorus 0.1887 


Water 1.0000 

Lead  (melted) 0.0402 

Sulphur    4i       0.2340 

Bismuth    "      0.0308 

Tin  "      0.0637 

Sulphuric  acid 0.3350 


LIQUIDS. 


Mercury 0.0333 

Alcohol  (absolute)  0.7000 

Fusel  oil 0.5640 

Benzine 0.4500 

Ether 0.5034 


458 


HEAT. 


Constant  Volume. 
0.16847 
0.15507 
2.41 226 
0.17273 
0.346 
0.1535 
0.173 
0.1758 
0.299 
0.3411 
0.3200 


GASES. 
Constant  Pressure 

Air 0.23751 

Oxygen 0.21751 

Hydrogen 3.40900 

Nitrogen 0.24380 

Superheated  steam 0.4805 

Carbonic  acid 0.217 

Olefiant  Gas  (CH2) 0.404 

Carbonic  oxide 0.2479 

Ammonia 0.508 

Ether 0.4797 

Alcohol ., 0.4534 

Acetic  acid ....... 0.4125 

Chloroform.. 0.1567  

In  addition  to  the  above,  the  'following  are  given  by  other  authorities. 
(Selected  from  various  sources.) 

METALS. 

Wrought  iron  (Petit  &  Dulong). 

32°  to  212° 1098 

32°to39-,>° 115 

"  32°  to  572° 1218 

"  32°  to  062° 1255 

Wrought  iron  ^J.  C.  Hoadley, 
A.  S.  M.  E.,  vi.  713), 

Wrought  iron,  32°  to    200° 1129 

u  32°  to    600° 1327 

32°  to  2000° 2619 


Platinum,  32°  to  446°  F 0333 

(increased  .000305  for  each  100°  F.) 

Cadmium .05G7 

Brass 0939 

Copper,  32°  to  212°  F 094 

32°  to572°F 1013 

Zinc        32°  to  212°  F 0927 

32°  to  572°  F 1015 

Nickel 1086 

Aluminum,  0°  F.  to  melting- 
point  (A.  E.  Hunt) 0.2185 

OTHER  SOLIDS. 


Brickwork  and  masonry,  about.  .20 

Marble 210 

Chalk  215 

Quicklime 217 

Magnesian  limestone 217 

Silica 191 

Corundum 198 

Stones  generally 2  to  22 


Coal 20  to  241 

Coke 203 

Graphite 202 

Sulphate  of  lime 197 

Magnesia 222 

Soda 231 

Quartz 188 

River  sand 195 


WOODS. 

Pine  (turpentine) 467      Oak . . 

Fir  650       Pear. 


.570 
.500 


LIQUIDS. 


Alcohol,  density  .793 622 

Sulphuric  acid,  density  1.87 .335 

1.30 661 

Hydrochloric  acid 600 

GASES. 

At  Constant 
Pressure. 

Sulphurous  acid 1553 

Light  carburetted  hydrogen,  marsh  gas  (CH4).  .5929 
Blast-furnace  gases 2277 

Specific  Heat  of  Salt  Solution.    (Schuller.) 

Per  cent  salt  in  solution 5  10  15  20 

Specific  heat 9306        .8909        .8606        .8490 

Specific  Meat  of  Air.  — Regnault  gives  for  the  mean  value 

Between  — 30°  C.  and -f  10°  C 0.23771 

"  0°  C.    "        100°  C ,0.23741 

0°C.    "        200°C 0.23751 

Hanssen  uses  0.1686  for  the  specific  heat  of  air  at  constant  volume.  The 
value  of  this  constant  has  never  been  found  to  any  degree  of  accuracy  by 
direct  experiment.  Prof.  Wood  gives  0.2375  -t- 1.406  =  0.1689.  The  ratio  of 


Olive  oil 310 

Benzine 393 

Turpentine,  density  .872 472 

Bromine 1.111 


At  Constant 
Volume. 
.1246 


25 

.8073 


EXPANSION   BY   HEAT. 


459 


the  specific  heat  of  a  fixed  gas  at  constant  pressure  to  the  sp.  ht.  at  con- 
stant volume  is  given  as  follows  by  different  writers  (Eng^g,  July  12,  1889): 
Renault,  1.3053;  Moll  and  Beck,  1.4085;  Szathmari,  1.40^7;  J.  Macfarlane 
Gray,  1.4.  The  first  three  are  obtained  from  the  velocity  of  sound  in  air.  The 
fourth  is  derived  from  theory.  Prof.  Wood  says:  The  value  of  the  ratio  for 
air,  as  found  in  the  days  of  La  Place,  was  1.41,  and  we  have  0.2377  -e-  1.41 
=  0.1686,  the  value  used  by  Clausius,  Hanssen,  and  many  others.  But  this 
ratio  is  not  definitely  known.  Rankine  in  his  later  writings  used  1.408,  and 
Tait  in  a  recent  work  gives  1.404,  while  some  experiments  gives  less  than 
1.4  and  others  more  than  1.41.  Prof.  Wood  uses  1.406. 

Specific  Heat  of  Gases.— Experiments  by  Mallard  and  Le  Chatelier 
indicate  a  continuous  increase  in  the  specific  heat  at  constant  volume  of 
steam.  CO2.  and  even  of  the  perfect  gases,  with  rise  of  temperature.  The 
variation  is  inappreciable  at  100°  C.,  but  increases  rapidly  at  the  high  tem- 
peratures of  the  gas-engine  cylinder.  (Robinson's  Gas  and  Petroleum 
Engines.) 

Specific  Heat  and  Latent  Heat  of  Fusion  of  Iron  and 
Steel.    (H.  H.  Campbell,  Trans.  A.  I.  M.  E.,  xix.  181.) 


Akerman.    Troilius. 

Specific  heat  pig  iron,       0  to  1200°  C 0.16 

"         1200  to  1800°  C 0.21 

Oto  1500°  C 

"         "  "         1500tol800°C 


0.18 
0.20 


Calculating  by  both  sets  of  data  we  have  : 


Akerman.    Troilius. 

Heating  from  0  to  1800°  C 318  330  calories  per  kilo. 

Hence  probable  value  is  about 325  calories  per  kilo. 

Specific  heat,  steel  (probably  high  carbon) (Troilius) 1175 

soft  iron "        1081 

Hence  probable  value  solid  rail  steel 1125 

4     melted  rail  steel 1275 

Akerman.      Troilius. 
Latent  heat  of  fusion,  pig  iron,  calories  per  kilo..  46 

"      gray  pig 33 

white  pig 23 

From  which  we  may  assume  that  the  truth  is  about :  Steel,  20  ;  pig  iron,  30. 

EXPANSION  BY  HEAT. 

In  the  centigrade  scale  the  coefficient  of  expansion  of  air  per  degree  is 
0.003665  =  1/278;  that  is,  the  pressure  being  constant,  the  volume  of  a  perfect 
gas  increases  1/273  of  its  volume  at  0°  C.  for  every  increase  in  temperature 
of  1°  C.  In  Fahrenheit  units  it  increases  1/491.2  =  .002036  of  its  volume  at 
32°  F.  for  every  increase  of  1°  F. 

Expansion  of  Oases  by  Heat  from  32°  to  212°  F.  (Regnault.) 


Increase 
Pressur 
Volume 
=  1.0,  f( 

n  Volume, 
e  Constant. 
at32°Fahr. 
sir 

Increase  in  Pressure, 
Volume  Constant. 
Pressure  at  32° 
Fahr.  =  1.0,  for 

100°  C. 

1°F. 

100°  C. 

1°F. 

Hydrogen      

0.3661 
0.3670 
0.3670 
0.3669 
0.3710 
0.3903 

0.002034 
0.002039 
0.002039 
0.002038 
0.002061 
0.002168 

0.3667 
0.3665 
0.3668 
0.3667 
0.3688 
0.3845 

0.002037 
0.002036 
0.002039 
0.002037 
0.002039 
0.002136 

Atmospheric  air  

Nitrogen                        .   .  . 

Carbonic  oxide  

Carbonic  acid 

Sulphurous  acid  

If  the  volume  is  kept  constant,  the  pressure  varies  directly  as  tlje  absolute 
temperature. 


460 


HEAT. 


Lineal  Expansion  of  Solids  at  Ordinary  Temperatures. 

(British  Board  of  Trade;  from  CLARK.) 


For 
1°  Fahr. 

For 

1°  Cent. 

Coef- 
ficient 
of 
Expan- 
sion 
from 
32°  to 
212°  F. 

Accord- 
ing to 
Other 
Author- 
ities. 

Aluminum  (cast)  

Length  =  1 

.00001234 
.00000627 
.00000957 
.00001052 
.00000306 
.00000986 
.00000975 
.00000594 

Length=l 

.00002221 
.00001129 
.00001722 
.00001894 
.00000550 
.00001774 
.00001755 
.00001070 
.00001430 
.00001596 
.00007700 
.00000812 
.00000897 
.00000714 
.00000789 
.00000897 
.00001415 
.00000641 
.00001166 
.00001001 
.00002828 

.002221 
.001129 
.001722 
.001894 
.000550 
.001774 
.001755 
.001070 
.001430 
.001596 
007700 
.000812 
.000897 
.000714 
.000789 
.000897 
.001415 
.000641 
.001166 
.001001 
.002828 

.'001083 
.001868 

Antimony  (cryst  ) 

Brass,  cast...   . 

*4          plate 

Brick  

Bronze  (Copper,  17;  Tin,  2^;  Zinc  1). 
Bismuth 

.'(X)  1392 

Concrete:  cement,  mortar,  and  pebbles 
Copper      

.00000795 
.00000887 
.00004278 
.00000451 
.00000499 
.00000397 
.00000438 
.00000498 
.00000786 
.00000356 
.00000648 
.00000556 
.00001571 

.001718 

Ebonite              . 

Glass  English  flint 

"       thermometer  

"       hard 

Granite  gray  dry        .              . 

4  4        red,  dry  

Gold   pure 

Iridium  pure  

Iron,  wrought  ,  

.001235 
.001110 

!  002694 

4  '     cast 

Lead     

Magnesium 

,,     ,  ,              .          (  from 

.00000308 
.00000786 
.00000256 
.00000494 
.00009984 
.00000695 
.00001129 
.00000922 
.00000479 

.00000453 
.00000200 

.00000434 

.00000788 
.00001079 
.00000577 
.00000636 
.00000689 
.00000652 
.00000417 
.00001163 
.00000489 
.00000276 
.00001407 

.00001  190 

.00000554 
.00001415 
.00000460 
.00000890 
.00017971 
.00001251 
.00002033 
.00001660 
.00000863 

.00000815 
.00000360 

.00000781 

.00001419 
.00001943 
.00001038 
.00001144 
.00001240 
.00001174 
.00000750 
.00002094 
.00000881 
.00000496 
.00002532 

.00002692 

000554 
.001415 
.000460 
.000890 
.017971 
.001251 
.002033 
.001660 
.000863 

.000815 
.000360 

.000781 

.001419 
.001943 
.001038 
.001144 
.001240 
.001174 
.000750 
.002094 
.000881 
.000496 
.002532 

.002692 

Marbles,  various  -j  £0 

-»«•               v.  •  i    i  from 

Masonry,  brick  -J  J^ 

Mercury  (cubic  expansion)  —  
Nickel        

.018018 
.001279 

Pewter            ...... 

Plaster    white               

Platinum      

Platinum,  85  per  cent  | 

.000884 

Indium,     15    "      *4    )'  
Porcelain 

Quartz,  parallel  to  major  axis,  t  0°  to 
40°  C  

Quartz,  perpendicular  to  major  axis, 
t  0°  to  40°  C  

.001908 
.001079 

Silver  pure 

Slate  

Steel   cast 

i4     tempered  

Stone  (sandstone),  dry  

'•               "            Rauville  

.001938 

Tin  

Wedgwood  ware  

Wood,  pine  .... 

.002942 

Zinc  

Zinc,  8  t 

Tin,  1    $      

Cubical  expansion,  or  expansion  of  volume  ==  linear  expansion  x  3. 


LATENT  HEATS  OF  FUSION.  461 

Absolute  Temperature—  Absolute  Zero.—  The  absolute  zero  of  a 
gas  is  a  theoretical  consequence  of  the  law  of  expansion  by  heat,  assuming 
that  it  is  possible  to  continue  the  cooling  of  a  perfect  gas  until  its  volume  is 
diminished  to  nothing. 

If  the  volume  of  a  perfect  gas  increases  1/273  of  its  volume  at  0°  C.  for 
every  increase  of  temperature  of  1°  C.,  and  decreases  1/273  of  its  volume  for 
every  decrease  of  temperature  of  1°  C.,  then  at  -  273°  C.  the  volume  of  the 
imaginary  gas  would  be  reduced  to  nothing.  This  point  —  273°  C.,  or  491.2° 
F.  below  the  melting-point  of  ice  on  the  air  thermometer,  or  492.66°  F.  be- 
low on  a  perfect  gas  thermometer  —  —  459.2°  F.  (or  —  460.66°),  is  called  the 
absolute  zero;  and  absolute  temperatures  are  temperatures  measured,  on 
cither  the  Fahrenheit  or  centigrade  scale,  from  this  zero.  The  freezing 
point,  32°  F.,  corresponds  to  491.2°  F.  absolute.  If  p0  be  the  pressure  and 
r0  the  volume  of  a  gas  at  the  temperature  of  32°  F.  =  491.2°  on  the  absolute 
s?ale  =  y0,  and  p  the  pressure,  and  v  the  volume  of  the  same  quantity  of 
g  as  at  any  other  absolute  temperature  T,  then 

pv_  __    T_  _    £  +  459.2        pv  _  pQv0 
p0v0  ~  TO  ~        491.2      ;      T   ~  "TO"' 

The  value  of  p0v0  -H  T0  for  air  is  53.37,  and  pv  =  53.37T,  calculated  as  fol- 
lows by  Prof.  Wood: 

A  cubic  foot  of  dry  air  at  32°  F.  at  the  sea-level  weighs  0.080728  Ib.    The 

volume  of  one  pound  is  v0  =  •  =  12.387  cubic  feet.  The  pressure  per 


square  foot  is  2116.2  Ibs. 

POVO  _   2116.2  X  12.387   _    26214  _ 

TO    =  491.13  ~  49TI3-  5<U7' 

The  figure  491.13  is  the  number  of  degrees  that  the  absolute  zero  is  below 
?rhe  melting-point  of  ice,  by  the  air  thermometer.    On   the  absolute  scale, 
whose  divisions  would  be  indicated  by  a  perfect  gas  thermometer,  the  cal- 
culated value  approximately  is  492  66,  which  would  makepv  =  53.  2  IT.  Prof. 
Thomson  considers  that  —  273.  1°  C.,  =  —  459.4°  F.,  is  the  most  probable  value 
nt  the  absolute  zero.    See  Heat  in  Ency.  Brit. 

Expansion  of  Liquids  from  32°   to   212°  F.—  Apparent  ex- 
4>ansion  in  glass  (Clark).    Volume  at  212°,  volume  at  32°  being  1: 
Water  ..............   ..........  1.0466        Nitric  acid  ..................  ....  1.11 

Water  saturated  with  salt  —  1.05  Olive  and  linseed  oils  ...........  1.08 

Mercury  ......................  1.0182       Turpentine  and  ether  ..........  1.07 

A.lcohol  .....  „  ................  1.11  Hydrochlor.  and  sulphuric  acids  1  .06 

For  water  at  various  temperatures,  see  Water. 
For  air  at  various  temperatures,  see  Air. 

LATENT  HEATS  OF  FUSION  AND   EVAPORATION. 
Latent  Heat  means  a  quantity  of  heat  which  has  disappeared,  having 
oeen  employed  to  produce  some  change  other  than  elevation  of  temperature. 
By  exactly  reversing  that  change,  the  quantity  of  heat  which  has  dis^ 
•appeared  is  reproduced.     Maxwell  defines  it  as  the  quantity  of  heat  which 
must  be  communicated  to  a  body  in  a  given  state  in  order  to  convert  it  into 
another  state  without  changing  its  temperature. 

Latent  Heat  of  Fusion.—  When  a  body  passes  from  the  solid  to  the 
liquid  state,  its  temperature  remains  stationary,  or  nearly  stationary,  at  a 
certain  melting  point  during  the  whole  operation  of  melting;  aud  in  order 
to  make  that  operation  go  on,  a  quantity  of  heat  must  be  transferred  to  the 
substance  melted,  being  a  certain  amount  for  each  unit  of  weight  of  the 
substance.    This  quantity  is  called  the  latent  heat  of  fusion. 

When   a  body  passes  from  the  liquid  to  the  solid  state,  its  temperature 
remains  stationary  or  nearly  stationary  during  the  whole  operation  of  freez- 
ing: a  quantity  of  heat  equal  to  the  latent  heat  of  fusion  is  produced  in  the 
body  and  rejected  into  the  atmosphere  or  other  surrounding  bodies. 

The  following  are  examples  in  British  thermal  units  per  pound,  as  given 
by  Rankine: 

Substance*  Melting  Latent  Heat 

Points.  of  Fusion. 

Ice  (according  to  Person)  ............    32  142.65 

Spermaceti  ...........................    56  148 

Beeswax  .............................  140  175 

Phosphorus  ..........................  177  9.06 

Sulphur...,  ..................  ........  405  16.86 

Tin  ...................................  426  500 


462 

Prof.  Wood  considers  144  heat  units  as  the  most  reliable  value  for  the 
latent  heat  of  fusion  of  ice.  Box  gives  only  26.6  for  tin.  Clements  gives  233 
for  cast  iron. 

Latent  Heat  of  Evaporation.— When  a  body  passes  from  the 
solid  or  liquid  to  the  gaseous  state,  irs  temperature  during  the  operation 
remains  stationary  at  a  certain  boiling  point,  depending  on  the  pressure  of 
the  vapor  produced;  and  in  order  to  make  the  evaporation  go  on,  a  quantity 
of  heat  must  be  transferred  to  the  substance  evaporated,  whose  amount  for 
each  unit  of  weight  of  the  substance  evaporated  depends  on  the  temperature. 
That  heat  does  not  raise  the  temperature  of  the  substance,  but  disappears 
in  causing  it  to  assume  the  gaseous  state,  and  it  is  called  the  latent  heat  of 
evaporation. 

When  a  body  passes  from  the  gaseous  state  to  the  liquid  or  solid  state,  its 
temperature  remains  stationary,  during  that  operation,  at  the  boiling-point 
corresponding  to  the  pressure  of  the  vapor:  a  quantity  of  heat  equal  to  the 
latent  heat  of  evaporation  at  that  temperature  is  produced  in  the  body;  and 
in  order  that  the  operation  of  condensation  may  go  on,  that  heat  must  be 
transferred  from  the  body  condensed  to  some  other  body. 

The  following  are  examples  of  the  latent  heat  of  evaporation  in  British 
thermal  units,  of  one  pound  of  certain  substances,  when  the  pressure  of  the 
vapor  is  one  atmosphere  of  14.7  Ibs.  on  the  square  inch: 

QllVkQi,  Boiling-point  under  Latent  Heat  in 

bubstance.  Qne  aim  Fahr  British  units. 

Water 212.0  965.7  (Regnault,) 

Alcohol.,    172.2  364.3  (Andrews.) 

Ether 95.0  162.8 

Bisulphide  of  carbon 114.8  156.0 

The  latent  heat  of  evaporation  of  water  at  a  series  of  boiling-points  ex- 
tending from  a  few  degrees  below  its  r'reezing-point  up  to  about  375  degree;* 
Fahrenheit  has  been  determined  experimentally  by  M.  Regnault.  The  re 
suits  of  those  experiments  are  represented  approximately  by  the  formula 
in  British  thermal  units  per  pound, 

I  nearly  =  1091.7  -  0.7(C  -  32°)  =  965.7-  0.7(*  -  212°). 

The  Total  Heat  of  Evaporation  is  the  sum  of  the  heat  whiciM 
disappears  in  evaporating  one  pound  of  a  given  substance  at  a  given  tem- 
perature (or  latent  heat  of  evaporation)  and  of  the  heat  required  to  raise  its 
temperature,  before  evaporation,  from  some  fixed  temperature  up  to  the 
temperature  of  evaporation.  The  latter  part  of  the  total  heat  is  called  the 
sensible  heat. 

In  the  case  of  water,  the  experiments  of  M.  Regnault  show  that  the  total 
heat  of  steam  from  the  temperature  of  melting  ice  increases  at  a  uniform 
rate  as  the  temperature  of  evaporation  rises.  The  following  is  the  formub* 
in  British  thermal  units  per  pound: 

h  =  1091.7-f  0.305(*  -  32°). 

For  the  total  heat,  latent  heat,  etc.,  of  steam  at  different  pressures,  see 
table. of  the  Properties  of  Saturated  Steam.  For  tables  of  total  heat,  latent 
heat,  and  other  properties  of  steams  of  ether,  alcohol,  acetone,  chloroform, 
chloride  of  carbon,  and  bisulphide  of  carbon,  see  Rontgen's  Thermodynam- 
ics (Dubote's  translation.)  For  ammonia  and  sulphur  dioxide,  see  Wood's 
Thermodynamics;  also,  tables  under  Refrigerating  Machinery,  in  this  book. 

EVAPORATION  ANB  DRYING. 

In  evaporation,  the  formation  of  vapor  takes  place  on  the  surface;  in  boil- 
ing, within  the  liquid:  the  former  is  a  slow,  the  latter  a  quick,  method  of 
evaporation. 

If  we  bring  an  open  vessel  with  water  under  the  receiver  of  an  air-pump 
and  exhaust  the  air  the  water  in  the  vessel  will  commence  to  boil,  and  if  we 
keep  up  the  vacuum  the  water  will  actually  boil  near  its  freezing-point.  The 
formation  of  steam  in  this  case  is  due  to  the  heat  which  the  water  takes  out 
of  the  surroundings. 

Steam  formed  under  pressure  has  the  same  temperature  as  the  liquid  in 
which  it  was  formed,  provided  the  steam  is  kept  under  the  same  pressure. 

By  properly  cooling  the  rising  steam  from  boiling  water,  as  in  the  multiple- 
effect  evaporating  systems,  we  can  regulate  the  pressure  so  that  the  water 
boils  at  low  temperatures. 


EVAPORATION.  463 

Evaporation  of  Heater  in  Reservoirs.— Experiments  at  the 
Mount  Hope  Reservoir,  Rochester,  N.  Y.,  in  1891,  gave  the  following  results: 

July.  Aug.  Sept.  Oct. 

Mean  temperature  of  air  in  shade 70.5  70.3  68.7  53.3 

**  water  in  reservoir 68.2  70.2  66.1  54.4 

"      humidity  of  air,  per  cent 67.0  74.6  75.2  74.7 

Evaporation  in  inches  during  month 5.59  4.93  4.05  3.23 

Rainfall  in  inches  during  month 3.44  2.95  1.44  2.16 

Evaporation  of  Water  from  Open  Channels.  (Flyim's 
Irrigation  Canals  and  Flow  of  Water.)— Experiments  from  1881  to  1885  in 
Tulare  County,  California,  showed  an  evaporation  from  a  pan  in  the  river 
equal  to  an  average  depth  of  one  eighth  of  an  inch  per  day  throughout  the 
year. 

When  the  pan  was  in  the  air  the  average  evaporation  was  less  than  3/16 
of  an  inch  per  day.  The  average  for  the  month  of  August  was  1/3  inch  per 
day,  and  for  March  and  April  1/12  of  an  inch  per  day.  Experiments  in 
Colorado  show  that  evaporation  ranges  from  .088  to  .16  of  an  inch  per  day 
during  the  irrigating  season. 

In  -Northern  Italy  the  evaporation  was  from  1/12  to  1/9  inch  per  day,  while 
in  the  south,  under  the  influence  of  hot  winds,  it  was  from  1/6  to  1/5  inch 
per  day. 

In  the  hot  season  in  Northern  India,  with  a  decidedly  hot  wind  blowing, 
the  average  evaporation  was  ^  inch  per  day.  The  evaporation  increases 
with  the  temperature  of  the  water. 

Evaporation  by  the  Multiple  System.— A  multiple  effect  is  a 
series  of  evaporating  vessels  each  having  a  steam  chamber,  so  connected 
that  the  heat  of  the  steam  or  vapor  produced  in  the  first  vessel  heats  the 
second,  the  vapor  or  steam  produced  in  the  second  heats  the  third,  and  so 
on.  The  vapor  from  the  last  vessel  is  condensed  in  a  condenser.  Three 
vessels  are  generally  used,  in  wrhich  case  the  apparatus  is  called  a  Triple 
Effect.  In  evaporating  in  a  triple  effect  the  vacuum  is  graduated  so  that  the 
liquid  is  boiled  at  a  constant  and  low  temperature. 

Resistance  to  Boiling. — Brine.  (Rankine.)— The  presence  in  a 
liquid  of  a  substance  dissolved  in  it  (as  salt  in  water)  resists  ebullition,  and 
raises  the  temperature  at  which  the  liquid  boils,  under  a  given  pressure;  but 
unless  the  dissolved  substance  enters  into  the  composition  of  the  vapor,  the 
relation  between  the  temperature  and  pressure  of  saturation  of  the  vapor 
remains  unchanged.  A  resistance  to  ebullition  is  also  offered  by  a  vessel  of 
a  material  which  attracts  the  liquid  (as  when  water  boils  in  a  glass  vessel), 
and  the  boiling  take  place  by  starts.  To  avoid  the  errors  which  causes  of 
this  kind  produce  in  the  measurement  of  boiling-points,  it  is  advisable  to 
place  the  thermometer,  not  in  the  liquid,  but  in  the  vapor,  which  shows  the 
true  boiling-point,  freed  from  the  disturbing  effect  of  the  attractive  nature 
of  the  vessel.  The  boiling-point  of  saturated  brine  under  one  atmosphere 
is  226°  Fahr.,  and  that  of  weaker  brine  is  higher  than  the  boiling-point  of 
pure  water  by  1.2°  Fahr.,  for  each  1/32  of  salt  that  the  water  contains. 
Average  sea-water  contains  1/32;  and  the  brine  in  marine  boilers  is  not  suf- 
fered to  contain  more  than  from  2/32  to  3/32. 

Methods  of  Evaporation  Employed  in  the  Manufacture 
of  Salt.  (F.  E.  Engelhardt,  Chemist  Onondaga  Salt  Springs;  Report  for 
1889.)—!.  Solar  heat— solar  evaporation.  2.  Direct  fire,  applied  to  the  heat- 
ing surface  of  the  vessels  containing  brine— kettle  and  pan  methods.  3.  The 
steam-grainer  system — steam-pans,  steam-kettles,  etc.  4.  Use  of  steam  and 
a  reduction  of  the  atmospheric  pressure  over  the  boiling  brine— vacuum 
system. 

When  a  saturated  salt  solution  boils,  it  is  immaterial  whether  it  is  done 
under  ordinary  atmospheric  pressure  at  228°  F.,  or  under  four  atmospheres 
with  a  temperature  of  320°  F.,  or  in  a  vacuum  under  1/10  atmosphere,  the 
result  will  always  be  a  fine-grained  salt. 

The  fuel  consumption  is  stated  to  be  as  follows:  By  the  kettle  method,  40 
to  45  bu.  of  salt  evaporated  per  ton  of  fuel,  anthracite  dust  burned  on  per- 
forated grates ;  evaporation,  5.53  Ibs.  of  water  per  pound  of  coal.  By  the 
pan  method,  70  to  75  bu.  per  ton  of  fuel.  By  vacuum  pans,  single  effect,  86 
Ibs.  per  ton  of  anthracite  dust  (2000  Ibs.).  With  a  double  effect  nearly 
double  that  amount  can  be  produced. 


464 


HEAT. 


Solubility  of  Common  Salt  in  Pure  Water*  (Andrese.) 


Temp,  of  brine,  F 

100  parts  water  dissolve  parts.. 
100  parts  brine  contain  salt  — 


.  35.63 
,  26.27 


50 

35.69 
26.30 


36.03 
26.49 


104        140       176 
36.32    37.06    38.00 
26.64    27.04    27.54 


According  to  Poggial,  100  parts  of  water  dissolve  at  229.66°  F.,  40.35  parts 
of  salt,  or  in  per  cent  of  brine,  28.749.  Gay  Lussac  found  that  at  229.72°  F., 
100  parts  of  pure  water  would  dissolve  40.38  parts  of  salt,  in  per  cent  of 
brine,  28.764  parts. 

The  solubility  of  salt  at  229°  F.  is  only  2.5#  greater  than  at  32°.  Hence  we 
cannot,  as  in  the  case  of  alum,  separate  the  salt  from  the  water  by  allowing 
a  saturated  solution  at  the  boiling  point  to  cool  to  a  lower  temperature. 

Solubility  of  Sulphate  of  Lime  in  Pure  "Water.    (Marignac.) 
Temperature  F.  degrees^          32      64.5     89.6   100.4    105.8     127.4    186.8     212 
415      386     371      368       370       375       417      452 

525      488      470      466       468       474       528      572 

In  salt  brine  sulphate  of  lime  is  much  more  soluble  than  in  pure  water. 
In  the  evaporation  of  salt  brine  the  accumulation  of  sulphate  of  lime  tends 
to  stop  the  operation,  and  it  must  be  removed  from  the  pans  to  avoid  waste 
of  fuel. 

The  average  strength  of  brine  in  the  New  York  salt  districts  in  1889  was 
69.38  degrees  of  the  salinometer. 

Strength  of  Salt  Brines.— The  following  table  is  condensed  from 
one  given  in  U.  S.  Mineral  Resources  for  1888,  on  the  authority  of  Dr. 
Englehardt. 

Relations  between  Salinometer  Strength,  Specific  Gravity, 
Solid  Contents,  etc.,  of  Brines  of  Different  Strengths. 


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210.8 

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8.597 

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136.5 

1,118 

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5.300 

8.622 

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176.8 

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9,280 

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296.2 

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40.51 

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1.136 

18.550 

9.464 

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31.89 

245.9 

40.98 

48.80 

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1.158 

21.200 

9.647 

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27.38 

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34.69 

57.65 

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23.40 

1.182 

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9.847 

2.348 

23.84 

178.8 

29.80 

67.11 

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26.500 

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2.660 

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155.3 

77.26 

EVAPORATION".  465 

Concentration  of  Sugar  Solutions,,*  (From  "  Heating  and  Con- 
centrating Liquids  by  Steam,"  by  JohnG.  Hudson;  The  Engineer ',  June  13, 
1890.)— In  the  early  stages  of  the  process,  when  the  liquor  is  of  low  density,  the 
evaporative  duty  will  be  high,  say  two  to  three  (.British)  gallons  per  square 
toot  of  heating  surface  with  10  Ibs.  steam  pressure,  but  will  gradually  fall  to 
an  almost  nominal  amount  as  the  final  stage  is  approached.  Asa  generally 
safe  basis  for  designing,  Mr.  Hudson  takes  an  evaporation  of  one  gallon  per 
hour  for  each  square  foot  of  gross  heating  surface,  with  steam  of  the  pres- 
sure of  about  10  Ibs. 

As  examples  of  the  evaporative  duty  of  a  vacuum  pan  when  performing 
the  earlier  stages  of  concentration,  .during  which  all  the  heating  surface 
can  be  employed;  he  gives  the  following: 

COIL  VACUUM  PAN.— 4%  in.  copper  coils,  528  square  feet  of  surface; 
steam  in  coils,  15  Ibs.;  temperature  in  pan,  141°  to  148°;  density  of  feed,  25° 
Beaume,  and  concentrated  to  81°  Beaum6. 

First  Trial. — Evaporation  at  the  rate  of  2000  gallons  per  hour  =  3.8  gallons 
per  square  foot;  transmission,  376  units  per  degree  of  difference  of  tem- 
perature. 

Second  Trial.—  Evaporation  at  the  rate  of  1503  gallons  per  hour  =  2.8  gal- 
lons per  square  foot;  transmission,  265  units  per  degree. 

As  regards  the  total  time  needed  to  work  up  a  charge  of  massecuite  from 
liquor  of  a  given  density,  the  following  figures,  obtained  by  plotting  the 
results  from  a  large  number  of  pans,  form  a  guide  to  practical  working. 
The  pans  were  all  of  the  coil  type,  some  with  and  some  without  jackets, 
the  gross  heating  surface  probably  averaging,  and  not  greatly  differing 
from,  .25  square  foot  per  gallon  capacity,  and  the  steam  pressure  10  Ibs.  per 
square  inch.  Both  plantation  and  refining  pans  are  included,  making 
various  grades  of  sugar: 

Density  of  Feed  (degs.  Beaume1).  ' 
10°        15°         20°         25°       30° 
Evaporation  required  per  gallon  masse- 
cuite discharged 6.123     3.6         2.26       1.5          .97 

Average   working   hours   required   per 

charge 12.          9.  6#        5.          4. 

Equivalent  average  evaporation  per  hour 
per  square  foot  of  gross  surface,  as- 
suming .25  sq.  ft.  per  gallon  capacity..      2.04       1.6         1.39       1.2          .97 
Fastest   working   hours    required    per 

charge  8.5        5.5          3.8        2.75      2.0 

Equivalent    average    evaporation    per 
hour  per  square  foot 2.88      2.6         2.38      2.18       1.9 

The  quantity  of  heating  steam  needed  is  practically  the  same  in  vacuum 
A,s  in  open  pans.  The  advantages  proper  to  the  vacuum  system  are  pri- 
marily the  reduced  temperature  of  boiling,  and  incidentally  the  possibility 
of  using  heating  steam  of  low  pressure. 

In  a  solution  of  sugar  in  water,  each  pound  of  sugar  adds  to  the  volume 
of  the  water  to  the  extent  of  .061  gallon  at  a  low  density  to  .0638  gallon  at 
high  densities. 

A  Method  of  Evaporating  by  Exhaust  Steam  is  described 
by  Albert  Stearns  in  Trans.  A.  S.  M.  E.,  vol.  viii.  A  pan  17'  6"  x  II7  x  1'  6", 
fitted  with  cast-iron  condensing  pipes  of  about  250  sq.  ft.  of  surface,  evapo- 
rated 120  gallons  per  hour  from  clear  water,  condensing  only  about  one  half 
of  the  steam  supplied  by  a  plain  slide-valve  engine  of  14"  x  32"  cylinder, 
making  65  revs,  per  min.,  cutting  off  about  two  thirds  stroke,  with  steam  at 
75  Ibs.  boiler  pressure. 

It  was  foand  that  keeping  the  pan-room  warm  and  letting  only  sufficient 
air  in  to  carry  the  vapor  up  out  of  a  ventilator  adds  to  its  efficiency,  as  the 
average  temperature  of  the  water  in  the  pan  was  only  about  165°  F. 

Experiments  were  made  with  coils  of  pipe  in  a  small  pan,  first  with  no 
agitator,  then  with  one  having  straight  blades,  and  lastly  with  troughed 
blades;  the  evaporative  results  being  about  the  proportions  of  one,  two,  and 
three  respectively. 

In  evaporating  liquors  whose  boiling  point  is  220°  F.,  or  much  above  that 
of  water,  it  Is  found  that  exhaust  steam  can  do  but  little  more  than  bring 
them  up  to  saturation  strength,  but  on  weak  liquors,  syrups,  glues,  etc.,  it 
should  be  very  useful. 

*  For  other  sugar  data  see  Bagasse  as  Fuel,  under  Fuel. 


466  HEAT. 

Drying  in  Vacuum.— An  apparatus  for  drying  grain  and  other  sub- 
stances in  vacuum  is  described  by  Mr.  Emil  Passburgin  Proo.  Inst.  Mecb. 
Engrs.,  1889.  The  three  essential  requirements  for  a  successf  I  and  eco- 
nomical process  of  drying  are:  1.  Cheap  evaporation  of  the  moisture; 
2.  Quick  drying  at  a  low  temperature;  3.  Large  capacity  of  the  apparatus 
employed. 

The  removal  of  the  moisture  can  be  effected  in  either  of  two  ways:  either 
by  slow  evaporation,  or  by  quick  evaporation — that  is,  by  boiling. 

Slow  Evaporation.— The  principal  idea  carried  into  practice  in  machines 
acting  by  slow  evaporation  is  to  bring  the  wet  substance  repeatedly  into 
contact  with  the  inner  surfaces  of  the  apparatus,  which  are  heated  by 
steam,  while  at  the  same  time  a  current  of  hot  air  is  also*passing  through 
the  substances  for  carrying  off  the  moisture.  This  method  requires  much 
heat,  because  the  hot-air  current  has  to  move  at  a  considerable  speed  in 
order  to  shorten  the  drying  process  as  much  as  possible;  consequently  a 
great  quantity  of  heated  air  passes  through  and  escapes  unused.  As  a  car- 
rier of  moisture  hot  air  cannot  in  practice  be  charged  beyond  half  its  full 
saturation ;  and  it  is  in  fact  considered  a  satisfactory  result  if  even  this 
proportion  be  attained.  A  great  amount  of  heat  is  here  produced  which  is 
not  used;  while,  with  scarcely  half  the  cost  for  fuel,  a  much  quicker  re- 
moval of  the  water  is  obtained  by  heating  it  to  the  boiling  point. 

Quick  Evaporation  by  Boiling.— This  does  not  take  place  until  the  water 
is  brought  up  to  the  boiling  point  and  kept  there,  namely,  212°  F.,  under 
atmospheric  pressure.  The  vapor  generated  then  escapes  freely.  Liquids 
are  easily  evaporated  in  this  way,  because  by  their  motion  consequent  on 
boiling  the  heat  is  continuously  conveyed  from  the  heating  surfaces  through 
the  liquid,  but  it  is  different  with  solid  substances,  and  many  more  difficul- 
ties have  to  be  overcome,  because  convection  of  the  heat  ceases  entirely  in 
solids.  The  substance  remains  motionless,  and  consequently  a  much 
greater  quantity  of  heat  is  required  than  with  liquids  for  obtaining  ths 
same  results. 

Evaporation  in  Vacuum.— All  the  foregoing  disadvantages  are  avoided  if 
the  boiling-point  of  water  is  lowered,  that  is,  if  the  evaporation  is  carried 
out  under  vacuum. 

This  plan  has  been  successfully  applied  in  Mr.  Passburg's  vacuum  drying 
apparatus,  which  is  designed  to  evaporate  large  quantities  of  water  con- 
tained in  solid  substances. 

The  drying  apparatus  consists  of  a  top  horizontal  cylinder,  surmounted 
by  a  charging  vessel  at  one  end,  and  a  bottom  horizontal  cylinder  with  a 
discharging  vessel  beneath  it  at  the  same  end.  Both  cylinders  are  encased 
in  steam-jackets  heated  by  exhaust  steam.  In  the  top  cylinder  works  a  re- 
volving cast-iron  screw  with  hollow  blades,  which  is  also  heated  by  exhaust 
steam.  The  bottom  cylinder  contains  a  revolving  drum  of  tubes,  consisting 
of  one  large  central  tube  surrounded  by  24  smaller  ones,  all  fixed  in  tube- 
plates  at  both  ends;  this  drum  is  heated  by  live  steam  direct  from  the  boiler. 
The  substance  to  be  dried  is  fed  into  the  charging  vessel  through  two  man- 
holes, and  is  carried  along  the  top  cylinder  by  the  screw  creeper  to  the  back 
end,  where  it  drops  through  a  valve  into  the  bottom  cylinder,  in  which  it  is 
lifted  by  blades  attached  to  the  drum  and  travels  forwards  in  the  reverse 
direction ;  from  the  front  end  of  the  bottom  cylinder  it  falls  into  a  discharg- 
ing vessel  through  another  valve,  having  by  this  time  become  dried.  The 
vapor  arising  during  the  process  is  carried  off  by  an  air-pump,  through  a 
dome  and  air-valve  on  the  top  of  the  upper  cylinder,  and  also  through 
a  throttle-valve  on  the  top  of  the  lower  cylinder;  both  of  these  valves  are 
supplied  with  strainers. 

As  soon  as  the  discharging  vessel  is  fined  with  dried  material  the  valve 
connecting  it  with  the  bottom  c.ylinder  is  shut,  and  the  dried  charge  taken 
out  without  impairing  the  vacuum  in  the  apparatus.  When  the  charging 
vessel  requires  replenishing,  the  intermediate  valve  between  the  two  cylin- 
ders is  shut,  and  the  charging  vessel  filled  with  a  fresh  supply  of  wet  mate- 
rial: the  vacuum  still  remains  unimpaired  in  the  bottom  cylinder,  and  has 
to  be  restored  only  in  the  top  cylinder  after  the  charging  vessel  has  been 
closed  again. 

In  this  vacuum  the  boiling-point  of  the  water  contained  in  the  wet  mate- 
rial is  brought  down  as  low  as  110°  F.  The  difference  between  this  tempera- 
ture and  that  of  the  heating  surfaces  is  amply  sufficient  for  obtaining  good 
results  from  the  employment  of  exhaust  steam  for  heating  all  the  surfaces 
except  the  revolving  drum  of  tubes.  The  water  contained  in  the  solid  sub- 
stance to  be  dried  evaporates  as  soon  as  the  latter  is  heated  to  about  110°  F,; 


RADIATION"  OF  HEAT.  467 

and  as  long  as  there  is  any  moisture  to  be  removed  the  solid  substance  is 
not  heated  above  this  temperature. 

Wet  grains  from  a  brewery  or  distillery,  containing  from  75$  to  78$  of 
water,  have  by  this  drying  process  been  converted  in  some  localities  from 
a  worthless  incumbrance  into  a  valuable  food-stuff.  The  water  is  removed 
by  evaporation  only,  no  previous  mechanical  pressing  being  resorted  to. 

At  Messrs.  Guinness's  brewery  in  Dublin  two  of  these  machines  are  em- 
ployed. In  each  of  these  the  top  cylinder  is  20'  4"  long  and  2'  8"  diam.,  and 
the  screw  working  inside  it  makes  7  revs,  per  min.;  the  bottom  cylinder  is 
19'  2"  long  and  5'  4"  diam.,  and  the  drum  of  the  tubes  inside  it  makes  5  revs, 
per  min.  The  drying  surfaces  of  the  two  cylinders  amount  together  to  a 
total  area  of  about  1000  sq.  ft.,  of  which  about  40$  is  heated  by  exhaust  steam 
direct  from  the  boiler.  There  is  only  one  air-pump,  which  is  made  large 
enough  for  three  machines;  it  is  horizontal,  and  has  only  one  air-cylinder, 
which  is  double-acting,  17%  in.  diam.  and  17%  in.  stroke;  and  it  is  driven  at 
about  45  revs,  per  min.  As  the  result  of  about  eight  months'  experience,  the 
two  machines  have  been  drying  the  wet  grains  from  about  500  cwt.  of  malt 
per  day  of  24  hours. 

Roughly  speaking,  3  cwt.  of  malt  gave  4  cwt.  of  wet  grains,  and  the  latter 
yield  1  cwt.  of  dried  grains;  500  cwt.  of  malt  will  therefore  yield  about  670 
cwt.  of  wet  grains,  or  335  cwt.  per  machine.  The  quantity  of  water  to  be 
evaporated  from  the  wet  grains  is  from  75$  to  78$  of  their  total  weight,  or 
say  about  512  cwt.  altogether,  being  256  cwt.  per  machine. 

RADIATION   OF  HEAT. 

Radiation  of  heat  takes  place  between  bodies  at  all  distances  apart,  and 
follows  the  laws  for  the  radiation  of  light. 

The  heat  rays  proceed  in  straight  lines,  and  the  intensity  of  the  rays 
radiated  from  any  one  source  varies  inversely  as  the  square  of  their  distance 
from  the  source. 

This  statement  has  been  erroneously  interpreted  by  some  writers,  who 
have  assumed  from  it  that  a  boiler  placed  two  feet  above  a  fire  would  re- 
ceive by  radiation  only  one  fourth  as  much  heat  as  if  it  were  only  one  foot 
above.  In  the  case  of  boiler  furnaces  the  side  walls  reflect  those  rays  that 
are  received  at  an  angle— follow  ing  the  law  of  optics,  tliar,  the  angle  of  inci- 
dence is  equal  to  the  angle  of  reflection.— wilh  the  result  that  the  intensity 
of  heat  two  feet  above  the  fire  is  practically  the  same  as  at  one  foot  above, 
instead  of  only  one-fourth  as  much. 

The  rate  at  which  a  hotter  body  radiates  heat,  and  a  colder  body  absorbs 
heat,  depends  upon  the  state  of  the  surfaces  of  the  bodies  as  well  as  on  their 
temperatures.  The  rate  of  radiation  and  of  absorption  are  increased  by 
darkness  and  roughness  of  the  surfaces  of  the  bodies,  and  diminished  by 
smoothness  and  polish.  For  this  reason  the  covering  of  steam  pipes  and 
boilers  should  be  smooth  and  of  a  light  color:  uncovered  pipes  and  steam- 
cylinder  covers  should  be  polished. 

The  quantity  of  heat  radiated  by  a  body  is  also  a  measure  of  its  heat- 
absorbing  power,  under  the  same  circumstances.  When  a  polished  body  is 
struck  by  a  ray  of  heat,  it  absorbs  part  of  the  heat  and  reflects  the  rest. 
The  reflecting  power  of  a  body  is  therefore  the  complement  of  its  absorbing 
power,  which  latter  is  the  same  as  its  radiating  power. 

The  relative  radiating  and  reflecting  power  of  different  bodies  has  been 
determined  by  experiment,  as  shown  in  the  table  below,  but  as  far  as  quan- 
tities of  heat  are  concerned,  says  Prof.  Trowbridge  (Johnson's  Cyclopaedia, 
art.  Heat),  it  is  doubtful  whether  anything  further  than  the  said  relative 
determinations  can,  in  the  present  state  of  our  knowledge,  be  depended 
upon,  the  actual  or  absolute  quantities  for  different  temperatures  being  still 
uncertain.  The  authorities  do  not  even  agree  on  the  relative  radiating 
powers.  Thus,  Leslie  gives  for  tin  plate,  gold,  silver,  and  copper  the  figure 
12,  which  differs  considerably  from  the  figures  in  the  table  below,  given  by 
Clark,  stated  to  be  on  the  authority  of  Leslie,  De  La  Provostaye  and  De- 
sains,  and  Melloni. 


468 


HEAT. 


Relative  Radiating  and  Reflecting  Power   of  Different 
Substances. 


h 

be 

obJO 

to 

Jf?  ? 

'«! 

.sl  ® 

'o  ? 

|J° 

01  PH 

~ll 

il 

£** 

tf 

3 

& 

Lampblack       

100 

o 

Zinc  polished 

19 

81 

Water 

100 

o 

Steel  polished 

17 

83 

Carbonate  of  lead.  .  . 

100 

0 

Platinum,  polished.. 

24 

76 

W  riting-paper  

98 

2 

"          in  sheet  .  . 

17 

83 

Ivory,  jet,  marble 

93  to  98 

7  to  2 

Tin 

15 

85 

Ordinary  glass  

90 

10 

Brass,      cast,    dead 

Ice           .... 

85 

15 

polished 

89 

Gum  lac  

72 

28 

Brass,     bright    pol- 

Silver-leaf on  glass 

27 

73 

ished 

7 

93 

Cast  iron,  bright  pol- 
ished 

25 

75 

Copper,  varnished  .  . 
"       hammered 

14 

7 

86 
93 

Mercury,  about  

23 

77 

Gold,  plated  

5 

95 

Wrought    iron,    pol- 

tk   on  polished 

ished 

23 

77 

steel 

3 

97 

Silver,    polished 

bright  

3 

97 

Experiments  of  Dr.  A.  M.  Mayer  give  the  following:  The  relative  radia- 
tions from  a  cube  of  cast  iron,  having  faces  rough,  as  from  the  foundry, 
planed,  *'  drawfiled,"  and  polished,  and  from  the  same  surfaces  oiled,  are  as 
below  (Prof.  Thurston,  in  Trans.  A.  S.  M.  E.,  vol.  xvi.) : 


Surface. 

Oiled. 

Dry. 

Rough  

100 
60 
49 

45 

100 
32 

20 

18 

Planed      

Drawfiled  

Polished  

It  here  appears  that  the  oiling  of  smoothly  polished  castings,  as  of  cylin- 
der-heads of  steam-engines,  more  than  doubles  the  loss  of  heat  by  radiation, 
while  it  does  not  seriously  affect  rough  castings. 

CONDUCTION   AND  CONVECTION  OF  HEAT* 

Conduction  is  the  transfer  of  heat  between  two  bodies  or  parts  of  a 

body  which  touch  each  other.    Internal  conduction  takes  place  between  the 

parts  of  one  continuous  body,  and  external  conduction  through  the  surface 

of  contact  of  a  pair  of  distinct  bodies. 

The  rate  at  which  conduction,  whether  internal  or  external,  goes  on, 
being  proportional  to  the  area  of  the  section  or  surface  through  which  it 
takes  place,  may  be  expressed  in  thermal  units  per  square  foot  of  area  per 
hour 

Internal  Conduction  varies  with  the  heat  conductivity,  which  de- 
pends upon  the  nature  of  the  substance,  and  is  directly  proportional  to  the 
difference  between  the  temperatures  of  the  two  faces  of  a  layer,  and  in- 
versely as  its  thickness.  The  reciprocal  of  the  conductivity  is  called  the 
internal  thermal  resistance  of  the  substance.  If  r  represents  this  resistance, 
x  the  thickness  of  the  layer  in  inches,  T'  and  Tthe  temperatures  on  the  two 
faces,  and  q  the  quantity  in  thermal  units  transmitted  per  hour  per  square 

foot  of  area,    q  =  — ^  — - .  (Rankine.) 


P6clet  gives  the  following  values  of  r  : 


Gold,  platinum,  silver 0.0016 

Copper 0.0018 

Iron 0.0043 

Zinc 0.0045 


Lead 0.0090 

Marble 0.0716 

Brick 0.1500 


CONDUCTION  AND   CONVECTION  OF  HEAT. 


469 


Relative  Heat-conducting  Power  of  Metals. 

(*  Calvert  &  Johnson  ;  t  Weidemann  &  Franz.) 
Silver  =  1000. 


Metals.         *0.  &  J. 

Silver 1000 

Gold 981 

Gold,    with    \%     of 

silver 840 

Copper,  rolled 845 

Copper,  cast 811 

Mercury 677 

Mercury,  with  1.25g 

of  tin 412 

Aluminum 665 

Zinc,  rolled 641 

Zinc: 

cast  vertically 628 

cast  horizontally. .  608 


tW.  &  F. 
1000 
532 


736 


Metals.         *C.  &J.  tW.  &  F. 

Cadmium 577         

Wrought  iron 436  119 

Tin 422  145 

Steel 397  116 

Platinum 380  84 

Sodium' 365 

Castiron 359 

Lead 287  85 

Antimony  : 

cast  horizontally. . .  215  .... 

cast  vertically 192         

Bismuth 61  18 


INFLUENCE  OP  A  NON-METALLIC  SUBSTANCE  IN  COMBINATION  ON  THE 
CONDUCTING  POWER  OF  A  METAL. 


Influence  of  carbon  on  iron  : 

Wrought  iron 436 

Steel 397 

Cast  iron 359 


Influence  of  arsenic  on  copper  : 

Cast  copper 81 1 

Copper  with  \%  of  arsenic 570 

with  .5$  of  arsenic 669 

"       with  .25$  of  arsenic. ...  771 

Strain-pipe  Coverings. 

(Experiments  by  Prof.  Ordway,  Trans.  A.  S.  M.  E.,  v,73;  also  Circular  No.  27 

of  Boston  Mfrs.  Mutual  Fire  Ins.  Co.,  1890.) 

It  will  be  observed  that  several  of  the  incombustible  materials  are  nearly 
as  efficient  as  wool,  cotton,  and  feathers,  with  which  they  may  be  compared 
in  the  following  table.  The  materials  which  may  be  considered  wholly 
free  from  the  danger  of  being  carbonized  or  ignited  by  slow  contact  with 
pipes  or  boilers  are  printed  in  Roman  type.  Those  which  are  more  or  less 
liable  to  be  carbonized  are  printed  in  italics. 

TABLE  I. 


Substance  1  inch  thick.    Heat  applied, 
310°  F. 

Pounds  of 
Water 
heated 
10°  F.,  per 
hour, 
through 
1  square 
foot. 

Solid 
Matter  in 
1  square 
foot  1  inch 
thick,  parts 
in  1000. 

Air  Included, 
parts  in  1000. 

1    Loose  wool 

8  1 

56 

944 

2   Live-geese  feathers      

9.6 

50 

950 

10.4 

20 

980 

4.  Hair  felt         .          ... 

10  3 

185 

815 

5.  Loose  lampblack  

9  8 

56 

944 

6.  Compressed  lampblack  

10.6 

244 

756 

7.  Cork  charcoal  

11  9 

53 

947 

8.  White-pine  charcoal  

13.9 

119 

881 

9.  Anthracite-coal  powder  

35.7 

506 

494 

10.  Loose  calcined  magnesia  

12.4 

23 

977 

11.  Compressed  calcined  magnesia. 

42  6 

285 

715 

12.  Light  carbonate  of  magnesia  

13.7 

60 

940 

13.  Compressed  carbonate  of  magnesia  
14    Loose  fossil-meal 

15.4 
14  5 

150 
60 

850 
940 

15.  Crowded  fossil-meal 

15  7 

112 

888 

16.  Ground  chalk  (Paris  white)  

20  6 

253 

747 

17    Dry  plaster  of  Paris  

30  9 

368 

632 

J8.  Fine  asbestos  

49  0 

81 

919 

19   Air  alone  ... 

48  0 

o 

1000 

20.  Sand  

62.1 

527 

471 

470                                                HEAT. 
TABLE  II. 

Covering. 

Pounds  of  Water 
heated  10°  F., 
per  hour,  by 
1  square  foot. 

21    Best  slag-wool                  -  .               ... 

13 

22    Paper                        

14 

23    Blottinq-'pct'peY  wound  tight                   .. 

21 

24    .^Isfrcs'fos  paper  itwiind  tight  

21  7 

25    Cork  strips  bound  on  

14  6 

26    Straw  Tope  wound  spirally  

18 

18  7 

28    Paste  of  fossil-meal  with  hair      .        

16  7 

29    Paste  of  fossil-meal  with  asbestos  

22 

30    Loose  bituminous-  coal  ashes  ..       .       ........ 

21 

31    Loose  anthracite-coal  ashes  

27 

32.  Paste  of  clay  and  vegetable  fibre  .  .     

30.9 

Professor  Ord way's  report  says:  Careful  experiments  have  been  made 
with  various  non-conductors,  each  used  in  a  mass  one  inch  thick,  placed  on 
a  flat  surface  of  iron  kept  heated  by  steam  to  310°  Fahr.  Table  I  gives  the 
amount  of  heat  transmitted  per  hour  through  each  kind  of  non-conductor 
one  inch  thick,  reckoned  in  pounds  of  water  heated  10°  Fahr.,  the  unit  of  area 
being  one  square  foot  of  covering. 

The  substances  given  in  Table  II  were  actually  tried  as  coverings  for 
two-inch  steam-pipe,  but  for  convenience  of  comparison  the  results  have 
been  reduced  by  calculation  to  the  same  terms  as  in  Table  I. 

Later  experiments  have  given  results  for  still  air  which  differ  little  from 
those  of  Nos.  3,  4,  and  6.  In  fact  the  bulk  of  matter  in  the  best  non-conduc- 
tors is  relatively  too  small  to  have  any  specific  effect,  except  to  entrap  the 
air  and  keep  it  stagnant.  These  substances  keep  the  air  still  by  virtue  ot 
the  roughness  of  their  fibres  or  particles.  The  asbestos,  No.  18,  had  smooth 
fibres,  which  could  not  prevent  the  air  from  moving  about. 

Later  trials  with  an  asbestos  of  exceedingly  fine  fibre  have  made  a  some- 
what better  showing,  but  asbestos  is  really  one  of  the  poorest  non-conduc- 
tors. By  reason  of  its  fibrous  character  it  may  be  used  advantageously 
to  hold  together  other  incombustible  substances,  but  the  less  the  better. 
We  have  made  trials  of  two  samples  of  a  <l  magnesia  covering,"  consisting 
of  carbonate  of  magnesia  with  a  small  percentage  of  good  asbestos  fibre. 
One  transmitted  heat  which,  reduced  to  the  terms  of  Table  I,  would  amount 
to  15  IDS.:  the  denser  one  gave  20  Ibs.  The  former  contained  250/1000 
of  solid  matter;  the  latter  396/1000. 

Any  suitable  substance  which  is  used  to  prevent  the  escape  of  steam 
heat  should  not  be  less  than  one  inch  thick. 

Any  covering  should  be  kept  perfectly  dry,  for  not  only  is  water  a  good 
carrier  of  heat,  but  it  has  been  found  that  still  water  conducts  heat  about 
eight  times  as  rapidly  as  still  air. 

Heat-conducting  Power  of  Covering  Materials. 

(J.  J.  Coleman,  Eng'g,  Sept.  5,  1884,  p.  237.) 
Experiments  were  made  by  filling  a  10-in.  cube  with   ice,  surrounding  it 

with  the  different  materials   to  be  tested,  and  noting  the  quantity  of  ice 

melted  per  hour  with  each  insulator. 
The  relative  results  were  as  follows  : 

Silicate  cotton  (mineral  wool) ...  100 

Hair  felt 117 

Cotton  wool 122 


Sheep's  wool  136 

Infusorial  earth 136 


Charcoal 140 

Sawdust 163 

Gas-works  breeze i?30 

Wood  and  air-space. 280 


The  Rate  of  External  Conduction  through  the  bounding  sur- 
face between  a  solid  body  and  a  fluid  is  approximately  proportional  to  the 
difference  of  temperature,  when  that  is  small;  but  when  that  difference  is 
considerable  the  rate  of  conduction  increases  faster  than  the  simple  ratio 
pf  that  difference.  (Rankine,) 


CONDUCTION"  AND   CONVECTION   OF   HEAT.          471 

If  r,  as  before,  is  the  coefficient  of  internal  thermal  resistance,  e  and  e'  the 
coefficient  of  external  resistance  of  the  two  surfaces,  x  the  thickness  of  the 
plate,  and  T'  and  Tthe  temperatures  of  the  two  fluids  in  contact  with  the 

T'  —  T 

two  surfaces,  the  total  thermal  resistance  is  q  =  —  — .   According  to 

e  +  e'  +  rx 

Peclet,  e  +  e'  =  ^  -y/  _        ,  in  which  the  constants  A  and  B  have 

the  following  values  : 

B  for  polished  metallic  surfaces 0028 

B  for  rough  metallic  surfaces  and  for  non-metallic  surfaces..     .0037 

A  for  polished  metals,  about 90 

A  for  glassy  and  varnished  surfaces 1 .34 

A  for  dull  metallic  surfaces 1 .58 

A  for  lamp-black 1 .78 

When  a  metal  plate  has  a  liquid  at  each  side  of  it,  it  appears  from  experi- 
ments by  Peclet  that  B  =  .058,  A  -  8.8. 

The  results  of  experiments  on  the  evaporative  power  of  boilers  agree  very 
well  with  the  following  approximate  formula  for  the  thermal  resistance  of 
boiler  plates  and  tubes  : 

e+e'=  <r=a>' 

which  gives  for  the  rate  of  conduction,  per  square  foot  of  surface  per  Lour, 

(Tf  -  T)* 
q  =     —^ ' 

This  formu'a  is  proposed  by  Rankine  as  a  rough  approximation,  near 
enough  to  the  truth  for  its  purpose.  The  value  of  a  lies  between  160  and  200. 

Convection,  or  carrying  of  heat,  means  the  transfer  and  diffusion  of 
the  heat  in  a  fluid  mass  by  means  of  the  motion  of  the  particles  of  that 
mass. 

The  conduction,  properly  so  called,  of  heat  through  a  stagnant  mass  of 
fluid  is  very  slow  in  liquids,  and  almost,  if  not  wholly,  inappreciable  in 
gases.  It  is  only  by  the  continual  circulation  and  mixture  of  the  particles  of 
tirie  fluid  that  uniformity  of  temperature  can  be  maintained  in  the  fluid 
mass,  or  heat  transferred  between  the  fluid  mass  and  a  solid  body. 

The  free  circulation  of  each  of  the  fluids  which  touch  the  side  of  a  solid 
plate  is  a  necessary  condition  of  the  correctness  of  Rankine's  formulae  for 
the  conduction  of  heat  through  that  plate;  and  in  these  formulae  it  is  im- 
plied that  the  circulation  of  each  of  the  fluids  by  currents  and  eddies  is  such 
as  to  prevent  any  considerable  difference  of  temperature  between  the  fluid 
particles  in  contact  with  one  side  of  the  solid  plate  and  those  at  considerable 
distances  from  it. 

When  heat  is  to  be  transferred  by  convection  from  one  fluid  to  another, 
through  an  intervening  layer  of  metal,  the  motions  of  the  two  fluid  masses 
should,  if  possible,  be  in  opposite  directions,  in  order  that  the  hottest  par- 
ticles of  each  fluid  may  be  in  communication  with  the  hottest  particles  of 
the  other,  and  that  the  minimum  difference  of  temperature  between  the 
adjacent  particles  of  the  two  fluids  may  be  the  greatest  possible. 

Thus,  in  the  surface  condensation  of  steam,  by  passing  it  through  metal 
tubes  immersed  in  a  current  of  cold  water  or  air,  the  cooling  fluid  should  be 
made  to  move  in  the  opposite  direction  to  the  condensing  steam. 

Transmission  of  Heat,  through  Solid  Plates,  from 
Water  to  Water.  (Clark,  S.E.).— M.  Peclet  found,  from  experiments 
made  with  plates  of  wrought  iron,  cast  iron,  copper,  lead,  zinc,  and  tin, 
that  when  the  fluid  in  contact  with  the  surface  of  the  plate  was  not  circu- 
lated by  artificial  means,  the  rate  of  conduction  was  the  same  for  different 
metals  and  for  plates  of  the  same  metal  of  different  thicknesses.  But 
when  the  water  was  thoroughly  circulated  over  the  surfaces,  and  when 
these  were  perfectly  clean,  the  quantity  of  transmitted  heat  was  inversely 
proportional  to  the  thickness,  and  directly  as  the  difference  in  temperature 
of  the  two  faces  of  the  plate.  When  the  metal  surface  became  dull,  the 
rate  of  transmission  of  heat  through  all  the  metals  was  very  nearly  the 
same. 

It  follows,  says  Clark,  that  the  absorption  of  heat  through  metal  plates  is 
more  active  whilst  evaporation  is  in  progress — when  the  circulation  of  the 
water  is  more  active— than  while  the  water  i$  being  heated  up  to  the  boiling 
point. 


473 


HEAT. 


Transmission  from  Steam  to  Water.— M.  Peclet's  principle  is 
supported  by  the  results  of  experiments  made  in  1867  by  Mr.  Isherwood  on 
the  conductivity  of  different  metals.  Cylindrical  pots,  10  inches  in  diameter, 
21*4  inches  deep  inside,  and  ^  inch,  14  inch,  and  %  inch  thick,  turned  and 
bored,  were  formed  of  pure  copper,  brass  (60  copper  and  40  zinc),  rolled 
wrought  iron,  and  remelted  cast  iron.  They  were  immersed  in  a  steam 
bath,  which  was  varied  from  220°  to  320°  F.  Water  at  21a°  was  supplied  to 
the  pots,  which  were  kept  filled.  It  was  ascertained  that  the  rate  of  evapora- 
tion was  in  the  direct  ratio  of  the  difference  of  the  temperatures  inside  and 
outside  ol  the  pots;  that  is,  that  the  rate  of  evaporation  per  degree  of 
difference  of  temperatures  was  the  same  for  all  temperatures;  and  that  the 
rate  of  evaporation  was  exactly  the  same  for  different  thicknesses  of  the 
metal.  The  respective  rates  of  conductivity  of  the  several  metals  were  as 
follows,  expressed  in  weight  of  water  evaporated  from  and  at  212°  F.  per 
square  foot  of  the  interior  surface  of  the  pots  per  degree  of  difference  of 
temperature  per  hour,  together  with  the  equivalent  quantities  of  heat-units: 
Water  at  212°.  Heat-units.  Ratio. 

Copper 665  Ib.  642.5  1.00 

Brass 577"  556.8  .87 

Wrought  iron 387"  373.6  .58 

Cast  iron 327"  315.7  .49 

Whitham,  "Steam  Engine  Design,"  p.  283,  also  Trans.  A.  S.  M.  E.  ix,  425,  in 
using  these  data  in  deriving  a  formula  for  surface  condensers  calls  these 
figures  those  of  perfect  conductivity,  and  multiplies  them  by  a  coefficient 
C,  which  he  takes  at  0.323,  to  obtain  the  efficiency  of  condenser  surface  in 
ordinary  use.  i.e.,  coated  with  saline  and  greasy  deposits. 

Transmission  of  Heat  from  Steam  to  Water  through 
Coils  of  Iron  Pipe.— H.  G.  C.  Kopp  and  F.  J.  Meystre  (Stevens  Indi- 
cator, Jan.,  1894),  give  an  account  of  some  experiments  on  transmission  of 
heat  through  coils  of  pipe.  They  collate  the  results  of  earlier  experiments 
as  follows,  for  comparison: 


Experimenter. 

3 

1 
1 

Steam  Con- 
densed per 
Square  foot  per 
degree  differ- 
ence of  temper- 
ature per  hour. 

Heat  trans- 
mitted per 
square  foot  per 
degree  differ- 
ence of  temper- 
ature per  hour. 

Eemarks. 

£•9 

III 

!* 

II 

Laurens 

Havrez.. 
Perkins. 

Box  
Havrez.. 

Copper  coils... 
2  Copper  coils. 
Copper  coil  .  .  . 

Iron  coil  

.292 
.268 

.981 
1.20 
1.26 

.24 

315 

"280 

974 
1120 
1200 

215 

208.2 

100 

j  Steam  pressure 
1     =  100. 
i  Steam  pressure 
i     =  10. 

.22 

Iron  tube  

Cast-iron  boi'l- 
er  

.235 
.196 
.206 

.077 

.105 

230 
207 
210 

82 

From  the  above  it  would  appear  that  the  efficiency  of  iron  surfaces  is  less 
than  that  of  copper  coils,  plate  surfaces  being  far  inferior. 

In  all  experiments  made  up  to  the  present  time,  it  appears  that  the  tem- 
perature of  the  condensing  water  was  allowed  to  rise,  a  mean  between  the 
initial  and  final  temperatures  being  accepted  as  the  effective  temperature. 
But  as  water  becomes  warmer  it  circulates  more  rapidly,  thereby  causing: 
the  water  surrounding  the  coil  to  become  agitated  and  replaced  bj  cooler 
water,  which  allows  more  heat  to  be  transmitted,. 


CONDUCTION  AND  CONVECTION  OF  HEAT.        473 


Again,  in  accepting  the  mean  temperature  as  that  of  the  condensing  me- 
dium, the  assumption  is  made  that  the  rate  of  condensation  is  in  direct  pro- 
portion to  the  temperature  of  the  condensing  water. 

In  order  to  correct  and  avoid  any  error  arising  from  these  assumptions 
and  approximations,  experiments  were  undertaken,  in  which  all  the  condi- 
tions were  constant  during  each  test. 

The  pressure  was  maintained  uniform  throughout  the  coil,  and  provision 
was  made  for  the  free  outflow  of  the  condensed  steam,  in  order  to  obtain 
at  all  times  the  full  efficiency  of  the  condensing  surface.  The  condensing 
water  was  continually  stirred  to  secure  uniformity  of  temperature,  which 
was  regulated  by  means  of  a  steam-pipe  and  a  cold-water  pipe  entering  the 
tank  in  which  the  coil  was  placed. 

The  following  is  a  condensed  statement  of  the  results 

HEAT  TRANSMITTED  PER  SQUARE  FOOT  OF  COOLING  SURFACE,  PEH  DEGREE 
OF  DIFFERENCE  OF  TEMPERATURE.    (British  Thermal  Units.) 


Temperature 
of  Condens- 
ing Water. 

1-in.  Iron  Pipe; 
Steam  inside, 
60  Ibs.  Gauge 
Pressure. 

1*4  in.  Pipe; 
Steam  inside. 
10  Ibs. 
Pressure. 

1^  in.  Pipe; 
Steam  inside, 
10  Ibs. 
Pressure. 

V&  in.  Pipe; 
Steam  inside, 
60  Ibs. 
Pressure. 

80 
100 
120 
140 
160 
180 
200 

265 
269 
272 

277 
281 
299 
313 

128 
130 
137 
145 
158 
174 

200 
230 
260 
267 
271 
270 

*239 
247 
276 

306 
349 
419 

The  results  indicate  that  the  heat  transmitted  per  degree  of  difference  of 
temperature  in  general  increases  as  the  temperature  of  the  condensing 
water  is  increased. 

The  amount  transmitted  is  much  larger  with  the  steam  on  the  outside  of 
the  coil  than  with  the  steam  inside  the  coil.  This  may  be  explained  in  part  by 
the  fact  that  the  condensing  water  when  inside  the  coil  flows  over  the  sur- 
face of  conduction  very  rapidly,  and  is  more  efficient  for  cooling  than  when 
contained  in  a  tank  outside  of  the  coil. 

This  result  is  in  accordance  with  that  found  by  Mr.  Thomas  Craddock, 
which  indicated  that  the  rate  of  cooling  by  transmission  of  heat  through 
metallic  surfaces  was  almost  wholly  dependent  on  the  rate  of  circulation  of 
the  cooling  medium  over  the  surf  ace  to  be  cooled. 

Transmission  of  Heat  in  Condenser  Tabes*  (Eng'g,  Dec. 
10,  1875,  p.  449.).— In  1874  B.  C.  Nichol  made  experiments  for  determining  the 
rate  at  which  heat  was  transmitted  through  a  condenser  tube.  The  results 
went  to  show  that  the  amount  of  heat  transmitted  through  the  walls  of  the 
tube  per  estimated  degree  of  mean  difference  of  temperature  increased 
considerably  with  this  difference.  For  example: 
Estimated  mean  difference  of  Vertical  Tube. 


mean 

temperature  between  inside  and 
outside  of  tube,  degrees  Fahr.  . 

Heat-units  transmitted  per  hour 
per  square  foot  of  surface  per 
degree  of  mean  diff.  of  temp. . 


Horizontal  Tube 
128     151.9     J5273        111.6     146.2     150^4 


610        737        823 


422     531        561 

These  results  seem  to  throw  doubt  upon  Mr.  Isherwood's  statement  that 
the  rate  of  evaporation  per  degree  of  difference  of  temperature  is  the  same 
for  all  temperatures. 

Mr.  Thomas  Craddock  found  that  water  was  enormously  more  efficient 
than  air  for  the  abstraction  of  heat  through  metallic  surfaces  in  the  process 
of  cooling.  He  proved  that  the  rate  of  cooling  by  transmission  of  heat 
through  metallic  surfaces  depends  upon  the  rate  of  circulation  of  the  cool- 
ing medium  over  the  surface  to  be  cooled.  A  tube  filled  with  hot  water, 
moved  by  rapid  rotation  at  the  rate  of  59  ft.  per  second,  through  air,  lost  as 
much  heat  in  one  minute  as  it  did  in  still  air  in  12  minutes.  In  water,  at  a 
velocity  of  3  ft.  per  second,  as  much  heat  was  abstracted  in  half  a  minute  as 
was  abstracted  in  one  minute  when  it  was  at  rest  in  the  water.  Mr.  Crad- 
dock concluded,  further,  that  the  circulation  of  the  cooling  fluid  became  of 


474 


HEAT. 


greater  importance  as  the  difference  of  temperature  on  the  two  sides  of  the 
plate  became  less.  (Clark,  R.  T.  D.,  p.  461.) 

Heat  Transmission  through  Cast-iron  Plates  Pickled  in 
Nitric  Acid.— Experiments  by  R.  C.  Carpenter  (Trans.  A.  S.  M.  E.,  xii 
179)  show  a  marked  change  in  the  conducting  power  of  the  plates  (from 
steam  to  water),  due  to  prolonged  treatment  with  dilute  nitric  acid. 

The  action  of  the  nitric  acid,  by  dissolving  the'free  iron  and  not  attacking 
the  carbon,  forms  a  protecting  surface  to  the  iron,  which  is  largely  com- 
posed of  carbon.  The  following  is  a  summary  of  results: 


Character  of  Plates,  each  plate  8.4  in. 
by  5.4  in.,  exposed  surface  27  sq.  ft. 

Increase  in 
Tempera- 
ture of 
3.125  Ibs.  of 
Water 
each 
Minute. 

Proportionate 
Thermal  Units 
Transmitted  for 
each  Degree  of 
Difference  of 
Temperature  per 
Square  Foot  per 
Hour. 

Rela- 
tive 
Trans- 
mission 
of 
Heat. 

Cast    iron—  untreated    skin    on,    but 
clean  free  from  rust        .           .  . 

13  90 

113  2 

100  0 

Cast  iron—  nitric  acid,  \%  sol.,  9  days.  . 
l^sol.,  18  days. 
l#sol.,  40  days. 
5f0  sol.,  9  days.. 
**                               5%  sol.,  40  days. 
Plate  of  pine  wood,  same  dimensions 
as  the  plate  of  cast  iron  

11.5 
9.7 
9.6 
9.93 
10.6 

0.33 

97.7 
80.08 
77.8 
87.0 
77.4 

1.9 

86.3 
70.7 
68.7 
76.8 
68.5 

1.6 

The  effect  of  covering  cast-iron  surfaces  with  varnish  has  been  investi- 
gated by  P.  M.  Chamberlain.  He  subjected  the  plate  to  the  action  of  strong 
acid  for  a  few  hours,  and  then  applied  a  non  conducting  varnish.  One  sur- 
face only  was  treated.  Some  of  his  results  are  as  follows: 

170.  As  finished— greasy. 

152.    **  .     "  washed  with  benzine  and  dried. 

169.  Oiled  with  lubricating  oil. 

162.  After  exposure  to  nitric  acid  sixteen  hours,  then  oiled  (lin- 
seed oil.) 

166  After  exposure  to  hydrochloric  acid  twelve  hours,  then  oiled 
(linseed  oil.) 

'    r  After  exposure  to  sulphuric  acid  1,  water  2,  for  48  hours, 
jjy    i    then  oiled,  varnished,  and  allowed  to  dry  for  24  hours. 

Transmission  of  Heat  through  Solid  Plates  from  Air 
or  other  Dry  Gases  to  Water.  (From  Clark  on  the  Steam  Engine.) 
—The  law  of  the  transmission  of  heat  from  hot  air  or  other  gases  to  water, 
through  metallic  plates,  has  not  been  exactly  determined  by  experiment. 
The  general  results  of  experiments  on  the  evaporative  action  of  different 
portions  of  the  heating  surface  of  a  steam  boiler  point  to  the  general  law 

.!__.  ^ x...-  _*!_„_.,.  . -»jtted  per  degree  difference  of  temperature 

3  differences  of  temperature, 
rom  the  gas  to  the  plate  surface  is  much 
accelerated  by  mechanical  impingement  of  the  gaseous  products  upon  the 
surface. 

Clark  says  that  when  the  surfaces  are  perfectly  clean,  the  rate  of  trans- 
mission of  heat  through  plates  of  metal  from  air  or  gas  to  water  is  greater 
for  copper,  next  for  brass,  and  next  for  wrought  iron.  But  when  the  sur- 
faces are  dimmed  or  coated,  the  rate  is  the  same  for  the  different  metals. 

With  respect  to  the  influence  of  the  conductivity  of  metals  and  of  the 
thickness  of  the  plate  on  the  transmission  of  heat  from  burnt  gases  to 
water,  Mr.  Napier  made  experiments  with  small  boilers  of  iron  and  copper 
placed  over  a  gas-flame.  The  vessels  were  5  inches  in  diameter  and  '% 
inches  deep.  From  three  vessels,  one  of  iron,  one  of  copper,  and  one  of  iron 
sides  and  copper -bottom,  each  of  them  1/30  inch  in  thickness,  equal  quanti- 
ties of  water  were  evaporated  to  dryness,  in  the  times  as  follows  : 


pui  tjiuiis  ui    i/iif  iicettiug  suiifcico   ui-   a, 

that  the  quantity  of  heat  transmitted 

is  practically  uniform  for  various  diff( 

The  communication  of  heat  from 


CONDUCTION  AND   CONVECTION   OF   HEAT.         475 

Water.  Iron  Vessel.         Copper  Vessel.      Iron 

4  ounces  19  minutes  18.5  minutes       .  

11        "  33        "  30.75        "  

5^    "  50  44  "  

4        "  35.7    "  36.83  minutes. 

Two  other  vessels  of  iron  sides  1/30  inch  thick,  one  having  a  ^-inch  copper 
oottom  and  the  other  a  !4-inch  lead  bottom,  were  tested  against  the  iron 
and  copper  vessel,  1/30  inch  thick.  Equal  quantities  of  water  were  evapo- 
rated in  54,  55,  and  53^  minutes  respectively.  Taken  generally,  the  results 
of  these  experiments  show  that  there  are  practically  but  slight  differences 
between  iron,  copper,  and  lead  in  evaporative  activity,  and  that  the  activity 
is  not  affected  by  the  thickness  of  the  bottom. 

Mr.  W.  B.  Johnson  formed  a  like  conclusion  from  the  results  of  his  obser- 
vations of  two  boilers  of  160  horse-power  each,  made  exactly  alike,  ex- 
cept that  one  had  iron  flue-tubes  and  the  other  copper  flue-tubes.  No  dif- 
ference could  be  detected  between  the  performances  of  these  boilers. 

Divergencies  between  the  results  of  different  experimenters  are  attribut- 
able probably  to  the  difference  of  conditions  under  which  the  heat  was 
transmitted,  as  between  water  or  steam  and  water,  and  between  gaseous 
matter  and  water.  On  one  point  the  divergence  is  extreme:  the  rate  of 
transmission  of  heat  per  degree  of  difference  of  temperature.  Whilst  from 
400  to  600  units  of  heat  are  transmitted  from  water  to  water  through  iron 
plates,  per  degree  of  difference  per  square  foot  per  hour,  the  quantity  of 
heat  transmitted  between  water  and  air,  or  other  dry  gas,  is  only  about 
from  2  to  5  units,  according  as  the  surrounding  air  is  at  rest  or  in  movement. 
In  a  locomotive  boiler,  where  radiant  heat  was  brought  into  play,  17  units 
of  heat  were  transmitted  through  the  plates  of  the  fire-box  per  degree  of 
difference  of  temperature  per  square  foot  per  hour. 

Transmission  of  Heat  through  Plates  and  Tubes  from 
Steam  or  Hot  Water  to  Air. — The  transfer  of  heat  from  steam  or 
water  through  a  plate  or  tube  into  the  surrounding  air  is  a  complex  opera- 
tion, in  which  the  internal  and  external  conductivity  of  the  metal,  the  radi- 
ating power  of  the  surface,  and  the  convection  of  heat  in  the  surrounding 
air  are  ail  concerned.  Since  the  quantity  of  heat  radiated  from  a  surface 
varies  with  the  condition  of  the  sun  ace  and  with  the  surroundings,  according 
to  laws  not  yet  determined,  and  since  the  heat  carried  away  by  convection 
varies  with  the  rate  of  the  flow  of  the  air  over  the  surface,  it  is  evident  that 
no  general  law  can  be  laid  down  for  the  total  quantity  of  heat  emitted. 

The  following  is  condensed  from  an  article  on  Loss  of  Heat  from  Steam- 
pipes,  in  The  Locomotive,  Sept.  and  Oct.,  1892. 

A  hot  steam  pipe  is  radiating  heat  constantly  off  into  space,  but  at  the 
same  time  it  is  cooling  also  by  convection.  Experimental  data  on  which  to 
base  calculations  of  the  heat  radiated  and  otherwise  lost  by  steam-pipes  are 
neither  numerous  nor  satisfactory. 

In  Box's  Practical  Treatise  on  Heat  a  number  of  results  are  given  for  the 
amount  of  heat  radiated  by  different  substances  when  the  temperature  of 
the  air  is  1°  Fahr.  lower  than  the  temperature  of  the  radiating  body.  A 
portion  of  this  table  is  given  below.  It  is  said  to  be  based  on  Peclet's  ex- 
periments. 

HEAT  UNITS  RADIATED  PER  HOUR,  PER  SQUARE  FOOT  OF  SURFACE,  FOR 
1°  FAHRENHEIT  EXCESS  IN  TEMPERATURE. 


Copper,  polished 03*27 

Tin,  polished   0440 

Zinc  and  brass,  polished 0491 

Tinned  iron,  polished 0858 

Sheet-iron,  polished  0920 

Sheet  lead  .  1329 


Sheet-iron ,  ordinary 5662 

Glass 51)48 

Cast  iron,  new 6480 

Common  steam-pipe,  inferred..  .6400 

Cast  and  sheet  iron,  rusted 6868 

Wood,  building  stone,  and  brick  .7358 


When  the  temperature  of  the  air  is  about  50° .or  60°  Fahr.,  and  the  radiat- 
ing body  is  not  more  than  about  30°  hotter  than  the  air,  we  may  calculate 
the  radiation  of  a  given  surface  by  assuming  the  amount  of  heat  given  off 
by  it  in  a  given  time  to  be  proportional  to  the  difference  in  temperature  be- 
tween the  radiating  body  and  the  air.  This  is  "  Newton's  law  of  cooling." 
But  when  the  difference  in  temperature  is  great,  Newton's  law  does  not  hold 
good;  the  radiation  is  no  longer  proportional  to  the  difference  in  tempera- 
ture, but  must  be  calculated  by  a  complex  formula  established  experiment, 
ally  by  Dulong  and  Petit.  Box  has  computed  a  table  from  this  formula, 
which  greatly  facilitates  its  application,  and  which  is  given  below  : 


476  HEAT. 

FACTORS  FOR  REDUCTION  TO  DULONG'S  LAW  OF  RADIATION. 


Differences  in  Tem- 
perature between 
Radiating  Body 
and  the  Air. 

Temperature  of  the  Air  on  the  Fahrenheit  Scale. 

32° 

50° 

59° 

68° 

86° 

104° 

122° 

140° 

158° 

176° 

194° 

212° 

Deg.  Fahr. 

18 

1.00 

1.07 

1.12 

1.16 

1.25 

1.36 

1.47 

1.58 

1.70 

1.85 

1.99 

2.15 

36 

1.03 

1.08 

1.16 

1.21 

1.30 

1.40 

1.52 

1.68 

1.76 

1.91 

2.06 

2.23 

54 

1.07 

1.161.20 

1.25 

1.35 

1.45 

1.58 

1.70 

1.83 

1.992.14 

2.31 

72 

1.12 

1.20 

1.25 

1.30 

1.40 

1.52 

1.64 

1.76 

1.90 

2.07 

2.23 

2.40 

90 

1.16 

1.25 

1.31 

1.36 

1.46 

1.58 

1.71 

1.84 

1.98 

2.15 

2.33 

2.51 

108 

1.81 

1.31 

1.36 

1.42 

1.52 

1.65 

1.78 

1.92 

2.07 

2.282.42 

2.62 

126 

1.26 

1.36 

1.42 

1.48 

1.50 

1.72 

1.86 

2.00 

2.16 

2.34 

2.52 

2.72 

144 

1.32 

1.42 

1.48 

1.54 

1.65 

1.79 

1.94 

2.08 

2.24 

2.442.64 

2.83 

162 

1.37 

1.48|1.54 

1.60 

1.73 

1.86 

2.02 

2.17 

2.34 

2.542.74 

2.96 

180 

1.44 

1.55 

1.61 

1.68 

1.81 

1.95 

2.11 

2.27 

2.46 

2.66 

2.87 

3.10 

198 

1.50 

1.62 

1.69 

1.75 

1.89 

2.04 

2.21 

2.38 

2.56 

2.783.00 

3.24 

216 

1.58 

1.691.76 

1.83 

1.97 

2.13 

2.32 

2.48 

2.68 

2.91 

3.13 

3.38 

234 

1.64 

1.77 

1.84 

1.90 

2.06 

2.28 

2.43 

2.52 

2.80 

3.033.28 

3.46 

252 

1.71 

1.85 

1.92 

2.00 

2.15 

2.33 

2.52 

2.71 

2.92 

3.18 

3.43 

3.70 

270 

1.79 

1.93 

2.01 

2.09 

2.22 

2.44 

2.64 

2.84 

3.06 

3.323.58 

3.87 

288 

1.89 

2.03 

2.12 

2.20 

2.37 

2.56 

2.78 

2.99 

3.22 

3.50 

3.77 

4.07 

306 

1.98 

2.13 

2.22 

2.31 

2.49 

2.69 

2.90 

3.12 

3.37 

3.663.95 

4.26 

324 

2.07 

2.23 

2.33 

2.42 

2.62 

2.81 

3.04 

3.28 

3.53 

3.844.14 

4.46 

342 

2.17 

2.34 

2.44 

2.54 

2.73 

2.95 

3.19 

3.44 

3.70 

4.024.34 

4.68 

3S° 

2.27 

2.45 

2.56 

2.66 

2.86 

3.09 

3.35 

3.60 

3.88 

4.22 

4.55 

4.91 

2.39 

2.57 

2.68 

2.79 

3.00 

3.24 

3.51 

3.78 

4.08 

4.424.77 

5.15 

396 

2.50 

2.70 

2.81 

2.93 

3.15 

3.40 

3.68 

3.97 

4.28 

4.645.01 

5.40 

414 

2.63 

2.842.95 

3.07 

3.31 

3.51 

3.87 

4.12 

4.48 

4.87 

5.26 

5.67 

432 

2.76 

2.98^.10 

3.233.47 

3.76 

4.10 

4.32 

4.61 

5.12 

5.33 

6.04 

The  loss  of  heat  by  convection  appears  to  be  independent  of  the  nature  of 
the  surface,  that  is,  it  is  the  same  for  iron,  stone,  wood,  and  other  materials. 
It  is  different  for  bodies  of  different  shape,  however,  and  it  varies  with  the 
position  of  the  body.  Thus  a  vertical  steam-pipe  will  not  lose  so  much  heat 
by  convection  as  a  horizontal  one  will;  for  the  air  heated  at  the  lower  part 
of  the  vertical  pipe  will  rise  along  the  surface  of  the  pipe,  protecting  it  to 
some  extent  from  the  chilling  action  of  the  surrounding  cooler  air.  For  a 
similar  reason  the  shape  of  a  body  has  an  important  influence  on  the  result, 
those  bodies  losing  most  heat  whose  forms  are  such  as  to  allow  the  cool  air 
free  access  to  every  part  of  their  surface.  The  following  table  from  Box 
gives  the  number  of  heat  units  that  horizontal  cylinders  or  pipes  lose  by 
convection  per  square  foot  of  surface  per  hour,  for  one  degree  difference  in 
temperature  between  the  pipe  and  the  air. 

HKAT  UNITS  LOST  BY  CONVECTION  FROM  HORIZONTAL  PIPES,  PER  SQUARE 

FOOT  OF  SURFACE  PER  HOUR,  FOR  A  TEMPERATURE 

DIFFERENCE  OF  1°  FAHR. 


External 

External 

External 

Diameter  of 

Heat  Units 

Diameter 

Heat  Units 

Diameter 

Heat  Units 

Pipe 
in  inches. 

Lost. 

of  Pipe 
in  inches. 

Lost. 

of  Pipe 
in  inches. 

Lost. 

2 

0.728 

7 

0.509 

18 

0.455 

3 

0.626 

8 

0.498 

24 

0.447 

4 

0.574 

9 

0.489 

36 

0.433 

5 

0.544 

10 

0.482 

48 

0.434 

6 

0.523 

12 

0.472 

The  loss  of  heat  by  convection  is  nearly  proportional  to  the  difference  in 
temperature  between  the  hot  body  and  the  air;  but  the  experiments  of 


CONDUCTION  AND   CONVECTION   OF   HEAT.         477 


Dulong  and  PSclet  show  that  this  is  not  exactly  true,  and  we  may  here  also 
resort  to  a  table  of  factors  for  correcting  the  results  obtained  by  simple 
proportion. 

FACTORS  FOR  REDUCTION  TO  DULONG'S  LAW  OF  CONVECTION. 


Difference 

Difference 

Difference 

in  Temp, 
between  Hot 

Factor. 

in  Temp, 
between  Hot 

Factor. 

in  Temp, 
between 

Factor. 

Body  and 
Air. 

Body  and 
Air. 

Hot  Body 
and  Air. 

18°  F. 

0.94 

180°  F. 

1.62 

342°  F. 

1.87 

36° 

1.11 

198° 

1.65 

360° 

1.90 

54° 

1.22 

216° 

1.68 

378° 

1.92 

72° 

1.30 

234° 

1.72 

396° 

1.94 

90° 

1.37 

252° 

1.74 

414° 

1.96 

108° 

1.43 

270° 

1.77 

432° 

1.98 

126° 

1.49 

288° 

1.80 

450° 

2.00 

144° 

1.53 

306° 

1.83 

468° 

2.02 

162° 

1.58 

324° 

1.85 

EXAMPLE  IN  THE  USE  OF  THE  TABLES. — Required  the  total  loss  of  heat  by 
both  radiation  and  convection,  per  foot  of  length  of  a  steam-pipe  2  11/32 
in.  external  diameter,  steam  pressure  60  Ibs.,  temperature  of  the  air  m  the 
room  68°  Fahr. 

Temperature  corresponding  to  60  Ibs.  equals  307°;  temperature  difference 
=  307  -  68  =  239°. 

Area  of  one  foot  length  of  steam-pipe  =  2  11/32  X  3.1416  -5-  12  =  0.614  sq. 
ft. 

Heat,  radiated  per  hour  per  square  foot  per  degree  of  difference,  from 
table,  0.64. 

Radiation  loss  per  hour  by  Newton's  law  =  239°  X  .614  ft.  X  .64  =  93.9 
heat  units.  Same  reduced  to  conform  with  Dulong's  law  of  radiation:  factor 
from  table  for  temperature  difference  of  239°  and  temperature  of  air  68°  = 
1.93.  93.9  X  1.93  =  181.2  heat  units,  total  loss  by  radiation. 

Convection  loss  per  square  foot  per  hour  from  a  2  11/32-inch  pipe:  by  in- 
terpolation from  table,  2"  =  .728.  3"  =  .626,  2  11/32"  =  .693. 

Area,  .614  X  -093  X  239°  =  101.7  heat  units.  Same  reduced  to  conform  with 
Dulong^s  law  of  convection:  101.7  X  1.73  (from  table)  =  175.9  heat  units  per 
hour.  Total  loss  by  radiation  and  convection  =  181.2  -j-  175.9  =  357.1  heat 
units  per  hour.  Loss  per  degree  of  difference  of  temperature  per  linear 
foot  of  pipe  per  hour  =  357.1  -H  239  =  1.494  heat  units  =  2.433  per  sq.  ft. 

It  is  not  claimed,  says  The  Locomotive,  that  the  results  obtained  by  this 
method  of  calculation  are  strictly  accurate.  The  experimental  data  are  not 
sufficient  to  allow  us  to  compute  the  heat-loss  from  steam-pipes  with  any 
great  degree  of  refinement;  yet  it  is  believed  that  the  results  obtained  as 
indicated  above  will  be  sufficiently  near  the  truth  for  most  purposes.  An 
experiment  by  Prof.  Ordway,  in  a  pipe  2  11/32  in.  diam.  under  the  above 
conditions  (Trans.  A.  S.  M.  E.,  v.  73),  showed  a  condensation  of  steam  of  181 
grammes  per  hour,  which  is  equivalent  to  a  loss  of  heat  of  358.7  heat  units 
per  hour,  or  within  half  of  one  per  cent  of  that  given  by  the  above  calcula- 
tion. 

According  to  different  authorities,  the  quantity  of  heat  given  off  by  steam 
and  hot-water  radiators  in  ordinary  practice  of  heating  of  buildings  by 
direct  radiation  varies  from  1.8  to  about  3  heat  units  per  hour  per  square 
foot  per  degree  of  difference  of  temperature. 

The  lowest  figure  is  calculated  from  the  following  statement  by  Robert 
Briggs  in  his  paper  on  "American  Practice  in  Warming  Buildings  by 
Steam  "  (Proc.  Inst.  C.  E.,  1882,  vol.  Ixxi):  "  Each  100  sq.  ft.  of  radiating 
surface  will  give  off  3  Fahr.  heat  units  per  minute  for  each  degree  F.  of  dif- 
ference in  temperature  between  the  radiating  surface  and  the  air  in  which 
it  is  exposed." 

The  figure  2  1/2  heat  units  is  given  by  the  Nason  Manufacturing  Company 
in  their  catalogue,  and  2  to  2  1/4  are  given  by  many  recent  writers. 

For  the  ordinary  temperature  difference  in  low-pressure  steam-heating, 
say  212°  —  70°  =  142°  F,,  1  Ib.  steam  condensed  from  212°  to  water  at  the 


478  HEAT. 

same  temperature  gives  up  965.7  heat  units.  A  loss  of  2  heat  units  per  sq. 
ft.  per  hour  per  degree  of  difference,  under  these  conditions,  is  equivalent 
to  2  X  142 -T- 965  =  0.3  Ibs.  of  steam  condensed  per  hour  per  sq.  ft.  of  heating 
surface.  (See  also  Heating  and  Ventilation.) 

Transmission  of  Heat  through  Walls,  etc.,  of  Buildings 
(Nason  Manufacturing  Co.).  (See  also  Heating  and  Ventilation.) — Heat 
has  the  remarkable  property  of  passing  through  moderate  thicknesses  of  air 
and  gases  without  appreciable  loss,  so  that  air  is  not  warmed  by  radiant 
lu- at,  but  by  contact  with  surfaces  that  have  absorbed  the  radiation. 

POWERS  OF  DIFFERENT  SUBSTANCES  FOB  TRANSMITTING  HEAT. 

Window-glass 1000        Bricks,  rough 200  to    250 

Oak  or  walnut ...  66        Bricks,  whitewashed 200 

White  pine 80       Granite  or  slate 250 

Pitch-pine 100       Sheet  iron 1030tolllO 

Lath  or  plaster  75  to    100 

A  square  foot  of  glass  will  cool  1.2T9  cubic  feet  of  air  from  the  tempera- 
ture inside  to  that  outside  per  minute,  and  outside  wall  surface  is  generally 
estimated  at  one  fifth  of  the  rate  of  glass  in  cooling  effect. 

Box,  in  his  4k  Practical  Treatise  on  Heat,"  gives  a  table  of  the  conducting 
powers  of  materials  prepared  from  the  experiments  of  Peclet.  It  gives  the 
quantity  of  heat  in  units  transmitted  per  square  foot  per  hour  by  a  plate  1 
inch  in  thickness,  the  two  surfaces  differing  in  temperature  1  degree: 

Fine-grained  gray  marble 28.00 

Coarse-grained  white  marble.. 22.4 

Stone,  calcareous,  fine 16.7 

Stone,  calcareous,  ordinary 13.68 

Baked  clay,  brickwork  4 . 83 

Brick-dust,  sifted 1 .33 

Hood,  in  his  "Warming  and  Ventilating  of  Buildings  "  p.  249,  gives  the 
results  of  M.  Depretz,  which,  placing  the  conducting  power  of  marble  at  1.00, 
give  .483  as  the  value  for  firebrick. 

THERMODYNAMICS. 

Thermodynamics,  the  science  of  heat  considered  as  a  form  of 
energy,  is  useful  in  advanced  studies  of  the  theory  of  steam,  gas,  and  air 
engines,  refrigerating  machines,  compressed  air,  etc.  The  method  of  treat- 
ment adopted  by  the  standard  writers  is  severely  mathematical,  involving 
constant  application  of  the  calculus.  The  student  will  find  the  subject 
thorougly  treated  in  the  recent  works  by  Rontgen  (Dubois's  translation), 
Wood,  and  Peabody. 

First  l,aw  of  Thermodynamics.  -Heat  and  mechanical  energy 
are  mutually  convertible  in  the  ratio  of  about  778  foot-pounds  for  the  British 
thermal  unit.  (Wood.)  Heat  is  the  living  force  or  vis  viva  due  to  certain 
molecular  motions  of  the  molecules  of  bodies,  and  this  living  force  may  be 
stated  or  measured  in  units  of  heat  or  in  foot-pounds,  a,  unit  of  heat  in 
British  measures  being  equivalent  to  772  [778]  foot-pounds.  (Trow bridge, 
Trans.  A.  S.  M.  E.,  vii.  727.) 

Second  Law  of  Thermodynamics.— The  second  law  has  by  dif- 
ferent writers  been  stated  in  a  variety  of  ways,  and  apparently  with  ideas 
so  diverse  as  not  to  cover  a  common  principle.  (Wood,  Therm.,  p.  389.) 

It  is  impossible  fora  self-act  ing  machine,  unaided  by  any  external  agency, 
to  convert  heat  from  one  body  to  another  at  a  higher  temperature.  (Clau- 
sins.) 

If  all  the  heat  absorbed  be  at  one  temperature,  and  that  rejected  be  at 
one  lower  temperature,  then  will  the  heat  which  is  transmuted  into  work  be 
to  the  entire  heat  absorbed  in  the  same  ratio  as  the  difference  between  the 
absolute  temperature  of  the  source  and  refrigerator  is  to  the  absolute  tem- 
perature of  the  source.  In  other  words,  the  second  law  is  an  expression  for 
the  efficiency  of  the  perfect  elementary  engine.  (Wood.) 

The  living  force,  or  vis  viva,  of  a  body  (called  heat)  is  always  proportional 
to  the  absolute  temperature  of  the  body.  (Trowbridge.) 


f-\  rn      rrt 

The  expression  V1  -  =  !  — -  may  be  called  the  symbolical  or  al- 
gebraic enunciation  of  the  second  law, — the  law  which  limits  the  efficiency 
of  heat  engines,  and  which  does  not  depend  on  the  nature  of  the  working 
medium  employed.  (Trowbridge.)  Ql  and  TI  =  quantity  and  absolute 


PHYSICAL   PROPERTIES   OF   GASES.  479 

temperature  of  the  heat  received,  Q2  aud  T2  =  quantity  and  absolute  tem- 
perature of  the  heat  rejected. 

T       -     Tr, 

The  expression  -  represents  the  efficiency  of  a  perfect  heat  engine 

which  receives  all  its  heat  at  the  absolute  temperature  2\,  and  rejects  heat 
at  the  temperature  7'2,  converting  into  work  the  difference  between  the 
quantity  received  and  rejected. 

EXAMPLE.—  What  is  the  efficiency  of  a  perfect  heat  engine  which  receives 
heat  at  888°  F.  (the  temperature  of  steam  of  200  Ibs.  gauge  pressure)  and 
rejects  heat  at  100°  F.  (temperature  of  a  condenser,  pressure  1  Ib.  above 
vacuum). 

-  1004-459,3 

-         =34^,  nearly. 


In  the  actual  engine  this  efficiency  can  never  be  attained,  for  the  difference 
between  the  quantity  of  heat  received  into  the  cylinder  and  that  rejected 
into  the  condenser  is  not  all  converted  into  work,  much  of  it  being  lost  by 
radiation,  leakage,  etc.  In  the  steam  engine  the  phenomenon  of  cylinder 
condensation  also  tends  to  reduce  the  efficiency. 

PHYSICAL  PROPERTIES  OP  QASES. 

(Additional  matter  on  this  subject  will  be  found  under  Heat,  Air,  Gas,  and 
Steam.) 

When  a  mass  of  gas  is  enclosed  in  a  vessel  it  exerts  a  pressure  against  the 
walls.  This  pressure  is  uniform  on  every  square  inch  of  the  surface  of  the 
vessel;  also,  at  any  point  in  the  fluid  mass  the  pressure  is  the  same  in  every 
direction. 

In  small  vessels  containinirig  gases  the  increase  of  pressure  due  to  weight 
may  be  neglected,  since  all  gases  are  very  light;  but  where  liquids  are  con- 
cerned, the  increase  in  pressure  due  to  their  weight  must  always  be  taken 
into  account. 

Expansion  of  .Gases,  Marriotte's  Law*—  The  volume  of  a  gas 
diminishes  in  the  same  ratio  as  the  pressure  upon  it  is  increased. 

This  law  is  by  experiment  found  to  be  very  nearly  true  for  all  gases,  and 
is  known  as  Boyle's  or  Mariotte's  law. 

If  p  =  pressure  at  a  volume  v,  and  p:  =  pressure  at  a  volume  vlt  piVi  = 

v 
pv;  Pi  =•  —  p;  pv  =  a  constant. 

Vl 

The  constant,  C,  varies  with  the  temperature,  everything  else  remaining 
\;he  samo. 

Air  compressed  by  a  pressure  of  seventy-five  atmospheres  has  a  volume 
about  2%  less  than  that  computed  from  Boyle's  law,  but  this  is  the  greatest 
divergence  that  is  found  below  160  atmospheres  pressure. 

Law  of  Charles.  —  The  volume  of  a  perfect  gas  at  a  constant  pressure 
is  proportional  to  its  absolute  temperature.  If  VQ  be  the  volume  of  a  gas 
F.,  and  v^_  the  volume  at  any  other  temperature,  ft,  then 


is  pro 
at  3~° 


or       Vi  =  [1  +  0.002036^  -  32°)]  v0. 
If  the  pressure  also  change  fromp0  to  p^ 


*  -  491.8- 

The  Densities  of  Gases  and  Vapors  are  simply  proportional  to 
their  atomic  weights. 

Avogadro's  I^aw.—  Equal  volumes  of  all  gases,  under  the  same  con- 
ditions of  temperature  and  pressure,  contain  the  same  number  of  mole- 
cules. 

To  find  the  weight  of  a  gas  in  pounds  per  cubic  foot  at  32°  F.,  multiply 
half  the  molecular  weight  of  the  gas  by  .00559.  Thus  1  cu.  ft.  marsh-gas,  CH4, 

~  ^^  x  <00559  =  >0447  lb* 


480  PHYSICAL   PROPERTIES  OF   GASES. 

When  a  certain  volume  of  hydrogen  combines  with  one  half  its  volume  of 
oxygen,  there  is  produced  an  amount  of  water  vapor  which  will  occupy  the 
same  volume  as  that  which  was  occupied  by  the  hydrogen  gas  when  at  the 
same  temperature  and  pressure. 

Saturation-point  of  Vapors. — A  vapor  that  is  not  near  the  satura- 
tion-point behaves  like  a  gas  under  changes  of  temperature  and  pressure; 
but  if  it  is  sufficiently  compressed  or  cooled,  it  reaches  a  point  where  it  be- 
gins to  condense:  it  then  no  longer  obeys  the  same  laws  as  a  gas,  but  its 
pressure  cannot  be  increased  by  diminishing  the  size  of  the  vessel  containing 
it,  but  remains  constant,  except  when  the  temperature  is  changed.  The 
only  gas  that  can  prevent  a  liquid  evaporating  seems  to  be  its  own  vapor. 

JDalton's  I^aw  of  Gaseous  Pressures.— Every  portion  of  a  mass 
of  gas  inclosed  in  a  vessel  contributes  to  the  pressure  against  the  sides  of 
the  vessel  the  same  amount  that  it  would  have  exerted  by  itself  had  no 
other  gas  been  present. 

Mixtures  of  Vapors  and  Gases.— The  pressure  exerted  against 
the  interior  of  a  vessel  by  a  given  quantity  of  a  perfect  gas  enclosed  in  it 
is  the  sum  of  the  pressures  whicli  any  number  of  parts  into  which  such  quan- 
tity might  be  divided  would  exert  separately,  if  each  were  enclosed  in  a 
vessel  of  the  same  bulk  alone,  at  the  same  temperature.  Although  this  law 
is  not  exactly  true  for  any  actual  gas,  it  is  very  nearly  true  for  many.  Thus 
if  0.080728  Ib.  of  air  at  32°  F.,  being  enclosed  in  a  vessel  of  one  cubic  foot 
capacity,  exerts  a  pressure  of  one  atmosphere  or  14.7  pounds,  on  each  square 
inch  of  the  interior  of  the  vessel,  then  will  each  additional  0.0807:28  Ib.  of  air 
which  is  enclosed,  at  32°,  in  the  same  vessel,  produce  very  nearly  an  addi- 
tional atmosphere  of  pressure.  The  same  law  is  applicable  to  mixtures  of 
gases  of  different  kinds.  For  example,  0,12344  Ib.  of  carbonic-acid  gas,  at 
32°,  being  enclosed  in  a  vessel  of  one  cubic  foot  in  capacity,  exerts  a  pressure 
of  one  atmosphere;  consequently,  if  0.080728  Ib.  of  air  and  0.12344  Ib.  of 
carbonic  acid,  mixed,  be  enclosed  at  the  temperature  of  32°,  in  a  vessel  of 
one  cubic  foot  of  capacity,  the  mixture  will  exert  a  pressure  of  two  atmos- 
pheres. As  a  second  example:  Let  0.080728  Ib.  of  air,  at  212°,  be  enclosed  in 
a  vessel  of  one  cubic  foot;  it  will  exert  a  pressure  of 

232  + 459.2  =  °66  atmosPheres- 

Let  0.03797  Ib.  of  steam,  at  212°,  be  enclosed  in  a  vessel  of  one  cubic  foot;  it 
will  exert  a  pressure  of  one  atmosphere.  Consequently,  if  0.080728  Ib.  of  air 
and  0.03797  Ib.  of  steam  be  mixed  and  enclosed  together,  at  212°,  in  a  vessel  of 
one  cubic  foot,  the  mixture  will  exert  a  pressure  of  2.366  atmospheres.  It  is 
a  common  but  erroneous  practice,  in  elementary  books  on  physics,  to  de- 
scribe this  law  as  constituting  a  difference  between  mixed  and  homogeneous 
gases;  whereas  it  is  obvious  that  for  mixed  and  homogeneous  gases  the  law 
of  pressure  is  exactly  the  same,  viz.,  that  the  pressure  of  the  whole  of  a 
gaseous  mass  is  the  sum  of  the  pressures  of  all  its  parts  This  is  one  of  thf/ 
laws  of  mixture  of  gases  and  vapors. 

A  second  law  is  that  the  presence  of  a  foreign  gaseous  substance  in  con 
tact  with  the  surface  of  a  solid  or  liquid  does  not  affect  the  density  of  the 
vapor  of  that  solid  or  liquid  unless  there  is  a  tendency  to  chemical  com- 
bination between  the  two  substances,  in  which  case  the  density  of  the 
vapor  is  slightly  increased.  (Rankine,  S.  E.,  p.  239.) 

Flow  of  Gases.— By  the  principle  of  the  conservation  of  energy,  it  may 
be  shown  that  the  velocity  with  which  a  gas  under  pressure  will  escape  into 
a  vacuum  is  inversely  proportional  to  the  square  root  of  its  density;  that  is, 
oxygen,  which  is  sixteen  times  as  heavy  as  hydrogen,  would,  under  exactly 
the  same  circumstances,  escape  through  an  opening  only  one  fourth  as  fast 
as  the  latter  gas. 

Absorption  of  Gases  l>y  liquids.— Many  gases  are  readily  ab- 
sorbed by  water.  Other  liquids  also  possess  this  power  in  a  greater  or  less 
degree.  Water  will  for  example,  absorb  its  own  volume  of  carbonic-acid 
gas,  430  times  its  volume  of  ammonia,  2^  times  its  volume  of  chlorine,  and 
only  about  1/20  of  its  volume  of  oxygen. 

The  weight  of  gas  that  is  absorbed  by  a  given  volume  of  liquid  is  propor- 
tional to  the  pressure.  But  as  the  volume  of  a  mass  of  gas  is  less  as  the 
pressure  is  greater,  the  volume  which  a  given  amount  of  liquid  can  absorb 
at  a  certain  temperature  will  be  constant,  whatever  the  pressure.  Water, 
for  example,  can  absorb  its  own  volume  of  carbonic-acid  gas  at  atmospheric 
pressure;  it  will  also  dissolve  its  own  volume  if  the  pressure  is  twice  as 
great,  but  in  that  case  the  gas  will  be  twice  as  dense,  and  consequently  twice 
the  weight  of  gas  is  dissolved. 


PRESSURE   OF   THE    ATMOSPHERE. 


481 


AIR. 

Properties  of  Air.  Air  is  a  mechanical  mixture  of  the  gases  oxygen 
and  niu-ouen ;  yO.7  purls  O  and  79.3  parts  N  by  volume,  23  parts  O  and  77  parts 
N  by  weight. 

The  weight  of  pure  air  at  32°  F.  and  a  barometric  pressure  of  29.92  inches 
of  mercury,  or  14.6963  Ibs.  per  sq.  in.,  or  2116.3  Ibs.  per  sq.  ft.,  is  .080728  Ib.  per 
cubic  foot.  Volume  of  1  Ib.  =  12.387  cu.  ft.  At  any  other  temperature  and 

barometric  pressure  its  weight  in  Ibs.  per  cubic  foot  is  W  ~    '        ~r~^' 

4o". «  -\-  J. 

where  B  =  height  of  the  barometer,  T=  temperature  Fahr.,  and  1.3253  = 
weight  in  Ibs.  of  459.2  c.  ft.  of  air  at  0°  F.  and  one  inch  barometric  pressure. 
Air  expands  1/491,2  of  its  volume  at  32°  F.  for  every  increase  of  1°  F.,  and 
its  volume  varies  inversely  as  the  pressure. 

Volume,  Density,  and.  Pressure  of  Air  at  Various 
Temperatures.    (D.  K.  Clark.) 


Volume  at  Atrnos. 

Pressure  at  Constant 

Pressure. 

Density,  Ibs. 

Volume. 

Fahr. 

per  Cubic  Foot  at 
Atmos.  Pressure. 

Cubic  Feet 
in  1  Ib. 

Compara- 
tive Vol. 

Lbs.  per 
Sq.  In. 

Compara- 
tive Pres. 

0 

11.583 

.881 

.086331 

12.96 

.881 

32 

12.387 

.943 

.080728 

13.86 

.943 

40 

12.586 

.     .958 

.079439 

14.08 

.958 

50 

12.840 

.977 

.077884 

14.36 

.977 

62 

13.141 

1.000 

.076097 

14.70 

1.000 

70 

13.342 

1.015 

.074950 

14.92 

1.015       : 

80 

13.593 

1.034 

.073565 

15.21 

1.034       ; 

90 

13.845 

1.054 

.072230 

15.49 

.054 

100 

14.096 

1.073 

.070942 

15.77 

.073 

110 

14.344 

1.092 

.069721 

16.05 

.092 

120 

14.592 

1.111 

.068500 

16.33 

.111 

130 

14.846 

1.130 

.067361 

16.61 

.130 

140 

15.100 

1.149 

.066221 

16.89 

.149 

150 

15.351 

1.168 

.065155 

17.19 

.168 

160 

15.603 

1.187 

.064088 

17.50 

.187 

170 

15.854 

1.206 

.063089 

17.76 

.206 

180 

16.106 

1.226 

.062090 

18.02 

.226 

200 

16.606 

1.264 

.060210 

18.58 

.264 

210 

16.860 

1.283 

.059313 

18.86 

.283 

212 

16.910 

1.287 

.059135 

18.92 

.287 

The  Air-ma.nom.eter  consists  of  a  long  vertical  glass  tube,  closed  at 
the  upp  M-  end,  open  at  the  lower  end,  containing  air,  provided  with  a  scale, 
and  immersed,  along  with  a  thermometer,  in  a  transparent  liquid,  such  as 
water  or  oil,  contained  in  a  strong  cylinder  of  glass,  which  communicates 
with  the  vessel  in  which  the  pressure  is  to  be  ascertained.  The  scale  shows 
the  volume  occupied  by  the  air  in  the  tube. 

Let  VQ  be  that  volume,  at  the  temperature  of  32°  Fahrenheit,  and  mean 
pressure  of  the  atmosphere,  pQ:  let  vl  be  the  volume  of  the  air  at  the  tem- 
perature t,  and  under  the  absolute  pressure  to  be  measured  p}  ;  then 


_ 

Pl  ~    '  .         , 

Pressure  of  the  Atmosphere  at  Different  Altitudes. 

At  the  sea-level  the  pressure  of  the  air  is  14.7  pounds  per  square  inch;  at 
VA  of  a  mile  above  the  sea-level  it  is  14.  02  pounds;  at  y%  mile,  13.33;  at  % 
mile,  12.66;  at  1  mile,  12.02;  at  1J4  mile,  11.42;  at  1J^  mile,  10.88;  and  at  2 


482 


AIR. 


miles,  9.80  pounds  per  square  inch.  For  a  rough  approximation  we  may 
assume  that  the  pressure  decreases  ^  pound  per  square  inch  for  every  1000 
feet  of  ascent. 

It  is  calculated  that  at  a  height  of  about  3^  miles  above  the  sea-level  the 
weight  of  a  cubic  foot  of  air  is  only  one  half  what  it  is  at  the  surface  of  the 
earth,  at  seven  miles  only  one  fourth,  at  fourteen  miles  only  one  sixteenth, 
at  twenty-one  miles  only  ona  sixty-fourth,  and  at  a  height  of  over  forty- 
five  miles  it  becomes  so  attenuated  as  to  have  no  appreciable  weight. 

The  pressure  of  the  atmosphere  increases  with  the  depth  of  shafts,  equal 
to  about  one  inch  rise  in  the  barometer  for  each  900  feet  increase  in  depth: 
this  may  be  taken  as  a  rough-and-ready  rule  for  ascertaining  the  depth  of 
shafts. 

Pressure    of  tlie   Atmosphere  per    Square    Inch  and   per 
Square  Foot  at  Various  Readings  of  the  Barometer. 

RULE.— Barometer  in  inches  x  .4908  =  pressure  per  square  inch;  pressure 
per  square  inch  x  144  =  pressure  per  square  foot. 


Barometer. 

Pressure 
per  Sq.  In. 

Pressure 
per  Sq.  Ft. 

Barometer. 

Pressure 
per  Sq.  In. 

Pressure 
per  Sq.  Ft. 

in. 

Ibs. 

Ibs.* 

in. 

Ibs. 

Ibs.* 

28.00 

13.74 

1978 

29.75 

14.60 

2102 

28.25 

13.86 

1995 

30.00 

14.72 

2119 

28.50 

13.98 

2013 

30.25 

14.84 

2136 

28.75 

14.11 

2031 

30.50 

14.96 

2154 

29.00 

14.23 

2049 

30.75 

15.09 

2172 

29.25 

14.35 

2066 

31.00 

15.21 

2190 

29.50 

14.47 

2083 

*  Decimals  omitted. 

For  lower  pressures  see  table  of  the  Properties  of  Steam. 
Barometric  Readings  corresponding  with  .Different 
Altitudes,  in  French  and  English  Measures. 


Read- 

Reading 

Reading 

Reading 

Alti- 
tude. 

ing  of 
Barom- 

Altitude. 

of 
Barom- 

Alti- 
tude. 

of 
Barom- 

Altitude. 

of 
Barom- 

eter. 

eter. 

eter. 

eter. 

meters. 

mm. 

feet. 

inches. 

meters. 

mm. 

feet. 

inches. 

0 

762 

0. 

30. 

1147 

660 

3763.2 

25.98 

21 

760 

68.9 

29.92 

1269 

650 

4163.3 

25.59 

127 

750 

416.7 

29.52 

1393 

640 

4568.3 

25.19 

234 

740 

767.7 

29.13 

1519 

630 

4983.1 

24.80 

342 

730 

1122.1 

28.74 

1647 

6-20 

5403.2 

24.41 

453 

720 

1486.2 

28.35 

1777 

610 

5830.2 

24.01 

564 

710 

1850.4 

27.95 

1909 

600 

6243. 

23.62 

678 

700 

2224.5 

27.55 

2043 

590 

6702.9 

23.22 

793 

690 

2599.7 

27.16 

2180 

580 

7152.4 

22.83 

909 

680 

2962.1 

26.77 

2318 

570 

7605.1 

22.44 

1027 

670 

3369.5 

26.38 

2460 

560 

8071. 

22.04 

Levelling   by   the    Barometer    and    by   Boiling   Water. 

(Trautwine.) — Many  circumstances  combine  to  render  the  results  of  this 
kind  of  levelling  unreliable  where  great  accuracy  is  required.  It  is  difficult 
to  read  off  from  an  aneroid  (the  kind  of  barometer  usually  employed  for 
engineering  purposes)  to  within  from  two  to  five  or  six  feet,  depending  on 
its  size.  The  moisture  or  dryriess  of  the  air  affects  the  results;  also  winds, 
the  vicinity  of  mountains,  and  the  daily  atmospheric  tides,  which  cause 
incessant  and  irregular  fluctuations  in  the  barometer.  A  barometer  hang- 
ing quietly  in  a  room  will  often  vary  1/4  of  an  inch  within  a  few  hours,  cor- 
responding to  a  difference  of  elevation  of  nearly  100  feet.  No  formula  can 
possibly  be  devised  that  shall  embrace  these  sources  of  error. 


MOISTURE   IN    THE    ATMOSPHERE. 


483 


To  Find  the  Difference  in  Altitude  of  Two  Places.— Take 
from  the  table  the  altitudes  opposite  to  the  two  boiling  temperatures,  or  to 
the  two  barometer  readings.  Subtract  the  one  opposite  the  lower  reading 
from  that  opposite  the  upper  reading.  The  remainder  will  be  the  required 
height,  as  a  rough  approximation.  To  correct  this,  add  together  the  two 
thermometer  readings,  and  divide  the  sum  by  2,  for  their  mean.  From 
table  of  corrections  for  temperature,  take  out  the  number  under  this  mean. 
Multiply  the  approximate  height  just  found  by  this  number. 

At  70°  F.  pure  water  will  boil  at  1°  less  of  temperature  for  an  average  of 
about  550  feet  of  elevation  above  sea-level,  up  to  a  height  of  1/2  a  mile.  At 
the  height  of  1  mile,  1°  of  boiling  temperature  will  correspond  to  about  500 
feet  of  elevation.  In  the  table  the  mean  of  the  temperatures  at  the  two 
stations  is  assumed  to  be  32°F.,  at  which  no  correction  for  temperature  is 
necessary  in  using  the  table. 


u     -r 

<D       "^ 

3-       "3 

ilia 

1.2 

+J    O    ®    ^ 

+3'°'3«s 

b£-£  be  . 

a     fl     02  rS 

I.S 

Ills 

Ift 

|  = 

®  P<  a 

PQ     - 

M 

o^.Sfe 

PQ 

?hr 

(§ft.S 

1 

$*¥ 

184° 

16.79 

15,221 

196 

21.71 

8,481 

208 

27.73 

2,063 

185 

17.16 

14,649 

197 

22.17 

7,932 

208.5 

28.00 

1,809 

186 

17.54 

14,075 

198 

22.64 

7,381 

209 

28.29 

1,539 

187 

17.93 

13,498 

199 

23.  1  1 

6,843 

209.5° 

28.56 

1,290 

188 

18.32 

12.934 

200 

23.59 

6,304 

210 

28.85 

1,025 

189 

18.72 

12,367 

201 

24.08 

5,764 

210.5 

29.15 

754 

190 

19.13 

11,799 

202 

24.58 

5,225 

211 

29.42 

512 

191 

19.54 

11,243 

203 

25.08 

4,697 

211.5 

29.71 

255 

192 

19.96 

10,685 

204 

25.59 

4,169 

212 

30.00 

S.  L  =  0 

193 

20.39 

10,127 

205 

26.11 

3,642 

212.5 

30.30 

-261 

194 

20.82 

9,579 

206 

26.64 

3,115 

S13 

30.59 

-511 

195 

21.26 

9,031 

207 

27.18 

2,589 

CORRECTIONS  FOR  TEMPERATURE. 


Mean  temp.  F.  in  shade.  0  i  10°   20° I  30° [  40°  I  50°  I  60°  j  70°   80°     90°    I  100°| 
Multiply  by  .933  (.954  .975|.996|l.016|l. 03611. 058|1.079  1.100  1.121|1.142| 


jSloisture  in  the  Atmosphere.— Atmospheric  air  always  contains 
a  small  quantity  of  carbonic-acid  gas  and  a  varying  quantity  of  aqueous 
vapor.  Pure  mountain  air  contains  about  3  to  4  parts  of  carbonic  acid  in 
10,000.  A  properly  ventilated  room  should  contain  not  more  than  six  parts 
in  10,000. 

The  degree  of  saturation  or  relative  humidity  of  the  air  is  determined  by 
the  use  of  the  dry  and  wet  bulb  thermometer.  The  degree  of  saturation  for 
a  number  of  different  readings  of  the  thermometer  is  given  in  the  following 
table  : 

INDICATIONS  OF  THE  HYGROMETER  (DRY  AND  WET  BULB),  FROM 
MR.  GLAISHER'S  OBSERVATIONS  AT  GREENWICH. 


Difference  of  Temperature  or  Degrees  of  Cold  in  the  Wet- 
bulb  Thermometer. 


of  the  Air 

Fahrenheit. 

1 

2 

3 

4 

r> 

('' 

7' 

8 

9 

10 

1! 

12 

13 

14 

15 

10 

17 

18 

19 

20 

21 

22  23 

Degrees  of  Humidity,  Saturation  being  100. 

32° 

87 

75 

42° 

92 

85 

78 

72 

00 

60 

54 

19 

44 

40 

36 

33 

30 

27 

52° 

93 

8(5 

80 

74 

69 

04 

59 

54 

50 

40 

42 

39 

36 

:;:5 

30 

27 

25 

62° 

94 

88 

82 

77 

72 

07 

02 

58 

54 

50 

47 

44 

11 

3H 

35 

:J,2 

30 

28 

& 

21 

72° 

94 

89 

84 

79 

74 

69 

65 

01 

57 

54 

51 

48 

45 

42 

39 

36 

34 

:I2 

3i» 

28 

26 

2423 

82° 

95 

90 

85 

80 

76 

OK 

(54 

60 

57 

51 

51 

48 

45 

42 

4038 

35 

33 

31 

29 

27  20 

92° 

95 

90 

85 

81 

77 

78 

70 

00 

02 

59 

56 

53 

50 

47' 

45 

43 

41 

38 

36 

34 

32 

3028 

484 


AIR. 


Weight*  of  Air,  Vapor  of  Water,  and  Saturated  ^fixtures 

of  Air  and  Vapor  at  Different  Temperatures,  under 

the  Ordinary  Atmospheric  Pressure  of  29.921 

inches  of  Mercury. 


-i-j  ^ 

£ 

MIXTURES  OF  AIR  SATURATED  WITH  VAPOR. 

fe  § 

o 

2  . 

t-1   <y      . 

Ill 

Sgs 

Ib 
**i 

ll 

Elastic 
Force  of 

Weight  of  Cubic  Foot  of  the 
Mixture  of  Air  and  Vapor. 

Weight 
of 

3.13 

c3  oS  g 

&§ 

the  Air  in 
Mixture 

Vapor 

Tempera 
Fahrerih< 

o3  g 

fibi 

.5PQS 

O>:M  0> 

£OH 

Elastic  Fo 
Inches  of 

of  Air  and 

Vapor, 
Inches  of 
Mercury. 

Weight 
of  the 
Air,  Ibs. 

Weight 
of  the 
Vapor, 
pounds. 

Total 
W'ght  of 
Mixture, 
pounds. 

mixed 
with  1  Ib. 
of  Air, 
pounds. 

0° 

.0864 

.044 

29.877 

.0863 

.000079 

.086379 

.00092 

12 

.0842 

.074 

29.849 

.0840 

.000130 

.084130 

.00155 

22 

.0824 

.118 

29.803 

.0821 

.000202 

.082302 

.00245 

32 

.0807 

.181 

29.740 

.0802 

.000304 

.080504 

.00379 

42 

.0791 

.267 

29.654 

.0784 

.000440 

.078840 

.00561 

52 

.0776 

.388 

29.533 

.0766 

.000627 

.077227 

.00819 

62 

.0761 

.556 

29.365 

.0747 

.000881 

.075581 

.01179 

72 

.0747 

.785 

29.136 

.0727 

.001221 

.073921 

.01680 

82 

.0733 

1.092 

28.829 

.0706 

.001667 

.072267 

.02361 

92 

.0720 

1.501 

28.420 

.0684 

.002250 

.070717 

.03289 

102 

.0707 

2.036 

27.885 

.0659 

.002997 

.068897 

.04547 

112 

.0694 

2.731 

27.190 

.0631 

.003946 

.067046 

.06253 

122 

.0682 

3.621 

26.300 

.0599 

.005142 

.065042 

.08584 

132 

.0671 

4.752 

25.169 

.0564 

.006639 

.063039 

.11771 

142 

.0660 

6.165 

23.756 

.0524 

.008473 

.060873 

.16170 

152 

.0649 

7.930 

21.991 

.0477 

.010716 

.058416 

.22465 

162 

.0638 

10.099 

19.822 

.0423 

.013415 

.055715 

.31713 

172 

.0628 

12.758 

17.163 

.0360 

.016682 

.052682 

.46338 

182 

.0618 

15.960 

13.961 

.0288 

.020536 

.049336 

.71300 

192 

.0609 

19.828 

10.093 

.0205 

.025142 

.045642 

1.22643 

202 

.0600 

24.450 

5.471 

.0109 

.030545 

.041445 

2.80230 

212 

.0591 

29  921 

0.000 

.0000 

.036820 

.036820 

Infinite. 

The  weight  in  Ibs.  of  the  vapor  mixed  with  100  Ibs.  of  pure  air  at  any 
given  temperature  and  pressure  is  given  by  the  formula 

62.3  X  E       29.92 
29.92  -  E  X      p   ' 

where  E  =  elastic  force  of  the  vapor  at  the  given  temperature,  in  inches  of 
mercury;  p  =  absolute  pressure  in  inches  of  mercury,  =  2992  for  ordinary 
atmospheric  pressure. 

Specific  Heat  of  Air  at  Constant  Volume  and  at  Constant 
Pressure. — Volume  of  1  Ib.  of  air  at  32°  F.  and  pressure  of  14.7  Ibs.  per  sq. 
in.  —  12.387  cu.  ft.  =  a  column  1  sq.  ft.  area  X  12.387  ft.  high.  Raising  temper- 
ature 1°  F.  expands  it  jqj-^  or  to  12.4122  ft.  high— a  rise  of  .02522  foot. 

Work  done  =  21 16  Ibs.  per  sq,  ft.  X  .02522  =  53.37  foot-pounds,  or  53.37  -f- 778 
=  .0686  heat  units. 

The  specific  heat  of  air  at  constant  pressure,  according  to  Regnault,  is 
0  2TT5;  but  this  includes  the  work  of  expansion,  or  .0686  heat  units;  hence 
the  specific  heat  at  constant  volume  =  0.2375  —  .0686  =  0.1689. 

Ratio  of  specific  heat  at  constant  pressure  to  specific  heat  at  constant 
vojume  =  .2375  -*-  .1689  =  1.406.  (See  Specific  Heat.  p.  458.) 

Flow  of  Air  through.  Orifices.— The  theoretical  velocity  in  feet 
per  second  of  flow  of  any  fluid,  liquid,  or  gas  through  an  orifice  is  v  = 
y2yh  =  8.02  ^h,  in  which  h  =  the  "  head  "  or  height  of  the  fluid  in  feet 
required  to  produce  the  pressure  of  the  fluid  at  the  level  of  the  orifice. 

v* 
h  =   — .  The  quantity  of  flow  in  cubic  feet  per  second  is  equal  to  the  product 


FLOW   OF   AIR  IN   PIPES.  485 

of  this  velocity  by  the  area  of  the  orifice,  in  square  feet,  multiplied  by  a 
"  coefficient  of  flow,1'  which  takes  into  account  the  contraction  of  the  vein 
or  flowing  stream,  the  friction  of  the  orifice,  etc. 

For  air  flowing  through  an  orifice  or  short  tube,  from  a  reservoir  of  the 
pressure  P!  into  a  reservoir  of  the  pressure  ps,  Weisbach  gives  the  follow- 
ing values  for  the  coefficient  of  flow,  obtained  from  his  experiments. 

FLOW  OP  AlR  THROUGH   AN  ORIFICE. 

Coefficient  c  in  formula  v  =  c  4/2#/i. 

Diameter       \  Ratio  of  pressures  p1-^-pz  1.05    1.09    1.43    1.65    1.89    2.15 
1  centimetre,    f  Coefficient  .................  555    .589    .692    .724    .754    .788 

Diameter       f  Ratio  of  pressures  ........  1.05    1.09    1.36    1.67    2.01     .... 

2.14  centimetres  {Coefficient  .................  558    .573    .634    .678    .723  .... 

FLOW  OP  AIR  THROUGH  A  SHORT  TUBE. 

Diam.  1  cm.,     \  Ratio  of  pressures  Pi-s-pa  1.05    1.10    1.30     ............ 

Length3cm.   (Coefficient  ...............  .     .730    .771    .830  ............ 

Diam.  1.414  cm.,  I  Ratio  of  pressures  ........  1.41    1.69      ................ 

Length  4.  242  cm.  \  Coefficient  .................  813  .822  ................ 

Diam   1cm..     (Rati0  of  pressures........  1.24    1.38    1.59    1.85    2.14     .... 

..............  979  -986  •«*  -971  -978" 


FLIEGNER'S  EQUATIONS  FOR  FLOW  OF  AIR  FROM  A  RESERVOIR  THROUGH  AN 
ORIFICE.     (Peabody's  Thermodynamics,  p.  135.) 

For  pl  >  2pa,     G  =  0.530  F  -^  ; 


p    <  2pa,     G  =  1.060  F 


G  =  flow  of  air  through  the  orifice  in  Ibs.  per  sec.,  F  =  area  of  orifice  in  ?q. 
in.,  pl  =  absolute  pressure  in  reservoir  in  Ibs.  per  sq.  in.,  pa  —  pressure  of 
atmosphere,  T\  =  absolute  temperature,  Fahr.,  of  air  in  reservoir. 

Clark  (Rules.  Tables,  and  Data,  p.  891)  gives,  for  the  velocity  of  flow  of  air 
through  an  orifice  due  to  small  differences  of  pressure, 


v  -  r  A  /?ffh  y  773  2  x  (i±  *  -  32")*  29'92 

C  \    12    X  ~~493~/X  ~£~' 


or,  simplified, 


V  =  352  C|/(l  -f  .00203«  -  32)  -  ; 


in  which  V—  velocity  in  feet  per  second  ;  2.g  =  64.4;  h  =  height  of  the  column 
of  water  in  inches,  measuring  the  difference  of  pressure;  i  =  the  tempera- 
ture Fahr.;  and  p  =  barometric  pressure  in  inches  of  mercury.  773.2  is  the 
volume  of  air  at  32°  under  a  pressure  of  29.92  inches  of  mercury  when  that  of 
an  equal  weight  of  water  is  taken  as  1. 

For  62°  F.,  the  formula  becomes  V  —  363C  A  /  -',  and  if  p  -  29.92  inches  V  = 

V  p 

66.35C  Vh 

The  coefficient  of  efflux  C,  according  to  Weisbach,  is: 
For  conoidal  mouthpiece,  of   form   of  the  contracted  vein, 

with  pressures  of  from  .23  to  1.1  atmospheres  ............   C  =  .97  to  .99 

Circular  orifices  in  thin  plates  .................................   C  —  .56  to  .79 

Short  cylindrical  mouthpieces  ..........  .  ......    ..............  C*  =  .81  to  .84 

The  same  rounded  at  the  inner  end  .....    ......................   C  —  .92  to  .93 

Conical  converging  mouthpieces  ..............................   C  —  .90  to  .99 

Flour   of  Air  in  Pipes.—  Hawksley  (Proc.    Inst.  C.  E..    xxxiii.   K) 

/'fjfi 

states  that  his  formula  for  flow  of  water  in  pipes  v  =  48  A/  -   may  also 


=  48  A/ 


be  employed  for  flow  of  air.    In  this  case  H  =  height  in  feet  of  a  column  of 
air  required  to  produce  the  pressure  causing  the  flow,  or  the  loss  of  head 


486 


AIR. 


for  a  given  flow;  v  =  velocity  in  feet  per  second,  1)  -  diameter  in  feet    L  - 
length  in  feet. 

If  the  head  is  expressed  in  inches  of   water,  7i,  the  air  being  taken  at 
62°  F  ,  its  weight  per  cubic  foot  at  atmospheric  pressure  =  .0761  Ib.    Then 

H  ~  0761  x  12  =  68-3/'-    If  d  =  Diameter  in  inches,  D  =  ^-,  and  the  formula 

becomes  v  =  114.5  A/  — ,  in  which  h  =  inches  of  water  column,  d  —  diam- 
f     L 


Lv* 


Lv* 


eter  in  inches  and  L  —  length  in  feet;  h  =   .•""    ;  d  ^  • . 

The  quantity  in  cubic  feet  per  second  is 


The  horse-power  required  to  drive  air  through  a  pipe  is  the  volume  O  in 
cubic  feet  per  second  multiplied  by  the  pressure  in  pounds  per  square  foot 
and  divided  by  550.  Pressure  in  pounds  per  square  foot.  =  p  =  inches  of 
water  column  x  5.196,  whence  horse-power  = 

Hp        QP  _     Qh  Q3L 

550  T  105.9  ~  41.3d5' 

If  the  head  or  pressure  causing  the  flow  is  expressed  in  pounds  per  square 
inch  =  p,  then  h  =  27.71p,  and  the  above  formulae  become 


•-  602.7V  ^; 


Lv* 


Lv* 


- 

363,300d  363,300p 


HP.  = 


Volume  of  Air  Transmitted  in  Cubic  Feet  per  Minute  in 
Pipes  of  Various  Diameters. 

Formula  Q  =  '-dtoi  x  60. 


.h* 
o  o 

.2E 
$* 


Actual  Diameter  of  Pipe  in  Inches. 


l! 

1 

2 

3 

4 

5 

6 

8 

10 

12 

16 

20 

24 

i 

.327 

1.31 

2.95 

5.24 

8.18 

11.78 

20.94 

32.73 

47.12 

83.77 

130.9 

188.5 

2   .655 

2.62 

5.89 

10.47 

16.36 

23.56 

41  89 

65.45 

94.25 

167.5 

261.8 

377 

3 

.982 

3.93 

8.84 

15.7 

24.5 

35.3 

62.8 

98.2 

141.4 

251.3 

392.7 

565.5 

4 

1.31 

5,24 

11.78 

20.9 

32.7 

47.1 

83.8 

131 

188 

335 

523 

754 

5 

1.64 

6.54 

14.7 

26.2 

41 

59 

104 

163 

235 

419 

654 

942 

6 

1.96 

7.85 

17.7 

31.4 

49.1 

70.7 

125 

196 

283 

502 

785 

1131 

7 

2.29 

9.16 

20.6 

36.6 

57.2 

82.4 

146 

229 

330 

586 

916 

1319 

8  2.62 

105 

23.5 

41.9 

65.4 

94 

167 

262 

377 

670 

1047 

1508 

9 

2.95 

11.78 

26.5 

47 

73 

106 

188 

294 

424 

754 

1178 

1696 

10 

3.27 

13.1 

29.4 

52 

82 

118 

209 

327 

471 

838 

1309 

1885 

12 

3.93 

15.7 

35.3 

63 

98 

141 

251 

393 

565 

1005 

1571 

2262 

15 

4.91 

19.6 

44.2 

78 

122 

177 

314 

491 

707 

1256 

1963 

2827 

18 

5.89 

23.5 

53 

94 

147 

212 

377 

589 

848 

1508 

2356 

3393 

20  ,6.54 

26.2 

59 

105 

164 

235 

419 

654 

942 

1675 

2618 

3770 

24 

7.85 

31.4 

71 

125 

196 

283 

502 

785 

1131 

2010 

3141 

4524 

25 

8.18 

32  7 

73 

131 

204 

294 

523 

818 

1178 

2094 

3272 

4712 

28 

9.16 

36  6 

82 

146 

229 

330 

586 

916 

1319 

2346 

3665 

5278 

30 

9.8  (39.3 

88 

157 

245 

353 

628 

982 

1414 

2513 

3927 

5655 

•  -; 

OF  AiR^ir-rBipfe^n   >  4B7 

^ 


in  Hawksley's  formula  and  its  derivatives  the  numerical  coefficients  are 
constant.  It  is  scarcely  possible,  however,  that  they  can  be  accurate  except 
within  a  limited  range  of  conditions.  In  the  case  of  water  it  is  found  that 
the  coefficient  of  friction,  on  w  hich  the  loss  of  head  depends,  varies  with  the 
length  and  diameter  of  the  pipe,  and  with  the  velocity,  as  well  as  with  the 
condition  of  the  interior  surface.  In  the  case  of  air  and  other  gases  we 
have,  in  addition,  the  decrease  in  density  and  consequent  increase  in  volume 
and  in  velocity  due  to  the  progressive  loss  of  head  from  one  end  of  the  pipe 
to  the  other. 

Clark  states  that  according  to  the  experiments  of  D'Aubuisson  and  those  of 
H  Sardinian  commission  on  the  resistance  of  air  through  long  conduits  or 
pipes,  the  diminution  of  pressure  is  very  nearly  directly  as  the  length,  and 
as  the  square  of  the  velocity  and  inversely  as  the  diameter.  The  resistance 
is  not  varied  by  the  density. 

If  these  statements  are  correct,  then  the  formulae  h  =  — r-  and  h  =  ~__ 

cd  c'd6 

and  their  derivatives  are  correct  in  form,  and  they  may  be  used  when  the 
numerical  coefficients  c  and  c'  are  obtained  by  experiment. 

If  we  take  the  forms  of  the  above  formulae  as  correct,  and  let  C  be  a  vari- 
able coefficient,  depending  upon  the  length,  diameter,  and  condition  of  sur- 
face of  the  pipe,  and  possibly  also  upon  the  velocity,  the  temperature  and 
the  density,  to  be  determined  by  future  experiments,  then  for  h  =  head  in 
inches  of  water,  d  =  diameter  in  inches,  L  =  length  in  feet,  v  =  velocity  in 
feet  per  second,  and  Q  =  quantity  in  cubic  feet  per  second:  • 

Lv*  Lv* 

V  =  CA/~;  <*  =  — -;  h : 


g=.005454C|/~-; 

For  difference  or  loss  of  pressure  p  in  pounds  per  square  inch, 
h  =  27.71p  Vh  =  5.264  VI 


(For  other  formulae  for  flow  of  air,  see  Mine  Ventilation.) 

Loss  of  Pressure  in  Ounces  per  Square  Incli.—  B.  F.  Sturte- 

vaiit  Company  uses  the  following  formulae  : 


Lv* 


25000px  ' 

in  which  pt  =  loss  of  pressure  in  ounces  per  square  inch,  y  —  velocity  of  air 
in  feet  per  second,  and  L,  =  length  of  pipe  in  feet.  If  p  is  taken  in  pounds 
per  square  inch,  these  formulae  reduce  to 

nnnnno^2  -00158  \/dp  .00000251^2 

.0000025-  * 


2  -00158  \/dp  .0000025 

-—-  ;    v  =  -  _       *  I    d  = 
d  L  p 


These  are  deduced  from  the  common  formula  (Weisbach's),  p  =  /•=  £-,  in 

which/=  .0001608. 

The  following  table  is  condensed  from  one  given  in  the  catalogue  of  B.  F. 
Sturtevant  Company. 

Loss  of  pressure  in  pipes  100  feet  long,  in  ounces  per  square  inch.  For 
any  other  length,  the  loss  is  proportional  to  the  length. 


488 


AIR. 


Velocity  of  Air,j 
feet  per  min.  i 

Diameter  of  Pipe  in  Inches. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

Loss  of  Pressure  in  Ounces. 

600 

1200 
1800 
2400 
300u 
3«500 
4200 
4800 
6000 

600 
1200 
1800 
2400 
3600 
4200 
4800 
6000 

.400 
1.000 
3.600 
6.400 
10. 
14.4 

.200 
.800 
1.800 
3.200 
5. 
7.2 
9.8 
12.8 
20. 

.133 
.533 
1.200 
2.133 
3.333 
4.8 
6.553 
8.533 
13.333 

.100 
.400 
.900 
1.600 
2.5 
3.6 
4.9 
6.4 
10.0 

.080 
.320 
.720 
1.280 
2. 
2.88 
3.92 
5.12 
8.0 

.067 
.267 
.600 
1.067 
1.667 
3.4 
3.267 
4.267 
6.6(57 

.057 
.229 
.514 
.914 
1  429 
2.057 
2.8 
3.657 
5.714 

.050 
.200 
.450 
.800 
1.250 
1.8 
2.45 
3.2 
5.0 

.044 
.178 
.400 
.711 
1.111 
1.6 
2.178 
2.844 
4.444 

.040 

.160 
.360 
.640 
1.000 
1.44 
1.96 
2.56 
4.0 

.036 

.145 
.327 
.582 
.909 
1.309 
1.782 
2.327 
3.636 

.033 
.133 
.300 
.533 
.833 
1.200 
1.633 
2.133 
3.333 

Diameter  of  Pipe  in  Inches. 

14 

16 

18 

20 

22 

24 

28; 

32 

36 

40 

44 

48 

Loss  of  Pressure  in  Ounces. 

.029 
.114 
.257 
.457 
1.029 
1.400 
1.829 
2.857 

.026 

.100 
.225 
.400 
.900 
1.225 
1.600 
2.500 

.022 

.089 
.200 
.356 
.800 
1.089 
1  .42-2 
2.222 

.020 
.080 
.180 
.320 
.720 
.980 
1.280 
2.000 

.018 
.073 
.164 
.291 
.655 
.891 
1.164 
1.818 

.017 
.067 
.156 
.267 
.600 
.817 
1.067 
1.667 

.014 
.057 
.129 
.239 
.514 
.700 
.914 
1.429 

.012 
.050 
.112 

.200 
.450 
.612 
.800 
1.25L 

.011 
.044 
.100 
.178 
.400 
.544 
.711 
.111 

.010 
.040 
.090 
.160 
.360 
.490 
640 
1.000 

.009 
.036 
.082 
.145 
.327 
.445 
.582 
.909 

.008 
.033 
.075 
.133 
.300 
.408 
.533 
.833 

Effect  of  Bends  in  Pipes.    (Norwalk  Iron  Works  Co.) 
Radius  of  elbow,  in  diameter  of  pipe  =  5      3       2      1^     1J4      1       M     ^ 
Equivalent  Igths.  of  straight  pipe,  diams  7.85  8.24  9.03  10.36  12.72 17.51  35.09 12L2 

Compressed-air  Transmission.  (Frank  Richards.  Am.  Mack., 
March  8,  1894  )— The  volume  of  free  air  transmitted  may  be  assumed  to  be 
directly  as  the  number  of  atmospheres  to  which  the  air  is  compressed. 
Thus,  if  the  air  transmitted  be  at  75  pounds  gauge-pressure,  or  six  atmos- 
pheres, the  volume  of  free  air  will  be  six  times  the  amount  given  in  the 
table  (page  486).  It  is  generally  considered  that  for  economical  transmission 
the  velocity  in  main  pipes  should  not  exceed  20  feet  per  second.  In  the 
smaller  distributing  pipes  the  velocity  should  be  decidedly  less  than  this. 

The  loss  of  power  in  the  transmission  of  compressed  air  in  general  is  not 
a  serious  one,  or  at  all  to  be  compared  with  the  losses  of  power  in  the  opera- 
tion of  compression  and  in  the  re-expansion  or  final  application  of  the  air. 

The  formulas  for  loss  by  friction  are  all  unsatisfactory.  The  statements 
of  observed  facts  in  this  line  are  in  a  more  or  less  chaotic  state,  and  self- 
evidently  unreliable. 

A  statement  of  the  friction  of  air  flowing  through  a  pipe  involves  at  least 
all  the  following  factors:  Unit  of  time,  volume  of  air,  pressure  of  air,  diam- 
eter of  pipe,  length  of  pipe,  and  the  difference  of  pressure  at  the  ends  of 
the  pipe  or  the  head  required  to  maintain  the  flow.  Neither  of  these  factors 
can  be  allowed  its  independent  and  absolute  value,  but  is  subject  to  modifi- 
cations in  deference  to  its  associates.  The  flow  of  air  being  assumed  to  be 
uniform  at  the  entrance  to  the  pipe,  the  volume  and  flow  are  not  uniform 
after  that.  The  air  is  constantly  losing  some  of  its  pressure  and  its  volume 
is  constantly  increasing.  The  velocity  of  flow  is  therefore  also  somewhat 
accelerated  continually.  This  also  modifies  the  use  of  the  length  of  the 
pipe  as  a  constant  factor. 

Then,  besides  the  fluctuating  valuns  of  these  factors,  there  is  the  condition 
of  the  pipe  itself.  The  actual  diameter  of  the  pipe,  especially  in  the 
smaller  sizes,  is  different  from  the  nominal  diameter.  The  pipe  m&y  be 
straight,  or  it  may  be  crooked  and  have  numerous  elbows.  Mr.  Richards 
considers  one  elbow  as  equivalent  to  a  length  of  pipe. 


FLOW   OF   COMPRESSED    AIR 


PIPES. 


489 


Head  or  Additional  Pressure  in  pounds  per  sq.  in. 
required  to  deliver  Air  at  75  Pounds  Gau^e-pressure 
through  Pipes  of  Various  Sizes  and  Lengths.  (Frank 

liicharus.) 


1"  PIPE. 

4"  PIPE. 

«  u  fl 

If! 

•2  ££ 

3-~ 

Length  in  feet. 

Cubic  ft. 
free  air 
per  min. 

Length  in  feet. 

50 

100 

300 

500 

1,000 

200 

300 

400 

1,000 

2,000 

25 
50 
100 
150 

Loss  of  pre 
.245      .49 
.981!  1.962 
3.925    7.85 
8.829  17.66 

ssure, 

1.47 
5.886 

ibs.  p. 
2.45 
981 

sq.  in. 
4.9 

500 
750 
1,000 
1,250 
1,500 

Loss 
.16 
.36 
.64 
1. 
1.44 

of  pre 
.24 
.54 
.96 
1.5 
2.16 

ssure, 
.4 
.9 
1.6 
2.5 
3.6 

Ibs.  p. 
.8 
1.8 
3.2 
5. 
7.2 

sq.  in. 
1.6 
3.6 
6.4 
10. 
14.4 

1*4"  PIPE. 

25 

50 
100 
150 

200 

.056 
.224 
.897 
2.02 
3.59 

.112 
.449 
1.79 
3.94 
7.18 

.336 
1.35 
5.38 
12.11 

..561 
2.24 
8.97 

1.12 
4.49 

5"  PIPE. 

500 

1,000 

2,000 

4,000 

5,000 

500 
1,000 
1,500 
2,000 
2,500 

.11 
.44 
.99 
1.76 

2.75 

.22 
.881 
1.98 
3.52 
5.5 

.44 
1.76 
3.96 
7.04 
11. 

.88 
3.52 
7.92 
14.08 

1.1 

4.4 
9.9 

W  PIPE. 

25 
50 
100 
150 
200 

.017 
.068 
274 
!«J6 
1.09 

.034 
.137 
.548 
1.23 
2.19 

103 
.411 
1.64 
3.69 
6.57 

.171 

.685 
2.74 
6.16 
10.96 

.34 
1.37 

5.48 
12.33 
21.9 

6"  PIPE. 

1,000 

2,000 

4,000 

5,000 

10,000 

3.54 
7.99 
14.17 

2"  PIPE. 

50 

100 
150 
200 
250 
300 

.019 
.076 
.171 
.304 
.476 
.685 

.038 
.152 
.343 
.609 
.952 
1.37 

.114 
.457 
1.03 
1.83 
2.86 
4.11 

.19 
.761 
1.71 
3  04 
4.76 
6.85 

.38 
1.52 
3.44 
6.09 
9.53 
13.72 

1,000 
1,500 
2,000 
2.500 
3,000 

.354 
.799 
1.417 
2.22 
3.18 

.708 
1.599 
2.83 
4.44 
6.37 

1.42 
3.2 
5.67 

8.89 
12.7 

1.77 
3.99 
7.09 
11.1 
15.9 

8"  PIPE. 

2J$"  PIPE. 

2,000 

4,000 

8,000 

10,000 

15,000 

200 

300 

500 

1,000 

2,000 

.87 
3.47 
7.81 
13.89 
21.7 

2,000 
2,500 
3,000 
4.000 
5,000 

.598 
.935 
1.25 
2.39 
3.74 

1.19 

1.87 
2.49 
4.79 

7.48 

2.39 
3.74 
4.99 
9.58 
14.97 

2.99 
4.68 
6.24 
11.97 
18.71 

4.48 
7.02 
9.36 

100 
200 
300 
400 
500 

.087 
.347 
.781 
1.39 
2.17 

.13 

.521 
1.17 
2.08 
3.25 

.217 
.868 
1.95 
3.47 
5.42 

.434 
1.74 
3.91 
6.94 
10.85 

10"  PIPE. 

3"  PIPE. 

2,500 
5,000 
7,500 
10,000 

.286 
1.14 
2.57 
4.57 

.57 
2.29 
5.15 
9.14 

1.14 
4.57 
10.29 

1.43 
5.71 
12.86 

2.15 
8.56 

100 
200 
300 
400 
500 

.0333 
.133 
.3 

.533 
.833 

.05 
2 

'.45 

.8 
1.25 

.0833 
.333 
.75 
1.33 

2.08 

.166 
.666 
1.5 
2.66 
4.16 

.33 
1.33 
3 
5.33 
8.33 

12"  PIPE. 

3^2"  PIPE. 

2,000 

4,000 

8,000 

10,000 

20,000 

250 

500 
750 
1,000 
1,250 

.0832 
.332 

.748 
1.328 
2.08 

.125 
.499 
1.12 
1.99 
3.12 

.208 
.832 
1.87 
3.33 
5.2 

.416 
1.66 
3.75 
6.66 
10.4 

83 

3.32 
7.49 
13.3 

20.8 

2,500 
5,000 
7,500 
10.000 

.11 
.44 
.99 
1.76 

.22 

.88 
1.98 
3.52 

.44 

1  .76 
3.96 
7.05 

.55 
2.2 

4.95 

8.81 

1.101 
4.4 
9.91 
17.6 

Although   Mr.  Richards  does  not  give  any  formula  with  this  table,  an 
nspection  of  it  shows  that  for  any  given  diameter  the  loss  of  head  is 


490 


AIR. 


taken  to  vary  directly  as  the  length  and  as  the  square  of  the  quantity 
delivered,  but  for  a  given  quantity  and  length  the  loss  of  head  appears  to 
vary  inversely  as  some  higher  power  of  the  diameter  than  the  fifth,  ap- 
proximately the  5.5  power;  or,  in  other  words,  that  the  coefficient  of  fric- 


tion  is  variable.     If  we  take   the  formula  of  the  form  Q' 


/ 
=  c'A/  - 


p  =  —,irrv  and  solve  for  c'= 


per  minute,  we  find  values  of  the  coefficient  as  follows: 


which  Q'=  cubic  feet  of  free  air 


For  diameter,  inches      1 
Value  of  c'  =  357 


2 

453 


4 
552 


6 
603 


8 


10 

664 


12 
676 


The  following  table  is  condensed  from  one  given  by  F.  A.  Halsey  in  the 
catalogue  of  the  Rand  Drill  Co. : 


Nominal  Diameter 
of  Pipe,  in  inches. 

Cubic  feet  of  free  air  compressed  to  a  gauge-pressure  of  60  Ibs. 
and  passing  through  the  pipe  each  minute. 

50 

100 

200 

400 

600 

800 

1000 

1500 

2000 

3000 

4000 

5000 

Loss  of  pressure  in  Ibs.  per  square  inch  for  each  1000  ft. 
of  straight  pipe. 

1 
1*4 

r* 
p 

4 
5 
6 
8 
10 
12 
14 

10.40 
2.63 
1.22 
.35 
.14 

4.89 
1.41 
.57 
.20 

5.64 
2.30 
.78 
.20 

9.20 
3.14 

.80 
.26 

7.05 

1.81 
.59 
.23 

3.22 

1.04 
.41 
.10 

5.02 
1.63 
.64 
.16 

3.66 
1.46 
.37 
.12 

6.50 
2.59 
.65 
.21 

5.81 
1.47 

.47 
.19 

10.30 
2.61 

.84 
.34 
.16 

4.08 
1.30 
.53 
.24 



This  table  appears  to  follow  more  closely  than  does  Richards'  table  the 
law  of  the  formula  p  =  !~a  „,  but  the  coefficients  differ  considerably  from 
those  of  Richards.  Solving  for  C',  we  obtain— 


For  diameter,  inches  . .    2 
Value  of  V 471 


4 

44° 


5 
443 


448        437 


10 

436 


12 

435 


14 

431 


Comparing  some  of  the  losses  of  pressure  in  the  two  tables,  we  find- 
Length,  feet 1000  1000  1000  5000  5000  5000 

Quantity,  cu.  ft 1000  1000  1000  4000  4000  4000 

Diameter,  inches 4  5  6  8  10  12 

Loss,  Richards  3.2  .881  .354  7.48  2.29  .88 

"     Halsey 5.02         1.63  .64  13.05          4.20  1.70 

The  two  tables  are  not  calculated  for  the  same  amount  of  compression, 
but  the  difference  is  not  sufficient  to  account  for  the  difference  in  the  coeffi- 
cients. If  we  multiply  the  coefficients  derived  from  Halsey's  table  by  5/4, 
the  ratio  of  the  pressures  75  and  60  Ibs.,  they  become  for  a  2-inch  pipe  589, 
and  for  a  12-inch  pipe  531,  against  Richards's  figures  of  453  and  676  for  the 
same  pipes.  To  compare  Richards's  figures  for  loss  of  pressure  with  Hal- 
sey's, the  former  should  be  multiplied  by  25/16.  In  the  absence  of  experi- 
mental data  no  opinion  can  be  f  orined  as  to  which  table  is  the  more  accurate, 
but  either  one  is  probably  of  sufficient  accuracy  for  practical  purposes. 


MEASUREMENT  OF   VELOCITY   OF   AIR. 


491 


Mr.  Richards,  in  Am.  Mach.,  Dec.  27,  1894,  publishes  a  new  formula,  viz.: 


'  10,000d5a  ' 


/10, 

~  Y 


10,000d»ap      r  _ 

L       ; 


, 

°     ~  ; 


in  which  F  =  actual  volume  of  compressed  air  delivered,  in  cubic  feet  per 
minute  (not  the  volume  of  free  air,  as  in  the  other  formulae),  L  =  length  of 
pipe  in  feet,  d  =  internal  diameter  of  pipe  in  inches,  p  =  head  or  additional 
pressure  in  pounds  per  square  inch  required  to  maintain  the  flow,  and  a  is 
a  coefficient  varying  with  the  diameter  of  the  pipe.  Its  value  for  different 
nominal  diameters  of  wrought-iron  pipe  is  given  by  Mr.  Richards  as  follows: 


Diam.  in. 

Val.  of  a. 

Diam.  in. 

Val.  of  a. 

Diam.  in. 

Val.  of  a. 

Diam 

in.  Val.  of  a 

1 

.35 

2y> 

.65 

5 

.93 

12 

1.26 

VA 

.5 

3 

.73 

6 

1. 

16 

1.34 

1% 

.66 

31^ 

.79 

8 

1.125 

20 

1.4 

2 

.56 

4 

.84 

10 

1.2 

24 

1.45 

The  values  of  a  for  the  1  and  1*4  inch  pipes  appear  inconsistent  with  the 
values  for  the  other  sizes,  because  the  nominal  diameters  of  these  two  sizes 
are  relatively  much  less  than  their  actual  diameters,  1.38  and  1.61  inches,  re- 
spectively. 

The  following  values  of  the  fifth  power  of  d  and  of  d5a  are  given  by  Mr. 
Richards  to  facilitate  calculations: 


Fifth  Powers  of  d. 


Value  of  d&a. 


1" 

1 

5" 

3  125 

1" 

35 

5". 

2918  75 

WA"  ... 

3  05 

6" 

7  776 

WA"  . 

...  1.525 

6"... 

7  776 

1^X/ 

7  59 

8" 

32  768 

\V»" 

5  03 

8" 

36  864 

2" 

32 

10" 

100  000 

w  ... 

.  .  18  08 

10".  . 

.  .  .   120,000 

2U" 

97  65 

12" 

248  832 

2W 

63  47 

12" 

313  528 

3-  :: 

243 

16" 

1  048  576 

3"  " 

177  4 

16" 

.  .  1  405  091 

3U"... 

.  .  .  525 

20" 

3  200  000 

3}4"  .  .  . 

...413  2 

20"  .  .  . 

...  4,480.000 

4"~  ... 

...1024 

24"  .  .  . 

..  7,962,624 

4"  ... 

...860.2 

24"... 

...11,545,805 

In  order  to  compare  Mr.  Richards'  new  formula  for  volume  of  compressed 
air  transmitted  with  the  formula  Q'  =  c' A/  ^=r~,  in  which  Q'  is  the  volume 
of  free  air,  =  5F  if  the  air  is  compressed  to  5  atmospheres,  we  have 


and  from  the  values  of  a  given  by  Mr.  Richards  we  find  values  of  c'  as 
follows: 

For  diameter,  nominal,  inches  =..     1      2      4      6      8      10      12 
Value  of  c' 296  374  453  500  530   548    561 

Measurement  of  the  Velocity  of  Air  in  Pipes  by  an  Ane- 
mometer.—-Tests  were  made  by  B.  Donkin,  Jr.  (Inst.  Civil  Enyrs.  1892), 
to  compare  the  velocity  of  air  in  pipes  from  8  in.  to  24  in.  cliam.,  as  shown  by 
an  anemometer  2%  in.  diam.  with  the  true  velocity  as  measured  by  the  time 
of  descent  of  a  gas-holder  holding  1622  cubic  feet.  A  table  of  the  results 
with  discussion  is  given  in  Encfg  News,  Dec.  22, 1892.  In  pipes  from  8  in.  to  20 
in.  diam.  with  air  velocities  of  from  140  to  690  feet  per  minute  the  anemome- 
ter showed  errors  varying  from  14.5$  fast  to  10$  slow.  With  a  24-inch  pipe 
and  a  velocity  of  73  ft.  per  minute,  the  anemometer  gave  from  44  to  63  feet, 
or  from  13.6  to  39.6$  slow.  The  practical  conclusion  drawn  from  these  ex- 
periments is  that  anemometers  for  the  measurement  of  velocities  of  air  in 
pipes  of  these  diameters  should  be  used  with  great  caution.  The  percentage 
of  error  is  not  constant,  and  varies  considerably  with  the  diameter  of  the 
pipes  and  the  speeds  of  air.  The  use  of  a  baffle,  consisting  of  a  perforated 
plate,  which  tended  to  equalize  the  velocity  in  the  centre  and  at  the  sides  in 
some  cases  diminished  the  error, 


492 


AIR. 


The  impossibility  of  measuring  the  true  quantity  of  air  by  an  anemometer 
held  stationary  in  one  position  is  shown  by  the  following  figures,  given  by 
Wm.  Daniel  (Proc.  Inst.  M.  E.,  1875),  of  the  velocities  of  air  found  at  different 
points  in  the  cross-sections  of  two  different  airways  in  a  mine. 

DIFFERENCES  OF  ANEMOMETER  READINGS  IN  AIRWAYS. 
8  ft.  square.  5  X  8  ft. 


1712 

1795 

1859 

1329 

1622 

1635 

1782 

1091 

1477 

1344 

1524 

1049 

1262 

1356 

1293 

1333 

Average  1469. 


Average  1132. 


Equation  of  Pipes.— It  is  frequently  desired  to  know  what  number 
of  pipes  of  a  given  size  are  equal  in  carrying  capacity  to  one  pipe  of  a  larger 
size.  At  the  same  velocity  of  flow  the  volume  delivered  by  tivo  pipes  of 
different  sizes  is  proportional  to  the  squares  of  their  diameters;  thus,  one 
4-inch  pipe  will  deliver  the  same  volume  as  four  2-inch  pipes.  With  the  same 
head,  however,  the  velocity  is  less  in  the  smaller  pipe,  and  the  volume  de- 
livered varies  about  as  the  square  root  of  the  fifth  power  (i.e.,  as  the  2.5 
power).  The  following  table  has  been  calculated  on  this  basis.  The  figures 
opposite  the  intersection  of  any  two  sizes  isjbne  number  of  the  smaller-sized 
pipes  required  to  equal  one  of  the  larg 


5.7  2-inch  pipes. 


<rger.    Thus,  one  4-inch  pipe  is  equal  ta 


S  a 
5"" 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

12 

14 

16 

18 

20 

21 

2 

5.7 

1 

3 

15.6 

2.8 

1 

4 

32 

5.7 

2.1 

1 

5 

55.9 

9.9 

3.6 

1.7 

1 

6 

88.2 

15.6 

5.7 

2.8 

1.6 

1 

7 

130 

22.9 

8.3 

4.1 

2.3 

1.5 

1 

8 

181 

32 

11.7 

5.7 

3.2 

2.1 

1.4 

1 

9 

243 

43. 

15.6 

7.6 

4.3 

2.8 

1.9 

1.3 

1 

10 

316 

55.9 

20.3 

9.9 

5.7 

3.6 

2.4 

1.7 

1.3 

1 

11 

401 

70.9 

25.7 

12.5 

7.2 

4.6 

3.1 

2.2 

1.7 

1.3 

12 

499 

88.2 

32 

15.6 

8.9 

5.7 

3.8 

2.8 

2.1 

1.6 

1 

13 

609 

108 

39.1 

19 

10.9 

7.1 

4.7 

3.4 

2.5 

1.9 

1.2 

14 

733 

130 

47 

22.9 

13.1 

8.3 

5.7 

4.1 

3.0 

2.3 

1.5 

1 

15 

787 

154 

55.9 

27.2 

15.6 

9.9 

6.7 

4.8 

3.6 

2.8 

1.7 

1.2 

16 

181 

65.7 

32 

18.3 

11.7 

7.S 

5.7 

4.2 

3.2 

2.1 

1.4 

1 

17 

211 

76.4 

37.2 

21.3 

13.5 

9.2 

6.6 

4.9 

3.8 

2.4 

1.6 

1.2 

18 

243 

88.2 

43 

24.6 

15.6 

10.6 

7.6 

5.7 

4.3 

2.8 

1.9 

1.3 

1 

19 

278 

101 

49.1 

28.1 

17.8 

12.1 

8.7 

6.5 

5 

3.2 

2.1 

1.5 

1.1 

20 

316 

115 

55.9 

32 

20.3 

13.8 

9.9 

7.4 

5.7 

3.6 

2.4 

1.7 

1.3 

1 

22 

401 

146 

?'0.9 

40.6 

25.7 

17.5 

12.5 

9.3 

7.2 

4.6 

3.1 

2.2 

1.7 

1.3 

24 

499 

181 

88.2 

50.5 

32 

21.8 

15.6 

11.6 

8.9 

5.7 

3.8 

2.8 

2.1 

1.6 

1 

26 

609 

221 

108 

61.7 

39.1 

26.6 

19. 

14.2 

10.9 

7.1 

4.7 

3.4 

2.5 

1.9 

l.fe 

28  ~ 

733 

266 

130 

74.2 

47 

32 

22.9 

17.1 

13.1 

8.3 

5.7 

4.1 

3 

2.3 

1.5 

30 

787 

316 

154 

88.2 

55.9 

38 

27.220.3 

15.6 

9.9 

6.7 

4.8 

3.6 

2.8 

1.7 

36 

499 

243 

130 

88.2 

60 

43   32 

24.6 

15.6 

10.6 

7.6 

5.7 

4.3 

2.8 

42 

733 

357 

205 

130 

88.2 

63.247 

36.2 

19 

15.6 

11.2 

8.3!  6.4 

4.1 

48 

499 

286 

181 

123 

88.262.7 

50.5 

32 

21.8 

15.6 

11.6  8.9 

5.7 

54 

670 

383 

243 

165 

118  88.2 

67.8 

43 

29.2 

20.9 

15.6 

12 

7.6 

60 

787 

499 

316 

215 

154J115 

88.2 

55.9 

38 

27.2 

20.3 

15.6 

9.9 

WIND. 


493 


Loss  of  Pressure  in  Compressed  Air  Pipe-main,  at 
St.  Gothard  Tunnel. 

(E.  Stockalper.) 


§ 

Il«-   • 

1!* 

=4-1  -~ 

fe 

c'S 

Observed  Pressures. 

£ 

I^llf' 

a;  c5  55 
*  x  fl 

O  03 

?| 

*1 

<M 

0 

o5 

Value 
of  c' 

cperinien1 

Q 

1 

illfl 

^JM  c3->->  p 

f->  P  *& 

&h 

gil 

HOC 

3ei_i  4^ 

!«  n 

l|| 

ight  of  ai 
nff  per  se 

S  M 
o  ^ 

la 
|| 

|!  . 

*§&• 

i! 

5n  O 

Loss  of 
Pressure. 

in  for- 
mula 

3 

«! 

^  O  >  03  55 

'O  0  G3 

1°'^ 

^ 

^u 

g.« 

Ibs. 

per 

No, 

in. 

cu.ft. 

cu.ft. 

den. 

Ibs. 

feet. 

at. 

at. 

sq.in 

% 

7.87 
5  91 

J-33.053  j 

6.534 
7.063 

.00650 
.00603 

2.669 
2.669 

19.32 
37.14 

5.60 
5.24 

5.24 
5.00 

5.292 
3.528 

6.4 
4.6 

610 
515 

8i 

7.87 
5  91 

J-22.002-J 

5.509 
5863 

.00514 
00482 

1.776 
1  776 

16.30 

4.35 
4  13 

4.13 

3.234 

5.1 

519 

•i 

7.87 
5.91 

f  18.884  | 

5.262 
5.580 

.00449 
.00423 

1.483 
1.483 

15.58 
29.34 

3.84 
3.65 

3.65 
3.54 

2793 
1.617 

5.0 
3.0 

466 
422 

The  length  of  the  pipe  7.87  in  diameter  was  15,092  ft.,  and  of  the  smaller 
pipe  1712.6  ft.  The  mean  temperature  of  the  air  in  the  large  pipe  was  70°  F. 
and.  in  the  small  pipe  80°  F. 

WIND. 

Force  of  the  Wind.— Smeaton  in  1759  published  a  table  of  the 
velocity  and  pressure  of  wind,  as  follows: 

VELOCITY  AND  FORCE  OP  WIND,  IN  POUNDS  PER  SQUARE  INCH. 


L 

Mo 

^ 
ftfl 

33     oj 

&^"o 

§V-I      £j 

Common    Appella- 
tion of  the 

N 

02   0 

fc-d 

&  = 

SL--3 
*^  9 

Common  Appella- 
tion of  the 

£% 

£>  Oi 

Q  ff. 

CT"  O 
O   CB   ft 

Force  of  Wind. 

.-Sw 

Qi  a^ 

2  crc 
o  «  a, 

Force  of  Wind. 

£ 

ft 

§ 

ft  * 

ft 

1 

1.47 

0.005 

\  Hardly  percepti- 
j     ble. 

18 
20 

26.4 
29.34 

1.55 
1.968 

>Very  brisk. 

2 
3 

4 

2.93 
4.4 

5.87 

0.020 
0.044 
0.079 

h  Just  perceptible. 
] 

25 
30 
35 

36.67 
44.01 
51.34 

3.075 
4.429 

6.027 

\ 
{-  High  wind. 

5 

7.33 

0.123 

1  Gentle  pleasant 

40 

58.68 

7.873 

] 

6 

7 

8.8 
10.25 

0.177 
0.241 

j     wind. 

j 

45 
50 

66.01 
73.35 

9.963 
12.30 

}-  Very  high  storm. 

8 

11.75 

0.315 

55 

80.7 

14.9 

j 

9 

13.2 

0.400 

60 

88.02 

17.71 

10 
12 

14.67 
17.6 

0.492 

0.708 

Pleasant  brisk 

66 
70 

95.4 
102.5 

20.85 
24.1 

>•  Great  Storm  . 

14 
15 

20.5 
22.00 

0.964 
1.107 

|     gale. 

75 

80 

110. 
117.36 

27.7 
31.49 

!•  Hurricane. 

16 

23.45 

1.25 

J 

100 

146.67 

49.2 

j  Immense  hurri- 

1     cane. 

The  pressures  per  square  foot  in  the  above  table  correspond  to  the 
formula  P  =  0.005 F«,  in  which  V  is  the  velocity  in  miles  per  hour.  Eng'g 
News.  Feb.  9,  1893,  says  that  the  formula  was  never  well  established,  and 
has  floated  chiefly  on  Smeaton 's  name  and  for  lack  of  a  better.  It  was  put 
forward  only  for  surfaces  for  use  in  windmill  practice.  The  trend  of 
modern  evidence  is  that  it  is  approximately  correct  only  for  such  surfaces, 
and  that  for  large  solid  bodies  it  often  gives  greatly  too  large  results. 
Observations  by  others  are  thus  compared  with  Smeaton's  formula: 

Old  Smeaton  formula P=    .005 V2 

As  determined  by  Prof.  Martin P  =     .004F2 

Whipple  and  Dines P-  .0029 F2 


494  AIR. 

At  60  miles  per  hour  these  formulas  give  for  the  pressure  per  square  foot, 
18,  14.4  and  10.44  Ibs.,  respectively,  the  pressure  varying  by  all  of  them  as 
the  square  of  the  velocity.  Lieut.  Crosby's  experiments  (Eng^g,  June  13, 
1890),  claiming  to  prove  that  P  =  fV  instead  of  P  =  /F2,  are  discredited. 

A.  R.  Wolff  (The  Windmill  as  a  Prime  Mover,  p.  9)  gives  as  the  theoretical 

pressure  per  sq.  ft.  of  surface,  P  =  —  —  ,  in  which  d  =  density  of  air  in  pounds 

.018743(p  4  P) 
per  cu.  ft.  =  —      —  .       •—  ;   p  being  the  barometric  pressure  per  square 

foot  at  any  level,  and  temperature  of  32°  F.,  t  any  absolute  temperature, 
Q  =  volume  of  air  carried  along  per  square  foot  in  one  second,  v  —  velocity 

dv* 
of  the  wind  in  feet  per  sec.,  g  =  32.16.    Since  Q  =  v  cu.  ft.  per  sec.,  P=  —  . 

Multiplying  this  by  a  coefficient  0.93  found  by  experiment,  and  substituting 

0.017431  X  p 
the  above  value  of  d,  he  obtains  P  =  —  -  ^—  T^  —    —  -  ,    and     when     p 


-  .018743 


=•  2116.5  Ibs.  per  sq  ft.  or  average  atmospheric  pressure  at  the  sea-level, 

36  8929 
P=T—  —  ,  an  expression  in  which  the  pressure  is  shown  to  vary 

**^16-  0.18743 

with  the  temperature;  and  he  gives  a  table  showing  the  relation  between 
velocity  and  pressure  for  temperatures  from  0°  to  100°  F.,  and  velocities 
from  1  to  80  miles  per  hour.  For  a  temperature  of  45°  F.  the  pressures  agree 
with  those  in  Smeaton's  table,  for  0°  F.  they  are  about  10  per  cent  greater, 
and  for  100°  10  per  cent  less.  Prof.  H.  Allen  Hazen,  Eng'g  News,  July  5, 
1890,  says  that  experiments  with  whirling  arms,  by  exposing  plates  to  direct 
wind,  and  on  locomotives  with  velocities  running  up  to  40  miles  per  hour. 
have  invariably  shown  the  resistance  to  vary  with  F2.  In  the  formula 
P  —  .005SF2,  in  which  P  —  pressure  in  pounds,  S  =  surface  in  square  feet, 
V  —  velocity  in  miles  per  hour,  the  doubtful  question  is  that  regarding 
the  accuracy  of  the  first  two  factors  in  the  second  member  of  this  equation. 
The  first  factor  has  been  variously  determined  from  .003  to  .005  [it  has  been 
determined  as  low  as  .0014.—  Ed.  Eng'g  News]. 

The  second  factor  has  been  found  in  some  experiments  with  very  short 
whirling  arms  and  low  velocities  to  vary  with  the  perimeter  of  the  plate, 
but  this  entirely  disappears  with  longer  arms  or  straight  line  motion,  and 
the  only  question  now  to  be  determined  is  the  value  of  the  coefficient.  Per- 
haps some  of  the  best  experiments  for  determining  this  value  were  tried  in 
France  in  1886  by  carrying  flat  boards  on  trains.  The  resulting  formula  in 
this  case  was,  for  44.5  miles  per  hour,  p  =  .005358F2. 

Mr.  Crosby's  whirling  experiments  were  made  with  an  arm  5.5  ft.  long. 
It  is  certain  that  most  serious  effects  from  centrifugal  action  would  be  set 
up  by  using  such  a  short  arm,  and  nothing  satisfactory  can  be  learned  with 
arms  less  than  20  or  30  ft.  long  at  velocities  above  5  miles  per  hour. 

Prof.  Kernot,  of  Melbourne  (Engineering  Record,  Feb.  20,  1894),  states  that 
experiments  at  the  Forth  Bridge  showed  that  the  average  pressure  on  sur- 
faces as  large  as  railway  carriages,  houses,  or  bridges  never  exceeded  two 
thirds  of  that  upon  small  surfaces  of  one  or  two  square  feet,  such  as  have 
been  used  at  observatories,  and  also  that  an  inertia  effect,  which  is  frequently 
overlooked,  may  cause  some  forms  of  anemometer  to  give  false  results 
enormously  exceeding  the  correct  indication.  Experiments  of  Mr.  O.  T. 
Crosby  showed  that  the  pressure  varied  directly  as  the  velocity,  whereas  all 
the  early  investigators,  from  the  time  of  Smeaton  onwards,  made  it  vary  as 
the  square  of  the  velocity.  Experiments  made  by  Prof.  Kernot  at  speeds 
varying  from  2  to  15  miles  per  hour  agreed  with  the  earlier  authorities,  and 
tended  to  negative  Crosby's  results.  The  pressure  upon  one  side  of  a  cube, 
or  of  a  block  proportioned  like  an  ordinary  carriage,  was  found  to  be  .9  of 
that  upon  a  thin  plate  of  the  same  area.  The  same  result  was  obtained  for 
a  square  tower.  A  square  pyramid,  whose  height  was  three  times  its  base, 
experienced  .8  of  the  pressure  upon  a  thin  plate  equal  to  one  of  its  sides,  but 
if  an  angle  was  turned  to  the  wind  the  pressure  was  increased  by  full}'  20$. 
A  bridge  consisting  of  two  plate-girders  connected  by  a  deck  at  the  top  was 
found  to  experience  .9  of  the  pressure  on  a  thin  plate  equal  in  size  to  one 
girder,  when  the  distance  between  the  girders  was  equal  to  their  depth,  and 
this  was  increased  by  one  fifth  when  the  distance  between  the  girders  was 


WINDMILLS.  495 

double  the  depth.  A  lattice-work  in  which  the  area  of  the  openings  was  55$ 
of  the  whole  area  experienced  a  pressure  of  80$  of  that  upon  a  plate  of  the 
same  area.  The  pressure  upon  cylinders  and  cones  was  proved  to  be  equal 
to  half  that  upon  the  diametral  planes,  and  that  upon  an  octagonal  prism  to 
be  20$  greater  than  upon  the  circumscribing  cylinder.  A  sphere  was  sub- 
ject to  a  pressure  of  .36  of  that  upon  a  thin  circular  plate  of  equal  diameter. 
A  hemispherical  cup  gave  the  same  result  as  the  sphere;  when  its  concavity 
was  turned  to  the  wind  the  pressure  was  1.15  of  that  on  a  flat  plate  of  equal 
diameter.  When  a  plane  surface  parallel  to  the  direction  of  the  wind  was 
brought  nearly  into  contact  with  a  cylinder  or  sphere,  the  pressure  on  the 
latter  bodies  was  augmented  by  about  20$,  owing  to  the  lateral  escape  of  the 
air  being  checked.  Thus  it  is  possible  for  the  security  of  a  tower  or  chimney 
to  be  impaired  by  the  erection  of  a  building  nearly  touching  it  on  one  side. 

Pressures  of  "Wind  Registered  in  Storms.—  Mr.  Frizell  has 
examined  the  published  records  of  Greenwich  Observatory  from  1849  to  1869, 
and  reports  that  the  highest  pressure  of  wind  he  finds  recorded  is  41  Ibs. 
per  sq.  ft.,  and  there  are  numerous  instances  in  which  it  was  between  30  and 
40  Ibs.  per  sq.  ft.  Prof.  Henry  says  that  on  Mount  Washington.  N.  H.,  a  ve- 
locity of  150  miles  per  hour  has  been  observed,  and  at  New  York  City  60 
miles  an  hour,  and  that  the  highest  winds  observed  in  1870  were  of  72  and  63 
miles  per  hour,  respectively. 

Lieut.  Dunwoody,  U.  S.  A.,  says,  in  substance,  that  the  New  England  coast 
is  exposed  to  storms  which  produce  a  pressure  of  50  Ibs.  per  sq.  ft.  Engi- 
neering News,  Aug.  20,  1880. 

WINDMILLS. 

Power  and  Efficiency  of  Windmills.—  Eankine,  S.  E.,  p.  215, 
gives  the  following:  Let  Q  =  volume  of  air  which  acts  on  the  sail,  or  part 
of  a  sail,  in  cubic  feet  per  second,  v  =  velocity  of  the  wind  in  feet  per 
second,  s  =  sectional  area  of  the  cylinder,  or  annular  cylinder  of  wind, 
through  which  the  sail,  or  part  of  the  sail,  sweeps  in  one  revolution,  c  =  a 
coefficient  to  be  found  by  experience;  then  Q  =  cvs.  Raukine,  from  experi- 
mental data  given  by  Smeaton,  and  taking  c  to  include  an  allowance  for 
friction,  gives  for  a  wheel  with  four  sails,  proportioned  in  the  best  manner, 
c  =  0.75.  Let  A  =  weather  angle  of  the  sail  at  any  distance  from  the  axis, 
i.e.,  the  angle  the  portion  of  the  sail  considered  makes  with  its  plane  of 
revolution.  This  angle  gradually  diminishes  from  the  inner  end  of  the  sail 
to  the  tip;  u  =  the  velocity  of  the  same  portion  of  the  sail,  and  E  =  the  effi- 
ciency. The  efficiency  is  the  ratio  of  the  useful  work  performed  to  whole 
energy  of  the  stream  of  wind  acting  on  the  surface  s  of  the  wheel,  which 

Dsv3 
energy  is  —  —  ,  D  being  the  weight  of  a  cubic  foot  of  air.    Rankine's  formula 

for  efficiency  is 


in  which  c  =  0.75  and  /  is  a  coefficient  of  friction  found  from  Smeaton's 
data  =  0.016.    Rankine  gives  the  following  from  Smeaton's  data: 

A  =  weather-angle  ....................  =7°  13°  19° 

Y~-v  =  ratio  of  speed  of  greatest  effi- 

ciency, for  a  given  weather- 

angle,  to  that  of  the  wind  .....   =2.63  1  .86  1.41 

E  =  efficiency  .......................   =0.24  0.29  0.31 

Rankine  gives  the  following  as  the  best  values  for  the  angle  ol  weather  at 
different  distances  from  the  axis: 

Distance  in  sixths  of  total  radius.  ..       1          23456 
Weather  angle  ....................     18°      19°      18°      16°      12^°    7° 

But  Wolff  (p.  125)  shows  that  Smeaton  did  not  term  these  the  best  angles, 
but  simply  says  they  "  answer  as  well  as  any,11  possibly  any  that  were  in  ex- 
istence in'  his  time.  Wolff  says  that  they  "cannot  in  the  nature  of  things 
be  the  most  desirable  angles."  Mathematical  considerations,  he  says,  con- 
clusively show  that  the  angle  of  impulse  depends  on  the  relative  velocity  of 
each  point  of  the  sail  and  the  wind,  the  angle  growing  larger  as  the  ratio  be- 
comes greater.  Smeaton's  angles  do  not  fulfil  this  condition.  Wolff  devel- 


496 


AIE. 


ops  a  theoretical  formula  for  the  best  angle  of  weather,  and  from  it 
calculates  a  table  for  different  relative  velocities  of  the  blades  (at  a  distance 
of  one  seventh  of  the  total  length  from  the  centre  of  the  shaft)  and  the  wind, 
from  which  the  following  is  condensed: 


Ratio  of  the 
Speed  of  Blade 
at  1/7  of  Radius 
to  Velocity  of 
Wind. 

Distance  from  the  axis  of  the  wheel  in  sevenths  of  radius. 

1 

2 

3 

4 

5 

6 

7 

Best  angles  of  weather. 

0.10 
0.15 

0.20 
0.25 
0.30 
0.35 
0.40 
0.45 
0.50 

42°  9' 
40  44 
39  21 
37  59 
36  39 
35  21 
34   6 
32  53 
31  43 

39°  21' 
36  39 
34   6 
36  43 
29  31 
27  30 
25  40 
24   0 
22  30 

36°  39' 
32  53 
29  31 
26  34 
24   0 
21  48 
19  54 
18  16 
16  51 

34°  6' 
29  31 
25  40 
22  30 
19  54 
17  46 
16   0 
14  32 
13  17 

31°  43' 
26  34 
22  30 
19  20 
16  51 
14  52 
13  17 
11  59 
10  54 

29°  31' 
24   0 
19  54 
16  51 
14  32 
12  44 
11  19 
10  10 
9  13 

27°  30' 
21  48 
17  46 
14  52 
12  44 
11   6 
9  50 
8  48 
7  58 

The  effective  power  of  a  windmill,  as  Smeaton  ascertained  by  experiment, 
varies  as  s,  the  sectional  area  of  the  acting  stream  of  wind;  that  is,  for  simi- 
lar wheels,  as  the  squares  of  the  radii. 

The  value  0.75,  assigned  to  the  multiplier  c  in  the  formula  Q  =  cvs,  is 
founded  on  the  fact,  ascertained  by  Smeaton,  that  the  effective  power  of  a 
windmill  with  sails  of  the  best  form,  and  about  15^  ft.  radius,  with  a  breeze 
of  13  ft.  per  second,  is  about  1  horse-power.  In  the  computations  founded 
on  that  fact,  the  mean  angle  of  weather  is  made  —  13°.  The  efficiency  of 
this  wheel,  according  to  the  formula  and  table  given,  is  0.29,  at  its  best 
speed,  when  the  tips  of  the  sails  move  at  a  velocity  of  2.6  times  that  of  the 
wind. 

Merivale  (Notes  and  Formulae  for  Mining  Students),  using  Smeaton's  co- 
efficient of  efficiency,  0.29,  gives  the  following: 
U  =  units  of  work  in  foot  Ibs.  per  sec.; 

W  =  weight,  in  pounds,  of  the  cylinder  of  wind  passing  the  sails  each 
second,  the  diameter  of  the  cylinder  being  equal  to  the  diameter 
of  the  sails  ; 

V  =  velocity  of  wind  in  feet  per  second; 
H.P.  =  effective  horse-power; 


64 


64  X550' 


A.  R.  Wolff,  in  an  article  in  the  American  Engineer,  gives  the  following 
(see  also  his  treatise  on  Windmills): 
Let  c  =  velocity  of  wind  in  feet  per  second  ; 

n  =  number  of  revolutions  of  the  windmill  per  minute; 

bo»  &n  &2i  bx  be  the  breadth  of  the  sail  or  blade  at  distances  Z0,  ^n  'a» 

/a,  and  Z,  respectively,  from  the  axis  of  the  shaft; 
10  =  distance  from  axis  of  shaft  to  beginning  of  sail  or  blade  proper; 
I   =  distance  from  axis  of  shaft  to  extremity  of  sail  proper; 
voi  vu  vi->  vsi  vx  =  tne  velocity  of  the  sail  in  feet  per  second  at  dis- 

tances 10,  Zj,  Z2<  l-i  respectively,  from  the  axis  of  the  shaft; 
a0,  ax,  «2»  a^  ax  —  tne  angles  of  impulse  for  maximum  effect  at  dis- 

tances Z0,  Zx,  Z2,  Z3,  Z  respectively  from  the  axis  of  the  shaft; 
a  =  the  angle  of  impulse  when  the  sails  or  blocks  are  plane  surfaces, 

so  that  there  is  but  one  angle  to  be  considered; 
JV  =  number  of  sails  or  blades  of  windmill  ; 
K  =  .93. 
d  =  density  of  wind  (weight  of  a  cubic  foot  of  air  at  average  tempera- 

ture and  barometric  pressure  where  mill  is  erected); 
W  =  weight  of  wind-wheel  in  pounds; 
/  =  coefficient  of  friction  of  shaft  and  bearings; 
D  —  diameter  of  bearing  of  windmill  in  feet. 


WINDMILLS. 


49? 


The  effective  horse-power  of  a  windmill  with  plane  sails  will  equal 

^  .(  v0 

X  mean  of  (  i?0(sm  a  --  2  cos  a)b0  cos  a 

fW  X  .05236nZ> 
-  -  —  - 


~ 

oovg 


vx  \ 

vx  (sin  a  --  —  cos  a)  bx  cos  aj  — 


— 


The  effective  horse-power  of  a  windmill  of  shape  of  sail  for  maximum 
effect  equals 


l  -  10}Kdc* 


22000 


p/2sm2a0-l,          2  sin2  c^-l, 

nofl ;     — 60,      :   ^ 6,  . 

^      sin2  a0  sin2  ax 


X  meai 
2  sin2  ax  -  1 


tf  sin*  ax  —  i      \ 
sin,^     bx)  ~ 


fW  X  .05236nD 
550  ' 


hose  pr  e  any  comp.  - 

sults obtained  are  in  close  agreement  with  those  obtained  by  theoretical 
analysis  of  the  impulse  of  wind  upon  windmill  blades. 

Capacity  of  the  Windmill. 


a 

"o3 
e 

pl 

H-g 

1 

w 

•ofa 

.sj 

?! 

Gallons  of  Water  raised  per  Minute  to 
an  Elevation  of— 

Cg  0) 

3  £ 

*t| 

a 

•^  ^ 

§'s 

<!  ?* 

o*  3« 

0 

>•>:« 

.2  g 

p  cc    •  ,f^>  "  3 
£  o  1)  !  <D  ^'  cS  _: 

c 

•"£,2 

|p< 

25 

50 

75 

100 

150 

200 

KSIjpSl 

'1 

5  2 

> 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

'|S  >  is  ss's 

p 

£ 

(2 

w 

•j 

wheel 

8V  ft 

16 

70  to  75 

6.162 

3016 

0.04 

8 

io2"' 

16 

60  to  65 

19.179 

9.563 

6.638 

4.750 

0.12 

8 

12    " 

16 

55  to  60 

33.941 

17.952 

11.851 

8.485 

'  5.680 

0.21 

8 

14    " 

16 

50  to  55 

45.139 

22.569 

15.304 

11.246 

7.807 

4998 

0.28 

8 

16    " 

16 

45  to  50 

64600 

31.654 

19.542 

16.150 

9.77! 

8.075 

0.41 

8 

18    " 

16 

40  to  45 

97.682 

52.165 

32.513 

24.421 

17.485 

12.211 

0.61 

8 

20    " 
25    " 

16 
16 

35  to  40  124.950 
30  to  35|  212.^81 

63.750 
106.964 

40.800 
71.604 

31.248 
49  .  725 

19.284 
37.349 

15.938 
26.741 

0.78 
1.34 

8 
8 

These  windmills  are  made  in  regular  sizes,  as  high  as  sixty  feet  diameter  of 
wheel;  but  the  experience  with  the  larger  class  of  mills  is  too  limited  to 
enable  the  presentation  of  precise  data  as  to  their  performance. 

If  the  wind  can  be  relied  upon  in  exceptional  localities  to  average  a  higher 
velocity  for  eight  hours  a  day  than  that  stated  in  the  above  table,  the  per- 
formance or  horse-power  of  the  mill  will  be  increased,  and  can  be  obtained 
by  multiplying  the  figures  in  the  table  by  the  ratio  of  the  cube  of  the  higher 
average  velocity  of  wind  to  the  cube  of  the  velocity  above  recorded. 

He  also  gives  the  following  table  showing  the  economy  of  the  windmill. 
All  the  items  of  expense,  including  both  interest  and  repairs,  are  reduced  to 
the  hour  by  dividing  the  costs  per  annum  l>y  365  X  8  —  2920;  the  interest, 


498 


AIR. 


etc.,  for  the  twenty-four  hours  being  charged  to  the  eight  hours  of 
work.  By  multiplying  the  figures  in  the  5th  column  by  584,  the  first 
the  windmill,  in  dollars,  is  obtained. 

Economy  of  the  Windmill. 


actual 
cost  of 


"8 

3hi 

bo 

E 

Expense  of  Actual  Useful  Power 

.22 

j»  §*  ^'g-b 

Developed,  in  cents,  per  hour. 

i 

t>-3       0  "'3 

Designation 

11 

ll  ;3*i« 

•*•'        *& 

cc_o"cc 

o> 
1 

£  <»" 

0  a 

of  Mill. 

£  a 

+-*  ^    \Zz  9"£  $ 

^  S^K*    S^ 

sS  "^O 

'O 

33  G 

O   4J 

v  ° 

0>   w  ^  ® 

o^O.S'ofS  t-'^ 

'III^ 

e 

<D 

®'t; 

J5oi 

1| 

ffils 

^  •-  o  o  ^  o  5 

S|s| 

5 

0 

"3 

111 

"5 

CTh5 

>  K  ^  ^ 

3faOO  C  E-1  c3 

0Q  O  ?g 

O 

o 

^g 

rx  »^ 

O 

fa 

<J 

fa 

fa 

fa 

E-i 

8^  ft.  wheel 

370 

0.04 

8 

0.25 

0.25 

0.06 

0.04 

0.60 

15.0 

10 

1151 

0.12 

8 

0.30 

0.30 

0.06 

0.04 

0.70 

5.8 

12 

2036 

0.21 

8 

0.36 

0.36 

0.06 

0.04 

0.82 

3.9 

14       ' 

2708 

0.28 

8 

0.75 

0.75 

0.06 

0.07 

1.63 

5.8 

16       * 

3876 

0.41 

8 

1.15 

1.15 

0.06 

0.07 

2.43 

5.9 

18       • 

5861 

0.61 

8 

1.35 

1  35 

0.06 

0.07 

2.83 

4.6 

20 

7497 

0.79 

8 

1.70 

1.70 

0.06 

0.10 

3.56 

4.5 

.25 

12743 

1.34 

8 

2.05 

2.05 

0.06 

0.10 

4.26 

3.2 

Lieut.  I.  N.  Lewis  (Eng'g  Mag..  Dec.  1894)  gives  a  table  of  results  of  ex- 
periments with  wooden  wheels,  from  which  the  following  is  taken : 


Velocity  of  Wind,  miles  per  hour. 


juiameter 
of  wheel, 
Feet. 

8 

10 

12              16 

20        |       25 

30 

Actual  Useful  Horse-power  developed. 

12 
16 
20 
25 
30 

0 
2 

3  4 

M 

3 
4 

* 

1 

4 
6 

7 

8p 

r 

9 

2 

4 
7 
10 
12 

The  wheels  were  tested  by  driving  a  differentially  wound  dynamo.  The 
"  usefiil  horse-power  "  was  measured  by  a  voltmeter  and  ammeter,  allow- 
ing 500  watts  per  horse-power.  Details  of  the  experiments,  including  the 
means  used  for  obtaining  the  velocity  of  the  wind,  are  not  given.  The  re- 
sults are  so  far  in  excess  of  the  capacity  claimed  by  responsible  manufactu- 
rers that  they  should  not  be  given  credence  until  established  by  further 
experiments. 

A  recent  article  on  windmills  in  the  Iron  Age  contains  the  following:  Ac- 
cording to  observations  of  the  United  States  Signal  Service,  the  average 
velocity  of  the  wind  within  the  range  of  its  record  is  9  miles  per  hour  for 
the  year  along  the  North  Atlantic  border  and  Northwestern  States,  10  miles 
on  the  plains  of  the  West,  and  6  miles  in  the  Gulf  States. 

The  horse-powers  of  windmills  of  the  best  construction  are  proportional 
to  the  squares  of  their  diameters  and  inversely  as  their  velocities;  for  ex- 
ample, a  10-ft.  mill  in  a  16-rnile  breeze  will  develop  0.15  horse-power  at  65 
revolutions  per  minute;  and  with  the  same  breeze 

A  20-ft.  mill,  40  revolutions,  1  horse-power. 

A  25-ft.  mill,  35  revolutions,  1%  horse-power. 

A  30-ft.  mill,  28  revolutions,  3^  horse-power. 

A  40-ft.  mill,  22  revolutions.  7^£  horse-power. 

A  50-ft.  mill.  18  revolutions,  12  horse-power. 

The  increase  in  power  from  increase  in  velocity  of  the  wind  is  equal  to  the 
square  of  its  proportional  velocity;  as  for  example,  the  25-ft.  mill  rated 


COMPRESSED   AIR.  499 

above  for  a  16-mile  wind  will,  with  a  3'2-mile  wind,  have  its  horse-power  in- 
creased to  4  X  !•%  =  7  horse-power,  a  40-ft.  mill  in  a  32-mile  wind  will  run 
up  to  30  horse-power,  and  a  50- ft.  mill  to  48  horse-power,  with  a  small  de 
duction  for  increased  friction  of  air  on  the  wheel  and  the  machinery. 

The  modern  mill  of  medium  and  large  size  will  run  and  produce  work  in  a 
4-mile  breeze,  becoming  very  efficient  in  an  8  to  16-mile  breeze,  and  increase 
its  power  with  safety  to  the  running-gear  up  to  a  gale  of  45  miles  per  hour. 

Prof.  Thurston.  in  an  article  on  modern  vises  of  the  windmill,  Engineer- 
ing Magazine,  Feb.  1893,  says  :  The  best  mills  cost  from  about  $600  for  the 
10-ft.  wheel  of  %  horse-power  to  $1200  for  the  25-ft.  wheel  of  1^  horse-power 
or  less.  In  the  estimates  a  working-day  of  8  hours  is  assumed ;  but  the  ma- 
chine, when  used  for  pumping,  its  most  common  application,  may  actually 
do  its  work  24  hours  a  day  for  days,  weeks,  and  even  months  together, 
whenever  the  wind  is  ''stiff'1'  enough  to  turn  it.  It  costs,  for  work  done  in 
situations  in  which  its  irregularity  of  action  is  no  objection,  only  one  half  or 
one  third  as  much  as  steam,  hot-air,  and  gas  engines  of  similar  power.  At 
Faversham,  it  is  said,  a  15-horse-power  mill  raises  2,000,000  gallons  a  month 
from  a  depth  of  100  ft.,  saving  10  tons  of  coal  a  month,  which  would  other- 
wise be  expended  in  doing  the  work  by  steam. 

Electric  storage  and  lighting  from  the  power  of  a  windmill  has  been  tested 
on  a  large  scale  for  several  years  by  Charles  F.  Brush,  at  Cleveland,  Ohio. 
In  1887  he  erected  on  the  grounds  of  his  dwelling  a  windmill  56  ft.  in  diam- 
eter, that  operates  with  ordinary  wind  a  dynamo  at  500  revolutions  per 
minute,  with  an  output  of  12,000  amperes — 16  electric  horse-power— charging 
a  storage  system  that  gives  a  constant  lighting  capacity  of  100  16  to  20 
candle-power  lamps.  The  current  from  the  dynamo  is  automatically  regu- 
lated to  commence  charging  at  330  revolutions  and  70  volts,  arid  cutting  the 
circuit  at  75  volts.  Thus,  by  its  24  hours'  work,  the  storage  system  of  408 
cells  in  12  parallel  series,  each  cell  having  a  capacity  of  100  ampere  hours,  is 
kept  in  constant  readiness  for  all  the  requirements  of  the  establishment,  it 
being  fitted  up  with  350  incandescent  lamps,  about  TOO  being  in  use  each 
evening.  The  plant  runs  at  a  mere  nominal  expense  for  oil.  repairs,  and  at- 
tention. (For  a  fuller  description  of  this  plant,  and  of  a  more  recent  one  at 
MarbleheadNeck,  Mass.,  see  Lieut.  Lewis's  paper  in  Engineering  Magazine, 
Dec.  1894,  p.  475.) 

COMPRESSED  AIR. 

Heating  of  Air  by  Compression.— Kimball,  in  his  treatise  on  Physi- 
cal Properties  of  Gases,  says:  When  air  is  compressed,  all  the  work  which  is 
done  in  the  compression  is  converted  into  heat,  and  shows  itself  in  the  rise  in 
temperature  of  the  compressed  gas.  As  the  gas  becomes  hotter  it  is  com- 
pressed with  more  difficulty;  so  in  practice  many  devices  are  employed  to 
carry  off  the  heat  as  fast  as  it  is  developed,  and  keep  the  temperature  down. 
But  it  is  not  possible  in  any  way  to  totally  remove  this  difficulty.  But.  it  may 
be  objected,  if  all  the  work  done  in  compression  is  converted  into  heat,  and 
if  this  heat  is  got  rid  of  as  soon  as  possible,  then  the  work  may  be  virtually 
thrown  away,  and  the  compressed  air  can  have  no  more  energy  than  it  had 
before  compression.  It  is  true  that  the  compressed  gas  has  no  more  energy 
than  the  gas  had  before  compression,  if  its  temperature  is  no  higher,  but 
the  advantage  of  the  compression  lies  in  bringing  its  energy  into  more  avail- 
able form. 

The  total  energy  of  the  compressed  and  uncompressed  gas  is  the  same  at 
the  same  temperature,  but  the  available  energy  is  much  greater  in  tiie  former. 

The  rise  in  temperature  due  to  compression  is  so  great  that  if  a  mass  of 
air  at  32°  F.  is  compressed  to  one  fourth  its  original  volume,  its  temperature 
will  be  raised  3T6°  F.,  if  no  heat  is  allowed  to  escape. 

Whan  the  compressed  air  is  used  in  driving  a  rock-drill,  or  any  other  piece 
of  machinery,  it  gives  up  energy  equal  in  amount  to  the  work  it  does,  and 
its  temperature  is  accordingly  greatly  reduced. 

Causes  of  L.OSS  of  Energy  in  Use  of  Compressed  Air. 
(Zahner,  on  Transmission  of  Power  by  Compressed  Air.)— 1.  The  compression 
of  air  always  develops  heat,  and  as  the  compressed  air  always  cools  down  to 
the  temperature  of  the  surrounding  atmosphere  before  it  is  used,  the  me- 
chanical equivalent  of  this  dissipated  heat  is  work  lost. 

2.  The  heat  of  compression  increases  the  volume  of  the  air,  and  hence  it 
is  necessary  to  carry  the  air  to  a  higher  pressure  in  the  compressor  in  order 
that  we  may  finally  have  a  given  volume  of  air  at  a  given  pressure,  and  at 
the  temperature  of  the  surrounding  atmosphere.  The  work  spent  in  effect- 
ing this  excess  of  pressure  is  work  lost. 


500 


AIR. 


3.  The  great  cold  which  results  when  air  expands  against  a  resistance 
forbids  expansive  working,  which  is  equivalent  to  saying,  forbids  the  reali 
zation  of  a  high  degree  of  efficiency  in  the  use  of  compressed  air. 

4.  Friction  of  the  air  in  the  pipes,  leakage,  dead  spaces,  the  resistance  of 
fered  by  the  valves,  insufficiency  of  valve-area,  inferior  workmanship,  and 
slovenly  attendance,  are  all  more  or  less  serious  causes  of  loss  of  power. 

The  first  cause  of  loss  of  work,  namely,  the  heat  developed  by  compres- 
sion, is  entirely  unavoidable.  The  whole  of  the  mechanical  energy  which 
the  compressor-piston  spends  upon  the  air  is  converted  into  heat.  This  heat 
is  dissipated  by  conduction  and  radiation,  and  its  mechanical  equivalent  is 
work  lost.  The  compressed  air,  having  again  reached  thermal  equilibrium 
with  the  surrounding  atmosphere,  expands  and  does  work  in  virtue  of  its 
intrinsic  energy. 

The  intrinsic  energy  of  a  fluid  is  the  energy  which  it  is  capable  of  exert- 
ing against  a  piston  in  changing  from  a  given  state  as  to  temperature  and 
volume,  to  a  total  privation  of  heat  and  indefinite  expansion. 

Volumes,  Mean  Pressures  per  Stroke,  Temperatures,  etc., 
in  the  Operation  of  Air-compression  from  1  Atmosphere 
and  6O°  Fahr.  (F.  Richards,  Am.  Mack.,  March  30,  1893.) 


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.975 

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28.16 

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7.62 

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.2189 

31.39 

43.91 

507 

2.02 

.495 

.606 

10.33 

11.51 

178 

115    8.823  .1133 

.2129 

31.98 

44.98 

518 

2.36 

.4237 

.543 

12.62 

14.4 

207 

120    9.163 

.1091 

.2073 

32.54 

46.04 

529 

2.7 

.3703 

.494 

14.59 

17.01 

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33.07 

47.06 

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3.04 

.3289 

.4538 

16.34 

19.4 

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33.57 

48.1 

550 

3.381 

.2957 

.42 

17.92 

21.6 

281 

135  10.183 

.0981 

.1922 

34.05 

49.1 

560 

3.721 

.2687 

.393 

19.32 

23.66 

302 

140  10.523 

.095 

.1878 

34.57 

50.02 

570 

L061 

.2462 

.37 

20.57 

25.59 

321 

14510.864 

.0921 

.1837 

35.09 

51. 

580 

4.401 

.2272 

.35 

21.69 

27.39 

339 

15011.204 

.0892 

.1796 

35.48 

51.89 

589 

4.741 

.2109 

.331 

22.76 

29.11 

357 

160  11.88 

.0841 

.1722 

36.29 

53.65 

607 

5,081 

.1968 

.3144 

23.78 

30.75 

375 

170  12.56 

.0796 

.1657 

37.2 

55.39 

624 

5.422 

.1844 

.301 

24.75 

32.32 

389 

180  13.24 

.0755 

.1595 

37.96 

57.01 

640 

5.762 

.1735 

.288 

25.67 

33.83 

405 

190  13.93 

.0718 

.154 

38.68 

58.5? 

657 

6.102 

.1639 

.276 

26.55 

35.27 

420 

200 

14.61 

.0685 

.149 

39.42 

60  14 

672 

Column  3  gives  the  volume  of  air  after  compression  to  the  given  pressure 
and  after  it  is  cooled  to  its  initial  temperature.  After  compression  air  loses 
its  heat  very  rapidly,  and  this  column  may  be  taken  to  represent  the  volume 
of  air  after  compression  available  for  the  purpose  for  which  the  air  has 
been  compressed. 

Column  4  gives  the  volume  of  air  more  nearly  as  the  compressor  has  to 
deal  with  it.  In  any  compressor  the  air  will  lose  some  of  its  heat  during 
compression.  The  slower  the  compressor  runs  the  cooler  the  air  and  the 
smaller  the  volume. 

Column  5  gives  the  mean  effective  resistance  to  be  overcome  by  the  air- 
cylinder  piston  in  the  stroke  of  compression,  supposing  the  air  to  remain 
constantly  at  its  initial  temperature.  Of  course  it  will  not  so  remain,  but 
this  column  is  the  ideal  to  be  kept  in  view  in  economical  air-compression. 


COMPRESSED   AIR. 


501 


Column  6  gives  the  mean  effective  resistance  to  be  overcome  by  the  pis- 
:on,  supposing  that  there  is  no  cooling  of  the  air.  The  actual  mean  effec- 
tive pressure  will  be  somewhat  less  than  as  given  in  this  column;  but  for 
computing  the  actual  power  required  for  operating  air-compressor  cylinders 
the,  figures  in  this  column  may  be  taken  and  a  certain  percentage  added — 
say  10  per  cent— and  the  result  will  represent  very  closely  the  power  required 
by  the  compressor. 

The  mean  pressures  given  being  for  compression  from  one  atmosphere 
upward,  they  will  not  be  correct  for  computations  in  compound  compression 
or  for  any  other  initial  pressure. 

Loss  Due  to  Excess  of  Pressure  caused  by  Heating  In 
the  Compression-cylinder.— If  the  air  during  compression  were 
kept  at  a  constant  temperature,  the  compression-curve  of  an  indicator-dia- 
gram taken  from  the  cylinder  would  be  an  isothermal  curve,  and  would  fol- 
low the  law  of  Boyle  and  Marriotte,  pv=a.  constant,  or  p,-i>,  =  p0v0  ,  or 

Pi  =  Po  —  i  Po  and  ^o  being  the  pressure  and  volume  at  the  beginning  of 

compression,  andp^  the  pressure  and  volume  at  the  end,  or  at  any  inter- 
mediate point.  But  as  the  air  is  heated  during  compression  the  pressure 
increases  faster  than  the  volume  decreases,  causing  the  work  required  for 
any  given  pressure  to  be  increased.  If  none  of  the  heat  were  abstracted 
by' radiation  or  by  injection  of  water,  the  curve  of  the  diagram  would  be  an 

adiabatic  curve,  with  the  equation  px  =  p0^— )  '  Cooling  the  air  dur- 

ing compression,  or  compressing  it  in  two  cylinders,  called  compounding, 
and  cooling  the  air  as  it  passes  from  one  cylinder  to  the  other,  reduces  the 
exponent  of  this  equation,  and  reduces  the  quantity  of  work  necessary  to 
effect  a  given  compression.  F.  T.  Gause  (Am.  Mach.\  Oct.  20,  1892),  describ- 
ing the  operations  of  thePopp  air-compressors  in  Paris,  says  :  The  greatest 
saving  realized  in  compressing  in  a  single  cylinder  was  33  per  cent  of  that 
theoretically  possible.  In  cards  taken  from  the  2000  H.P.  compound  com- 
pressor at  Quai  De  La  Gare,  Paris,  the  saving  realized  is  85  per  cent  of  the 
theoretical  amount.  Of  this  amount  only  8  per  cent  is  due  to  cooling  dur- 
ing compression,  so  that  the  increase  of  economy  in  the  compound  com- 
pressor is  mainly  due  to  cooling  the  air  between  the  two  stages  of  compres- 
sion. A  compression-curve  with  exponent  1.25  is  the  best  result  that  was 
obtained  for  compression  in  a  single  cylinder  and  cooling  with  a  very  fine 
spray.  The  curve  with  exponent  1.15  is  that  which  must  be  realized  in  a 
single  cylinder  to  equal  the  present  economy  of  the  compound  compressor 
at  Quai  De  La  Gare. 


Horse-power      required     to 
compress  and   deliver   one 
cubic   foot    of  Free  Air   per 

minute  to  a  given  pressure  with  no 
cooling  of  the  air  during  the  com- 
pression; also   the  horse-power  re- 
quired, supposing  the  air  t<  -,  be  main- 
tained    at     constant    temperature 
during  the  compresion. 
Gauge-           Aii1  not        Air  constant 
pressure.         cooled.        temperature. 
5                  .0196                   .0188 
10                  .0361                    .0333 
20                  .06:28                   .0551 
30                  .0846                   .0713 
40                 .1032                  .0843 
50                  .1195                   .0946 
60                  .1312                   .1036 
70                  .1476                   .1120 
80                  .1599                   .1195 
90                  .1710                   .15:61 
100                 .1815                   .1318 

Horse-power      required      to 
compress   and  deliver   one 
cubic   foot   of   Compressed 

Air  per  minute  at  a  given  pressure 
with  no  cooling  of  ihe  ail  during 
the  compression;    also    the  horse- 
power required,  supposing  the  air  to 
be  maintained  at  constant  tempera 
ture  during  the  compression. 
Gauge-          Air  not          Air  constant 
pressure.        cooled.          temperature. 
5                  .0263                   .0251 
10                 .0606                  .0559 
20                 .1483                   .1300 
30                 .2573                  .2168 
40                 .3842                  .3138 
50                  .5261                   .4166 
60                 .6818                  .5266 
70                 .8508                   .6456 
80               1.0302                  .7700 
90               1.2177                  .8979 
100               1.4171                 1.0291 

The  horse-power  given  above  is  the  theoretical  power,  no  allowance  being 
made  for  friction  of  the  compressor  or  other  losses,  which  may  amount  to 
10  per  cent  or  more. 


502 


AIR. 


Table  for  Adiabatic  Compression  or  Expansion  of  Air. 

(Proc.  lust.  M.E.,  Jan.  1881,  p.  123.) 


Absolute  Pressure. 

Absolute  Temperature. 

Volume. 

Ratio  of 

Ratio  of 

Ratio  of 

Ratio  of 

Ratio  of 

Ratio  of 

Greater 

Less  to 

Greater 

Less  to 

Greater 

Less  to 

to  Less. 

Greater. 

to  Less. 

Greater. 

to  Less. 

Greater. 

(Expan- 

(Compres- 

(Expan- 

(Compres- 

(Compres- 

(Expan- 

sion.) 

sion.) 

sion.) 

sion.) 

sion.) 

sion.) 

1.2 

.833 

.054 

.948 

1.138 

.879 

1.4 

.714 

.102 

.907 

1.270 

.788 

1.6 

.625 

.146 

.873 

1.396 

.716 

1.8 

.556 

.186 

.843 

1.518 

.659 

2.0 

.500 

.222 

.818 

1.636 

.611 

2.2 

.454 

.257 

.796 

1.750 

.571 

2.4 

.417 

.289 

.776 

1.862 

.537 

2.6 

.385 

.319 

.758 

1.971 

.507 

2.8 

.357 

.348 

.742 

2.077 

.481 

3.0 

.333 

1.375 

.727 

2.182 

.458 

3.2 

.312 

1.401 

.714 

2.284 

.438 

3.4 

.294 

1.426 

.701 

2.384 

.419 

3.6 

.278 

1.450 

.690 

2.483 

.403 

3.8 

.263 

1.473 

.679 

2.580 

.388 

4.0 

.250 

1.495 

.669 

2.676 

.374 

4.2 

.238 

1.516 

.660 

2.770 

.361 

4.4 

.227 

1.537 

.651 

2.863 

.349 

4.6 

.217 

1.557 

.642 

2.955 

.338 

4.8 

.208 

1.576 

.635 

3.046 

.328 

5,0 

.200 

1.595 

.627 

3.135 

.319 

6.0 

.167 

1.681 

.595 

3.569 

.280 

7.0 

.143 

1.758 

.569 

3.981 

.251 

8.0 

.125 

1.828 

.547 

4.377 

.228 

9.0 

.111 

1.891 

.529 

4.759 

.210 

10.0 

.100 

1.950 

.513 

5.129 

.195 

Mean  Effective  Pressures  for  tlie  Compression  Part  only 
of  tlie  Stroke  wlien  compressing  and  delivering  Air 
from  one  Atmosphere  to  given  Gauge-pressure  in  a  Sin- 
gle Cylinder.  (F.  Richards,  Am.  Mach.,  Dec.  14,  1893.) 


Gauge- 

Adiabatic 

Isothermal 

Gauge- 

Adiabatic 

Isothermal 

pressure. 

Compression. 

Compression. 

pressure. 

Compression. 

Compression. 

1 

.44 

.43 

45 

13.  -05 

12.62 

2 

.96 

.95 

50 

15.05 

13.48 

3 

1.41 

1.4 

55 

15.98 

14.3 

4 

1.86 

1.84 

60 

16.89 

15.05 

5 

2.26 

2.22 

65 

17.88 

15.76 

10 

4.26 

4.14 

70 

18.74 

16  43 

15 

5.99 

5.77 

75 

19.54 

17.09 

20 

7.58 

7.2 

80 

20.5 

17  7 

25 

9.05 

8.49 

85 

91.22 

18.3 

30 

10.39 

9.66 

90 

22 

18.87 

35 

11.59 

10.72 

95 

22.77 

19.4 

40 

12.8 

11.7 

100 

23.43 

19.92 

The  mean  effective  pressure  for  compression  only  is  always  lower  than 
the  mean  effective  pressure  for  the  whole  work 


COMPRESSED    AIR. 


503 


Mean   and  Terminal  Pressures  of  Compressed  Air  used 
Expansively  for  Gauge-pressures  from  6O  to  lOOlbs. 

(Frank  Richards,  Am.  Much.,  April  13,  1893.) 


Initial 
Pres- 
sure. 

60. 

70. 

80. 

90. 

100. 

o»j 

p  -  g 

£3     1    '-> 

t 

1  ,  g 

a     '—   *     g 

P  ,  g 

1      g* 

P..  | 

"3     gj 

•43    O 

Sis. 

•Sis 

•S  •'  s 

g'^l 

£'•**   0! 
^      -g 

Ito'l 

t->  ^  a? 

Ifllpl 

1)  -r-     tt> 

S^  | 

rl 

1^1 

§•<! 

&H 

ft 

EH      ft 

ft 

EH      ft 

~    H      ft 

ft 

H      ft 

ft  H      ft 

.25 

23.6 

1O.65 

28.74 

12.O7 

33  89  13.49 

39.04 

14.91 

44.19 

1.33 

.30 

28.9 

13.77 

34.75 

!e 

40.611     2.44 

46.46 

4  27 

53.32 

6.11 

32.13 

.96 

38.41 

3.09 

44.69!     5.22 

50.98 

7  '.35 

57.26 

9.48 

35 

33.66 

2.33 

40.15 

4.38 

46.  641     6.66 

53.13 

8.95 

59.62 

11.23 

3X 

35.85 

3.85 

42.63 

6.36 

49.41     7.88, 

56.2 

11.39 

62.98 

13.89 

40 

37.93 

5.64 

44.99 

8.39 

52.05    11.14 

59.11 

13.88 

66.16 

16.64 

45 

41.75 

10.71 

49.31 

12.61 

56.9  j  15.86 

64  45 

19.11 

72.02 

22.36 

'.50 

45.14 

13.26 

53.16 

17. 

61.18    20.81 

69.19 

24.56 

77.21 

28.33 

.60 

50.75 

21.53 

59.51 

26.4 

68.28    31.27 

77.05 

36.14 

85.82 

41.01 

51.92 

23.69 

60.84 

28.85 

69.76    34.01 

78.69 

39.16 

87.61 

44.32 

?1 

53.67 

27.94 

62  83 

33.03 

71.99    38.68 

81.14 

44.33 

90.32 

49.97 

70 

54.93 

30.39 

64  25 

36.44 

73.57    42.49 

82.9 

48.54 

92.22 

54.59 

!75 

56.52 

35.01 

66.05 

41.68 

75.59    48.35 

85.12 

55.02 

94.66 

61.69 

.80 

57.79 

39.78 

67.5 

47.08 

77.2  !  54.38 

86.91 

61.69 

96.61 

68.99 

59.15 

47.14 

69.03 

55.43 

78.92J  63.81 

88.81 

72. 

98.7 

80.28 

.90     ;  59.46 

49.65 

69.38 

58.27 

79.31    66.89 

89.24 

75.52 

99.17 

87.82 

The  pressures  in  the  table  are  all  gauge-pressures  except  those  in  italics, 
which  are  absolute  pressures  (above  a  vacuum). 

Straight-line  Air-compressors,  Ingersoll-Sergeant 
Rock-drill  Co. 


Diameter 
Steam- 
cylinder. 
inches. 

Diameter 
of  Air- 
cylinder, 
inches. 

Length 
of 
Stroke, 
inches. 

No.  of 
Revolu- 
tions 
per 
minute. 

Piston 
Speed 
in  feet 
per 
minute. 

Cubic  Feet 
Free  Air 
per  minute 
(Theo- 
retical). 

Horse- 
power 
of 
Boiler 
required. 

4 

414 

10 

175 

291 

28 

6 

5 

5H 

10 

175 

291 

42 

8 

6 

6U 

12 

160 

320 

66 

10 

7 

7M 

12 

160 

320 

91 

12 

8 

8M 

12 

160 

320 

117 

15 

9 

9^ 

12 

160 

320 

148 

20 

10 

1014 

14 

155 

361 

207 

30 

12 

12J4 

14 

155 

361 

295 

40 

14 

14J4 

18 

120 

360 

398 

55 

16 

16^ 

18 

120 

360 

518 

70 

18 

18H 

24 

94 

3;e 

683 

100 

20 

2014 

24 

94 

376 

840 

130 

22 

22J4 

8-J 

75 

375 

1011 

155 

24 

2414 

30 

75 

375 

1202 

200 

The  same  sizes  are  made  to  be  driven  by  belt  or  gearing. 
Compressors  at  High  Altitudes.— Cubic  feet  of  compressed  air 
delivered  by  air-compressors  at  high  altitudes,  expressed  as  a  percentage  of 
the  air  delivered  at  the  sea-level. 


Altitude  above  Sea-       1 
level,  feet.            f 

0 

100 

1000 
97 

2000 
94 

3000 
91 

4000 

~89~ 

5000 

6000 

7000 

81 

8000 

78 

9000 

10000 
74 

Air  delivered,  per  cent.. 

Bo 

84 

76 

504 


AIR. 


Standard  Air-compressors  driven  by  Steam. 

(Norwalk  Iron  Works  Co.) 

In  the  following  list  the  large  air-cylinder  gives  the  capacity  of  the  ma- 
chine. For  actual  capacity,  allowance  of  10  per  cent  may  be  made  for 
contingencies.  The  small  piston  only  encounters  the  pressure  of  the  final 
compression. 


I*       ti 

4)    ,    0> 

131 

!«» 

Length  of 
Stroke. 

s-   •   ttfe* 

2S.5-0 

0)  O  CC  C 

12  8S 

|oaO 

Diameter 
of  Steam- 
cylinder. 

Revolutions 
or  Double 
Strokes  per 
minute. 

<t> 

"i^lai 

ipn 

0  &.Q  '„  V 
Qj  eg  3  o>  t* 

gOo  P.&- 

!• 

a 

£ 

o3 

& 

W 

Exhaust- 
pipe. 

Air-pipe. 

Water-pipe. 

Horse- 
power. 

8 
10 
14 
20 
26 
32 

10 
12 
16 
24 
30 
36 

5 
6M 
9^ 

ny2 

1% 

2JH 

8 
10 
14 
20 
24 
30 

200 
190 
150 
110 
90 
80 

116 
207 
42? 

960 
1659 

2686 

ly* 

5 
6 

f 

4 
6 
8 
10 

2 

2^ 
4 
5 

6 

8 

| 

i 

ig 

15 
28 
55 
125 
215 
350 

Double-compound  Compressors. 

(Norwalk  Iron  Works  Co.) 


Diameter  of  — 

Capac'y 

Diameter 
Air- 
cylinder. 

Length 
of 
Stroke. 

Com- 
pressing 
cylinder. 

High- 
pressure 
Steam- 
cylinder. 

Low- 
pressure 
Steam- 
cylinder. 

Steam- 
pipe. 

Revolu- 
tions 
per 
minute. 

cubic 
feet 
Free 
Air  per 
minute. 

10 

12 

5 

7^ 

12 

2 

190 

207 

12 

12 

5 

7^jj 

12 

2 

190 

298 

14 

16 

9^ 

10 

16 

2l^> 

150 

427 

16 

16 

9^ 

10 

16 

gi^ 

150 

558 

20 

20 

13J4 

14 

22 

3 

120 

872 

20 

24 

m* 

14 

22 

3 

110 

960 

22 

24 

13^ 

14 

22 

3 

110 

1160 

26 

30 

17^i> 

18 

28 

4^£ 

90 

1659 

28 

30 

1% 

18 

28 

41^ 

90 

1924 

32 

36 

*% 

22 

35 

6 

80 

2686 

Mountain  or  High-altitude  Compressors. 

(Norwalk  Iron  Works  Co.) 


be 

At  Sea- 

At  2000 

At  6000 

At  10,000 

2, 

o5 

level. 

feet. 

feet. 

feet. 

Tifc 

o    • 

O  to  .• 

•~  y  5 

!.'fe 

c  S 
O  C 

. 

-i 

oj.g 

O  <£> 

,dr* 

1i2 

?OD 

111 

rt   W  ~ 

!a$ 

s=i 
lit 

.5  02  0' 

fl 

||| 

orse- 
power 

I 
• 

orse- 
power 

1 
a 

orse- 
power 

1 

orse- 
power. 

Q 

h3 

« 

ft 

PH 

O 

K 

0 

n 

o 

m 

0 

W 

12 

12 

7 

10 

190 

298 

35 

280 

34 

244 

32 

214 

30 

16 

16 

14 

150 

558 

70 

524 

68 

462 

64 

405 

60 

20 

20 

13^6 

18 

120 

872 

110 

819 

107 

722 

100 

634 

94 

22. 

24 

13Vi 

20 

110 

1160 

145 

1090 

140 

960 

132 

843 

124 

26 

30 

17J^ 

24 

90 

1659 

215 

1560 

207 

1373 

195 

1200 

184 

The  delivery  and  power  of  the  compressors  decrease  as  the  height  in- 
creases. As  the  capacity  decreases  in  a  greater  ratio  than  the  power 
necessary  to  compress,  it  follows  that  operations  at  a  high  altitude  are  more 
expensive  than  at  sea-level.  At  10,000  feet  this  extra  expense  amounts  to 
over  20  per  cent. 


COMPRESSED   AIR.  505 

Rand  Drill  Co.'s  Air-compressors. 


^ 

Theoretical  Volume  of  Air  delivered  in  cubic 

ft 

feet  per  minute,  at  Sea-level. 

Dimensions 

cc  ^ 

of  Air- 

Class. 

cylinders 

'2  n 

Compressed  to  a  Gauge-pressure  of  — 

in 

3  '2 

inches. 

'o  fi 

Free. 

1 

10 

20 

40 

60 

80 

100 

PH 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

1  fl  v  1  R  '         '  ' 

100 

145.44 

86.56 

61.61 

39.08 

28.62 

22.57 

18.64 

J 

1  D*.. 

100 

290.88 

173.12 

123.23 

78.17 

57.24 

45.15 

37.28 

i 
' 

11*00  f  S..'.' 

85 

333.20 

198.31 

141.10 

89.51 

65.54 

51.93 

42.67 

ID-;- 

85 

666.40 

396.61 

282.20 

179.01 

131.07 

103.86 

85.34 

75 

556.83 

331.39 

235.89 

149.64 

109.5? 

86.43 

71.36 

r 

10>*3  x  OVA  j-^ 

75 

1113.66 

662.79 

471.79 

299.28 

219.15 

172.86 

142.72 

1  i{  v   °O    Jo... 

75 

662.68 

394.39 

280.73 

178.08 

130.40 

102.86 

84.92 

A 

i8x30jD;;; 

75 

1325.36 

788.78 

561.46 

356.17 

260.81 

205.72 

169.84 

and     -[ 

.  o    \    S  .  .  . 

50 

872.66 

519.36 

309.69 

234.51 

171.72 

135.46 

111.84 

B 

/  D. 

50 

1745.32 

1038.72 

739.38 

469.03 

343.45 

270.92 

223.68 

i 

.JQ  v-  /<G    i   S.  .  . 

40 

1368.34 

814.36 

579.67 

367.72 

269.2-J 

212.40 

175.36 

1  :  ~°  *  •*  J  1  D 

40 

2736.68 

1628.71 

1159.34 

735.45 

538.54 

424.80 

350.73 

/•   oo  ..  <o  )  O.  .  . 

40 

1787.22 

1063.65 

757.12 

480.29 

351.70 

277.42 

229.05 

A 

O~  A  -10  -\    -pv 

40 

3574.44 

2127.30 

1514.24 

960.58 

703.40 

554.85 

458,10 

and 

00         £«A  JO... 

35 

1954.77 

1163.37 

828.10 

525.32 

384.67 

303.43 

250.52 

B 

'3~xb0"JD... 

35 

3909.55 

2326.73 

1656.20 

1050.63 

769.34 

606.86 

501.05 

Geared 

oo       />n  J  S  .  . 

30 

2120.61 

1262.07 

898.35 

572.07 

417.72 

3-,>9.16 

272.82 

I 

00  X  OU  •(  -r} 

30 

4241.22 

2524.14 

1796.70 

1144.14 

835.44 

658.32 

545.64 

r 

8x12.....'' 

120 

83.78 

49.86 

35.49 

22.51 

16.49 

13.00 

10.74 

10x14  

110 

139.95 

83.27 

59  29 

37.62 

27.50 

21.72 

17.94 

12x16  

100 

209.44 

124.65 

88.73 

56.28 

41.22 

32.51 

26.66 

C     - 

14x22  

95 

372.40 

221.64 

15^.70 

100.04 

73.25 

58.04 

47  69 

16x24,  

90 

502.66 

299.15 

212.94 

135.08 

98.92 

78.03 

64.42 

17U  x  24  .  .  . 

90 

601.29 

357.85 

254.95 

161.60 

118.33 

93.33 

77.06 

[20x"30...    . 

80 

872.67    519.36 

369.69 

234.52 

171.73 

135.46 

111.84 

*S,  Single;  D,  Duplex. 

Practical  Results  witli  Compressed  Air.— Compressed-air 
System  at  the  Chapln.  Mines,  Iron  Mountain,  Mich. — These  mines  are  three 
miles  from  the  fails  which  supply  the  power.  There  are  four  turbines  at 
the  falls,  one  of  1000  horse-power  and  three  of  900  horse-power  each.  The 
pressure  is  60  pounds  at  60°  Fahr.  Each  turbine  runs  a  pair  of  compressors. 
The  pipe  to  the  mines  is  24  inches  in  diameter.  The  power  is  applied  at  the 
mines  to  Corliss  engines,  running  pumps,  hoists,  etc.,  and  direct  to  rock- 
drills. 

A  test  made  in  1888  gave  1430.27  horse-power  at  the  compressors,  and  390.17 
horse-power  as  the  sum  of  the  horse-power  of  the  engines  at  the  mines. 
Therefore,  only  27$  of  the  power  generated  was  recovered  at  the  mines. 
This  includes  the  loss  due  to  leakage  and  the  loss  of  energy  in  heat,  but  not 
the  friction  in  the  engines  or  compressors.  (F.  A.  Pocock,  Trans.  A.  I.  M.  E., 
1890.) 

W.  L.  Saunders  (Jour.  F.  I.  1892)  says:  "There  is  not  a  properly  designed 
compressed  air  installation  in  operation  to-day  that  loses  over  5$  by  trans- 
mission alone.  The  question  is  altogether  one  of  the  size  of  pipe;  and  if 
the  pipe  is  large  enough,  the  friction  loss  is  a  small  item.  The  largest  com- 
pressed-air power  plant  in  America  is  that  at  the  Chapin  Mines  in  Michigan, 
where  power  is  generated  at  Quinnesec  Falls,  and  transmitted  three  miles. 
This  is  is  not  an  economical  plant,  but  the  loss  of  pressure  as  shown  by  the 
gauge  is  only  2  Ibs.,  and  this  is  the  loss  which  may  be  laid  strictly  to  trans- 
mission. 

"  The  loss  of  power  in  common  practice,  where  compressed  air  is  used  to 
dr,ive  machinery  in  mines  and  tunnels,  is  about  70$.  I  refer  to  cases  where 
common  American  air-compressors  are  used,  and  where  the  air  is  trans- 
mitted far  enough  to  lose  its  heat  of  compression  and  is  exhausted  without 


506 


AIR. 


reheating.    In  the  best  practice,  with  the  best  air-compressors,  and  without 
reheating,  the  loss  is  about  60$. 

"  These  losses  may  be  reduced  to  a  point  as  low  as  20#  by  combining  the 
best  systems  of  reheating  wiih  the  best  air-compressors.11 

Prof.  Kennedy  says  compressed  air  transmission  system  is  now  being 
carried  on.  on  a  large  commercial  scale,  in  such  a  fashion  that  a  small  motor 
four  miles  away  from  the  central  station  can  indicate  in  round  numbers  10 
horse-power,  for  20  horse  power  at  the  station  itself,  allowing  for  the  value 
of  the  coke  used  in  heating  the  air. 

The  limit  to  successful  reheating  lies  in  the  fact  that  air-engines  cannot 
work  to  advantage  at  temperatures  over  350°. 

The  efficiency  of  the  common  system  of  reheating  is  shown  by  the  re- 
sults obtained  with  the  Popp  system  in  Paris.  Air  is  admitted  to  the  re- 
heater  at  about  83°,  and  passes' to  the  engine  at  about  315°,  thus  being  in- 
creased in  volume  about  42$.  The  air  used  in  Paris  is  about  11  cubic  feet  of 
free  air  per  minute  per  horse-power.  The  ordinary  practice  in  America 
with  cold  air  is  from  15  to  25 cubic  feet  per  minute  per  horse-power.  When 
the  Paris  engines  were  worked  without  reheating  the  air  consumption  was 
increased  to  about  15  cubic  feet  per  horse-power  per  minute.  The  amount 
of  fuel  consumed  during  reheating  is  trifling. 

Efficiency  of  Compressed-air  Engines.— The  efficiency  of  an 
air-engine,  that  is,  the  percentage  which  the  power  given  out  by  the  air-en- 
gine bears  to  that  required  to  compress  the  air  in  the  compressor,  depends 
on  the  loss  by  friction  in  the  pipes,  valves,  etc.,  as  well  as  in  the  engine  itself. 
This  question  is  treated  at  length  in  the  catalogue  of  the  Norwalk  Iron  Works 
Co.,  from  which  the  following  is  condensed.  As  the  friction  increases  the 
most  economical  pressure  increases.  In  fact,  for  any  given  friction  in  a 
pipe,  the  pressure  at  the  compressor  must  not  be  carried  below  a  certain 
limit.  The  following  table  gives  the  lowest  pressures  which  should  be  used 
at  the  compressor  with  varying  amounts  of  friction  in  the  pipe: 

Friction,  Ibs 2.9      5.8      8.8    11.7    14.7    17.6    20.5    23.5    26.4    29.4 

Lbs.  at  Compressor...  20.5    29.4    38.2    47.      52.8    61.7    70.5    76.4    82.3    88.2 
Efficiency  % 70.9    61.5    606    57.9    55.7    54.0    52.5    51.3    50.2    49.2 

An  increase  of  pressure  will  decrease  the  bulk  of  air  passing  the  pipe  and 
its  velocity.  This  will  decrease  the  loss  by  friction,  but  we  subject  ourselves 
to  a  new  loss,  i.e.  the  diminishing  efficiencies  of  increasing  pressures.  Yet  as 
each  cubic  foot  of  air  is  at  a  higher  pressure  and  therefore  carries  more 
power,  we  will  not  need  as  many  cubic  feet  as  before,  for  the  same  work. 
With  so  many  sources  of  gain  or  loss,  the  question  of  selecting  the  proper 
pressure  is  not  to  be  decided  hastily. 

The  losses  are,  first,  friction  of  the  compressor.  This  will  amount  ordinarily 
to  15  or  20  percent,  and  cannot  probably  be  reduced  below  10  per  cent. 
Second,  the  loss  occasioned  by  pumping  the  air  of  the  engine-room,  rather 
than  the  air  drawn  from  a  cooler  place.  This  loss  varies  wirh  t  he  season  and 
amounts  from  3  to  10  per  cent.  This  can  all  be  saved.  The  third  loss,  or  series 
of  losses,  arises  in  the  compressing  cylinder,  viz.,  insufficient  supply,  difficult 
discharge,  defective  cooling  arrangements,  poor  lubrication,  etc  The  fourth 
loss  is  found  in  the  pipe.  This  loss  varies  with  the  situation,  and  is  subject 
to  somewhat  complex  influences.  The  fifth  loss  is  chargeable  to  fall  of 
temperature  in  the  cylinder  of  the  air-engine.  Losses  arising  from  leaks 
are  often  serious. 

Air  should  be  drawn  from  outside  the  engine-room,  and  from  as  cool  a 
place  as  possible.  The  gain  amounts  to  one  per  cent  for  every  five  degrees 
that  the  air  is  taken  in  lower  than  the  temperature  of  the  engine-room. 
The  inlet  conduit  should  ha.ve  an  area  at  least,  50$  of  the  area  of  the  air 
piston,  and  should  be  made  of  wood,  brick,  or  other  non-conductor  of  heat. 

Discharge  of  a  compressor  having  an  intake  capacity  of  1000  cubic  feet 
pnr  minute,  and  volumes  of  the  discharge  reduced  to  cubic  feet  at  atmos- 
pheric pressure  and  at  temperature  of  62  degrees  Fahrenheit: 

Temperature  of  Intake,  F 0°    32°    62°  75°  80°  90°  100°    110° 

Keiaiive  volume  discharged,  cubic  ft.. .   1135  1060  1000  975  966  949    932    916 

Requirements  of  Rock-drills  Driven  by  Compressed 
Air.  (Norwalk  Iron  Works  Co.) — The  speed  of  the  drill,  the  pressure  ot 
air,  and  the  nature  of  the  rock  affect  the  consumption  of  power  of  rock- 
drills. 

A  three-inch  drill  using  air  at  30  Ibs.  pressure  made  300  blows  per  miriute 
and  consumed  the  equivalent  of  64  cubic  feet  of  free  air  per  minute.  The 


COMPRESSED   AIR. 


507 


Same  drill,  with  air  of  58  Ibs.  pressure,  made  450  blows  per  minute  and  con- 
sumed 160  cubic  f  i-et  of  free  air  per  minute.  At  Hell  Gate  different  machines 
doing  the  same  work  used  from  80  to  150  cubic  feet  free  air  per  minute. 

An  average  consumption  may  be  taken  generally  from  80  to  100  cubic  feet 
per  minute,  according  to  the  nature  of  the  work. 

The  Popp  Compressed-air  System  in  Paris.— A  most  exten- 
sive system  of  distribution  of  power  by  means  of  compressed  air  is  that  of 
M.  Popp,  in  Paris.  One  of  the  central  stations  is  laid  out  for  24,000  horse- 


power. For  a  very  complete  description  of  the  system,  see  Engineering, 
Feb.  15,  June  7,  21.  and  28,  1889,  and  March  13  and '20,  April  10,  and  May  1. 
1891.  Also  Prop.  Insfc.  M.  E.,  July,  1889.  A  condensed  description  will  be 


found  in  Modern  Mechanism,  p.  12. 
Utilization  of  Compressed  Air  in  Small  Motors.— In  the 

earliest  stages  of  the  Popp  system  in  Paris  it  was  recognized  that  no  good 
results  could  be  obtained  if  the  air  were  allowed  to  expand  direct  into  the 
motor-;  not  only  did  the  formation  of  ice  due  to  the  expansion  of  the  air 
rapidly  accumulate  and  choke  the  exhaust,  but  the  percentage  of  useful 
work  obtained,  compared  with  that  put  into  the  air  at  the  central  station, 
was  so  small  as  to  render  commercial  results  hopeless. 

After  a  number  of  experiments  M.  Popp  adopted  a  simple  form  of  cast- 
iron  stove  lined  with  fire-clay,  heated  either  by  a  gas  jet  or  by  a  small  coke 
fire.  This  apparatus  answered  the  desired  purpose  until  some  better  ar- 
rangement was  perfected,  and  the  type  was  accordingly  adopted  through- 
out the  whole  system.  The  economy  resulting  from  the  use  of  an  improved 
form  was  very  marked,  as  will  be  seen  from  the  following  table. 

EFFICIENCY  OF  AIR-HEATING  STOVES. 


CD 

u 

Temperature 

Value  of  Heat  Absorbed 

1 

ft 

of  Air  in  Oven. 

per  Hour. 

Nature  of 

9 
O2 

i>  3 

C  u 

2o^  • 

*o 

Stove. 

&JC 

1  ° 

14 

$  . 

SuS$ 

§5 

C 

te 

.S2fe 

°^ 

,j 

o"o  -g^5 

£o 

~c3 

S  si 

.•s  * 

3 

^  O  OJ  3 

HH  ^ 

02 

'C  cu 

o 

K 

d 

H 

H 

£ 

f^° 

sq.  ft. 

cub.  ft. 

cal. 

cal. 

cal. 

Cast-iron  box  j 

14 

20,342 

45 

215 

17,900 

1278 

2032 

stoves           j 

14 

11,054 

45 

364 

17,200 

1228 

2058 

W  rough  t-i  r  o  n 
coiled  tubes.. 

46.3 

38,428 

41 

347 

39,200 

830 

2545 

The  results  given  in  this  table  were  obtained  from  a  large  number  of 
trials.  From  these  trials  it  was  found  that  more  than  70$  of  the  total  num- 
ber of  calories  in  the  fuel  employed  was  absorbed  by  the  air  and  trans- 
formed into  useful  work.  Whether  gas  or  coal  be  employed  as  the  fuel,  the 
amount  required  is  so  small  as  to  be  scarcely  worth  consideration;  accord- 
ing to  the  experiments  carried  out  it  does  not  e:xceed  0.2  Ib.  per 
horse-power  per  hour,  but  it  is  scarcely  to  be  expected  that  in  regular  prac- 
tice this  quantity  is  not  largely  exceeded.  The  efficiency  of  fuel  consumed 
in  this  way  is  at  least  six  times  greater  than  when  utilized  in  a  boiler  and 
steam-engine. 

According  to  Prof.  Riedler,  from  15$  to  20$  above  the  power  at  the  central 
station  can  be  obtained  by  means  at  the  disposal  of  the  power  users,  and  it 
has  been  shown  by  experiment  that  by  heating  the  air  to  480°  F.  an  in- 
creased efficiency  of  30$  can  be  obtained. 

A  large  number  of  motors  in  use  among  the  subscribers  to  the  Compressed 
Air  Company  of  Paris  are  rotary  engines  developing  1  horse-power  and 
less,  and  these  in  the  early  times  of  the  industry  were  very  extravagant  in 
their  consumption.  Small  rotary  engines,  working  cold  air  without  expan- 
sion, used  as  high  as  2330  cu  ft.  of  air  per  brake  horse-power  per 
hour,  and  with  heated  air  1624  cu.  ft.  Working  expansively,  a  1  horse- 
power rotary  engine  used  1469  cu.  ft.  of  cold  air,  or  960  cu.  ft.  of  heated  air, 
and  a  2-horse-power  rotary  engine  1059  cu.  ft.  of  cold  air,  or  847  cu.  ft.  of  air, 
heated  to  about  50°  C. 

The  efficiency  of  this  type  of  rotary  motors,  with  air  heated  to  50°  C  ,  may 
now  be  assumed  at  43$.  With  such  an  efficiency  the  use  of  small  motors  iu 


508  AIR. 

many  industries  becomes  possible,  while  in  cases  where  it  is  necessary  to 
have  a  constant  supply  of  cold  air  economy  ceases  to  be  a  matter  of  the 
first  importance. 

The  following  table  shows  the  results  of  tests  of  a  small  rotary  engine  used 
for  driving  sewing-machines,  and  indicating  about  a  tenth  of  a  horse-power: 

TRIALS  OF  A  SMALL  ROTARY  RIEDINGER  ENGINE. 

Numbers  of  trials I.  II. 

Initial  air-pressure,  Ibs.  per  sq.  in .....   . .  .      86 

Initial  temperature,  deg.  Fahr 54°  338° 

Ft.-lbs.  per  sec.,  measured  on  the  brake. 51 .63  34.07 

Revolutions  per  minute 384  300 

Consumption  of  air  per  1  horse-power  per  hour 1377  988 

The  following  table  shows  the  results  obtained  with  a  one-half  horse- 
power variable  expansive  Riedinger  rotary  engine.  These  trials  represent 
the  best  practice  that  has  been  obtained  up  to  I  he  present  time  (1890).  The 
volumes  of  air  were  in  all  cases  taken  at  atmospheric  pressure: 

TRIALS  OF  A  .B-HORSE-POWER  RIEDINGER  ROTARY  ENGINE. 

Numbers  of  trials  I.  II.  III.  IV. 

Initial  pressure  of  air,  Ibs.  per  sq.  in....      54          69.7  85          71.8 

"     temperature  of  air,  deg.  Fahr 338  356  388  46 

Final  "  "         "         kk         ..77  68  ...  77 

Revolutions  per  minute 335  350  310  243 

Ft.-lbs.  per  second,  measured  on  brake..    271  477  376  316 
Consumption  of  air  per  horse-power  per 

hour 883  791  900  1148 

Trials  made  with  an  old  single-cylinder  80-horse-power  Farcot  steam-en 
gine,  indicating  72  horse-power,  gave  a  consumption  of  air  per  brake  horse- 
power as  low  as  465  cu.  ft.  per  hour.  The  temperature  of  admission  was 
320°  F.,  and  of  exhaust  95°  F. 

Prof.  Elliott  gives  the  following  as  typical  results  of  efficiency  for  various 
systems  of  compressors  and  air-motors  : 

Simple  compressor  and  simple  motor,  efficiency 39.  \% 

Compound  compressor  and  simple  motor,    "       44.9 

44    compound  motor,  efficiency ........  50 . 7 

Triple  compressor  and  triple  motor,  "        55.3 

The  efficiency  is  the  ratio  of  the  indicated  horse-power  in  the  motor  cylin 
ders  to  the  indicated  horse-power  in  the  steam-cylinders  of  the  compressor. 
The  pressure  assumed  is  6  atmospheres  absolute,  and  the  losses  are  equal 
to  those  found  in  Paris  over  a  distance  of  4  miles. 

Summary  of  Efficiencies  of  Compressed-air  Transmission 
at  Paris,  between  the  Central  Station  at  St.  Fargeau  and 
a  lO-horse-power  Motor  Working  with  Pressure  Re- 
duced to  4J4  Atmospheres. 

(The  figures  below  correspond  to  mean  results  of  two  experiments  cold  and 

two  heated.) 

1  indicated  horse-power  at  central  station  gives  0.845  indicated  horse-power 
in  compressors,  aud  corresponds  to  the  compression  of  348  cubic  feet  of  air 
per  hour  from  atmospheric  pressure  to  6  atmospheres  absolute.  (The  weight 
of  this  air  is  about  25  pounds.) 

0.845  indicated  horse-power  in  compressors  delivers  as  much  air  as  will  do 
0.52  indicated  horse-power  in  adiabatic  expansion  after  it  has  fallen  in  tem- 
perature to  the  normal  temperature  of  the  mains. 

The  fall  of  pressure  in  mains  between  central  station  an  1  Paris  (say  5  kilo- 
metres) reduces  the  possibility  of  work  from  0.52  to  0.51  indicated  horse- 
power. 

The  further  fall  of  pressure  through  the  reducing  valve  to  4%  atmospheres 
(absolute)  reduces  the  possibility  of  work  from  0.51  to  0.50. 

Incomplete  expansion,  wire-drawing,  and  other  such  causes  reduce  the 
actual  indicated  horse-power  of  the  motor  from  0.50  to  0.39. 

By  heating  the  air  before  it  enters  the  motor  to  about  3201-  F.,  the  actual 
indicated  horse-power  at  the  motor  is.  however,  increased  to  f.54.  The  ratio 

0  54 
of  gain  by  heating  the  air  is,  therefore,  ~^.  —  1.38. 


COMPRESSED   AIR.  509 

In  this  process  additional  heat  is  supplied  by  the  combustion  of  about  0.39 
pounds  of  coke  per  indicated  horse-power  per  hour,  and  if  this  be  taken  into 
account,  the  real  indicated  efficiency  of  the  whole  process  becomes  0.4? 
instead  of  0.54. 

Working  with  cold  air  the  work  spent  in  driving  the  motor  itself  reduces 
the  available  horse-power  from  0.89  to  0.26. 

Working  with  heated  air  the  work  spent  in  driving  the  motor  itself  reduces 
the  available  horse-power  from  0.54  to  0.44. 

A  summary  of  the  efficiencies  is  as  follows  : 

Efficiency  of  main  engines  0.845. 

Efficiency  of  compressors  0.52  H-  0.845  —  0.61. 

Efficiency  of  transmission  through  mains  0.51  -*-  0.52  =  0.98. 

Efficiency  of  reducing  valve  0.50-e-  0.51  =  0.98. 

The  combined  efficiency  of  the  mains  and  reducing  valve  between  5  and 
414  atmospheres  is  thus  0.98  X  0.98  =  0.96.  If  the  reduction  had  been  to  4, 
3^,  or  3  atmospheres,  the  corresponding  efficiencies  would  have  been  0.93, 
0.89,  and  0.85  respectively. 

Indicated  efficiency  of  motor  0.39  -4-  0.50  -  0.78. 

Indicated  efficiency  of  whole  process  with  cold  air  0.39.  Apparent  indi- 
cated efficiency  of  whole  process  with  heated  air  0.54. 

Real  indicated  efficiency  of  whole  process  with  heated  air  0.47. 

Mechanical  efficiency  of  motor,  cold,  0.67. 

Mechanical  efficiency  of  motor,  hot,  0.81. 

Most  of  the  compressed  air  in  Paris  is  used  for  driving  motors,  but  the 
work  done  by  these  is  of  the  most  varied  kind.  A  list  of  motors  driven  from 
St.  Fargeau  station  shows  225  installations,  nearly  all  motors  working  at 
from  1^  horse-power  to  50  horse-power,  and  the  great  majority  of  them  more 
than  two  miles  away  from  the  station.  The  new  station  at  Quai  de  la  Gare 
is  much  larger  than' the  one  at  St.  Fargeau.  Experiments  on  the  Riedler 
air-compressors  at  Paris,  made  in  December,  1891,  to  determine  the  ratio 
between  the  indicated  work  done  by  the  air-pistons  and  the  indicated  work 


1 893,  describes  the  shops  or  the  Wuerpel  Switch  and  Signal  Co. ,  East  St.  Louis, 
the  machine  tools  of  which  are  operated  by  compressed  air,  each  of  the 
larger  tools  having  its  own  air  engine,  and  the  smaller  tools  being  belted 
from  shafting  driven  by  an  air  engine.  Power  is  supplied  by  a  compound 
compressor  rated  at  55  horse-power.  The  air  engines  are  of  the  Kriebel 
make,  rated  from  2  to  8  horse-power. 

Pneumatic  Postal  Transmission.— A  paper  by  A.  Falkerau, 
Eng'rs  Club  of  Philadelphia,  April  1894,  entitled  the  "First  United  Stares 
Pneumatic  Postal  System,"  gives  a  description  of  the  system  used  in  London 
and  Paris,  and  that  recently  introduced  in  Philadelphia  between  the  main 
post-office  and  a  substation.  In  London  the  tubes  are  2*4  and  3  inch  lead 
pipes  laid  in  cast-iron  pipes  for  protection.  The  carriers  used  in  2*4 -inch 
tubes  are  but  \V±  inches  diameter,  the  remaining  space  being  taken  up  by 
packing.  Carriers  are  despatched  singly.  First,  vacuum  alone  was  used; 
later,  vacuum  and  compressed  air.  The  tubes  used  in  the  Continental  cities 
in  Europe  are  wrought  iron,  the  Paris  tubes  being  2^  inches  diameter. 
There  the  carriers  are  despatched  in  trains  of  six  to  ten,  propelled  by  a 
piston.  In  Philadelphia  the  size  of  tube  adopted  is  6)4  inches,  the  tubes 
being  of  cast  iron  bored  to  size.  The  lengths  of  the  outgoing  and  return 
tubes  are  2928  feet  each.  The  pressure  at  the  main  station  is  7  Ibs.,  at  the 
substation  4  Ibs.,  and  at  the  end  of  the  return  pipe  atmospheric  pressure. 
The  compressor  has  two  air-cylinders  18  X  24  in.  Each  carrier  holds  about 
200  letters,  but  100  to  150  are  taken  as  an  average.  Eight  carriers  may  be 
despatched  in  a  minute,  giving  a  delivery  of  48,000  to  72,000  letters  per  hour. 
The  time  required  in  transmission  is  about  57  seconds. 

The  Iflekarski  Compressed-air  Tramway  at  Berne, 
Switzerland.  (Eng^g  News,  April  20,  1893.)— The  Mekarski  system  has 
been  introduced  in  Berne,  Switzerland,  on  a  line  about  two  miles  long,  with 
grades  of  0.25$  to  3.7$  and  5.2#.  A  special  feature  of  the  Mekarski  system  is 
the  heating  of  the  air,  to  maintain  it  at  a  constant  temperature,  by  passing 
it  through  superheated  water  at  330°  F.  The  air  thus  becomes  saturated 
with  steam,  which  subsequently  partly  condenses,  its  latent  heat  being 
absorbed  by  the  expanding  air.  The  pressure  in  the  car  reservoirs  is  440 
Ibs.  per  sq.  in. 

The  engine  is  constructed  like  an  ordinary  steam  tramway  locomotive, 


510  AIR. 

and  drives  two  coupled  axles,  the  wheel-base  being  5.2  ft.  It  has  a  pair  of 
outside  horizontal  cylinders,  5.1  X  8.6  in.;  four  coupled  wheels,  27.5  in. 
diameter.  The  total  weight  of  the  car  including  compressed  air  is  7.25  tons, 
and  with  30  passengers,  including  the  driver  and  conductor,  about  9.5  tons. 

The  authorized  speed  is  about  7  miles  per  hour.  Taking  the  resistance 
due  to  the  grooved  rails  and  to  curves  under  unfavorable  conditions  at  30 
Ibs.  per  ton  of  car  weight,  the  engine  has  to  overcome  on  the  steepest  grade, 
5$,  a  total  resistance  of  about  0.63  ton,  and  has  to  develop  25  H.P.  At  the 
maximum  authorized  working  pressure  in  cylindersof  176 Ibs.  persq.  in.  the 
motors  can  develop  a  tractive  force  of  0.64  ton.  This  maximum  is,  there- 
fore, just  sufficient  to  take  the  car  up  the  5.2%  grade,  while  on  the  flatter 
sections  of  the  line  the  working  pressure  does  not  exceed  73  to  147  Ibs.  per 
sq.  in.  Sand  has  to  be  frequently  used  to  increase  the  adhesion  on  the  2%  to 
5%  grades. 

Between  the  two  car  frames  are  suspended  ten  horizontal  compressed-air 
storage-cylinders,  varying  in  length  according  to  the  available  space,  but  of 
uniform  inside  diameter  of  17.7  in.,  composed  of  riveted  0.27-in.  sheet  iron, 
and  tested  up  to  588  Ibs.  per  sq.  in.  These  cylinders  have  a  collective 
capacity  of  84.25  cu.  ft.,  which,  according  to  Mr.  Mekarski's  estimate, 
should  have  been  sufficient  for  a  double  trip,  3%  miles.  The  trial  trips, 
however,  showed  this  estimate  to  be  inadequate,  and  two  further  small 
storage-cylinders  had  therefore  to  be  added  of  5.3  cu.  ft.  capacity  each, 
bringing  the  total  cubic  contents  of  the  12  storage-cylinders  per  car  up  to 
75  cu.  ft.,  divided  into  two  groups,  the  working  and  the  reserve  battery,  the 
former  of  49  cu.  ft.  the  latter  of  26  cu.  ft.  capacity. 

From  the  results  of  six  official  trips,  the  pressure  arid  the  mean  consump- 
tion of  air  during  a  double  journey  per  motor  car  are  as  follows: 

Working,  Reserve, 
Storage-cylinders.  ^  m®r    ^  P«r 

Pressure  of  air  on  starting    440  440 

Pressure  of  air  at  end  of  up  journey 176  260 

Pressure  of  air  at  end  of  down  journey 103  176 

Lbs. 

Consumption  of  air  at  end  of  up  journey 92 

Consumption  of  air  during  down  journey 31 

This  has  been  fully  confirmed  by  the  working  experience  of  1891,  when 
the  consumption  of  air  per  motor  car  and  double  journey  was  as  follows: 

Minimum,  103  Ibs „.   .     28  Ibs.  per  car-mile- 

Maxirnum,  154  Ibs 42      " 

Mean,  123  Ibs 35      **        "        " 

The  principal  advantages  of  the  compressed-air  system  for  urban  and 
suburban  trnmwray  traffic  a,s  worked  at  Berne  consist  in  the  smooth 
and  noiseless  motion;  in  the  absence  of  smoke,  steam,  or  heat,  of  overhead 
or  underground  conductors,  of  the  more  or  less  grinding  motion  of  most 
electric  cars,  and  of  the  jerky  motion  to  which  underground  cable  traction 
is  subject.  On  all  these  grounds  the  system  has  vindicated  its  claims  a? 
being  preferable  to  any  other  so  far  known  system  of  mechanical  traction 
for  street  tramways.  Its  disadvantages,  on  the  other  hand,  consist  in  the 
extremely  delicate  adjustment  of  the  different  parts  of  th«  system,  in  the 
comparatively  small  supply  of  air  carried  by  one  motor  car,  which  necessi- 
tates the  car  returning  to  the  depot  for  refilling  after  a  run  of  only  four 
miles  or  40  minutes,  although  on  the  Nogent  and  Paris  lines  the  cars, 
which  are,  moreover,  larger,  and  carry  outside  passengers  on  the  top, 
run  seven  miles,  and  the  loading  pressure  is  517  Ibs.  per  sq.  in.  as  against 
only  440  Ibs.  at  Berne. 

Longer  distances  in  the  same  direction  would  involve  either  more  power- 
ful motors,  a  larger  number  of  storage-cylinders,  and  consequently  heavier 
cars,  or  loading  stations  every  four  or  seven  miles;  and  in  this  respect  the 
system  is  manifestly  inferior  to  electric  traction,  which  easily  admits  of  a 
line  of  10  to  15  miles  in  length  being  continuously  fed  from  one  central 
station  without  the  loss  of  time  and  expense  caused  by  reloading. 

The  cost  of  working  the  Berne  line  is  compared  in  the  annexed  table 
with  some  other  tra;i.wavs  worked  under  similar  conditions  by  horse  and 
mechanical  traction  for  the  year  1891.  As  is  seen,  both  in  the  case  of  com- 
pressed air  and  of  electric  traction,  the  cost  of  working  is  considerably 


FAXS  AND   BLOWERS.  511 

increased  where  steam  at  a  high  cost  of  fuel  has  to  be  used  instead  of 
hydraulic  power.  Given  the  latter,  the  cost  of  working  by  air  is  about  the 
same  as  that  by  steam-locomotives  or  steam-cars;  but  over  both  of  these 
last-named,  compressed-air  offers,  at  equal  cost  and  for  such  short  lines 
wilh  constant  traffic,  certain  advantages: 

Constr.        Opera 


1891.  Length  of  Line, 

miles. 

Geneva,  city 8.68 

Zurich,  city 5.58 

Geneva,  suburban 40.30 

Mulhouse,  city     18.00 

Montreux,  subu  rban 6 . 82 

Florence,  suburban 4.96 

Tours,  suburban  6.20 

Nogent  (Paris),  suburban    7.44 
Berne,  city 1.86 


Motive  Power,  and  equip't,      tion, 
per  mile.    p.  car  mi 

Horse $60,800  19.4  cts. 

Horse  39,700  11  6 

Steam  locomotive. 32,000  13.2 

Steam  locomotive.22,400  17.8 

Hydro-electric  . .  20,800  10.4 

Steam  electric ...  32,000  20.0 

Steam  cars 19,200  17.2 

Steam-compr.  air.46,100  2f>.6 

Hydro-conipr.  air.48,950  17.8 


For  description  of  the  Mekarski  system  as  used  at  Nantes,  France,  see 
paper  by  Prof.  D.  S.  Jacobus.  Trans.  A.  I.  M.  E.  xix.  553. 

Compressed  Air  for  Working  Underground  Pumps  in 
Fillies.— Eng'g  Record,  May  19,  1894,  describes  an  installation  of  com- 
pressors for  working  a  number  of  pumps  in  the  Nottingham  No.  15  Mine, 
Plymouth,  Pa.,  which  is  claimed  to  be  the  largest  in  America.  The  com- 
pressors develop  above  2300  H.P.,  and  the  piping,  horizontal  and  vertical,  is 
6000  feet  in  length.  About  25,000  gallons  of  water  per  hour  are  raised. 

FANS  AND  BLOWERS. 

Centrifugal  Fans.— The  ordinary  centrifugal  fan  consists  of  a  num- 
ber of  blades  fixed  to  arms,  revolving  on  a  shaft  at  high  speed.  The  width 
of  the  blade  is  parallel  to  the  axis  of  the  shaft.  Most  engineers1  reference 
books  quote  the  experiments  of  W.  Buckle,  Proc.  Inst.  M.E.,  1847,  as  still 
standard.  Mr.  Buckle's  conclusions  are  given  below,  together  with  data  of 
more  recent  experiments. 

Experiments  were  made  as  to  the  proper  size  of  the  inlet  openings  and  on 
the  proper  proportions  to  be  given  to  the  vane.  The  inlet  openings  in  the 
sides  of  the  fan-chest  \\  ere  contracted  from  17^  m-*  the  original  diameter, 
to  12  and  6  in.  diam.,  when  the  following  results  were  obtained: 

First,  that  the  power  expended  with  the  opening  contracted  to  12  in.  diam. 
was  as  2J/£  to  1  compared  with  the  opening  of  17J4  in-  diam.;  the  velocity  of 
the  fan  being  nearly  the  same,  as  also  the  quantity  and  density  of  air 
delivered. 

Second,  that  the  power  expended  with  the  opening  contracted  to  6  in. 
diam.  was  as  2^  to  1  compared  with  the  opening  of  17^  in.  diam.;  the 
velocity  of  the  fan  being  nearly  the  same,  and  also  the  area  of  the  efflux 
pipe,  but  the  density  of  the  air  decreased  one  fourth. 

These  experiments  show  that  the  inlet  openings  must  be  made  of  sufficient 
size,  that  the  air  may  have  a  free  and  uninterrupted  action  in  its  passage  to 
the  blades  of  the  fan;  for  if  we  impede  this  action  we  do  so  at  the  expense 
of  power. 

With  a  vane  14  in.  long,  the  tips  of  which  revolve  at  the  rate  of  236.8  ft. 
per  second,  air  is  condensed  to  9.4  ounces  per  square  inch  above  the  pres- 
sure of  the  atmosphere,  with  a  power  of  9.6  H.  P. ;  but  a  vane  8  inches  long, 
the  diameter  at  the  tips  being  the  same,  and  having,  therefore,  the  same 
velocity,  condenses  air  to  6  ounces  per  square  inch  only,  and  takes  12  H.  P. 

Thus  the  density  of  the  latter  is  little  better  than  six  tenths  of  the  former, 
while  the  power  absorbed  is  nearly  1.25  to  1.  Although  the  velocity  of  the 
tips  of  the  vanes  is  the  same  in  each  case,  the  velocities  of  the  heels  of  the 
respective  blades  are  very  different,  for,  while  the  tips  of  the  blades  in  each 
case  move  at  the  same  rate,  the  velocity  of  the  heel  of  the  14-inch  is  in  the 
ratio  of  1  to  1.67  to  the  velocity  of  the  heel  of  the  8-inch  blade.  The 
longer  blades  approaching  nearer  the  centre,  strikes  the  air  with  less  velo- 
city, and  allows  it  to  enter  on  the  blade  with  greater  freedom,  and  with 
considerably  less  force  than  the  shorter  one.  The  inference  is,  that  the 
short  blade  must  take  more  power  at  the  same  time  that  it  accumulates  a 
less  quantity  of  air.  These  experiments  lead  to  the  conclusion  that  the 
length  of  the  vane  demands  as  great  a  consideration  as  the  proper 
diameter  of  the  inlet  opening.  If  there  were  no  other  object  in  view,  it 


AIR. 


would  be  useless  to  make  the  vanes  of  the  fan  of  a  greater  width  than  the 
inlet  opening  can  freely  supply.  On  the  proportion  of  the  length  and  width 
of  the  vane  and  the  diameter  of  the  inlet  opening  rest  the  three  most  im- 
portant points,  viz.,  quantity  and  density  of  air,  arid  expenditure  of  power. 

In  the  14-inch  blade  the  tip  has  a  velocity  2,6  times  greater  than  the 
heel;  and,  by  the  laws  of  centrifugal  force,  the  air  will  have  a  density  2.G 
times  greater  at  the  tip  of  the  blade  than  that  at  the  heel.  The  air  cannot 
enter  on  the  heel  with  a  density  higher  than  that  of  the  atmosphere;  but  in 
its  passage  along  the  vane  it  becomes  compressed  in  proportion  to  its 
centrifugal  force.  The  greater  the  length  of  the  vane,  the  greater  will  be 
the  difference  of  the  centrifugal  force  between  the  heel  and  the  tip  of  the 
blade;  consequently  the  greater  the  density  of  the  air. 

Reasoning  from  these  experiments,  Mr.  Buckle  recommends  for  easy  ref- 
erence the  following  proportions  for  the  construction  of  the  fan: 

1.  Let  the  width  of  the  vanes  be  one  fourth  of  the  diameter;  2.  Let  the 
diameter  of  the  inlet  openings  in  the  sides  of  the  fan-chest  be  one  half  the 
diameter  of  the  fan;  3.  Let  the  length  of  the  vanes  be  one  fourth  of  the 
diameter  of  the  fan. 

In  adopting  this  mode  of  construction,  the  area  of  the  inlet  openings  in 
the  sides  of  the  fan-chest  will  be  the  same  as  the  circumference  of  the  heel 
of  the  blade,  multiplied  by  its  width;  or  the  same  area  as  the  space 
described  by  the  heel  of  the'  blade. 

Best  Proportions  of  Fans.    (Buckle.) 

PRESSURE  FROM  3  OUNCES  TO  6  OUNCES  PER  SQUARE  INCH;  OR  5.2  INCHES 
TO  10.1  INCHES  OF  WATER. 


Diameter 

Vanes. 

Diameter 
of  Inlet 

Diameter 

Vanes. 

Diameter 
of  Inlet 

of  Fan. 

Open- 

of Fan. 

Open- 

Width. 

Length. 

ings. 

Width. 

Length. 

ings. 

ft.    ins. 

ft.  ins. 

ft.  ins. 

ft.   ins. 

ft.  ius. 

ft.  ins. 

ft.  ins. 

ft.  ins. 

3      0 

0     9 

0      9 

1       6 

4       6 

1      1^ 

1      1^ 

2      3 

3      6 

0   10H 

0    1(% 

1       9 

5       0 

1      3 

1      3 

2      6 

4      0 

1     0 

1      0 

2       0 

0       0 

1      6 

1      6 

3      0 

PRESSURE  FROM  6  OUNCES  TO  9  OUNCES  PER  SQUARE  INCH,  AND  UPWARDS, 
OR  10.4  INCHES  TO  15.6  INCHES  OF  WATER. 


3      0 

0     7 

1      0 

1       0 

4       6 

0   10J$ 

1     4y2 

1       9 

3      6 

0     8J4 

1      1^ 

1       3 

5       0 

1      0 

1      6 

2      0 

4      0 

0     9^ 

1     3fc 

1       6 

6       0 

1     2 

1    10 

2       4 

The  dimensions  of  the  above  tables  are  not  laid  clown  as  prescribed  limits, 
but  as  approximations  obtained  from  the  best  results  in  practice. 

Experiments  were  also  made  with  reference  to  the  admission  of  air  into 
the  transit  or  outlet  pipe.  By  a  slide  the  width  of  the  opening  into  this  pipe 
was  varied  from  12  to  4  inches.  The  object  of  this  was  to  proportion  the 
opening  to  the  quantity  of  air  required,  and  thereby  to  lessen  the  power 
necessary  to  drive  the  fan.  It  was  found  that  the  less  this  opening  is  made, 

Erovided  we  produce  sufficient  blast,  the  less  noise  will  proceed  from  the 
3,11 ;  and  by  making  the  tops  of  this  opening  level  with  the  tips  of  the  vane, 
the  column  of  air  has  little  or  no  reaction  on  the  vanes. 

The  number  of  blades  may  be  4  or  6.  The  case  is  made  of  the  form  of 
an  arithmetical  spiral,  widening  the  space  between  the  ease  and  the  revolv- 
ing blades,  circumferentially,  from  the  origin  to  the  opening  for  discharge. 

The  following  rules  deduced  from  experiments  are  given  in  Spretson's 
treatise  on  Casting  and  Founding: 

The  fan-case  should  be  an  arithmetical  spiral  to  the  extent  of  the  depth 
of  the  blade  at  least. 

The  diameter  of  the  tips  of  the  blades  should  be  about  double  the  diameter 
of  the  hole  in  the  centre;  the  width  to  be  about  two  thirds  of  the  radius  of 
the  tips  of  the  blades.  The  velocity  of  the  tips  of  the  blades  should  be  rather 


FANS  AND   BLOWERS.  513 

more  than  the  velocity  due  to  the  air  at  the  pressure  required,  say  one 
eighth  more  velocity. 

In  some  cases,-  two  fans  mounted  on  one  shaft  would  be  more  useful  than 
one  wide  one,  as  in  such  an  arrangement  twice  the  area  of  inlet  opening  is 
obtained  as  compared  with  a  single  wide  fan.  Such  an  arrangement  may 
be  adopted  where  occasionally  half  the  full  quantity  of  air  is  required,  as 
one  of  them  may  be  put  out  of  gear,  thus  saving  power. 

Pressure  due  to  Velocity  ol'tlie  Fan-blades.—  "  By  increas- 
ing the  number  of  revolutions  of  the  fan  the  head  or  pressure  is  increased, 
the  law  being  that  the  total  head  produced  is  equal  (in  centrifugal  fans)  to 
twice  the  height  due  to  the  velocity  of  the  extremities  of  the  blades,  or 

H  =  —  approximatelyin  practice"  (W.  P.  Trowbridge,  Trans.  A.  S.  M.  E  , 

vii.  536.)  This  law  is  analogous  to  that  of  the  pressure  of  a  jet  striking  a 
plane  surface.  T.  Hawksley,  Proc.  lust.  M.  E.,  1882,  vol.  Ixix..  says:  ''The 
pressure  of  a  fluid  striking  a  plane  surface  perpendicularly  and  then  escap- 
ing at  right  angles  to  its  original  path  is  that  due  to  twice  the  height  h  due 
the  velocity." 

(For  discussion  of  this  question,  showing  that  it  is  an  error  to  take  the 
pressure  as  equal  to  a  column  of  air  of  the  height  h  =  v"2  H-  2(/,  see  Wolff  on 
Windmills,  p.  17.) 

Buckle  says:  '•  From  the  experiments  it  further  appears  that  the  velocity 
of  the  tips  of  the  fan  is  equal  to  nine  tenths  of  the  velocity  a  body  would 
acquire  in  falling  the  height  of  a  homogeneous  column  of  air  equivalent  to 
the  density."  D.  K.  Clark  (R.  T.  &  D.,  p.  924),  paraphrasing  Buckle,  appar 
ently,  says:  "  It  further  appears  that  the  pressure  generated  at  the  circum 
ference  is  one  ninth  greater  than  that  which  is  due  to  the  actual  circumfer- 
ential  velocity  of  the  fan."  The  two  statements,  however,  are  not  in 

harmony,  for  itv  =  0.9  V*gH,  H  =  Q  ^  ^  =  1-234  1-   and  not  1$  £ 

If  we  take  the  pressure  as  that  equal  to  a  head  or  column  of  air  of  twice 
the  height  due  the  velocity,  as  is  correctly  stated  by  Trowbridge.  the  para- 
doxical statements  of  Buckle  and  Clark—  which  would  indicate  that  the 
actual  pressure  is  greater  than  the  theoretical—  are  explained,  and  the 

— 


formula  becomes  H=  .617  —  and   v  =  1.273  VgH  =  0.9  V%gH,  in  which  H 

is  the  head  of  a  column  producing  the  pressure,  which  is  equal  to  twice  the 

/  v'2\ 

theoretical  head  due  the  velocity  of  a  falling  body  (or  h  =  —  1,  multiplied 

by  the  coefficient  .617.  The  difference  between  1  and  this  coefficient  ex- 
presses the  loss  of  pressure  due  to  friction,  to  the  fact  that  the  inner  por- 
tions of  the  blade  have  a  smaller  velocity  than  the  outer  edge,  and  probably 
to  other  causes.  The  coefficient  1.273  means  that  the  tip  of  the  blade  must 
be  given  a  velocity  1.273  times  that  theoretically  required  to  produce  the 
head  H. 

To  convert  the  head  //  expressed  in  feet  to  pressure  In  Ibs.  per  sq.  in. 
multiply  it  by  the  weight  of  a  cubic  foot  of  air  at  the  pressure  and  tempera- 
ture of  the  air  expelled  from  the  fan  (about  .08  Ib.  usually)  and  divide  by 
141.  Multiply  this  by  16  to  obtain  pressure  in  ounces  per  sq.  in.  or  by  2.035 
to  obtain  inches  of  mercury,  or  by  27.71  to  obtain  pressure  in  inches  of 
water  column.  Taking  .08  as  the  weight  of  a  cubic  foot  of  air, 

p  Ibs.  per  sq.  in.          =  .00001066*;2;  v  =  310  linearly; 

Pi  ounces  per  sq.  in.  =  .0001  706v2;  v  =    80  j  p±      " 

p2  inches  of  mercury  =  .00002169u2;  v  =  220  1  p,      " 

ps  inches  of  water       —  .0002954v2;  v  =    60  4/p3      '* 

in  which  v  =  velocity  of  tips  of  blades  in  feet  per  second. 

Testing  the  above  formula  by  the  experiment  of  Buckle  with  the  vane 
14  inches  long,  quoted  above,  we  have  p  =  .  00001  OOCu8  =  9.5G  oz.  The  ex- 
periment gave  9.4  oz. 

Testing  it  by  the  experiment  of  H.  I.  Snell,  given  below,  in  which  the 
circumferential  speed  was  about  150  ft.  per  second,  we  obtain  3.85  ounces, 
wnile  the  experiment  gave  from  2.38  to  3.50  ounces,  according  to  the  amount 
of  opening  for  discharge.  The  numerical  coefficients  of  the  above  formulae 
are  all  based  on  Buckle's  statement  that  the  velocity  of  the  tips  of  the  fan 
is  equal  to  nine  tenths  of  the  velocity  a  body  would  acquire  in  falling  the 


514 


AIE. 


height  of  a  homogeneous  column  of  air  equivalent  to  the  pressure.  Should 
other  experiments  show  a  different  law,  the  coefficients  can  be  corrected 
accordingly.  It  is  probable  that  they  will  vary  to  some  extent  with  differ- 
ent proportions  of  fans  and  different  speeds. 

Taking  the  formula  v  =  80  1/pj,  we  have  for  different  pressures  in  ounces 
per  square  inch  the  following  velocities  of  the  tips  of  the  blades  in  feet  per 
second: 

Pi  =  ounces  per  square  inch 2      3      4      5      6      7      8      10      12      14 

v    =  feet  per  second 113  139  160  179  196  212  226  253    277    299 

A  rule  in  App.  Cyc.  Mecli,  article  "  Blowers,"  gives  the  following  velocities 
of  circumference  for  different  densities  of  blast  in  ounces:  3, 170;  4,  180;  5, 
195;  6,  205;  7,  215. 

The  same  article  gives  the  following  tables,  the  first  of  which  shows  that 
the  density  of  blast  is  not  constant  for  a  given  velocity,  but  depends  on  the 
ratio  of  area  of  nozzle  to  area  of  blades: 

Velocity  of  circumference,  feet  per  second.  150  150  150  170  200  200  220 

Area  of  nozzle -*- area  of  blades 2      1     ^    14    %  1/6  y% 

Density  of  blast,  oz.  per  square  inch 1      2      3      4      4      6      6 

QUANTITY  OP  AIR  OF  A  GIVEN  DENSITY  DELIVERED  BY  A  FAN. 
Total  area  of  nozzles  in  square  feet  X  velocity  in  feet  per  minute  corre- 
sponding to  density  (see  table)  =  air  delivered  in  cubic  feet  per  minute. 


Velocity,  feet 

5000 

7000 

8600 

10,000 


Velocity,  feet 


per  sq.  in. 
5 
6 

7 


ounces 


Velocity,  feet 
per  minute. 


per  mm. 

11,000 
12,250 
13,200 
14,150 

(Henry  I.  Snell,  Trans.  A.  S.  M.  E. 


10 
11 
12 


15,000 
15,800 
16,500 
17,300 


Experiments  with  Blowers. 

ix.  51.)— The  following  tables  give  velocities  of  air  discharging  through  an 
aperture  of  any  size  under  the  given  pressures  into  the  atmosphere.  The 
volume  discharged  can  be  obtained  by  multiplying  the  area  of  discharge 
opening  by  the  velocity,  and  this  product  by  the  coefficient  of  contraction: 
.65  for  a,  thin  plate  and  .93  when  the  orifice  is  a  conical  tube  with  a  conver- 
gence of  about  3.5  degrees,  as  determined  by  the  experiments  of  Weisbach. 

The  tables  are  calculated  for  a  barometrical  pressure  of  14.69  Ibs.  (= 
235  oz.),  and  for  a  temperature  of  50°  Fahr.,  from  the  formula  V=  y2gfi. 

Allowances  have  been  made  for  the  effect  of  the  compression  of  the  air, 
but  none  for  the  heating  effect  due  to  the  compression. 

At  a  temperature  of  50  degrees,  a  cubic  foot  of  air  weighs  .078  Ibs.,  and 
calling  g  =  32.1602,  the  above  formula  may  be  reduced  to 


Fj  =  60  V31.5812  X  (235  +  P)  X  P, 

where  V\  =  velocity  in  feet  per  minute. 

P  —  pressure  above  atmosphere,  or  the  pressure  shown  by  gauge,  in  oz. 
per  square  inch. 


Pressure 
pei-  sq.  in. 
in  inches  of 
water. 

Corre- 
sponding 
Pressure  in 
oz.  per  sq. 
inch. 

Velocity 
due  the 
Pressure  in 
feet  per 
minute. 

Pressure 
per  sq.  in. 
in  inches  of 
water. 

Corre- 
sponding 
Pressure  in 
oz,  per  sq. 
inch. 

Velocity  due 
the  Pressure 
in  feet  per 
minute. 

1/32 

.01817 

696.78 

% 

.36340 

3118.38 

1/16 

.03634 

987.66 

a/ 

.43608 

3416.64 

^ 

.07268 

1393.75 

% 

.50870 

3690.62 

3/16 

.10902 

1707.00 

1 

.58140 

3946.17 

% 

.14536 

1971.30 

1$ 

.7267 

4362.62 

5/16 

.18170 

2204.16 

.8721 

4836.06 

% 

.21804 

2414.70 

1% 

1  .0174 

5224.98 

^ 

.29072 

2788.74 

2 

1.1628 

5587.58 

FAKS   AND   BLOWERS. 


515 


Press- 

Velocity 

Press- 

Velocity 

Press- 

Velocity 

Velocity 

ure 

due  the 

ure 

due  the 

ure 

due  the 

Pressure 

due  the 

in  oz. 

Pressure 

in  oz. 

Pressure 

in  oz. 

Pressure 

in  oz. 

Pressure 

per  sq. 
inch. 

in  ft.  per 
minute. 

per  sq. 
inch. 

in  ft.  per 
minute. 

persq. 
inch. 

in  ft.  per 
minute. 

persq.  in. 

in  ft.  per 
minute. 

.25 

2,582 

2.25 

7,787 

5.50 

12,259 

11.00 

17,534 

.50 

3,658 

2.50 

8,213 

6.00 

12,817 

12.00 

18,350 

.75 

4.482 

2.75 

8,618 

6.50 

13.854 

13.00 

19,138 

1.00 

5,178 

3.00 

9,006 

7.00 

13.873 

14.00 

19,901 

1.25 

5,792 

3.50 

9,739 

7.50 

14.374 

15.00 

20.641 

1.50 

6,349 

4.00 

10,421 

8.00 

14.861 

16.00 

21,360 

1.75 

6.801 

4.50 

11,065 

9.00 

15,795 

2.00 

7,338 

5.00 

11,676 

10.00 

16,684 

Pressure  in  ounces 
per  square  inch. 

Velocity  in  feet 
per  minute. 

Pressure  in  ounces 
per  square  inch. 

Velocity  in  feet  per 
minute. 

.01 
.02 
.03 
.04 
.05 

516.90 
722.64 
895.26 
1033.86 
1155.90 

.06 
.07 
.08 
.09 
.10 

12C6  24 
1367.76 
1462.20 
1550.70 
1635.00 

on  a  Fan  witli  Varying  Discharge-opening. 
Revolutions  nearly  constant. 


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The  fan  wheel  was  23  inches  in  diameter,  6%  inches  wide  at  its  periphery, 
and  had  an  inlet  of  12i/o  inches  in  diameter  on  either  side,  which  was 
partially  obstructed  by  the  pulleys,  which  were  5  9/16  inches  in  diameter.  It 
had  eight  blades,  each  of  an  area  of  45.49  square  inches. 

The  discharge  of  air  was  through  a  conical  tin  tubs  with  sides  tapered  at 
an  angle  of  3*4  degrees.  The  actual  area  of  opening  was  1%  greater  than 
given  in  the  tables,  to  compensate  for  (he  vena  coutracta. 

In  the  last  experiment,  89.5  sq.  in.  represents  the  actual  area  of  the  mouth 
of  the  blower  less  a  deduction  for  a  narrow  strip  of  wood  placed  across  it  for 
the  purpose  of  holding  the  pressure  gauge.  In  calculating  the  volume  of  air 
discharged  in  the  last  experiment  the  value  of  vena  contracta  is  taken  at  .80. 


516 


AIR. 


Experiments  were  undertaken  for  the  purpose  of  showing  the  results  ob- 
tained by  running  the  same  fan  at  different  speeds  with  th/e  discharge-open- 
ing the  same  throughout  the  series. 

The  discharge-pipe  was  a  conical  tube  8J^  inches  inside  diameter  at  the 
end,  having  an  area  of  56.74,  which  is  1%  larger  than  53  sq.  inches  ;  therefore 
£8  square  inches,  equal  to  .368  square  feet,  is  called  the  area  of  discharge,  as 
that  is  the  practical  area  by  which  the  volume  of  air  is  computed. 

Experiments  on  a  Fan  with  Constant  Discharge-open- 
ing and  Varying  Speed.— The  first  four  columns  are  given  by  Mr. 
Snell,  the  others  are  calculated  by  the  author. 


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60.2 

56.6 

85.1 

3,630 

.182 

73 

800 

.88 

1787 

.70 

80  3 

75.0 

85.6 

4,856 

.429 

61 

1000 

1.38 

2245 

1.35 

100.4 

94. 

85.4 

6,100 

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1.479 

67 

1400 

2.75 

3177 

3.45 

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84.8 

8,633 

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1600 

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3670 

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156. 

82.4 

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3.803 

74 

1800 

4.80 

4172 

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180.6 

175. 

82.4 

11,337 

5.462 

68 

2000 

5.95 

4674 

11.40 

200.7 

195. 

85.6 

12,701 

7.586 

67 

Mr.  Snell  has  not  found  any  practical  difference  between  the  efficiencies 
of  blowers  with  curved  blade's  and  those  with  straight  radial  ones. 

From  these  experiments.  sa>  s  Mr.  Snell,  it  appears  that  we  may  expect  to 
receive  back  65$  to  75^  of  the  power  expended,  and  no  more. 

The  great  amount  of  power  often  used  to  run  a  fan  is  not  due  to  the  fan 
itself,  but  to  the  method  of  selecting,  erecting,  and  piping  it. 

(For  opinions  on  the  relative  merits  of  fans  and  positive  rotary  blowers, 
see  discussion  of  Mr.  Sr.elFs  paper,  Trans.  A.  S.  M.  E.,  ix.  66,  etc.) 

Comparative  Efficiency  of  Fans  and  Positive  Blowers.— 
(H.  M.  Howe,  Trans.  A.  1.  M.  E.,  x.  482.)— Experiments  with  fans  and  positive 
(Bakery  blowers  working  at  moderately  low  pressures,  under  20  ounces,  show 
that  they  work  more  efficiently  at  a  given  pressure  when  delivering  large 
volumes  (i.e.,  when  working  nearly  up  to  their  maximum  capacity)  than 
when  delivering  comparatively  small  volumes.  Therefore,  when  great  vari- 
ations in  the  quantity  and  pressure  of  blast  required  are  liable  to  arise,  the 
highest  efficiency  would  be  obtained  by  having  a  number  of  blowers,  always 
driving  them  up  to  their  full  capacity,  and  regulating  the  amount  of  blast 
by  altering  the  number  of  blowers  at  work,  instead  of  having  one  or  two 
very  large  blowers  and  regulating  the  amount  of  blast  by  the  speed  of  the 
blowers. 

There  appears  to  be  little  difference  between  the  efficiency  of  fans  and  of 
Baker  blowers  when  each  works  under  favorable  conditions  as  regards 
quantity  of  work,  and  when  each  is  in  good  order. 

For  a  given  speed  of  fan,  any  diminution  in  the  size  of  the  blast-orifice  de- 
creases the  consumption  of  power  and  at  the  same  time  raises  the  pressure 
of  the  blast ;  but  it  increases  the  consumption  of  power  per  unit  of  orifice 
f<«r  a  given  pressure  of  blast.  When  the  orifice  has  been  reduced  to  the 
normal  size  for  any  given  fan,  further  diminishing  it  causes  but 
slight  elevation  of  the  blast  pressure;  and,  when  the  orifice  becomes  com- 
paratively small,  further  diminishing  it  causes  no  sensible  elevation  of  the 
blast  pressure,  which  remains  practically  constant,  even  when  the  orifice  is 
entirely  closed. 

Many  of  the.  failures  of  fans  have  been  due  to  too  low  speed,  to  too  small 
pulle3-s,  to  improper  fastening  of  belts,  or  to  the  belts  being  too  nearly  Ver- 
tical; in  brief,  to  bad  mechanical  arrangement,  rather  than  to  inherent  de- 
fects in  the  principles  of  the  machine. 


FANS  AND    BLOWERS. 


517 


If  several  fans-are  used,  it  is  probably  essential  to  high  efficiency  to  pro- 
vide a  separate  blast  pipe  for  each  (at  least  if  the  fans  are  of  different  size 
or  speed),  while  any  number  of  positive  blowers  may  deliver  into  the  same 
pipe  without  lowering  their  efficiency. 

Capacity  of  Fans  and  Blowers. 

The  following  tables  show  the  guaranteed  air-supply  and  air-removal  of 
leading  forms  of  blowers  and  exhaust  fans.  The  figures  given  are  often 
exceeded  in  practice,  especially  when  the  blowers  and  fans  are  driven  at 
higher  speeds  than  stated.  The  ratings,  particularly  of  the  blowers,  are 
below  those  generally  given  in  catalogues,  but  it  was  the  desire  to  present 
only  conservative  and  assured  practice.  (A.  R.  Wolff  on  Ventilation.) 

QUANTITY  OF  AIR  SUPPLIED  TO  BUILDINGS  BY  BLOWERS  OF  VARIOUS  SIZES. 


Capacity 

Capacitv 

Diam- 
eter of 
Wheel 
in  feet. 

Ordinary 
Number 
of  Revs, 
per  min. 

Horse- 
power 
to  Drive 
Blower. 

cu.  ft. 
per  min. 
against  a 
Pressure 
of  1  ounce 

Diam- 
eter of 
Wheel 
in  feet. 

Ordinary 
Number 
of  Revs, 
per  min. 

Horse- 
power 
to  Drive 
Blower. 

cu.  ft. 
per  min. 
against  a 
Pressure 
of  1  ounce 

per  sq.  in 

per  sq.  in. 

4 

350 

6. 

10,635 

9 

175 

29 

56,800 

5 

325 

9.4 

17,000 

10 

160 

35.5 

70,340 

6 

275 

13.5 

29,618 

12 

130 

49.5 

102,000 

7 

230 

18.4 

42,700 

14 

110 

66 

139,000 

8 

200 

24 

46,000 

15 

100 

77 

160,000 

If  the  resistance  exceeds  the  pressure  of  one  ounce  per  square  inch,  of 
above  table,  the  capacity  of  the  blower  will  be  correspondingly  decreased, 
or  power  increased,  and  allowance  for  this  must  be  made  when  the  distrib- 
uting ducts  are  small,  of  excessive  length,  and  contain  many  contractions 
and  bends. 

QUANTITY  OF  AIR  MOVED  BY   AN   APPROVED   FORM  OF   EXHAUST  FAN,  THE 
FAN  DISCHARGING  DIRECTLY  FROM  ROOM  INTO  THE  ATMOSPHERE. 


Diam- 
eter of 
Wheel 
in  feet. 

Ordinary 
Number 
of  Revs. 
per  min. 

Horse- 
power 
to  Drive 
Fan. 

Capacity 
in  cu.  ft. 
per  min. 

Diam- 
eter of 
Wheel 
in  feet. 

Ordinary 
Number 
of  Revs, 
per  min. 

Horse- 
power 
to  Drive 
Fan. 

Capacity 
in  cu.  ft. 
per  min. 

2.0 
2.5 
3.0 
3.5 

600 
550 
500 
500 

0.50 
0.75 
1.00 

2.50 

5,000 
8,000 
12,000 
20,000 

4.0 
5.0 
6.0 
7.0 

475 
350 
300 
250 

3.50 
4.50 
7.00 
9.00 

28,000 
35,000 
50,000 
80,000 

The  capacity  of  exhaust  fans  here  stated,  and  the  horse-power  to  drive 
them,  are  for  free  exhaust  from  room  into  atmosphere.  The  capacity  de- 
creases and  the  horse-power  increases  materially  as  the  resistance,  resulting 
from  lengths,  smallness  and  bends  of  ducts,  enters  as  a  factor.  The  differ- 
ence in  pressures  in  the  two  tables  is  the  main  cause  of  variation  in  the  re- 
spective records.  The  fan  referred  to  in  the  second  table  could  not  be  used 
with  as  high  a  resistance  as  one  ounce  per  square  inch,  the  rated  resistance 
of  the  blowers. 


518 


AIR. 


CENTRIFUGAL  FANS. 

Pressures,  Velocities,  Volume  of  Air,    Horse-Power 
Required,  etc.    (B.  F.  Sturtevant  Co.) 


£.£-§  . 

W  —  3  >, 
S'Q  Q  £ 

!!i! 

.s  --3  « 

OC+j   «3 

-i  i-  «:'_? 
.g  a  <&•£ 

Kb  P-3 
'^3  §.£ 

°r* 

3&|.S 

§s^:  . 

E-S-ep'S 
L»IS* 

per  minute  (at 
y  be  discharged 
shaped  mouth- 
leter  of  which 
iches,  the  area 
inches. 

111 

i^uiefji 

sSI-llf^N 

•s  o  £  *£  ®*  i  M 

•i5s!"lll" 

£'>  c  ^J      A*>  S 
l?.£a3iSi)'7rCcs 

fe*si-er>5sr>ic 

z  4)  *°       ^-i^co^c- 

43  §| 

^^ 
%  .=  c  ** 

l&wg 

a£o^'= 
l^'Il 

ressure  per  sq. 
from  y4  to  20  out 
eludes  the  strong 
on  any  cupola  in 

elocity  in  feet  pe 
(at50°F.)  escapil 
through  any  sha 
any  pipe  or  res( 
the  Air  is  comprt 

-•§s|-s 

"Nil 

^j^-5 

fi-&35S 

"^-  '  3  of.ua  tX 

its  ill 

•gss-as^ 

|1|| 

i!l«lli: 
i!l;!l!I|l 

StsAllli^i 

!S  cs  -.2  -^  a  cs  ^  *-  ^ 
gf««3BJBlIS 

Number  of  mo 
scribed  in  colum 
discharge  one  H. 
allowance  being 
tion  in  the  blast-i 

PH 

> 

o 

^ 

g 

•t— 

1 

2 

3 

4 

5 

6 

y 

2584.80 

17.944 

0.001224 

14662.76 

817.00 

r/ 

3657.60 

25.400 

0.003463 

7333.70 

288.70 

a/ 

4482.00 

31.124 

0.005659 

4889.11 

157.08 

1 

5175.00 

35.93 

0.0098 

3666.62 

102.05 

2 

7338.24 

50.96 

0.0278 

1833.00 

35.970 

3 

9006  42 

62.54 

0.0512 

1222.30 

19.540 

4 

10421.58 

72.37 

0.0789 

916.27 

12  660 

5 

11676.00 

81.08 

0.1106 

733.39 

9.045 

6 

12817.08 

89.01 

0.1456 

611.10 

6.867 

7 

13872.72 

96.34 

0.1839 

523.81 

5.440 

8 

14861.16 

103.20 

0.2251 

458.43 

4.440 

9 

15795.06 

109.69 

0.2692 

407.42 

3.715 

10 

16683.51 

115.86 

0.3160 

366.69 

3.165 

11 

17533.50 

121.76 

0  3652 

333.40 

2.738 

12 

18350  34 

127.43 

0.4170 

305.56 

2.398 

13 

19138.26 

132.90 

0.4712 

282.05 

2.136 

14 

19900.68 

138.20 

0.5277 

261.91 

1.895 

15 

20640.48 

143.34 

0.5864 

244.44 

.705 

16 

21360.00 

148.33 

0.6473 

229.17 

.545 

17 

22060.80 

153.26 

0.7103 

215.77 

.408 

18 

22745.40 

157.96 

0.7754 

203.71 

.290 

19 

23415.00 

162.60 

0.8426 

192.98 

.187 

20 

24070.80 

167.16 

0.9118 

183.33                      .097 

*  Always  give  the  wind  a  good  wide  opening  into  the  furnace  or  forge  : 
see  by  this  table  how  much  more  wind  can  be  discharged  with  one  H.  P.  at 
low  pressure  than  at  high. 

This  table  shows  the  great  advantage  of  large  tuyeres,  large  pipes,  large 
blower,  and  slow  speed  when  the  nature  of  the  work  will  admit. 

t  Number  of  forges  driven  with  1.2  H.  P.  with  Sturtevant  blower. 

Caution  in  Regard  to  Use  of  Fan  and  Blower  Tables.— 

Msiiiy  engineers  report  that  manufacturers'  tables  overrate  the  capacity 
of  their  fans  and  underestimate  the  horse-power  required  to  drive  them. 
In  some  cases  the  complaints  may  be  due  to  restricted  air  outlets,  long 
and  crooked  pipes,  slipping  of  belts,  too  small  engines,  etc. 


CEKTKIFITGAL  FAtfS. 


519 


Engines,  Fans,  and  Steam-coil 
Blower  System  of  Heating. 


and  Steam-coils  combined  for  the 

(Buffalo  Forge  Co.) 


d« 

«M         ~g 

tit 

d 

Sd  cL 

s 

a 

^  & 

fc,   *   * 

o'coj 

§  *  •  s 

-"-•^ 
33  ^^ 

•a*-" 

43  03  fl 

§*H 

"o  ® 

S| 

.H  ^ 
j» 

i 

tp 
'So 

fllll 

Ssl1- 

g«H 

p 

III1 

F1 

*i° 

£W£ 
t> 

pi 

4x3 

52 

450 

8,740 

1,200 

49  x    38 

3.1 

1,000 

12 

4x4 

60 

425 

11,000 

1,525 

51  x    45 

4 

1,200 

15 

5x4 

70 

390 

15,280 

1,700 

52  x    50 

4.5 

1,600 

20 

5x5 

80 

360 

19,900 

2,200 

52  x    56 

6 

2,000 

25 

6x5 

90 

330 

25,900 

2,450 

59  x    74 

7.2 

2,500 

30 

6x6 

100 

290 

32,500 

2,7'00 

62  x    84 

9.1 

3,000 

35 

7x6 

110 

260 

39,300 

3,200 

69  x    94 

11 

3,500 

42 

7x7 

120 

235 

49,161 

3,900 

79  x  104 

13.5 

4,000 

48 

8x7 

130 

210 

57,720 

4,500 

83  x  111 

15 

4,500 

54 

8x8 

150 

180 

81,120 

5.300 

87  x  133 

20 

5,000 

62 

10  x  9 

170 

165 

101,250 

6,000 

92  x  148 

22 

6,000 

72 

The  Sturtevant  Steel  Pressure-blower,  applied  to 
Cupola  Furnaces. 


Is 

c^o 

& 

"O  O. 

§16 
5" 

& 

.s 

wtf3 

| 

o    5 

^.'•3 

3   1 

'd* 

9 

1 

_d 

Horse-power 
Required. 

Power  Saved  by  Reducing 
the  Speed  and  Pressure  of 
Blast. 

o> 
DQ 

4 

5 
6 
7 
8 
10 
12 
12 
14 
14 

P-i 

w 

02 

*! 

W 

1 

0 

3 
4 
5 
6 
7 
8 
9 
10 

22 
26 
30 
35 

40 
46 
53 
60 

72 
84 

1200 
1900 
2880 
4130 
6178 
8900 
12500 
16560 
23800 
33300 

5.7 
8 
10.7 
14.2 
18.7 
24.3 
32 
43 
60 

324 

507 
768 
1102 
1646 
2375 
3353 
4416 
6364 
8880 

4135 
3756 
3250 
3100 
2900 
2820 
2600 
2270 
2100 
1815 

5 
6 
7 
8 
10 
12 
14 
14 
16 
16 

0.5 
1 
1.8 
3 
5.5 
9.7 
16. 
22. 
35. 
48. 

3445 
3000 
2900 
2560 
2550 
2380 
2100 
1960 
1700 

0.8 
1.5 
2.5 
4. 
7.4 
12.7 
16.7 
28.4 
39.6 

3100 
2750 
2700 
2390 
2-260 
2150 
1900 
1800 
1566 

4 
5 

(f, 
7 
8 
10 
10 
12 
12 

0.6 
1.1 
2. 
3.3 
5.3 
9.4 
12.7 
22.5 
31.7 

*One  square  inch  of  blast  is  sufficient  for  one  forge-fire,  or  90  square 
inches  area  of  cupola  furnaces. 

The  speed  given  is  regulated  so  as  to  give  the  pressure  of  blast  stated  in 
ounces  per  square  inch. 

The  term  "  square  inches  of  blast  "  refers  to  the  area  of  a  proper  shaped 
mouth-piece  discharging  blast  into  the  open  air. 

The  melting  capacity  per  hour  in  pounds  of  iron  is  made  up  from  an 
average  of  tests  on  a  few  of  the  best  cupolas  found,  and  is  reliable  in  cases 
where  the  cupolas  are  well  constructed  and  driven  with  the  greatest  force 
of  blast  given  in  the  table. 

For  tables  of  the  steel  pressure -blower  as  applied  to  forge-fires,  and  for 
sizes,  etc.,  of  other  patterns  of  blowers  and  exhausters,  see  catalogue  of 
B.  F.  Sturtevant  Co. 

(For  other  data  concerning  Cupolas,  see  Foundry  Practice.) 

Diameter  of  Blast-pipes  for  Pressure-blowers  for  Cupola 
Furnaces  and  Forges.    (B.  F.  Sturtevant  Co.) 

The  following  table  has  been  constructed  on  this  basis,  namely  :  Allowing 
a  loss  of  pressure  of  ^  oz.  in  the  process  of  transmission  through  any  length 
of  pipe  of  any  size  as  a  standard,  the  increased  friction  due  to  lengthening 
the  pipe  has  been  compensated  for  by  an  enlargement  of  the  pipe  sufficient 


520 


AIR. 


to  keep  the  loss  still  at  ^  oz.  The  quantities  of  air  in  the  left-hand  column 
of  each  division  indicate  the  capacity  of  the  given  blower  when  working 
under  pressures  of  4,  8,  12,  and  16  ozs.  Thus  a  No.  6  Blower  will  force  2678 
cubic  ft.  of  air,  at  8  oz.  pressure,  through  50  ft.  of  12*4-in.  pipe,  with  a  loss 
of  ^  oz.  pressure.  If  it  is  desired  to  force  the  air  300  ft.  without  an  increased 
loss  by  friction,  the  pipe  must  be  enlarged  to  17*4  in.  diameter. 


BLOWER  No.  1, 


BLOWER  No.  6. 


Ill 
111 


Lengths  of  Blast-pipe  in  Feet. 


50  I  100   150   200   300 


Diameter  in  inches. 


ic  Fee 
transmi 
per  minu 


Lengths  of  Blast-pipe  in  Feet. 


50   100   150   200   300 


Diameter  in  inches. 


360 
515 
635 
740 


3* 

9 


10*4 


1872 

2678 
3302 
3848 


12*4 

13*4 


13% 
16 


BLOWER  No.  2. 


BLOWER  No.  7. 


504 
721 

889 
1036 


8* 
9 
9*6 


m 


8% 


2592 
3708 
4572 
5328 


12 
13% 

16  8 


15 

17*4 
18% 
20 


BLOWER  No.  3. 


BLOWER  No.  8. 


720 
1030 
1270 
1480 


8*4 


3312 

4738 
5842 
6808 


15% 
17% 
19*6 
20M 


18% 
21% 


BLOWER  No.  4. 


BLOWER  No.  9. 


1008 
1442 

1778 
2072 


10% 


4320 

6180 
7620 

8880 


17 


21*6 

24% 
26*^> 
28*6 


BLOWER  No.  5. 


BLOWER  No.  10. 


1440 
2060 
2540 
2960 


11% 


5760 
8240 
10160 
11840 


23% 

27*4 
29% 
31*6 


CENTRIFUGAL   FANS.  521 

Centrifugal  Ventilators  for  Mines.— Of  different  appliances  for 
ventilating  mines  various  forms  of  centrifugal  machines  having  proved  their 
efficiency  have  now  almost  completely  replaced  all  others.  Most  if  not  all 
of  the  machines  in  use  in  this  country  are  of  this  class,  being  either  open- 
periphery  fans,  or  closed,  with  chimney  and  spiral  casing,  of  a  more  or  less 
modified  Guibal  type.  The  theory  of  such  machines  has  been  demonstrated 
by  Mr.  Daniel  Murgue  in  "  Theories  and  Practices  of  Centrifugal  Ventilating 
Machines,"  translated  by  A.  L.  Stevenson,  and  is  discussed  in  a  paper  by  R. 
Van  A.  Norris,  Trans.  A.  I.  M.  E.  xx.  637.  From  this  paper  the  following  for- 
mulas are  taken: 

Let  a  =  area  in  sq.  ft.  of  an  orifice  in  a  thin  plate,  of  such  area  that  its  re- 
sistance to  the  passage  of  a  given  quantity  of  air  equals  the 
resistance  of  the  mine; 

o  =  orifice  in  a  thin  plate  of  such  area  that  its  resistance  to  the  pas- 
sage of  a  given  quantity  of  air  equals  that  of  the  machine; 
Q  =  quantity  of  air  passing  in  cubic  feet  per  minute; 
V=  velocity  of  air  passing  through  a  in  feet  per  second; 
F0  =  velocity  of  air  passing  through  o  in  feet  per  second; 
h  =  head  in  feet  air -column  to  produce  velocity  F; 
h0  =  head  in  feet  air-column  to  produce  velocity  F0. 

Q  =  0.65aF;    V  =  V2gh\     Q  =  0.65a  \/2gh\ 

a  = ^         =  equivalent  orifice  of  mine; 

0.65  \/2gh 

or,  reducing  to  water-gauge  in  inches  and  quantity  in  thousands  of  feet  per 
minute, 

.403Q 


3          =  equivalent  orifice  of  machine. 

The  theoretical  depression  which  can  be  produced  by  any  centrifugal  ven- 
tilator is  double  that  due  to  its  tangential  speed.    The  formula 


in  which  Tis  the  tangential  speed,  Fthe  velocity  of  exit  of  the  air  from  the 
space  between  the  blades,  and  H  the  depression  measured  in  feet  of  air- 
column,  is  an  expression  for  the  theoretical  depression  which  can  be  pro- 
duced by  an  uncovered  ventilator;  this  reaches  a  maximum  when  the  air 
leaves  the  blades  without  speed,  that  is,  F  =  0,  and  H  =  T2  -r-  2.17. 

Heuce  the  theoretical  depression  which  can  be  produced  by  any  uncovered 
ventilator  is  equal  to  the  height  due  to  its  tangential  speed,  and  one  half- 
tliMt  which  can  be  produced  by  a  covered  ventilator  with  expanding 
chimney. 

So  long  as  the  condition  of  the  mine  remains  constant: 

The  volume  produced  by  any  ventilator  varies  directly  as  the  speed  of 
rotation. 

The  depression  produced  by  any  ventilator  varies  as  the  square  of  the 
speed  of  rotation. 

For  the  same  tangential  speed  with  decreased  resistance  the  quantity  of 
air  increases  and  the  depression  diminishes. 

The  following  table  shows  a  few  results,  selected  from  Mr.  Norris's  paper, 
giving  the  range  of  efficiency  which  may  be  expected  under  different  cir- 
cumstances. Details  of  these  and  other  fans,  with  diagrams  of  the  results 
are  given  in  the  paper. 


522 


AIK. 


Experiments  on  Mine-ventilating  Fans. 


0)     • 

1  = 

•<j  o5 

£ 

ll 

lid 

£ 

a 

o'So 

o 

3 

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5517 

236,684 

2818 

3040 

4290 

1.80 

67.13 

88.40 

75.9 

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A  J 

100 

6282 

336,862 

3369 

3040 

5393 

2.50 

132.70 

155.4385.4 

1? 

1 

111 

6973 

347,396 

3130 

3040 

5002 

3.20 

175.17 

209.6483.6 

[ 

123 

7727 

394,100 

3204 

3040 

5100 

3.60 

223.56 

295.21J75.7 

fs 

100 

6282 

188,888 

1889 

1520 

3007 

1.40 

41.67 

97.9942.5 

1 

130 

8167 

274,876 

2114 

1520 

3366 

2.00 

86.63 

194.9544.6 

22 

( 

59 

3702 

59,587 

1010 

1520 

1610 

1.20 

11.27 

16.7667.83 

1 

83 

5208 

82,969 

1000 

1520 

1593 

2.15 

27.86 

48.54  57.38 

( 

40 

3140 

49,611 

1240 

3096 

1580 

0.87 

6.80 

13.8249.2 

32 

D 

70 

5495 

137,760 

1825 

3096 

2507 

2.55 

55.35 

67.44  82.07 

i 

50 

2749 

147,232 

2944 

1522 

5356 

0.50 

11.60 

28.55140.63 

&•< 

69 

3793 

205,761 

2982 

1522 

5451 

1.00 

32.42    45.  98  170.50 

83 

j 

96 

5278 

299,600 

3121 

1522 

5076 

2.15 

101.50  120.64  84.  10j 

200 

7540 

133,198 

666 

746 

1767 

3.35 

70.  30  102.  7968.40|     26.9 

F-| 

200 

7540 

180,809 

904 

746 

2398 

3  05 

86.89-129.0767.30     38.3 

200 

7540 

209,150 

1046 

746 

2774 

2.80 

92.50  150.08  61.70 

46.3 

r 

10 

785 

28,896 

2890 

3022 

3680 

0.10 

0.45 

1.30 

35. 

20 

1570 

57,120 

2856 

3022 

3637 

0.20 

1.80 

3.70 

49. 

25 

1962 

66,640 

2665 

3022 

3399 

0.29 

2.90 

6.10 

48. 

30 

2355 

73,080 

2436 

3022 

3103 

0.40 

4.60 

9.70 

47. 

52 

35 

2747 

94,080 

2688 

3022 

3425 

0.50 

7.40 

15.00 

48. 

G  - 

40 

3140 

112,000 

2800 

3022 

3567 

0.70 

12.30 

24.90 

49. 

50 

3925 

132,700 

2654 

3022 

3381 

0.90 

18.80 

38.80 

48. 

60 

4710 

173,600 

2893 

3022 

3686 

1.35 

36.90    66.40 

55. 

70 

5495 

203,280 

2904 

3022 

3718 

1.80 

57.70107.10 

54. 

I 

80 

6280 

222,320 

2779 

3022 

3540 

2.25 

78.80  152.60 

52. 

Type  of  Fan.  Diam. 

A.  Guibal,  double 20ft. 

B.  Same,  only  left  hand  running.  20 
0.  Guibal 20 

D.  Guibal 25 

E.  Guibal,  double 17^ 

F.  Capell ....  12 

G.  Guibal 25 


Width.    No.  Inlets.     Diam.  Inlets 


6ft. 
6 
6 
8 
4 

10 
8 


4 
4 
2 
1 
4 
2 
1 


8  ft.  10  in. 
8       10 
8       10 
11         6 

8 

7 

12 


An  examination  of  the  detailed  results  of  each  test  in  Mr.  Norris's  table 
sbows  a  mass  of  contradictions  from  which  it  is  exceedingly  difficult  to  draw 
any  satisfactory  conclusions.  The  following,  he  states,  appear  to  be  more 
or  less  warranted  by  some  of  the  figures  : 

1.  Influence  of  the  Condition  of  the  Airways  on  the  Fan.— Mines  with 
varying  equivalent  orifices  give  air  per  100  feet  periphery-motion  of  fan, 
witkin  limits  as  follows,  the  quantity  depending  on  the  resistance  of  the 
mine : 


Equivalent      Cu  Ft.  Air  per 
Orifice.       100  ft.  Periphery- 
speed. 
1100  to  1700 
1300  to  1800 
1500  to  2500 
2300  to  3500 


Under  20  sq.  ft. 
20  to  30 
80  to  40 
40  to  50 
50  to  60 


Aver-    Equivalent    Cu.  Ft.  Air  per   Aver- 
age.       Orifice.      ICO  ft.  Periphery-    age. 

speed. 
3300  to  5100 
4000  to  4700 


2700  to  4800 


1300 
1600 
2100 
2700 
3500 


60  to  70 
70  to  80 
80  to  90 
90  to  100 
100  to  114 


3000  to  5600 
5200  to  6200 


4000 
4400 

4800 

5700 


The  influence  of  the  mine  on  the  efficiency  of  the  fan  does  not  seem  to  be 
very  clear.    Eight  fans,  with  equivalent  orifices  over  50  square  feet,  give 


CENTRIFUGAL  FANS.  523 

efficiencies  over  70^  ;  four,  with  smaller  equivalent  mine-orifices,  give  about 
tbe  same  figures  ;  while,  on  the  contrary,  six  fans,  with  equivalent  orifices  of 
over  50  square  feet,  give  lower  efficiencies,  as  do  ten  fans,  all  drawing  from 
mines  with  small  equivalent  orifices. 

It  would  seem  that,  on  the  whole,  large  airways  tend  to  assist  somewhat 
in  attaining  large  efficiency. 

2.  Influence  of  the  Diameter  of  the  Fan.— This  seems  to  be  practically  nil, 
the  only  advantage  of  large  fans  being  in  their  greater  width  and  the  lower 
speed  required  of  the  engines. 

3.  Influence  of  the  Width  of  a  Fan.— This  appears  to  be  small  as  regards 
the  efficiency  of  the  machine  ;  but  the  wider  fans  are,  as  a  rule,  exhausting 
more  air. 

4.  Influence  of  Shape  of  Blades.— This  appears,  within  reasonable  limits, 
to  be  practically  nil.    Thus,  six  fans  with  tips  of  blades  curved  forward, 
three  fans  with  flat  blades,  and  one  with  blades  curved  back  to  a  tangent 
with  the  circumference,  all  give  very  high  efficiencies-  over  70$. 

5.  Influence  of  the  Shape  of  the  Spiral  Casing. — This  appears  to  be  con- 
siderable    The  shapes  of  spiral  casing  in  use  fall  into  two  classes,  the  first 
presenting  a  large  spiral,  beginning  at  or  near  the  point  of  cut-off,  and  the 
second  a  circular  casing  reaching  around  three  quarters  of  the  circumference 
of  the  fan,  with  a  short  spiral  reaching  to  the  evasee  chimney. 

Fans  having  the  first  form  of  casing  appear  to  give  in  almost  every  case 
large  efficiencies. 

Fans  that  have  a  spiral  belonging  to  the  first  class,  but  very  much  con- 
tracted, give  only  medium  efficiencies.  It  seems  probable  that  the  proper 
shape  of  spiral  casing  would  be  one  of  such  form  that  the  air  between  each 
pair  of  blades  could  constantly  and  freely  discharge  into  the  space  between 
the  fan  and  casing,  the  whole  being  swept  along  to  the  evasee  chimney.  This 
would  require  a  spiral  beginning  near  the  point  of  cut-off,  enlarging  by 
gradually  increasing  increments  to  allow  for  the  slowing  of  the  air  caused  by 
its  friction  against  the  casing,  and  reaching  the  chimney  with  an  area  such 
that  the  air  could  make  its  exit  with  its  then  existing  speed— somewhat  less 
than  the  periphery-speed  of  the  fa,n. 

6.  Influence  of  the  Shutter.— This  certainly  appears  to  be  an  advantage,  as 
by  it  the  exit  area  can  be  regulated  to  suit  the  varying  quantity  of  air  given 
by  the  fan,  and  in  this  way  re-entries  can  be  prevented.    It  is  not  uncommon 
to  find  shutterless  fans  into  the  chimneys  of  which  bits  of  paper  may  be 
dropped,  which  are  drawn  into  the  fan,  make  the  circuit,  and  are  again 
thrown  out.    This  peculiarity  has  not  been  noticed  with  fans  provided  with 
shutters. 

7.  Influence  of  the  Speed  at  which  a  Fan  is  Run.— It  is  noticeable  that 
most  of  the  fans  giving  high  efficiency  were  running  at  a  rather  high 
periphery  velocity.    The  best  speed  seems  to  be  between  5000  and  6000  feet 
per  minute. 

The  fans  appear  to  reach  a  maximum  efficiency  at  somewhere  about  the 
speed  given,  and  to  decrease  rapidly  in  efficiency  when  this  maximum  point 
is  passed. 

In  discussion  of  Mr.  Norris's  paper,  Mr.  A.  H.  Storrs  says:  From  the  "cu- 
bic feet  per  revolution  "  and  "  cubical  contents  of  fan-blades,"  as  given  in  the 
table,  we  find  that  the  enclosed  fans  empty  themselves  from  one  half  to 
twice  per  revolution,  while  the  open  fans  are  emptied  from  one  and  three- 
quarter  to  nearly  three  times.  This  for  fans  of  both  types,  on  mines  cover- 
ing the  same  range  cf  equivalent  orifices.  One  open  fan,  on  a  very  large 
orifice,  was  emptied  nearly  four  times,  while  a  closed  fan,  on  a  still  larger 
orifice,  only  shows  one  and  one-half  times.  For  tbe  open  fans  the  "  cubic 
feet  per  100  ft.  motion  "  is  greater,  in  proportion  to  the  fan  width  and  equiv- 
alent orifice,  than  for  the  enclosed  type.  Notwithstanding  this  apparently 
free  discharge  of  the  open  fans,  they  snow  very  low  efficiencies. 

As  illustrating  the  very  large  capacity  of  centrifugal  fans  to  pass  air,  if 
the  conditions  of  the  mine  are  made  favorable,  a  16-ft.  diam.  fan,  4  ft.  6  in. 
wide,  at  130  revolutions,  passed  360,000  cu.  ft.  per  min.,  and  another,  of  same 
diameter,  but  slightly  wider  and  with  larger  intake  circles,  passed  500,000  cm 
ft ,  the  water-gauge  in  both  instances  being  about  14  in. 

T.  D.  Jones  says :  The  efficiency  reported  in  some  cases  by  Mr.  Norris  is 
larger  than  I  have  ever  been  able  to  determine  by  experiment.  My  own  ex- 
periments, recorded  in  the  Pennsylvania  Mine  Inspectors'  Reports  from  1875 
to  1881,  did  not  show  more  than  60$  to  65^. 


524 


AIR. 


DISK  FANS. 

Experiments    made  with   a  Blackman  Disk   Fan,  4  ft. 

diam.,  by  Geo.  A.  Suter,  to  determine  the  volumes  of  air  delivered  under 
various  conditions,  and  the  power  required;  with  calculations  of  efficiency 
and  ratio  of  increase  of  power  to  increase  of  velocity,  by  G.  H.  Babcock. 
(Trans.  A.  S.  M.  E.,  vii.  54?) : 


o 

1 

1 

i 

h 

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<%££  . 
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&> 

Ratio  of  In- 
crease  of 
Speed. 

Ratio  of  In- 
crease of 
Delivery. 

Ratio  of  In- 
crease of 
Power. 

Exponent  #, 
HP  <x  Fx  . 

Exponent  y, 
h*Vy. 

Efficiency 
of  Fan. 

350 

25,797 

0  65 

1  682 

440 

32,575 

2.29 

1.257 

1.262 

3.523 

5  4 

.9553 

534 
612 

41,929 
47,756 

4.42 
7.41 

1.186 
1.146 

1.287 
1.139 

1.843 
1.677 

2.4 
3  97 



1.062 
.9358 

For 

series 

1.749 

1.851 

11.140 

4. 

340 

20,372 

0  76 

7110 

453 

26,660 

1.99 

1.332 

1.308 

2  618 

3  55 

6063 

536 

31,649 

3.86 

1.183 

1.187 

1.940 

3  86 

5205 

627 

36,543 

6.47 

1.167 

1.155 

1  676 

3  59 

4802 

For 

series 

1  761 

1.794 

8  513 

3  63 

340 

9,983 

1.12 

0.28 

.3939 

430 
534 

570 

13,017 
17,018 
18,649 
For 

3.17 
6.07 
8.46 
series 

0.47 
0.75 
0.87 

1.265 
1.242 

1.068 
1.676 

1.304 
1.307 
1.096 
1.704 

2.837 
1.915 
1.394 
7.554 

3.93 
2.25 
3.63 
3  24 

1.95 
1.74 
1.60 
1  81 

.3046 
.3319 
.3027 

330 

8,399 

1  31 

0  26 

2631 

437 

516 

10,071 
11,157 
For 

3.27 

6.00 
series 

0.45 
0.75 

1.324 

1.181 
1.563 

1.199 
1.108 
1.329 

3.142 

1.457 

4.580 

6.31 
3.66 
5.35 

3.06 
4.96 
3.72 

.2188 
.2202 

Nature  of  the  Experiments.— First  Series:  Drawing:  air  through  30  ft.  of 
48-in.  diam.  pipe  on  inlet  side  of  the  fan. 

Second  Series:  Forcing  air  through  30  ft.  of  48-in.  diam.  pipe  on  outlet  side 
of  the  fan. 

Third  Series:  Drawing  air  through  30  ft.  of  48-in.  pipe  on  inlet  side  of  the 
fan— the  pipe  being  obstructed  by  a  diaphragm  of  cheese-cloth. 

Fourth  Series:  Forcing  air  through  30  ft.  of  48-in.  pipe  on  outlet  side  of  fan 
—the  pipe  being  obstructed  by  a  diaphragm  of  cheese-cloth. 

Mr.  Babcock  says  concerning  these  experiments  :  The  first  four  experi- 
ments are  evidently  the  subject  of  some  error,  because  the  efficiency  is  such 
as  to  prove  on  an  average  that  the  fan  was  a  source  of  power  sufficient  to 
overcome  all  losses  and  help  drive  the  engine  besides.  The  second  series  is 
less  questionable,  but  still  the  efficiency  in  the  first  two  experiments  is  larger 
than  might  be  expected.  In  the  third  and  fourth  series  the  resistance  of  the 
cheese-cloth  in  the  pipe  reduces  the  efficiency  largely,  as  would  be  expected. 
In  this  case  the  value  has  been  calculated  from  the  height  equivalent  to  the 
water-pressure,  rather  than  the  actual  velocity  of  the  air. 

This  record  of  experiments  made  with  the  disk  fan  shows  that  this  kind  of 
fan  is  not  adapted  for  use  where  there  is  any  material  resistance  to  the  flow 
of  the  air.  In  the  centrifugal  fan  the  pover  used  is  nearly  proportioned  to 
the  amount  of  air  moved  under  a  given  head,  while  in  this  fan  the  power  re- 
quired for  the  same  number  of  revolutions  of  the  fan  increases  very  mate- 
rially with  the  resistance,  notwithstanding  the  quantity  of  air  moved  is  at  the 
same  time  considerably  reduced.  In  fact,  from  the  inspection  of  the  third 
and  fourth  series  of  tests,  it  would  appear  that  the  power  required  is  very 
nearly  the  same  for  a  given  pressure,  whether  more  or  less  air  be  in  motion. 
It  would  seem  that  the  main  advantage,  if  any.  of  the  disk  fan  over  the  cen- 
trifugal fan  for  slight  resistances  consists  in  the  fact  that  the  delivery  is  the 
full  area  of  the  disk,  while  with  centrifugal  fans  intended  to  move  the  same 
quantity  of  air  the  opening  is  much  smaller. 


DISK  FAKS. 


525 


It  will  be  seen  by  columns  8  and  9  of  the  table  that  the  power  used  in- 
creased much  more  rapidly  than  the  cube  of  the  velocity,  as  in  centrifugal 
fans.  The  different 'experiments  do  not  agree  with  each  other,  but  a  general 
average  may  be  assumed  as  about  the  cube  root  of  the  eleventh  power. 

Cubic  Feet  of  Air  removed  l>y  Exhaust  IMsk-Avlieel  per 
minute.    (Buffalo  Forge  Co.) 


Number 
of  Revo- 
lutions of 
Wheel 
per 
minute. 

Diameter  of  Wheel. 

24  Inch. 

30  Inch. 

36  Inch. 

42  Inch. 

48  Inch. 

54  Inch. 

60  Inch. 

72  Inch. 

Amount  of  Air  in  cubic  feet  per  minute. 

100... 

4,245 
6,405 
8,686 
11,098 
13,641 
16,315 
19,119 
22,055 
25,127 
28,325 
31,518 
34,310 
36,940 

6,059 
9,154 
12,410 
15,822 
19,408 
23,147 
27,048 
31,112 
35,338 
39,727 
44,277 
48,992 
53,858 

:  8,387 
12,822 
17,457 
22,292 
27,327 
32,565 
37,997 
43,632 
49,467 
55,152 
60,401 

14,936 
22,926 

31,267 
39,956 
48,996 
58,386 
67,985 
76,900 

150.     .  . 

200  

3,594 
4,541 
5,550 
6.621 
7,755 
8,950 
10,210 
11,430 
12,816 
14,265 
15,776 

5,607 
7,079 
8,621 
10,233 
11,915 
13,967 
15,489 
17,381 
19,345 
21,375 
23,420 

250. 

1,307 
1,084 
2,014 
2,375 
2,770 
3,197 
3,656 
4,148 
4,671 
5,221 

2  696 
3^338 
4,042 
4,808 
5,636 
6,516 
7,446 
8,426 
9,456 
10,536 

300.     .  .  . 

350. 

400      .... 

450  

500  

550.   .   .. 

600  
650  

700  

Efficiency  of  Disk  Fans.— Prof .  A.  B.  W.  Kennedy  (Industries,  Jan. 
17,  1890)  made  a  series  of  tests  on  two  disk  fans,  2  and  3  ft.  diameter,  known 
as  the  Verity  Silent  Air-propeller.  The  principal  results  and  conclusions 
are  condensed  below. 

In  each  case  the  efficiency  of  the  fan,  that  is,  the  quantity  of  air  delivered 
per  effective  horse-power,  increases  very  rapidly  as  the  speed  diminishes, 
so  that  lower  speeds  are  much  more  economical  than  higher  ones.  On  the 
other  hand,  as  the  quantity  of  air  delivered  per  revolution  is  very  nearly 
constant,  the  actual  useful  work  done  by  the  fan  increases  almost  directly 
with  its  speed.  Comparing  the  large  and  small  fans  with  about  the  same 
air  delivery,  the  former  (running  at  a  much  lower  speed,  of  course)  is  much 
the  more  economical.  Comparing  the  two  fans  running  at  the  same  speed, 
however,  the  smaller  fan  is  very  much  the  more  economical.  The  delivery 
of  air  per  revolution  of  fan  is  very  nearly  directly  proportional  to  the  area 
of  the  fan's  diameter. 

The  air  delivered  per  minute  by  the  3-ft.  fan  is  nearly  12.5.R  cubic  feet 
(R  being  the  number  of  revolutions  made  by  the  fan  per  minute).  For  the 
2-t't.  fan  the  quantity  is  5.7R  cubic  feet.  For  either  of  these  or  any  other 
similar  fans  of  which  the  area  is  A  square  feet,  the  delivery  will  be  about 
1.8AR  cubic  feet.  Of  course  any  change  in  the  pitch  of  the  blades  might 
entirely  change  these  figures. 

The  net  H.P.  taken  up  is  not  far  from  proportional  to  the  square  of  the 
number  of  revolutions  above  100  per  minute.  Thus  for  the  3-ft.  fan  the  net 

H-p-  is  naff  { while  for  the  2-ft- fan  the  net  H-p- is  f w  • 

The  denominators  of  these  two  fractions  are  very  nearly  proportional  in- 
versely to  the  square  of  the  fan  areas  or  the  fourth  power  of  the  fan  diam- 
eters. The  net  H.P.  required  to  drive  a  fan  of  diameter  D  feet  or  area  A 
square  feet,  at  a  speed  of  R  revolutions  per  minute,  will  therefore  be  ap- 

— *  - 

The  2-ft.  fan  was  noiseless  at  all  speeds.  The  3-ft.  fan  was  also  noiseless 
up  to  over  450  revolutions  per  minute. 


526 


Alfi. 


Propeller, 
2  ft.  diam. 

Propeller, 
3ft.  diam. 

Speed  of  fan,  revolutions  per  minute. 
Net  H.P.  to  drive  fan  and  belt  

750 
0.42 

676 
0.32 

577 
0.227 

576 
1.02 

459 
0.575 

373 
0.324 

Cubic  feet  of  air  per  minute  

4,183 

3,830 

3,410 

7,400 

5,800 

4,470 

Mean  velocity  of  air  in  3-f  t.  flue,  feet 

per  minute               .... 

593 

543 

482 

1  046 

820 

632 

Mean   velocity  of  air  in  flue,   same 

diameter  as  fan  

1,330 

1,220 

1,085 

Cu.ft.of  air  perm  in.  per  effective  H.P. 

9,980 

11,970 

15,000 

7,250 

10,070 

13,800 

Motion  given  to  air  per  rev.  of  fan,  ft. 
Cubic  feet  of  air  per  rev.  of  fan  

1.77 

5.58 

1.81 
5.66 

1.88 
5.90 

1.82 
12.8 

1.79 
12.6 

1.70 
12.0 

POSITIVE    ROTARY    BLOWERS.    (P.  H.  &  F.  M.  Roots.) 


Size  number  

V£ 

1 

2 

3 

4 

5 

6 

7 

Cubic  feet  per  revolution  

11^3 

3 

5 

8 

13 

23 

42 

65 

Revolutions      per      minute, 
Smith  fires  

•{  to 
/350 

to 
300 

225 
to 
275 

200 
to 
250 

175 
to 
225 

150 
to 

200 

125 
to 
175 

100 
to 
150 

75 
to 

125 

Furnishes    blast    for    Smith 

(     2 

6 
to 

10 
to 

16 
to 

24 
to 

32 
to 

47 
to 

70 
to 

80 
to 

1  *  4 

8 

14 

20 

30 

43 

67 

100 

135 

Revolutions  per  minute  for 
cupola,  melting  iron  

i:: 

275 
to 
375 

275 
to 
325 

200 
to 
300 

185 
to 
275 

170 
to 

250 

150 
to 
200 

137 
to 
175 

Size    of   cupola,    inches,   in- 
side lining  

I: 

18 
to 

24 
to 

30 

30 
to 
36 

36 
to 
42 

42 
to 
50 

50        72 
to        or 
60  2-55's 

(  ... 

\\/^ 

2^£ 

3 

4% 

8 

12J^> 

17*^» 

Will  melt  iron  per  hour,  tons 

] 

to 

to 

to 

to 

to 

to 

to 

... 

2 

3 

4% 

7 

12 

WM 

22% 

Horse-power  required 1        2    3^    5^       8    11^    17%       27       40 

The  amount  of  iron  melted  is  based  on  30,000  cubic  feet  of  air  per  ton  of 
iron.  The  horse-power  is  for  maximum  speed  and  a  pressure  of  %  pound, 
ordinary  cupola  pressure.  (See  also  Foundry  Practice.) 

BLOWING-ENGINES. 

Blast-furnace   Blowing-engines  of  the  Variable  Puppet- 
valve  Cut-off  Type.    (Philada.  Engineering  Works.) 


Diameter 

Diameter 

Shop 

Revolu- 

Displace- 

Maximum 

of 
Steam- 
cylinder. 

of 
Blowing- 
cylinder. 

Stroke. 

Weights, 
approxi- 
mate. 

tions, 
ordinary 
speed. 

Piston  per 
minute  at 
ordinary 

Blast-pres- 
sure for  Reg- 
ular Work. 

speed. 

in. 

in. 

in. 

pounds. 

cubic  feet. 

Ibs.  per  so.  in. 

28 

66 

36 

80,000 

60 

8,550 

10 

28 

66 

48 

90,000 

50 

9,500 

10 

32 

72 

48 

106,000 

50 

11,308 

12 

36 

72 

48 

130,000 

50 

11,308 

15 

36 

84 

48 

140,000 

50 

15,392 

11 

36 

84 

60 

165,000 

40 

15,392 

11 

42 

84 

48 

165,000 

50 

15,392 

15 

42 

84 

60 

190,000 

40 

15,392 

15 

42 

90 

48 

170,000 

50 

17,700 

13 

42 

90 

60 

195,000 

40 

17,700 

13 

48 

96 

48 

220,000 

50 

20,000 

15 

48 

96 

60 

280,000 

40 

20,000 

15 

The  blowing-engines  of  the  country  are  usually  very  wasteful  of  steam, 
by  reason  of  wire-drawing  valve-gear,  and  especially  of  slow  piston-speed. 
The  latter  is  perhaps  the  greatest  and  the  least  recognized  of  all  steam- 
engine  defects.  Almost  any  expense  to  increase  the  economy  of  blowing- 
engines  is  warranted.  (A.  L.  Holley,  Trans.  A.  I.  M.  E.,  vol.  iv.  p.  81.) 


STEAM-JET  BLOWER  AND   EXHAUSTER. 


527 


The  calculations  of  power,  capacity,  etc.,  of  blowing-engines  are  the  same 
as  those  for  air-compressors.  They  are  built  without  any  provision  for 
cooling  the  air  during  compression.  About  400  feet  per  minute  is  the  usual 
piston-speed  for  recent  forms  of  engines,  but  with  positive  air-valves,  which 
have  been  introduced  to  some  extent,  this  speed  may  be  increased.  The 
efficiency  of  the  engine,  that  is,  the  ratio  of  the  I.H.P.  of  the  air  cylinder  to 
that  of  the  steam  cylinder,  is  usually  taken  at  90  per  cent,  the  losses  by 
friction,  leakage,  etc.,  being  taken  at  10  per  cent. 

STEAM-JET  BLOWER  AND  EXHAUSTER. 

A  blower  and  exhauster  is  made  by  L.  Schutte  &  Co.,  Philadelphia,  on 
the  principle  of  the  steam-jet  ejector.  The  following  is  a  table  of  capacities: 


Size 
No. 

Quantity  of 
Air  per  hour 
in 
cubic  feet. 

Diameter  of 
Pipes  in  inches. 

Size 
No. 

Quantity  of 
Air  per  hour 
in 
cubic  feet. 

Diameter  of 
Pipes  in  inches. 

Steam. 

Air. 

Steam. 

Air. 

000 
00 
0 

1 

2 

3 

4 

1,000 
2,000 
4,000 
6,000 
12,000 
18,000 
24,000 

1  4 

2 
2 

^ 

•Hi 

3^ 
4 

5 
6 

7 
8 
9 
10 

30,000 
36,000 
42,000 
48,000 
54,000 
60,000 

3 
3 

5 
6 
6 

7 
7 
8 

The  admissible  vacuum  and  counter  pressure,  for  which  the  apparatus  is 
constructed,  is  up  to  a  rarefaction  of  20  inches  of  mercury,  and  a  counter- 
pressure  up  to  one  sixth  of  the  steam-pressure. 

The  table  of  capacities  is  based  on  a  steam- pressure  of  about  60  Ibs.,  and 
a  counter-pressure  of  about  8  Ibs.  With  an  increase  of  steam-pressure  or 
decrease  of  counter-pressure  the  capacity  will  largely  increase. 

Another  steam- jet  blower  is  used  for  boiler-firing,  ventilation,  and  similar 
purposes  where  a  low  counter-pressure  or  rarefaction  meets  the  require- 
ments. 

The  volumes  as  given  in  the  following  table  of  capacities  are  under  the 
supposition  of  a  steam-pressure  of  45  Ibs.  and  a  counter-pressure  of,  say, 
2  inches  of  water  : 


Size 
No. 

Cubic 
feet  of 
Air 
delivered 
per  hour. 

Diameter 
of 
Steam- 
pipe  in 
inches. 

Diameter  in 
inches  of  — 

Size 
No. 

Cubic 
feet  of 
Air  de- 
livered 
per  hour 

Diam. 
of 
Steam- 
pipe  in 
inches. 

Diameter  in 
inches  of  — 

Inlet 

Disch. 

Tnlet. 

Disch. 

00 
0 
1 
2 
3 

6,000 
12,000 
30,000 
60,000 
125,000 

1 

4 
5 

8 
11 
14 

3 

4 
6 
8 
10 

4 
6 
8 
10 

250,000 
500,000 
1,000,000 
2,000,000 

1 

*M 

P 

17 
24 
32 
42 

14 
20 

27 
36 

The  Steam-jet  as  a  Means  for  Ventilation.— Between  1810 
and  1850  the  steam-jet  was  employed  to  a  considerable  extent  for  ventilat- 
ing English  collieries,  and  in  1852  a  committee  of  the  House  of  Commons 
reported  that  it  was  the  most  powerful  and  at  the  same  time  the  cheapest 
method  for  the  ventilation  of  mines  ;  but  experiments  made  shortly  after- 
wards proved  that  this  opinion  was  erroneous,  and  that  furnace  ventilation 
was  less  than  half  as  expensive,  and  in  consequence  the  jet  was  soon  aban- 
doned as  a  permanent  method  of  ventilation. 

For  an  account  of  these  experiments  see  Colliery  Engineer,  Feb.  1890. 
The  jet,  however,  is  sometimes  advantageously  used  as  a  substitute,  for 
instance,  in  the  case  of  a  fan  standing  for  repairs,  or  after  an  explosion, 
when  the  furnace  may  not  be  kept  going,  or  in  the  case  of  the  fan  having 
been  rendered  useless. 


528  HEATIKG  AHD  VEOTILATIOH. 


HEATING   AND   VENTILATION. 

Ventilation.  (A.  R.  Wolff,  Stevens  Indicator,  April,  1890.)—  The  pop- 
ular impression  that  the  impure  air  falls  to  the  bottom  of  a  crowded  room 
is  erroneous.  There  is  a  constant  mingling  of  the  fresh  air  admitted  with 
the  impure  air  due  to  the  law  of  diffusion  of  gases,  to  difference  of  temper- 
ature, etc.  The  process  of  ventilation  is  one  of  dilution  of  the  impure  pir 
by  the  fresh,  and  a  room  is  properly  ventilated  in  the  opinion  of  the  hygien- 
ists  when  the  dilution  is  such  that  the  carbonic  acid  in  the  air  does  not  ex- 
ceed from  6  to  8  parts  by  volume  in  10,000.  Pure  country  air  contains  about 
4  parts  CO2  in  10,000,  and  badly-ventilated  quarters  as  high  as  80  parts. 

An  ordinary  man  exhales  0.6  of  a  cubic  foot  of  COa  per  hour.  New  York 
gas  gives  out  0.75  of  a  cubic  foot  of  CO2  for  each  cubic  foot  of  gas  burnt. 
An  ordinary  lamp  gives  out  1  cu.  ft.  of  CO2  per  hour.  An  ordinary  candle 
gives  out  0'.3  cu.  ft.  per  hour.  One  ordinary  gaslight  equals  in  vitiating 
effect  about  5J4  men,  an  ordinary  lamp  \%  men,  and  an  ordinary  candle  ^ 
man. 

To  determine  the  quantity  of  air  to  be  supplied  to  the  inmates  of  an  un- 
lighted  room,  to  dilute  the  air  to  a  desired  standard  of  purity,  we  can  estab- 
lish equations  as  follows: 
Let  v  =  cubic  feet  of  fresh  air  to  be  supplied  per  hour; 

r  =  cubic  feet  of  CO2  in  each  10,000  cu.  ft.  of  the  entering  air: 

R  =  cubic  feet  of  CO2  which  each  10,000  cu.  ft.  of  the  air  in  the  room 

may  contain  for  proper  health  conditions; 
n  —  number  of  persons  in  the  room  ; 
.6  =  cubic  feet  of  CO2  exhaled  by  one  man  per  hour. 

Then  v  ,  J*  +  .6n  equals  cubic  feet  of  C02  communicated  to  the  room  dur- 
ing one  hour. 

This  value  divided  by  v  and  multiplied  by  10,000  gives  the  proportion  of 
CO2  in  10,000  parts  of  the  air  in  the  room,  and  this  should  equal  JR,  the  stan- 
dard of  purity  desired.  Therefore 


600071 
or  v  =  -—  —  ......   (1) 


If  we  place  r  at  4  and  R  at  6,  v  =    -^~n  =  30°0?i, 


or  the  quantity  of  air  to  be  supplied  per  person  is  3000  cubic  feet  per  hour. 

If  the  original  air  in  the  room  is  of  the  purity  of  external  air,  and  the  cubic 
contents  of  the  room  is  equal  to  100  cu.  ft.  per  inmate,  only  3000  -  100  =  2900 
cu.  ft.  of  fresh  air  from  without  will  have  to  be  supplied  the  first  hour  to 
keep  the  air  within  the  standard  purity  of  6  parts  of  CO2  in  10,000.  If  the 
cubic  contents  of  the  room  equals  200  cu.'ft.  per  inmate,  only  3000  -  200  =  2800 
cu.  ft.  will  have  to  be  supplied  the  first  hour  to  keep  the  air  within  the 
standard  purity,  and  so  on. 

Again,  if  we  only  desire  to  maintain  a  standard  of  purity  of  8  parts  of 
carbonic  acid  in  10,000,  equation  (1)  gives  as  the  required  air-supply  per  hour 

6000 
v  =  -=  —  -n  =  1500?i,  or  1500  cu.  ft.  of  fresh  air  per  inmate  per  hour. 

Cubic  feet  of  air  containing  4  parts  of  carbonic  acid  in  10,000  necessary  per 
person  per  hour  to  keep  the  air  in  room  at  the  composition  of 

„  ft  1A         IK         on    f  parts  of  carbonic  acid  in 

6  7  10         15         20    -^     10?ooa 

3000       2000       1500       1200       1000       545       375     cubic  feet. 

If  the  original  air  in  the  room  is  of  purity  of  external  atmosphere  (4  parts 
of  carbonic  acid  in  10,000),  the  amount  of  air  to  be  supplied  the  first  hour, 
for  given  cubic  spaces  per  inmate,  to  have  given  standards  of  purity  not 
exceeded  at  the  end  of  the  hour  is  obtained  from  the  following  table  : 


VENTILATION. 


529 


Cubic  Feet 
of 
Space 
in  Room 
per 
Individual. 

Proportion  of  Carbonic  Acid  in  10,000  Parts  of  the  Air,  not  to 
be  Exceeded  at  End  of  Hour. 

6 

7 

8 

9 

10 

15 

20 

Cubic  Feet  of  Air,  of  Composition  4  Parts  of  Carbonic  Acid  in 
10,000,  to  be  Supplied  the  First  Hour. 

100 
200 
300 
400 
500 
600 
700 

aoo 

900 
1000 
1500 
2000 
2500 

2900 
2800 
2700 
2600 
2500 
2400 
2300 
2200 
2100 
2000 
1500 
1000 
500 

1900 
1800 
1700 
1600 
1500 
1400 
1300 
1200 
1100 
1000 
500 
None 

1400 
1300 
1200 
1100 
1000 
900 
800 
700 
600 
500 
None 

1100 
1000 
900 
800 
700 
600 
500 
400 
300 
200 
None 

900 
800 
700 
600 
500 
400 
300 
200 
100 
None 

445 
345 
245 
145 
45 
None 

275 
175 
75 
None 

It  is  exceptional  that  systematic  ventilation  supplies  the  3000  cubic  feet 
per  inmate  per  hour,  which  adequate  health  considerations  demand.  Large 
auditoriums  in  which  the  cubic  space  per  individual  is  great,  and  in  which 
the  atmosphere  is  thoroughly  fresh  before  the  rooms  are  occupied,  and  the 
occupancy  is  of  two  or  three  hours'  duration,  the  systematic  air-supply  may 
be  reduced,  and  2000  to  2500  cubic  feet  per  inmate  per  hour  is  a  satisfactory 
allowance. 

Hospitals  where,  on  account  of  unhealthy  excretions  of  various  kinds,  the 
air-dilution  must  be  largest,  an  air-supply  of  from  4000  to  6000  cubic  feet  per 
inmate  per  hour  si  ionic!  be  provided,  and  this  is  actually  secured  in  some 
hospitals.  A  report  dated  March  15,  1882,  by  a  commission  appointed  to 
examine  the  public  schools  of  the  District  of  Columbia,  says  : 

"In  each  class-room  not  less  than  15  square  feet  of  floor-space  should  be 
allotted  to  each  pupil.  In  each  class-room  the  window-space  should  not  be 
less  than  one  fourth  the  floor-space,  and  the  distance  of  desk  most  remote 
from  the  window  should  not  be  more  than  one  and  a  half  times  the  height  of 
the  top  of  the  window  from  the  floor.  The  height  of  the  class  room  should 
never  exceed  14  feet.  The  provisions  for  ventilation  should  be  such  as  to 
provide  for  each  person  in  a  class-room  not  less  than  30  cubic  feet  of  fresh 
air  per  minute  (1800  per  hour),  which  amount  must  be  introduced  and 
thoroughly  distributed  without  creating  unpleasant  draughts,  or  causing  any 
two  parts  of  the  room  to  differ  in  temperature  more  than  2°  Fahr.,  or  the 
maximum  temperature  to  exceed  70°  Fahr." 

When  the  air  enters  at  or  near  the  floor,  it  is  desirable  that  the  velocity  of 
inlet  should  not  exeee.l  2  feet  per  second,  which  means  larger  sizes  of 
register  openings  and  fines  than  are  usually  obtainable,  and  much  higher 
velocities  of  inlet  than  two  feet  per  second  are  the  rule  in  practice.  The 
velocity  of  current  into  vent-flues  can  safely  be  as  high  as  6  or  even  10  feet 
per  second,  without  being  disagreeably  perceptible. 

The  entrance  of  fresh  air  into  a  room  is  co-incident  with,  or  dependent  on, 
the  removal  of  an  equal  amount  of  air  from  the  room.  The  ordinary  means 
of  removal  is  the  vertical  vent-duct,  rising  to  the  top  of  the  building.  Some- 
times reliance  for  the  production  of  the  current  in  this  vent-duct  is  placed 
solely  on  the  difference  of  temperature  of  the  air  in  the  room  and  that  of 
the  external  atmosphere:  sometimes  a  steam  coil  is  placed  within  the  flue 
near  its  bottom  to  heat  the  air  within  the  duct;  sometimes  steam  pipes 
(risers  and  returns)  run  up  the  duct  performing  the  same  functions;  or  steam 
jets  within  the  flue,  or  exhaust  fans,  driven  by  steam  or  electric  power,  act 
directly  as  exhausters;  sometimes  the  heating  oE  the  air  in  the  flue  is  ac- 
complished by  gas-jets. 

The  draft  of  such  a  duct  is  caused  by  the  difference  of  weight  of  thd 


530 


HEATING  AKD  VENTILATION. 


heated  air  in  the  duct,  and  a  column  of  equal  height  and  cross-sectional  area 
of  weight  of  the  external  air. 

Let  d  =  density,  or  weight  in  pounds,  of  a  cubic  foot  of  the  external  air. 

Let  dl  =  density,  or  weight  in  pounds,  of  a  cubic  foot  of  the  heated  air 
within  the  duct. 

Let  h  =  vertical  height,  in  feet,  of  the  vent-duct. 

h(d  —  d^  =  the  pressure,  in  pounds  per  square  foot,  with  which  the  air  is 
forced  into  and  out  of  the  vent-duct. 

This  pressure  can  be  expressed  in  height  of  a  column  of  the  air  of  density 
within  the  vent-duct,  and  evidently  the  height  of  such  column   of  equal 
.    ,  h(d  —  d,) 

presssu re  would  be,,       — -; — - (3) 

.  "i 

Or,  if  t  =  absolute  temperature  of  external  air,  and  tv  —  absolute  temper- 
ature of  the  air  in  vent-duct  in  the  form,  then  the  pressure  equals 


afr3 (4) 

The  theoretical  velocity,  in  feet  per  second,  with  which  the  air  would 
travels  through  the  vent-duct  under  this  pressure  is 


=  8.02  , 


The  actual  velocity  will  be  considerably  less  than  this,  on  account  of  loss 
due  to  friction.  This  friction  will  vary  with  the  form  and  cross-sectional 
area  of  the  vent-duct  and  its  connections,  and  with  the  degree  of  smooth- 
ness of  its  interior  surface.  On  this  account,  as  well  as  to  prevent  leakage 
of  air  through  crevices  in  the  wall,  tin  lining  of  vent-flues  is  desirable. 

The  loss  by  friction  may  be  estimated  at  approximately  50$,  and  so  we  find 
for  the  actual  velocity  of  the  air  as  it  flows  through  the  vent-duct : 


2gh- 


-O 
t 


,  or,  approximately,  v  =  4  4 


(6) 


If  V=  velocity  of  air  in  vent-duct,  in  feet  per  minute,  and  the  external  air 
be  at  32°  Fahr.,  since  the  absolute  temperature  on  Fahrenheit  scale  equals 
thermometric  temperature  plus  459.4, 


V  =  240  A 


from  which  has  been  computed  the  following  table  : 

Quantity  of  Air,  in  Cubic  Feet,  Discharged  per  Minute 
through  a  Ventilating  Duet,  of  which  the  Cross-sec- 
tional Area  is  One  Square  Foot  (the  External  Tempera- 
ture of  Air  being  32°  Fahr.). 


Height  of 
Vent-duct  in 


Excess  of  Temperature  of  Air  in  Vent-duct  above  that  of 
External  Air. 


feet. 

5° 

10° 

15° 

20° 

25° 

30° 

50° 

100° 

150° 

10 

77 

108 

133 

153 

171 

188 

242 

342 

419 

15 

94 

133 

362 

188 

210 

230 

297 

419 

514 

20 

108 

153 

188 

217 

242 

265 

342 

484 

593 

25 

121 

171 

210 

242 

271 

297 

383 

541 

663 

30 

133 

188 

230 

265 

297 

325 

419 

593 

726 

35 

143 

203 

248 

286 

320 

351 

453 

640 

784 

40 

153 

217 

265 

306 

342 

375 

484 

656 

838 

45 

162 

230 

282 

325 

363 

398 

514 

476 

889 

50 

171 

242 

297 

342 

383 

419 

541 

278 

937 

Multiplying  the  figures  in  above  table  by  60  gives  the  cubic  feet  of  air  dis- 
charged per  hour  per  square  foot  of  cross-section  of  vent-duct.    Knowing 


MINE-VEKTILATIOtf.  531 

the  cross-sectional  area  of  vent-ducts  we  can  find  the  total  discharge;  or 
for  a  desired  air-removal,  we  can  proportion  the  cross-sectional  area  of 
vent-ducts  required. 

Artificial  Cooling  of  Air  for  Ventilation.  (Engineering 
Neivs,  July  7,  1892.) — A  pound  of  coal  used  to  make  steam  for  a  fairly  effi- 
cient refrigerating-machine  can  produce  an  actual  cooling  effect  equal  to 
that  produced  by  the  melting  of  16  to  46  Ibs.  of  ice,  the  amount  varying 
with  the  conditions  of  working.  Or,  855  heat-units  per  Ib.  of  coal  converted 
into  work  in  the  refrigerating  plant  (at  the  rate  of  3  Ibs.  coal  per  horse- 
power hour)  will  abstract  2275  to  0545  heat-units  of  heat  from  the  refriger- 
ated body.  If  we  allow  2000  cu.  ft.  of  fresh  air  per  hour  per  person  as  suffi- 
cient for  fair  ventilation,  with  the  air  at  an  initial  temperature  of  80°  F.,  its 


ng  0.238.  will  requir 
units  per  person  per  hour. 

Taking  the  figures  given  for  the  refrigerating  effect  per  pound  of  coal  as 
above  stated,  and  the  required  abstraction  of  350  heat-units  per  person  per 
hour  to  have  a  satisfactory  cooling  effect,  the  refrigeration  obtained  from  a 
pound  of  coal  will  produce  this  cooling  effect  for  2275  -s-  350  =  6J4  hours  with 
the  least  efficient  working,  or  6545  -^-  3~>0  =  18.7  hours  with  the  tnost  efficient 
working.  With  ice  at  $5  per  ton,  Mr.  Wolff  computes  the  cost  of  cooling  with 
ice  at  about  $5  per  hour  per  thousand  persons,  and  concludes  that  this  is  too 
expensive  for  any  general  use.  With  mechanical  refrigeration,  however,  if 
we  assume  10  hours'  cooling  per  person  per  pound  of  coal  as  a  fair  practical 
service  in  regular  work,  we  have  an  expense  of  only  15cts.  per  thousand 
persons  per  hour,  coal  being  estimated  at  $3  per  short  ton.  This  is  for  fuel 
alone,  and  the  various  items  of  oil,  attendance,  interest,  and  depreciation  on 
the  plant,  etc.,  must  be  considered  in  making  up  the  actual  total  cost  of 
mechanical  refrigeration. 

Mine-ventilation—  Friction  of  Air  in  Underground  Pas- 
sages.— In  ventilating  a  mine  or  other  underground  passage  the  resistance 
to  be  overcome  is,  according  to  most  w  liters  on  the  subject,  proportional  to 
the  extent  of  the  frictional  surface  exposed;  that  is,  to  the  product  lo  of  the 
length  of  the  gangway  by  its  perimeter,  to  the  density  of  the  air  in  circula- 
tion, to  the  square  of  its  average  speed,  v,  and  lastly  to  a  coefficient  fc,  whose 
numerical  value  varies  according  to  the  nature  of  the  sides  of  the  gangway 
and  the  irregularities  of  its  course. 

The  formula  for  the  loss  of  head,  neglecting  the  variation  in  density  as 

ksv^ 
unimportant,  is  p  =  -  ,  in  which  p  =  loss  of  pressure  in  pounds  per  square 

foot,  s  =  square  feet  of  rubbing-surface  exposed  to  the  air,  v  the  velocity  of 
the  air  in  feet  per  minute,  a  the  area  of  the  passage  in  square  feet,  and  k  the 
coefficient  of  friction.  W.  Fairley,  in  Colliery  Engineer,  Oct.  and  Nov. 
1893,  gives  the  following  formulae  for  all  the  quantities  involved,  using  the 
same  notation  as  the  above,  with  these  additions  :  h  =  horse-power  of  ven- 
tilation; I  =  length  of  air-channel;  o  =  perimeter  of  air-channel;  q  =  quan- 
tity of  air  circulating  in  cubic  feet  per  minute;  u  =  units  of  work,  in  foot- 
pounds, applied  to  circulate  the  air:  w  =  water-gauge  in  inches.  Then, 

_  7csi>2_  Jcsv^q  __  ksv3       u  _  q 
p   ~      u  pv  ~  pv~  v 

o   ;,  _  9P        5-2gw 

~~ 


_  _ 

33,000  "  33,000  ~  33,000  * 

p  5. 


*  -*-  a~  sv*  -T-  a" 


4    j-=L 
;  o      kv*o  ' 


pa 


6        ^=u  =  52w=     /Mfcf  =  ^!  =  JL, 

a        q  V  r    *»/    a        g         au 


532 


HEATIKG  AKD   VENTILATION. 


/      3    —  \2 

7.  pa  =  ksv*  -  I  A/~\  ks  =  *;    pa3  =  ksq*. 
\V   ksj  v 


11    «=--  =     =  =  A 

pa      a      Y   ks       y 


To  find  the  quantity  of  air  with  a  given  horse-power  and  efficiency  (e)  of 
engine: 

_  h  X  33,000  X  e 

P 

The  value  of  fe,  the  coefficient  of  friction,  as  stated,  varies  according  to 
the  nature  of  the  sides  of  the  gangway.  Widely  divergent  values  have  been 
given  by  different  authorities  (see  Colliery  Engineer,  Nov.  1893),  the  most 
generally  accepted  one  until  recently  being  probably  that  of  J.  J.  Atkinson, 
.0000000217,  which  is  the  pressure  per  square  foot  in  decimals  of  a  pound  for 
each  square  foot  of  rubbing-surface  and  a  velocity  of  one  foot  per  minute. 
Mr.  Fairley,  in  his  "  Theory  and  Practice  of  Ventilating  Coal-mines,"  gives  a 
value  less  than  half  of  Atkinson's,  or  .00000001 ;  and  recent  experiments  by  D. 
Murgue  show  that  even  this  value  is  high  under  most  conditions.  Murgue's 
results  are  given  in  his  paper  on  Experimental  Investigations  in  the  Loss  of 
Head  of  Air  currents  in  Underground  Workings,  Trans.  A.  I.  M.  EJ.,  1893. 
vol.  xxiii.  63.  His  coefficients  are  given  in  the  following  table,  as  determined 
in  twelve  experiments: 

Coefficient  of  Loss  of 

Head  by  Friction. 
French.        British. 

f  Straight,  normal  section 00092      . 000.000,00486 

Rock.        J  Straight,  normal  section 00094      .000,000,00497 

gangways,    j  Straight,  large  section 00104      .000,000.00549 

[Straight,  normal  section ...   .00122      .000,000,00645 

f  Straight,  normal  section 00030      .000,000,00158 

Brick-lined    |  Straight,  normal  section 00036      . 000,000,00190 

arched       *i  Continuous  curve,  normal  section 00062       .000.000  00328 

gangways.    |  Sinuous,  intermediate  section 00051       .000,000,00269 

L  Sinuous,  small  section 00055      .000.000,00291 

rp.    .    „   ,     (  Straight,  normal  section .00168      .000.000,00888 

a    •<  Straight,  normal  section 00144       .000,000,00761 

;angways.    j  slightly  sinuous,  small  section .00238      .000,000,01257 

The  French  coefficients  which  are  given  by  Murgue  represent  the  height 
of  water-gauge  in  millimetres  for  each  square  metre  of  rubbing-surface  and 
a  velocity  of  one  metre  per  second.  To  convert  them  to  the  British  measure 
of  pounds  per  square  foot  for  each  square  foot  of  rubbing-surface  and  a 
velocity  of  one  foot  per  minute  they  have  been  multiplied  by  the  factor  of 
conversion,  .000005283.  For  a  velocity  of  1000  feet  per  minute,  since  the  loss 
of  head  varies  as  v2,  move  the  decimal  point  in  the  coefficients  six  places  to 
the  right 


FAKS  AtfD  HEATED  CHIMKEYS  FOE  VEHTILATIOtf.  533 

Equivalent  Orifice.—  The  head  absorbed  by  the  working-chambers 
of  a  mine  cannot  be  computed  a  priori,  because  the  openings,  cross-pas- 
sages, irregular-shaped  gob-piles,  and  daily  changes  in  the  size  and  shape  of 
the   chambers   present    much  too   complicated  a  network   for   accurate 
analysis.    In  order  to  overcome  this  difficulty  Murgue  proposed  in  1872  the 
method  of  equivalent  orifice.    This  method  consists  in  substituting  for  the 
mine  to  be  considered  the  equivalent  thin-lipped  orifice,  requiring  the  same 
height  of  head  for  the  discharge  of  an  equal  volume  of  air.    The  area  of 
this  orifice  is  obtained  when  the  head  and  the  discharge  are  known,  by 
means  of  the  following  formulae,  as  given  by  Fairley: 
Let  Q  —  quantity  of  air  in  thousands  of  cubic  feet  per  minute; 
w  =  inches  of  water-gauge; 
A  —  area  in  square  feet  of  equivalent  orifice. 
Then 


Motive  Column  or  the  Head  of  Air  Due  to  Differences 
of  Temperature^  etc.    (Fairley.) 
Let  Jf  =  motive  column  in  feet; 
T  =  temperature  of  upcast; 
/  =  weight  of  one  cubic  foot  of  the  flowing  air; 
t  =  temperature  of  downcast; 
D  —  depth  of  downcast. 
Then 

v-fxM-     w-fXM-    P 
•  '~~- 


To  find  diameter  of  a  round  airway  to  pass  the  same  amount  of  air  as  a 
square  airway  the  length  and  power  remaining  the  same: 

Let  D  =  diameter  of  round  airway,  A  =  area  of  square  airway;  O—  peri- 

6/~A*  X  3.1416 
meter  of  square  airway.    ThenD3  =  /4/     .78543  x  Q  ' 

If  two  fans  are  employed  to  ventilate  a  mine,  each  of  which  when  worked 
separately  produces  a  certain  quantity,  which  may  be  indicated  by  A  and  B 
then  the  quantity  of  air  that  will  pass  when  the  two  fans  are  worked  together 

will  be  A/ A3  -j-  fi*.     (For  mine-ventilating  fans,  see  page  521.) 

Relative  Efficiency  of  Fans  and  Heated  Chimneys  for 
Ventilation.— W.  P.  Trow  bridge,  Trans.  A.  S.  M.  E.  vii.  53J,  gives  a  theo- 
retical solution  of  the  relative  amounts  of  heat  expended  to  remove  a  given 
volume  of  impure  air  by  a  fan  and  by  a  chimney.  Assuming  the  total  effi- 
ciency of  a  fan  to  be  only  1/25,  which  is  made  up  of  an  efficiency  of  1/10  for 
the  engine,  5/10  for  the  fan  itself,  and  8/10  for  efficiency  as  regards  friction, 
the  fan  requires  an  expenditure  of  heat  to  drive  it  of  only  1/38  of  the  amount 
that  would  be  required  to  produce  the  same  ventilation  by  a  chimney  100  ft. 
high.  For  a  chimney  500  ft.  high  the  fan  will  be  7.6  times  more  efficient. 

In  all  cases  of  moderate  ventilation  of  rooms  or  buildings  where  the  air 
is  heated  before  it  enters  the  rooms,  and  spontaneous  ventilation  is  pro- 
duced by  the  passage  of  this  heated  air  upwards  through  vertical  flues, 
no  special  heat  is  required  for  ventilation;  and  if  such  ventilation  be  suffi- 
cient, the  process  is  faultless  as  far  as  cost  is  concerned.  This  is  a  concjit''^. 
of  things  which  may  be  realized  in  most  dwelling  houses,  and  in  many  halls, 
schoolrooms,  and  public  buildings,  provided  inlet  and  outlet  flues  of  ample 
cross-section  be  provided,  and  the  heated  air  be  properly  distributed. 

If  a  more  active  ventilation  be  demanded,  but  such  as  requires  the  small- 
est amount  of  power,  the  cost  of  this  power  may  outweigh  the  advantages 
of  the  fan.  There  are  many  cases  in  which  steam-pipes  in  the  base  of  a 
chimney,  requiring  no  care  or  attention,  may  be  preferable  to  mechanical 
ventilation,  on  the  ground  of  cost,  and  trouble  of  attendance,  repairs,  etc. 

*  Murgue  gives  A  =       _ ,  and  Norris  A  —  — — ~.    See  page  521,  ante, 


534  HEATING   AHD   VENTILATION. 

The  following  figures  are  given  by  Atkinson  (Coll.  Engr.,  1889),  showing 
.the  minimum  depth  at  which  a  furnace  would  be  equal  to  a  ventilating- 
machine,  assuming  that  the  sources  of  loss  are  the  same  in  each  case,  i.e., 
that  the  loss  of  fuel  in  a  furnace  from  the  cooling  in  the  upcast  is  equivalent 
to  the  power  expended  in  overcoming  the  friction  in  the  machine,  and  also 
assuming  that  the  veutilatiug-machine  utilizes  60$  of  the  engine-power.  The 
coal  consumption  of  the  engine  per  I.H.P.  is  taken  at  8  Ibs.  per  hour: 

Average  temperature  in  upcast 100°  F.          150°  F.         200°  F. 

Minimum  depth  for  equal  economy. ..  960  yards.  1040 yards.  1130  yards. 

Heating:    and    Ventilating:  of   Large    Buildings.     (A.  R. 

"Wolff,  Jour.  Frank.  Inst.,  1893.) — The  transmission  of  heat  from  the  interior 
to  the  exterior  of  a  room  or  building,  through  the  walls,  ceilings,  windows, 
etc.,  is  calculated  as  follows  : 

S  =  amount  of  transmitting  surface  in  square  feet; 
t  =  temperature  F.  inside,  /0  =  temperature  outside; 

K  =  a  coefficient  representing,  for  various  materials  composing  buildings, 
the  loss  by  transmission  per  square  foot  of  surface  in  British  ther- 
mal units  per  hour,  for  each  degree  of  difference  of  temperature 
on  the  two  sides  of  the  material ; 
Q  =  total  heat  transmission  =  SK  (t  -  to). 

This  quantity  of  heat  is  also  the  amount  that  must  be  conveyed  to  the 
room  in  order  to  make  good  the  loss  by  transmission,  but  it  does  not  cover 
the  additional  heat  to  be  conveyed  on  account  of  the  change  of  air  for  pur- 

Eoses  of  ventilation.  The  coefficients  K  given  below  are  those  prescribed  by 
iw  by  the  German  Government  in  the  design  of  the  heating  plants  of  its 
Eublic  buildings,  and  generally  used  in  Germany  for  all  buildings.  They 
ave  been  converted  into  American  units  by  Mr.  Wolff,  and  he  finds  that 
they  agree  well  with  good  American  practice: 

VALUE  OF  K  FOR  EACH  SQUARE  FOOT  OF  BRICK  WALL. 

TlbrickewaUf }         4"      8//     12"     16"    a°"     24"     28"      32"      36"       40// 
K  =  0.68    0.46    0.32    0.26    0.23    0.20    0.174     0.15     0.129     0.115 

1  sq.  ft.,  wooden-beam  construction, )  as  flooring,  K  =  0.083 

planked  over  or  ceiled,  f as  ceiling,    K=  0.104 

1    sq.    ft.,    fireproof    construction,  j  as  flooring,  K  —  0. 124 

floored  over,  f as  ceiling,    .K"  =  0.145 

1  sq.  ft.,  single  window K  =  1.030 

1  sq.  ft.,  single  skylight K  =  1.118 

1  sq.  ft.,  double  window K=  0.518 

1  sq.  ft.,  double  skylight K  =  0.621 

1  sq.  ft.,  door K  =  0.414 

These  coefficients  are  to  be  increased  respectively  as  follows:  10$  when  the 
exposure  is  a  northerly  one,  and  winds  are  to  be  counted  on  as  important 
factors;  10$  when  the  building  is  heated  during  the  daytime  only,  and  the 
location  of  the  building  is  not  an  exposed  one;  30$  when  the  building  is 
heated  during  the  daytime  only,  and  the  location  of  the  building  is  exposed; 
50$  when  the  building  is  heated  during  the  winter  months  intermittently, 
with  long  intervals  (say  days  or  weeks)  of  non-heating. 

The  value  of  the  radiating-surface  is  about  as  follows:  Ordinary  bronzed 
cast-iron  radiating-surfaces,  in  American  radiators  (of  Bundy  or  similar 
type),  located  in  rooms,  give  out  about  250  heat-units  per  hour  for  each 
square  foot  of  surface,  with  ordinary  steam-pressure,  say  3  to  5  Ibs.  per  sq. 
in.,  and  about  0.6  this  amount  with  ordinary  hot-water  heating. 

Non-painted  radiating-surfaces,  of  the  ordinary  "indirect"  type  (Climax 
or  pin  surfaces),  give  out  about  400  heat-units  per  hour  for  each  square  foot 
of  heating-surface,  with  ordinary  steam-pressure,  say  3  to  5  Ibs.  per  sq.  in.; 
and  about  0.6  this  amount  with  ordinary  hot-water  heating. 

A  person  gives  out  about  400  heat-units  per  hour;  an  ordinary  gas-burner, 
about  4800  heat-units  per  hour;  an  incandescent  electric  (16  candle-power) 
light,  about  1600  heat-units  per  hour. 

The  following  example  is  given  by  Mr.  Wolff  to  show  the  application  of 
the  formula  and  coefficients: 

Lecture-room  40  x  60  ft.,  20  ft.  high,  48,000  cubic  feet,  to  be  heated  to 
69°  F.;  exposures  as  follows:  North  wall,  60  X  20  ft.,  with  four  windows, 
each  14  X  4  feet,  outside  temperature  0°  F.  Room  beyond  west  wall  agq 


HEATING  AND  VENTILATING  OF  LARGE  BUILDINGS.  535 


room  overhead  heated  to  69°,  except  a  double  skylight  in  ceiling,  14  X  24  ft., 
exposed  to  the  outside  temperature  of  0°.    Store-room  beyond  east  wall  at 
36°.    Door  6  X  12ft.  in  wall.    Corridor  beyond  south  wall  heated  to  59°. 
Two  doors.  6  X  12,  in  wall.    Cellar  below,  temperature  36°. 
The  following  table  shows  the  calculation  of  heat  transmission: 


t*'    . 

69° 
69 
33 
33 
10 
10 
10 
10 
69 

as 

Kind  of  Transmitting 
Surface. 

Thickness 
of  Wall  in 
inches. 

Calculation 
of  Area  of 
Transmitting 
Surface. 

1 

I 

Thermal 
Units. 

Outside  wall  .        

36" 
36" 
24" 
36" 

63  X  22  -  448 
4X    8X    14 
42X22-    72 
6X12 
45  X  22  -    72 
6X12 
17X22-    72 
6X12 
32  X  42  -  336 
14X24 
62  X  42 

utside  wall,  1C 
mtside  windov 

day  or  night  i 

938 

448 
852 
72 
018 
72 
302 
72 
1,008 
336 
2,604 

w  

use,  30, 

9 
72 
4 
19 
2 
5 
1 
5 
10 
43 
4 

*  ... 

8,442 
32,256 
3,408 
1,368 
1,836 
360 
302 
360 
10,080 
14,448 
10.416 

Four  windows  (single) 

Inside  wall  (store-room)  

Roof        

Floor  

Supplementary  allowance,  north  o 
north  c 

Exposed  location  and  intermittent 
Total  thermal  units  

83,276 
814 
3.226 

87,346 
26.204 

113.550 

If  we  assume  that  the  lecture-room  must  be  heated  to  69  degrees  Fahr.  in 
•(be  daytime  when  unoccupied,  so  as  to  be  at  this  temperature  when  first 
persons  arrive,  there  will  be  required,  ventilation  not  being  considered,  and 
Lronzed  direct  low-pressure  steam-  radiators  being  the  heating  media,  about 
/13,  550  -5-  250  =  455  sq.  ft.  of  radiating-surface.  (This  gives  a  ratio  of  about 
^05  cu.  ft.  of  contents  of  room  for  each  sq.  ft.  of  heating-surface.) 

If  we  assume  that  there  are  160  persons  in  the  lecture-room,  and  we  pro- 
vide 2500  cubic  feet  of  fresh  air  per  person  per  hour,  we  will  supply  160  X 

4500  =  400,000  cubic  feet  of  air  per  hour  (i.e.,       '       -  over  eight  changes  of 


Contents  of  room  per  hour). 
To  heat  this  air  from  0°  Fahr.  to  69°  Fahr.  will  require  400,000  X  0.0189  X 

09  =  521,640  thermal  units  per  hour  (0.0189  being  the  product  of  a  weight  of 
ft,  cubic  foot  by  the  specific  heat  of  air).  Accordingly  there  must  be  provided 
ii21,640-r-400  =  1304  sq.  ft.  of  indirect  surface,  to  heat  the  air  required  for 
ventilation,  in  zero  weather.    If  the  room  were  to  be  warmed  entirely  indi- 
rectly, that  is,  by  the  air  supplied  to  room  (including  the  heat  to  be'conveyed 

10  cover  loss  by  transmission  through  walls,  etc.),  there  would   have  to  be 
conveyed  to  the  fresh-air  supply  521,640  -4-  113,550  =  635.190  heat-units.    This 
would  imply  the  provision  of  an  amount  of  indirect  heating-surface  of  the 
"  Climax  "  type  of  635,190  -*-  400  =  1589  sq.  ft.,  and  the  fresh  air  entering  the 
room  would  have  to  be  at  a  temperature  of  about  84°  Fahr.,  viz.,  69°  = 

4-00,^0189'  <"  69  +  15  =  84°  Fah, 

The  above  calculations  do  not,  however,  take  into  account  that  160  per- 
sons in  the  lecture-room  give  out  160  X  400  =  64,000  thermal  units  per  hour; 
and  that,  say,  50  electric  lights  give  out  50  X  1600  =  80,000  thermal  units  per 
hour;  or,  say,  50  gaslights.  50  X  4800  =  240,000  thermal  units  per  hour.  The 
presence  of  160  people  and  the  gas-lighting  would  diminish  considerably  the 
amount  of  heat  required.  Practically,  it  appears  that  the  heat  generated 
by  the  presence  of  160  people,  64,000  heat-units,  and  by  50  electric  lights, 
80,000  heat-units,  a  total  of  144,000  heat-units,  more  than  covers  the  amount 
of  heat  transmitted  through  walls,  etc.  Moreover,  that  if  the  50  gaslights 
give  out  240,000  thermal  units  per  hour,  the  air  supplied  for  ventilation  must 
enter  considerably  below  69°  Fahr.,  or  the  room  will  be  heated  to  an 
unbearably  high  temperature.  If  400,000  cubic  feet  of  fresh  air  per  hour 


536 


HEATING  AKD   VENTILATION. 


are  supplied,  and  240,000  thermal  units  per  hour  generated  by  the  gas  must 
be  abstracted,  it  means  that  the  air  must,  under  these  conditions,  enter 

240  000 

.*n";"A.Qft  =  about  32°  less  than  84°,  or  at  about  52°  Fahr.    Further- 

4UU,UUU  X  .vlow 

more,  the  additional  vitiation  due  to  gaslighting  would  necessitate  a  much 
larger  supply  of  fresh  air  than  when  the  vitiation  of  the  atmosphere  by  the 
people  alone  is  considered,  one  gaslight  vitiating  the  air  as  much  as  five 
men. 

Various  Rules  for  Computing  Radiating-stirface.—  The 
following  rules  are  compiled  from  various  sources.  They  are  more  in  the 
nature  of  4'rule-of -thumb  "  rules  than  those  given  by  Mr.  Wolff,  quoted 
above,  but  they  may  be  useful  for  comparison. 

Divide  the  cubic  feet  of  space  of  the  room  to  be  heated,  the  square  feet 
of  wall  surface,  and  the  square  feet  of  the  glass  surface  by  the  figures 
given  under  these  headings  in  the  following  table,  and  add  the  quotients 
together;  the  result  will  be  the  square  feet  of  radiating-surface  required. 
(F.  Schumann.) 

SPACE,  WALL  AND  GLASS  SURFACE  WHICH  ONE  SQUARE  FOOT  OF  RADIATING- 
SURFACE  WILL  HEAT. 


Air  Change. 

Steam-pressure 
in  pounds. 

Space  in  cubic 
feet.  1 

Exposure  of  Rooms. 

All  Sides. 

Northwest. 

Southeast. 

Wall 
Surface, 
sq.  ft. 

Glass 
Surface, 
sq.  ft. 

Wall 
Surface, 
sq.  ft. 

Glass 
Surface, 
sq.  ft. 

Wall 
Surface, 
sq.  ft. 

Glass 
Surface, 
sq.  ft. 

Once 
per 
hour. 

1 
3 
5 

190 
210 
225 

13.8 
15.0 
16.5 

7 
7.7 
8.5 

15.87 
17.25 
18.97 

8.05 
8.85 
9.77 

16.56 
18.00 
19.80 

8.4 
9.24 
10.20 

Twice 
per 

hour. 

1 
3 
5 

75 
82 
90 

11.1 
12.1 
13.0 

5.7 
6.2 
6.7 

12.76 
13.91 
14.52 

6.55 
7.13 
7.60 

13.22 
14.52 
15.60 

6.84 
7.44 
8.04 

EMISSION  OF  HEAT-UNITS  PER  SQUARE  FOOT  PER  HOUR  FROM  CAST-IRON  PIPES 
OR  RADIATORS.    TEMP.  OF  AIR  IN  ROOM,  70°  F.    (F.  Schumann.) 


Mean  Temperature  of 
Heated  Pipe,  Radia- 
tor, etc. 

By  Contact. 

By  Radi- 
ation. 

By  Radiation 
and  Contact. 

Air  quiet. 

Air 
moving. 

Air  quiet. 

Air 
moving. 

Hot  water        140° 

55.51 
65.45 
75.68 
86.18 
96.93 
107.90 
119.13 
130.49 
142.20 
153.95 
165.90 
178.00 
189.90 
202.70 
215.30 
228.55 
240.85 

92.52 
109.18 
126.13 
143.30 
161.55 
179.83 
198.55 
217.48 
237.00 
256.58 
279.83 
296.65 
316.50 
337.83 
358.85 
380.91 
401.41 

59.63 
69.69 
80.19 
91.12 
102.15 
114.45 
127.00 
139.96 
155.27 
169.56 
184.58 
200.18 
214.36 
233.42 
251.21 
267.73 
279.12 

115.14 
135.14 
155.87 
177.30 
199.43 
222.35 
246.13 
270.49 
297.47 
323.51 
350.48 
378.18 
404.26 
436.12 
466.51 
496.28 
519.97 

152.15 
178.87 
206.32 
234.42 
264.05 
294.28 
325.55 
357.48 
392.27 
426.14 
464.41 
496.81 
530.86 
571.25 
610.06 
648.64 
680.53 

"               150° 

"               ....  160° 

"               170° 

"                  180° 
•*                190° 

««                200° 

"              or  steam  .  .210° 
Steam                          220° 

"       .     .        .           230° 

••        240° 

"        250° 

"        260° 

"    -    270° 

••        280° 

"        290° 

300° 

INDIRECT  HEATING-SURFACE.  537 

RADIATING-SURFACE  REQUIRED  FOR  DIFFERENT  KINDS  OF  BUILDINGS.  (From 
practice  of  the  Dubuque  Steam  Supply  Co.,  External  Air  0°  F.  Chas.  A. 
Smith.) 


Cubic  ft.  of  Room  heated 
by  1  sq.  ft.  of  Surface. 
Direct      Indirect 
System.     System. 

Dwellings 50  40 

Stores,  wholesale 125  100 

'V       retail  100  80 


Cubic  ft.  of  Room  heated 
by  1  sq.  ft.  of  Surface. 
Direct      Indirect 
System.    System. 
Banks,  offices,  drug-stores  70          60 

Large  hotels 125         100 

Churches 200         150 


The  Nason  Mfg.  Co.'s  catalogue  gives  the  following:  One  square  foot  of 
surface  will  heat  from  40  to  100  cu.  ft.  of  space  to  75°  in  —  10°  latitudes. 
This  range  is  intended  to  meet  conditions  of  exposed  or  corner  rooms  of 
buildings,  and  those  less  so,  as  intermediate  ones  of  a  block.  As  a  general 
rule,  1  sq.  ft.  of  surface  will  heat  70  cu.  ft.  of  air  in  outer  or  front  rooms  and 
100  cu.  ft.  in  inner  rooms.  In  large  stores  in  cities  with  buildings  on  each 
side,  1  to  100  is  ample. 

APPROXIMATE  PROPORTIONS  OP  RADIATING-SURPACES. 
One  square  foot  radiating-surface  will  heat: 

Indwellings,        In  hall,  stores,  In  churches,  large 

schoolrooms,       lofts,  factories,  auditoriums, 

offices,  etc.                     etc.  etc. 

By  direct  radiation...        60  to  80  ft.              75  to  100  ft.  150  to  200  ft. 

By  indirect  radiation.        40  to  50  4i                50  to   70  4t  100  to  140  " 

Isolated  buildings  exposed  to  prevailing  north  or  west  winds  should  have 
a  generous  addition  made  to  the  heating-surface  on  their  exposed  sides. 

The  following  rule  is  given  in  the  catalogue  of  the  Babcock  &  Wilcox  Co., 
and  is  also  recommended  by  the  Nason  Mfg.  Co.: 

Radiating  surf  ace  may  be  calculated  by  the  rule:  Add  together  the  square 
feet  of  glass  in  the  windows,  the  number  of  cubic  feet  of  air  required  to  be 
changed  per  minute,  and  one  twentieth  the  surface  of  external  wall  and 
roof;  multiply  this  sum  by  the  difference  between  the  required  temperature 
of  the  room  and  that  of  the  external  air  at  its  lowest  point,  and  divide  the 
product  by  the  difference  in  temperature  between  the  steam  in  the  pipes 
and  the  required  temperature  of  the  room.  The  quotient  is  the  required 
radiating-surface  in  square  feet. 

Overhead  Steam-pipe*.  (A.  R.  Wolff,  Stevens  Indicator,  1887.)— 
When  the  overhead  system  of  steam-heating  is  employed,  in  which  system 
direct  radiating-pipes,  usually  1*4  in.  in  diarn.,  are  placed  in  rows  overhead, 
suspended  upon  horizontal  racks,  the  pipes  running  horizontally,  and  side 
by  side,  around  the  whole  interior  of  the  building,  from  2  to  3  ft.  from  the 
walls,  and  from  2  to  4  ft.  from  the  ceiling,  the  amount  of  1%  in.  pipe  re- 
quired, according  to  Mr.  C.  J.  H.  Woodbury,  for  heating  mills  (for  which 
use  this  system  is  deservedly  much  in  vogue),  is  about  1  ft.  in  length  for 
every  90  cu.  ft.  of  space.  Of  course  a  great  range  of  difference  exists,  due 
to  the  special  character  of  the  operating  machinery  in  the  mill,  both  in  re- 
spect to  the  amount  of  air  circulated  by  the  machinery,  and  also  the  aid  to 
warming  the  room  by  the  friction  of  thie  journals. 

Indirect  Heating-surface.—  J.  H.  Kinealy,  in  Heating  and  Ven- 
tilation, May  15,  1894,  gives  the  following  formula,  deduced  from  results  of 
experiments  by  C.  B.  Richards,  W.  J.  Baldwin,  J.  H.  Mills,  and  others,  upon 
indirect  heaters  of  various  kinds,  supplied  with  varying  amounts  of  air  per 
hour  per  square  foot  of  surface: 


JV=  cubic  feet  of  air,  reduced  to  70°  F.,  supplied  to  the  heater  per  square 

foot  of  heating-surface  per  hour; 

T0  =  temperature  of  the  steam  or  water  in  the  heater; 
%\  =  temperature  of  the  air  when  it  enters  the  heater; 
Ta  =  temperature  of  the  air  when  it  leaves  the  heater. 

As  the  formula  is  based  upon  an  average  of  experiments  made  upon  all 
sorts  of  indirect  heaters,  the  results  obtained  by  the  use  of  the  equation 
may  in  some  cases  be  slightly  too  small  and  in  others  slightly  too  large, 


538  HEATING   AND   VENTILATION. 

although  the  error  will  in  no  case  be  great.  No  single  formula  ought  to  be 
expected  to  apply  equally  well  to  all  dispositions  of  heating-surface  in  in- 
direct heaters,  as  the  efficiency  of  such  heater  can  be  varied  between  such 
wide  limits  by  the  construction  and  arrangement  of  the  surface. 

In  indirect  heating,  the  efficiency  of  the  radiating-surface  will  increase, 
and  the  temperature  of  the  air  will  diminish,  when  the  quantity  of  the  air 
caused  to  pass  through  the  coil  increases.  Thus  1  sq.  ft.  radiating-surface, 
with  steam  at  212°,  has  been  found  to  heat  100  cu.  ft.  of  air  per  hour  from 
zero  to  150°,  or  300  cu.  ft.  from  zero  to  100°  in  the  same  time.  The  best  re- 
sults are  attained  by  using  indirect  radiation  to  supply  the  necessary  venti- 
lation, and  direct  radiation  for  the  balance  of  the  heat.  (Steam.) 

In  indirect  steam-heating  the  least  flue  area  should  be  1  to  \Y\  sq.  in. 
to  every  square  foot  of  heating-surface,  provided  there  are  no  long  horizon- 
tal reaches  in  the  duct,  with  little  rise.  The  register  should  have  twice  the 
area  of  the  duct  to  allow  for  the  fretwork.  For  hot  water  heating  from  25# 
to  30#  more  heating-surface  and  flue  area  should  be  given  than  for  low- 
pressure  steam.  (Engineering  Record,  May  26,  1894.) 

Boiler  Heating-surface  Required.  (A.  R.  Wolff,  Stevens  Indi- 
cator, 1887.) — When  the  direct  system  is  used  to  heat  buildings  in  which  the 
street  floor  is  a  store,  and  the  upper  floors  are  devoted  to  sales  and  stock- 
rooms and  to  light  manufacturing,  and  in  which  the  fronts  are  of  stone  or 
iron,  and  the  sides  and  the  rear  of  building  of  brick— a  safe  rule  to  follow  is  to 
supply  1  sq.  ft.  of  boiler  heating-surface  for  each  700  cu.  ft.,  and  1  sq.  ft.  of 
radiating-surface  for  each  100  cu.  ft.  of  contents  of  building. 

For  heating  mills,  shops,  and  factories,  1  sq.  ft.  of  boiler  heating-surface 
should  be  supplied  for  each  475  cu.  ft.  of  contents  of  building;  and  the  same 
allowance  should  also  be  made  for  heating  exposed  wooden  dwellings.  For 
heating  foundries  and  wooden  shops,  1  sq.  ft.  of  boiler  heating- surf  ace 
should  be  provided  for  each  400  cu.  ft.  of  contents;  and  for  structures  in 
which  glass  enters  very  largely  in  the  construction — such  as  conservatories, 
exhibition  buildings,  and  the  like— 1  sq.  ft.  of  boiler  heating-surface  should 
be  provided  for  each  275  cu.  ft.  of  contents  of  building. 

When  the  indirect  system  is  employed,  the  radiator-surface  and  the  boiler 
capacity  to  be  provided  will  each  have  to  be,  on  an  average,  about  25#  more 
than  where  direct  radiation  is  used.  This  percentage  also  marks  approxi- 
mately the  increased  fuel  consumption  in  the  indirect  system. 

Steam  (Babcock&  Wilcox  Co.)  has  the  following:  1  sq.  ft.  of  boiler-surface 
will  supply  from  7  to  10  sq.  ft.  of  radiating-surface,  depending  upon  the  size 
of  boiler  and  the  efficiency  of  its  surface,  as  well  as  that  of  the  radiating- 
surface.  Small  boilers  for  house  use  should  be  much  larger  proportionately 
than  large  plants.  Each  horse-power  of  boiler  will  supply  from  240  to  300 
ft.  of  1-in.  steam-pipe,  or  80  to  120  sq.  ft.  of  radiating  surface.  Cubic  feet 
of  space  has  little  to  do  with  amount  of  steam  or  surface  required,  but  is  a 
convenient  factor  for  rough  calculations.  Under  ordinary  conditions  1 
horse-power  will  heat,  approximately,  in- 
Brick  dwellings,  in  blocks,  as  in  cities 15,000  to  20,000  cu.  ft. 

"      stores         '*        " 10,000    "   15,000      " 

41       dwellings,  exposed  all  round 10,000    "  15,000      " 

"       mills,  shops,  factories,  etc 7,000    "  10,000      " 

Wooden  dwellings,  exposed 7,000    "   10,000      " 

Foundries  and  wooden  shops.... 6,000    "10,000      " 

Exhibition  buildings,  largely  glass,  etc 4,000    "  15,000 

Proportion  of  Grate-surface  to  Radiator-surface. 

(J.  R.  Willett,  Heating  and  Ventilation,  Feb.  1894.) 


Radiator-surf., 

sq.  ft 

Grate-surface, 


100  200  400  600  800  1000  1200  1400  1600  1800  20CO 
120  208  362  501  630   754   872   986  1100  1210  1310 


sq.  in . 

Steam-consumption  in  Car-heating. 

C.,  M.  &  ST.  PAUL  RAILWAY  TESTS.    (Engineering,  June  27,  1890,  p.  764.) 

Water  of  Condensation 

Outside  Temperature.         Inside  Temperature.  per  Car  per  Hour. 

40  70  70  Ibs. 

30  70  85 

10  70  100 


REGISTERS  AND   COLD-AIR   DUCTS. 


539 


Internal  Diameters  of  Steam  Supply-mains,  with  Total 
Resistance  equal  to  2  inches  of  Water-column.* 

Steam,  Pressure  10  Ibs.  per  square  inch  above  atm.,  Temperature  239°  F. 

Formula,   d  —  0.5374  A/  ~ ;  where  d  =  internal  diameter  in  inches; 

•  minute  Der  100  so.  1.. 0 , 

'  steam  to  produce  flow. 


Q  =  9.2  cubic  feet  of  steam  per  minute  per  100  sq.  ft.  of  radiating-surface  ; 
/  =  length  of  mains  in  feet;  h    =  159.3  feet  head  of  stear 


hq*j 

Internal  Diameters  in  inches  for  Lengths  of  Mains  from  1  ft.  to  600  ft. 

>r5  3 

03   W 

tf 

1  ft. 

10ft. 

20ft. 

40ft. 

60ft. 

80ft. 

100  ft. 

200  ft. 

300  ft. 

400  ft. 

600ft. 

sq.ft. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

inch. 

1 

0.075 

0  119 

0.136 

0.157 

0.170 

0.180 

0.189 

0.210 

0.234 

0.248 

0.270 

10 

0.19 

0.30 

0.34 

0.39 

0.43 

0.45 

0.47 

0.54 

0.59 

0.62 

0.68 

20 

0.25 

0.39 

0.45 

0.52 

0.56 

0.60 

0.62 

0.72 

0.78 

0.82 

0.89 

40 

0.33 

0.52 

0.60 

0.69 

0.74 

0.79 

0.82 

0.95 

1.03 

1.09 

1.18 

60 

0.39 

0.61 

0.71 

0.81 

0.87 

0.93 

0.9T 

1.11 

1.21 

1.28 

1.39 

80 

0.43 

0.68 

0.79 

0.90 

0.98 

.04 

1.09 

1.25 

1.35 

1.43 

1.55 

100 

0.47 

0.75 

0.86 

0.99 

1.07 

.14 

1.19 

1.36 

1.48 

1.57 

1.70 

200 

0  62 

0.99 

.14 

1.30 

1.41 

.50 

1.57 

1.80 

1.95 

2.07 

2.24 

300 

0.73 

1.16 

.34 

1.53 

1.66 

.76 

1.84 

2  12 

2.30 

.2.43 

2.64 

400 

0.82 

1.30 

.50 

1.72 

1.86 

.98 

2.07 

2.37 

2.57 

2.73 

2.96 

500 

0.90 

1.43 

.64 

1.88 

2.04 

2.16 

2.26 

2.60 

2.81 

2.98 

3.23 

600 

0.97 

1.53 

.76 

2.03 

2.20 

2.33 

2.43 

2.79 

3.03 

3.21 

3.48 

800 

1.09 

1.72 

.98 

2.27 

2  46 

2.61 

2.73 

3.13 

3.40 

3.60 

3.90 

1,000 

.19 

1.88 

2.16 

2.48 

2.69 

2.85 

2.98 

3.43 

3.71 

3.94 

4.27 

1,200 

.28 

2.04 

2.33 

2.67 

2.90 

3.07 

3.21 

3.68 

4.00 

4.23 

4.59 

1,400 

.36 

2.15 

2.47 

2.84 

3.08 

3.26 

3.41 

3.92 

4.25 

4.50 

4.88 

1,600 

.43 

2.27 

2.61 

3.00 

3.25 

3.44 

3.60 

4.13 

4.49 

4.75 

5.15 

1,800 

.50 

2.38 

2.74 

3.14 

3.41 

3.61 

3.78 

4.34 

4.70 

4.98 

5.40 

2,000 

.57 

2.48 

2.85 

3.28 

3.55 

3.76 

3.93 

4.52 

4.90 

5.19 

5.63 

3,000 

.84 

2.92 

3.36 

3.85 

4.18 

4.43 

4  63 

5.32 

5.77 

6  11 

6.63 

4,000 

2.07 

3.28 

3.76 

4.32 

4.69 

4.96 

5.19 

5.96 

6.47 

6.85 

7.44 

*  From  Robert  Briggs's  paper  on  American  Practice  of  Warming  Buildings 
by  Steam  (Proc.  lust.  0.  E.,  1882,  vol.  Ixxi). 

For  other  resistances  and  pressures  above  atmosphere  multiply  by  the 
respective  factors  below : 

Water  col  .     G  in.      12  in.      24  in.  I  Press,  ab.  atm.  0  Ibs.  3  Ibs.  30  Ibs.  60  Ibs. 
Multiply  by  0.8027    0.6988      0.6084  |  Multiply  by        1.023   1.015    0.973     0.948 

Registers  and  Cold-air  Ducts  for  Indirect  Steam  Heating. 
—The  Locomotive  gives  the  following  table  of  openings  for  registers  and 
cold-air  ducts,  which  has  been  found  to  give  satisfactory  results.  The  cold- 
air  boxes  should  have  \V%  sq.  in.  area  for  each  square  foot  of  radiator  suface, 
and  never  less  than  %  the  sectional  area  of  the  hot-air  ducts.  The  hot  air 
ducts  should  have  2  sq.  in.  of  «PC  tional  area  to  each  square  foot  of  radiator 
surface  on  the  first  floor,  and  from  1^  to  2  inches  on  the  second  floor. 


Heating  Surface 
in  Stacks. 

Cold-air  Supply,  First  Floor. 

Size 

Register. 

Cold-air 
Supply. 
2d  Floor. 

30  square  feet 
40 
50 
60 
70 
80 
90 
100 

iuches 
45  square  inches  =   5  by   9 
60       "         '        =    6  by  10 
75       "                  =    8  by  10 
90        "         '        =    9  by  10 
108       4t         »        =    9  by  12 
120        "         '        =10  by  12 
135       "         •*       =  11  by  12 
150        '          "       =12  by  12 

inches 
9  by  12 
10  by  14 
10  by  14 
12  by  15 
12  by  19 
12  by  22 
14  by  24 
16  by  20 

inches 
4  by  10 
4  by  14 
5  by  15 
6  by  15 
6  by  18 
8  by  15 
9  by  15 
12  by  12 

The  sizes  in  the  table  approximate  to  the  rules  given,  and  it  will  be  found 
that  they  will  allow  an  easy  flow  of  air  and  a  full  distribution  throughout  the 
room  to  be  heated. 


540 


HEATIHG  AHD  VENTILATION. 


Physical  Properties  of  Steam  and  Condensed  Water, 
under  Conditions  of  Ordinary  Practice  in  Warming  by 
Steam,  (firlggs.) 


1  Steam-pressure  i  above  atm.  .  . 
^  per  square  inch  |  total  

Ibs. 
Ibs. 

0 

14.7 

3 

17.7 

10 
24.7 

30 
44.7 

60 

74.7 

Fahr. 

212° 

222° 

239° 

274° 

307° 

Temperature  of  air 

Fahr. 

60° 

60 

60° 

60° 

60* 

Difference  —  B  —  C                ... 

Fahr. 

152° 

162° 

179° 

214° 

247° 

(  Heat  given  out  per  minute  per 
•<     100  sq.  ft.  of  radiating-sur- 

>•  units 

456 

486 

537 

642 

741 

(     face  =  D  X  3 

Latent  heat  of  steam 

Fahr. 

965° 

958° 

946° 

921° 

898° 

Volume  of  1  Ib.  weight  of  steam 

cu.  ft. 

26.4 

22.1 

16.2 

9.24 

5.70 

Weight  of  1  cubic  foot  of  steam 

Ib. 

0.0380 

0.04520.0618 

0.1082 

0.1752 

(  Volume  Q  of  steam  per  minute 
•<     to  give  out  E  units 

tcu.ft. 

12.48 

11.21 

9.20 

6.44 

4.70 

(               =  K  X  G  H-  P. 

i 

i  Weight  of  1  cubic  foot  of  con- 

) 

densed    water   at   tempera- 

V Ibs. 

59.64 

59.51 

59.05 

58.07 

57.03 

ture  B, 

i 

(  Volume  of  condensed  water  to 

•<     return  to  boiler  per  minute 

f-cu.ft. 

0.0079 

0.0085  0.0096 

0.0120 

0.0144 

/                 =  J  X  H  -*-  K, 

i 

! 

i  Head  of  steam  equivalent  to 
•<     12  inches  water-column 
(                    =K-*-H. 

i  feet 

1569 

1317 

955.5 

536.7 

325.5 

STEAM-SUPPLY  MAINS. 

[Head  h  of  steam,  equivalent 

] 

to  assumed  2  inches  water- 
1     column  for  producing  steam 

[  feet 

261.5 

219.5 

159.3 

89.45 

54.25 

[     flow  6,  =  M  H-  6, 

j 

j  Internal  diameter  d  of   tube* 
I     for  flow  Q  when  /  =      1  foot, 

j-  inch 

0.484 

0.481 

0.474 

0.461 

0.449 

Do.        do.  when  1  =  100  feet, 

inch 

1.217 

1.207 

1.190 

1.158 

1.128 

Ratios  of  values  of  d. 

ratio 

1.023 

1.015 

1.000 

0.973 

0.948 

WATER-RETURN  MAINS. 

(  Head   h   assumed    at    J^-inch 

| 

-j     water-column  for  producing 

V  foot 

0.0417 

0.0417 

0.0417 

0.0-117 

0.0417 

f     full-bore  water-flow  Q, 

} 

j  Internal  diameter  d  of  tube* 

I   • 

1     for  flow  Q  when  I  =      1  foot, 

r  inch 

0.147 

0  151 

0.158 

0.173 

0.186 

Do.        do.  when  I  =  100  feet, 

inch 

0.368 

0.379 

0.896 

0.434 

0.468 

Ratios  of  values  of  d  ...    

ratio 

0.926 

0.952 

1.000 

1.092 

1.176 

*  P,  I?,  U,  V  are  each  determined  from  the  formula  d  =  0.5374  j  /  -^—  . 


Size  of  Steam  Pipes  for  Steam  Heating.  (See  also  Flow  of 
Steam  in  Pipes.)— Sizes  of  vertical  main  pipes.  Direct  radiation.  (J.  R. 
Willett,  Heating  and  Ventilation,  Feb.,  1894.) 

Diameter  of  pipe,  inches.    1      1J4      1)^      2     2^      3      3^      4         5         6 
Sq.  ft.  of  radiator  surface  40      70       110    220    360    560    810    1110    2000    3000 
A  horizontal  branch  pipe  for  a  given  extent  of  radiator  surface  should  be 
one  size  larger  than  a  vertical  pipe  for  the  same  surface. 

The  Nason  Mfg.  Co.  gives  the  following: 

Diameter  of  pipe,  in 1J4    l^j      2       2^>       3       3^ 

Radiator  surface  sq  ft.  (maximum)..     125    200    500    1000    1500    2500 

When  mains  and  surfaces  are  very  much  above  the  boiler  the  pipes  need 
not  be  as  large  as  given  above;  under  very  favorable  circumstances  and 


HEATIXG   A   GREENHOUSE   BY    STEAM. 


541 


conditions  a  •1-inch  pipe  may  supply  from  2000  to  2500  sq.  ft.  of  surface,  a  6- 
ineh  pipe  for  5000  sq.  ft ,  and  a  10-inch  pipe  for  15,000  to  20.000  sq  ft.,  if  the 
distance  of  run  from  boiler  is  not  too  great.  Less  than  1^-inch  pipe  should 
not  be  used  horizontally  in  a  main  unless  Tor  a  single  rndiator  connection 

Steam,  by  the  Babcock  &  Wilcox  Co.,  says:  Where  the  condensed  water 
is  returned  to  the  boiler,  or  where  low  pressure  of  steam  is  used,  the  diarne- 
ier  of  mains  leading  from  the  boiler  to  the  radiati  rig-surf  ace  should  be 
equal  in  inches  to  one  tenth  the  square  root  of  the  radiating-surf  ,ce.  mains 
included,  in  square  feet.  Thus  a  1-inch  pipe  will  supply  100  square  feet  of 
surface,  itself  included.  Return-pipes  should  be  at  least  %  inch  in  diame- 
ter, and  never  less  than  one  half  the  diameter  of  the  main— longer  returns 
requiring  larger  pipe.  A  thorough  drainage  of  steam-pipes  will  effectually 
prevent  all  cracking  and  pounding  noises  therein. 

A.  R.  Wolff's  Practice. — Mr.  Wolff  gives  the  following  figures  showing  his 
present  practice  (1897)  in  proportioning  mains  and  returns.  They  are  based 
on  an  estimated  loss  of  pressure  of  2$  for  a  length  of  100  ft.  of  pipe,  not  in- 
cluding allowance  for  bends  and  valves  (see  p.  078)  For  longer  runs  divide 
the  thermal  units  given  in  the  table  by  0.1  I/length  in  ft.  Besides  giving  the 
thermal  units  the  table  also  indicates  the  amount  of  direct  radial  ing  surface 
which  the  steam-pipes  can  supply,  on  the  basis  of  an  emission  of  250  thermal 
units  per  hour  for  e-ich  square  foot  of  direct  radiating  surface. 
Size  of  Pipes  for  Steam  Heating. 


C'E 
J  5 

In. 
1 

1M 

3 
4  3 

^  Diam.  of 
r  Return. 

2  ibs.  Pressure 

5  Ibs.  Pressure 

®"p, 
IM 
In. 

H-I  Diam.  of 
=  Return. 

2  Ibs  Pressure  5  Ibs.  Pressure 

Isril 

Sso1 

'^  P  £  2 

®  5  a 
M  aco 

_.       ;  03 

f|| 

1 

1 

2 

~Hj 

3  ~ 
3 

9 

18 
30 
70 

225 
330 
480 

690 

38 

120 
280 
528 
900 
1320 
1920 
2760 

15 
30 
50 
120 
220 
375 
550 
800 
1150 

60 
120 
200 

480 
880 
1500 
2200 
3200 
4(500 

6 

8 
9 
10 
12 
14 
16 

3>l 
4 

5 

6 

s 

930 
1500 
2250 
3200 
4450 
5800 
9250 
1  3500 
19000 

3720        1550 
6000        2500 
9000        3750 
12800       5400 
1  78<X)        7500 
23200        9750 
37000      15500 
51000      23000 
76000      32500 

6200 
10000 
150HO 
21600 
30000 
39000 
(52000 
9-)000 
130000 

Heating  a  Greenhouse  Tby  Steam.— Wm.  J.  Baldwin  answers  a 
question  in  the  American  Machinist  as  below:  With  five  pounds  steam- 
pressure,  how  many  square  feet  or  inches  of  heating-surface  is  necessary  to 
heat  100  square  feet  of  glass  on  the  roof,  ends,  and  sides  of  a  greenhouse 
in  order  to  maintain  a  night  heat  of  55°  to  65°,  while  the  thermometer  out- 
side ranges  at  from  15°  to  20°  below  zero  ;  also,  what  boiler-surface  is  neces- 
sary ?  Which  is  the  best  for  the  purpose  to  use — 2"  pipe  or  1*4"  pipe  ? 

Ans.— Reliable  authorities  agree  that  1.25  to  1.50  cubic  feet  or  air  in  an 
enclosed  space  will  be  cooled  per  minute  per  sq.  ft.  of  glass  as  many  degrees 
as  the  internal  temperature  of  the  house  exceeds  that  of  the  air  outside. 
Between  -f-  65°  and  —  20°  there  will  be  a  difference  of  85°,  or,  say,  one  cubic 
foot  of  air  cooled  127.5°  F.  for  each  sq  ft.  of  glass  for  the  most  extreme 
condition  mentioned.  Multiply  this  by  the  number  of  square  feet  of 
glass  and  by  60,  and  we  have  the  number  of  cubic  feet  of  air  cooled  1°  per 
hour  within  the  building  or  house.  Divide  the  number  thus  found  by  48,  and 
it  gives  the  units  of  heat  required,  approximately.  Divide  again  by  953, 
and  it  will  give  the  number  of  pounds  of  steam  that  must  be  condensed  from 
a  pressure  and  temperature  of  five  pounds  above  atmosphere  to  water  at 
the  same  temperature  in  an  hour  to  maintain  the  heat.  Each  square  foot 
of  surface  of  pipe  will  condense  from  J4  to  nearly  y%  Ib.  of  steam  per  hour, 
according  as  the  coils  are  exposed  or  well  or  poorly  arranged,  for  which 
an  average  of  ^  Ib.  may  be  taken.  According  to  this,  it  will  require  3  sq.  ft. 
of  pipe  surface  per  ib.  of  steam  to  be  condensed.  Proportion  the  heating- 
surface  of  the  boiler  to  have  about  one  fifth  the  actual  radiating-surface,  if 
you  wish  to  keep  steam  over  night,  and  proportion  the  grate  to  burn  not 
more  than  six  pounds  of  coal  per  sq.  ft.  of  grate  per  hour.  With  very  slow 
combustion,  such  as  takes  place  in  base-burning  boilers,  the  grate  might  be 
proportioned  for  four  to  five  pounds  of  coal  per  hour.  It  is  cheaper  to  make 
coils  of  1J4"  pipe  than  of  2",  and  there  is  nothing  to  be  gained  by  using  2' 
pipe  unless  the  coils  are  very  long.  The  pipes  in  a  greenhouse  should  be 


542  HEATING   AND   VENTILATION. 

under  or  in  front  of  the  benches,  with  every  chance  for  a  good  circulation 
of  air.  "  Header"  coils  are  better  than  "return-bend"  coils  for  this  purpose. 

Mr.  Baldwin's  rule  may  be  given  the  following  form  :  Let  H  =  heat-units 
transferred  per  hour,  T  =  temperature  inside  the  greenhouse,  t  =  tempera- 
ture outside,  S  =  sq.  ft.  of  glass  surface;  then  H  =  1.5S(T  —  t)  X  60  -*-  48 
=  1.8755(7'-  t).  Mr.  Wolff's  coefficient  K  for  single  skylights  would  give 
H=  1.118S(r-#. 

Heating  a  Greenhouse  by  Hot  Water.— W.  M.  Mackay,  of  the 
Richardson  &  Boynton  Co.,  in  a  lecture  before  the  Master  Plumbers'  Asso- 
ciation, N.  Y.,  1889,  says :  I  find  that  while  greenhouses  were  formerly 
heated  by  4-inch  and  3-inch  cast-iron  pipe,  on  account  of  the  large  body  of 
water  which  they  contained,  and  the  supposition  that  they  gave  better  satis- 
faction and  a  more  even  temperature,  florists  of  long  experience  who 
have  tried  4-inch  and  3-inch  cast-iron  pipe,  and  also  2  inch  wrought-iron 
pipe  for  a  number  of  years  in  heating  their  greenhouses  by  hot  water, 
and  who  have  also  tried  steam-heat,  tell  me  that  they  get  better  satisfaction, 
greater  economy,  and  are  able  to  maintain  a  more  even  temperature  with  2- 
inch  wrought-iron  pipe  and  hot  water  than  by  any  other  system  they  have 
used.  They  attribute  this  result  principally  to  the  fact  that  this  size  pipe 
contains  less  water  and  on  this  account  the  heat  can  be  raised  and  lowered 
quicker  than  by  any  other  arrangement  of  pipes,  and  a  more  uniform  tem- 
perature maintained  than  by  steam  or  any  other  system. 

HOT- WATER  HEATING. 

(Nason  Mfg.  Co.) 

There  are  two  distinct  forms  or  modifications  of  hot-water  apparatus,  de- 
pending upon  the  temperature  of  the  water. 

In  the  first  or  open-tank  system  the  water  is  never  above  212°  tempera- 
ture, and  rarely  above  200°.  This  method  always  gives  satisfaction  where 
the  surface  is  sufficiently  liberal,  but  in  making  it  so  its  cost  is  considerably 
greater  than  that  for  a  steam-heating  apparatus. 

In  the  second  method,  sometimes  called  (erroneously)  high-pressure  hot- 
water  heating,  or  the  closed-system  apparatus,  the  tank  is  closed.  If  it  is 
provided  with  a  safety-valve  set  at  10  Ibs.  it  is  practically  as  safe  as  the  open- 
tank  system. 

Law  of  Velocity  of  Flow.— The  motive  power  of  the  circulation 
in  a  hot- water  apparatus  is  the  difference  between  the  specific  gravities  of 
the  ascending  and  the  descending  pipes.  This  effective  pressure  is  very 
small,  and  is  equal  to  about  one  grain  for  each  foot  in  height  for  each  de- 
gree difference  between  the  pipes;  thus,  with  a  height  of  12"  in  "  up  "  pipe, 
and  a,  difference  between  the  temperatures  of  the  up  and  clown  pipes  of  8°, 
the  difference  in  their  specific  gravities  is  equal  to  8. 16  grains  on  each  square 
inch  of  the  section  of  return-pipe,  and  the  velocity  of  the  circulation  is  pro- 
portioned to  these  differences  in  temperature  and  height. 

To  Calculate  Velocity  of  Flow.—  Thus,  \\ith  a  height  of  ascend- 
ing pipe  equal  to  10'  and  a  difference  in  temperatures  of  the  flow  and  return 
pipes  of  8°,  the  difference  in  their  specific  gravities  will  equal  81  6  grains,  or 
-f-  7000  =  .01166  Ibs.,  or  X  2.31  (feet  of  water  in  one  pound)  =  .0269  ft.,  and  by 
the  law  of  falling  bodies  the  velocity  will  be  equal  to  8  |/?o769  =  1-312  ft.  per 
second,  or  X  60  =  78.7  ft.  per  minute.  In  this  calculation  the  effect  of  fric- 
tion is  entirety  omitted.  Considerable  deduction  must,  be  made  on  this 
account.  Even  in  apparatus  where  length  of  pipe  is  not  great,  and  with 
pipes  of  larger  areas  and  with  few  bends  or  angles,  a  large  deduction  for 
friction  must  be  made  from  the  theoretical  velocity,  while  in  large  and 
complex  apparatus  with  small  head,  the  velocity  is  so  much  reduced  by 
friction  that  sometimes  as  much  as  from  50$  to  QOfc  must  be  deducted  to  ob- 
tain the  true  rate  of  circulation. 

Main  flow-pipes  from  the  heater,  from  which  branches  may  be  taken,  are 
to  be  preferred  to  the  practice  of  taking  off  nearly  as  many  pipes  from  the 
heater  as  there  are  radiators  to  supply. 

It  is  not  necessary  that  the  main  flow  and  return  pipes  should  equal  in 
capacity  that  of  all  their  branches.  The  hottest  water  will  seek  the  highest 
level,  while  gravity  will  cause  an  even  distribution  of  the  heated  water  if  the 
surface  is  properly  proportioned. 

It  is  good  practice  to  reduce  the  size  of  the  vertical  mains  as  they  ascend, 
say  at  the  rate  of  one  size  for  each  floor. 

As  with  steam,  so  with  hot  water,  the  nin««  ^'jst  be  uuconfined  to  allow 


HOT-WATER  HEATING. 


543 


for  expansion  of  the  pipes  consequent  on  having  their  temperatures  in- 
creased. 

An  expansion  tank  is  required  to  keep  the  apparatus  filled  with  water, 
which  latter  expands  1/24  of  its  bulk  on  being  heated  from  40°  to  212°,  and 
the  cistern  must  have  capacity  to  hold  certainly  this  increased  bulk.  It  is 
recommended  that  the  supply  cistern  be  placed  on  level  with  or  above  the 
highest  pipes  of  the  apparatus,  in  order  to  receive  the  air  which  collects  in 
the  mains  and  radiators,  and  capable  of  holding  at  least  1/20  of  the  water 
in  the  entire  apparatus. 

Approximate  Proportions  of  Radiatiug-siirfaces  to 
Cubic  Capacities  of  Space  to  be  Heated. 


One  Square  Foot  of  Ra- 
diat  ing-surf  ace  will 
heat  with— 

In  Dwellings, 
School-rooms, 
Offices,  etc. 

In  Halls,  Stores, 
Lofts,  Facto- 
ries, etc. 

In  Churches, 
Large  Audito- 
riums, etc. 

High  temperature  di-  ) 
rect  hot-  water  radi-  > 
ation  ) 
Low   temperature   di-  J 
rect  hot-  water  radi-  > 
ation    .  .                        ) 

50  to  70  cu.  ft. 
30  to  50  "      " 

65  to  90  cu.  ft. 
35  to  65  t4    " 

130  to  180  cu.  ft. 
70  to  130  "    " 

High  temperature  in-  ) 
direct  hot-water  ra-  V 
diatioii  \ 
Low   temperature  in-  j 
direct  hot-water  ra-  >• 
diation  ) 

30  to  60  "     " 
20  to  40"     " 

35  to  75  "    " 
25  to  50  "    " 

70  to  150  "    •* 

50  to  100  "    " 

Diameter  of  Main  and  Branch  Pipes  and  square  feet  of  coil 
surface  they  will  supply,  in  a  low-pressure  hot-water  apparatus  (212°)  for 
direct  or  indirect  radiation,  when  coils  are  at  different  altitudes  for  direct 
radiation  or  in  the  lower  story  for  indirect  radiation: 


s  »" 

I'l 

Direct  Radiation.  Height  of  Coil  above  Bottom  of  Boiler, 

ll 

11 

in  feet. 

s" 

0 

10 

20 

30  |  40 

50 

60 

70 

80 

90 

100 

so.  ft. 

sq.  ft. 

sq.  ft. 

sq.  ft.'sq  ft. 

sq.  ft. 

sq.  ft. 

sq.  ft. 

sq.ft. 

sq.  ft. 

sq.  ft. 

% 

49 

50 

52 

53 

55 

57 

59 

61 

63 

65 

68 

1 

87 

89 

92 

95 

98 

101 

103 

108 

112 

116 

121 

136 

140 

144 

149 

153 

158 

161 

169 

175 

182 

189 

1  Vi> 

196 

202 

209 

214 

222 

228 

235 

243 

252 

261 

271 

o 

349 

359 

370 

380 

393 

405 

413 

433 

449 

465 

483 

2V^ 

546 

561 

577 

595 

613 

633 

643 

678 

701 

727 

755 

3 

785 

807 

835 

856 

888 

912 

941 

974 

1009 

1046 

1086 

1069 

1099 

1132 

1166 

1202 

1241 

1283 

1327 

1374 

1425 

1480 

4 

1395 

1436 

1478 

1520  1571 

1621 

1654 

1733 

1795 

1861 

1933 

1767 

1817 

1871 

1927  1988 

2052 

2120 

2193 

2272 

2356 

2445 

5 

2185 

2244 

2309 

2376 

2454 

2531 

2574 

2713 

2805 

2907 

3019 

6 

3140 

3228 

3341 

3424 

3552 

3648 

3763 

3897 

4036 

4184 

4344 

7 

4276 

4396 

4528 

4664 

4808 

4964 

5132 

5308 

5496 

5700 

5920 

8 

5580 

5744 

5912 

6080  6284 

6484 

6616 

6932 

7180 

7444 

7735 

9 

7068 

7268 

7484 

7708 

7952 

8208 

8482 

877'4 

9088 

9424 

9780 

10 

8740 

8976 

9236 

9516 

9816 

10124 

10296 

10852 

11220 

11628 

12076 

11 

10559 

10860 

11180 

11519  11879 

12262 

12666 

13108 

13576 

14078 

14620 

12 

12560 

12912 

13364 

13696  14208 

14592 

15052 

15588 

16144 

16736 

17376 

13 

14748 

15169 

15615 

16090  16591 

17126 

17697 

18307 

18961 

19633 

20420 

14 

17104 

17584 

18109 

18656  19232 

19856 

20528  1  21  232 

21984 

22800 

23680 

15 

19634 

20195 

20789 

21419  '22089 

22801 

23561 

24373 

25244 

26179 

27168 

16 

22320 

22978 

23643 

24320  25136 

25936 

26464 

27728 

28720 

29776 

30928 

544  HEATING   AND   VENTILATION. 

The  best  forms  of  hot-water-heating  boilers  are  proportioned  about  as 
follows: 

1  sq.  ft.  of  grate-surface  to  about  40  sq.  ft.  of  boiler-surface. 
1   "    "        boiler-      "  "         5  **    "        radiating-surface. 

1   "    "        grate-       "  "     200  "     " 

Rules  for  Hot- water  Heating.— J.  L.  Saunders  (Heating  and 
Ventilation,  Dec.  15, 1894)  gives  the  following :  Allow  1  sq.  ft.  of  radiating 
surface  for  every  3  ft.  of  glass  surface,  and  1  sq.  ft.  for  every  30  sq.  ft.  of 
wall  surface,  also  1  sq.  ft.  for  the  following  numbers  of  cubic  feet  of  space 
in  the  several  cases  mentioned. 

In  dwelling-bouses:  Libraries  and  dining-rooms,  first  floor..  35  to  40  cu.  ft. 

Reception  halls,  first  floor 40  to  50 

Stair  halls,  'k      "    40  to  55 

Chambers  above,  "      "    50  to  65 

Libraries,  sewing-rooms,  nurseries,  etc., 

above  first  floor 45  to  55 

Bath  rooms 30  to  40 

Public-schoolrooms .  60  to  85 

Offices 50  to  65 

Factories  and  stores 65  to  90 

Assembly  halls  and  churches 90  to  150 

To  find  the  necessary  amount  of  indirect  radiation  required  to  beat  a  room: 
Find  the  required  amount  of  direct  radiation  according  to  the  foregoing 
method  and  add  50#.  This  if  wrought-ii  on  pipe  coil  surface  is  used ;  if  cast- 
iron  pin  indirect-stack  surface  is  used  it  is  advisable  to  add  from  7'0#  to  80$. 

Sizes  of  hot-air  flues,  cold-air  ducts,  and  registers  for  indirect  work. — 
Hot-air  flues,  first  floor:  Make  the  net  internal  area  of  the  flue  equal  to 
%  sq.  in.  to  every  square  foot  of  radiating  surface  in  the  indirect  stack.  Hot- 
air  flues,  second  floor:  Make  the  net  internal  area  of  the  flue  equal  to  %  sq.  in. 
to  every  square  foot  of  radiating  surface  in  the  indirect  stack. 

Cold-air  ducts,  first  floor  :  Make  the  net  internal  area  of  the  duct  equal 
to  %  sq.  in.  to  every  square  foot  of  radiating  surface  in  the  indirect  stack. 
Cold  air  ducts,  second  floor :  Make  the  net  internal  area  of  the  duct  equal 
to  y%  sq.  in.  to  every  square  foot  of  radiating  surface  in  the  indirect  stack. 

Hot-air  registers  should  have  their  net  area  equal  in  full  to  the  area  of  the 
hot-air  flues.  Multiply  the  length  by  the  width  of  the  register  in  inches  ;  % 
of  the  product  is  the  net  area  of  register. 

Arrangement  of  Mains  for  Hot-water  Heating:.  (W.  M. 
Mackay,  Lecture  before  Master  Plumbers'  Assoc.,  N.  Y.,  1889  )— There  are 
two  different  systems  of  mains  in  general  use,  either  of  which,  if  properly 
placed,  will  give  good  satisfaction.  One  is  the  taking  of  a  single  large-flow 
main  from  the  heater  to  supply  all  the  radiators  on  the  several  floors,  with  a 
corresponding  return  main  of  the  same  size.  The  other  is  the  taking  of  a 
number  of  2-inch  wrought-iron  mains  from  the  heater,  with  the  same  num- 
ber of  return  mains  of  the  same  size,  branching  off  to  the  several  radiators 
or  coils  with  l^-inch  or  1-inch  pipe,  according  to  the  size  of  the  radiator  or 
coil.  A  2-inch  main  will  supply  three  l)4-inch  or  four  1-inch  branches,  and 
these  branches  should  be  taken  from  the  top  of  the  horizontal  main  with  a 
nipple  and  elbow,  except  in  special  cases  where  it  is  found  necessary  to  retard 
the  flow  of  water  to  the  near  radiator,  for  the  purpose  of  assisting  the  circu- 
lation in  the  far  radiator  ;  in  this  case  the  branch  is  taken  from  the  side  of 
the  horizontal  main.  The  flow  and  return  mains  are  usually  run  side  by  side, 
suspended  from  the  basement  ceiling,  and  should  have  a  gradual  ascent  from 
the  heater  to  the  radiators  of  at  least  1  inch  in  10  feet.  It  is  customary,  and 
an  advantage  where  2-inch  mains  are  used,  to  reduce  the  size  of  the  main  at 
every  point  where  a  branch  is  taken  off. 

The  single  or  large  main  system  is  best  adapted  for  large  buildings  ;  but 
there  is  a  limit  as  to  size  of  main  which  it  is  not  wise  to  go  beyond— gener- 
ally 6- inch,  except  in  special  cases. 

The  proper  area  of  cold-air  pipe  necessary  for  100  square  feet  of  indirect 
radiation  in  hot-water  heating  is  75  square  inches,  while  the  hot-air  pipe 
should  have  at  least  100  square  inches  of  area.  There  should  be  a  damper  in 
the  cold-air  pipe  for  the  purpose  of  controlling  the  amount  of  air  admitted  to 
the  radiator,  depending  on  the  severity  of  the  weather. 


BLOWER  SYSTEM  OF  HEATING  AND  VENTILATING.    545 

Til  10    BLOW  Kit    SYSTEM  OF    HEATING  AND 
VENTILATING. 

The  system  provides  for  the  use  of  a  fan  or  blower  which  takes  its  supply 
of  fresh  air  from  the  outside  of  the  building  to  be  heated,  forces  it  over 
steam  coils,  located  either  centrally  or  divided  up  into  a  number  of  indepen- 
dent groups,  and  then  into  the  several  ducts  or  flues  leading  to  the  various 
rooms.  The  movement  of  the  warmed  air  is  positive,  and  the  delivery  of 
the  air  to  the  various  points  of  supply  is  certain  and  entirely  independent 
of  atmospheric  conditions.  For  engines,  fans,  and  steam-coils  used  with  the 
blower  system,  see  page  519. 

Experiments  with  Radiators  of  60  sq.  ft.  of  Surface. 
(Mech.  News,  Dec.,  1893.) — After  having  determined  the  volume  and  tem- 
perature of  the  warm  air  passing  through  the  flues  and  radiators  from 
natural  causes,  a  fan  was  applied  to  each  flue,  forcing  in  air,  and  new  sets  of 
measurements  were  made.  The  results  showed  that  more  than  t\\  o  and  one- 
third  times  as  much  air  was  warmed  with  the  fans  in  use,  and  the  falling  off 
in  the  temperature  of  this  greatly  increased  air-volume  was  only  about  12.6$. 
The  condensation  of  steam  in  the  radiators  with  the  forced-air  circulation 
also  was  only  66%%  greater  than  with  natural  air  draught.  One  of  the 
several  sets  of  test  figures  obtained  is  as  follows  : 

Natural      Forced- 
Draught         air 
in  Flue.  Circulation. 

Cubic  feet  of  air  per  minute 457.5        1227 

Condensation  of  steam  per  minute  in  ounces  11.7  19.6 

Steam  pressure  in  radiator,  pounds 9  9 

Temperature  of  air  after  leaving  radiator 142°  124° 

"     "  before  passing  through  radiator.     61°  61° 

Amount  of  radiating  surface  in  square  feet 60  60 

Size  of  flue  in  both  cases  12  x  18  inches. 

There  was  probably  an  error  in  the  determination  of  the  volume  of  air  in 
these  tests,  as  appears  from  the  following  calculation.  (W.  K.)  Assume 
that  1  Ib.  of  steam  in  condensing  from  9  Ibs.  pressure  and  cooling  to  the  tem- 
perature at  which  the  water  may  have  been  discharged  from  the  radiator 
gave  up  1000  heat-units,  or  62.5  h.  u.  per  ounce;  that  the  air  weighed  .076  Ib. 
per  cubic  foot,  and  that  its  specific  heat  is  .238.  We  have 

Natural      Forced 
Draught.   Draught. 

Heat  given  up  by  steam,  ounces  x  62.5 =    731  1225H.U. 

Heat  received  by  air,  cu.  ft.  x. 076  xdiff.  of  tern.  x. 238=    673  1399    " 

Or,  in  the  case  of  forced  draught  t'he  air  received  \\%  more  heat  than  the 
steam  gave  out,  which  is  impossible.  Taking  the  heat  given  up  by  the  steam 
as  the  correct  measure  of  the  work  done  by  the  radiator,  the  temperature 
of  the  steam  at  237°,  and  the  average  temperature  of  the  air  in  the  case  of 
natural  draught  at  102°  and  in  the  other  case  at  93°,  we  have  for  the  tem- 
perature difference  in  the  two  cases  135°  and  144°  respectively;  dividing 
these  into  the  heat- units  we  find  that  each  square  foot  of  radiating  surface 
transmitted  5.4  heat-units  per  hour  per  degree  of  difference  of  temperature, 
in  the  case  of  natural  draught,  and  8.5  heat-units  in  the  case  of  forced 
draught  (—  8.5  X  144°  =  1224  heat-units  per  square  foot  of  surface). 

In  the  Women's  Homoeopathic  Hospital  in  Philadelphia.  2000  feet  of 
one-inch  pipe  heats  250.000  cubic  feet  of  space,  ventilating  as  well;  this 
equals  one  square  foot  of  pipe  surface  for  about  350  cubic  feet  of  space,  or 
less  than  3  square  feet  for  1000  cubic  feet.  The  fan  is  located  in  a  sepa- 
rate building  about  100  feet  from  the  hospital,  and  the  air,  after  being  heated 
to  about  135°,  is  conveyed  through  an  underground  brick  duct  with  a  loss  of 
only  five  or  six  degrees  it»  cold  weather.  (H.  I.  Snell,  Trans.  A.  S.  M.E  .ix.  106. 

Heating  a  Building  to  7O°  F.  Inside  when  the  Outside 
Temperature  is  Zero.— It  is  customary  in  some  contracts  for  heating 
to  guarantee  that  the  apparatus  will  heat  the  interior  of  the  building  to  70° 
in  zero  weather.  As  it  may  not  be  practicable  to  obtain  zero  weather  for 
the  purpose  of  a  test,  it  may  be  difficult  to  prove  the  performance  of  the 
guarantee.  E.  E.  Macgovern,  in  Engineering  Record,  Feb.  3,  1894,  gives  a 
calculation  tending  to  show  that  a  test  may  be  made  in  weather  of  a  higher 
temperature  than  zero,  if  the  heat  of  the  interior  is  raised  above  70°.  The 
higher  the  temperature  of  the  rooms  the  lower  is  the  efficiency  of  the  radi- 
ating-surface,  since  the  efficiency  depends  upon  the  difference  between  the 


546  HEATING   AND   VENTILATION. 

temperature  inside  of  the  radiator  and  the  temperature  of  the  room.  He 
concludes  that  a  heating  apparatus  sufficient  to  heat  a  given  building  to  70° 
in  zero  weather  with  a  given  pressure  of  steam  will  be  found  to  heat  the 
same  building,  steam-pressure  constant,  to  110°  at  60°,  95°  at  50°,  82°  at  40°, 
and  74°  at  3vJ°,  outside  temperature.  The  accuracy  of  these  figures,  however 
has  not  been  tested  by  experiment. 

The  following  solution  of  the  question  is  proposed  by  the  author.  It  gives 
resultsquite  different  from  those  of  Mr.  Macgovern,  but,  like  them,  lacks  ex- 
perimental confirmation. 

Let    S  =  sq.  ft.  of  surface  of  the  steam  or  hot-  water  radiator; 
W  =  sq.  ft.  of  surface  of  exposed  walls,  windows,  etc.; 
Ts  =  temp,  of  the  steam  or  hot  water,  jT,  =  temp,  of  inside  of  building 

or  room,  T0  =  temp,  of  outside  of  building  or  room; 
a  =  heat-units  transmitted  per  sq.  ft.  of  surface  of  radiator  per  hour 

per  degree  of  difference  of  temperature; 

b  =  average  heat-units  transmitted  per  sq.  ft.  of  walls  per  hour,  per 
degree  of  difference  of  temperature,  including  allowance  for 
ventilation. 

It  is  assumed  that  within  the  range  of  temperatures  considered  Newton's 
law  of  cooling  holds  good,  viz.,  that  it  is  proportional  to  the  difference  of 
temperature  between  the  two  sides  of  the  radiating-surface. 

hW 
Then  aS(T8  -  T,)  =  bW(T±  -  T0).    Let  ~   =  C  ;    then 


=  70,  and  T0  =  0,  C  =  Ts  ~ 


. 

Let  Ts  =  140°,  213.5°,  308°; 

Then  C  =      1,  2.05,  3.4. 

From  these  we  derive  the  following: 

Temperature  of  Outside  Temperatures,  TQ. 

Steam  or  Hot  -20°  -10°             0°        10°           20°           30°           40° 

Water,  Ts.  Inside  Temperatures,  T1,. 

140°  60  65             70          75             80             85             90 

213.5  56.6  63.3          70         76.7          83.4         90.2         96.9 

308  54.5  62.3         70         77.7         85.5          93.2        100.9 

Heating  by  Electricity.—  If  the  electric  currents  are  generated  r>y 
a  dynamo  driven  by  a  steam-engine,  electric  heating  will  prove  very  expen- 
sive, since  the  steam-t  ngine  wastes  in  the  exhaust-steam  and  by  radiation 
about  90$  of  the  heat-units  supplied  to  it.  In  direct  steam  -heating,  with  a 
good  boiler  and  properly  covered  supply-pipes,  we  can  utilize  about  60$  of 
the  total  heat  value  of  the  fuel.  One  pound  of  coal,  with  a  heating  value  of 
13,000  heat-units,  would  supply  to  the  radiators  about  13,000  X  .60  -  7800 
heat-  units.  In  electric  heating,  suppose  we  have  a  first-class  condensing- 
engine  developing  1  H.P.  for  every  2  Ibs.  of  coal  burned  per  hour. 
This  would  be  equivalent  to  1,980,000  ft.-lbs.  -f-  778  =  2545  heat-units,  or  1272 
heat-units  for  1  Ib.  of  coal.  The  friction  of  the  engine  and  of  the  dynamo  and 
the  loss  by  electric  leakage,  and  by  heat  radiation  from  the  conducting 
wires,  might  reduce  the  heat-units  delivered  as  electric  current  to  the  elec- 
tric radiator,  and  these  converted  into  heat  to  50$  of  this,  or  only  636  heat- 
units,  or  less  than  one  twelfth  of  that  delivered  to  the  steam-radiators  in 
direct  steam  -heating.  Electric  heating,  therefore,  will  prove  uneconomical 
unless  the  electric  current  is  derived  from  water  or  wind  power,  which  would 
otherwise  be  wasted.  (See  Electrical  Engineering.) 


WEIGHT  OF   WATER. 


547 


WATER. 


Expansion  of  "Water.— The  following  table  gives  the  relative  vol- 
i>mes  of  water  at  different  temperatures,  compared  with  its  volume  at  4°  C. 
according  to  Kopp,  as  corrected  by  Porter. 


Cent, 

Fahr. 

Volume. 

Cent. 

Fahr. 

Volume. 

Cent. 

Fahr. 

Volume. 

4° 

39.1° 

1.00000 

35° 

95° 

1.00586 

70° 

158° 

1.02241 

5 

41 

1.00001 

40 

104 

1.00767 

75 

167 

1.02548 

10 

50 

1.00025 

45 

113 

1  .00967 

80 

176 

1.02872 

15 

59 

1.00083 

50 

122 

1.01186 

85 

185 

1.03213 

20 

68 

1.00171 

55 

131 

1.01423 

90 

194 

1.03570 

25 

77 

1.00286 

60 

140 

1.01678 

95 

203 

1.03943 

30 

80 

1.00425 

65 

149 

1.01951 

100 

212 

1.04332 

Weight  of  1  cu.  ft.  at  39.1°  F.  =  62.4245  Ib. 
ft.  at  212°  F. 


1.04332  =  59.833,  weight  of  1  cu. 


Weiglit  of  Water  at  Different  Temperatures.— The  weight 
of  water  at  maximum  density,  39.1°,  is  generally  taken  at  the  figure  given 
by  Rankine,  62.425  Ibs.  per  cubic  foot.  Some  authorities  give  as  low  as 
62.379.  The  figure  62.5  commonly  given  is  approximate.  The  highest 
authoritative  figure  is  62.425.  At  62°  F.  the  figures  range  from  62.291  to  62.360. 
The  figure  62.355  is  generally  accepted  as  the  most  accurate. 

At  32°  F.  figures  given  by  different  writers  range  from  62379  to  62.418. 
Clark  gives  the  latter  figure,  and  Hamilton  {Smith,  Jr.,  (from  Rosetti.)  gives 
62.416. 

Weight  of  Water  at  Temperatures  above  £12°  F.— Porter 
(Richards'  "Steam-engine  Indicator.'1  p.  52)  says  that  nothing  is  known 
about  the  expansion  of  water  above  212°.  Applying  formulae  derived  from 
experiments  made  at  temperatures  below  212°,  however,  the  weight  and 
volume  above  212°  may  be  calculated,  but  in  the  absence  of  experimental 
data  we  are  not  certain  that  the  formulae  hold  good  at  higher  temperatures. 

Thurston.  in  his  "  Engine  and  Boiler  Trials,"  gives  a  table  from  which  we 
take  the  following  (neglecting  the  third  decimal  place  given  by  him) : 


~  .2  T3 

03  y 

Irt 

bfir,  O 

«£,£ 

t> 

| 

^^  fcic 

£  3  * 

|| 

III 

l| 

4»  S 

|il 

H 

£ 

EH" 

| 

£ 

EH 

fc. 

220 
230 
240 
250 
260 
270 

59.71 
59.64 
59.37 
59.10 
58.81 
58.52 
58.21 

280 
290 
300 
310 
3^0 
330 
310 

57.90 
57.59 
57.26 
56.93 
56.58 
56.24 
55.88. 

350 
360 
370 
380 
390 
400 
410 

55.52 
55.16 
54.79 
54.41 
54.03 
53.64 
53.26 

420 
430 
440 
450 
460 
470 
480 

52.86 
52.47 
52.07 
51.66 
51.26 
50.85 
50.44 

490 
500 
510 
520 
530 
540 
550 

50.03 
49.61 
49.20 
48.78 
48.36 
47.94 
47.52 

Box  on  Heat  gives  the  following  : 

Temperature  F...       ,.    212°      250°      300°      350°      400°      450°      500°      600° 
Lbs.  per  cubic  foot....  59.82    58,85    57. -12    55.94    54.34    52.70    51.02    47.64 

At  212°  figures  given  by  different  writers  (see  Trans.  A.  S.  M,  EM  xiii.  409) 
range  from  59,56  to  59,845,  averaging  about  59,77, 


548 


WATER. 


Weight  of  Water  per  Cubic  Foot,  from  32°  to  212°  F.,  and  heat- 
units  per  pound,  reckoned  above  32°  F.:  The  following  table,  made  by  in- 
terpolating the  table  given  by  Clark  as  calculated  from  Rankine's  formula, 
with  corrections  for  apparent  errors,  was  published  by  the  author  in  1884, 
Trans.  A.  S.  M.  E.,  vi.  90.  (For  heat  units  above  212°  see  Steam  Tables.) 


Jj? 

dtJQ 

C  0) 

S'O 
H 

Weight,  Ibs. 
per  cubic 
foot. 

Heat-units. 

k* 

i5^ 

I| 

3'O^j 

2>*  o 

l^2 

Heat-units. 

IA 

IBS 

8  ° 

5  3 

111 

®   ft«M 

Heat-units. 

,    !|| 

*£&ci£s 
JS&2&S 

H         P 

Heat-units. 

32 

62.42 

0. 

78 

62.25 

46.03 

123 

61.68 

91.16 

168 

60.81 

136.44 

33 

62.42 

1. 

79 

62.24 

47.03 

124 

61.67 

92.17 

169 

60.79 

137.45 

34 

62.42 

80 

62.23    48.04 

125 

61.65 

93.17 

170 

60.77 

138.45 

35 

62.42 

5! 

81 

62.22    49.04 

126 

61.03 

94.17 

171 

60.75 

139.41) 

36 

62.42 

4. 

82 

62.21 

50.04 

127 

61.61 

95.18 

172 

60.73 

140.47 

37 

62.42 

5. 

83 

62.20 

51.04 

128 

61.60 

96.18 

173 

60.70 

141.48 

38 

62.42 

6. 

84 

62.19 

52.04 

129 

61.58 

97.19 

174 

60.68 

142.40 

39 

62.42 

7. 

85 

62.18 

53.05 

130 

61.56 

98.19 

175 

60.66 

143.f.0 

40 

62.42 

8. 

86 

62.17 

54.05 

131 

61.54 

99.20 

176 

60.64 

144.51 

41 

62.42 

9. 

87 

62.16 

55.05 

132 

61.52 

100.20 

177 

60.62 

145.52 

42 

62.42 

10. 

88 

62.15 

56.05 

133 

61.51 

101.21 

178 

60.59 

146.52 

43 

62.42 

11. 

89 

62.14 

57.05 

134 

61.49 

102.21 

179 

60.57 

147.53 

44 

62.42 

12. 

90 

62.13 

58.06 

135 

61.47 

103.22 

180 

60.55 

148.54 

45 

62.42 

13. 

91 

62.12 

59.06 

136 

61.45 

104.22 

181 

60.53 

149.55 

46 

62.42 

14. 

92 

62.11 

60.06 

137 

61.43 

105.23 

182 

60.50150.56 

47 

62.42 

15. 

93 

62.10 

61.06 

138 

61.41 

106.23 

183 

60.48 

151.57 

48 

62.41 

16. 

94 

62.09 

62.06 

139 

61.39 

107.24 

184 

69.46 

152.58 

49 

62.41 

17. 

95 

62.08 

63.07 

140 

61.37 

108.25 

185 

60.44 

153.59 

50 

62.41 

18. 

96 

62.07 

64.07 

141 

61.36 

109.25 

186 

60.41 

154.60 

51 

62.41 

19. 

97 

62.06 

65.07 

142 

61.34 

110.26 

187 

60.39 

155.61 

52 

62.40 

20. 

98 

62.05 

66.07 

143 

61  32 

111.26 

188 

60.37 

156.62 

53 

62.40 

21.01 

99 

62.03 

67.08 

144 

61.30 

112.27 

189 

60.34 

157.63 

54 

62.40 

22.01 

100 

62.02 

68.08 

145 

61.28 

113.28 

190 

60.32 

158.64 

55 

62.39 

23.01 

101 

62.01 

69.08 

146 

61.  2f 

114.28 

191 

60.29 

159.65 

56 

62.39 

24.01 

102 

62.00 

70.09 

147 

61.24 

115.29 

192 

60.27 

160.67 

57 

62.39 

25.01 

103 

61.99 

71.09 

148 

61.22 

116.29 

193 

60.25 

161.08 

58 

62.38 

26.01 

104 

61.97 

72.09 

149 

61.20 

117.30 

194 

60.22 

162.69 

59 

62.38 

27.01 

105 

61.96 

73.10 

150 

61.18 

118.31 

195 

60.20 

163.70 

60 

62.37 

28.01 

106 

61.95 

74.10 

151 

61.16 

119.31 

196 

60.17 

164.71 

61 

62.37 

29.01 

107 

61.93 

75.10 

152 

61.14 

120.32 

197 

60.15 

165.72 

62 

62.36 

30.01 

108 

61.92 

76.10 

153 

61.12 

121.33 

198 

60.12 

166.73 

63 

62.36 

31.01 

109 

61.91 

77.11 

154 

61.10 

122.33 

199 

60.10 

167.74 

64 

62.35 

32.01 

110 

61.89 

78.11 

155 

61.08 

123.34 

200 

60.07 

168.75 

05 

62.34 

33.01 

111 

61.88 

79.11 

156 

61.06 

124.35 

201 

60.05 

169.77 

66 

62.34 

34.0'v 

112 

61.86 

80.12 

157 

61.04 

125.35 

202 

60.02 

170.78 

67 

62.33 

35.02 

113 

61.85 

81.12 

158 

61.02 

126.36 

203 

60.00 

171.79 

68 

62.33 

36.02 

114 

61.83 

82.13 

159 

61.00 

127.37 

204 

59.97 

172.80 

69 

62.32 

37.02 

115 

61.82 

83.13 

160 

60.98 

128.37 

205 

59.95 

173.81 

70 

62.31 

38.02 

116 

61.80 

84.13 

161 

60.96 

129.38 

206 

59.92 

174.83 

71 

62.31 

39.02 

117 

61.78 

85.14 

162 

60.94 

130.39 

207 

59.89 

175.84 

72 

62.30 

40.02 

118 

61.77 

86.14 

163 

60.92 

131.40 

208 

59.87 

176.85 

73 

62.29 

41.02 

119 

61.75 

87.15 

164 

60.90 

132.41 

209 

59.84 

177.86 

74 

62.28 

42.03 

120 

61.74 

88.15 

165 

60.87 

133.41 

210 

59.82 

178.87 

75 

62.28 

43.03 

121 

61.72 

89.15 

166 

60.85 

134.4* 

211 

59.79 

179.89 

76 

62.27 

44.03 

122 

61.70 

90.16 

167 

60.83 

135.43 

212 

59.76 

180.90 

77 

62.26 

45.03 

Comparison  of  Heads  of  Water  in  Feet  with  Pressures  in 
Various  Units. 

One  foot  of  water  at  39°. 1  Fahr.  =   62.425  Ibs.  on  the  square  foot; 
=     0.4335  Ibs.  on  the  square  inch; 
=     0.0295  atmosphere; 
=     0.8826  inch  of  mercury  at  32° ; 
M  u  «<  _  r,r-o  o  j  feet  of  air  at  32°  and 

I         atmospheric  pressure ; 


PRESSURE   OF   WATER. 


549 


One  Ib.  on  the  square  foot,  at  39°. 1  Fahr 

One  Ib.  on  the  square  inch  

One  atmosphere  of  29.922  inches  of  mercury 

One  inch  of  mercury  at  32°. 1 

One  foot  of  air  at  32  deg.,  and  one  atmosphere.. 

One  foot  of  average  sea-water 

One  foot  of  water  at  62°  F 

"      "      "        "      "  62°  F 

One  inch  of  water  at  62°  F 

One  pound  of  water  on  the  square  inch  at  62°  F. 


=  0.01602  foot  of  water; 
=  2.307  feet  of  water; 
=  33.9  "  "  " 

=    1.133         "    "      " 
=    0.001293    "    "      " 
=  1.026  foot  of  pure  water; 
=  62.355  Ibs.  per  sq.  foot; 
=    0.43302  Ibs.  per  sq.  inch; 
--=    0.036085"      "     "      " 
=    2.3094  feet  of  water. 


Pressure  in  Pounds  per  Square  Inch  for  Different  Meads 
of  Water. 

At  62°  F.  1  foot  head  =  0.433  Ib.  per  square  inch,  .433  X  144  =  62.352  Ibs. 
per  cubic  foot. 


Head,  feet. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

0.433 

0.866 

1.299 

1.732 

2.165 

2.598 

3.031 

3.464 

3.897 

10 

4.330 

4.763 

5.196 

5.629 

6.062 

6.495 

6.928 

7.361 

7.794 

8.227 

20 

8.660 

9.093 

9.526 

9.959 

10.392 

10.825 

11.258 

11.691 

12.124 

12.557 

30 

12.990 

13.423 

13.856 

14.289 

14.722 

15.155 

15.588 

16.021 

16.454 

16.887 

40 

17.320 

17.753 

18.186 

18.619 

19.052 

19.485 

19.918 

20.351 

20.784 

21.217 

50 

21.650 

22.083 

22.516 

22.949 

23.382 

23.815 

24.248 

24.681 

25.114 

25.547 

60 

25.980 

26.413 

26.846 

27.279 

27.712 

28.145 

28.578 

29.011 

29.444 

29.877 

70 

30.310 

30.743 

31.176 

31.609 

32.042 

32.475 

32.908 

33.341 

33.774 

34.207 

80 

34.640 

85.073 

35.506 

35.939 

36.372 

36.805 

37.238 

37.671 

38.104 

38.537 

90 

38.970 

39.403 

39.836 

40.269 

40.702 

41.135 

41.568 

42.001 

42.436 

42.867 

Head  in  Feet  of  "Water,  Corresponding  to  Pressures  in 
Pounds  per  Square  Inch. 

1  Ib.  per  square  inch  =  2.30947  feet  head,  1  atmosphere  =  14.7  Ibs.  per  sq 
inch  =  33.94  ft,  head. 


Pressure. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

2.309 

4.619 

6.928 

9.238 

11.547 

13.857 

16.166 

18.476 

20.785 

10 

23.0947  25.404:27.714  30.023  32.333 

34.642 

36.952 

39.261 

41.570 

43.880 

20 

46.189448.49950.80853.11855.427 

57.737 

60.046 

62.356 

64.66566.975 

30 

69.2841  71.594  73.903  76.213  78.522 

80.831 

83.141 

85.450 

87.  760  190.069 

40 

92.378894.68896.998 

99.307,101.62 

103.93 

106.24 

108.55 

110.85  113.16 

50 

115.4735  117.78  120.09 

122.40  124.71 

126.02 

129.33 

131.64 

133.95 

136.26 

60 

138.5682140.88  143.19 

145.50  147.81 

150.12 

152.42 

154.73 

157.04 

159.35 

70 

161.6629163.971166.28 

168.59170.90 

173.21 

175.52 

177.83 

180.14 

182.45 

80 

184.7576  187.07  189.38 

191.69194  00 

196.31 

198.61 

200.92 

203.23 

205.54 

90 

207.8523 

210.16 

212.47 

214.78 

217.09 

219.40 

221.71 

224.02 

226.33 

228.64 

Pressure  of  Water  due  to  its  Weight.— The  pressure  of  still 
water  in  pounds  per  square  inch  against  the  sides  of  any  pipe,  channel,  or 
vessel  of  any  shape  whatever  is  due  solely  to  the  "head,"  or  height  of  the 
level  surface  of  the  water  above  the  point  at  which  the  pressure  is  con- 
sidered, and  is  equal  to  .43302  Ib.  per  square  inch  for  every  foot  of  head, 
or  62.355  Ibs.  per  square  foot  for  every  foot  of  head  (at  62°  F.). 

The  pressure  per  square  inch  is  equal  in  all  directions,  downwards,  up- 
wards, or  sideways,  and  is  independent  of  the  shape  or  size  of  the  containing 
vessel. 

The  pressure  against  a  vertical  surface,  as  a  retaining- wall,  at  any  point 
is  in  direct  ratio  to  the  head  above  that  point,  increasing  from  0  at  the  level 
surface  to  a  maximum  at  the  bottom.  The  total  pressure  against  a  vertical 
Strip  of  a  unit's  breadth  increases  as  the  area  of  a  right-angled  triangle 


550  WATER. 

whose  perpendicular  represents  the  height  of  the  strip  and  whose  base 
represents  the  pressure  on  a  unit  of  surface  at  the  bottom;  that  is,  it  in- 
creases as  the  square  of  the  depth.  The  sum  of  all  the  horizontal  pressures 
is  represented  by  the  area  of  the  triangle,  and  the  resultant  of  this  sum  is 
equal  to  this  sum  exerted  at  a  point  one  third  of  the  height  from  the  bottom. 
(The  centre  of  gravity  of  the  area  o£  a  triangle  is  one  third  of  its  height.) 

The  horizontal  pressure  is  the  same  if  the  surface  is  inclined  instead  of 
vertical. 

(For  an  elaboration  of  these  principles  see  Trautwine's  Pocket-Book,  or 
the  chapter  on  Hydrostatics  in  any  work  on  Physics.  For  dams,  retainirig- 
walls,  etc.,  see  Trautwine.) 

The  amount  of  pressure  on  the  interior  walls  of  a  pipe  has  no  appreciable 
effect  upon  the  amount  of  flow. 

Buoyancy.— When  a  body  is  immersed  in  a  liquid,  whether  it  float  or 
sink,  it  is  buoyed  up  by  a  force  equal  to  the  weight  of  the  bulk  of  the  liquid 
displaced  by  the  body.  The  weight  of  a  floating  body  is  equal  to  the  weight 
of  the  bulk  of  the  liquid  that  it  displaces.  The  upward  pressure  or  buoy- 
ancy of  the  liquid  may  be  regarded  as  exerted  at  the  centre  of  gravity  of 
the  displaced  water,  which  is  called  the  centre  of  pressure  or  of  buoyancy. 
A  vertical  line  drawn  through  it  is  called  the  axis  of  buoyancy  or  of  flota- 
tion. In  a  floating  body  at  rest  a  line  joining  the  centre  of  gravity  and  the 
centre  of  buoyancy  is  vertical,  and  is  called  the  axis  of  equilibrium.  When 
an  external  force  causes  the  axis  of  equilibrium  to  lean,  if  a  vertical  line  be 
drawn  upward  from  the  centre  of  buoyancy  to  this  axis,  the  point  where  it 
cuts  the  axis  is  called  the  metacentre.  If  the  rnetacentre  is  above  the  centre 
of  gravity  the  distance  between  them  is  called  the  rnetacentric  height,  and 
the  body  is  then  said  to  be  in  stable  equilibrium,  tending  to  return  to  its 
original  position  when  the  external  force  is  removed. 

Boiling-point.— Water  boils  at  212*  V.  (100°  C.)  at  mean  atmospheric 
pressure  at  the  sea-level,  14  696  Ibs.  per  square  inch.  The  temperature  at 
which  water  boils  at  any  given  pressure  is  the  same  as  the  temperature  of 
saturated  steam  at  the  same  pressure.  For  boiling-point  of  water  at  othei 
pressure  than  14.696  Ibs.  per  square  inch,  see  table  of  the  Properties  of 
Saturated  Steam. 

The  Boiling-point  of  Water  may  toe  Raised.— When  water 
is  entirely  freed  of  air,  which  ma}'  be  accomplished  by  freezing  or  boiling, 
the  cohesion  of  its  atoms  is  greatly  increased,  so  that  its  temperature  may 
be  raised  over  50°  above  the  ordinary  boiling-point  before  ebullition  taken 
place.  It  was  found  by  Faraday  that  when  such  air-freed  water  did  boil 
the  rupture  of  the  liquid  was  like  an  explosion.  When  water  is  surrounded 
by  a  film  of  oil,  its  boiling  temperature  may  be  raised  considerably  above 
its  normal  standard.  This  has  been  applied  as  a  theoretical  explanation  in 
the  instance  of  boiler-explosions. 

The  freezing-point  also  may  be  lowered,  if  the  water  is  perfectly  quiet,  to 
-  10°  C.,  or  18°  Fahrenheit 'below  the  normal  freezing-point.  ('Hamilton 
Smith,  Jr.,  on  Hydraulics,  p.  13.)  The  density  of  water  at  14°  F.  is  .99814,  its 
density  at  39°.  1  being  1,  and  at  32°,  .99987. 

Freezing-point.— Wat er  freezes  at  32°  F.  at  the  ordinary  atmospheric 
pressure,  and  ice  melts  at  the  same  temperature.  In  the  melting  of  1  pound 
of  ice  into  water  at  32°  F.  about  142  heat-units  are  absorbed,  or  become 
latent:  and  in  freezing  1  Ib.  of  water  into  ice  a  like  quantity  of  heat  is  given 
out  to  the  surrounding  medium. 

Sea-water  freezes  at  27°  F.    The  ice  is  fresh.    (Trautwine.) 

Ice  and  Snow.  (From  Clark.)—!  cubic  foot  of  ice  at  32°  F.  weighs 
57.50  Ibs. ;  1  pound  of  ice  at  32°  F.  has  a  volume  of  .0174  cu  ft,  =  30.067  cu.  in. 

Relative  volume  of  ice  to  water  at  32°  F.,  1.0855,  the  expansion  in  passing 
into  the  solid  state  being  8.55$.  Specific  gravity  of  ice  =  0.922,  water  at 
02°  F.  being  1. 

At  high  pressures  the  melting  point  of  ice  is  lowrer  than  32°  F.,  being  at 
the  rate  of  .0133°  K.  for  each  additional  atmosphere  of  pressure 

The  specific  heat  of  ice  is  .504,  that  of  water  being  1. 

1  cubic  foot  of  fresh  snow,  according  to  humidity  of  atmosphere:  5  Ibs.  ti> 
12  Ibs.  1  cubic  foot  of  snow  moistened  and  compacted  by  rain:  15  Ibs.  to 
50  Ibs.  (Trautwio«). 

Specific  Heat  of  Water.  (From  Clark's  Steam-engine.)— Calcu- 
lated by  means  of  Regnault's  formula,  c  =  1  +  0. 00004 1  -j-  0.0000009 *2,  in 
which  e^is  the  specific  heat  of  water  at  any  temperature  t  in  centigrade  de- 
grees, the  specific  heat  at  the  freezing-point  being  1. 


THE   IMPURITIES   OF  WATER. 


551 


• 

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Tempera- 

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tures. 

£*  £•  8  2$ 

W*B.  *fl 

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tures. 

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H^  .M    C3 

lie  ® 

A£>  °  ® 

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"*'*•* 

xp2  * 

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Cent. 

Fahr. 

lid 

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111 

Cent. 

Fahr. 

Cfi          P*> 
S'cj  ^  5 

PI 

|ll 

0° 

32- 

0.000 

1.0000 

120° 

248° 

217.449 

1.0177 

1.0067 

10 

50 

18.004 

1.0005 

.0002 

130 

266 

235.7911  1.0204 

.0076 

20 

68 

36.018 

1.0012 

.0005 

140 

284 

254.187 

1.0232 

.0087 

30 

86 

54.047 

1.0020 

.0009 

150 

302 

272.628    1.0262 

.0097 

40 

104 

72.090 

.0030 

.0013 

160 

320 

291.132    1.0294 

.0109 

50 

122 

90.157 

.0042 

.0017 

170 

338 

309.690 

1.0328 

.0121 

60 

140 

108.247 

.0056 

.0023 

180 

356 

328.320 

1.0364 

.0133 

70 

158 

126.378 

.0072 

.0030 

190 

374 

347.004 

1.0401 

.0146 

80 

176 

144.508 

.0089 

1.0035 

200 

392 

365.760 

1.0440 

.0160 

90 

194 

162.686 

.0109 

1.0042 

210 

410 

384.588 

1.0481 

1.0174 

100 

212 

180.900 

.0130 

1.0050 

220 

428 

403.488 

1.0524 

1.0189 

110 

230 

199.152 

.0153 

1  .0058 

230 

446 

422.478 

1.0568 

1.0204 

Compressibility  of  Water.—  Water  is  very  slightly  compressible. 
Its  compressibility  is  from  .000040  to  .000051  for  one  atmosphere,  decreasing 

with  increase  of  temperature.  For  each  foot  of  pressure  distilled  water  will 
be  diminished  in  volume  .0000015  to  .0000013.  Water  is  so  incompressible 
that  even  at  a  depth  of  a  mile  a  cubic  foot  of  water  will  weigh  only  about 
half  a  pound  more  than  at  the  surface. 

Till;  IMPURITIES  OF  WATER. 

(A.  E.  Hunt  and  G.  H.  Clapp,  Trans.  A.  I.  MT.  E.  xvii.  338.) 

Commercial  analyses  are  made  to  determine  concerning  a  given  water: 
(1)  its  applicability  for  making  steam;  (2)  its  hardness,  or  the  facility  with 
which  it  will  "  form  a  lather1'  necessary  for  washing;  or  (3)  its  adaptation 
to  other  manufacturing  purposes. 

At  the  Buffalo  meeting  of  the  Chemical  Section  of  the  A.  A.  A.  S.  it  was  de- 
cided to  report  all  water  analyses  in  parts  per  thousand,  hundred-thousand, 
and  million. 

To  convert  grains  per  imperial  (British)  gallons  into  parts  per  100,000,  di- 
vide by  0.7.  To  convert  parts  per  100,000  into  grains  per  U.  S.  gallon,  mul- 
tiply by  7/12  or  .583. 

The  most  common  commercial  analysis  of  water  is  made  to  determine  its 
fitness  for  making  steam.  Water  containing  more  than  5  parts  per  100,000 
of  free  sulphuric  or  nitric  acid  is  liable  to  cause  serious  corrosion,  not  only 
of  the  metal  of  the  boiler  itself,  but  of  the  pipes,  cylinders,  pistons,  and 
valves  with  which  the  steam  comes  in  contact. 

The  total  residue  in  water  used  for  making  steam  causes  the  interior  lin- 
ings of  boilers  to  become  coated,  and  often  produces  a  dangerous  hard 
scale,  which  prevents  the  cooling  action  of  the  water  from  protecting  the 
metal  against  burning. 

Lime  and  magnesia  bicarbonates  in  water  lose  their  excess  of  carbonic 
acid  on  boiling,  and  often,  especially  when  the  water  contains  sulphuric 
acid,  produce,  with  the  other  solid  residues  constantly  beinj;  formed  by  the 
evaporation,  a  very  hard  and  insoluble  scale.  A  larger  amount  than  100 
parts  per  100.000  of  total  solid  residue  will  ordinarily  cause  troublesome 
scale,  and  should  condemn  the  water  for  use  in  steam-boilers,  unless  a 
better  supply  cannot  be  obtained. 

The  following  is  a  tabulated  form  of  the  causes  of  trouble  with  water  for 
steam  purposes,  and  the  proposed  remedies,  given  by  Prof.  L.  M.  Norton. 

CAUSES  OF  INCRUSTATION. 

1.  Deposition  of  suspended  matter. 

2.  Deposition  of  deposed  salts  from  concentration. 

3.  Deposition  of  carbonates  of  lime  and  magnesia  by  boiling  off  carbonic 
acid,  which  holds  them  in  solution. 


552 


WATER. 


4.  Deposition  of  sulphates  of  lime,  because  sulphate  of  lime  is  but  slightly 
soluble  in  cold  water,  less  soluble  in  hot  water,  insoluble  above  270°  F. 

5.  Deposition  of  magnesia,  because  magnesium  salts  decompose  at  high 
temperature. 

6.  Deposition  of  lime  soap,  iron  soap,  etc.,  formed  by  saponification  of 
grease. 

MEANS  FOR  PREVENTING  INCRUSTATION. 

1.  Filtration. 

2.  Blowing  off. 

3.  Use  of  internal  collecting  apparatus  or  devices  for  directing  the  cir- 
culation. 

4.  Heating  feed-water. 

5.  Chemical  or  other  treatment  of  water  in  boiler. 

6.  Introduction  of  zinc  into  boiler. 

7.  Chemical  treatment  of  water  outside  of  boiler. 


TABULAR  VIEW. 

Troublesome  Substance.  Trouble. 

Sediment,  ntud,  clay,  etc.  Incrustation. 

Readily  soluble  salts. 

Bicarbonates  of  lime,  magnesia,  )  tt 

iron.  j" 

Sulphate  of  lime.  " 

Chloride  and  sulphate  of  magne- )    Corrosion 

Carbonate     of    soda    in    large )      primin~ 

amounts.  f 

Acid  (in  mine  waters).  Corrosion. 

carbonic    acid    and }  4t 


Dissolved 
oxygen. 


Grease  (from  condensed  water). 

Organic  matter  (sewage). 
Organic  matter. 


Priming. 
Corrosion. 


Remedy  or  Palliation. 
Filtration ;  blowing  off. 
Blowing  off. 
Heating  feed.    Addition  of 

caustic   soda,  lime,    or 

magnesia,  etc. 
Addition     of    carb.    soda, 

barium  chloride,  etc. 
Addition   of  carbonate  of 

soda,  etc. 

Addition   of   barium  chlo- 
ride, etc. 
Alkali. 
Heating  feed.    Addition  of 

caustic    soda,     slacked 

lime,  etc. 
Slacked  lime  and  filtering. 

Carbonate  of  soda. 

Substitute  mineral  oil. 
Precipitate  with    alum  or 

ferric  chloride  and  filter. 
Ditto. 


The  mineral  matters  causing  the  most  troublesome  boiler-scales  are  bicar- 
bonates  and  sulphates  of  lime  and  magnesia,  oxides  of  iron  and  alumina, 
and  silica.  The  analyses  of  some  of  the  most  common  and  troublesome 
boiler-scales  are  given  in  the  following  table  : 

Analyses  of  Boiler-scale.    (Chandler.) 


Sul- 

Per- 

Car- 

phate 
of 

Mag- 
nesia. 

Silica. 

oxide 
of 

Water. 

bonate 
of 

Lime. 

Iron. 

Lime. 

N.Y.  C.  &H.R.Ry.,No.    1 

74.07 

9.19 

0.65 

0.08 

1.14 

14.78 

1        "        "            No     2 

71  37 

1  76 

No.    3 

62.86 

18.95 

2.60 

0.92 

1.28 

12.62 

No     4 

53  05 

4  79 

No     5 

46  83 

5  32 

No.    6 

30.80 

31.17 

7.75 

1.08 

2.44 

26.93 

No.    7 

4.95 

2.61 

2.07 

1.03 

0.63 

86.25 

No.    8 

0.88 

2.84 

0.65 

0  36 

0.15 

93.19 

No.    9 

4.81 

2.92 

No.  10 

30.07 

8.24 

THE   IMPURITIES   OF  WATER. 


553 


Analyses  in   Parts    per    1OO,OOO    of     Water   giving    Bad 
Results   in    Steam-boilers.    (A.  E.  Hunt.) 


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1  04 

98 

1   90 

38 

Allegheny  R.,  near  Oil-works 

30 

50 

41 

68 

690 

42 

23 

Many  substances  have  been  added  with  the  idea  of  causing  chemical 
action  which  will  prevent  boiler-scale.  As  a  general  rule,  these  do  more 
harm  than  good,  for  a  boiler  is  one  of  the  worst  possible  places  in  which  to 
carry  on  chemical  reaction,  where  it  nearly  always  causes  more  or  less 
corrosion  of  the  metal,  and  is  liable  to  cause  dangerous  explosions. 

In  cases  where  water  containing  large  amounts  of  total  solid  residue  is 
necessarily  used,  a  heavy  petroleum  oil,  free  from  tar  or  wax,  which  is  not 
acted  upon  by  acids  or  alkalies,  not  having  sufficient  wax  in  it  to  cause 
saponification,  and  which  has  a  vaporizing-point  at  nearly  600°  F.,  will  give 
the  best  results  in  preventing  boiler-scale.  Its  action  is  to  form  a  thin 
greasy  film  over  the  boiler  linings,  protecting  them  largely  from  the  action 
of  acids  in  the  water  and  greasing  the  sediment  which  is  formed,  thus  pre- 
venting the  formation  of  scale  and  keeping  the  solid  residue  from  the 
evaporation  of  the  water  in  such  a  plastic  suspended  condition  that  it  can 
be  easily  ejected  from  the  boiler  by  the  process  of  "  blowing  off."  If  the 
water  is  not  blown  off  sufficiently  often,  this  sediment  forms  into  a  "  putty" 
that  will  necessitate  cleaning  the  boilers.  Any  boiler  using  bad  water  should 
be  blown  off  every  twelve  hours. 

Hardness  oi'  Water.—  The  hardness  of  water,  or  its  opposite  quality, 
indicated  by  the  ease  with  which  it  will  form  a  lather  with  soap,  depends 
almost  altogether  upon  the  presence  of  compounds  of  lime  and  magnesia. 
Almost  all  soaps  consist,  chemically,  of  oleate,  stearate,  and  palmitate,  of 
an  alkaline  base,  usually  soda  and  potash.  The  more  lime  and  magnesia  in  a 
sample  of  water,  the  more  soap  a  given  volume  of  the  water  will  decompose, 
so  as  to  give  insoluble  oleate,  palmitate,  and  stearate  of  lime  and  magnesia, 
and  consequently  the  more  soap  must  be  added  to  a  gallon  of  water  in  order 
that  the  necessary  quantity  of  soap  may  remain  in  solution  to  form  the  lather. 
The  relative  hardness  of  samples  of  water  is  generally  expressed  in  terms 
of  the  number  of  standard  soap-measures  consumed  by  a  gallon  of  water  in 
yielding  a  permanent  lather. 

The  standard  soap-measure  is  the  quantity  required  to  precipitate  one 
grain  of  carbonate  of  lime. 

It  is  commonly  reckoned  that  one  gallon  of  pure  distilled  water  takes  one 
soap-measure  to  produce  a  lather.  Therefore  one  is  deducted  from  the 
total  number  of  soap-measures  found  to  be  necessary  to  use  to  produce  a 
lather  in  a  gallon  of  water,  in  reporting  the  number  of  soap-measures,  or 
"  degrees  "  of  hardness  of  the  water  sample.  In  actually  making  tests  for 
hardness,  the  "  miniature  gallon,"  or  seventy  cubic  centimetres,  is  used 
rather  than  the  inconvenient  larger  amount.  The  standard  measure  is  made 
by  completely  dissolving  ten  grammes  of  purecastile  soap  (contain ing  60  per 
cent  olive-oil)  in  a  litre  of  weak  alcohol  (of  about  35  per  cent  alcohol).  This 
yields  a  solution  containing  exactly  sufficient  soap  in  one  cubic  centimeter 
of  the  solution  to  precipitate  one  milligramme  of  carbonate  of  lime,  or,  in 
other  words,  the  standard  soap  solution  is  reduced  to  terms  of  the  "  minia- 
ture gallon ' '  of  water  taken. 

If  a  water  charged  with  a  bicarbonate  of  lime,  magnesia,  or  iron  is  boiled. 


554 


WATEE. 


it  will,  on  the  excess  of  the  carbonic  acid  being  expelled,  deposit  a  consid- 
erable quantity  of  the  lime,  magnesia,  or  iron,  and  consequently  the  water 
will  be  softer.  The  hardness  of  the  water  after  this  deposit  of  lime,  afte< 
long  boiling,  is  called  the  permanent  hardness  and  the  difference  between  it, 
and  the  total  hardness  is  called  temporary  hardness. 

Lime  salts  in  water  react  immediately  on  soap-solutions,  precipitating  the 
oleate,  palmitate,  or  stearate  of  lime  at  once.  Magnesia  salts,  on  the  con- 
trary, require  some  considerable  time  for  reaction.  They  are,  however, 
more  powerful  hardeners  ;  one  equivalent  of  magnesia  salts  consuming  as 
much  soap  as  one  and  one-half  equivalents  of  lime. 

The  presence  of  soda  and  potash  salts  softens  rather  than  hardens  water. 
Each  grain  of  carbonate  of  lime  per  gallon  of  water  causes  an  increased 
expenditure  for  soap  of  about  2  ounces  per  100  gallons  of  water.  (Eng^g. 
News,  Jan.  31,  1885.) 

Purifying  Feed-water  for  Steam-boilers.— To  effect  the 
purification  of  water  before  and  after  being  fed  into  a  boiler,  a  device  man- 
ufactured by  the  Albany  Steam  Trap  Company,  Albany,  N.  Y.  removes 
the  impurities  by  the  process  of  a  continuous  circulation  of  the  water  from 
the  boiler,  through  the  filter  and  back  into  the  boiler,  The  scale  forming 
impurities  that  are  held  in  suspension  are  thus  brought  in  contact  with 
and  "arrested"  by  the  filtering  agent  contained  in  the  filter  while  under 
pressure,  and  at  a  temperature  limited  only  by  that  contained  in  the  boiler. 

It  is  sometimes  desirable,  in  the  removal  of  the  sulphates  and  carbonates 
from  the  feed- water,  to  heat  the  water  up  to  nearly  the  same  temperature 
as  it  is  in  the  boiler,  and  then  to  filter  the  same  before  feeding  it  into  the 
boiler.  The  operation  in  a  general  way  is  :  The  water  is  first  forced  into  the 
usual  exhaust-heater  by  the  feed-pump,  and  there  it  is  heated  by  the  ex- 
haust from  the  engine,  say  to  200°,  and  at  this  temperature  it  enters  the  re- 
heater.  The  reheater  consists  of  a  vertical,  cylindrical  shell  containing  a 
series  of  water  pans  or  shelves,  and  so  arranged  that  as  the  water  enters  it 
it  delivered  into  the  top  pan,  and  then  overflows  into  the  second,  and  so  on 
down  the  series  to  the  bottom,  and  during  its  transit  deposits  the  scale- 
forming  material.  The  circulating-pump  takes  the  water  from  the  bottom  of 
the  reheater  and  forces  it  through  the  filter  on  its  way  into  the  boiler. 

Mr.  W.  B.  Coggswell,  of  the  Solvay  Process  Co.'s  Soda  Works  in  Syracuse, 
N.  Y.,  thus  describes  the  system  of  purification  of  boiler  feed-water  in  use 
at  these  works  (Trans.  A.  S.  M.  E.,  xiii.  255): 

For  purifying,  we  use  a  weak  soda  liquor,  containing  about  12  to  15  grams. 
Na2Cos  per  litre.  Say  1^  to  2  M3  (or  397  to  530  gals.)  of  this  liquor  is  run 
into  the  precipitating  tank.  Hot  water  about  60°  C.  is  then  turned  in.  and 
the  reaction  of  the  precipitation  goes  on  while  the  tank  is  filling,  which  re- 
quires about  15  minutes.  When  the  tank  is  full  the  water  is  filtered  through 
the  Hyatt  (4),  5  feet  diameter,  and  the  Jewell  (1),  10  feet  diameter,  filters  in 
30  minutes.  Forty  tanks  treated  per  24  hours. 

Charge  of  water  purified  at  once 35  M3,  9.275  gallons. 

Soda  in  purifying  reagent 15  kgs.  Na,2CO3. 

Soda  used  per  1 ,000  gallons 3.5  Ibs. 

A  sample  is  taken  from  each  boiler  every  other  day  and  tested  for  deg. 
Baume,  soda  and  salt.  If  the  deg.  B  is  more  than  2,  that  boiler  is  blown  to 
reduce  it  below  2  deg.  B. 

The  following  are  some  analyses  given  by  Mr.  Coggswell : 


Lake 
Water, 
grams  per 
litre. 

Mud  from 
Hyatt 
Filter. 

Scale  from 
Boiler- 
tube. 

Scale 
found 
in 
Pump. 

Calcium  sulphate 

.261 

3.70 

51  24 

10  9 

Calcium  chloride             

.186 

Calcium  carbonate  

.091 

63.37 

19.76 

87. 

Magnesium  carbonate  . 

015 

1.11 

25  21 

Magnesium  chloride 

087 

Salt  NaCl 

.63 

14 

Silica            

15  17 

2.29 

.8 

Iron  and  aluminum  oxide 

3.75 

1.10 

1  2 

Total  

1.270 

87.10 

99.74 

99.9 

FLOW   OF   WATER.  555 


of  Arthur  Pennell,  of  Kansas  City.  The  general  plan  adopted  is  to  first  dis- 
solve the  chemicals  in  a  closed  tank,  and  then  connect  this  to  the  supply  main 
so  that  its  contents  will  be  forced  into  the  main  tank,  the  supply-pipe  being 
so  arranged  that  thorough  mixture  of  the  solution  with  the  water  is  ob- 
tained. A  waste-pipe  from  the  bottom  of  the  tank  is  opened  from  time  to 
time  to  draw  off  the  precipitate.  The  pipe  leading  to  the  tender  is  arranged 
to  draw  the  water  from  near  the  surface. 

A  water-tank  24  feet  in  diameter  and  16  feet  high  will  contain  about  46,600 
gallons  of  water.  About  three  hours  should  be  allowed  for  this  amount  of 
water  to  pass  through  the  tank  to  insure  thorough  precipitation,  giving  a 
permissible  consumption  of  about  15,000  gallons  per  hour.  Should  more 
than  this  be  required,  auxiliary  settling-tanks  should  be  provided. 

The  chemicals  added  to  precipitate  the  scale-forming  impurities  are  so- 
dium carbonate  and  quicklime,  varying  in  proportions  according  to  the  rela- 
tive proportions  of  sulphates  and  carbonates  in  the  water  to  be  treated. 
Sufficient  sodium  carbonate  is  added  to  produce  just  enough  sodium  sulphate 
to  combine  with  the  remaining  lime  and  magnesia  sulphate  and  produce 
glauberite  or  its  corresponding  magnesia  salt,  thereby  to  get  rid  of  the 
sodium  sulphate,  which  produces  foaming,  if  allowed  to  accumulate. 


HYDRAULICS—  PLOW  OP  WATER. 

Formulae  for  Discharge  of  Water  though  Orifices  and 
\Veirs.  —  For  rectangular  or  circular  orifices,  with  the  head  measured  from 
centre  of  the  orifice  to  the  surface  of  the  still  water  in  the  feeding  reservoir. 


Q=  CVfyHX  a  ............    (1) 

For  weirs  with  no  allowance  for  increased  head  due  to  velocity  of  approach: 
Q  =  C%  V^H  X  LH.  ..........    (2) 


For  rectangular  and  circular  or  other  shaped  vertical  or  inclined  orifices; 
formula  based  on  the  proposition  that  each  successive  horizontal  layer  of 
water  passing  through  the  orifice  has  a  velocity  due  to  its  respective  head: 

Q  =  cL%  V%/  X  (  VHb*  -  VHt*)  ......    (3) 

For  rectangular  vertical  weirs: 

Q  =  c%  V^gHxLh  ...........    (4) 

Q  —  quantity  of  water  discharged  in  cubic  feet  per  second;  C  =  approxi- 
mate coefficient  for  formulas  (1)  and  (2)  ;  c  —  correct  -coefficient  for  (3) 
and  (4). 

Values  of  thejjoefficients  c  and  C  are  given  below. 

g  =  3-2.16;  \(2g  =  8.02;  H  -  head  in  feet  measured  from  centre  of  orifice 
to  level  of  still  water;  Hb  =  head  measured  from  bottom  of  orifice;  Ht  — 
head  measured  from  top  of  orifice;  h  =  H  ,  corrected  for  velocity  of  ap- 

4  yai 
proach,  Fa,  —  H  -\-  -  —  —  ;  a  =  area  in  square  feet;  L  =  length  in  feet. 

Flow  of  Water  from  Orifices.—  The  theoretical  velocity  of  water 
flowing  from  an  orifice  is  the  same  as  the  velocity  of  a  falling  body  which 
has  fallen  from  a  height  equal  to  the  head  of  water,  =  \'2gH.  The  actual 
velocity  at  the  smaller  section  of  the  vena  contracta  is  substantially  the 
same  as  the  theoretical,  but  the  velocity  at  the  plane  of  the  orifice  is 
C  \  2gH,  in  which  the  coefficient  C  has  the  nearly  constant  value  of  .62.  The 
smallest  diameter  of  the  vena  contracta  is  therefore  about  .79  of  that  of  the 
orifice.  If  C  be  the  approximate  coefficient  =  .62,  and  c  the  correct  cpeffl- 


556 


HYDRAULICS. 


cient,  the  ratio  -  varies  with  different  ratios  of  the  head  to  the  diameter 
c 

TT 

of  the  vertical  orifice,  or  to  — .    Hamilton  Smith,  Jr.,  gives  the  following: 


For|=    .5 

—  =  .9604 


.875 


.1 


1.5 


2.5 


10. 


.9849     .9918        .9965       .9980       .9987        .9997  1. 

c 

For  vertical  rectangular  orifices  of  ratio  of  head  to  width  W : 
For^.=    .5          .6         .8         .1          1.5         2.          3.         4.         5.        8. 

—  =  .9428    .9657    .9823    .9890    .9953    .9974    .9988    .9993    .9996    .9998 
c 

For  H  -5-  D  or  H  -*-  W  over  8,  C  =  c,  practically. 

Weisbacb  gives  the  following  values  of  c  for  circular  orifices  in  a  thin  wall. 
H  —  measured  head  from  centre  of  orifice. 


Dft. 

H  ft. 

.066 

.33 

.82 

2.0 

3.0 

45. 

340. 

.033 
.066 
.10 
.13 

.711 

.665 

.637 
.629 
.622 
.614 

.628 
.621 
.614 
.607 

.641 

.632 

.600 

For  an  orifice  of  D  =  .033  ft.  and  a  well-rounded  mouthpiece,  H  being  the 
effective  head  in  feet, 


H  =  .066 
c  =  .959 


1.64 


11.5 
.975 


56 
.994 


.994 


Hamilton  Smith,  Jr.,  found  that  for  great  heads,  312  ft.  to  336  ft.,  with  con- 
verging mouthpieces,  c  has  a  value  of  about  one.  and  for  small  circular 
orifices  in  thin  plates,  with  full  contraction,  c  =  about  .60.  Some  of  Mr, 
Smith's  experimental  values  of  c  for  orifices  in  thin  plates  discharging  into 
air  are  as  follows.  All  dimensions  in  feet. 


Circular,  in  steel,  D  =  .020,  j 
Circular,  in  brass,  D  =  .050,  \  • 


H  = 


Circular,  in  brass,!)  =  .100,  -j 
Circular,  in  iron,  D  =  .100,  -J 
Square,  in  brass,  .05  X  .05,  -j  & 

Square,  in  brass,  .10  X  .10,  -j  -^ 

Rectangular,  in  brass,          j  H 
L=  .300,  W=  .050 1    c 


:  .739 

.6495 

:  .185 

2.43 
.6298 
.536 

3 

1 

.19 
.6:264 

.74 

2.73 

3.57 

4 

.63 

.6525 

.6265 

.6113 

.6070 

.6060 

.6051 

:  .129 

.457 

.900 

1 

.73 

2 

.05 

3 

.18 

.6337 

.6155 

.6096 

.6042 

,6038 

.6025 

1.80 

1.81 

2 

.81 

4 

.68 

.6061 

.6041 

.6033 

.6026 

.313 

.877 

i! 

.79 

2 

.81 

3 

70 

4, 

,63 

.6410 

.6238 

.6157 

.6127 

6113 

,6097 

.181 

.939   1.71 

2 

.75 

3! 

74 

4, 

.59 

.6292 

.6139 

.6084 

.6076 

,6060 

,6005 

.261 

.917 

1^82 

2 

.83 

3' 

75 

4, 

,70 

.6476 

.6:280 

,6203 

.6180 

.6176 

.6168 

For  the  rectangular  orifice,  Z/,  the  length,  is  horizontal. 

Mr.  Smith,  as  the  result  of  the  collation  of  much  experimental  data  of 
others  as  well  as  his  own,  gives  tables  of  the  value  of  c  for  vertical  orifices, 
with  full  contraction,  with  a  free  discharge  into  the  air,  with  the  inner  face 
of  the  plate,  in  which  the  orifice  is  pierced,  plane,  and  with  sharp  inner 
corners,  so  that  the  escaping  vein  only  touches  these  inner  edges.  These 
tables  are  abridged  below.  The  coefficient  c  is  to  be  used  in  the  formulae  (3) 

and  (4)  above.    For  formulae  (1)  and  (2j  use  the  coefficient  (7  found  from  the 
ri 

values  of  the  ratios  —  above, 

Q 


HYDEAULIC   FORMULAE. 


557 


Values  of  Coefficient  c  for  Vertical  Orifices  witli  Sliarp 
Edges,  Full  Contraction,  and  Free  Discharge  into 
Air.  (Hamilton  Smith,  Jr.) 


Head  from 
Centre  of 
Orifice  H. 

Square  Orifices.    Length  of  the  Side  of  the  Square,  in  feet. 

.02 

.03 

.04 

.05 

.07 

.10 

.12 

.15 

.20 

.40 

.60 

.80 

1.0 

A 
.6 

1.0 
3.0 
6.0 

10. 
20. 
100.  (?) 

.660 
.648 
.632 
.623 
.616 
.606 

.645 
.636 
.622 
.616 
.611 
605 

.643 

.636 
.628 
.616 
.612 
608 
604 

.637 
.630 
.622 
.612 
.609 
.606 
603 

.628 
.623 
.618 
.609 
.607 
.605 
.602 

.621 
.617 
.613 
.607 
.605 
.604 
602 

.616 
.613 
.610 
.606 
.605 
.604 
.602 

.611 
.610 
.608 
.606 
.605 
.603 
602 

.605 
.605 
.605 
.604 
.603 
602 

.601 
.603 
.605 
.604 
.603 
601 

.598 
.601 
.604 
.603 
.602 
.601 

.596 
.600 
.603 
.602 
.602 
.601 

.599 
.603 
.602 
.601 
.600 

.599 

.598 

.598 

.598|   .598 

.598 

.598 

.598 

.598 

598 

.598 

.598 

.598 

H. 

Circular  Orifices.    Diameters,  in  feet. 

.02 

.03 

.04 

.05      .07 

.10 

.12 

.15 

.20 

.40 

.60 

.80 

1.0 

A 
.6 
1.0 
2. 

4. 
6. 
10. 

20. 
50.(?) 

100.(?) 

.655 
.644 
.632 
.623 
.618 
.611 
.601 
.596 
.593 

.640 
.631 
.621 
.614 
.611 
.606 
.600 
.596 
.593 

.630 
.623 
.614 
.609 
.607 
.603 
.599 
.595 
.592 

.637 
.624 
.617 
.610 
.605 
.604 
.601 
.598 
.595 
.592 

.628 
.618 
.612 
.607 
.603 
.602 
.599 
.597 
.594 
.592 

.618 
.613 
.608 
.604 
.602 
.600 
.598 
.596 
.594 
.592 

.612 
.609 
.605 
.601 
.600 
.599 
.598 
.596 
.594 
.592 

.606 
.605 
.603 
.600 
.599 
.599 
.597 
.596 
.594 
.592 

.601 
.600 
.599 
.599 
.598 
.597 
.596 
.594 
.592 

.596 
.598 
.599 
.598 
.598 
.597 
.596 
.594 
.592 

.593 
.595 
.597 
.597 
.597 
.596 
.596 
.594 
.592 

.590 
.593 
.596 
.597 
.596 
.596 
.595 
.593 
.592 

.591 

.595 
.596 
.596 
.595 
.594 
.593 
.592 

HYDRAFLIC  FORMUL.JE.— FI^OW  OF  WATER  IN 
OPEN  AND  CLOSED  CHANNELS. 

Flow  of  Water  in  Pipes.— The  quantity  of  water  discharged 
through  a  pipe  depends  on  the  "head;11  that  is,  the  vertical  distance  be- 
tween the  level  surface  of  still  water  in  the  chamber  at  the  entrance  end  of 
the  pipe  and  the  level  of  the  centre  of  the  discharge  end  of  the  pipe ; 
also  upon  the  length  of  the  pipe,  upon  the  character  of  its  interior  surface 
as  to  smoothness,  and  upon  the  number  and  sharpness  of  the  bends:  but 
it  is  independent  of  the  position  of  the  pipe,  as  horizontal,  or  inclined 
upwards  or  downwards. 

The  head,  instead  of  being  an  actual  distance  between  levels,  may  be 
caused  by  pressure,  as  by  a  pump,  in  which  case  the  head  is  calculated  as  a 
vertical  distance  corresponding  to  the  pressure  1  Ib.  per  sq.  in.  =  2.309  ft. 
head,  or  1  ft.  head  =  .433  Ib.  per  sq.  in. 

The  total  head  operating  to  cause  flow  is  divided  into  three  parts:  1.  The 
velocity-head,  which  is  the  height  through  which  a  body  must  fall  in  vacua 
to  acquire  the  velocity  with  which  the  water  flows  into  the  pipe  =  v2  -t-2g,  in 
which  v  is  the  velocity  in  ft.  per  sec.  and  2g  =  64.32;  2.  the  entry-head,  that 
required  to  overcome  the  resistance  to  entrance  to  the  pipe.  With  sharp- 
edged  entrance  the  entry-head  =  about  \4  the  velocity-head;  with  smooth 
rounded  entrance  the  entry-head  is  inappreciable;  3.  the  friction-head,  due 
to  the  friction al  resistance  to  flow  within  the  pipe. 

In  ordinary  cases  of  pipes  of  considerable  length  the  sum  of  the  entry  and 
velocity  heads  required  scarcely  exceeds  1  foot.  In  the  case  of  long  pipes 
with  low  heads  the  sum  of  the  velocity  and  entry  heads  is  generally  so  small 
that  it  may  be  neglected. 

General  Formula  for  Flow  of  Water  in  Pipes  or  Conduits, 
Mean  velocity  in  ft.  per  sec.  =  c  j/mean  hydraulic  radius  X  slope 

Do.  for  pipes  running  full  =  CA/  dia™eter  x  siope, 
in  which  c  is  a  coefficient  determined  by  experiment.    (See  pages  559-564.) 


553 


SYDKAULICS. 


The  mean  hydraulic  radius  = 


£.rea  of  wet  cross-section 


wet  perimeter. 

In  pipes  running  full,  or  exactly  half  full,  and  in  semicircular  open  chan- 
nels running  full  it  is  equal  to  %  diameter. 

The  slope  —  the  head  (or  pressure  expressed  as  a  head,  in  feet) 

-7-  length  of  pipe  measured  in  a  straight  line  from  end  to  end. 

In  open  channels  the  slope  is  the  actual  slope  of  the  surface,  or  its  fall  per 
unit  of  length,  or  the  sine  of  the  angle  of  the  slope  with  the  horizon. 

If  r  =  mean  hydraulic  radius,  s  =  slope  =  head  H-  length,  v  =  velocity  in 
feet  per  second  all  dimensions  in  feet),  v  =  c  \'r  \/s  =  c  \/rs. 

Quantity  of  Water  Discharged.  -If  Q  —  discharge  in  cubic  feet 
per  second  and  a  —  area  of  channel,  Q  —  av  =  ac  VVs. 

a  Vr  is  approximately  proportional  to  the  discharge.  It  is  a  maximum  a« 
308°,  corresponding  to  19/20  of  the  diameter,  and  the  flow  of  a  conduit  19/20 
full  is  about  5  per  cent  greater  than  that  of  one  completely  filled. 

Table  giving  Fall  in  Feet  per  Mile,  the  Distance  on  Slope 
corresponding  to  a  Fall  of  1  Ft.9  and  also  the  Values 

of  s  and  V*  for  Use  in  the  Formula  v  =  c  VW. 

s  =  H-*-L=  sine  of  angle  of  slope  =  fall  of  water-surface  (H),  in  any  dis- 
tance (L),  divided  by  that  distance. 


Fall  in 
Feet 
per  Mi. 

Slope, 
1  Foot 
in 

Sine  of 
Slope, 
s. 

Vs. 

Fall  in 
Feet 
per  Mi. 

Slope, 
1  Foot 
in 

Sine  of 
Slope, 
s. 

Vs. 

0.25 

21120 

.0000473 

.006881 

17 

310.6 

.0032197 

.056742 

.30 

17600 

.0000568 

.007538 

18 

293.3 

.0034091 

.058S88 

.40 

13200 

.0000758 

.008704 

19 

277.9 

.0035985 

.059988 

.50 

10560 

.0000947 

.009731 

20 

264 

.0037879 

.061546 

.60 

8800 

.0001136 

.010660 

22 

240 

.0041667 

.064549 

.702 

7520 

.0001330 

.011532 

24 

220 

.0045455 

.067419 

.805 

6560 

.0001524 

.012347 

26 

203.1 

.0049242 

.070173 

.904 

5840 

.0001712 

.013085 

28 

188.6 

.0053030 

.072822 

1. 

5280 

.0001894 

.013762 

30 

176 

.0056818 

.075378 

1.25 

4224 

.0002367 

.015386 

35.20 

150 

.0066667 

.081650 

1.5 

3520 

.0002841 

.016854 

40 

132 

.0075758 

.087039 

1.75 

3017 

.0003314 

.018205 

44 

120 

.00833,33 

.091287 

2. 

2640 

.0003788 

.019463 

48 

110 

.0090909 

.095346 

2.25 

2347 

.0004261 

.020641 

52.8 

100 

.010 

.1 

2.5 

2112 

.0004735 

.021760 

60 

88 

.0113636 

.1066 

2.75 

1920 

.0005208 

.022822 

66 

80 

.0125 

.111803 

3. 

1760 

.0005682 

.023837 

70.4 

75 

.0133333 

.115470 

3.25 

1625 

.0006154 

.024807 

80 

66 

.0151515 

123091 

3.5 

1508 

.0006631 

.025751 

88 

60 

.0166667 

.1291 

3.75 

1408 

.0007102 

.026650 

96 

55 

.0181818 

.134839 

4 

1320 

.0007576 

.027524 

105.6 

50 

.02 

141421 

5 

1056 

.0009470 

.030773 

120 

44 

.0227273 

.150756 

6 

880 

.0011364 

.03371 

132 

40 

.025 

.158114 

7 

754.3 

.0013257 

.036416 

160 

33 

.0303030 

.174077 

8 

660 

.0015152 

.038925 

220 

24 

.0416667 

.204124 

9 

586.6 

.0017044 

.041286 

264 

20 

.05 

.223607 

10 

528 

.0018939 

.043519 

330 

16 

.0625 

.25 

11 

443.6 

.0020833 

.045643 

440 

12 

.0833333 

.288675 

12 

440 

.0022727 

.047673 

528 

10 

.1 

,316228 

13 

406.1 

.0024621 

.04962 

660 

8 

.125 

.353553 

14 

377.1 

.0026515 

.051493 

880 

6 

.1666667 

.408248 

15 

352 

.0028409 

.0533 

1056 

5 

.2 

447214 

16 

330 

.0030303 

.055048 

1320 

4 

.25 

.5 

HYDRAULIC   FOKMTTIJE. 


559 


Values  of  \/r  for  Circular  Pipes,  Sewers,  and  Conduits  of 
different  Diameters. 


r  =  mean  hydraulic  depth  = 
ning  full  or  exactly  half  full. 


perimeter 


=  14  diam.  for  circular  pipes  run- 


Diam.. 
ft.  in. 

\Tr 
in  Feet. 

Diam., 
ft.  in. 

i/v 

in  Feet. 

Diam., 
ft.  in. 

Vr 
in  Feet. 

Diam., 
ft.  in. 

Vi 
in  Feet. 

% 

.088 

2 

.707 

4      6 

.061 

9 

1.500 

Vz 

.102 

2      1 

.722 

4      7 

.070 

9      3 

1.521 

% 

.125 

2      2 

.736 

4      8 

.080 

9      6 

1.541 

1 

.144 

2      3 

.750 

4      9 

.089 

9      9 

1.561 

Ujl 

.161 

2      4 

.764 

4    10 

.099 

10 

1.581 

.177 

2      5 

.777 

4    11 

.109 

10      3 

1.601 

1% 

•191 

2      6 

.790 

5 

.118 

10      6 

1.620 

2 

.204 

2      7 

.804 

5      1 

.127 

10      9 

1.639 

2)4 

.228 

2      8 

.817 

5      2 

.137 

11 

1.658 

3 

.251 

2      9 

.829 

5      3 

.146 

11      3 

1.677 

4 

.290 

2    10 

.842 

5      4 

.155 

11      6 

1.696 

5 

.323 

2    11 

.854 

5      5 

.164 

11      9 

.1.714 

6 

.354 

3 

.866 

5      6 

.173 

12 

1.732 

7 

.382 

3      1 

.878 

5      7 

.181 

12      3 

1.750 

8 

.408 

3      2 

.890 

5      8 

.190 

12      6 

1.768 

9 

.433 

3      3 

.901 

5      9 

.199 

12      9 

1.785 

10 

.456 

3      4 

.913 

5    10 

.208 

13 

1.083 

11 

.479 

3      5 

.924 

5    11 

.216 

13      3 

1.820 

.500 

3      6 

.935 

6 

.225 

13      6 

1.837 

1 

.520 

3      7 

.946 

6      3 

.250 

14 

1.871 

2 

.540 

3      8 

.957 

6      6 

.275 

14      6 

1.904 

3 

.559 

3      9 

.968 

6      9 

.299 

15 

1.936 

4 

.577 

3    10 

.979 

7 

.323 

15      6 

1.968 

5 

.595 

3    11 

.990 

7      3 

.346 

16 

2. 

6 

.612 

4 

7      6 

.369 

16      6 

2.031 

7 

.629 

4      1 

!oio 

7      9 

.392 

17 

2.061 

8 

.646 

4      2 

.021 

8 

.414 

17      6 

2.091 

1    9 

.661 

4      3 

.031 

8      3 

.436 

18 

2.121 

1  10 

.677 

4      4 

.041 

8      6 

.458 

19 

2.180 

1  11 

.692 

4      5 

1.051 

8      9 

1.479 

20 

2.236 

Values  of  the  Coefficient  c.  (Chiefly  condensed  from  P.  J.  Flynn 
on  Flow  of  Water.)— Almost  all  the  old  hydraulic  formulae  for  finding  the 
mean  velocity  in  open  and  closed  channels  have  constant  coefficients,  and  are 
therefore  correct  for  only  a  small  range  of  channels.  They  have  often  been 
found  to  give  incorrect  results  with  disastrous  effects.  Ganguillet  and  Kut- 
ter  thoroughly  investigated  the  American,  French,  and  other  experiments, 
and  they  gave  as  the  result  of  their  labors  the  formula  now  generally  known 
as  Kutter's  formula.  There  are  so  many  varying  conditions  affecting  the 
flow  of  water,  that  all  hydraulic  formulae  are  only  approximations  to  the 
correct  result. 

When  the  surface-slope  measurement  is  good,  Kutter's  formula  will  give 
results  seldom  exceeding  7^  error,  provided  the  rugosity  coefficient  of  the 
formula  is  known  for  the  site.  For  small  open  channels  D'Arcy's  and 
Bazin's  formulae,  and  for  cast-iron  pipes  D'Arcy's  formulae,  are  generally 
accepted  as  being  approximately  correct. 

flutter's  Formula  for  measures  in  feet  is 


in  which  v  =  mean  velocity  in  feet  per  second ;  r  =  -  =  hydraulic  mean 


560  HYDRAULICS. 

depth  in  feet  =  area  of  cross-section  in  square  feet  divided  by  wetted  perim- 
eter in  lineal  feet ;  s  =  fall  of  water-surface  (h)  in  any  distance  (I)  divided 

by  that  distance,  =  -,  =  sine  of  slope  ;  n  =  the  coefficient  of  rugosity,  de- 
pending on  the  nature  of  the  lining  or  surface  of  the  channel.  If  we  let  the 
first  term  of  the£ight-hand  side  of  the  equation  equal  c,  we  have  Chezy's 
formula,  v  =  c  \^rs  =  c  X  -Vr  X  Vs* 

Values  of  n  in  Kutter's  Formula.— The  accuracy  of  Kutter's  for- 
mula depends,  in  a  great  measure,  on  the  proper  selection  of  the  coefficient 
of  roughness  n.  Experience  is  required  in  order  to  give  the  right  value  to 
this  coefficient,  and  to  this  end  great  assistance  can  be  obtained,  in  making 
this  selection,  by  consulting  and  comparing  the  results  obtained  from  Ex- 
periments on  the  flow  of  water  already  made  in  different  channels. 

In  some  cases  it  would  be  well  to  provide  for  the  contingency  of  future 
deterioration  of  channel,  by  selecting  a  high  value  of  ?i,  as,  for  instance, 
where  a  dense  growth  of  weeds  is  likely  to  occur  in  small  channels,  and  also 
where  channels  are  likely  not  to  be  kept  in  a  state  of  good  repair. 

The  foliowing  table,  giving  the  value  of  n  for  different  materials,  is  com- 
piled from  Kutter,  Jackson,  and  Hering,  and  this  value  of  n  applies  also  in 
each  instance,  to  the  surfaces  of  other  materials  equally  rough. 

VALUE  OF  n  IN  KUTTER'S  FORMULA  FOR  DIFFERENT  CHANNELS. 

n  =  .009,  well-planed  timber,  in  perfect  order  and  alignment ;  otherwise, 
perhaps  .01  would  be  suitable. 

n  =  .010,  plaster  in  pure  cement ;  planed  timber  ;  glazed,  coated,  or  en- 
amelled stoneware  and  iron  pipes  ;  glazed  surfaces  of  every  sort  in  perfect 
order. 

n  =  .011,  plaster  in  cement  with  one  third  sand,  in  good  condition  ;  also  for 
iron,  cement,  and  terra  cotta  pipes,  well  joined,  and  in  best  order. 

n  =  .012,  unplaned  timber,  when  perfectly  continuous  on  the  inside  ; 
flumes. 

n  =  .013,  ashlar  and  well-laid  brickwork  ;  ordinary  metal ;  earthen  and 
stoneware  pipe  in  good  condition,  but  not  new  ;  cement  and  terra-cotta  pipe 
not  well  jointed  nor  in  perfect  order  ,  plaster  and  planed  wood  in  imperfect 
or  inferior  condition  ;  and,  generally,  the  materials  mentioned  with  n  =  .010, 
when  in  imperfect  or  inferior  condition. 

n  =  .015,  second  class  or  rough-faced  brickwork  ;  well-dressed  stonework  ; 
foul  and  slightly  tuberculated  iron  ;  cement  and  terra-cotta  pipes,  with  im- 
perfect joints  and  in  bad  order  ;  and  canvas  lining  on  wooden  frames. 

?i  =  .017,  brickwork,  ashlar,  and  stoneware  in  an  inferior  condition  ;  tu- 
berculated iron  pipes  ;  rubble  in  cement  or  plaster  in  good  order  ;  fine  gravel, 
well  rammed,  ^  to  %  inch  diameter  ;  and,  generally,  the  materials  men- 
tioned with  n  =  .013  when  in  bad  order  and  condition. 

n  —  .020,  rubble  in  cement  in  an  inferior  condition  ;  coarse  rubble,  rough 
set  in  a  normal  condition  ;  coarse  rubble  set  dry  ;  ruined  brickwork  and 
masonry  ;  coarse  gravel  well  rammed,  from  1  to  1^  inch  diameter  ;  canals 
with  beds  and  banks  of  very  firm,  regular  gravel,  carefully  trimmed  and 
rammed  in  defective  places  ;  rough  rubble  with  bed  partially  covered  with 
silt  and  mud  ;  rectangular  wooden  troughs,  with  battens  on  the  inside  two 
inches  apart ;  trimmed  earth  in  perfect  order. 

n  =  .0225,  canals  in  earth  above  the  average  in  order  and  regimen. 

n  =  .025,  canals  and  rivers  in  earth  of  tolerably  uniform  cross-section  ; 
slope  and  direction,  in  moderately  good  order  and  regimen,  and  free  from 
stones  and  weeds. 

n  —  .0^75,  canals  and  rivers  in  earth  below  the  average  in  order  and  regi- 
men. 

n  =  .030,  canals  and  rivers  in  earth  in  rather  bad  order  and  regimen,  hav- 
ing stones  and  weeds  occasionally,  and  obstructed  by  detritus. 

n  =  .035,  suitable  for  rivers  and  canals  with  earthen  beds  in  bad  order  and 
regimen,  and  having  stones  and  weeds  in  great  quantities. 

n  =  .05,  torrents  encumbered  with  detritus. 

Kutter's  formula  has  the  advantage  of  being  easily  adapted  to  a  change 
in  the  surface  of  the  pipe  exposed  to  the  flow  of  water,  by  a  change  in  the 
value  of  n.  For  cast-iron  pipes  it  is  usual  to  use  n  —  .013  to  provide  for  the 
future  deterioration  of  the  surface.  _,.  _ 

Reducing  Kutter'*  formula  to  the  form  v  =  c  X  Vr  X  4/s,  and  taking  n,  the 
coefficient  of  roughness  in  the  formula  =  .011,  .012,  and  .013,  and  s  =  .001,  we 
have  the  following  values  of  the  coefficient  c  for  different  diameters  of 
conduit. 


HYDRAULIC  FORMULA. 


561 


Values  of  c  in  Formula  v  =  c  x  Vr  x  Vs  for  Metal  Pipes  and 
Moderately  Smooth  Conduits  Generally. 

By  KUTTKB'S  FORMULA,     (s  =  .001  or  greater.) 


Diameter. 

n  =  .011 

n  =  .012 

n  =  .013 

Diameter. 

n  =  .011 

n  =  .012 

n  =  .013 

ft.    in. 
0       1 
2 
4 
6 

6 
2 
3 
4 
5 
6 

c  — 
47.1 
61.5 
77.4 
87.4 
105.7 
116.1 
123.6 
133.6 
140.4 
145.4 
149.4 

c  — 

c  — 

ft. 
7 
8 
9 
10 
11 
12 
14 
16 
18 
20 

c  = 
152.7 
155.4 
157.7 
159.7 
161.5 
163 
165.8 
168 
169.9 
171.6 

139~.2 
141.9 
144.1 

146 
147.8 
149.3 
152 
154.2 
156.1 
157.7 

127~.9 
130.4 
132.7 
134.5 
136.2 
137.7 
140.4 
142.1 
144.4 
146 

77.5 
94.6 
104.3 
111.3 
120.8 
127.4 
132.3 
136.1 

69.5 
85.3 
94.4 
101.1 
110.1 
116.5 
121.1 
124.8 

For  circular  pipes  the  hydraulic  mean  depth  r  equals  V±  of  the  diameter. 

According  to  Kutter's  formula  the  value  of  c,  the  coefficient  of  discharge, 
is  the  same  for  all  slopes  greater  than  1  in  1000;  that  is,  within  these  limits 
c  is  constant.  We  further  find  that  up  to  a  slope  of  1  in  2640  the  value  of  c 
is,  for  all  practical  purposes,  constant,  and  even  up  to  a  slope  of  1  in  5000 
the  difference  in  the  value  of  c  is  very  little.  This  is  exemplified  in  the 
following : 

Value  of  c  for  Different  Values  of  V^and  s  in  Kutter's 
Formula,  with  n_=  .013. 

v  =  c  V~r  X  Vs.  


Slopes. 


Vr 

1  in  1000 

1  in  2500 

1  in  3333.3 

1  in  5000 

1  in  10,000 

.6 
1 
2 

93.6 
116.5 
142.6 

91.5 
115.2 
142.8 

90.4 
114.4 
143.0 

88.4 
113.2 
143.1 

83.3 
109.7 
143.8 

The  reliability  of  the  values  of  the  coefficient  of  Kutter's  formula  for 
pipes  of  less  than  6  in.  diameter  is  considered  doubtful.  (See  note  under 
table  on  page  564.) 

Values  of  c  for  Earthen  Channels,  by  Kutter's  Formula, 
for  Use  in  Formula  v  =  c  yrs. 


Coefficient  of  Roughness, 

Coefficient  of  Roughness, 

n  =  .0225. 

n  =  .035. 

Vr  in  feet. 

Vr  in  feet. 

0.4 

1.0 

1.8 

2.5 

4.0 

0.4 

1.0 

1.8 

2.5 

4.0 

Slope,  1  in 

c 

c 

c 

c 

c 

c 

c 

c 

c 

c 

1000 

35.7 

62.5 

80.3 

89.2 

99.9 

19.7 

37.6 

51.6 

59.3 

69.2 

1250 

35  5 

62.3 

80.3 

89.3 

100.2 

19.6 

37.6 

51.6 

59.4 

69.4 

1667 

35.2 

62.1 

80.3 

89.5 

100.6 

19.4 

37.4 

51.6 

59.5 

69.8 

2500 

34.6 

61.7 

80.3 

89.8 

101.4 

19.1 

37.1 

51.6 

59.7 

70.4 

3333 

34. 

61.2 

80.3 

90.1 

102.2 

18.8 

36.9 

51.6 

59.9 

71.0 

5000 

33. 

60.5 

80.3 

90.7 

103.7 

18.3 

36.4 

51.6 

60.4 

72.2 

7500 

31.6 

59.4 

80.3 

91.5 

106.0 

17.6 

35.8 

51.6 

60.9 

73.9 

10000 

30.5 

58.5 

80.3 

92.3 

107.9 

17.1 

35.3 

51.6 

60.5 

75.4 

15840 

28.5 

56.7 

80.2 

93.9 

112.2 

16.2 

34.3 

51.6 

62.5 

78.6 

20000 

27.4 

55.7 

80.2 

94.8 

115.0 

15.6 

33.8 

51.5 

63.1 

80.6 

562 


HYDBAULICS. 


Mr.  Molesworth,  in  the  22d  edition  of  his  "  Pocket-book  of  Engineering 
Formulae,"  gives  a  modification  of  Kutter's  formula  as  follows  :  For  flow  in 
cast-iron  pipes,  v  =  c  Vrs,  in  which 

181  +  ="« 


.00281 


.026 


in  which  d  =  diameter  of  the  pipe  in  feet. 

(This  formula  was  given  incorrectly  in  Molesworth's  21st  edition.) 
JVloleswortn's  Formula.— v  =  4/fcrs,  in  which  the  values  of  k  are 

as  follows  : 


Values  of  k  for  Velocities. 


ixaiure  01  unannei. 

Less  than 
4  ft.  per  sec. 

More  than 
4  ft.  per  sec. 

8800 

8500 

Earth  

7200 

6800 

Shingle.     .        .                

6400 

5900 

Rough,  with  bowlders  

5300 

4700 

In  very  large  channels,  rivers,  etc.,  the  description  of  the  channel  affects 
the  result  so  slightly  that  it  may  be  practically  neglected,  and  k  assumed  = 
from  8500  to  9000. 

Fly nu's  Formula.— Mr.  Flynn  obtains  the  following  expression  of 
the  value  of  Kutter's  coefficient  for  a  slope  of  .001  and  a  value  of  n  =  .013 : 

183.72 


1-f- 


The  following  table  shows  the  close  agreement  of  the  values  of  c  obtained 
from  Kutter's,  Molesworth's,  and  Flyun's  formulae  : 


Diameter. 
6  inches 
6  inches 
4  feet 
4  feet 
8  feet 
8  feet 


Slope. 
lin  40 
1  in  1000 
1  in  400 
1  in  1000 
1  in  700 
1  in  2600 


Kutter. 
71.50 
69.50 

117. 

116.5 

130.5 

129.8 


Molesworth. 
71.48 
69.79 
117. 
116.55 
130.68 
129.93 


Flynn. 
69.5 
69.5 
116.5 
116.5 
130.5 
130.5 


Mr.  Flynn  gives  another  simplified  form  of  Kutter's  formula  for  use  with 
different  values  of  n  as  follows  : 


Vrs. 


In  the  following  table  the  value  of  K  is  given  for  the  several  values  of  n  : 


n 

K 

n 

K 

n 

K 

n 

K 

n 

K 

.009 
.010 

.011 

245.63 
225.51 

209.05 

.012 
.013 
.014 

195.33 
183.72 
137.77 

.015 
.016 
.017 

165.14 
157.6 
150.94 

.018 
.019 
.020 

145.03 
139.73 
134.96 

.021 
.022 
.0225 

130.65 
126.73 
124.9 

If  in  the  application  of  Mr.  Flynn's  formula  given  above  within  the  limits 
of  n  as  given  in  the  table,  we  substitute  for  n,  K,  and  i/r  their  values,  wo 
have  a  simplified  form  of  Kutter's  formula. 


HYDRAULIC   FORMULA  563 


For  instance,  when  n  =  .011,  and  d  =  3  feet,  we  have 
209.05 


.  . 

7-     ~on\        rs' 

^44.41X^61 


Bazlii'K   Formulae  : 

For  very  even  surfaces,  flue  plastered  sides  and  bed,  planed  planks,  etc., 


v  =A/1  -*-  .0000045(l0.16  -fj)  X  Vrs. 

For  even  surfaces  such  as  cut-stone,  brickwork,  unplaned  planking,  mortar, 
etc.  : 


v  =  4/1  H-  .000013(4.354  +  ^)  X  Vrs 
For  slightly  uneven  surfaces,  such  as  rubble  masonry  i 


v  -  A/1  -*-  .00006(l.219  H-  i)  X  |/rs. 
For  uneven  surfaces,  such  as  earth : 


-  .00035(0.2438  -f  *)  X  Vrs- 
A  modification  of  Bazin's  formula,  known  as  D'Arcy's  Bazin's : 


1000s 


r  -f  0.35 

For  small  channels  of  less  than  20  feet  bed  Bazin's  formula  for  earthen 
channels  in  good  order  gives  very  fair  results,  but  Kutter's  formula  is  super- 
seding it  in  almost  all  countries  where  its  accuracy  has  been  investigated. 

The  last  table  on  p.  561  shows  the  value  of  c,  in  Kutter's  formula,  for  a  wide 
range  of  channels  in  earth,  that  will  cover  anything  likely  to  occur  in  the 
ordinary  practice  of  an  engineer. 

D'Arcy's  Formula  for  clean  iron  pipes  under  pressure  is 


'"F 


.00007726  + 


Flynn's  modification  of  D'Arcy's  formula  is 


in  which  d  —  diameter  in  feet. 

D'Arcy's  formula,  as  given  by  J.  B.  Francis,  C.E.,  for  old  cast-iron  pipe, 
lined  with  deposit  and  under  pressure,  is 


Flynn's  modification  of  D'Arcy's  formula  for  old  cast-iron  pipe  is 


564 


HYDRAULICS. 


For  Pipes  Less  tliaii  5  in  dies  in  Diameter,  coefficients  (c) 
in  the  formula  v  =  c  Vrs,  from  the  formula  of  D'Arcy,  Kutter,  and  Fanning. 


Diam. 
in 
inches. 

D'Arcy, 
for  Clean 
Pipes. 

Kutter, 
for 
n  =  .011 
s=  .001 

Fanning, 
for  Clean 
Iron 
Pipes 

Diam. 
in 
inches 

D'Arcy, 
for  Clean 
Pipes. 

Kutter, 
for 
n  =  .011 
s=  .001 

Fanning, 
for  Clean 
Iron 
Pipes. 

% 

59.4 

32. 

m 

90.7 

58.8 

92.5 

i^f 

65.7 

36.1 

2 

92.9 

61.5 

94.8 

M 

74.5 

42.6 

%Y2 

96.1 

66. 

1 

80.4 

47.4 

80.4 

3 

98.5 

70.1 

96.6 

1/4 

84.8 

51.9 

4 

101.7 

77.4 

103.4 

* 

88.1 

55.4 

88. 

5 

103.8 

82.9 

Mr.  Flynn,  in  giving  the  above  table,  says  that  the  facts  show  that  the  co- 
efficients diminish  from  a  diameter  of  5  inches  to  smaller  diameters,  and  it 
is  a  safer  plan  to  adopt  coefficients  varying  with  the  diameter  than  a  con- 
stant coefficient.  No  opinion  is  advanced  as  to  what  coefficients  should  be 
used  with  Kutter's  formula  for  small  diameters.  The  facts  are  simply 
stated,  giving  the  results  of  well-known  authors. 

Older  Formulae.— The  following  are  a  few  of  the  many  formulae  for 
flow  of  water  in  pipes  given  by  earlier  writers.  As  they  have  constant  coef- 
ficients, they  are  not  considered  as  reliable  as  the  newer  formulae. 


Prony,  v  =  97  \/rs  -  .08; 


Eytelwein,    v  =  50  , 


-,    or    v  =  108  Vr~s  -  0.13 ; 


Hawksley,    v  =  48  A/     dh     ;      Neville,  v  =  140  Vrs  -  11  i/rs. 
Y    I  ~T~  j4c* 

In  these  formulae  d  =  diameter  in  feet;  h  =  head  of  water  in  feet;  Z  = 
length  of  pipe  in  feet;  s  =  sine  of  slope  =  —  ;  r  =  mean  hydraulic  depth, 

=  area  -*-  wet  perimeter  =  —  for  circular  pipe. 
4 

Mr.  Santo  Crimp  (Eng'g,  August  4,  1893)  states  that  observations  on  flow 
in  brick  sewers  show  that  the  actual  discharge  is  83J6  greater  than  that  cal- 
culated by  Eytelwein's  formula.  He  thinks  Kutter's  formula  not  superior 
to  D'Arcy 's  for  brick  sewers,  the  usual  coefficient  of  roughness  in  the 
former,  viz.,  .013,  being  too  low  for  large  sewers  and  far  too  small  in  the  case 
of  small  sewers. 

D'Arcy's  formula  for  brickwork  is 

4/2a  /         7?  \ 

v  =    —rs  ;    m  -  a(  1  -f  —  ) ;    a  -  .0037285;    B  =  .229663. 
m  V        r  / 

VELOCITY  OF  WATER  IN  OPEN  CHANNELS. 

Irrigation  Canals. — The  minimum  mean  velocity  required  to  prevent 
the  deposit  of  silt  or  the  growth  of  aquatic  plants  is  in  Northern  India, 
taken  at  \y»  feet  per  second.  It  is  stated  that  in  America  a  higher  velocity 
is  required  for  this  purpose,  and  it  varies  from  2  to  3^  feet  per  second.  Tin- 
maximum  allowable  velocity  will  vary  with  the  nature  of  the  soil  of  the 
bed.  A  sandy  bed  will  be  disturbed  if  the  velocity  exceeds  3  feet  per 
second.  Good  loam  with  not  too  much  sand  will  bear  a  velocity  of  4  feet 
per  second.  The  Cavour  Canal  in  Italy,  over  a  gravel  bed,  has  a  velocity  of 
about  5  per  second.  (Flynn's  "Irrigation  Canals.") 

Mean  Surface  and  Bottom  Velocities.— According  to  the  for- 
mula of  Bazin, 

v  =  vmax  -  25.4  Vrs;   v  =  vb  +  10.87  1/rsT 


VELOCITY   OF   WATER  IK   OPEK  CHANNELS.        565 


.-.  vb  =  v  —  10.87  |/rs,  in  which  v  =  mean  velocity  in  feet  per  second, 
umax  =  maximum  surface  velocity  in  feet  per  second,  vb  =  bottom  velocity 
in  feet  per  second,  r  =  hydraulic  mean  depth  in  feet  =  area  of  cross-section 
iu  square  feet  divided  by  wetted  perimeter  in  feet,  s  =  sine  of  slope. 

The  least  velocity,  or  that  of  the  particles  in  contact  with  the  bed,  is 
almost  as  much  less  than  the  mean  velocity  as  the  greatest  velocity  is 
greater  than  the  mean. 

Rankine  states  that  in  ordinary  cases  the  velocities  may  be  taken  as  bear- 
ing to  each  other  nearly  the  proportions  of  3,  4,  and  5.  In  very  slow  cur- 
rents they  are  nearly  as  2,  3,  and  4. 

Safe  Bottom  and  Mean  Velocities.— Ganguillet  &  Kutter  give 
the  following  table  of  safe  bottom  and  mean  velocity  in  channels,  calculated 
from  the  formula  v  =  vb  -\-  10.87  \^rs' 


Material  of  Channel. 

Safe  Bottom  Veloc 
ity  vb,  in  feet 
per  second. 

Mean  Velocity  v, 
in  feet  per 
second. 

Soft  brown  earth          

0.249 

0.328 

Soft  loam  

0.499 

0.656 

Sand                    .              

1  000 

1.312 

Gravel       

1.998 

2.625 

Pebbles 

2  999 

3  938 

Broken  stone  flint        

4  003 

5.579 

Conglomerate  soft  slate 

4  988 

6  564 

Stratified  rock                       

6.006 

8.204 

Hard  rock  

10.009 

13.127 

Ganguillet  &  Kutter  state  that  they  are  unable  for  want  of  observations 
to  judge  how  far  these  figures  are  trustworthy.  They  consider  them  to  be 
rather  disproportionately  small  than  too  large,  and  therefore  recommend 
them  more  confidently. 

Water  flowing  at  a  high  velocity  and  carrying  large  quanties  of  silt  is  very 
destructive  to  channels,  even  when  constructed  of  the  best  masonry. 

Resistance  of  Soils  to  Erosion  by  Water.— W.  A.  Burr,  Eng'g 
News,  Feb.  8,  1894,  gives  a  diagram  showing  the  resistance  of  various  soils  to 
erosion  by  flowing  water. 

Experiments  show  that  a  velocity  greater  than  1.1  feet  per  second  will 
erode  sand,  while  pure  clay  will  stand  a  velocity  of  7.35  feet  per  second. 
The  greater  the  proportion  of  clay  carried  by  any  soil,  the  higher  the  per- 
missible velocity.  Mr.  Burr  states  that  experiments  have  shown  that  the  line 
describing  the  power  of  soils  to  resist  erosion  is  parabolic.  From  his  dia- 
gram the  following  figures  are  selected  representing  different  classes  of 
soils: 

Pure  sand  resists  erosion  by  flow  of 1.1  feet  per  second. 

Sandy  soil,  15$  clay  1.2         ' 

Sandy  loam,  40$  clay 1..8 

Loamy  soil,  65$  clay 3.0 

Clay  loam,  85$  clay 4.8 

Agricultural  clay,  95$  clay 6.2 

Clay , 7.35 

Abrading  and  Transporting  Power  of  Water.—  Prof.   J. 

LeConte,  in  his  %'  Elements  of  Geology,"  states  : 

The  erosive  power  of  water,  or  its  power  of  overcoming  cohesion,  varies  as 
the  square  of  the  velocity  of  the  current. 

The  transporting  power  of  a  current  varies  as  the  sixth  power  of  the  ve- 
locity. *  *  *  if  the  velocity  therefore  be  increased  ten  times,  the  transport- 
ing power  is  increased  1,000,000  times.  A  current  running  three  feet  per 
second,  or  about  two  miles  per  hour,  will  bear  fragments  of  stone  of  the 
size  of  a  hen's  egg,  or  about  three  ounces  weight.  A  current  of  ten  miles  an 
hour  will  bear  fragments  of  one  and  a  half  tons,  and  a  torrent  of  twenty 
miles  an  hour  will  carry  fragments  of  100  tons. 

The  transporting  power  of  water  must  not  be  confounded  with  its  erosive 
power.  The  resistance  to  be  overcome  in  the  one  case  is  weight,  in  the 
other,  cohesion  ;  the  latter  varies  as  the  square  :  the  former  as  the  sixth 
power  of  the  velocity. 

In  many  cases  of  removal  of  slightly  cohering  material,  the  resistance  is  a 


566  HYDRAULICS. 

mixture  of  these  two  resistances,  and  the  power  of  removing  material  will 
vary  at  some  rate  between  v  2  and  v*. 

Baldwin  Latham  has  found  that  in  order  to  prevent  deposits  of  sewage  silt 
in  small  sewers  or  drains,  such  as  those  from  6  inches  to  9  inches  diameter, 
a  mean  velocity  of  not  less  than  3  feet  per  second  should  be  produced. 
Sewers  from  12  to  24  inches  diameter  should  have  a  velocity  of  not  less  than 
2^  feet  per  second,  and  in  sewers  of  larger  dimensions  in  no  case  should  the 
velocity  be  less  than  2  feet  per  second. 

The  specific  gravity  of  the  materials  has  a  marked  effect  upon  the  mean 
velocities  necessary  to  move  them.  T.  E.  Blackwell  found  that  coal  of  a 
sp  gr.  of  1.26  was  moved  by  a  current  of  from  1.25  to  1.50  ft.  per  second, 
while  stones  of  a  sp.  gr.  of  2  32  to  3.00  required  a  velocity  of  2.5  to  2.75  ft.  per 
second. 

Chailly  gives  the  following  formula  for  finding  the  velocity  required  to 
move  rounded  stones  or  shingle  : 


in  which  v  —  velocity  of  water  in  feet  per  second,  a  =  average  diameter  in 
feet  of  the  body  to  be  moved,  g  =  its  specific  gravity. 

Geo.  Y.  Wisner,  Eng'g  News,  Jan  10,  1895,  doubts  the  general  accuracy  of 
statements  made  by  many  authorities  concerning  the  rate  of  flow  of  a  cur- 
rent and  the  size  of  particles  which  different  velocities  will  move.  He  says: 

The  scouring  action  of  any  river,  for  any  given  rate  of  current,  must  be  an 
inverse  function  of  the  depth.  The  fact  that  some  engineer  has  found  that 
a  given  velocity  of  current  on  some  stream  of  unknown  depth  will  move 
sand  or  gravel  has  no  bearing  whatever  on  what  may  be  expected  of  cur- 
rents of  the  same  velocity  in  streams  of  greater  depths.  In  channels  3  to  5 
ft.  deep  a  mean  velocity  of  3  to  5  ft.  per  second  may  produce  rapid  scouring, 
while  in  depths  of  18  ft.  and  upwards  current  velocities  of  6  to  8  ft.  per 
second  often  have  no  effect  whatever  on  the  channel  bed. 

Grade  of  Sewers.—  The  following  empirical  formula  is  given  in  Bau- 
meister's  "  Cleaning  and  Sewerage  of  Cities,"  for  the  minimum  grade  for  a 
sewer  of  clear  diameter  equal  to  d  inches,  and  either  circular  or  oval  in 
section  : 

_,.  .  ,     .  100 

Minimum  grade,  in  per  cent,  =  . 

od  -j-  ou 

As  the  lowest  limit  of  grades  which  can  be  flushed,  0.1  to  0.2  per  cent  may 
be  assumed  for  sowers  which  are  sometimes  dry,  while  0.3  per  cent  is  allow- 
able for  the  trunk  sewers  in  large  cities.  The  sewers  should  run  dry  as 
rarely  as  possible 

Relation  of  Diameter  of  Pipe  to  Quantity  Discharged.— 
In  many  cases  which  arise  in  practice  the  information  sought  is  the  diame- 
ter necessary  to  supply  a  given  quantity  of  water  under  a  given  head.  The 
diameter  is  commonly  taken  to  vary  as  the  two-fifth  power  of  the  dis- 
charge. This  is  almost  certainly  too  large.  Hagen's  formula,  with  Prof. 

/    O      \  387 
Un  win's  coefficients,  give  d  =  cl-~r-\       ,  where  c  =  .239  when  d  and  Q 


J    Q     V387 

((?)*)     ' 


are  in  feet  and  cubic  feet  per  second. 

Mr.  Thrupp  has  proposed  a  formula  which  makes  d  vary  as  the  .383  power 
of  the  discharge,  and  the  formula  of  M.  Vallot,  a  French  engineer,  makes  d 
vary  as  the  .375  power  of  the  discharge.  (Engineer ing.) 

FLOW  OF  WATER-EXPERIMENTS  AND  TARLES. 

Tiie  Flow  of  Water  through   New   Cast-iron   Pipe   was 

recently  measured  by  S.  Bent  Russell,  of  the  St.  Louis,  Mo  ,  Water-works. 
The  pipe  was  12  inches  in  diameter,  1631  feet  long,  and  laid  on  a  uniform 
grade  from  end  to  end.  Under  an  average  total  head  of  3.36  feet  the  flow 
was  43,200  cubic  feet  in  seven  hours;  under  an  average  head  of  3.37  feet  the 
flow  was  the  same;  under  an  average  total  head  of  3.41  feet  the  flow  was 
46,700  cubic  feet  in  8  hours  and  35  minutes.  Making  allowance  for  loss 
of  head  due  to  entrance  and  to  curves,  it  was  found  that  the  value  of  c  in 
the  formula  v  =  c  Vrs  was  from  88  to  93.  (Eng'g  Record,  April  14,  1894. 

Flow  of  Water  in  a  20-inch  Pipe  75,OOO  Feet  l.ong.— A 
comparison  of  experimental  data  with  calculations  by  different  formulae  is 


FLOW   OF  WATER — EXPERIMENTS  AND  TABLES.    567 


given  by  Chas.  B.  Brush,  Trans.  A.  S.  C.  E.,  1888.    The  pipe  experimented 
with  was  that  supplying  the  city  of  Hoboken,  N.  J. 

RESULTS  OBTAINED  BY  THE  HACKENSACK  WATER  COMPANY,  FROM  1882-1887, 
IN  PUMPING  THROUGH  A  20-iN.  CAST-IRON  MAIN  75,000  FEET  LONG. 

Pressure  in  Ibs.  per  sq.  in.  at  pumping-station: 
95          100          105          110          115 


Total  effective  head  in  feet : 
55  66  77 


100 


120 
112 


125 


130 
135 


Discharge  in  U.  S.  gallons  in  24  hours,  1  =  1000  : 

2,848  3,165  3,354  3,566  3,804  3,904  4,116  4,255 
Actual  velocity  in  main  in  feet  per  second  : 

2.00  2.24  2.36  2.52  2.68  2.76  292  3.00 
Cost  of  coal  consumed  in  delivering  each  million  gals,  at  given  velocities : 

$8.40  $8.15  $8.00  $8.10  $8.30  $8.60  $9.00  $9.GO 
Theoretical  discharge  by  D'Arcy's  formula  : 

2,743       3,004       3,244        3,488       3,699       3,915       4,102       4,297 

Velocities  In  Smooth  Cast-iron  Water-pipes  from  1  Foot 
to  9  Feet  in  Diameter,  on  Hydraulic  Grades  of*  O.5 
Foot  to  8  Fee£  per  Mile  ;  witn  Corresponding  Values 

of  c  in  F=  c  \/rs.    (D.  M.  Greene,  in  Eng'g  News,  Feb.  24,  1894.) 


il 

B  * 

ll-s 

lis'S 

Hydraulic  Grade;  Feet  per  Mile  =  h. 

Sp 

>>  oftj 
m^ 

h  =  0.5 

1.0 

1.5 

2.0 

3.0 

4.0 

D. 

r. 

s  -  0.0000947 

0.0001894 

0.0002841 

0.0003788 

0.0005682 

0.0007576 

1. 

0.25  1 

V=      0.4542 
c=    92.7 

0.6673 
97.0 

0.8356 
99.1 

0.9803 
100.7 

1.2277 
103.0 

1.4402 
104.7 

n  *    I 

F=     0.7359 

1.0793 

1.3516 

1.5856 

1.9857 

2.3294 

c=  106.6 

110.9 

113.4 

115.2 

117.9 

119.7 

1 

V-      0.9733 

1.4298 

1.7906 

2.1017 

2.6306 

3.0860 

3. 

0.7oj 

c=  115.5 

119.9 

122.6 

124.4 

127.5 

129.5 

1  n  J 

V=      1.1883 

1.7456 

2.1861 

2.5645 

3.2116 

3.7676 

1.0  ^ 

c=  122.1 

126.8 

129.7 

131.8 

134.7 

136.9 

had 

V=      1.3872 

2.0379 

2.5521 

2.9939 

3.7493 

4.3983 

c  -  127.5 

132.4 

135.5 

137.6 

140.7 

142.9 

1  ^  ] 

V=      1.5742 

2.3126 

2.8961 

3.3975 

4.2548 

4.9913 

1.0     ^ 

c  -  132.1 

137.8 

140.3 

142.6 

145.8 

148.1 

7. 

1.75-j 

F=      1.7518 
c  =  135.9 

2.5736 
141.4 

3.2230 
146.0 

3.7809 
146,8 

4.7350 
150.2 

5.5546 
152.5 

i 

V=      1,9218 

2.8234 

3.5358 

4.1479 

5.1945 

6.0936 

8. 

2.0  •< 

c  =  139.7 

145  1 

148.4 

150.7 

154.1 

156.5 

o  9*j 

V=     2.0854 

3.0638 

3.8368 

4.5010 

5.6368 

6.6125 

J.25} 

c  =  142.9 

148.4 

151.7 

154.2 

157.6 

160.1 

The  velocities  in  this  table  have  been  calculated  by  Mr.  Greene's  modifi- 
cation of  the  Chezy  formula,  which  modification  is  found  to  give  results 
which  differ  by  from  1.29  to  —  2.65  per  cent  (average  0.9  per  cent)  from  very 
carefully  measured  flows  in  pipes  from  16  to  48  inches  in  diameter,  on  grades 
from  1.68  feet  to  10.296  feet  per  mile,  and  in  which  the  velocities  ranged 
from  1.577  to  6.195  feet  per  second.  The  only  assumption  made  is  that  the 
modified  formula  for  V  gives  correct  results  in  conduits  from  4  feet  to  9 
feet  in  diameter,  as  it  is  known  to  do  in  conduits  less  than  4  feet  in  diameter. 

Other  articles  on  Flow  of  Water  in  long  tubes  are  to  be  found  in  Eng'g 
News  as  follows  :  G.  B.  Pearsons,  Sept.  23,  18^6;  E.  Sherman  Gould,  Feb.  16, 
23,  March  9, 16,  and  23, 1889;  J.  L.  Fitzgerald,  Sept,  6  and  13,  1890;  Jas.  Duane, 
Jan.  2,  18.92;  J.  T,  Fanning,  July  14,  1892;  A.  N.  Talbot,  Aug.  11,  18.92,, 


568 


HYDRAULICS. 


Flow  of  Water  In  Circular  Pipes,  Sewer*,  etc..  Flowing 
Full.    Based  on  Kutter's  Formula,  with  n  =  .013. 

Discharge  in  cubic  feet  per  second. 


Diam- 
eter. 

Slope,  or  Head  Divided  by  Length  of  Pipe. 

Iin40 

Iin70 

lin  100 

1  in  200 

1  in  300 

1  in  400 

lin  500 

lin  600 

5  in. 
6  " 

7  " 
8  " 
9  " 

.456 
.762 
1.17 
1.70 
2.37 

.344 
.576 
.889 
1.29 
1.79 

.288 
.482 
.744 
1.08 
1.50 

.204 
.341 
.526 
.765 
1.06 

.166 
.278 
.430 
.624 
.868 

.144 
.241 
.372 
.54 
.75 

.137 
.230 
.355 
.516 
.717 

.118 
.197 
.304 
.441 
.613 

Slope  .... 
10  in. 
11  " 
12  " 
13  " 
14  " 

lin6T 
*.<*. 

3.34 

4.32 
5.38 
6.60 

1  in  80 
2.24 
2.94 
3.74 
4.66 
5.72 

1  in  100 
2.01 
2.63 
3.35 
4.16 
5.15 

1  in  200 
1.42 
1.86 
2.37 
2.95 
3.62 

1  in  300 
1.16 
1.52 
1.93 
2.40 
2.95 

1  in  400 
1.00 
1.31 
1.67 
2.08 
2.57 

1  in  500 
.90 
1.17 
1.5 
1.86 
2.29 

lin  600 
.82 
1.07 
1.37 
1.70 
2.09 

Slope  
15  in. 
16  " 
18  " 
20  " 
22  " 

1  in  100 
6.18 
7.38 
10.21 
13.65 
17.  7J 

1  in  200 
4.37 
5.22 
7  22 
9.65 
12.52 

1  in  300 
3.57 
4.26 
5.89 
7.88 
10.22 

1  in  400 
3.09 
3.69 
5.10 
6.82 
8.85 

lin  500 
2.77 
3.30 
4.56 
6.10 
7.92 

1  in  600 
2.52 
3.01 
4.17 
5.57 
7.23 

1  in  700 
2.34 
2.79 
3.86 
5.16 
6.69 

1  in  800 
2.19 
2.61 
3.61 
4.83 
6.26 

Slope  .... 
2ft. 
2fr.2iu. 
t  u  4  « 
2  u  6  " 
2  "  8  " 

1  in  200 
15.88 
19.73 
24.15 
29.08 
34.71 

1  in  400 
11.23 
13.96 
17.07 
20.56 
24.54 

1  in  750 
21.10 
24.61 
28.50 
32  72 
37.28 

1  in  600 
9.17 
11.39 
13  94 
16.79 
20.04 

1  in  1000 
18.27 
21.31 
24.68 
28.34 
32.28 

lin  800 
7.94 
9.87 
12.07 
14.54 
11.35 

1  in  1250 
16.34 
19.06 
22.07 
25.35 
28.87 

1  in  1000 
7.10 
8.82 
10.80 
13.00 
15.52 

1  in  1500 
14.92 
17.40 
20.15 
23.14 
26.36 

1  in  1250 
6.35 
7.89 
9.66 
11.63 
13.88 

lin  1500 
5.80 
7.20 
8.82 
10.62 
12.67 

1  in  2000 
12.92 
15.07 
17.45 
20.04 
22.83 

1  in  1800 
5.29 
6.58 
8.05 
9.69 
11.57 

iln~2500 
11.55 
13.48 
15.61 
17.93 
20.41 

Slope  — 
2ft.  10  in. 
3    " 
3  "  2  in. 
3  «*  4  44 

3  "  6  " 

1  in  500 
25.84 
30.14 
34.90 
40.08 
45.66 

1  in  1750 
13.81 
16.11 
18.66 
21.42 
24.40 

Slope  .... 
3ft.    8  in. 
3  "  10  " 
4  «» 

4  "   6  in. 

5  " 

1  in  500 
51.74 
58.36 
65.47 
89.75 
118.9 

1  in  750 
42.52 
47.65 
53.46 
73.28 
97.09 

lin  1000 
36.59 
41.27 
46.30 
63.47 
84.08 

1  in  1250 
32.72 
36.91 
41.41 
56.76 
75.21 

1  in  1500 
29.87 
33.69 
37.80 
51.82 
68.65 

1  in  1750 
27.66 
31.20 
34.50 
47.97 
63.56 

1  in  2000 
25.87 
29.18 
32.74 
44.88 
59.46 

1  in  2500 
23.14 
26.10 
29.28 
40.14 
53.18 

Slope  
5  ft.  6  in. 

6  " 
6  "  6  " 

7  " 
7  "  6  " 

1  in  750 
125.2 
157.8 
195.0 
237.7 
285.3 

1  in  1000 
108.4 
136.7 
168.8 
205.9 
247.1 

1  in  1500 
88.54 
111.6 
137.9 
168.1 
201.7 

1  in  2000 
76.67 
96.66 
119.4 
145.6 
174.7 

1  in  2500 
68.58 
86.45 
106.8 
130.2 
156.3 

1  in  3000 
62.60 
78.92 
97.49 
118.8 
142.6 

1  in  3500 
57.96 
73.07 
90.26 
110.00 
132.1 

1  in  4000 
54.21 
68  35 
84.43 
102.9 
123.5 

Slope  .... 
8ft. 
8  "  6  in. 
9  " 
9  "  6  " 
10  " 

1  in  1500 
239.4 
281.1 
327.0 
376.9 
431.4 

1  in  2000 
207.3 
243.5 
283.1 
326.4 
373.6 

1  in  2500 
195.4 
217.8 
253.3 
291.9 
334.1 

1  in  3000 
169.3 
198.8 
231.2 
266.5 
305.0 

1  in  3500 
156.7 
184.0 
214.0 
246.7 
282.4 

1  in  4000 
146.6 
172.2 
200.2 
230.8 
264.2 

1  in  4500 
138.2 
162.3 
188.7 
217.6 
249.1 

1  in  5000 
131.1 
154.0 
179.1 
206.4 
236.3 

For  U.  S.  gallons  multiply  the  figures  in  the  table  by  7.4805. 
For  a  given  diameter  the  quantity  of  flow  varies  as  the  square  root  of  the 
sine  of  the  slope.    From  this  principle  the  flow  for  other  slopes  than  those 


FLOW  OF  WATER  IK  CIKCtTLAB  PIPES,    ETC.      569 


given  in  the  table  may  be  found.  Thus,  what  is  the  flow  for  a  pipe  8  feet 
diameter,  slope  1  in  125  ?  From  the  table  take  Q  =  207.3  for  slope  1  in  2000. 
The  given  slope  1  in  125  is  to  1  in  2000  as  16  to  1,  and  the  square  root  of  this 
ratio  is  4  to  1.  Therefore  the  flow  required  is  207.3  X  4  =  829.2  cu.  ft. 

Circular  Pipes,  Conduits,  etc.,  Flowing  Full. 

Values  of  the  factor  ac  \'r  in  the  formula  Q  =.  ac  |/r  X  Vt>  correspond- 
ing to  different  values  of  the  coefficient  of  roughness,  n.  (Based  on  Kutter's 
formula.) 


1 
s 

ft.  in. 

Value  of  ac  |/r. 

n  =  .010. 

n  =  .011. 

n  =  .012. 

n  =  .013. 

n  =  .015. 

n  =  .017. 

6 

6.906 

6.0627 

5.3800 

4.8216 

3.9604 

3  329 

9 

21.25 

18.742 

16.708 

15.029 

12.421 

10.50 

1 

46.93 

41.487 

37.149 

33.497 

27.803 

23  60 

1  3 

86.05 

76.347 

68.44 

61.867 

51.600 

43.93 

1  6 

141.2 

125.60 

112.79 

102.14 

85.496 

72.99 

1  9 

214.1 

190.79 

171.66 

155.68 

130.58 

111.8 

2 

307.6 

274.50 

247.33 

224.63 

188.77 

164 

2  3 

421.9 

377.07 

340.10 

309.23 

260.47 

223.9 

2  6 

559.6 

500.78 

452.07 

411.27 

347.28 

299.3 

2  9 

722.4 

647.18 

584.90 

532.76 

451.23 

388.8 

3 

911.8 

817.50 

739.59 

674.09 

570.90 

493.3 

3  3 

1128.9 

1013.1 

917.41 

836.69 

709.56 

613.9 

3  6 

1374.7 

1234.4 

1118.6 

1021.1 

866.91 

750.8 

3  9 

1652.1 

1484.2 

1345.9 

1229.7 

1045 

906 

4 

1962.8 

1764.3 

1600.9 

1463.9 

1245.3 

1080.7 

4  6 

2682.1 

2413.3 

2193 

2007 

1711.4 

1487.3 

5 

3543 

3191.8 

2903.6 

2659 

2272.7 

1977 

5  6 

4557.8 

4111.9 

3742.7 

3429 

2934.8 

2557.2 

6 

5731.5 

5176.3 

4713.9 

4322 

3702.3 

3232.5 

6  6 

7075.2 

6394.9 

5825.9 

5339 

4588.3 

4010 

7 

8595.1 

7774  .  3 

7087 

6510 

5591.6 

4893 

7  6 

10296 

9318.3 

8501.8 

7814 

6717 

5884.2 

8 

12196 

11044 

10083 

9272 

7978.3 

6995.3 

8  6 

14298 

12954 

11832 

10889 

9377.9 

8226.3 

9 

16604 

15049 

13751 

12663 

10917 

9580.7 

9  6 

19118 

17338 

15847 

14597 

12594 

11061 

10 

21858 

19834 

18134 

16709 

14426 

12678 

10  6 

*4823 

22534 

20612 

18996 

16412 

14434 

11 

28020 

25444 

23285 

21464 

18555 

16333 

11  6 

31482 

28593 

26179 

24139 

20879 

18395 

12 

35156 

31937 

29254 

26981 

23352 

20584 

12  6 

39104 

35529 

32558 

30041 

26012 

22938 

13 

43307 

39358 

36077 

33301 

28850 

25451 

13  6 

47751 

43412 

39802 

36752 

31860 

28117 

14 

52491 

47739 

43773 

40432 

35073 

30965 

14  6 

57496 

52308 

47969 

44322 

38454 

33975 

15 

62748 

57103 

52382 

48413 

42040 

37147 

16 

74191 

67557 

62008 

57343 

49823 

44073 

17 

86769 

79050 

72594 

67140 

58387 

51669 

18 

100617 

91711 

84247 

77932 

67839 

60067 

19 

115769 

105570 

96991 

89759 

78201 

69301 

20 

132133 

120570 

110905 

102559    J 

89423 

79259 

Flow  of  Water  in  Circular  Pipes,  Conduits,  etc.,  Flowing 
under  Pressure. 

Based  on  D'Arcy^  formulae  for  the  flow  of  water  through  cast-iron  pipes. 
With  comparison  of  results  obtained  by  Kutter's  formula,  with  n  =  .013! 
(Condensed  from  Flynn  on  Water  Power.) 

Values  of  a,  and  also  the  values  of  the  factors  c  \/r  and  ac  tfr  for  use  in 
the  formulae  Q  =  at;;  v  =  c  |/r  X  Vst  and  Q  =  ac  |/f  X  fs- 


570 


HYDRAULICS. 


Q  =  discharge  in  cubic  feet  per  second,  a  =  area  in  square  feet,  v  =  veloc* 
ity  in  feet  per  second,  r  =  mean  hydraulic  depth,  J4  diam.  for  pipes  running 
rail,  s  —  sine  of  slope. 

(For  values  of  V«  see  page  558.) 


Size  of  Pipe. 

Clean  Cast-iron 
Pipes. 

Value  of 

Old  Cast-iron  Pipes 
Lined  with  Deposit. 

ac  Vr  by 

d=  diam. 
in 
ft.    in. 

a  =  area 
in 
square 
feet. 

For 
Velocity, 

c  1/r. 

For  Dis- 
charge, 
ac  Vr- 

Kutter's 
Formula, 
when 
n  =  .013. 

For 
Velocity, 
c  yr> 

For 
Discharge, 
ac  |/r. 

K 

.00077 
.00136 

5.251 
6.702 

.00403 
.00914 

3.532 

4.507 

.00272 

.00613 

% 

.00307 

9.309 

.02855 

6.261 

.01922 

1 

.00545 

11.61 

.06334 

7.811 

.04257 

V/A 

.00852 

13.68 

.11659 

9.255 

.07885 

Itfi 

.01227 

15.58 

.19115 

10.48 

.12855 

\% 

.01670 

17.32 

.28936 

11.65 

.19462 

2 

.02182 

18.96 

.41357 

12.75 

.27824 

2^ 

.0341 

21.94 

.74786 

14.76 

.50321 

3 

.0491 

24.63 

1  .2089 

16.56 

.81333 

4 

.0873 

29.37 

2.5630 

19.75 

1.7246 

5 

.136 

33.54 

4.5610 

22.56 

3.0681 

6 

.196 

37.28 

7.3068 

4  822 

25  07 

4.9147 

7 

.267 

40.65 

10.852 

27.34 

7.2995 

8 

.349 

43.75 

15.270 

29.43 

10.271 

9 

.442 

46.73 

20.652 

15.03 

31.42 

13.891 

10 

.545 

49.45 

26.952 

33.26 

18.129 

11 

.660 

52.16 

34.428 

35.09 

23.158 

1 

.785 

54.65 

42.918 

33.50 

30.75 

28.867 

1      2 

1.000 

59.34 

63.435 

39  91 

42  668 

1      4 

1.396 

63.67 

88.886 

42.83 

59.788 

1      6 

1.767 

67.75 

119.72 

102.14 

45.57 

80.531 

1      8 

2.182 

71.71 

156.46 

48.34 

105.25 

1    10 

2.640 

75.32 

198.83 

50.658 

133.74 

2 

3.142 

78.80 

247.57 

224.63 

52.961 

166.41 

2      2 

3.687 

82.15 

302.90 

55.258 

203.74 

2      4 

4.276 

85.39 

365.14 

57.436 

245.60 

2      6 

4.909 

88.39 

433.92 

411.37 

59.455 

291.87 

2      8 

5.585 

91.51 

511.10 

61.55 

343.8 

2    10 

6.305 

94.40 

595.17 

63.49 

400.3 

3 

7.068 

97.17 

686.76 

674.09 

65.35 

461.9 

3      2 

7.875 

99.93 

786.94 

67.21 

529.3 

3      4 

8.726 

102.6 

895.7 

69 

602 

3      6 

9.621 

105.1 

1011.2 

1021.1 

70.70 

680.2 

3      8 

10  559 

107.6 

1136.5 

72.40 

764.5 

3    10 

11.541 

110.2 

1271.4 

74.10 

855.2 

4 

12.566 

112.6 

1414.7 

1463.9 

75.73 

951.6 

4      3 

14.186 

116.1 

1647.6 

78.12 

1108.2 

4      6 

15.904 

119.6 

1901.9 

2007 

80.43 

1279.2 

4      9 

17.721 

122.8 

2176.1 

82.20 

1456.8 

5 

19.  6i  5 

126.1 

2476.4 

2659 

84  83 

1665.7 

5      3 

21.648 

129.3 

2799.7 

fO.99 

1883.2 

5      6 

23.758 

132.4 

3146.3 

3429 

89.07 

2116.2 

5      9 

25.967 

135.4 

3516 

91.08 

2365 

6 

28.274 

138.4 

3912.8 

4322 

93.08 

2681.7 

6      6 

33.183 

144.1 

4782.1 

5339 

96.93 

3216.4 

7 

38.485 

149.6 

5757.5 

6510 

100.61 

3872.5 

7      6 

44.179 

154  9 

6841.6 

7814 

104.11 

4601.9 

8 

50.266 

160 

8043 

9272 

107.61 

5409.9 

8      6 

56.745 

165 

9364.7 

10889 

111 

6299.1 

9 

63.617 

169.8 

0804 

12663 

114.2 

7267.3 

9      6 

70.882 

174.5 

12370 

14597 

117,4 

8320.6 

10 

78.540 

179.1 

14066 

16709 

120.4 

9460.9 

FLOW  OF   WATER  IK   CIRCULAR   PIPES,    ETC.        571 


Size  of  Pipe. 

Clean  Cast-iron 
Pipes. 

Value  of 

Old  Cast-iron  Pi  pet 
Lined  with  Deposit. 

ac  W  by 

Kutter's 

d—  diam. 
in 
ft.    in. 

a  =  area 
in 
square 
feet. 

For 
Velocity, 
c  |/r. 

For  Dis- 
charge, 
ac  |/r« 

Formula, 
when 
n  =  .013 

For 
Velocity, 
c4/r. 

For 
Discharge, 

ac  |/r. 

10      6 
11 

86.590 
95.033 

183.6 
187.9 

15893 

17855 

18996 
21464 

123.4 
126.3 

10690 
12010 

11      6 

103.869 

192.2 

19966 

24139 

129.3 

13429 

12 

113.098 

196.3 

22204 

26981 

132 

14935 

12      6 

122  719 

200.4 

24598 

30041 

134.8 

16545 

13 

132.733 

204.4 

27134 

33301 

137.5 

18252 

13      6 

143.139 

208.3 

29818   - 

36752 

140.1 

20056 

14 

153.938 

212.2 

32664 

40432 

142.7 

21971 

14      6 

165.130 

216.0 

35660 

44322 

145.2 

23986 

15 

176.715 

219.6 

38807 

48413 

147.7 

26103 

15      6 

188.692 

223.3 

42125 

52753 

150.1 

28335 

16 

201.062 

226.9 

45621 

57343 

152.6 

30686 

16      6 

213.825 

230  .4 

49273 

62132 

155 

33144 

17 

226.981 

233.9 

53082 

67140 

157.3 

35704 

17      6 

240.529 

237.3 

57074 

72409 

159.6 

38389 

18 

254.470 

240.7 

61249 

77932 

161.9 

41199 

19 

283.529 

247.4 

70154 

89759 

166.4 

47186 

30 

314.159 

253.8 

79736 

102559 

170.7 

53633 

Flow  of  Water  in  Circular  Pipes  front  %  Inch  to  12  inches 
Diameter. 

Based  on  D'Arcy's  formula  for  clean  cast-iron  pipes.    Q  =  ac  Vr  Vs. 


Value  of 

Dia. 

Slope,  or  Head  Divided  by  Length  of  Pipe. 

ac  ^r- 

in. 

1  in  10. 

1  in  20. 

1  in  40. 

1  in  60. 

1  in  80. 

1  in 
100. 

1  in 
150. 

lin 

200. 

Quau 

tity  in 

cubic 

feet  p 

er   sec 

ond. 

.00403 

ax 

.00127 

.00090 

.00064 

.00052 

.00045 

.00040 

.00033 

.00028 

.00914 

IX 

.00289 

.00204 

.00145 

.00118 

.00102 

.00091 

.00075 

.00065 

.02855 

3/ 

.00903 

.00638 

.00451 

.00369 

.00319 

.00286 

.00233 

.00202 

.06334 

1 

.02003 

.01416 

.01001 

.00818 

.00708 

.00633 

.00517 

.00448 

.11659 

V/4        03687 

.02607 

.01843 

.01505 

.01303 

.01166 

.00952 

.00824 

.19115 

.06044 

.04274 

.03022 

.02468 

.02137 

.01912 

.01561 

.01352 

.28936 

I/I 

.09140 

.06470 

.04575 

.03736 

.03235 

.02894 

.02363 

.02046 

.41357 

o 

.13077 

.09247 

.06539 

.05339 

.04624 

.04136 

.03377 

.02927 

.74786 

gix 

.23647 

.16722 

.  11824 

.09655 

.08361 

.07479 

.06106 

.05288 

1.2089 

3 

.38225 

.27031 

.19113 

.15607 

.13515 

.12089 

.09871 

.08548 

2.5630 

4 

.81042 

.57309 

.40521 

.33088 

.28654 

.25630 

.20927 

.18123 

4.5610 

5 

1.4422 

1.0198 

.72109 

.58882 

.50992 

.45610 

.37241 

.32251 

7.3068 

6 

2.3104 

1.6338 

1.1552 

.94331 

.81690 

.73068 

.59660 

.51666 

10.852 

7 

3.4314 

2.4265 

1.7157 

1.4110 

1.2132 

1.0852 

.88607 

.76734 

15.270 

8 

4.8284 

3.4143 

2.4141 

1.9713 

1.7072 

1.5270 

1.2468 

1  .0797 

20.652 

9 

6.5302 

4.6178 

3.2651 

2.6662 

2.3089 

2.0652 

1.6862 

1.4603 

26.952 

10 

8.5222 

6.0265 

4.2611 

3.4795 

3.0132 

2.6952 

2.2006 

1.9058 

34.428 

11 

10.886 

7.6981 

5.4431 

4.4447 

3.8491 

3.4428 

2.8110 

2  4344 

42.918 

12 

13.571 

9.5965 

6.7853 

5.5407 

4.7982 

4.2918 

3.5043 

3.0347 

Value  of  Vl  = 

.3162 

.2236 

.1581 

.1291 

.1118 

.1 

.08165 

.07071 

572 


HYDRAULICS. 


Slope,  or  Head  Divided  by  Length  of  Pipe. 

Value  of 

Dia. 

ac  \/~r. 

in. 

1  in 

lin 

1  in 

1  in 

lin 

lin 

lin 

1  in  250. 

300. 

350. 

400. 

450. 

500. 

550. 

600. 

.00403 

% 

.00025 

.00023 

.00022 

.00020 

.00019 

.00018 

.00017 

.00016 

.00914 

TL£ 

.00058 

.00053 

.00049 

.00046 

.00043|  .00041 

.00039 

.00037 

.02855 

% 

.00181 

.00165 

.00153 

.00143 

.00134|  .00128 

.00122 

.00117 

.06334 

1 

.00400 

.00366 

.00339 

.00317 

.00-298  .00283 

.00270 

.00259 

.11659 

\YA 

.00737 

.00673 

.00623 

.00583 

.005491  .00521 

.00497 

.00476 

.19115 

$2 

.01209 

.01104 

.01022 

.00956 

.009011  .00855 

.00815 

.00780 

.28936 

m 

.01830 

.01671 

.01547 

.01447 

.01363 

.01294 

.01234 

.01181 

.41357 

2 

.02615 

.02388 

.02211 

.02068 

.01948 

.01849 

.01763 

.01688 

.74786 

% 

.04730 

.04318 

.03997 

.03739 

.03523  .03344 

.03189!  .03053 

1.2089 

3 

.07645 

.06980 

.06462 

.06045 

.05695 

.05406 

.05155 

.04935 

2.5630 

4 

.16208 

.14799 

.13699 

.12815 

.12074 

.11461 

.10929 

.10463 

4.5610 

5 

.28843 

.26335 

.24379 

.22805 

.21487 

.20397 

.19448 

.19620 

7.3068 

6 

.46208 

.42189 

.39055 

.36534 

.34422 

.32676 

.31158 

.29830 

10.852 

7 

.68628 

.62660 

.58005 

.54260 

.51124 

.48530 

.46273 

.44303 

15.270 

8 

.96567 

.88158 

.81617 

.76350 

.71936 

.68286 

.65111 

.62340 

20.652 

9 

1.3060 

1.1924 

1.1038 

1.0326 

.97292 

.92356 

.88060 

.84310 

26.952 

10 

1.7044 

1.5562 

1.4405 

1.3476 

1.2697 

1  2053 

1.1492 

1.1003 

34.428 

11 

2.1772 

1.9878 

1.8402 

1.7214 

1.6219 

1.5396 

1.4680 

1.4055 

42.918 

12 

2.7141 

2.4781 

2.2940 

2.1459 

•2.0219 

1.9193 

1.8300 

1.7521 

Value  of  |/8  = 

.06324 

.05774 

.05345 

.05 

.04711 

.04472 

.04264 

.04082 

For  U.  S.  gals,  per  sec.,  multiply  the  figures  in  the  table  by 7.4805 

"    min.,        "  "        "          448.83 

"      "       "      "    hour,        *  "  "        "          26929.8 

44      44        "      4t    24hu.,    4<  "  "  646315. 

For  any  other  slope  the  flow  is  proportional  to  the  square  root  of  the 
slope  ;  thus,  flow  in  slope  of  1  in  100  is  double  that  in  slope  of  1  in  400. 

Flow     of    Water    in    Pipes    from    %    Inch    to    12    In  olios 
Diameter  for  a  Uniform  Velocity  of  100  Ft.  per  Min. 


Diameter 
in 
Inches. 

Area 
in 
Square  Feet. 

Flow  in  Cubic 
Feet  per 
Minute. 

Flow  in  U.  S 
Gallons  per 
Minute. 

Flow  in  U.  S. 
Gallons  per 
Hour. 

% 

.00077 

0.077 

.57 

34 

% 

.00136 

0.136 

1.02 

61 

% 

.00307 

0.307 

2.30 

138 

1 

.00545 

0.545 

4.08 

245 

IM 

.00852 

0.852 

6.38 

383 

1*6 

.01227 

1.227 

9.18 

551 

m 

.01670 

1.670 

12.50 

750 

2 

.02182 

2.182 

16.32 

979 

«W 

.0341 

3.41 

25.50 

1,530 

3 

.0491 

4.91 

36.72 

2,203 

4 

.0873 

8.73 

65.28 

3,917 

5 

.136 

13.6 

10:2.00 

6,120 

6 

.196 

19.6 

146.88 

8,813 

7 

.267 

26.7 

199.92 

11,995 

8 

.349 

34.9 

261.12 

15,667 

9 

.442 

44.2 

330.48 

19,829 

10 

.545 

54.5 

408.00 

24,480 

11 

.660 

66.0 

493.68 

29,621 

12 

.785 

78.5 

587.52 

35,251 

Given  the  diameter  of  a  pipe,  to  find  the  quantity  in  gallons  it  will  deliver, 
the  velocity  of  flow  being  100  ft.  per  minute.  Square  the  diameter  in  inches 
and  multiply  by  4.08. 


LOSS  OF  HEAD.  573 

If  Q'  =  quantity  in  gallons  per  minute  and  d  =  diameter  in  inches,  then 

_  d»  X  .7854  X  100  X  7.4805  _ 
V  ~  144 

V 
For  any  other  velocity,  F',  in  feet  per  minute,  Q'  —  4.06d*^  =  .0408daF'. 

Given  diameter  of  pipe  in  inches  and  velocity  in  feet  per  second,  to  find 
discharge  in  cubic  feet  and  in  gallons  per  minute. 

Q'  =  <*2  X  •785^X  v  x  60  =  o.32725c*2u  cubic  feet  per  minute. 
=  .32725  X  7,4805  or  2.448d2v  U.  S.  gallons  per  minute. 

To  find  the  capacity  of  a  pipe  or  cylinder  in  gallons,  multiply  the  square 
of  the  diameter  in  inches  by  the  length  in  inches  and  by  .0034.  Or  multiply 
the  square  of  the  diameter  in  inches  by  the  length  in  feet  and  by  .0408. 

Q  -  — 23i~  =  -W84daJ  (exact)  .0034  X  12  =  .0408. 

LOSS  OF  HEAD. 

The  loss  of  head  due  to  friction  when  water,  steam,  air,  or  gas  of  any  kind 
flows  through  a  straight  tube  is  represented  by  the  formula 

i  =  /==S        whence^,'"4'4  hd 


in  which  I  —  the  length  and  d  =  the  diameter  of  the  tube,  both  in  feet;  v  = 
velocity  in  feet  per  second,  and  /  is  a  coefficient  to  be  determined  by  experi- 
ment. According  to  Weisbach,  /  =  .00614,  in  which  case 

and    v  =  I 

which  is  one  of  the  older  formulae  for  flow  of  water  (Downing's).  Prof.  Un- 
win  says  that  the  value  of  /  is  possibly  too  small  for  tubes  of  small  bore, 
and  he  would  put/  =  .006  to  .01  for  4-inch  tubes,  and/  =  .0084  to  .012  for  2- 
inch  tubes.  Another  formula  by  Weisbach  is 


2g 
Rankine  gives 


From  the  general  equation  for  velocity  of  flow  of  water  v  =  c  tfr  Vs,  = 
for  round  pipes  C;4/j  A/p   w«  have  v2  =  c2-  5   and  h  =  ^,  in  which 

c  is  the  coefficient  c  of  D'Arcy's,  Bazin's,  Kutter's.  or  other  formula,  as  found 
by  experiment.  Since  this  coefficient  varies  with  the  condition  of  the  inner 
surface  of  the  tube,  as  well  as  with  the  velocity,  it  is  to  be  expected  that 
values  of  the  loss  of  head  given  by  different  writers  will  vary  as  much  as  those 
of  quantity  of  flow.  Two-tables  for  loss  of  head  per  100  ft.  in  length  in  pipes 
of  different  diameters  with  different  velocities  are  given  below.  The  first 
is  given  by  Clark,  based  on  Ellis'  and  Rowland's  experiments;  the  second  is 
from  the  Pelton  Water-wheel  Co.'s  catalogue,  authority  not  stated.  The 
loss  of  head  as  given  in  these  two  tables  for  any  given  diameter  and  velocity 
differs  considerably.  Either  table  should  be  used  with  caution  and  the  re- 
sults compared  with  the  quantity  of  flow  for  the  given  diameter  and  head 
as  given  in  the  tables  of  flow  based  on  Kutter's  and  D'Arcy's  formulae. 


574 


HYDRAULICS. 


Relative   Loss  of   Head   by  Friction  for  each    100   Feet 
Length  of  Clean  Cast-iron  Pipe. 

(Based  on  Ellis  and  Rowland's  experiments.) 


Velocity 
in  Feet 
pei- 
Second. 

Diameter  of  Pipes  in  Inches. 

3 

4    |    a 

6     |     7 

8 

9 

10    1     12    j     14 

Loss  of  Head  in  Feet,  per  100  Feet  Long. 

Feet 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

Feet 
of 
Head 

.12 
.19 
.27 
.37 
.49 
.61 
.76 
.92 

2 
2.5 
3 
3.5 
4 
4.5 
5 
5.5 
6 

.97 
1.49 
1.9 
2.6 
3.3 

.55 
.92 
1.2 
1.6 
2.2 

.41 
.64 
.82 
1.2 
1.7 

.32 

.50 
.72 
1.0 
1.3 
1.6 

.27 
.43 
.61 
.7 
.9 
1.2 

.23 

.36 
.51 
.71 
.92 
1.2 

.19 
.30 
.44 
.61 
.79 
1.01 
1.2 

.18 
.27 
.39 
.52 
.69 
.87 
1.1 

.15 
.23 
.33 
.45 
.59 
.75 
.90 

15 

18 

21 

24 

27 

30 

33 

36 

42 

48 

2 
2.5 
3 
3.5 
4 
4.5 
5 
5.5 
6 

.11 
.17 
.25 
.34 
.44 
.50 
.70 
.84 

.095 
.147 
.21 
.29 
.36 
.46 
.58 
.70 

.075 
.117 
.17 
.23 
.31 
.39 
.48 
.59 

.065 
.109 
.15 
.20 
.27 
.34 
.41 
.50 
.59 

.055 
.088 
.13 
.18 
.23 
.30 
.37 
.44 
.53 

.052 
.085 
.12 
.16 
.2-2 
.28 
.34 
.39 
.49 

.049 
.076 
.108 
.15 
.20 
.25 
.30 
.36 
43 

.047 
.067 
.10 
.14 
.  17 
22 
.27 
.32 
.4 

.036 
.056 
.081 
.111 
.14 
.18 
.22 
.27 
.32 

.030 
.046 
.067 
.092 
.116 
.15 
.18 
.22 
.27 

Loss  of  Head  in  Pipe  by  Friction.— Loss  of  head  by  friction  in 
each  100  feet  in  length  of  different  diameters  of  pipe  when  discharging  the 
following  quantities  of  water  per  minute  (Pelton  Water-wheel  Co.) : 


Inside  Diameter  of  Pipe  in  Inches. 


ft 
*-» 

ll 

'o 
"V 

To 

3.0 
4.0 
5.0 
6.0 
7.0 

1 

2 

3 

4 

5 

6 

•a 

1 

a  . 

p 

/I 

Cubic  Feet  per 
<°  Minute. 

1 

*«• 

?£ 

^Cubic  Feet  per 
<°  Minute. 

1 

a  . 

O  Q) 

h 

Cubic  Feet  per 
10  Minute. 

a 

Cubic  Feet  per 
<°  Minute. 

1 

o! 

.-Cubic  Feet  per 
0  Minute. 

1 
fa 

.395 

.815 
1.37 
2.05 

2.87 
2.81 

.Cubic  Feet  per 
0  Minute. 

2.37 

4.89 
8.20 
12.33 
17.23 
22.89 

.65 
.99 
1.32 
1.65 
1.98 
2.31 

1.185 
2.44 
4.10 
6.17 
8.61 
11.45 

2.62 
3.92 
5.23 
6.54 
7.85 
9.16 

.791 
1.62 
2.73 

4>n 

5.74 

7.62 

5.89 
8.83 
11.80 
14.70 
17.70 
20.6 

.593 
1.22 
2.05 
3.08 
4.31 
5.72 

10.4 
15.7 
20.9 
26.2 
31.4 
36.6 

.474 
.978 
1.64 
2.46 
3.45 
4.57 

16.3 
24.5 
32.7 
40.9 
49.1 
57.2 

23.5 
35.3 
47.1 

58.9 
70.7 

82.4 

LOSS   OF   HEAD. 


575 


Inside  Diameter  of  Pipe  in  Inches. 

7 

8 

9 

10 

11 

12 

V 

h 

Q 

h 

Q 

h 

Q 

h 

g 

h 

Q 

h 

Q 

2.0 
3.0 
4.0 
5.0 
6.0 
7.0 

.338 
.698 
1  .  175 
1.76 
2.46 
3.26 

32.0 

48.1 
64.1 
80.2 
96.2 
112.0 

.296 
.611 
1.027 
1.54 
2  15 
2.85 

41.9 
62.8 
83.7 
105 
125 
146 

.264 
.544 
.913 
1.37 
1.92 
2.52 

53 
79.5 
106 
132 
159 
185 

.237 

.488 
.822 
1.23 
1.71 

2.28 

65.4 
98.2 
131 
163 
196 
229 

.216 
.444 
.747 
1.122 
1.56 
2  07 

79.2 
119 
158 
198 
237 
277 

.198 
.407 
.685 
1.028 
1.43 
1.91 

94.2 
141 
188 
235 
283 
330 

V 

Inside  Diameter  of  Pipe  in  Inches. 

13 

14 

15 

16 

18 

20 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

167 

251 
335 
419 
502 

586 

h 

.132 
.271 
.456 
.685 
.957 
1.27 

Q 

212 

318 
424 
530 
636 

742 

h 

.119 
.245 
.410 
.617 
.861 
1.143 

Q 

2.0 
3.0 
4.0 
5.0 
6,0 
7.0 

.183 
.375 
.632 
.949 
1.325 
1.75 

no 

166 
821 

276 
332 

387 

.1(59 
.349 
.587 
.881 
1.229 
1.63 

128 
192 
256 
321 
385 
449 

.158 
.325 
.548 
.822 
1.148 
1.52 

147 
221 
294 
368 
442 
515 

.147 
.306 
.513 
.770 
1.076 
1.43 

262 
393 
523 
654 

185 
916 

Inside  Diameter  of  Pipe  in  Inches. 

22 

24 

26 

28 

30 

36 

V 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

h 

Q 

2.0 
3.0 

4.0 
5.0 
6.0 
7.0 

.108 
.222 
.373 
.561 
.782 
1.040 

316 
475 
633 
792 
950 
1109 

.098 
.204 
.342 
.513 
.717 
.953 

377 
565 
754 
942 
1131 
1319 

.091 
.188 
.315 
.474 
.662 
.879 

442 

663 
885 
1106 
1327 
1548 

.084 
.174 
293 
.440 
.615 
.817 

513 
770 
1026 
1283 
1539 
1796 

.079 
.163 
.273 
.411 
.574 
.762 

589 
883 
1178 
1472 
1767 
2061 

.066 
.135 
.228 
.342 
.479 
.636 

848 
1273 
1697 
2121 
2545 
2868 

EXAMPLE.—  Given  200  ft.  head  and  600  ft.  of  11  -inch  pipe,  carrying  119  cubic 
\  eet  of  water  per  minute.  To  find  effective  head  :  In  right-hand  column, 
under  11-inch  pipe,  find  119  cubic  ft.;  opposite  this  will  be  found  the  loss  by 
friction  in  100  ft.  of  length  for  this  amount  of  water,  which  is  .444.  Multiply 
this  by  the  number  of  hundred  feet  of  pipe,  which  is  6,  and  we  have 
,v.66  ft.,  which  is  the  loss  of  head.  Therefore  the  effective  head  is  200  -  2.66 
.-=  197.34. 

EXPLANATION.—  The  loss  of  head  by  friction  in  pipe  depends  not  only  upon 
Diameter  and  length,  but  upon  the  quantity  of  water  passed  through  it.  Th^ 
head  or  pressure  is  what  would  be  indicated  by  a  pressure-gauge  attached 
to  the  pipe  near  the  wheel.  Readings  of  gauge  should  be  taken  while  the 
\vater  is  flowing  from  the  nozzle. 

To  reduce  heads  in  feet  to  pressure  in  pounds  multiply  by  .433.  To  reduce 
pounds  pressure  to  feet  multiply  by  2.309. 

Cox's  Formula.—  WeisbactTs  formula  for  loss  of  head  caused  by  the 
friction  of  water  in  pipes  is  as  follows  : 

Friction-head  =  /0.0144  +  °^\  L^l, 
\  4/F  /  5.367d 

where  L  =  length  of  pipe  in  feet; 

V  =  velocity  of  the  water  in  feet  per  second  ; 
d  =  diameter  of  pipe  in  inches. 

William  Cox  (Amer.  Mack.,  Dec.  28,  1893)  gives  a  simpler  formula  which 
gives  almost  identical  results  : 


U  a  friction-head  in  feet  = 


Hd 


~ 

4V*  4-5F-  2 
1200          * 


(D 
• 


576 


HYDEAULICS. 


He  gives  a  table  by  means  of  which  the  value  of  : 
obtained  when  F  is  known,  and  vice  versa. 

4F2-f  5F-  2 


—— 


_ 

is  at  once 


VALUES  OF 


1200 


V 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1 

.00583 

.00695 

.00813 

.00938 

.01070 

.01208 

.01353  .01505 

.01663 

.01828 

2 

.02000 

.02178 

.02.363 

.02555 

.02753 

.02958 

.031  70  .  .03388 

.03613 

.03845 

3 

.04083  .04328 

.04580 

.04838 

.05103 

.05375 

.05653  .05938 

.06230 

.06528 

4 

.06833  .07145 

.07463 

.07788 

.08120 

.08458 

.08803  .09155 

.09513 

.09878 

5 

.10250 

.1062S 

.11013 

.11405 

.11803 

.12208 

.12620,  ,13038 

.13403 

.13895 

6 

.14333 

.14778 

.15230 

.15688 

.16153 

.16625 

.17103  .17588 

.18080 

.  18578 

7 

.19083 

.19595 

.20113 

.20638 

.21170 

.21708 

.22253:  .22805 

.22363 

.23928 

S 

.24500 

.25078 

.25663 

.26255 

.26853 

.27458 

.28070;  .28688 

.29313 

.29945 

9 

.30583 

.31228 

.31880 

.32538 

.33203 

.33875 

.345531  .35238 

.35930 

.36628 

10 

.37333 

.38045 

.38763 

.39488 

.40220 

.40958 

.41703  .42455 

.43213 

.43978 

11 

.44750 

.45528 

.46313 

.47105 

.47903 

.48708 

.49520  .50338 

.51163 

.51995 

12 

.52833 

.53678 

.54530 

.55388 

.56253 

.57125 

.58003 

.58888 

.59780 

.60678 

13 

.61583 

.62495 

.63413 

.64338 

.65270 

.66208 

.67153 

.68105 

.69063 

.70028 

14 

.71000 

.71978 

.72963 

.73955 

.74953 

.75958 

.76970 

.77988 

.79013 

.80045 

15 

.81083 

.82128 

.83180 

.84238 

.85303 

.86375 

.87453 

.88538 

.89630 

.90728 

10 

.91833 

.92945 

.94063 

.95188 

.96320 

.97458 

.98603 

.99755 

1.00913 

1.02078 

17 

.03250 

1.04428 

1.05613 

1.06805 

1.08003 

1.09208 

1.10420 

1.11638 

1  .  12863 

1.14095 

18 

.15333 

1.16578 

1.17830 

1.19088 

1.20353 

1.21625 

1.229031.24188 

1.25480 

1.26778 

10 

.28083 

1  .29395 

1.30713 

1.32038 

1.33370 

1.34708 

1.36053  1.37405 

1.38763 

1.40128 

20 

.41500 

1.42878 

1.44263 

1.45655 

1.47053 

1  .  48458 

1.498701.51288 

1.52713 

1.54145 

21 

.55583 

1.57028 

1.58480 

1.59938 

1.61403 

1.62875 

1.64353 

1.65838 

1.67330 

1.68828 

The  use  of  the  formula  and  table  is  illustrated  as  follows: 
Given  a  pipe  5  inches  diameter  and  1000  feet  long,  with  49  feet  head,  what 
will  the  discharge  be? 

If  the  velocity  Pis  known  in  feet  per  second,  the  discharge  is  0.32725d2F 
cubic  foot  per  minute. 
By  equation  2  we  have 

4F*  +  5F-2  _  Hd         49X5  . 

~1200~~        -  ~L~    =  ~1000~  : 
whence,  by  table,  V  =  real  velocity  =  8  feet  per  second. 

The  discharge  in  cubic  feet  per  minute,  if  V  is  velocity  in  feet  per  second 
and  d  diameter  in  inches,  is  0.32725c?2F,  whence,  discharge 

=  0.32725  X  25  X  8  =  65.45  cubic  feet  per  minute. 

The  velocity  due  the  head,  if  there  were  no  friction,  is  8.025  ^H  =  56.175 
feet  per  second,  and  the  discharge  at  that  velocity  would  be 
0.32725  x  25  X  56.175  =  460  cubic  feet  per  minute. 

Suppose  it  is  required  to  deliver  this  amount,  460. cubic  feet,  at  a  velocity 
of  2  feet  per  second,  what  diameter  of  pipe  will  be  required  and  what  will  be 
the  loss  of  head  by  friction? 


d  —  diameter  = 


FX  0.32725 


460 


=    4/703  =  26.5  inches. 

Having  now  the  diameter,  the  velocity,  and  the  discharge,  the  friction-head 
is  calculated  by  equation  1  and  uce  of  the  table;  thus, 
Z,4P2  +  5F-2        1000.,  20 


2  X  0.32725 


thus  leaving  49  —  0.75  =  say  48  feet  effective  head  applicable  to  power-pro- 
ducing: purposes. 

Problems  of  the  loss  of  head  may  be  solved  rapidly  by  means  of  Cox's 
Pipe  Computer,  a  mechanical  device  on  the  principle  of  the  slide-rule,  for 
sale  by  Keuffel  &  Esser,  New  York. 


LOSS   OF   HEAD. 


Friclioiial  Heads  at  Given  Rates  of  Discharge  in  Clean 
Castriron  Pipes  for  Each  100O  Feet  of  Length. 

(Condensed  from  Ellis  and  Rowland's  Hydraulic  Tables.) 


fl-tf  * 

III 

a  %S 

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05.2  35 

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25 
50 
100 
150 
200 
250 
300 
350 
400 
500 
600 
700 
800 
000 
1000 
1200 
1400 
1600 
1800 
2000 
2500 
3000 
4000 

4-inch 
Pipe. 

6-inch 
Pipe. 

8-inch 
Pipe. 

10-inch 
Pipe. 

12-inch 
Pipe. 

14-inch 
Pipe. 

El 
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2.72 
3.66 
4.73 
5.93 
7.28 
10.38 
14.02 
18.22 
22.96 
28.25 
43.87 
62.92 


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.43 
.57 
.71 
.85 
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1.13 
1.42 
1.70 
1.98 
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2.84 
3.40 
3.97 
4.54 
5.11 
5.67 
7.09 
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2.72 
3.51 
4.41 
5.41 
8.35 
11.93 
21.00 

.64 
1.28 
2.55 
3.83 
5.11 
6.37 
7.66 
8.94 
10.21 
12.77 
15.32 
17.87 

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7.36 
16.05 
28.09 
43.47 
62.20 
84.26 
109.68 
170.53 
244.76 
332.36 

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1.13 
1.70 
2.27 
2.84 
3.40 
3.97 
4.54 
5.67 
6.81 
7.94 
9.08 
10.21 
11.35 
13.61 
15  88 
18.15 
20.42 
22.69 

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2.28 
3.92 
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8.52 
11.48 
14.89 
23.01 
32.89 
44.54 
57.95 
73.12 
90.05 
129.20 
175.38 
228  62 
288.90 
356.22 

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.32 
.64 
.96 
1.28 
1.60 
1.91 
2.23 
2.55 
3.19 
3.83 
4,47 
5.09 
5.74 
6.38 
7.66 
8.94 
10.21 
11.47 
12.77 
15.96 

.04 
.10 
.29 
.60 
1.01 
1.52 
2.13 
2.85 
3.68 
5.64 
8.03 
10.83 
14.05 
17.68 
21.74 
31.10 
42.13 
54.84 
69.22 
85  27 
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1.23 
1.43 
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1500 
2000 
2500 
3000 
3500 
4000 
4500 
5000 
6000 
7000 
8000 
9000 
10000 
12000 
14000 
16000 
18000 
20000 

16-inch 
Pipe. 

18-inch 
Pipe. 

20-inch 
Pipe. 

24-inch 
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30-inch 
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36-inch 
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6.38 
7.18 
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2.82 
4.34 
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8.37 
10.87 
13.70 
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6.30 

578 


HYDRAULICS. 


Effect  of  Bends  and  Curves  in  Pipes.— Weisbach's  rule  for 
bends:  Loss  of  head  in  feet  =  .131  -f-  1.847  /— )*> 


180' 


in  which 


:  internal  radius  of  pipe  in  feet,  R  —  radius  of  curvature  of  axis  of  pipe,  v 
=  velocity  in  feet  per  second,  and  a  =  the  central  angle,  or  angle  subtended 
by  the  bend. 

Hamilton  Smith,  Jr.,  in  his  work  on  Hydraulics,  says:  The  experimental 
data  at  hand  are  entirely  insufficient  to  permit  a  satisfactory  analysis  of 
this  quite  complicated  subject;  in  fact,  about  the  only  experiments  of  value 
are  those  made  by  Bossut  and  Dubuat  with  small  pipes. 

Curves.— If  the  pipe  has  easy  curves,  say  with  radius  not  less  than  5 
diameters  of  the  pipe,  the  flow  will  not  be  materially  diminished,  provided 
the  tops  of  all  curves  are  kept  below  the  hydraulic  grade-line  and  provision 
be  made  for  escape  of  air  from  the  tops  of  all  curves.  (Trautwine.) 

Hydraulic  Grade-line.— In  a  straight  tube  of  uniform  diameter 
throughout,  running  full  and  discharging  freely  into  the  air,  the  hydraulic 
grade-line  is  a  straight  line  drawn  from  the  discharge  end  to  a  point  imme- 
diately over  the  entry  end  of  the  pipe  and  at  a  depth  below  the  surface 
equal  to  the  entry  and  velocity  heads.  (Trautwine.) 

In  a  pipe  leading  from  a  reservoir,  no  part  of  its  length  should  be  above 
the  hydraulic  grade-line. 

Flow  of  Water  in  House-service  Pipes. 

Mr.  E.  Kuichling,  C.E.,  furnished  the  following  table  to  the  Thomson 
Meter  Co.: 


Condition 
of 
Discharge. 

Pressure  in  Main, 
pounds  pei- 
square  inch. 

Discharge,  or  Quantity  capable  of  being  delivered,  in 
Cubic  Feet  per  Minute,  from  the  Pipe, 
under  the  conditions  specified  in  the  first  column. 

Nominal  Diameters  of  Iron  or  Lead  Service-pipe  in 
Inches. 

H 

% 

% 

1 

1« 

2 

33.34 
38.50 
43.04 
47.15 

52.71 
60.87 
69.40 

3           4 

6 

Through  35 
feet  of 
service- 
pipe,  no 
back 
pressure. 

30 
40 
50 
60 
75 
100 
130 

1.10 
1.27 
1.42 
1.56 
1.74 
2.01 
2.29 

1.92 
2.22 
2.48 
2.71 
3.03 
3.50 
3.99 

3.01 
3.48 
3.89 
4.26 
4.77 
5.50 
6.28 

6.13 
7.08 
7.92 
8.67 
9.70 
11.20 
12.77 

16.58 
19.14 
21.40 
23.44 
26.21 
30.27 
34.51 

88.16  173.85 
101.80|200.75 
113.82224.44 
124.68'245.87 
139.  391274.89 
160.96317.41 
183.52361.91 

444.63 
513.42 
574.02 
628.81 
703.03 
811.79 
925.58 

Through 
100  feet  of 
service- 
pipe,  no 
back 
pressure. 

30 
40 
50 
60 
75 
100 
130 

0.66 
0.77 
0.86 
0.94 
1.05 
1.22 
1.39 

1.16 
1.34 
1.50 
1.65 
1.84 
2.13 
2.42 

1.84 
2.12 
2.37 
2.60 
2.91 
3.36 
3.83 

3.78 
4.36 
4.88 
5.34 
5.97 
6.90 
7.86 

10.40 
12.01 
13.43 
14.71 
16.45 
18.99 
21.66 

21.30 
24.50 
27.50 
30.12 
33.68 
38.89 
44.34 

58.19  118.13 
67.19136.41 
75.13  152.51 
82.30167.06 
92.01  186.78 
106.24215.68 
121.HS46.9J 

317.23 
366.30 
409.54 
448.63 
501.58 
579.18 
660.36 

Through 
100  feet  of 
service- 
pipe  and 
15  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.55 
0.66 
0.75 
0.83 
0.94 
1.10 
1.26 

0.96 
1.15 
1.31 
1.45 
1.64 
1.92 
2.20 

1.52 
1.81 
2.06 
2.29 
2.59 
3.02 
3.48 

3.11 
3  72 
4.24 
4.70 
5.32 
6.21 
7.14 

8.57 
10.24 
11.67 
12.94 
14.64 
17.10 
19.66 

17.55 
20.95 
23.87 
26.48 
29.96 
35.00 
40.23 

47.90i  97.171260.56 
57.20116.01  311.09 
65.18  132.20354.49 
72.28146  61  !  393.  13 
81.79  165.  90!444.  85 
95.  55'193.  821519.  72 
109.82222.75597.31 

Through 
100  feet  of 
service- 
pipe,  and 
30  feet 
vertical 
rise. 

30 
40 
50 
60 
75 
100 
130 

0.44 
0.55 
0.65 
0.73 
0.84 
1.00 
1.15 

0.77 
0.97 
1.14 
1.28 
1.47 
1.74 
2.02 

1.22 
1.53 
1.79 
2.02 
2.32 
2.75 
3.19 

2.50 
3.15 
3.69 
4.15 
4.77 
5.65 
6.55 

6.80 
8.68 
10.16 
11.45 
13.15 
15.58 
18.07 

14.11 
17.79 
20.82 
23.47 
26.95 
31  .  93 
37.02 

38.63    78.54 
48.  68'  98.98 
56.98  115.87 
64.22130.59 
73.76:149.99 
87.38177.67 
101.33206.04 

211.54 
266.59 
312.08 
351.73 
403.98 
i  478.  55 
'554.96 

FIRE-STREAMS. 


579 


In  this  table  it  is  assumed  that  the  pipe  is  straight  and  smooth  inside;  that 
the  friction  of  the  main  and  meter  are  disregarded;  that  the  inlet  from  the 
main  is  of  ordinary  character,  sharp,  not  flaring  or  rounded,  and  that  the 
outlet  is  the  full  diameter  of  pipe.  The  deliveries  given  will  be  increased  if, 
first,  the  pipe  between  the  meter  and  the  main  is  of  larger  diameter  than  the 
outlet;  second,  if  the  main  is  tapped,  say  for  1-inch  pipe,  but  is  enlarged 
from  the  tap  to  1*4  or  114  inch;  or,  third,  if  pipe  on  the  outlet  is  larger  than 
that  on  the  inlet  side  of  the  meter.  The  exact  details  of  the  conditions  given 
are  rarely  met  in  practice;  consequently  the  quantities  of  the  table  may  be 
expected  to  be  decreased,  because  the  pipe  is  liable  to  be  throttled  at  the 
joints,  additional  bends  may  interpose,  or  stop-cocks  may  be  used,  or  the 
back-pressure  may  be  increased. 

Air-^>ound  JPipes.—  A  pipe  is  said  to  be  air-bound  when,  in  conse- 
quence of  air  being  entrapped  at  the  hign  points  of  vertical  curves  in  the 
line,  water  will  not  flow  out  of  the  pipe,  although  the  supply  is  higher  than 
the  outlet.  The  remedy  is  to  provide  cocks  or  valves  at  the  high  points, 
through  which  the  air  may  be  discharged.  The  valve  may  be  made  auto- 
matic by  means  of  a  float. 

Vertical  Jets.  (Molesworth.)—  H  =  head  of  water,  h  =  height  of  jet, 
d  —  diameter  of  jet,  K  =  coefficient,  varying  with  ratio  of  diameter  of  jet 
to  head;  then  h  =  KH. 

If  H  =  d  X  300       600         1000         1500         1800         2800       3500       4500, 
K=  .96         .9  .85  .8  .7  .6  .5  .25 

Water  Delivered  through  Meters.    (Thomson  Meter  Co.).—  The 
best  modern  practice  limits  the  velocity  in  water-pipes  to  10  lineal  feet  per 
second.    Assume  this  as  a  basis  of  delivery,  and  we  find,  for  the  several  sizes 
of  pipes  usually  metered,  the  following  approximate  results: 
Nominal  diameter  of  pipe  in  inches: 

%  %           %  1         •  1«         2  3  4  6 

Quantity  delivered,  in  cubic  feet  per  minute,  due  to  said  velocity: 

0.46         1.28        1.85        3.28        7.36        13.1        29.5        52.4        117.9 
Prices   Charged    for    Water  in    Different   Cities   (National 
Meter  Co.;: 
Average  minimum  price  for  1000  gallons  in  163  places  ............    9.4  cents. 

maximum    »••,*«     »»          *«        "    "        "•      ..  .........  28       " 

Extremes,  2^  cents  to  .......................................  100       ** 


FIRE-STREAMS. 

Discharge  from  Nozzles  at  Different  Pressures. 

(J.  T.  Fanning,  Am.  Water-works  Ass'n,  1892,  Eny'g  News,  July  14,  1892.) 


i 

Nozzle 
diam., 
in. 

Height 
of 
stream, 
ft 

Pressure 
at  Play- 

P/vp6' 

Horizon- 
tal Pro- 
jection of 
Streams, 

Gallons 
per 
minute. 

Gallons 
per  24 
hours. 

Friction 
per  100 
ft.  Hose, 

Ihe 

Friction 
per  100 
ft.  Hose, 
Net 

los. 

ft. 

IDS. 

Head,  ft. 

1 

70 

46.5 

59.5 

303 

292,298 

10.75 

24.77 

1 

80 

59.0 

67.0 

230 

331,200 

13.00 

31.10 

1 

90 

79.0 

76.6 

267 

384.500 

17.70 

40.78 

1 

100 

130  0 

88.0 

311 

447.900 

22.50 

54.14 

1^6 

70 

44.5 

61.3 

249 

358,520 

15.50 

35.71 

li^j 

80 

55.5 

69.5 

281 

404,700 

19.40 

44.70 

1^ 

90 

72.0 

78.5 

324 

466,600 

25.40 

58.52 

1^ 

100 

103.0 

89.0 

376 

541,500 

33.80 

17.88 

m 

70 

43.0 

66.0 

306 

440,613 

22.75 

52.42 

m 

80 

53.5 

72.4 

343 

493.900 

28.40 

65.43 

m 

90 

68.5 

81.0 

388 

558,800 

35.90 

82.71 

1$ 

100 

93.0 

92.0 

460 

662,500 

57.75 

86.98 

70 

41.5 

77.0 

368 

530,149 

32.50 

74.88 

1% 

80 

51.5 

74.4 

410 

590,500 

40.00 

92.16 

1% 

90 

65.5 

82.6 

468 

674,000 

51.40 

118.43 

1% 

100 

88.0 

92.0 

540 

777,700 

72.00 

165.89 

580 


HYDRAULICS. 


Friction  Losses  in  Hose.— In  the  above  table  the  volumes  of 
water  discharged  per  jet  were  for  stated  pressures  at  the  play-pipe. 

In  providing  for  this  pressure  due  allowance  is  to  be  made  for  friction 
losses  in  each  hose,  according  to  the  streams  of  greatest  discharge  which  are 
to  be  used. 

The  loss  of  pressure  or  its  equivalent  loss  of  head  (h)  in  the  hose  may  by 

found  by  the  formula  h  =  v2(4m)— -%. 

«(/Ct 

In  this  formula,  as  ordinarily  used,  for  friction  per  100  ft.  of  2J4-in.  hose 
there  are  the  following  constants  :  2^£  in.  diameter  of  hose  d  =  .20833  ft.; 
length  of  hose  I  =  100  ft.,  and  2g  =  64.4.  The  variables  are  :  v  =  velocity  in 
feet  per  second;  h  =  loss  of  head  in  feet  per  100  ft.  of  hose;  TO  —  a  coeffi- 
cient found  by  experiment  ;  the  velocity  v  is  found  from  the  given  dis- 
charges of  the  jets  through  the  given  diameter  of  hose. 

Head   and    Pressure    Losses    by  Friction    in    lOO-ft. 
Lengths  of  Rubber-lined  Smooth  2jj-tii.  Hose. 


Discharge 
per  minute, 
gallons. 

Velocity 
per  second, 
ft. 

Coefficient, 
m. 

Head  Lost, 
ft. 

22.89 
35.55 
46.80 
61.53 
68.48 
88.83 
111.80 
137.50 
148.40 

Pressure 
Lost,  Ibs. 
per  sq.  in. 

9.93 
15.43 
20.31 
26.70 
29.73 
38.55 
48.52 
59.67 
64.40 

Gallons  per 
24  hours. 

288,000 
360,000 
432,000 
499,680 
504,000 
576,000 
648,000 
720,000 
748,800 

200 
250 
300 
347 
350 
400 
450 
500 
520 

13.072 
16.388 
18.858 
21.677 
22.873 
26.144 
29.408 
32.675 
33.982 

.00450 
.00446 
.00442 
.00439 
.00439 
.00436 
.00434 
.00432 
.00431 

These  frictions  are  forgiven  volumes  of  flow  in  the  hose  and  the  veloci- 
ties respectively  due  to  those  volumes,  and  are  independent  of  size  of 
nozzle.  The  changes  in  nozzle  do  not  affect  the  friction  in  the  hose  if  there 
is  no  change  in  velocity  of  flow,  but  a  larger  nozzle  with  equal  pressure  at 
the  nozzle  augments  the  discharge  and  velocity  of  flow,  and  thus  materially 
increases  the  friction  loss  in  the  hose. 

Loss  of  Pressure  (p)  and  Head  (/*)  in  Rubber-lined 
Smooth  2}/2-iii.  Hose  may  be  found  approximately  by  the  formulae! 

/a2  /o2 

p  =      j*       and  h  —  •,  in  which  p  =  pressure   lost    by    friction,    in 

pounds  per  square  inch;  I  —  length  of  hose  in  feet;  q  —  gallons  of  water 
discharged  per  minute ;  d  =  diam.  of  the  hose  in  inches,  2^  in.;  h  =  friction- 
head  in  feet.  The  coefficient  of  d6  would  be  decreased  for  rougher  hose. 

The  loss  of  pressure  and  head  for  a  1^-in.  stream  with  power  to  reach  a 
height  of  80  ft.  is,  in  each  100  ft.  of  2i^-in.  hose,  approximately  20  Ibs.,  or  45 
ft.  net,  or,  say,  including  friction  in  the  hydrant,  J4  ft.  l°ss  °f  head  for  each 
foot  of  hose. 

If  we  change  the  nozzles  to  1*4  or  1%  in.  diameter,  then  for  the  same  80  ft. 
height  of  stream  we  increase  the  friction  losses  on  the  hose  to  approxi- 
mately %  ft.  and  1  ft.  head,  respectively,  for  each  foot-length  of  hose. 

These  computations  show  the  great  difficulty  of  maintaining  a  high 
stream  through  large  nozzles  unless  the  hose  is  very  short,  especially  for  a 
gravity  or  direct-pressure  system. 

This  single  IJ^-in.  stream  requires  approximately  56  Ibs  pressure,  equiva 
lent  to  129  ft.  head,  at  the  play-pipe,  and  45  to  50'ft.  head  for  each  100  ft. 
length  of  smooth  2^-in.  hose,  so  that  for  100,  200.  and  300  ft.  of  hose  we 
must  have  available  heads  at  the  hydrant  or  fire-engine  of  1(6,  156,  and  206 
ft.,  respectively.  If  we  substitute  lJ4-in.  nozzles  for  same  height  of  stream 
we  must  have  available  heads  at  the  hydrants  or  engine  of  185,  255  and  325 
ft.,  respectively,  or  we  must  increase  the  diameter  of  a  portion  at  least  of 
th^  long  hose  and  save  friction-loss  of  head. 

Rated  Capacities  of  Steam  Fire-engines,  which  is  perhaps 
one  third  greater  than  their  ordinary  rate  of  work  at  fires,  are  substantially 
as  follows  : 

3d  size,     550  gals,  per  min.,  or     792,000  gals,  per  24  hours. 
2d    "         700    "  "  1,008.000 

1st   "         900    "  1,296,000 

1  ext.,    1,100    "  *•  1,584,000 


THE   SIPHON. 


581 


Pressures  required  at  Nozzle  and  at  Pump, with  Quantity 
and  Pressure  of  \Vater  Necessary  to  throw  Water 
Various  Distances  through  DifFerent-sized  Nozzles— 
using  2j/»-inch  Rubber  Hose  and  Smooth  Nozzles. 

(From  Experiments  of  Ellis  &  Leshure,  Farming's  "  Water  Supply/1) 


•size  or  iNozzies. 

i  ir 

icn. 

17S   J 

incn. 

Pressure  at  nozzle  Ibs  per  sq  in 

40 

GO 

SO 

100 

40 

60 

80 

100 

*  Pressure    at  pump  or    hydrant  with 
100  ft  2J^  inch  rubber  hose 

48 

73 

97 

191 

54 

81 

108 

135 

Gallons  per  minute  

155 

189 

919 

945 

196 

940 

977 

310 

Horizontal  distance  thrown   feet 

109 

142 

1HH 

186 

113 

148 

175 

193 

Vertical  distance  thrown,  feet  

79 

108 

131 

148 

81 

112 

137 

157 

Size  of  Nozzles. 

1J4  ] 

rnch 

Ws 

;nch 

Pressure  at  nozzle  Ibs  per  sq  in 

40 

60 

80 

100 

40 

60 

80 

100 

*  Pressure  at  pump    or  hydrant  with 
100  feet  2J^j-inch  rubber  hose 

61 

92 

1<>3 

154 

71 

107 

144 

180 

Gallons  per  minute     .              

949 

997 

349 

3S3 

993 

358 

413 

469 

Horizontal  distance  thrown,  feet  

118 

156 

186 

9,07 

194 

166 

900 

2?,4 

Vertical  distance  thrown,  feet  

82 

115 

142 

164 

85 

118 

146 

169 

*  For  greater  length  of  2i^-inch  hose  the  increased  friction  can  be  ob- 
tained by  noting  the  differences  between  the  above  given  "  pressure  at 
nozzle"  and  "pressure  at  pump  or  hydrant  with  100  feet  of  hose."  For 
instance,  if  it  requires  at  hydrant  or  pump  eight  pounds  more  pressure 
than  it  does  at  nozzle  to  overcome  the  friction  when  pumping  through  100 
feet  of  2^-inch  hose  (using  1-inch  nozzle,  with  40-pound  pressure  at  said 
nozzle)  then  it  requires  16-pounds  pressure  to  overcome  the  friction  in 
forcing  through  200  feet  of  same  size  hose. 

^Decrease  of  Flow  due  to  Increase  of  Length  of  Hose. 
(J.  R.  Freeman's  Experiments,  Trans.  A.  S.  C.  E.  1889.)— If  the  static  pres- 
sure is  80  Ibs.  and  the  hydrant-pipes  of  such  size  that  the  pressure  at  the  hy- 
drant is  70  Ibs.,  the  hose  2%  in.  nominal  diam.,  and  the  nozzle  1%  m-  diam., 
the  height  of  effective  fire-stream  obtainable  and  the  quantity  in  gallons  per 
minute  will  be : 


With    50  ft.  o 
"      250  " 

"      500  " 


in.  hose.  . 


Linen  Hose. 
Height,        Gals. 

feet.       per  in  in. 
.     73  261 

. .     42  184 

. .     27  146 


Best  Rubber- 
lined  Hose. 
Height,        Gals. 
feet.      per  min. 

81  282 

61  229 

46  192 


With  500  ft.  of  smoothest  and  best  rubber-lined  hose,  if  diameter  be 
exactly  2^4  in.,  effective  height  of  stream  will  be  39ft.  (177  gals.);  if  diameter 
be  J4  in.  larger,  effective  height  of  stream  will  be  46  ft.  (192  gals.) 

THE  SIPHON. 

The  Siphon  is  a  bent  tube  of  unequal  branches,'  open  at  both  ends,  and 
is  used  to  convey  a  liquid  from  a  higher  to  a  lower  level,  over  an  intermedi- 
ate point  higher  than  either.  Its  parallel  branches  being  in  a  vertical  plane 
and  plunged  into  two  bodies  of  liquid  whose  upper  surfaces  are  at  different 
levels,  the  fluid  will  stand  at  the  same  level  both  within  and  witfrout  each 
branch  of  the  tube  when  a  vent  or  small  opening  is  made  at  the  bend.  If 
the  air  be  withdrawn  from  the  siphon  through  this  vent,  the  water  will  rise 
in  the  branches  by  the  atmospheric  pressure  without,  and  when  the  two 
columns  unite  and  the  vent  is  closed,  the  liquid  will  flovy  from  the  upper 
reservoir  as  long  as  the  end  of  the  shorter  branch  of  the  siphon  is  below  the 
surface  of  the  liquid  in  the  reservoir. 

If  the  water  was  free  from  air  the  height  of  the  bend  above  the  supply 
level  might  be  as  great  as  33  feet. 


582  HYDRAULICS. 

If  A  =  area  of  cross-section  of  the  tube  in  square  feet,  H  —  the  difference 
in  level  between  the  two  reservoirs  in  feet,  D  the  density  of  the  liquid  in 
pounds  per  cubic  foot,  then  A DH  measures  the  intensity  of  the  force  which 
causes  the  movement  of  the  fluid,  and  V  —  \/'ZgH=  8.02  ^H  is  the  theoretical 
velocity,  in  feet  per  second,  which  is  reduced  by  the  loss  of  head  for  entry 
and  friction,  as  in  other  cases  of  flow  of  liquids  through  pipes.  In  the  case 
of  the  difference  of  level  being  greater  than  33  feet,  however,  the  velocity  of 
the  water  in  the  shorter  leg  is  limited  to  that  due  to  a  height  of  33  feet,  or 
that  due  to  the  difference  between  the  atmospheric  pressure  at  the  entrance 
and  the  vacuum  at  the  bend. 

Leicester  Allen  (Am.  Mach.,  Nov.  2,  1893)  says:  The  supply  of  liquid  to  a 
siphon  must  be  greater  than  the  flow  which  would  take  place  from  the  dis- 
charge end  of  the  pipe,  provided  the  pipe  were  filled  with  the  liquid,  the 
supply  end  stopped,  and  the  discharge  end  opened  when  the  discharge  end 
is  left  free,  unregulated,  and  unsubmerged. 

To  illustrate  this  principle,  let  us  suppose  the  extreme  case  of  a  siphon 
haying  a  calibre  of  1  foot,  in  which  the  difference  of  level,  or  between  the 
point  of  supply  and  discharge,  is  4  inches.  Let  us  further  suppose  this 
siphon  to  be  at  the  sea-level,  and  its  highest  point  above  the  level  of  the 
supply  to  be  2?  feet.  Also  suppose  the  discharge  end  of  this  siphon  to  be  un- 
regulated, unsubmerged.  It  would  be  inoperative  because  the  water  in  the 
longer  leg  would  not  be  held  solid  by  the  pressure  of  the  atmosphere  against 
it,  and  it  would  therefore  break  up  and  run  out  faster  than  it  could  be  re- 
placed at  the  inflow  end  under  an  effective  head  of  only  4  inches. 

Long  Siphons.— Prof.  Joseph  Torrey,  in  the  Aiuer.  Machinist, 
describes  a  long  siphon  which  was  a  partial  failure. 

The  length  of  the  pipe  was  1792  feet.  The  pipe  was  3  inches  diameter,  and 
rose  at  one  point  9  feet  above  the  initial  level.  The  final  level  was  20  feet 
below  the  initial  level.  No  automatic  air  valve  was  provided.  The  highest 
point  in  the  siphon  was  about  one  third  the  total  distance  from  the  pond  and 
nearest  the  pond.  At  this  point  a  pump  was  placed,  whose  mission  was  to 
fill  the  pipe  when  necessary.  This  siphon  would  flow  for  about  two  hours 
and  then  cease,  owing  to  accumulation  of  air  in  the  pipe.  V\  hen  in  full 
operation  it  discharged  43^  gallons  per  minute.  The  theoretical  discharge 
from  such  a  sized  pipe  with  the  specified  head  is  55^  gallons  per  minute. 

Siphon  on  the  Water-supply  of  Mount  Vernon,  N.  Y. 
(Eng^g  News,  May  4, 1893.) — A  12-inch  siphon,  925  feet  long,  with  a  maximum 
lift  of"22.12  feet  and  a  45°  change  in  alignment,  was  put  in  use  in  1892  by  the 
New  York  City  Suburban  Water  Co.,  which  supplies  Mount  Vernon,  N.  Y. 

At  its  summit  the  siphon  crosses  a  supply  main,  which  is  tapped  to  charge 
the  siphon. 

The  air-chamber  at  the  siphon  is  12  inches  by  16  feet  long.  A  J^-inch  tap 
and  cock  at  the  top  of  the  chamber  provide  an  outlet  for  the  collected  air. 

It  was  found  that  the  siphon  with  air-chamber  as  desc.ibed  would  run 
until  125  cubic  feet  of  air  had  gathered,  and  that  this  took  place  only  half  as 
soon  with  a  14-foot  lift  as  with  the  full  lift  of  22.12  feet.  The  siphon  will 
operate  about  12  hours  without  being  recharged,  but  more  water  can  be 
gotten  over  by  charging  every  six  hours.  It  can  be  kept  running  23  hours 
out  of  24  with  only  one  man  in  attendance.  With  the  siphon  as  described 
above  it  is  necessary  to  close  the  valves  at  each  end  of  the  siphon  to 
recharge  it. 

It  has  been  found  by  weir  measurements  that  the  discharge  of  the  siphon 
before  air  accumulates  at  the  summit  is  practically  the  same  as  through  a 
straight  pipe. 

MEASUREMENT  OF  FLOWING  WATER. 

IPiezonieter. — If  a  vertical  or  oblique  tube  be  inserted  into  a  pipe  con- 
taining water  under  pressure,  the  water  will  rise  in  the  former,  and  the  ver- 
tical height  to  which  it  rises  will  be  the  head  producing  the  pressure  at  the 
point  where  the  tube  is  attached.  Such  a  tube  is  called  a  piezometer  or 
pressure  measure.  If  the  water  in  the  piezometer  falls  below  its  proper 
level  it  shows  that  the  pressure  in  the  main  pipe  has  been  reduced  by  an 
obstruction  between  the  piezometer  and  the  reservoir.  If  the  water  rises 
above  its  proper  level,  it  indicates  that  the  pressure  there  has  been  in- 
creased by  an  obstruction  beyond  the  piezometer. 

If  we  imagine  a  pipe  full  of  water  to  be  provided  with  a  number  of  pie- 
zometers, then  a  line  joining  the  tops  of  the  columns  of  water  in  them  is 
the  hydraulic  grade-line. 


MEASUREMEHT   OF   FLOWING   WATER.  583 

Pitot  Tube  Gauge.—  The  Pitot  tube  is  used  for  measuring  the  veloc- 
ity of  fluids  in  motion.  It  has  been  used  with  great  success  in  measuring 
the  flow  of  natural  gas.  (S.  W.  Robinson,  Report  Ohio  Geol.  Survey,  1890.) 
(See  also  Van  NostrancVs  Mag.,  vol.  xxxv.)  It  is  simply  a  tube  so  bent  that 
a  short  leg  extends  into  the  current  of  fluid  flowing  from  a  tube,  with  the 
plane  of  the  entering  orifice  opposed  at  right  angles  to  the  direction  of  the 
current.  The  pressure  caused  by  the  impact  of  the  current  is  transmitted 
through  the  tube  to  a  pressure  gauge  of  any  kind,  such  as  a  column  of 
water  or  of  mercury,  or  a  Bourdon  spring-gauge.  From  the  pressure  thus 
indicated  and  the  known  density  and  temperature  of  the  flowing  gas  is  ob- 
tained the  head  corresponding' to  the  pressure,  and  from  this  the  velocity. 
In  a  modification  of  the  Fitot  tube  described  by  Prof.  Jlobinson,  there  are 
two  tubes  inserted  into  the  pipe  conveying  the  gas,  one  of  which  has  the 
plane  of  the  orifice  at  right  angles  to  the  current,  to  receive  the  static  pres- 
sure plus  the  pressure  due  to  impact;  the  other  has  the  plane  of  its  orifice 
parallel  to  the  current,  so  as  to  receive  the  static  pressure  only.  These 
tubes  are  connected  to  the  legs  of  a  £7  tube  partly  filled  with  mercury,  which 
then  registers  the  difference  in  pressure  in  the  two  tubes,  from  which  the 
velocity  may  be  calculated.  Comparative  tests  of  Pitot  tubes  with  gas- 
meters,  for  measurement  of  the  flow  of  natural  gas,  have  shown  an  agree- 
ment within  3$. 

The  Venturi  JHeter,  invented  by  Clemens  Herschel,  and  described  in 
a  pamphlet  issued  by  the  Builders'  Iron  Foundry  of  Providence,  R.  I.,  is 
named  from  Venturi,  who  first  called  attention,  in  1796,  to  the  relation  be- 
tween the  velocities  and  pressures  of  fluids  when  flowing  through  converging 
and  diverging  tubes. 

It  consists  of  two  parts— the  tube,  through  which  the  water  flows,  and  the 
recorder,  which  registers  the  quantity  of  water  that  passes  through  the 
tube. 

The  tube  takes  the  shape  of  two  truncated  cones  joined  in  their  smallest 
diameters  by  a  short  throat-piece.  At  the  up-stream  end  and  at  the  throat 
there  are  air-chambers,  at  which  points  the  pressures  are  taken. 

The  action  of  the  tube  is  based  on  that  property  which  causes  the  small 
section  of  a  gently  expanding  frustum  of  a  cone  to  receive,  without  material 
resultant  loss  of  head,  as  much  water  at  the  smallest  diameter  as  is  dis- 
charged at  the  large  end,  and  on  that  further  property  which  causes  the 
pressure  of  the  water  flowing  through  the  throat  to  be  less,  by  virtue  of  its 
greater  velocity,  than  the  pressure  at  the  up-stream  end  of  the  tube,  each 
pressure  being' at  the  same  time  a  function  of  the  velocity  at  that  point  and 
of  the  hydrostatic  pressure  which  would  obtain  were  the  water  motionless 
within  the  pipe. 

The  recorder  is  connected  with  the  tube  by  pressure-pipes  which  lead  to 
it  from  the  chambers  surrounding  the  up-stream  end  and  the  throat  of  the 
tube.  It  may  be  placed  in  any  convenient  position  within  1000  feet  of  the 
tube.  It  is  operated  by  a  weight  and  clockwork. 

The  difference  of  pressure  or  head  at  the  entrance  and  at  the  throat  of  the 
meter  is  balanced  in  the  recorder  by  the  difference  of  level  in  two  columns 
of  mercury  in  cylindrical  receivers,  one  within  the  other.  The  inner  carries 
a  float,  the  position  of  which  is  indicative  of  the  quantity  of  water  flowing 
through  the  tube.  By  its  rise  and  fall  the  float  varies  the  time  of  contact 
between  an  integrating  drum  and  the  counters  by  which  the  successive 
readings  are  registered. 

There  is  no  limit  to  the  sizes  of  the  meters  nor  the  quantity  of  water  that 
may  be  measured.  Meters  with  24-inch,  36-inch,  48-inch,  and  even  20-foot 
tubes  can  be  readily  made. 

Measurement  "by  Venturi  Tubes.  (Trans.  A.  S.  C.  E.,  Nov.,  1887, 
and  Jan.,  1888.) — Mr.  Herschel  recommends  the  use  of  a  Venturi  tube,  in- 
serted in  the  force-main  of  the  pumping  engine,  for  determining  the  quantity 
of  water  discharged.  Such  a  tube  applied  to  a  24-inch  main  has  a  total 
length  of  about  20  feet.  At  a  distance  of  4  feet  from  the  end  nearest  the 
engine  the  inside  diameter  of  the  tube  is  contracted  to  a  throat  having  a 
diameter  of  about  8  inches.  A  pressure-gauge  is  attached  to  each  of  two 
chambers,  the  one  surrounding  and  communicating  with  the  entrance  or 
main  pipe,  the  other  with  the  throat.  According  to  experiments  made  upon 
two  tubes  of  this  kind,  one  4  in.  in  diameter  at  the  throat  and  12  in.  at  the  en- 
trance, and  the  other  about  36  in.  in  diameter  at  the  throat  and  9  feet  at  its 
entrance,  the  quantity  of  water  which  passes  through  the  tube  is  very  nearly 
the  theoretical  discharge  through  an  opening  having  an  area  equal  to  that 
of  the  throat,  and  a  velocity  which  is  that  due  to  the  difference  in  head  Miown 


584 


HYDRAULICS. 


by  the  two  gauges.  Mr.  Herschel  states  that  the  coefficient  for  these  twd 
widely-varying  sizes  of  tubes  and  for  a  wide  range  of  velocity  through  the 
pipe,  was  found  to  be  within  two  per  cent,  either  way,  of  98$.  Tn  other 
words,  the  quantity  of  water  flowing  through  the  tube  per  second  is  ex- 
pressed within  two  per  cent  by  the  formula  W  —  0.98  X  A  X  1/20/1,  in  which 
A  is  the  area  of  the  throat  of  the  tube,  h  the  head,  in  feet,  correspond- 
ing to  the  difference  in  the  pressure  of  the  water  entering  the  tube  and  that 
found  at  the  throat,  and  g  =  32.16. 

measurement  of  Discharge  of  Pmnpiiig-engines  by 
Means  of  Nozzles.  (Trans.  A.  S.  M.  E.,  xiii,  557).-— The  measurement 
<»t'  water  by  computation  from  its  discharge  through  orifices,  or  through  the 
nozzles  of  nre-hose,*furnishes  a  means  of  determining  the  quantity  of  water 
delivered  by  a  pumping-engine  which  can  be  applied  without  much  difficulty. 
John  R.  Freeman,  Trans.  A.  S.  C.  E.,  Nov.,  1889,  describes  a  series  of  experi- 
ments covering  a  wide  range  of  pressures  and  sizes,  and  the  results  showed 
that  the  coefficient  of  discharge  for  a  smooth  nozzle  of  ordinary  good  form 
was  within  one  half  of  one  per  cent,  either  way,  of  0.977  ;  the  diameter  of 
the  nozzle  being  accurately  calipered,  and  the  pressures  being  determined 
by  means  of  an  accurate  gauge  attached  to  a  suitable  piezometer  at  the  base 
of  the  play-pipe. 

In  order  to  use  this  method  for  determining  the  quantity  of  water  dis- 
charged by  a  pumping-engine,  it  would  be  necessary  to  provide  a  pressure- 
box,  to  which  the  water  would  be  conducted,  and  attach  to  the  box  as  many 
nozzles  as  would  be  required  to  carry  off  the  water.  According  to  Mr. 
Freeman's  estimate,  four  lJ4-inch  nozzles,  thus  connected,  with  a  pressure 
of  80  Ibs.  per  square  inch,  would  discharge  the  full  capacity  of  a  two-and  a- 
half-million  engine.  He  also  suggests  the  use  of  a  portable  apparatus  with 
a  single  opening  for  discharge,  consisting  essentially  of  a  Siamese  nozzle, 
so-called,  the  water  being  carried  to  it  by  three  or  more  lines  of  fire  hose. 

To  insure  reliability  for  these  measurements,  it  is  necessary  that  the  shut 
off  valve  in  the  force-main,  or  the  several  shut  off  valves,  should  be  tight, 
so  that  all  the  water  discharged  by  the  engine  may  pass  through  the  nozzles. 

Flow  through  Rectangular  Orifices.   (Approximate.  Seep.  556.) 

CUBIC  FEET  OP  WATER  DISCHARGED  PER  MINUTE  THROUGH  AN  ORIFICE  ONE 
INCH  SQUARE,  UNDER  ANY  HEAD  OP  WATER  FROM  3  TO  72  INCHES. 

For  any  other  orifice  multiply  by  its  area  in  square  inches. 
Formula,  Q'  =  .624  1//i"X  <*.    Q'  =  cu.  ft.  per  min.;  a  —  area  in  sq.  in. 


Heads 
in  inches. 

Cubic  Feet 
Discharged 
per  min. 

Heads 
in  inches. 

Cubic  Feet 
Discharged 
per  min. 

cc 

03 

"1 

«s.S 
r- 

Cubic  Feet 
Discharged 
per  min. 

i 

CO  rC 

"3  ~ 

X  B 
li  '" 

Cubic  Feet 
Discharged 
per  min. 

g 

jj 

Cubic  Feet 
Discharged 
per  min. 

Heads 
in  inches. 

Cubic  Feet 
Discharged 
per  min. 

i 

ll 

(gfi 

Cubic  Feet 
Discharged 
per  min. 

3 

1.12 

13 

2.20 

23 

2.90 

33 

3.47 

43 

3  95 

53 

4.39 

63 

4.78 

4 

1.2? 

14 

2.28 

24 

2.97 

34 

3.52 

44 

4.00 

54 

4.42 

64 

4.81 

5 

1.40 

15 

2.36 

25 

3.03 

35 

3.57 

45 

4  05 

55 

4.46 

65 

4.85 

6 

1.52 

1C 

2.43 

26 

3.08 

36 

3.62 

46 

4.09 

56 

4.52 

66 

4.89 

7 

1.64 

17 

2.51 

27 

3.14 

37 

3.67 

47 

4.1,2 

57 

4.55 

67 

4.92 

8 

1.75 

18 

2.58 

28 

3.20 

38 

3.72 

48 

4.18 

58 

4.58 

68 

4.97 

9 

1.84 

19 

2.64 

29 

3.25 

39 

3.77 

49 

4.21 

59 

4.63 

69 

5.00 

10 

1.94 

20 

2.71 

30 

3.31 

40 

3.81 

50 

4.27 

60 

4.65 

70 

5.03 

11 

2.03 

21 

2.78 

31 

3.36 

41 

3.86 

51 

4.30 

61 

4.72 

71 

5.07 

12 

2.12 

22 

2.84 

32 

3.41 

42 

3.91 

52 

4.34 

62 

4.74 

72 

5.09 

Measurement  of  an  Open  Stream  by  Velocity  and  Cross- 
section. — Measure  the  depth  of  the  water  at  from  6  to  12  points  across 
the  stream  at  equal  distances  between.  Add  all  the  depths  in  feet  together 
and  divide  by  the  number  of  measurements  made;  this  will  be  the  average 
depth  of  the  stream,  which  multiplied  by  its  width  will  give  its  area  or  cross- 
section.  Multiply  this  by  the  velocity  o'f  the  stream  in  feet  per  minute,  and 
the  result  will  be  the  discharge  in  cubic  feet  per  minute  of  the  stream. 

The  velocity  of  the  stream  can  be  found  by  laying  off  100  feet  of  the  bank 
and  throwing  afloat  into  the  middle,  noting  the  time  taken  in  passing  over 
the  100  ft.  Do  this  a  number  of  times  and  take  the  average  ;  then,  dividing 


MEASUREMENT   OF   FLOWING   WATER. 


585 


this  distance  by  the  time  gives  the  velocity  at  the  surface.  As  the  top  of  the 
stream  flows  faster  than  the  bottom  or  sides— the  average  velocity  being 
about  83#  of  the  surface  velocity  at  the  middle— it  is  convenient  to  measure 
a  distance  of  120  feet  for  the  float  and  reckon  it  as  100. 


FIG.  130. 
.  Miners'  Inch  Measurements. 


(Pelton  Water  Wheel  Co.) 
The  cut,  Fig.  130,  shows  the  form  of  measuring-box  ordinarily  used,  and  the 
following  table  gives  the  discharge  in  cubic  feet  per  minute  of  a  miner's  inch 
of  water,  as  measured  under  the  various  heads  and  different  lengths  and 
heights  of  apertures  used  in  California. 


Length 

Openings  2  Inches  High. 

Openings  4  Inches  High. 

of 

Opening 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

Head  to 

in 

Centre, 

Centre, 

Centre, 

Centre, 

Centre, 

Centre, 

inches. 

5  inches 

6  inches. 

7  inches. 

5  inches. 

6  inches. 

7  inches. 

Cu.  ft. 

C  i.  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

Cu.  ft. 

4 

.348 

.473 

.589 

1.320 

.450 

.570 

6 

.355 

.480 

.596 

1.336 

.470 

.595 

8 

.359 

.484 

.600 

1.344 

.481 

.608 

10 

.361 

.485 

.602 

1.349 

.487 

.615 

12 

.363 

.487 

.604 

1.352 

.491 

.620 

14 

.364 

.488 

.604 

1.354 

.494 

.623 

16 

.365 

.489 

.605 

1.356 

.496 

.626 

18 

.365 

•489 

.606 

1.357 

.498 

.628 

20 

.365 

.490 

.606 

1.359 

.499 

.630 

22 

1.366 

.490 

.607 

1.359 

.500 

.631 

24 

1.366 

.490 

.607 

1.360 

.501 

.632 

26 

1.366 

.490 

.607 

1.361 

.502 

.633 

1.367 

.491 

.607 

1.361 

.503 

.634 

30 

1.367 

.491 

.608 

1.362 

.503 

.635 

40 

1.367 

.492 

.608 

1.363 

.505 

.637 

50 

1.368 

.493 

.609 

1.364 

.507 

.639 

60 

1.368 

.493 

.609 

1.365 

.508 

.640 

70 

1.368 

.493 

.609 

1.365 

.508 

1.641 

80 

1.368 

.493 

.609 

1.366 

.509 

1.641 

90 

1.369 

1.493 

.610 

1.366 

.509 

1.641 

100 

1.369 

1.494 

.610 

1.366 

.509 

1.642 

E.— The  apertures  from  which  the  above  measurements  were  obtained 


586 


HYDRAULICS. 


were  through  material  1*4  inches  thick,  and  the  lower  edge  2  inches  above 
the  bottom  of  the  measuring-box,  thus  giving  full  contraction 
Flow  of  Water  Over  Weirs.     Weir  Dam  Measurement. 

(Pelton  Water  Wheel  Co.)— Place  a  board  or  plank  in  the  stream,  as  shown 


FIG.  131. 

in  the  sketch,  at  some  point  where  a  pond  will  form  above.  The  length  of 
the  notch  in  the  dam  should  be  from  two  to  four  times  its  depth  for  small 
quantities  and  longer  for  large  quantities.  The  edges  of  the  notch  should 
be  bevelled  toward  the  intake  side,  as  shown.  The  overfall  below  the  notch 
should  not  be  less  than  twice  its  depth,  that  is,  12  inches  if  the  notch  is  6 
inches  deep,  and  so  on. 

In  the  pond,  about  6  ft.  above  fhe  dam,  drive  a  stake,  and  then  obstruct  the 
water  until  it  rises  precisely  to  the  bottom  of  the  notch  and  mark  the  stake 
at  this  level.  Then  complete  the  dam  so  as  to  cause  all  the  water  to  flow 
through  the  notch,  and,  after  time  for  the  water  to  settle,  mark  the  stake 
again  for  this  new  level.  If  preferred  the  stake  can  be  driven  with  its  top 
precisely  level  with  the  bottom  of  the  notch  and  the  depth  of  the  water  be 
measured  with  a  rule  after  the  water  is  flowing  free,  but  the  marks  are  pre- 
ferable in  most  cases.  The  stake  can  then  be  withdrawn :  and  the  distance 
between  the  marks  is  the  theoretical  depth  of  flow  corresponding  to  the 
quantities  in  the  table. 

Francis's  Formulas  for  Weirs. 

As  given  by  As  modified  by 

Francis.  Smith. 

Q  =  3.33Z/1*  3.29(7+  ^)t? 


Weirs  with  both  end  contractions  / 
suppressed 

Weirs  with  one  end  contraction     | 
suppressed 

Weirs  with  full  contraction 


=  3.33(Z  -  .l 


The  greatest  variation  of  the  Francis  formulae  from  the  values  of  c  given  by 
Smith  amounts  to  3^$.  The  modified  Francis  formulae,  says  Smith,  will  give 
results  sufficiently  exact,  when  great  accuracy  is  not  required,  within  the 
limits  of  fc,  from  .5  ft.  to  2  ft.,  I  being  not  less  than  3  h. 


MEASUREMENT   OF   FLOWING   WATEK. 


587 


Q  =  discharge  in  cubic  feet  per  second,  I  =  length  of  weir  in  feet,  h  =effec- 
tive  head  in  feet,  measured  from  the  level  of  the  crest  to  the  level  of  still 
water  above  the  weir. 

If  Q'  —  discharge  in  cubic  feet  per  minute,  and  I'  and  h'  are  taken  in 

inches,  the  first  of  the  above  formulae  reduces  to  Q'  =  0.41'h'?.  From  this 
formula  the  following  table  is  calculated.  The-values  are  sufficiently  accu- 
rate for  ordinary  computations  of  water-power  for  weirs  without  end  con- 
traction, that  is,  for  a  weir  the  full  width  of  the  channel  of  approach,  and 
are  approximate  also  for  weirs  with  end  contraction  when  I  ~  at  least  lO/i, 
but  about  6$  in  excess  of  the  truth  when  I  —  4h. 

Weir  Table. 

GIVING  CUBIC  FEET  OF  WATER  PER  MINUTE  THAT  WILL  FLOW  OVER  A  WEIR 
ONE  INCH  WIDE  AND  FROM  J^  TO  20%  INCHES  DEEP. 

For  other  widths  multiply  by  the  width  in  inches. 


fcin. 

^4  in. 

%i«. 

1-6  in. 

$8  in- 

34  in.  |    %in. 

in. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

cu.  ft, 

cu.  ft. 

cu.  ft. 

cu.  ft. 

cu.  ft. 

0 

.00 

.01 

.05 

.09 

.14 

.19 

.26 

.32 

1 

.40 

.47 

.55 

.64 

.73 

.82 

.92 

1.02 

2 

1.13 

1.23 

1.35 

1.46 

1.58 

1.70 

1.82 

1.95 

3 

2.07 

2.21 

2.34 

2.48 

2.61 

2.76 

2.90 

3.05 

4 

3.20 

3.35 

3.50 

3.66 

3.81 

3.97 

4.14 

4.30 

5 

4.47 

4.64 

4.81 

4.98 

5.15 

5.33 

5.51 

5.69 

6 

5.87 

6.06 

6.25 

6.44 

6.6v> 

6.82 

7.01 

7.21 

7 

7.40 

7.60 

7.80 

8.01 

8.21 

8.42 

8.63 

8.83 

8 

9.05 

9.26 

9.47 

9.69 

9.91 

10.13 

10.35 

10.57 

9 

10.80 

11.02 

11.25 

11.48 

11.71 

11.94 

12.17 

12.41 

10 

12.64 

•13.88 

13.12 

13.36 

13.60 

13.85 

14.09 

14.34 

11 

14.59 

14.84 

15.09 

15  34 

15.59 

15.85 

16.11 

16.36 

12 

16.62 

16.88 

17.15 

17.41 

17.67 

17.94 

18.21 

18.47 

13 

18.74 

19.01 

19.29 

19.56 

19.84 

20.11 

20.39 

20.67 

14 

20.95 

21.23 

21.51 

21.80 

22.08 

22.37 

22.65 

22.94 

15 

23.23 

23.52 

23.82 

24.11 

24.40 

24.70 

25.00 

25.30 

16 

25.60 

25.90 

26.20 

26.50 

26.80 

27.11 

27.42 

27.72 

17 

28.03 

28.34 

28.65 

28.97 

29.28 

29  59 

29.91 

30.22 

18 

30.54 

30.86 

31.18 

31.50 

31.82 

3-.M5 

32.47 

32.80 

19 

33.12 

33.45 

33.78 

34  11 

34.44 

34.77 

35.10 

35.44 

20 

35.77 

86.11 

36.45 

36.78 

37.12 

37.46 

37.80 

38.15 

For  more  accurate  computations,  the  coefficients  of  flow  of  Hamilton 
Smith,  Jr.,  or  of  Bazin  should  be  used.  In  Smith's  hydraulics  will  be  found 
a  collection  of  results  of  experiments  on  orifices  and  weirs  of  various  shapes 
made  by  many  different  authorities,  together  with  a  discussion  of  their 
several  formulae.  (See  also  Traut  wine's  Pocket  Book.) 

Bazin's  Experiments.  — M.  Bazin  (Annales  des  Fonts  et  Ghaussees, 
Oct.,  1888,  translated  by  Marichal  and  Trautwine,  Proc.  Engrs.  Club  of  Phila., 
Jan.,  1890),  made  an  extensive  series  of  experiments  with  a  sharp-crested 
weir  without  lateral  contraction,  the  air  being  admitted  freely  behind  the 
falling  sheet,  and  found  values  of  m  varying  from  0.42  to  0.50,  with  varia- 
tions of  the  length  of  the  weir  from  19%  to  78%  in.,  of  the  height  of  the  crt-st 
above  the  bottom  of  the  channel  from  0.79  to  2.46  ft.,  and  of  the  head  from 
1.97  to  23.62  in.  From  these  experiments  he  deduces  the  following  formula  : 

Q  =[o.425  +  0.2l 

in  which  Pis  the  height  in  feet  of  the  crest  of  the  weir  above  the  bottom  of 
the  channel  of  approach,  L  the  length  of  the  weir,  H  the  head,  both  in  feet, 
and  Q  the  discharge  in  cu.  ft.  per  sec.  This  formula,  says  M.  Bazin,  is  en- 
tirely practical  where  errors  of  2g  to  3#  are  admissible.  The  following 
table  is  condensed  from  M.  Bazin 's  paper  : 


588 


WATER-POWER. 


VALUES  OF  THE  COEFFICIENT  m  IN  THE  FORMULA  Q  =  mLH  V2(jH,  FOR  A 
SHARP-CRESTED  WEIR  WITHOUT  LATERAL  CONTRACTION  ;  THE  AIR  BEING 
ADMITTED  FREELY  BEHIND  THE  FALLING  SHEET. 


Head, 
H. 

Height  of  Crest  of  Weir  Above  Bed  of  Channel. 

Feet  ...0.66 
Inches  7.87 

0.98 
11.81 

1.31 
15.75 

1.64 
19.69 

1.97 
23.62 

2.62 
31.50 

3.28 
39.38 

4.92 
59.07 

6  56 

78.76 

00 
00 

Ft. 
.164 
.230 
.29o 
.394 
.525 
.656 
.787 
.919 
.050 
.181 
.312 
.444 
.575 
.706 
1.837 
1.969 

In. 
1.97 
2.76 
3.54 
4.72 
6.30 
7.87 
9.45 
11.02 
12.60 
14.17 
15.75 
17.32 
18.90 
20.47 
22.05 
23.62 

m 
0458 
0.455 
0.457 
0.462 
0.471 
0.480 
0.488 
0.496 

m 
0.453 
0.448 
0.447 
0.448 
0.453 
0.459 
0.465 
0.472 
0.478 
0.483 
0.489 
0.494 

m 
0.451 
0.445 
0.442 
0.442 
0.444 
0.447 
0.452 
0.457 
0.462 
0.467 
0.472 
0.476 
0.480 
0.483 
0.487 
0.490 

m 
0.450 
0.443 
0.440 
0.438 
0.438 
0.440 
0.444 
0.448 
0.452 
0.456 
0.459 
0.463 
0.467 
0.470 
0.473 
0.476 

m 
0.449 
0.442 
0.438 
0.436 
0.435 
0.436 
0.438 
0.441 
0.444 
0.448 
0.451 
0.454 
0.457 
0.460 
0.463 
0.466 

m 

0.449 
0.441 
0.436 
0.433 
0.431 
0.431 
0.432 
0.433 
0.436 
0.438 
0.440 
0.442 
0.444 
0.446 
0.448 
0.451 

m 
0.449 
0.440 
0.436 
0.432 
0.429 
0.428 
0.428 
0.429 
0.430 
0.432 
0.433 
0.435 
0.436 
0.438 
0.439 
0.441 

m 
0.448 
0.440 
0.435 
0.430 
0.427 
0.425 
0.424 
0.424 
0.424 
0.424 
0.424 
10.425 
0.425 
0.426 
,0.42? 
0.427 

m 
0.448 
0.439 
0.434 
0.430 
0.426 
0.423 
0.422 
0.422 
0.421 
0.421 
0.421 
0.421 
0.421 
0.421 
0.421 
0-421 

m 
0.4481 
0.4391 
0.4840 
0.4291 
0.4246 
0.4215 
0.4194 
0.4181 
0.4168 
0.4156 
0.4144 
0.4134 
0.4122 
0.4112 
0.4101 
0.4092 

A  comparison  of  the  results  of  this  formula  with  those  of  experiments, 
says  M.  Bazin,  justifies  us  in  believing  that,  except  in  the  unusual  case  of  a 
very  low  weir  (which  should  always  be  avoided),  the  preceding  table  will 
give  the  coefficient  in  in  all  cases  within  \%\  provided,  however,  that  the  ar- 
rangements of  the  standard  weir  are  exactly  reproduced.  It  is  especially 
important  that  the  admission  of  the  air  behind  the  falling  sheet  be  perfectly 
assured.  If  this  condition  is  not  complied  with,  m  may  vary  within  much 
wider  limits.  The  type  adopted  gives  the  least  possible  variation  in  th» 
coefficient. 


WATER-POWER. 


Power  of  a  Fall  of  Water—  Efficiency.—  The  gross  power  of 
a  fall  of  water  is  the  product  of  the  weight  of  water  discharged  in  a  unit  of 
time  into  the  total  head,  i.e.,  the  difference  of  vertical  elevation  of  the 
upper  surface  of  the  water  at  the  points  where  the  fall  in  question  begins 
and  ends.  The  term  "  head  "  used  in  connection  with  water-wheels  is  the 
difference  in  height  from  the  surface  of  the  water  in  the  wheel-pit  to  the 
surface  in  the  pen-stock  when  the  wheel  is  running. 

If  Q  =  cubic  feet  of  water  discharged  per  second,  D  =  weight  of  a  cubic 
foot  of  water  =  62.36  Ibs.  at  60°  F.,  H  =  total  head  in  feet;  then 


DQH  =  gross  power  in  foot-pounds  per  second, 
and  DQH  -*-  550  —M'WQH  —  gross  horse-power. 


If  O'  ifl  taken  in  cubic  feet  per  minute,  H.  P.  = 


=  .00189$'  J7. 


A  water-wheel  or  motor  of  any  kind  cannot  utilize  the  whole  of  the  head 
H,  since  there  are  losses  of  head  at  both  the  entrance  to  and  the  exit  from 
the  wheel.  There  are  also  losses  of  energy  clue  to  friction  of  the  water  in 
its  passage  through  the  wheel.  1'he  ratio'  of  the  power  developed  by  the 
wheel  to  the  gross  power  of  the  fall  is  the  efficiency  of  the  wheel.  For  75* 

efficiency,  net  horse-power  =  .QQ142Q'H  =——. 


MILL-POWER.  589 

A  head  of  water  can  be  made  use  of  in  one  or  other  of  the  following  ways 
viz. : 

1st.  By  its  weight,  as  in  the  water- balance  and  overshot-wheel. 

2d.  By  its  pressure,  as  in  turbines  and  in  the  hydraulic  engine,  hydraulic 
press,  crane,  etc. 

3d.   By  its  impulse,  as  in  the  undershot- wheel,  and  in  the  Pelton  wheel. 

4th.  By  a  combination  of  the  above. 

Horse-power  of  a  Running  Stream.— The  gross  horse-power 
is,  H.  P.  =  QH  X  62.30  -*-  550  =  M34QH,  in  which  Q  is  the  discharge  in  cubic 
feet  per  second  actually  impinging  on  the  float  or  bucket,  and  H  =  theoret- 
ical head  due  to  the  velocity  of  the  stream  =  ^-  =  ^7-7 ,  in  which  v  is  the 

2g      64.4 

velocity  in  feet  per  second.  If  0'  be  taken  in  cubic  feet  per  minute, 
H.P.  =  .001890'fl: 

Thus,  if  the*floats  of  an  undershot -wheel  driven  by  a  current  alone  be  5 
feet  X  1  foot,  and  the  velocity  of  stream  =•  210  ft.  per  minute,  or  3^  ft.  per 
-sec.,  of  which  the  theoretical  head  is  .19  ft.,  Q  =  5  sq.  ft.  X  210  =  1050  cu.  ft. 
per  minute  ;  H-  .19ft ;  H.  P.  =  1050  X  .19  X.00189  =  .377  H.  P. 

The  wheels  would  realize  only  about  .4  of  this  power,  on  account  of  friction 
and  slip,  or  .151  H.P.,  or  about  .03  H.P.  per  square  foot  of  float,  which  is 
equivalent  to  83  sq.  ft.  of  float  per  H.  P. 

Current  Motors* — A  current  motor  could  only  utilize  the  whole  power 
of  a  running  stream  if  it  could  take  all  the  velocity  out  of  the  water,  so  that 
it  would  leave  the  floats  or  buckets  with  no  velocity  at  all;  or  in  other  words, 
it  would  require  the  backing  up  of  the  whole  volume  of  the  stream  until  the 
actual  head  was  equivalent  to  the  theoretical  head  due  to  the  velocity  of  the 
stream.  As  but  a  small  fraction  of  the  velocity  of  the  stream  can  be  taken 
up  by  a  current  motor,  its  efficiency  is  very  small.  Current  motors  may  be 
used  to  obtain  small  amounts  of  power  from  large  streams,  but  for  large 
powers  they  are  not  practicable. 
Horse-power  of  "Water  Flowing  in  a  Tube. —The  head  due  to 

v^  f 

the  velocity  is  — ;  the  head  due  to  the  pressure  is  -  ;  the  head  due  to  actual 

height  above  the  datum  plane  is  h  feet.  The  total  head  is  the  sum  of  these  = 
!L.  4.  h  .j.  Z.^  in  feet,  in  which  v  =  velocity  in  feet  per  second,  /  =  pressure 
in  Ibs.  per  sq.  ft.,  w  —  weight  of  1  cu.  ft.  of  water  =  62.36  Ibs.  If  p  =  pres- 
sure in  Ibs.  per  sq.  in.,  —  =  2.309p.  In  hydraulic  transmission  the  velocity 

and  the  height  above  datum  are  usually  small  compared  with  the  pressure- 
head.  The  work  or  energy  of  a  given  quantity  of  water  under  pressure  = 
its  volume  in  cubic  feet  X  its  pressure  in  Ibs.  per  sq.  ft.;  or  if  Q  =  quantity 
in  cubic  feet  per  second,  and  p  =  pressure  in  Ibs.  per  square  inch,  W  = 

144pQ,  and  the  H.  P.  =  ^^  =  36l8pQ. 

Maximum  Efficiency  of  a  Long  Conduit.— A.  L.  Adams  and 
K.  Gr.  Gemmel  (Euy'y  News,  May  4, 1893),  show  by  mathematical  analysis  that 
the  conditions  for  securing  the  maximum  amount  of  power  through  a  long 
conduit  of  fixed  diameter,  without  regard  to  the  economy  of  water,  is  that 
the  draught  from  the  pipe  should  be  such  that  the  frictional  loss  in  the  pipe 
will  be  equal  to  one  third  of  the  entire  static  head. 

mill-Power. — A  "mill-power"  is  a  unit  used  to  rate  a  water-power  for 
the  purpose  of  renting  it.  The  value  of  the  unit  is  different  in  different 
localities.  The  following  are  examples  (from  Emerson) : 

Holyoke,  Mass. — Each  mill-power  at  the  respective  fall  sis  declared  to  be 
the  right  during  16  hours  in  a  day  to  draw  38  cu.  ft.  of  Avater  per  second  at 
the  upper  fall  when  the  head  there  is  20  feet,  or  a  quantity  proportionate  to 
the  height  at  the  falls.  This  is  equal  to  86.2  horse-power  as  a  maximum. 

Lowell,  Mass. — The  right  to  draw  during  15  hours  in  the  day  so  much  water 
as  shall  give  a  power  equal  to  25  cu.  ft.  a  second  at  the  great  fall,  when  the 
tali  there  is  30  feet.  Equal  to  85  H.  P.  maximum. 

Lawrence,  Mass. — The  right  to  draw  during  16  hours  in  a  day  so  much 
water  as  shall  give  a  horse-power  equal  to  30  cu.  ft.  per  second  when  the 
head  is  25  feet.  Equal  to  85  H.  P.  maximum. 

Minneapolis,  Minn.— 30  cu.  ft.  of  water  per  second  with  head  of  22  feet. 
Equal  to  74.8  H.  P. 

Manchester^  N.  #.— -Divide  725  by  the  number  of  feet  of  fall  minus  1,  and 


590  WATER-POWER. 

the  quotient  will  be  the  number  of  cubic  feet  per  second  in  that  fall.  For  20 
feet  fall  this  equals  38.1  cu.  ft.,  equal  to  86.4  H.  P.  maximum. 

Cohoes,  N.  Y. — *'  Mill-power  "  equivalent  to  the  power  given  by  6  cu.  ft. 
per  second,  when  the  fall  is  20  feet.  Equal  to  13.6  H.  P.,  maximum. 

Passaic,  N.  J. — Mill-power:  The  right  to  draw  8^  cu.  ft.  of  water  per  sec., 
fail  of  22  feet,  equal  to  21. a  horse-power.  Maximum  rental  $700  per  year  for 
each  mill-power  =  $33.00  per  H.  P. 

The  horse-power  maximum  above  given  is  that  due  theoretically  to  the 
weight  of  water  and  the  height  of  the  fall,  assuming  the  water-wheel  to 
have  perfect  efficiency.  It  should  be  multiplied  by  the  efficiency  of  the 
wheel,  say  75#  for  good  turbines,  to  obtain  the  H.  P.  delivered  by  the  wheel. 

Value  of  a  Water-power.— In  estimating  the  value  of  a  water- 
power,  especially  where  such  value  is  used  as  testimony  for  a  plain  tiff  whose 
water-power  has  beeii  diminished  or  confiscated,  it  is  a  common  custom  for 
the  person  making  such  estimate  to  say  that  the  value  is  represented  by  a 
sum  of  money  which,  when  put  at  interest,  would  maintain  a  steam-plant 
of  the  same  power  in  the  same  place. 

Mr.  Charles  T.  Main  (Trans.  A.  S.  M.  E.  xiii.  140)  points  out  that  this  sys- 
tem of  estimating  is  erroneous;  that  the  value  of  a  power  depends  upon  a 
great  number  of  conditions,  such  as  location,  quantity  of  wrater,  fall  or  head, 
uniformity  of  flow,  conditions  which  fix  the  expense  of  dams,  canals,  founda- 
tions of  buildings,  freight  charges  for  fuel,  raw  materials  and  finished  prod- 
uct, etc.  He  gives  an  estimate  of  relative  cost  of  steam  and  water-power 
for  a  500  H.  P.  plant  from  which  the  following  is  condensed: 

The  amount  of  heat  required  per  H.  P.  varies  with  different  kinds  of  busi- 
ness, but  in  an  average  plain  cotton-mill,  the  steam  required  for  heating  and 
slashing  is  equivalent  to  about  25$  of  steam  exhausted  from  the  high- 
pressure  cylinder  of  a  compound  engine  of  the  power  required  to  run  that 
mill,  the  steam  to  be  taken  from  the  receiver. 

The  coal  consumption  per  H.  P.  per  hour  for  a  compound  engine  is  taken 
at  1%  Ibs.  per  hour,  when  no  steam  is  taken  from  the  receiver  for  heating 
purposes.  The  gross  consumption  when  25$  is  taken  from  the  receiver  is 
about  2.06  Ibs. 

75#  of  the  steam  is  used  as  in  a  compound  engine  at  1.75  Ibs.  =  1.31  Ibs. 
25#  high-pressure    *  3.00  Ibs.  =    .75" 

~2M  " 

The  running  expenses  per  H.  P.  per  year  are  as  follows  : 
2.06  Ibs.  coal  per  hour  =  21.115  Ibs.  for  10*4  hours  or  one  day  =  6503.42 

Ibs.  for  308  days,  which,  at  $3".00  per  long  ton  =  $8  71 

Attendance  of  boilers,  one  man  @  $2.00,  and  one  man  @,  $1.25  =  2  00 

"          "  engine,     ••      '•     "  $3.50.  2  16 

Oil,  waste,  and  supplies.  80 

The  cost  of  such  a  steam- plant  in  New  England  and  vicinity  of  500 
H.  P.  is  about  $65  per  H.  P.  Taking  the  fixed  expenses  as  4%  on 
engine,  5%  on  boilers,  and  2#  on  other  portions,  repairs  at  2#,  in- 
terest at  5$,  taxes  at  \\fa%  on  %  cost,  an  insurance  at  y$  on  exposed 
portion,  the  total  average  per  cent  is  about  12^,  or  $65  X  .12^  =  8  13 

Gross  cost  of  power  and  low-pressure  steam  per  H.  P.  $21  80 

Comparing  this  with  water-power,  Mr.  Main  says  :  "  At  Lawrence  the  cost 
of  dam  and  canals  was  about  $650,000,  or  $65  per  H.  P.  The  cost  per  H.  P. 
of  wheel-plant  from  canal  to  river  is  about  $45  per  H.  P.  of  plant,  or  about 
$65  per  H.  P.  used,  the  additional  $20  being  caused  by  making  the  plant 
large  enough  to  compensate  for  fluctuation  of  power  due  to  rise  and  fall  of 
river.  The  total  cost  per  H.  P.  of  developed  plant  is  then  about  $130  per  H.  P. 
Placing  the  depreciation  on  the  whole  plant  at  2$,  repairs  at  1£.  iuterest  at 
5#,  taxes  and  insurance  at  1%,  or  a  total  of  9$,  gives: 

Fixed  expenses  per  H.  P.  $130  X  .09  =  $11  70 
Running    "  (Estimated)       2  00 

$13  70 

"  To  this  has  to  be  added  the  amount  of  steam  required  for  heating  pur- 
poses, said  to  be  about  25#  of  the  total  amount  used,  but  in  winter  months 
the  consumption  is  at  least  37^j$.  It  is  therefore  necessary  to  have  a  boiler 
plant  of  about  37^  of  the  size  of  the  one  considered  with  the  steam-plant, 


TURBINE   WHEELS.  59l 

costing  about  $20  X  .375  =  $7.50  per  H.  P.  of  total  power  used.    The  ex- 
peuse  of  running  this  boiler-plant  is,  per  H.  P.  of  the  the  total  plant  per  year: 

Fixed  expenses  12^*  on  $7.50 $0.94 

Coal 3.26 

Labor 1 .23 


Total $5.43 

Making  a  total  cost  per  year  for  water-power  with  the  auxiliary  boiler  plant 
$13. 70  +  $5. 43  =  $19.13  which  deducted  from  $21.80  make  a  difference  in 
favor  of  water-power  of  $2.67,  or  for  10,000  H.  P.  a  saving  of  $26,700  per 
year. 

"  It  is  fair  to  say,"  says  Mr.  Main,"  that  the  value  of  this  constant  power  is 
a  sum  of  money  which  when  put  at  interest  will  produce  the  saving ;  or  if  §% 
is  a  fair  interest  to  receive  on  money  thus  invested  the  value  would  be 
$26.700--  .06  =  $445,000." 

Mr.  Main  makes  the  following  general  statements  as  to  the  value  of  a 
water-power  :  "  The  value  of  an  undeveloped  variable  power  is  usually  noth- 
ing if  its  variation  is  great,  unless  it  is  to  be  supplemented  by  a  steam-plant. 
It  is  of  value  then  only  when  the  cost  per  horse-power  for  the  double-plant 
is  less  than  the  cost  of  steam-power  under  the  same  conditions  as  mentioned 
for  a  permanent  power,  and  its  value  can  be  represented  in  the  same  man- 
ner as  the  value  of  a  permanent  power  has  been  represented. 

"  The  value  of  a  developed  power  is  as  follows:  If  the  power  can  be  run 
cheaper  than  steam,  the  value  is  that  of  the  power,  plus  the  cost  of  plant, 
less  depreciation.  If  it  cannot  be  run  as  cheaply  as  steam,  considering  its 
cost,  etc.,  the  value  of  the  power  itself  is  nothing,  but  the  value  of  the  plant 
is  such  as  could  be  paid  for  it  new,  which  would  bring  the  total  cost  of  run- 
ning down  to  the  cost  of  steam-power,  less  depreciation.1' 

Mr.  Samuel  Webber,  Iron  Age,  Feb.  and  March,  1893,  writes  a  series  of 
articles  showing  the  development  of  American  turbine  wheels,  and  inci- 
dentally criticises  the  statements  of  Mr.  Main  and  others  who  have  made 
comparisons  of  costs  of  steam  and  of  water-power  unfavorable  to  the  latter. 
Hesays  :  "They  have  based  their  calculations  on  the  cost  of  steam,  on  large 
compound  engines  of  1000  or  more  H.  P.  and  120  pounds  pressure  of  steam 
in  their  boilers,  and  by  careful  10-hour  trials  succeeded  in  figuring  down 
steam  to  a  cost  of  about  $x)0  per  H.  P.,  ignoring  the  well-known  fact  that  its 
average  cost  in  practical  use,  except  near  the  coal  mines,  is  from  $40  to  $50. 
In  many  instances  dams,  canals,  and  modern  turbines  can  be  all  completed 
for  a  cost  of  $100  per  H.  P. :  and  the  interest  on  that,  and  the  cost  of  attend- 
ance and  oil,  will  bring  water-power  up  to  but  about  $10  or  $12 per  annum; 
and  with  a  man  competent  to  attend  the  dynamo  in  attendance,  it  can 
probably  be  safely  estimated  at  not  over  $15  per  H.  P." 

TURBINE   WHEEL.S. 

Proportions  of  Turbines.— Prof.  De  Volson   Wood  discusses  at 
length  the  theory  of  turbines  in  his  paper  on  Hydraulic  Reaction  Motors, 
Trans.  A.  S.  M.  E.  xiv.  266.    His  principal  deductions  which  have  an  imme- 
diate bearing  upon  practice  are  condensed  in  the  following  : 
Notation. 

Q  =  volume  of  water  passing  through  the  wheel  per  second, 

HI  =  head  in  the  supply  chamber  above  the  entrance  to  the  buckets, 

/<2  =  head  in  the  tail-race  above  the  exit  from  the  buckets, 

z,  =  fall  in  passing  through  the  buckets. 

H  =  hv  -f  %i  —  /'a-  tne  effective  head, 

/Uj  =  coefficient  of  resistance  along  the  guides, 

/xa  =  coefficient  of  resistance  along  the  buckets, 

?*!  =  radius  of  the  initial  rim, 

?-2  =  radius  of  the  terminal  rim, 
v  —  velocity  of  the  water  issuing  from  supply  chamber, 

t?i  =  initial  velocity  of  the  water  in  the  bucket  in  reference  to  the  bucket, 

v?  =  terminal  velocity  in  the  bucket, 

co  =  angular  velocity  of  the  wheel, 

a  =  terminal  angle  between  the  guide  and  initial  rim  =  CAB,  Fig.  132, 

Vi  =  angle  between  the  initial  element  of  bucket  and  initial  rim  =:  EAD. 

Ya  =  GFI,  the  angle  between  the  terminal  rim  and  terminal  element  of 
the  bucket. 

a  =  ebt  Fig.  133  =  the  arc  subtending  one  gate  opening, 


592 


WATER-POWER. 


ox  =  the  arc  subtending  one  bucket  at  entrance.    (In  practice  at  is  larger 
than  a,) 

aa  =  gh,  the  arc  subtending  one  bucket  at  exit, 

K  =  fc/i  normal  section  of  passage,  it  being  assumed  that  the  passages 
and  buckets  are  very  narrow, 

fcj  =  bd,  initial  normal  section  of  bucket, 
fca  =  fltf,  terminal  normal  section, 
wr  j  =  velocity  of  initial  rim, 
*>r«  =  velocity  of  terminal  rim, 

6  =  HFI,  angle  between  the  terminal  rim  and  actual  direction  of  the 
water  at  exit, 

Y  =  depth  of  K,  y,  of  «,,  and  2/2  of  K^  then 

K  =  Fa  siu  a;  Kv  =  2/x  ax  sin  Vi ;  -^3  =  2/aaa  sin  >»• 


Fro.  132. 


FIG.  133. 


Three  simple  systems  are  recognized,  rT  <  recalled  outward  flow;  rt  >  r2, 
called  inward  flow;  rt  =  r«,  called  parallel  flow.  The  first  and  second  may 
be  combined  with  the  third,  making  a  mixed  system. 

Value  of  Y?  (the  quitting  angle).— The  efficiency  is  increased  as  ya  de* 
creases,  and  is  greatest  for  y2  ==  0.  Hence,  theoretically,  the  terminal  ele- 
ment of  the  bucket  should  be  tangent  to  the  quitting  rim  for  best  efficiency. 
This,  however,  for  the  discharge  of  a  finite  quantity  of  water,  would 
require  an  infinite  depth  of  bucket.  In  practice,  therefore,  this  angle  must 
have  a  finite  value.  The  larger  the  diameter  of  the  terminal  rim  the  smaller 
may  be  this  angle  for  a  given  depth  of  wheel  and  given  quantity  of  water 
discharged.  In  practice  y2  is  from  10°  to  20°. 

In  a  wheel  in  which  all  the  elements  except  ya  are  fixed,  the  velocity  of 
the  wheel  for  best  effect  must  increase  as  the  quitting  angle  of  the  bucket 
decreases. 

Values  of  a  -f-  V)  must  be  less  than  180°,  but  the  best  relation  cannot  be 
determined  by  analysis.  However,  since  the  water  should  be  deflected  from 
its  course  as  much  as  possible  from  its  entering  to  its  leaving  the  wheel,  the 
angle  a  for  this  reason  should  be  as  small  as  practicable. 

In  practice,  a  cannot  be  zero,  and  is  made  from  20°  to  30°. 

The  value  »*i  =  1.4ra  makes  the  width  of  the  crown  for  internal  flow  about 
the  same  as  for  rx  =ra  \/%  for  outward  flow,  being  approximately  0.3  of  the 
external  radius. 

Values  G//U-!  and  /u2. — The  f fictional  resistances  depend  upon  the  construc- 
tion of  the  wheel  as  to  smoothness  of  the  surfaces,  sharpness  of  the  angles, 


TURBINE   WHEELS.  503 

regularity  of  the  curved  parts,  and  also  upon  the  speed  it  is  run.  These 
values  cannot  be  definitely  assigned  beforehand,  but  Weisbach  gives  for 
good  conditions  /u^  =  jx,,  =  0.05  to  0.10. 

They  are  not  necessarily  equal,  arid  t*-i  may  be  from  0.05  to  0.075,  and  /ma 
from  0.0(5  to  0.10  or  even  larger. 

Values  of  y^  must  be  less  than  180°  —  a. 

To  be  on  the  safe  side,  yt  may  be  20  or  30  degrees  less  than  180°— 2a,  giving 

Yl  =  180°  -  2a  -  25    (say)    =  155  -  2a. 

Then  if  a  =  30°,  y±  =  95°.  Some  designers  make  y^  90°;  others  more,  and 
still  others  less,  than  that  amount.  Weisbach  suggests  that  it  be  less,  so 
that  the  bucket  will  be  shorter  and  friction  less.  This  reasoning  appears  to 
be  correct  for  the  inflow  wheel,  but  not  for  the  outflow  wheel.  In  the  Tre- 
mont  turbines,  described  in  the  Lowell  Hydraulic  Experiments,  this  angle 
is  90°,  the  angle  a  20°,  and  v2  10°,  which  proportions  insured  a  positive 
pressure  in  the  wheel.  Fourneyron  made  y^  —  90°,  and  a  from  30°  to  33°, 
which  values  made  the  initial  pressure  in  the  wheel  near  zero. 

Form  of  Bucket. — The  form  of  the  bucket  cannot  be  determined  analytic- 
ally. From  the  initial  and  terminal  directions  and  the  volume  of  the  water 
flowing  through  the  wheel,  the  area  of  the  normal  sections  may  be  found. 

The  normal  section  of  the  buckets  will  be  : 


The  depths  of  those  sections  will  be : 

K                         Jc 
Y  =  — : ,*    ?/!  = r ;    2/3  =  — 


"  a  sin  a'         ""  ax  sin  y^ "  oa  sin  -ya "  t 

The  changes  of  curvature  and  section  must  be  gradual,  and  the  general 
form  regular,  so  that  eddies  and  whirls  shall  not  be  formed.  For  the  same 
reason  the  wheel  must  be  run  with  the  correct  velocity  to  secure  the  best 
effect.  In  practice  the  buckets  are  made  of  two  or  three  arcs  of  circles, 
mutually  tangential. 

The  Value  of  w.— So  far  as  analysis  indicates,  the  wheel  may  run  at  any 
speed;  but  in  order  that  the  stream  shall  flow  smoothly  from  the  supply 
chamber  into  the  bucket,  the  velocity  V  should  be  properly  regulated. 

If  /xj  =  f*a  =  0.10,  r2  -s-  i\  =  1.40,  a  =  25°,  yl  =  90°,  y2  =  12°,  the  velocity  of 
the  initial  rim  for  outward  flow  will  be  for  maximum  efficiency  0.614  of  the 
velocity  due  to  the  head,  or  corj  =  0.614  ^2gH. 
The  velocity  due  to  the  head  would  be  V2yH  =  1.414  ^gH. 
For  an  inflow  wheel  for  the  case  in  which  r,2  =  2ra2,  and  the  other  dimen 
sioris  as  given  above,  eo?-j  =  0.682  ]/2gH. 

The  highest  efficiency  of  the  Trem'ont  turbine,  found  experimentally,  was 
0.79375,  and  the  corresponding  velocity,  0.62645  of  that  due  to  the  head,  and 
for  all  velocities  above  and  below  this  value  the  efficiency  was  less. 

In  the  Tremont  wheel  a  =  20°  instead  of  25°,  and  y?  =  10°  instead  of  12°. 
These  would  make  the  theoretical  efficiency  and  velocity  of  the  wheel  some- 
what, greater.  Experiment  showed  that  the  velocity  might  be  considerably 
larger  or  smaller  than  this  amount  without  much  diminution  of  the  efficiency. 
It  was  found  that  if  the  velocity  of  the  initial  (or  interior)  rim  was  not  less 
than  44#  nor  more  than  75#  of  that  due  to  the  fall,  the  efficiency  was  75#  or 
more.  This  wheel  was  allowed  to  run  freely  without  any  brake  except  its 
own  friction,  and  the  velocity  of  the  initial  rim  was  observed  to  be 
1.335  V2gH,  half  of  which  is  0.6675  \/2g~H,  which  is  not  far  from  the  velocity 
giving  maximum  effect;  that  is  tosay,when  the  gate  is  fully  raised  the  coeffi- 
cient of  effect  is  a  maximum  when  the  wheel  is  moving  with  about  half  its 
maximum  velocity. 

Number  of  Buckets,— Successful  wheels  have  been  made  in  which  the  dis- 
tance between  the  buckets  was  as  small  as  0.75  of  an  inch,  and  others  as 
much  as  2.75  inches.  Turbines  at  the  Centennial  Exposition  had  buckets 
from  4J4  inches  to  9  inches  from  centre  to  centre.  If  too  large  they  will  not 
work  properly.  Neither  should  they  be  too  deep.  Horizontal  partitions 
are  sometimes  introduced.  These  secure  more  efficient  working  in  case  the 
gates  are  only  partly  opened.  The  form  and  number  of  buckets  for  com- 
mercial purposes  are  chiefly  the  result  of  experience. 


594  WATER-POWER. 

Ratio  of  Radii.— Theory  does  not  limit  the  dimensions  of  the  wheel.  In 
practice, 

for  outward  flow,  r2  -+-  rt  is  from  1.25  to  1.50; 
for  inward  flow,  r^^-i\  is  from  0.60  to  0.80. 

It  appears  that  the  inflow-wheel  has  a  higher  efficiency  than  the  outward- 
flow  wheel.  The  inflow-wheel  also  runs  somewhat  slower  for  best  effect. 
The  centrifugal  force  in  the  outward-flow  wheel  tends  to  force  the  water 
outward  faster  than  it  would  otherwise  flow  ;  while  in  the  inward-flow  wheel 
it  has  the  contrary  effect,  acting  as  it  does  in  opposition  to  the  velocity  in 
the  buckets. 

It  also  appears  that  the  efficiency  of  the  outward-flow  wheel  increases 
slightly  as  the  width  of  the  crown  is  less  and  the  velocity  for  maximum 
efficiency  is  slower  ;  while  for  the  inflow-wheel  the  efficiency  slightly  in- 
creases for  increased  width  of  crown,  and  the  velocity  of  the  outer  rim  at  the 
same  time  also  increases. 

Efficiency.— The  exact  value  of  the  efficiency  for  a  particular  wheel  must 
be  found  by  experiment. 

It  seems  hardly  possible  for  the  effective  efficiency  to  equal,  much  less 
exceed,  86#,  and  all  claims  of  90  or  more  per  cent  for  these  motors  should  be 
discarded  as  improbable.  A  turbine  yielding  from  75$  to  80$  is  extremely 
good.  Experiments  with  higher  efficiencies  have  been  reported. 

The  celebrated  Tremont  turbine  gave  79)4$  without  the  "diffuser,"  which 
might  have  added  some  2#.  A  Jonval  turbine  (parallel  flow)  was  reported 
as  yielding  0.75  to  0.90,  hut  Morin  suggested  corrections  reducing  it  to  0.63  to 
0.71.  Weisbach  gives  the  results  of  many  experiments,  in  which  the  effi- 
ciency ranged  from  50#  to  84$.  Numerous  experiments  give  E=  0.60 'to  0.65. 
The  efficiency,  considering  only  the  energy  imparted  to  the  wheel,  will  ex- 
ceed by  several  per  cent  the  efficiency  of  the  wheel,  for  the  latter  will  in- 
clude the  friction  of  the  support  and  leakage  at  the  joint  between  the  sluice 
and  wheel,  which  are  not  included  in  the  former  ;  also  as  a  plant  the  resist- 
ances and  losses  in  the  supply-chamber  are  to  be  still  further  deducted. 

The  Crowns. — The  crowns  may  be  plane  annular  disks,  or  conical,  or 
curved.  If  the  partitions  forming  the  buckets  be  so  thin  that  they  may  be 
discarded,  the  law  of  radial  flow  will  be  determined  bv  the  form  of  the 
crowns.  If  the  crowns  be  plane,  the  radial  flow  (or  radial  component)  will 
diminish,  for  the  outward  flow-wheel,  as  the  distance  from  the  axis  increases 
—the  buckets  being  full — for  the  angular  space  will  be  greater. 

Prof.  Wood  deduces  from  the  formulae  in  his  paper  the  tables  on  page  595. 

It  appears  fronVthese  tables:  1.  That  the  terminal  angle,  a,  has  frequently 
been  made  too  large  in  practice  for  the  best  efficiency. 

2.  That  the  terminal  angle,  a,  of  the  guide  should  be  for  the  inflow  less 
than  10®  for  the  wheels  here  considered,  but  when  the  initial  angle  of  the 
bucket  is  90°,  and  the  terminal  angle  of  the  guide  is  5°  28',  the  gain  of  effi- 
ciency is  not  2%  greater  than  when  the  latter  is  25°. 

3.  That  the  initial  angle  of  the  bucket  should  exceed  90°  for  best  effect  for 
outflow- wheels. 

4.  That  with  the  initial  angle  between  60°  and  120°  for  best  effect  on  inflow 
wheels  the  efficiency  varies  scarcely  \%. 

5.  In  the  outflow-wheel,  column  (9)  shows  that  for  the  outflow  for  best 
effect  the  direction  of  the  quitting  water  in  reference  to  the  earth  should  be 
nearly  radial  (from  76°  to  97°),  but  for  the  inflow  wheel  the  water  is  thrown 
forward  in  quitting.    This  shows  that  the  velocity  of  the  rim  should  some- 
what exceed  the  relative  final  velocity  backward  in  the  bucket,  as  shown  in 
columns  (4)  and  (5). 

6.  In  these  tables  the  velocities  given  are  in  terms  of  )/2<://i,  and  the  co- 
efficients of  this  expression  will  be  the  part  of  the  head  whicli  would  produce 
that  velocity  if  the  water  issued  freely.    There  is  only  one  case,  column  (5), 
where  the  coefficient  exceeds  unity,  and  the  excess  is  so  small  it  maybe  dis- 
carded; and  it  may  be  said  that  in  a  properly  proportioned  turbine  with  the 
conditions  here  given  none  of  the  velocities  will  equal  that  due  to  the  head 
in  the  supply-chamber  when  running  at  best  effect. 

7.  The  inflow  turbine  presents  the  best  conditions  for  construction  for 
producing  a  given  effect,  the  only  apparent  disadvantage  being  an  increased 
first  cost  due  to  an  increased  depth,  or  an  increased  diameter  for  producing 
a  given  amount  of  work.     The  larger  efficiency  should,  however,  more  than 
iieut;  alize  the  increased  first  cost. 


TUKBIKE   WHEELS. 


595 


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596 


WATER-fOWER. 


Tests  of  Turbines.— Emerson  says  that  in  testing  turbines  it  is  a  rnre 
thing  to  find  two  of  the  same  size  which  can  be  made  to  do  their  best  at  the 
same  speed.  The  best  speed  of  one  of  the  leading  wheels  is  invariably  wide 
from  the  tabled  rate.  It,  was  found  that  a  54-in.  Leffel  wheel  under  12  ft. 
head  gave  much  better  results  at  78  revolutions  per  minute  than  at  90. 

Overshot  wheels  have  been  known  to  give  75$  efficiency,  but  the  average 
performance  is  not  over  60$. 

A  fair  average  for  a  good  turbine  wheel  may  be  taken  at  75$.  In  tests  of  18 
wheels  made  at  the  Philadelphia  Water-works  in  1859  and  1860,  one  wheel 
gave  less  than  50$  efficiency,  two  between  50$  and  60$,  six  between  6  %  and 
70$,  seven  between  71$  and  77$,  two  82$,  and  one  87.77$.  (Emerson.) 

Tests  of  Turbine  Wheels  at  the  Centennial  Exhibition. 
1876.  (From  a  paper  by  R.  H.  Thurston  on  The  Systematic  Testing  of 
Turbine  Wheels  in  the  United  States,  Trans.  A.  S.  M.  E.,  viii.  359.)— In  1876 
the  judges  at  the  International  Exhibition  conducted  a  series  of  trials  of 
turbines.  Many  of  the  wheels  offered  for  tests  were  found  to  be  more  or 
less  defective  in  fitting  and  workmanship.  The  following  is  a  statement  of 
the  results  of  all  turbines  entered  which  gave  an  efficiency  of  over  75$. 
Seven  other  wheels  were  tested,  giving  results  between  65$  and  75$. 


a  i 

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Maker's  Name,  or  Name  the 

0 

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Wheel  is  Known  By. 

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£ 

PH 

£ 

PH 

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^ 

Risdon  

87.68 

86.20 

82.41 

75.35 

83.79 

7'0.79 

Geyelin  (single)        

83.30 

Thos.  Tait  

82.13 

70.40 

66.35 

55.00 

Goldie  &  McCullough  
Rodney  Hunt  Mach.  Co  

81.21 
78.70 

71.66 

71.01 

55.90 
68.60 

51.03 

Tyler  Wheel  ... 

79.59 

81.24 

79.92 

67.23 

69.59 

Geyelin  (duplex)  

77.57 

Knowlton  &  Dolan  

77.43 

74.25 

62.75 

E  T  Cope  &  Sons 

76  94 

6992 

Barber  &  Harris  

76.16 

73.33 

70.87 

71.74 

York  Manufacturing  Co.  .  .  
W.  F.  Mosser&Co...,  

75.70 
75.15 

74.89 

67.08 
71.90 

67.57 
70.52 

62.06 

66.04 

The  limits  of  error  of  the  tests,  says  Prof.  Thurston,  were  very  uncertain ; 
they  are  undoubtedly  considerable  as  compared  with  the  later  work  done  in 
the  permanent  flume  at  Holyoke — possibly  as  much  as  4$  or  5$. 

Experiments  with  "draught-tubes,11  or  "suction-tubes,11  which  were 
actually  "  diffusers"  in  their  effect,  so  far  as  Prof.  Thurston  has  analyzed 
them,  indicate  the  loss  by  friction  which  should  be  anticipated  in  such 
cases,  this  loss  decreasing  as  the  tube  increased  in  size,  and  increasing  as 
its  diameter  approached  that  of  the  wheel — the  minimum  diameter  tried. 
It  was  sometimes  found  very  difficult  to  free  the  tube  from  air  completelv, 
and  next  to  impossible,  during  the  interval,  to  control  the  speed  with  the 
brake.  Several  trials  were  often  necessary  before  the  power  due  to  the  full 
head  could  be  obtained.  The  loss  of  power  by  gearing  and  by  belting  was 
variable  with  the  proportions  and  arrangement  of  the  gears  and  pulleys, 
length  of  belt,  etc.,  but  averaged  not  far  from  30$  for  a  single  pair  of  bevel- 
gears,  uncut  and  dry,  but  smooth  for  such  gearing,  and  but  10$  for  the  same 
gears,  well  lubricated,  after  they  had  been  a  short  time  in  operation.  The 
amount  of  power  transmitted  was,  however,  small,  and  these  figures  are 
probably  much  higher  than  those  representing  ordinary  practice.  Intro- 
ducing a  second  pair— spur-gears— the  best  figures  were  but  little  changed, 
although  the  difference  between  (he  case  in  which  the  larger  gear  was  the 
driver,  and  the  case  in  wVoh  the  small  wheel  was  the  driver,  wns  perceiv- 
able, and  was  in  favor  of  the  former  arrangement.  A  single  straight  belt 
gave  a  loss  of  but  2$  or  3$,  a  crossed  belt  6$  to  8$,  when  transmitting  14 


TUKBLNE    WHEELS.  597 

-,  / 

horse-power  with  maximum  tightness  and  transmitting  power.   A  "  quarter 
turn  ""  wasted  about  10$  as  a  maximum,  and  a  "quarter  twist "  about  5#. 

Dimensions  of  Turbines.— For  dimensions,  power,  etc.,  of  stand- 
ard makes  of  turbines  consult  the  catalogues  of  different  manufacturers. 
The  wheels  of  different  makers  vary  greatly  in  their  proportions  for  any 
given  capacity. 

The  Pelton  Water- wheel.— Mr.  Ross  E.  Browne  (Eng'g  News,  Feb. 
20,  1892)  thus  outlines  the  principles  upon  which  this  water-wheel  is 
constructed : 

The  function  of  a  water-wheel,  operated  by  a  jet  of  water  escaping  from 
a  nozzle,  is  to  convert  the  energy  of  the  jet,  due  to  its  velocity,  into  useful 
work  In  order  to  utilize  this  energy  fully  the  wheel-bucket,  after  catching 
the  jet,  must  bring  it  to  rest  before  discharging  it,  without  inducing  turbu- 
lence or  agitation  of  the  particles. 

This  cannot  be  fully  effected,  and  unavoidable  difficulties  necessitate  the 
loss  of  a  portion  of  the  energy.  The  principal  losses  occur  as  follows: 
First,  in  sharp  or  angular  diversion  of  the  jet  in  entering,  or  in  its  course 
through  the  bucket,  causing  impact,  or  the  conversion  of  a  portion  of  the 
energy  into  heat  instead  of  useful  work.  Second,  in  the  so-called  frictional 
resistance  offered  to  the  motion  of  the  water  by  the  wetted  surfaces  of  the 
buckets,  causing  also  the  conversion  of  a  portion  of  the  energy  into  heat 
instead  of  useful  work,  Third,  in  the  velocity  of  the  water,  as  it  leaves  the 
bucket,  representing  energy  which  has  not  been  converted  into  work. 

Hence,  in  seeking  a  high  efficiency:  1.  The  bucket-surface  at  the  entrance 
should  be  approximately  ->arallel  to  the  relative  course  of  the  jet,  and 
the  bucket  should  be  curved  in  such 
a  manner  as  to  avoid  sharp  angular  de- 
flection of  the  stream.  If,  for  example, 
a  jet  strikes  >  surface  .-^  an  angle  and 
is  sharply  deflected,  a  portion  of  the 
water  is  backed,  the  smoothness  of  the 
stream  is  disturbed,  and  there  results 
considerable  loss  by  impact  and  other- 
wise. The  entrance  and  deflection  in 
thePelton  bucket  are  such  as  to  avoid  FIG.  134.  FIG.  135. 

these  losses  in  the  main.     (See  Fig.  136.) 

2.  The  number  of  buckets  should  be  small,  and  the  path  of  the  jet  in  the 
bucket  short;  in  other  words,  the  total  wetted  surface  should  be  small,  as 
the  loss  by  friction  will  be  proportional  to  this. 

3.  The  discharge  end  of  the  bucket  should  be  as  nearly  tangential  to  the 
wheel  periphery  as  compatible  with  the  clearance  of  the  bucket  which 
follows;  and  great  differences  of  velocity  in  the  parts  of  the  escaping  water 
should  be  avoided.    In  order  to  bring  the  water  to  rest  at  the  discharge  end 
of  the  bucket,  it  is  shown,  mathematically,  that  the  velocity  of  the  bucket 
should  be  one  half  the  velocity  of  the  jet. 

A  bucket,  such  as  shown  in  Kig.  135,  will  cause  the  heaping  of  more  or  less 
dead  or  turbulent  water  at  the  point  indicated  by  dark 
shading.  Tin's  dead  water  is  subsequently  thrown  from 
the  wheel  with  considerable  velocity,  and  represents  a 
large  loss  of  energy.  The  introduction  of  the  wedge  in 
the  Pel  ton  bucket  (see  Fig.  134)  is  an  efficient  means  of 
avoiding  this  loss. 

A  wheel  of  the  form  of  the  Pelton  conforms  closely  in 
construction  to  each  of  these  requirements. 

In  a  test  made  by  the  proprietors  of  the  Idaho  mine, 
Frr-   13fi  near  Grass  Valley,  Cal.,  the  dimensions  and  results  were 

as  follow  :  Main  supply-pipe,  22  in.  diameter,  6900  ft. 
long,  with  a  head  of  3S6^  feet  above  centre  of  nozzle.  The  loss  by  friction 
in  the  pipe  was  1.8  ft.,  reducing  the  effective  head  to  384.7  ft.  The  Pelton 
wheel  used  in  the  t  st  was  6  ft.  in  diameter  and  the  nozzle  was  1.89  in. 
diameter.  The  work  done  was  measured  by  a  Prony  brake,  and  the  mean 
of  13  tests  showed  a  useful  effect  of  87. 3#. 

The  Pelton  wheel  is  also  used  as  a  motor  for  small  powers.  A  test  by 
M.  E.  Cooley  of  a  12-inch  wheel, with  a  %-inch  nozzle,  under  100  Ibs.  pressure, 
gave  1.9  horse-power.  The  theoretical  discharge  was  .0935  cubic  feet  per 
second,  and  the  theoretical  horse-power  2  45;  the  efficiency  being  80  per 
cent.  Two  other  styles  of  water-motor  tested  at  the  same  time  each  gave 
efficiencies  of  55  per  cent „ 


598 


WATER-POWER. 


Pel  to  ii  Water-wheel  Tables.  (Abridged.) 

The  smaller  figures  under  those  denoting  the  various  heads  give   the 

spouting  velocity  of  the  water  in  feet  per  minute.  The  cubic-feet  measure- 
ment is  also  based  on  the  flow  per  minute. 


Head 
in  ft. 

Size  of 
Wheels. 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

6 
in. 

No.l 

.05 
1.67 
684 

12 
in. 
No.  2 

.12 
3.91 
342 

18 
in. 
No.  3 

.20 
6.62 

228 

18 
in. 

No.  4 

24 
in. 
No.  5 

3 

ft. 

4 

ft. 

5 
ft. 

6 
ft. 

6.00 

187.72 
57 

20 

2151.97 

.37 

11.72 
228 

.66 
20.83 
171 

1    5'! 

46.93 
114 

2.64 
83.32 

85 

4.18 

130.3M 
70 

30 

2635.6-2 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.10 
2.05 

837 

.23 
4.79 

418 

.38 
8.11 
279 

.69 
14.36 
279 

1.22 
25.51 
209 

2.76 
57.44 
139 

4.88 
102.04 
104 

7.69 
159.66 
83 

11.04 
229.76 
69 

40 

304?.  39 

Horse-power. 
Cubic  feet  
Revolutions.. 

.15 
2.37 
969 

.35 
5.53 

484 

.59 
9.37 
323 

1.06 
16.59 
323 

1.89 
29.46 
242 

4.24 
66.36 
161 

7.58 
107.84 
121 

11.85 
184.36 
96 

16.96 
265.44 

80 

23  93 
296.70 
90 

50 

3402.61 

Horse-power. 
Cubic  feet.... 
Revolutions.. 

.21 
2.64 
1083 

.49 
6.18 
541 

.84 
10.47 
361 

1.49 

18.54 
361 

2.65 
32.93 

270 

5.98 
74.17 
180 

10.60 
131.72 
135 

16.63 
206.13 

108 

60 

3727  37 

Horse-power. 
Cubic  feet.  .  .  . 
Revolutions.. 

Horse-  power. 
Cubic  feet.  .  .  . 
Revolutions.. 

.28 
2.90 

1185 

.65 
6.77 
592 

.82 
7.3! 
640 

1.00 

7.82 
684 

1.10 
11.47 
395 

1.96 
20.31 
395 

3.48 
36.08 
296 

7.84 
81.25 
197 

13.94 
144.32 

148 

21.77 
225.80 

118 

31.36 
325.00 

98 

70 

4026.00 

~To~ 

4303.99 

.35 
3.13 

1281 

.43 
3.35 
1368 

1.39 
12.39 
427 

1.70 
13  25 
456 

2  47 
2l!  94 
427 

4.39 
38.97 
320 

9.88 
87.76 
213 

17.58 
155.88 
160 

27.51 
243.89 
130 

39.52 
351.04 
106 

48.16 
375.3!) 
114 

Horse-power. 
Cubic  feet  
Revolutions.. 

3.01 
23.46 
456 

5.36 
41.66 
342 

12.04 
93  84 
228 

21.44 
166.64 
171 

33.54 
260.73 
137 

90 

4565.04 

Horse-power. 
Cubic  feet  
Revolutions.. 

.51 
3.55 
1452 

1.20 
8.29 
726 

2.03 

14.05 
484 

3  60 

24.88 
484 

6.39 
44.19 
363 

14.40 
99.52 
242 

25.59 
176.75 

181 

40.04 
276.55 
145 

57.60 
398.08 
121 

100 

4812.00 

Horse-power. 
Cubic  feet.  ... 
Revolutions.. 

Horse-power. 
Cubic  feet.  .  .  . 
Revolutions.. 

.60 

3.74 
1530 

.79 
4.10 
1677 

1.40 
8.74 
765 

1.84 
9.57 

838 

2.32 

14.81 
510 

4.21 
26.  •>•„' 
510 

7.49 
46.58 
382 

16.84 
104.  8S 
255 

29.93 
186.32 
191 

46.85 
291.51 
152 

67.36 
419.52 
127 

120 

5271.30 

3.12 
16.21 
559 

5.54 

28.72 
559 

9.85 
51.02 
419 

22.18 
114.91 
279 

39.41 
204.10 
209 

61.66 
319.33 
167 

88.75 
459.64 
139 

140 

5693.65 

Horse-power. 
Cubic  feet.  ... 
Revolutions.. 

.99 
4.43 
1812 

132 
4.73 

1938 

2.33 
10.34 
906 

2.84 
11.05 
969 

3.94 
17.53 
604 

6.99 
31.03 
604 

12.41 
55.11 
453 

27.96 
124.12 
302 

49.64 
220.44 
226 

344^92 

181 

111.85 
496.48 
151 

160 

6036  74 

Horse-power. 
Cubic  feet  
Revolutions.  . 

4.82 
18.74 
646 

8.54 
33.17 
646 

15.17 
58.92 
484 

34.16 
132.08 
323 

60.68 
235.68 
242 

94.94 
368.73 
193 

136.65 
530.75 
161 

180 

6455.97 

Horse-power. 
Cubic  feet..  . 
Revolutions.  . 

1.45 
5.02 
2049 

3.39 
11.72 
1024 

3.97 

12.36 
1080 

5.75 
19.87 
683 

10.19 
35.18 
683 

18.10 
62.49 
513 

40.77 
140.74 
342 

7-2.41 
249.97 
256 

113.30 
391.10 
206 

163.08 
562.96 
171 

200 

6805.17 

Horse-power. 
Cubic  feet.  .  . 
Revolutions.  . 

1.70 
5.29 

2160 

6.74 
20.94 
720 

11.93 
37.08 
720 

21.20 
65.87 
540 

47.75 
148.35 
360 

84.81 
263.49 
270 

132.70 
412  25 
216 

191.00 
593.40 

180 

250 

7608.44 

Horse-power. 
Cubic  feet.  .  .  . 
Revolutions.  . 

2.38 
5.92 

2418 

5.56 
13.82 
1209 

9.42 
23.42 

806 

16.68 
41.46 
806 

29.  C3 
73.64 
605 

66.74 
165.86 
403 

118.54 
•294.59 
302 

185.47 
460.91 
241 

266.96 
663.45 

202 

TOWER   OF    OCEAN   WAVES.  599 

Pelton  Water-wlieel  Tables.— Continued. 


Head 
in  ft. 

Size  of 
Wheels. 

6 
in. 
No.l 

3.13 
6.48 
2652 

12 
in. 

No.  2 

18 
in. 
No.  3 

18 
in. 
No.  ± 

24 
in. 
No.  5 

3 
ft. 

4 
ft. 

5 
ft. 

6 
ft. 

350.94 
726.76 
221 

300 

8334.62 

Sorse-pow'r 
Cubic  feet..  . 
Revolutions 

7.31 
15.13 
1326 

12.38 
25.66 

884 

21.93 
45.42 

884 

38.95: 
80.67 
663 

87.73 
181.69 
442 

155.83 
322.71 
331 

243.82 
504.91 
265 

350 

9002.43 
400 

9624.00 

Horse-pow'r 
Dubic  feet..  . 
Revolutions 

3.94 
7.00 
2865 

9.21 
16.35 
1432 

15.61 
27.71 
955 

27.64 
49.06 
955 

49.09 
87.14 
716 

110.56 
196.25 

477 

196.38 
348.57 
358 

307.25 
545.36 
285 

442.27 
785.00 
238 

Horse-pow'r 
Cubic  feet... 
Revolutions 

4.82 
7.49 
3063 

11.25 
17.48 
1531 

19.0 
29  63 
1021 

33.77 
52.45 
1021 

59.98 
93.16 
765 

135.08 
209.80 
510 

239.94 
372.64 
382 

375.40 
583.02 
306 

540.35 
839.20 
255 

450 

10-207.79 
500 
10759.96 

Horse-pow'r 
Oubic  feet... 
Revolutions 

5.75 
7.94 
3249 

13.43 

18.54 
1624 

15.73 
19.54 
1713 

22.76 
31.42 
1083 

40.29 
55.63 
1083 

71.57 
98.81 
812 

161.19 
222.52 
541 

286.31 
395.24 
406 

447.95 
618.38 
324 

644.78 
890.11 
270 

Horse-pow'r 
Cubic  feet... 
Revolutions 

6.74 
8.37 
3426 

26.66 
33.12 
1142 

47.20 
58.64 
1142 

83.83 
104.15 
856 

188.80 
234.56 
571 

335.34 
416.62 

428 

524.66 
651.83 
342 

755.20 
938.25 
285 

600 

11786.94 

Horse-pow'r 
Cubic  feet   . 

62.04 
64.24 
1251 

110.19 
114.09 
938 

248.16 
256.95 
625 

440.77 
456.38 
469 

689.63 
714.05 
375 

992.65 
1027.80 
315? 

Revolutions 

— 

_ni: 

;_^: 

650 

12268.24 

Horse-pow'r 

69.95 
66.86 
1302 

124.25 
118.75 
976 

279.82 
267.44 
651 

497.01 
475.02 

488 

777.62 
743.21 
390 

1119.29 
1069.77 
325 

Revolutions 

700 

12731.34 

Horse-pow'r 
Cubic  feet 

78.18 
69.38 
1351 

138.86 
123.23 
1013 

312.73 
277.54 
675 

555.46 
492.95 
506 

869.06 
771.26 
405 

1250.92 
1110.16 
337 

Revolutions 

111! 

750 

13178.19 
800 
13610.40 

Horse-pow'r 
Cubic  feet  .. 

86.70 

71.82 
1399 

154.00 
127.56 
1049 

346.83 

287.28 
699 

616.03 
510.25 
524 

963.82 
798.33 
419 

1387.34 
1149.13 
349 

Revolutions 

—  : 

_i^: 

Horse-pow'r 
Cubic  feet 

95  52 

169.66 
131.74 
1083 

382.09 
296.70 
722 

678.66 
526.99 
542 

1061.81 
824.51 
433 

1528.36 
1186.81 
361 

74.17 
1444 

Revolutions 

900 

14436.00 

Horse-pow'r 
Cubic  feet... 

113.98 
78.67 
1532 

202.45 
139.74 
1149 

455.94 
314.70 
766 

809.82 
558.96 
574 

1267.02 
874.53 
459 

1823.76 
1258.81 
383 

Revolutions 

1000 

15216.89 

Horse-pow'r 
Cubic  feet.  . 

133.50 
82.93 
1615 

237.12 
147.30 
1210 

534.01 
331.72 

807 

948.48 
589.19 
605 

1483.97 
921.83 

484 

2136.04 
1326.91 
1        403 

Revolutions 

.... 

THE  POWER   OF   OCEAN   WAVES. 

Albert  W.  Stahl,  U.  S.  N.  (Trans.  A.  S.  M.  E.,  xiii.  438),  gives  the  following 
formulae  and  table,  based  upon  a  theoretical  discussion  of  wave  motion: 

The  total  energy  of  one  whole  wave-length  of  a  wove  H  feet  high,  L  feet 
long,  and  one  foot  in  breadth,  the  length  being  the  distance  between  succes- 
sive crests,  and  the  height  the  vertical  distance  between  the  crest  and  the 

trough,  is  E  =  8£H2  (l  -  4.935  ^)  foot-pounds. 

The  time  required  for  each  wave  to  travel  through  a  distance  equal  to  its 
own  length  is  P  —  A/  — --  seconds,  and  the  number  of  waves  passing  any 


600 


WATER-POWER. 


given  point  in  one  minute  is  N  =  --  =  QQA/^—L.    Hence  the  total  energy 

of  an  indefinite  series  of  such  waves,  expressed  in  horse-power  per  foot  of 
breadth,  is 


EXN 

33000 


=  .0329H2I/1  -4.935^)- 


By  substituting  various  values  for  H  -*-  _L,  within  the  limits  of  such  values 
actually  occurring  in  nature,  we  obtain  the  following  table  of 

TOTAL  ENERGY  OF  DEEP-SEA  WAVES  IN  TERMS  OF  HORSE-POWER  PER  FOOT 
OF  BREADTH. 


Ratio  of 
Length  of 
Waves  to 
Height  of 
Waves. 

Length  of  Waves  in  Feet. 

25 

50 

75 

.64 
1.00 
1.77 
3.96 
6.97 
15.24 
51  48 

100 

150 

200 

[300 

400 

50 
40 
30 
20 
15 
10 
5 

.04 
.06 
.12 
.25 
.42 
.98 
3.30 

.23 
.36 
.64 
1.44 
2.83 
5.53 
18.68 

1.31 
2.05 
3.64 
8.13 
14.31 
31.29 
105.68 

3.62 
5.65 
10.02 
21  79 
39.43 
86.22 
291.20 

7.43 
11.59 
20.57 
45.98 
80.94 
177.00 
597.78 

20.46 
31.95 
56.70 
12C.70 
223.06 
487.75 
1647.01 

42.01 
65.58 
116.38 
260.08 
457.89 
1001.25 
3381.60 

The  figures  are  correct  for  trochoidal  deep-sea  waves  only,  but  they  give 
a  close  approximation  for  any  nearly  regular  series  of  waves  in  deep  water 
and  a  fair  approximation  for  waves  in  shallow  water. 

The  question  of  the  practical  utilization  of  the  energy  which  exists  in 
ocean  waves  divides  itself  into  several  parts  : 

*•  1.  The  various  motions  of  the  water  which  may  be  utilized  for  power 
purposes. 

2.  The  wave  motor  proper.  That  is,  the  portion  of  the  apparatus  in  direct 
contact  with  the  water,  and  receiving  and  transmitting  the  energy  thereof  ; 
together  with  the  mechanism  for  transmitting  this  energy  to  the  machinery 
for  utilizing  the  same. 

C.  Regulating  devices,  for  obtaining  a  uniform  motion  from  the  irregular 
and  more  or  less  spasmodic  action  of  the  waves,  as  well  as  for  adjusting  the 
apparatus  to  the  state  of  the  tide  and  condition  of  the  sea. 

4.  Storage  arrangements  for  insuring  a  continuous  and  uniform  output  of 
power  during  a  calm,  or  when  the  waves  are  comparatively  small. 

The  motions  that  may  be  utilized  for  power  purposes  are  the  following: 
1.  Vertical  rise  and  fall  of  particles  at  and  near  the  surface.  2.  Horizontal 
to-and-fro  motion  of  particles  at  and  near  the  surface.  3.  Varying  slope  of 
surface  of  wave.  4.  Impetus  of  waves  rolling  up  the  beach  in  the  form  of 
breakers.  5.  Motion  of  distorted  verticals.  All  of  these  motions,  except  the 
last  one  mentioned,  have  at  various  times  been  proposed  to  be  utilized  for 
power  purposes;  and  the  last  is  proposed  to  be  used  in  apparatus  described 
by  Mr.  Stahl. 

The  motion  of  distorted  verticals  is  thus  defined:  A  set  of  particles,  origi- 
nally in  the  same  vertical  straight  line  when  the  water  is  at  rest,  does  not 
remain  in  a  vertical  line  during  the  passage  of  the  wave;  so  that  the  line 
connecting  a  set  of  such  particles,  while  vertical  and  straight  in  still  water, 
becomes  distorted,  as  well  as  displaced,  during  the  passage  of  the  wave,  its 
upper  portion  moving  farther  and  more  rapidly  than  its  lower  portion. 

Mr.  StahFs  paper  contains  illustrations  of  several  wave-motors  designed 
upon  various  principles.  His  conclusions  as  to  their  practicability  is  as  fol- 
lows: "  Possibly  none  of  the  methods  described  in  this  paper  may  ever  prove 
commercially  successful;  indeed  the  problem  may  not  be  susceptible  of  a 
financially  successful  solution.  My  own  investigations,  however,  so  far  as  I 
have  yet  been  able  to  carry  them,  incline  me  to  the  belief  that  wave-power 
can  and  will  be  utilized  on  a  paying  basis.'1 

Continuous  Utilization  of  Tidal  Power.  (P.  Decceur,  Proc. 
Inst.  C.  E.  1890.)— In  connection  with  the  training-walls  to  be  constructed  in 


PUMPS   AND   PUMPING   ENGINES.  GOl 

the  estuary  of  the  Seine,  it  is  proposed  to  construct  large  basins,  by  means 
of  which  the  power  available  from  the  rise  and  fall  of  the  tide  could,  be  util- 
ized. The  method  proposed  is  to  have  two  basins  separated  by  a  bank  rising 
above  high  water,  within  which  turbines  would  be  placed.  The  upper  basin 
would  be  in  communication  with  the  sea  during  the  higher  one  third  of  the 
tidal  range,  rising,  and  the  lower  basin  during  the  lower  one  third  of  the 
tidal  range,  falling.  If  H  be  the  range  in  feet,  the  level  in  the  upper 
basin  would  never  fall  below  %//  measured  from  low  water,  and  the 
level  in  the  lower  basin  would  never  rise  above  %H.  The  available  head 
varies  between  0.53H  and  0.80H,  the  mean  value  being  %H.  If  S  square  feet 
be  the  area  of  the  lower  basin,  and  the  above  conditions  are  fulfilled,  a 
quantity  1/3SH  cu.  ft.  of  water  is  delivered  through  the  turbines  in  the  space 
of  9J4  hours.  The  mean  flow  is,  therefore,  SH  H-  99,900  cu.  ft.  per  sec  ,  and, 
the  mean  fall  being  %H,  the  available  gross  horse-power  is  about  l/SON'Jf8, 
where  <S"  is  measured  in  acres.  This  might  be  increased  by  about  one  third 
if  a  variation  of  level  in  the  basins  amounting  to  y^H  were  permitted.  But 
to  reach  this  end  the  number  of  turbines  would  have  to  be  doubled,  the 
mean  head  being  reduced  to  y%H,  and  it  would  be  more  difficult  to  transmit 
a  constant  power  from  the  turbines.  The  turbine  proposed  is  of  an  improved 
model  designed  to  utilize  a  large  flow  with  a  moderate  diameter.  One  has 
been  designed  to  produce  300  horse-power,  with  a  minimum  head  of  5  ft.  3 
in.  at  a  speed  of  15  revolutions  per  minute,  the  vanes  having  13  ft.  internal 
diameter.  The  speed  would  be  maintained  constant  by  regulating  sluices. 


PUMPS  AND  PUMPING  ENGINES. 

Theoretical    Capacity  of  a  Pump.— Let  Q'  =  cu.  ft.  per  min.; 

G'  =  Amer.  gals,   per  min.  =  7.4805$';  d  =  diam.  of  pump  in  inches;  I  = 
stroke  in  inches;  N  =  number  of  single  strokes  per  min. 

Capacity  in  cu.  ft.  per  min.  =  $'  =  ^  -  ~~  .  4-  =  ,0004545AW; 

Capacity  in  gals,  per  min.  G'  =  ^  .    — -' =  .0084JVd2Z; 

Capacity  in  gals,  per  hour =  *2Q4NdH. 

Diameter  required  for  a  )  ^  _  AR  Q  .  /  Q*        iff  1K  t  /  G' 
given  capacity  per  min.  \a      4b-9j/  ^  |/ jvT* 

If  v  =  piston  speed  in  feet  per  min.,  d  =  13.54^/  Q    —  4.95 A /         . 

If  the  piston  speed  is  100  feet  per  min.: 

Nl  =  1200,  and  d  =  1.354  4/$~'  =  .495  V~G'-,     G'  =  4.08d2  per  min. 

The  actual  capacity  will  be  from  60#  to  95$  of  the  theoretical,  according  to 
the  tightness  of  the  piston,  valves,  suction-pipe,  etc. 

Theoretical  Horse-power  required  to  raise  Water  to  a 
given  Height.— Horse-power  = 

Volume  incu.  ft.  per  min.  X  pressure  per  sq.  ft.  _  Weight  x  height  of  lift 
33,000  .  337)00 

Q'  =  cu.  ft.  per  min.;  G'  —  gals,  per  min.;  W  —  wt.  in  Ibs. ;  P  =  pressure 
in  Ibs.  per  sq.  ft.;  p  =  pressure  in  Ibs.  per  sq.  in.;  H  =.  height  of  lift  in  ft.; 
W=  62.36$',  P=  U4p,p  =  .433J?,  H  =  5>.309p,  6?'  =  7.4805$'. 

HP  =  ®'p  -  ®'H  x  144  x  -4;j3  -  9-H-  -  G'H  • 

~  33,000  f  33,000  ~  5S9.2  ~  3958.7' 

WH         $'  x  62.36  X  2.309p         Q'p          G'p 


HP  = 


-  =  = 

33,000  33,000  ;     229.^    .  1714.5' 


For  the  actual  horse-power  required  an  allowance  must  be  made  for  the 
friction,  slips,  etc.,  of  engine,  pump,  valves,  and  passages. 


602 


WATER-POWER. 


Depth  of  Suction. -Theoretically  a  perfect  pump  will  draw  water 
from  a  height  of  nearly  34  feet,  or  the  height  corresponding  to  a  perfect 
vacuum  (14.7  Ibs.  X  2.309  —  v3.95  feet);  but  since  a  perfect  vacuum  cannot  be 
obtained,  on  account  of  valve-leakage,  air  contained  in  the  water,  and  the 
vapor  of  the  water  itself,  the  actual  height  is  generally  less  than  30  feet. 
When  the  water  is  warm  the  height  to  which  it  can  be  lifted  by  suction  de- 
creases, on  account  of  the  increased  pressure  of  the  vapor.  In  pumping  hot 
water,  therefore,  the  water  must  flow  into  the  pump  by  gravity.  The  fol- 
lowing table  sh  >ws  the  theoretical  maximum  depth  of  suction  for  different 
temperatures,  leakage  not  considered: 


Temp. 
F. 

Absolute 
Pressure 
ofVapor, 
Ibs.  per 
sq.  in. 

Vacuum 
in 
Inches  of 
Mercury. 

Max. 
Depth 
of 
Suction, 
feet. 

Temp. 
F. 

Absolute 
Pressure 
ot  Vapor, 
Ibs.  per 
sq.  in. 

Vacuum 
in 
Inches  of 
Mercury. 

Max. 
Depth 
of 
Suction, 
feet. 

101.4 

1 

27.88 

31.6 

183.0 

8 

13.63 

15.5 

126.2 

2 

25.85 

29.3 

188.4 

9 

11.59 

13.2 

144.7 

3 

23.81 

27.0 

193.2 

10 

9.55 

10.9 

153.3 

4 

21.77 

24.7 

197.6 

11 

7.51 

8.5 

162.5 

5 

19.74 

22  4 

201.9 

12 

5.48 

6.2 

170.3 

6 

17.70 

20.1 

205.8 

13 

3.44 

3.9 

177.0 

7 

15.66 

17.8 

209.6 

14 

1.40 

1.6 

Amount  of  Water  raised  by  a  Single-acting  Lift-pump. 

— It  is  common  to  estimate  that  the  quantity  of  water  raised  by  a 
single-acting  bucket-valve  pump  per  minute  is  equal  to  the  number  of 
strokes  in  one  direction  per  minute,  multiplied  by  the  volume  traversed  by 
the  piston  in  a  single  stroke,  on  the  theory  that  the  water  rises  in  the  pump 
only  when  the  piston  or  bucket  ascends;  but  the  fact  is  that  the  column  of 
water  does  not  cease  flowing  when  the  bucket  descends,  but  flows  on  con- 
tinuously through  the  valve  in  the  bucket,  so  that  the  discharge  of  the 
pump,  if  it  is  operated  at  a  high  speecl,  may  amount  to  nearly  double  that 
calculated  from  the  displacement  multiplied  by  the  number  of  single  strokes 
in  one  direction. 

Proportioning   the    Steam-cylinder   of   a   Direct-acting 
Pump.— Let 

A  =  area  of  steam-cylinder;  a  =  area  of  pump-cylinder; 

D  =  diameter  of  steam-cylinder;      d  =  diameter  of  pump-cylinder; 

P  =  steam-pressure,  Ibs.  per  sq.  in. ;  p  =  resistance  per  sq.  in.  on  pumps: 

H  =  head  =  2.309p;  p  =  .433H: 

work  done  in  pump-cylinder 

E  =  efficiency  of  the  pump  =  — 

work  done  by  the  steam-cylinder 


EP* 


EA 


H=  2.309#P  -;    If  E  =  75*,  H  =  1.732P  -. 
_»  -...  a 

E  Is  commonly  taken  at  0.7  to  0.8  for  ordinary  direct-acting  pumps.  For 
the  highest  class  of  pnmping-engines  it  may  amount  to  0.9.  The  steam- 
pressure  Pis  the  mean  effective  pressure,  according  to  the  indicator-dia- 
gram; the  water-pressure  p  is  the  mean  total  pressure  acting  on  the  pump 
plunger  or  piston,  including  the  suction,  as  could  be  shown  by  an  indicator- 
diagram  of  the  water-cylinder.  The  pressure  on  the  pump-piston  is  fre- 
quently much  greater  than  that  due  to  the  height  of  the  lift,  on  account  of 
the  friction  of  the  valves  and  passages,  which  increases  rapidly  with  velocity 
of  flow. 

Speed  of  Water  through  Pipes  and  Pump-passages.— 
The  speed  of  the  water  is  commonly  from  100  to  ~00  feet  per  minute.  If  200 
feet  per  minute  is  exceeded,  the  loss  from  friction  may  be  considerable. 

/        gallons  per  minute 

The  diameter  of  pipe  required  is  4.95,4  /      .     ..  —  :  —  —  . 

|/    velocity  in  feet  per  minute 

For  a  velocity  of  200  feet  per  minute,  diameter  =.35  x  ^gallons  per  mitT 


PUMPS. 


GOB 


Sizes  of  Direct-acting  Pumps.— The  two  following  tables  are  se- 
lected fro iii  catalogues  of  manufacturers,  as  representing  the  two  common 
types  of  direct-acting  pump,    viz.,    the  single-cylinder  and  the  duplex. 
Both  types  are  now  made  by  most  of  the  leading  manufacturers. 
The  Deane  Direct-acting  Pump. 
STANDARD  SIZES  FOR  ORDINARY  SERVICE. 


g 

L 

6 

*> 

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a 

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ft 

M 

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SM 

JU 

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1 

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CO 

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cc 

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C    03 

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130        35 

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125        49 

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125        64 

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125        90 

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1.64 

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110      180 

58 

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1 

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714 

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10 

1.91 

to  250 

110      210 

58 

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714 

8 

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2.17 

to  250 

110      239 

58 

17 

1 

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5 

4 

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6 

12 

1.47 

to  250 

100      147 

67 

201^ 

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4 

4 

a 

7 

12 

2.00 

to  250 

100      200 

67 

i 

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4 

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8 

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2.61 

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100      261 

68 

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10 

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100      408 

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2.61 

1  to  250 

100      261 

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10 

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4.08 

1  to  250 

100      408 

681/2 

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5.87 

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100      587 

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100      408 

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70      428 

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100      587 

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70      616 

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70      840 

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4.08 

1  to  250 

100      408 

69 

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6.12 

1  to  175 

70      428 

93 

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50      408 

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5.87 

1  to  250 

100      587 

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70      616 

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13.92 

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80    1114 

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1  to  150 

50    1044 

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1  to  175 

70      840 

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50      800 

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80    1114 

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16 

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50    1044 

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26.43 

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50    1322 

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14 

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18 

16 

24 

20.88 

1  to  125 

50    1044 

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12 

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18 

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26.43 

1  to  125 

50    1322 

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14 

12 

18 

20 

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32.64 

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50    1632 

118 

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14 

20 

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24 

26.43 

1  to  125 

50    1322 

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I 

Efficiency  of  Small  Direct-acting  Pumps.—  Chas.  E.  Emery,  in 
Reports  of  Judges  of  Philadelphia  Exhibition,  1876,  Group  xx.,  says  :  "Ex- 
periments made  with  steam-pumps  at  the  American  Institute  Exhibition  of 
1867  showed  that  average  sized  steam-pumps  do  not,  on  the  average,  utilize 

more  than  50  per  cent  of  the  indicated  power  in  the  steam-  cylinders,  the  re- 
mainder being  absorbed  in  the  friction  of  the  engine,  but  more  particularly 
in  the  passage  of  the  water  through  the  pump.     Again,  all  ordinary  steam- 
pumps"  for  miscellaneous  uses  require  that  the  steam  -cylinder  shall  have 
three  to  four  times  the  area  of  the  water-cylinder  to  give  sufficient  power 

604 


WATER-POWER. 


when  the  steam  is  accidentally  low;  hence  as  such  pumps  usually  work 
against  the  atmospheric  pressure,  the  net  or  effective  pressure  forms  a 
small  percentage  of  the  total  pressure,  which,  with  the  large  extent  of 
radiating  surface  exposed  and  the  total  absence  of  expansion,  makes  the 
expenditure  of  steam  very  large.  One  pump  tested  required  120  pounds 
weight  of  steam  per  indicated  horse-power  per  hour,  and  it  is  believed  that 
the  cost  will  rarely  fall  below  60  pounds  ;  and  as  only  50  per  cent  of  the  in- 
dicated povyer  is  utilized,  it  may  be  safely  stated  that  ordinary  steam  pumps 
rarely  require  less  than  120  pounds  of  steam  per  hour  for  each  horse-power 
utilized  in  raising  water,  equivalent  to  a  duty  of  only  15.000,000  foot-pounds 
per  100  pounds  of  coal.  With  larger  steam-pumps,  particularly  when  they 
are  proportioned  for  the  work  to  be  done,  the  duty  will  be  materially  in- 
creased." 

Tlie  Wortliiiigton  Duplex  Pump. 

STANDARD  SIZES  FOR  ORDINARY  SERVICE. 


>>  ' 

a  o   . 

Sizes  of  Pipes  for 

cc 

00 

c 

h 

g|'. 

|l 

—  -c-o 
•_  .1  i 

Short  Lengths. 
To  be  increased  as 

1 

So 

&•• 

*  ^  = 

'3  2** 

length  increases. 

p 

c 

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100  to  150 

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100  to    150 

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135  to    230 

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180  to    300 

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245  to    410 

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14 

7 

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1.66 

75  to  125 

245  to    410 

97^ 

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3 

6 

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10 

2.45 

75  to  125 

365  to    610 

12 

2  Mi 

3 

6 

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2.45 

75  to  125 

365  to    610 

12 

214 

3 

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2.45 

75  to  125 

365  to    610 

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2.45 

75  to  125 

365  to    610 

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10 

2  45 

75  to  125 

365  to    610 

12 

4 

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10 

3^57 

75  to  125 

530  to    890 

1414 

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10*4 

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3.57 

75  to  125 

530  to    890 

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3 

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3.57 

75  to  125 

530  to    890 

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530  to    890 

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3.57 

75  to  125 

530  to    890 

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14 

12 

10 

4.89 

75  to  125 

730  to  1220 

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3 

10 

8 

16 

12 

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4.89 

75  to  125 

730  to  1220 

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10 

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12 

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4.89 

75  to  125 

730  to  1220 

17 

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730  to  1220 

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75  to  125 

990  to  1660 

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10 

20 

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6.66 

75  to  122 

990  to  1660 

19% 

4 

5 

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5.10 

50  to  100 

510  to  1020 

14 

3 

3^£ 

10 

8 

20 

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7.34 

50  to  100 

730  to  1460 

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12 

10 

20 

15 

15 

11  47 

50  to  100 

1145t.n2:29n    21 

25 

15 

15 

11.47 

50  to  100     1145  to  2290    21 

PUMPS. 


605 


Speed  of  Piston, — A  piston  speed  of  100  feet  per  minute  is  commonly 
u^.suined  as  correct  in  practice,  but  for  short-stroke  pumps  this  gives  too 
high  a  speed  of  rotation,  requiring  too  frequent  a  reversal  of  the  valves. 
For  long  stroke  pumps,  2  feet  and  upward,  this  speed  may  be  considerably 
exceeded,  if  valves  and  passages  are  of  ample  area. 

Number  of  Strokes   required   to    Attain  a  Piston    Speed 

from  5O  to  125  Feet  per  Minute  for  Pumps  having 

Strokes  from  3  to  18  Inches  in  JLength. 


W3  1£ 

'&£  .• 

Length  of  Stroke  in  Inches. 

CM   3 

°.£| 

3 

4 

5 

6 

7 

8 

10 

12 

15 

18 

111 

oj*^ 

Number  of  Strokes  per  Minute. 

50 

200 

150 

120 

100 

86 

75 

60 

50 

40 

33 

55 

220 

165 

132 

110 

94 

82.5 

66 

55 

44 

37 

60 

240 

180 

144 

120 

103 

90 

72 

60 

48 

40 

65 

260 

195 

156 

130 

111 

97.5 

78 

65 

52 

43 

70 

280 

210 

168 

140 

120 

105 

84 

70 

56 

47 

75 

300 

225 

180 

150 

128 

112.5 

90 

75 

60 

50 

80 

320 

240 

192 

160 

137 

120 

96 

80 

64 

53 

85 

340 

255 

204 

170 

146 

127.5 

102 

85 

68 

57 

90 

360 

270 

216 

180 

154 

135 

108 

90 

72 

60 

95 

380 

285 

228 

190 

163 

142.5 

114 

95 

76 

63 

100 

400 

300 

240 

200 

171 

150 

120 

100 

80 

67 

105 

420 

315 

252 

210 

180 

157.5 

126 

J05 

84 

70 

110 

440 

330 

264 

220 

188 

165 

132 

110 

88 

73 

115 

460 

345 

276 

230 

197 

H2.5 

138 

115 

92 

77 

120 

480 

360 

288 

240 

206 

180 

144 

120 

90 

80 

125 

500 

375 

300 

250 

214 

187.5 

150 

125 

100 

83 

Piston  Speed  of  Pumping-engines.  (John  Birkinbine,  Trans. 
A.  I.  M.  E.,  v.  459.)— In  dealing  with  such  a  ponderous  and  unyielding  sub- 
stance as  water  there  are  many  difficulties  to  overcome  in  making  a  pump 
work  with  a  high  piston  speed.  The  attainment  of  moderately  high  speed 
is,  however,  easily  accomplished.  Well-proportioned  pumping-engines  of 
large  capacity,  provided  with  ample  water-ways  and  properly  constructed 
valves,  are  operated  successfully  against  heavy  pressures  at  a  speed  of  250  ft. 
per  minute,  without  "thug,1'  concussion,  or  injury  to  the  apparatus,  and 
there  is  no  doubt  that  the  speed  can  be  still  further  increased. 

Speed  of  Water  through  Valves.— If  areas  through  valves  and 
water  passages  are  sufficient  u>  give  a  velocity  of  250  ft.  per  min.  or  less, 
they  are  ample.  The  water  should  be  carefully  guided  and  not  too  abruptly 
deflected.  (F.  W.  Dean.  Eng.  News,  Aug.  10,  1893.) 

Boiler»feed  Pumps.— Practice  has  shown  that  100  ft.  of  piston  speed 
per  minute  is  the  limit,  if  excessive  wear  and  tear  is  to  be  avoided. 

The  velocity  of  water  through  the  suction-pipe  must  not  exceed  200  ft. 
per  minute,  else  the  resistance  of  the  suction  is  too  great. 

The  approximate  size  of  suction-pipe,  where  the  length  does  not  exceed 
25  ft.  and  there  are  not  more  than  two  elbows,  may  be  found  as  follows  : 

7/10  of  the  diameter  of  the  cylinder  multiplied  by  1/100  of  the  piston  speed 
in  feet.  For  duplex  pumps  of  small  size,  a  pipe  one  size  larger  is  usually 
-employed.  The  velocity  of  flow  in  the  discharge-pipe  should  not  exceed 
500  ft.  per  minute.  The  volume  of  discharge  and  length  of  pipe  vary  so 
greatly  in  different  installations  that  where  the  water  is  to  be  forced  more 
than  50  ft.  the  size  of  discharge-pipe  should  be  calculated  for  the  particular 
conditions,  allowing  no  greater  velocity  than  500  ft.  per  minute.  The  size  of 
discharge-pipe  is  calculated  in  single-cylinder  pumps  from  250  to  400  ft.  per 
minute.  Greater  velocity  is  permitted 'in  the  larger  pipes. 

In  determining  the  proper  size  of  pnmp  for  a  steam-boiler,  allowances 
must  be  made  for  a  supply  of  water  sufficient  to  cover  all  the  demands  of 
engines,  steam-heating,  etc.,  up  to  the  capacity  of  generator,  and  should  not 
be  calculated  simply  according  to  the  requirements  of  the  engine.  In  prac- 
tice engines  use  all  the  way  from  12  up  to  50,  or  more,  pounds  of  steam  per 
H.P.  per  hour  when  being  worked  up  to  capacity.  When  an  engine  is  over- 
loaded or  underloaded  more  water  per  H.P.  will  be  required  than  when 
operating  at  its  rated  capacity.  The  average  run  of  horizontal  tubular 


606 


WATER-POWER. 


boilers  will  evaporate  from  2  to  3  Ibs.  of  water  per  sq.  ft.  of  heating-surface 
per  hour,  but  may  be  driven  up  to  6  Ibs.  if  the  grate-surface  is  too  large  or 
the  draught  too  great  for  economical  working. 

Pump-Valves.— A.  F.  Nagle  (Trans.  A.  S.  M.  E.,  x.  521)  gives  a  number 
of  designs  with  dimensions  of  double-beat  or  Cornish  valves  used  in  large 
pumping-engines,  with  a  discussion  of  the  theory  of  their  proportions.  The 
following  is  a  summary  of  the  proportions  of  the  valves  described. 

SUMMARY  OF  VALVE  PROPORTIONS. 


1 

'3 

11s  f 

is§ 

fl   r 

M 

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£b'£  a)*"* 

^-C-S; 

13  «r 

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Location  of  Engine. 

5111. 

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£  & 

§  *  J  5 

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Providence  high-ser- 

vice engine  ...   . 

12 

1  lb. 

IB?' 

377  Ibs. 

Good 

reduced  to 

.66  lb. 

Providence  Cornish- 

engine  ... 

16 

1.88 

12 

680 

Good 

St.  Louis  Water  Wks. 

16 

1.86 

67 

250 

Some  noise 

Milwaukee    "       ** 

7 

.40 

88 

120 

j  Some  noise  at 
{    high  speed. 

Chicago 

25 

1.41 

75 

151 

Noisy 

it                                    it                 4( 

15 

1.31 

85 

140 

4t 

wood  seats  

15 

1.16 

94 

132 

« 

Chicago  Water  Wks. 

8 

.96 

75 

151 

** 

Mr.  Nagle  says :  There  is  one  feature  in  which  the  Cornish  valves  are 
necessarily  defective,  namely,the  lift  must  always  be  quite  large,  unless  great 
power  is  sacrificed  to  reduce  it.  It  is  undeniable  that  a  small  lift  is  prefer- 
able to  a  great  one,  and  hence  ic  naturally  leads  to  the  substitution  of 
numerous  small  valves  for  one  or  several  large  ones.  To  what  extreme  re- 
duction of  size  this  view  might  safely  lead  must  be  left  to  the  judgment  of 
the  engineer  for  the  particular  case  in  hand,  but  certainly,  theoretically,  we 
must  adopt  small  valves.  Mr.  Corliss  at  one  time  carried  the  theory  so 
far  as  to  make  them  only  1%  inches  in  diameter,  but  from  3  to  4  inches  is 
the  more  common  practice  now.  A  small  valve  presents  proportionately  a 
larger  surface  of  discharge  with  the  same  lift  than  a  larger  valve,  so  that 
whatever  the  total  area  of  valve-seat  opening,  its  full  contents  can  be  dis- 
charged with  less  lift  through  numerous  small  valves  than  with  one  large 
one. 

Henry  R.  Worthington  was  the  first  to  use  numerous  small  rubber  valves 
in  preference  to  the  larger  metal  valves.  These  valves  work  well  under  all 
the  conditions  of  a  city  pumping-engine.  A  volute  spring  is  generally  used 
to  limit  the  rise  of  the  valve. 

In  theLeavitt  high-duty  sewerage-engine  at  Boston  (Am.  Machinist,  May 
31.  1884),  the  valves  are  of  rubber,  %-inch  thick,  the  opening  in  valve  seat 
being  13^  x  4^  inches.  The  valves  have  iron  face  and  back-plates,  and 
form  their  own  hinges. 

CENTRIFUGAL,  PUMPS. 

Relation  of  Height  of  Lift  to  Velocity.  -The  height  of  lift 
depends  only  on  the  tangential  velocity  of  the  circumference,  every  tangen- 
tial velocity  giving  a  constant  height  of  lift — sometimes  termed  "head  *"- 
whether  the  pump  is  small  or  large.  The  quantity  of  water  discharged  is  in 
proportion  to  the  area  of  the  discharging  orifices  at  the  circumference,  or  in 
proportion  to  the  square  of  the  diameter,  when  the  breadth  is  kept  the  same. 
R.  H.  Buel  (App.  Cyc.  Mech.,  ii,  606)  gives  the  following: 

Let  Q  represent  the  quantity  of  water,  in  cubic  feet,  to  be  pumped  per 
minute,  h  the  height  of  suction  in  feet,  h'  the  height  of  discharge  in  feet,  and 
d  the  diameter  of  suction-pipe,  equal  to  the  diameter  of  discharge-pipe,  iu 


CENTRIFUGAL   PUMPS. 


60? 


feet;  then,  according  to  Fink,  d  =  0.36  |/  -—^===  ,  g  being  the  accel- 
eration due  to  gravity. 

If  the  suction  takes  place  on  one  side  of  the  wheel,  the  inside  diameter  of 
the  wheel  is  equal  to  1.2d,  and  the  outside  to  2Ad.  If  the  suction  takes  place 
at  both  sides  of  the  wheel,  the  inside  diameter  of  the  wheel  is  equal  to  0.85d, 
and  the  outside  to  1.7d.  Then  the  suction-pipe  will  have  two  branches,  the 
area  of  each  equal  to  half  the  area  of  d.  The  suction-pipe  should  be  as  short 
as  possible,  to  prevent  air  from  entering  the  pump.  The  tangential  velocity 
of  the  outer  edge  of  wheel  for  the  delivery  Q  is  equal  to  1.25  Vfy  (li  -f  h'~) 
feet  per  second. 

The  arms  are  six  in  number,  constructed  as  follows:  Divide  the  central 
angle  of  60°,  which  incloses  the  outer  edges  of  the  two  arms,  into  any  num- 
ber of  equal  parts  by  dividing  the  radii,  and  divide  the  breadth  of  the  wheel 
in  the  same  manner  by  drawing  concentric  circles.  The  intersections  of  the 
several  radii  with  the  corresponding  circles  give  points  of  the  arm. 

In  experiments  with  Appold's  pump,  a  velocity  of  circumference  of  500 
ft.  per  min.  raised  the  water  1  ft.  high,  and  maintained  it  at  that  level 
without  discharging  any;  and  double  the  velocity  raised  the  water  to  four 
times  the  height,  as  the  centrifugal  force  was  proportionate  to  the  square 
of  the  velocity;  consequently, 

500  ft.  per  min.  raised  the  water    1  ft.  without  discharge. 
]000      «          »*          n        «          4t        4  .1 

2000      "          "          "        "         "      16  " 
4000      "          "          "        "         "      64  "          " 

The  greatest  height  to  which  the  water  had  been  raised  \\ithout  discharge, 
in  the  experiments  with  the  1-ft.  pump,  was  67.7  ft.,  with  a  velocity  of  4153 
ft.  per  min.,  being  rather  less  than  the  calculated  height,  owing  probably  to 
leakage  with  the  greater  pressure.  A  velocity  of  1128  ft.  per  min.  raised  the 
water  5^  ft.  without  any  discharge,  and  the  maximum  effect  from  the 
power  employed  in  raising  to  the  same  height  5^  ft.  was  obtained  at  the 
velocity  of  1678  ft.  per  min.,  giving  a  discharge  of  1400 gals,  per  min.  from 
the  1-ft.  pump.  The  additional  velocity  required  to  effect  a  discharge  of 
1400  gals,  per  min.,  through  a  1-ft.  pump  working  at  a  dead  level  without  any 
height  of  lift,  is  550  ft.  per  min.  Consequently,  adding  this  number  in  each 
case  to  the  velocity  given  above,  at  which  no  discharge  takes  place,  the  fol- 
lowing velocities  are  obtained  for  the  maximum  effect  to  be  produced  in 
each  case : 

1050  ft.  per  min.,  velocity  for    1  ft.  height  of  lift. 
1550      "  "  "      4  " 

2550      "          "  "  "     16  "        "          " 

4550      *•          "  "  "    64  "        "          u 

Or,  in  general  terms,  the  velocity  in  feet  per  minute  for  the  circumference 
of  the  pump  to  be  driven,  to  raise  the  water  to  a  certain  height,  is  equal  to 
550  +  500  j/lieight  of  lift  in  feet. 

Lawrence   Centrifugal   Pumps.   Class   B— For   Lifts  from 
15  to  35  ft. 


Size  of  Pipes. 

Economical 
Capacity, 
in  gallons 
per  min. 

Total 
Capacity, 
in  gallons 
per  min. 

Horse-power 
per  Ft.  Lift, 
for  sin  al  lei- 
quantity. 

Suction. 

Dis- 
charge. 

No.  1^ 

2  in. 

lUin 

20  to        50 

150 

.024 

"      2 

2^ 

2 

60  to        80 

300 

.035 

"      3 

31^ 

3 

80  to       160 

650 

.055 

44     4 

4^ 

4 

160  to       350 

1,250 

.075 

"      5 

6 

5 

330  to       600 

1,850 

.175 

'      6 

6 

6 

500  to       900 

2,600 

.22 

'     8 

8 

8 

1,1  00  to    2,000 

4,750 

.45 

4    10 

10 

10 

1,600  to    3,000 

7,500 

.62 

'    12 

12 

12 

2,000  to    3,000 

10,000 

1.00 

4    14 

14 

14 

3,000  to    5.000 

14,000 

1.25 

4    15 

15 

15 

3,500  to    7.000 

16,000 

1.40 

u    18 

18 

18 

6.000  to  11,000 

22,000 

2.40 

608 


WATER-POWER. 


Table  of  Diameters  and  Width  of  Pulleys,  Width  of  Belts, 
and  Number  of  Revolutions  per  Minute  Necessary  to 
raise  Minimum  Quantity  of  Water  to  Different  Heights 
with  Different  Sizes  of  Pumps  of  Class  B. 


•V. 

«M 

«M 

s**-  • 

Height  in  Feet  and  Revolutions  per 

s 

fjj 

jjft 

§33 

Minute. 

o  & 

33 

i* 

|£ 

3* 

a  2  *** 

6 

8 

10 

12 

16 

20 

25 

30 

35 

&£ 

Ins. 

Ins. 
5 

Ins. 
5 

Ins. 
3 

40 

465 

515 

560 

605 

680 

745 

820 

885 

945 

m 

2 

5 

5 

4 

60 

425 

47.", 

515 

560 

625 

680 

750 

810 

870 

2 

7L£ 

7 

6 

80 

390 

435 

475 

510 

575 

630 

695 

750 

800 

3 

4 

?L£ 

7 

7 

160 

365 

405 

445 

475 

535 

590 

645 

700 

745 

4 

5 

12 

11 

8 

330 

320 

355 

390 

415 

470 

520 

570 

610 

750 

5 

6 

14 

11 

9 

500 

285 

315 

345 

370 

415 

460 

500 

540 

580 

6 

8 

16 

12 

10 

1100 

215 

240 

260 

280 

310 

340 

375 

410 

435 

8 

10 

18 

12 

10 

1600 

170 

190 

210 

225 

250 

275 

300 

325 

350 

10 

12 

22 

14 

12 

2000 

150 

165 

185 

195 

220 

240 

265 

285 

310 

12 

14 

24 

14 

12 

3000 

135 

150 

165 

175 

195 

215 

240 

295 

275 

14 

15 

28 

15 

14 

3500 

125 

145 

155 

165 

190 

210 

230 

245 

360 

15 

18 

28 

16 

14 

6000 

110 

120 

130 

135 

160 

175 

190 

255 

220 

18 

Efficiencies  of  Centrifugal  and  Reciprocating  Pumps.— 

\V.  O.  Webber  (Trans.  A.  S.  M.  E.,  vii.  598)  gives  diagrams  showing  the 
relative  efficiencies  of  centrifugal  and  reciprocating  pumps,  from  which  the 
following  figures  are  taken  for  the  different  lifts  stated  : 
Lift,  feet: 

2      5    10    15    20    25    30    35    40    50    60    80    100    120    160    200    240    280 
Efficiency  reciprocating  pump: 

..     .     .30  .45  .55  .61  .66  .68  .71  .75  .77  .82    .85    .87     .90    .89    .88     .85 
Efficiency  centrifugal  pump: 

.50  .56  .64  .68  .69  .68  .66  .62  .58  .50  .40  

The  term  efficiency  here  used  indicates  the  value  of  W.  H.  P.  -H  I.  H.  P., 
or  horse-power  of  the  water  raised  divided  by  the  indicated  horse- power  of 
the  steam-engine,and  does  not  therefore  show  the  full  efficiency  of  the  pump, 
but  that  of  the  combined  pump  and  engine.  It  is,  however,  a  very  simple 
way  of  showing  the  relative  values  of  different  kinds  of  pumping-eugiues 
having  their  motive  power  forming  a  part  of  the  plant. 

The  highest  value  of  this  term,  given  by  Mr.  Webber,  is  .9164  for  a  lift  of 
170ft.,  and  3615  gals,  per  min.  This  was  obtained  in  a  test  of  the  Leavitt 
pumping- engine  at  Lawrence,  Mass.,  July  24,  1879. 

With  reciprocating  pumps,  for  higher  lifts  than  170  ft.,  the  curve  of  effl 
ciencies  falls,  and  from  200  to  300  ft.  lift  the  average  value  seem:;  about 
.84.  Below  170  ft.  the  curve  also  falls  reversely  and  slowly,  until  at  about  90 
ft.  its  descent  becomes  more  rapid,  and  at  35  ft.  .727  appears  the  best 
recorded  performance.  There  are  not  any  very  satisfactory  records  below 
this  lift,  but  some  figures  are  given  for  the  yearly  coal  consumption  and 
total  number  of  gallons  pumped  by  engines  in  Holland  under  a  16-ft.  lift, 
f  rom  which  an  efficiency  of  .44  has  been  deduced. 

With  centrifugal  pumps,  the  lift  at  which  the  maximum  efficiency  is  ob- 
tained is  approximately  17  ft.  At  lifts  from  12  to  18  ft.  some  makers  of 
large  experience  claim  now  to  obtain  from  65$  to  70$  of  useful  effect,  but 
.613  appears  to  be  the  best  done  at  a  public  test  under  14.7  ft.  head. 

The  drainage-pumps  constructed  some  years  ago  for  the  Haarlem  Lake 
were  designed  to  lift  70  tons  per  min.  15  ft.,  and  they  weighed  about  150 
tons.  Centrifugal  pumps  for  the  same  work  weigh  only  5  tons.  The  weight 
of  a  centrifugal  pump  and  engine  to  lift  10,000  gals,  per  miri.  35  ft.  high  is 
6  tons. 

The  pumps  placed  by  Gwynne  at  the  Ferrara  Marshes,  Northern  Italy,  in 
1865,  are,  it  is  believed,  capable  of  handling  more  water  than  other  set  of 
pumping-engines  in  existence.  The  work  performed  by  these  pumps  is  the 
lifting  of  2000  tons  per  min.— over  600.000,000  gals,  per  24  hours— on  a  mean 
lift  of  about  10  ft.  (maximum  of  12.5  ft.).  (See  Engineering,  1876.) 

The  efficiency  of  centrifugal  pumps  seems  to  increase  as  the  size  of  pump 


DUTY   TRIALS   OF   PUMPLtfG-ENGINES. 


609 


increases,  approximately  as  follows:  A  2"  pump  (this  designation  meaning 
always  the  size  of  discharge-outlet  in  inches  of  diameter),  giving  an  effi- 
ciency of  38$,  a  3"  pump  45$,  and  a  4"  pump  52$,  a  5"  pump  60$,  and  a  6" 
pump  64$  efficiency. 

Tests  of  Centrifugal  Pumps. 

W.  O.  Webber,  Trans.  A.  S.  M.  E.,  ix.  237. 


Maker. 

An- 
drews. 

An- 
drews. 

An- 
drews. 

Heald 
& 
Sisco. 

Heald 

& 
Sisco. 

Heald 
& 
Sisco. 

Berlin. 
Schwartz- 
kopff. 

Size               

No.  9. 
0U" 

9%" 
26" 
191.9 
1513.12 
12.25 
4.69 
10.09 
46.52 

No.  9. 

9X" 

9%" 
26" 
195.5 
2023.82 
12.62 
6.47 
12.2 
53.0 

No.  9. 

9%" 
26" 
200.5 
2499.33 
13.08 
8.28 
14.38 
57.57 

No.  10. 
10" 
12" 
30.5" 
188.3 
1673.37 
12.33 
5.22 
8.11 
64.5 

No.  10. 
10" 
12" 
30.5" 
20-J.7 
2044.9 
12.58 
6.51 
10  74 
60.74 

No.  10. 
10" 
12" 

30.5" 
213.7 
2371.67 
13.0 
7.81 
14.02 
55.72 

No.  9. 

9^4" 
10.3" 
20.5" 
500 
1944.8 
16.46 

Diam.  discharge  . 
'•     suction  ... 
"     disk  

Rev.  per  minute. 
Gal  Is.  per  minute 
Knight  in  feet..  .  . 
Water  H.P  
Dynam'eter  H.P. 
Efficiency  

11 
73.1 

?i 


Vanes  of  Centrifugal  Pumps,— For  forms  of  pump  vanes,  see 

Eaper  by  W.  O.  Webber,  Trajis.  A.  S.  M.  E.,  ix.  228,  and  discussion  thereon 
y  Profs.  Thurston,  Wood,  and  others. 

The  Centrifugal  Pump  used  as  a  Suction  Dredge.— The 
Andrews  centrifugal  pump  was  used  by  Gen.  Gillmore,  U.  S.  A.,  in  1871.  in 
deepening  the  channel  over  the  bar  at  the  mouth  of  the  St.  John's  River, 
Florida.  The  pump  was  a  No.  9,  with  suction  and  discharge  pipes  each  9 
inches  <iinm.  It  was  driven  at  300  revolutions  per  minute  by  belt  from  an 
engine  developing  26  useful  horse-power. 

Although  ~00  revolutions  of  the  pump  disk  per  minute  will  easily  raise 
3000  gallons  of  clear  water  12ft.  high,  through  a  straight  vertical  9-inch 

'ipe,  300  revolutions  were  required  to  raise  2500  gallons  of  sand  and  water 
1  ft.  high,  through  two  inclined  suction-pipes  having  two  turns  each,  dis- 
charged through  a  pipe  having  one  turn. 

The  proportion  of  sand  that  can  be  pumped  depends  greatly  upon  its 
specific  gravity  and  fineness.  The  calcareous  and  argillaceous  sands  flow 
more  freely  than  the  silicious,  and  fine  sands  are  less  liable  to  choke  the 
pipe  than  those  that  are  coarse.  Wlien  working  at  high  speed,  50$  to  55$  of 
sand  can  be  raised  through  a  straight  vertical  pipe,  giving  for  every  10  cubic 
yards  of  material  discharged  5  to  5^  cubic  yards  of  compact  sand.  With 
the  appliances  used  on  the  St.  John's  bar,  the  proportion  of  sand  seldom 
exceeded  45$,  generally  ranging  from  30$  to  35$  when  working  under  the 
most  favorable  conditions. 

In  pumping  2500  gallons,  or  12.6  cubic  yards  of  sand  and  water  per  minute, 
there  would  therefore  be  obtained  from  3.7  to  4.3  cubic  yards  of  sand.  Dur- 

had  been 
L  was  con- 
Edwards  &  Co., 


tnere  woma  tnererore  oe  oorainea  irom  z.i  to  4.3  cuoic  yaras  or  sa 
ing  the  early  stages  of  the  work,  before  the  teeth  under  the  drag 
properly  arranged  to  aid  the  flow  of  sand  into  the  pipes,  the  yield 
siderably  below  this  average.  (From  catalogue  of  Jos.  Edwar 


age. 
Mfrs.  of  the  Andrews  Purnp,  New  York.) 


V  TRIALS  OF  PUlttPING-JENGINES. 

A  committee  of  the  A.  S.  M.  E.  (Trans.,  xii.  530)  reported  in  1891  on  a 
standard  method  of  conducting  duty  trials.  Instead  of  the  old  unit  of 
duty  of  foot-pounds  of  work  per  100  Ibs.  of  coal  used,  the  committee  recom- 
mend a  new  unit,  foot-pounds  of  work  per  million  heat-units  furnished  by 
the  boiler.  The  variations  in  quality  of  coal  make  the  old  standard  unfit  a's 
a  basis  of  duty  ratings.  The  new  unit  is  the  precise  equivalent  of  100  Ibs.  of 
coal  in  cases  where  each  pound  of  coal  imparts  10,000  heat-  units  to  the 
water  in  the  boiler,  or  where  the  evaporation  is  10,000  -~  965.7  =  10.355  Ibs.  of 
water  from  and  at  212°  per  pound  of  fuel.  This  evaporative  result  is  readily 
obtained  from  all  grades  of  Cumberland  bituminous  coal,  used  in  horizontal 
return  tubular  boilers,  and,  in  many  cases,  from  the  best  grades  of  anthra- 
cite coal. 


610  WATER-POWER. 

The  committee  also  recommend  that  the  work  done  be  determined  by 
plunger  displacement,  after  making  a  test  for  leakage,  instead  of  by  meas 
urement  of  flow  by  weirs  or  other  apparatus,  but  advise  the  use  of  such 
apparatus  when  practicable  for  obtaining  additional  data.  The  following 
extracts  are  taken  from  the  report.  When  important  tests  are  to  be  made 
the  complete  report  should  be  consulted. 

The  necessary  data  having  been  obtained,  the  duty  of  an  engine,  and  other 
quantities  relating  to  its  performance,  may  be  computed  by  the  use  of  the 
following  formulae: 

'  Foot-pounds  of  work  done 

Total  number  of  heat-units  consumed 


x  1)0(X))000  (foot.pounds)> 

C  x  144 

2.  Percentage  of  leakage  =  - — ^ x  100  (per  cent). 

•a-    X   •*-•    X    -tV 

3.  Capacity  =  number  of  gallons  of  water  discharged  in  24  hours 

AXLXNX  7.4805  X  24          AxLx  NX  1.24675 
DX144  — D—          ~ 

4.  Percentage  of  total  frictions, 


xioo 


tD  X  60  X  33,T)00 
I.H.P. 


or,  in  the  usual  case,  where  the  length  of  the  stroke  and  number  of  strokes 
of  the  plunger  are  the  same  as  that  of  the  steam-piston,  this  last  formula 
becomes: 


Percentage  of  total  frictions  =1  --  .    J^J'u   1  X  100  (per  cent). 

1_  As  X  i'l  •  -Ej-  f  •  J 


In  these  formulae  the  letters  refer  to  the  following  quantities: 
A  =  Area,  in  square  inches,  of  pump  plunger  or  piston,  corrected  for  area 

of  piston  rod  or  rods; 
P  =  Pressure,  in  pounds  per  square  inch,  indicated  by  the  gauge  on  the 

force  main  ; 

p  =  Pressure,  in  pounds  per  square  inch,  corresponding  to  indication  of  the 
vacuum-gauge  on  suction  -main  (or  pressure-gauge,  if  the  suction- 
pipe  is  under  a  head).  The  indication  of  the  vacuum-gauge,  in 
inches  of  mercury,  may  be  converted  into  pounds  by  dividing  it  by 
2.035; 

s  =  Pressure,  in  pounds  per  square  inch,  corresponding  to  distance  be- 
tween the  centres  of  the  two  gauges.    The  computation  for  this 
pressure  is  made  by  multiplying  the  distance,  expressed  in  feet,  by 
the  weight  of  one  cubic  foot  of  water  at  the  temperature  of  the 
pump-  well,  and  dividing  the  product  by  144; 
L  =  Average  length  of  stroke  of  pump-plunger,  in  feet; 
N  =  Total  number  of  single  strokes  of  pump-plunger  made  during  the  trial; 
As  =  Area  of  steam-cylinder,  in  square  inches,  corrected  for  area  of  piston- 
rod.    The  quantity  As  X  M.E.P.,  in  an  engine  having  more  than  one 
cylinder,  is  the  sum  of  the  various  quantities  relating  to  the  respec- 
tive cylinders; 

Ls  =  Average  length  of  stroke  of  steam  -piston,  in  feet; 
_A7s  =  Total  number  of  single  strokes  of  steam-piston  during  trial; 
M.E.P.  =  Average  mean    effective  pressure,  in  pounds  per  square  inch, 
measured  from  the  indicator-diagrams  taken  from  the  steam-cylin- 
der; 

I.H.P.  =  Indicated  horse-power  developed  by  the  steam-cylinder; 
C  —  Total  number  of  cubic  feet  of  water  which  leaked  by  the  purnp-plunger 

during  the  trial,  estimated  from  the  results  of  the  leakage  test; 
D  =  Duration  of  trial  in  hours; 


DUTY   TRIALS   OF   PUMPLTO-EKGINES.  611 

H—  Total  number  of  heat-units  (B.  T.  IT.)  consumed  by  engine  =  weight  of 
water  supplied  to  boiler  by  main  feed-pump  x  total  heat  of  steam 
of  boiler  pressure  reckoned  from  temperature  of  main  feed-water  -f- 
weight  of  water  supplied  by  jacket-pump  X  total  heat  of  steam  of 
boiler-pressure  reckoned  from  temperature  of  jacket-water  -f-  weight 
of  any  other  water  supplied  X  total  heat  of  steam  reckoned  from  its 
temperature  of  supply.  The  total  heat  of  the  steam  is  corrected  for 
the  moisture  or  superheat  which  the  steam  may  contain.  No  allow- 
ance is  made  for  water  added  to  the  feed  water,  which  is  derived 
from  any  source,  except  the  engine  or  some  accessory  of  the  engine. 
Heat  added  to  the  water  by  the  use  of  a  flue -heater  at  the  boiler  is 
not  to  be  deducted.  Should  heat  be  abstracted  from  the  flue  by 
means  of  a  steam  reheater  connected  with  the  intermediate  re- 
ceiver of  the  engine,  this  heat  must  be  included  in  the  total  quantity 
supplied  by  the  boiler. 

Leakage  Test  of  Pump.— The  leakage  of  an  inside  plunger  (the 
only  type  which  requires  testing)  is  most  satisfactorily  determined  by  mak- 
ing the  test  with  the  cylinder-head  removed.  A  wide  board  or  plank  may 
be  temporarily  bolted  to  the  lower  part  of  the  end  of  the  cylinder,  so  as  to 
hold  back  the  water  in  the  manner  of  a  dam,  and  an  opening  made  in  the 
temporary  head  thus  provided  for  the  reception  of  an  overflow-pipe.  The 
plunger  is  blocked  at  some  intermediate  point  in  the  stroke  (or,  if  this  posi- 
tion is  not  practicable,  at  the  end  of  the  stroke),  and  the  water  from  the 
force  main  is  admitted  at  full  pressure  behind  it.  The  leakage  escapes 
through  the  overflow-pipe,  and  it  is  collected  in  barrels  and  measured.  The 
test  should  be  made,  if  possible,  with  the  plunger  in  various  positions. 

In  the  case  of  a  pump  so  planned  that  it  is  difficult  to  remove  the  cylinder- 
head,  it  may  be  desirable  to  take  the  leakage  from  one  of  the  openings 
which  are  provided  for  the  inspection  of  the  suction-valves,  the  head  being 
allowed  to  remain  in  place. 

It  is  assumed  that  there  is  a  practical  absence  of  valve  leakage.  Exami- 
nation for  such  leakage  should  be  made,  and  if  it  occurs,  and  it  is  found  to 
be  due  to  disordered  valves,  it  should  be  remedied  before  making  the  plunger 
test.  Leakage  of  the  discharge  valves  will  be  shown  by  water  passing  down 
into  the  empty  cylinder  at  either  end  when  they  are  under  pressure.  Leak- 
age of  the  suction-valves  will  be  shown  by  the  disappearance  of  water  which 
covers  them. 

If  valve  leakage  is  found  which  cannot  be  remedied  the  quantity  of  water 
thus  lost  should  also  be  tested.  One  method  is  to  measure  the  amount  of 
water  required  to  maintain  a  certain  pressure  in  the  pump  cylinder  when 
this  is  introduced  through  a  pipe  temporarily  erected,  no  water  being  al- 
lowed to  enter  through  the  discharge  valves  of  the  pump. 

Table  of  Data  and  Results.— In  order  that  uniformity  may  be  se- 
cured, it  is  suggested  that  the  data  and  results,  worked  out  in  accordance 
with  the  standard  method,  be  tabulated  in  the  manner  indicated  in  the  fol- 
lowing scheme : 

DUTY  TRIAL  OF  ENGINE. 

DIMENSIONS. 

1.  Number  of  steam -cylinders. 


2.  Diameter  of  steam-cylinders ins. 

3.  Diameter  of  piston-rods  of  steam-cylinders. ins. 

4.  Nominal  stroke  of  steam-pistons ft. 

5.  Number  of  water-plungers  

6.  Diameter  of  plungers ins. 

7.  Diameter  of  piston-rods  of  water-cylinders ins. 

8.  Nominal  stroke  of  plungers < ft. 

9.  Net  area  of  steam-pistons =, .:.  sq.  ins. 

10.  Net  area  of  plungers •>  sq.  ins. 

11.  Average  length  of  stroke  of  steam-pistons  during  trial ft. 

12.  Average  length  of  stroke  of  plungers  during  trial ft. 

(Give  also  complete  description  of  plant.) 

TEMPERATURES. 

13.  Temperature  of  water  in  pump- well degs. 

14.  Temperature  of  \vater  supplied  to  boiler  by  main  feed-pump. .  degs. 

15.  Temperature  of  water  supplied  to  boiler  from  various  other 

sources degs, 


612  WATER-POWER. 

FEED-WATER. 

16.  Weight  of  water  supplied  to  boiler  by  main  feed-pump Ibs. 

17.  Weight  of  water  supplied  to  boiler  from  various  other  sources.  Ibs. 

18.  Total  weight  of  feed-water  supplied  from  all  sources Ibs. 

PRESSURES. 

19.  Boiler  pressure  indicated  by  gauge Ibs. 

20.  Pressure  indicated  by  gauge  on  force  main Ibs. 

21 .  Vacuum  indicated  by  gauge  on  suction  main ins. 

22.  Pressure  corresponding  to  vacuum  given  in  preceding  line Ibs. 

'.'3.  Vertical  distance  between  the  centres  of  the  two  gauges ins. 

-'4.  Pressure  equivalent  to  distance  between  the  two  gauges ; Ibs. 

MISCELLANEOUS  DATA. 

25.  Duration  of  trial  hrs. 

20.  Total  number  of  single  strokes  during  trial 

27.  Percentage  of  moisture  in  steam  supplied  to  engine,  or  number 

of  degrees  of  superheating %  or  deg. 

28.  Total  leakage  of  pump  during  trial,  determined  from  results  of 

leakage  test Ibs. 

29.  Mean  effective  pressure,  measured  from  diagrams  taken  from 

steam-cylinders   i M.E.P. 

PRINCIPAL    RESULTS. 

30.  Duty ft.  Ibs. 

31.  Percentage  of  leakage . .  % 

32.  Capacity gals. 

33.  Percentage  of  total  friction % 

ADDITIONAL  RESULTS. 

34.  Number  of  double  strokes  of  steam-piston  per  minute    

35.  Indicated  horse-power  developed  by  the  various  steam-cylinders  I.H.P. 

36.  Feed- water  consumed  by  the  plant  per  hour Ibs. 

37.  Feed-water  consumed  by  the  plant  per  indicated  horse-power 

per  hour,  corrected  for  moisture  in  steam Ibs. 

38.  Number  of  heat  units  consumed  per  indicated   horse-power 

per  hour B.T.U, 

39.  Number  of  heat  units  consumed  per  indicated  horse-power 

per  minute B.T,U. 

40.  Steam  accounted  for  by  indicator  at  cut-off  and  release  in  the 

various  steam-cylinders Ibs. 

41.  Proportion  which  steam  accounted  for  by  indicator  bears  to 

the  feed-water  consumption 

42.  Number  of  double  strokes  of  pump  per  minute 

43.  Mean  effective  pressure,  measured  from  pump  diagrams M.E.P. 

44.  Indicated  horse-power  exerted  in  pump-cylinders I.H.P. 

45.  Work  done  (or  duty)  per  100  Ibs.  of  coal  ft.  Ibs. 

SAMPLE   DIAGRAM  TAKEN  FROM   STEAM-CYLINDERS. 

(Also,  if  possible,  full  measurement  of  the  diagrams,  embracing  pressures 
at  the  initial  point,  cut  off,  release,  and  compression  ;  also  back  pressure^ 
and  the  proportions  of  the  stroke  completed  at  the  various  points  noted.) 

SAMPLE   DIAGRAM  TAKEN  FROM  PUMP-CYLINDERS. 

These  are  not  necessary  to  the  main  object,  but  it  is  desirable  to  give 
them. 

DATA  AND   RESULTS  OF  BOILER  TEST. 

(In  accordance  with  the  scheme  recommended  by  the  Boiler-test  Com- 
mittee of  the  Society.) 

VACUUM  PUMPS— AIR-L.IFT  PUMP. 

Xlie  Pulsometer.— In  the  pulsometer  the  water  is  raised  by  suction 
into  the  pump-chamber  by  the  condensation  of  steam  within  it,  and  is  then 
forced  into  the  delivery-pipe  by  the  pressure  of  a  new  quantity  of  steam  on 
the  surface  of  the  water.  Two  chambers  are  used  which  work  alternately, 
one  raising  while  the  other  is  discharging. 

Test  of  a  Pulsometer. — A  test  of  a  pulsometer  is  described  by  De  Volspn 
Wood  in  Trans.  A.  S.  M.  E.  xiii.  It  had  a  3^-inch  suction-pipe,' stood  40  in. 
hiy;h.  and  weighed  695  Ibs. 

The  steam-pipe  was  1  inch  in  diameter.    A  throttle  was  placed  about 2  fee' 


VACUUM   PUMPS — AIR-LIFT   PUMP. 


613 


from  the  pump,  and  pressure  gauges  placed  on  both  sides  of  the  throttle, 
and  a  mercury  well  and  thermometer  placed  beyond  the  throttle.  The  wire 
drawing  due  to  throttling  caused  superheating. 

The  pounds  of  steam  used  were  computed  from  the  increase  of  the  tern 
perature  of  the  water  in  passing  through  the  pump. 
Pounds  of  steam  X  loss  of  heat  =  Ibs.  of  water  sucked  in  X  increase  of  temp. 

Tha  loss  of  heat  in  a  pound  of  steam  is  the  total  heat  in  a  pound  of  satu- 
rated steam  as  found  from  "steam  tables  "  for  the  given  pressure,  plus  the 
heat  of  superheating,  minus  the  temperature  of  the  discharged  water  ;  or 

Ibs.  water  X  increase  of  temp. 
Pounds  of  steam  =  — 

a.  —  U.4bt  —  J. . 

The  results  for  the  four  tests  are  given  in  the  following  table  : 


Data  and  Results. 


Number  of  Test. 


1 

2 

3 

4 

Strokes  per  minute  

71 

60 

57 

64 

Steam  press.  in  pipe  before  throttl'g 
Steam  press,  in  pipe  after  throttPg 
Steam  temp,  after  throttling,deg.F. 
Steam  am'nt  of  superheat'g.deg.F. 
Steam  used  as  det'd  from  temp.,  Ibs. 
Water  pumped  Ibs 

114 

19 
270.4 
3.1 
1617 
404  786 

110 
30 

277 
3.4 
931 
186  362 

127 
43.8 
309.0 
17.4 

1518 
228  425 

104.3 
26.1 
270.1 
1.4 
1019.9 
248  053 

Water  temp.  before  entering  pump, 
Water  temp    rise  of 

75.15 

80.6 
5  5 

76.3 
749 

70.25 
4  55 

Water  head  by  gauge  on  lift,  ft  
Water  head  by  gauge  on  suction... 
Water  head  by  gauge,  total  (H)  
Water  head  by  measure,  total  (h) 
Coeff.  of  friction  of  plant  (h)  -f-  (H) 
Efficiency  of  pulsometer  ... 
Effic.  of  plant  exclusive  of  boiler.  .  . 
Effic.  of  plant  if  that  of  boiler  be  0.7 
Duty,if  1  Ib.  evaporates  10  Ibs.  water 

29.90 
12.26 
42.16 
32.8 
0.777 
0.012 
0.0093 
0.0065 
10,511,400 

54.05 
12.26 
66.31 
57.80 
0.877 
0.0155 
0.0136 
0.0095 
13,391,000 

54.05 
19.67 
73.72 
66.6 
0.911 
0.0126 
0.0115 
0.0080 
11.059,000 

29.90 
19.67 
49.57 
41.60 
0.839 
0.0138 
0  0116 
0.0081 
12.036,300 

Of  the  two  tests  having  the  highest  lift  (54.05  ft.),  that  was  more  efficient 
which  had  the  smaller  suction  (12.26  ft.),  and  this  was  also  the  most  efficient 
of  the  four  tests.  But,  on  the  other  hand,  the  other  two  tests  having  the 
same  lift  (J29.9  ft.),  that  was  the  more  efficient  which  had  the  greater  suction 
(19.67),  so  that  no  law  in  this  regard  was  established.  The  pressures  used, 
19,  30,  43.8,  26.1,  follow  the  order  of  magnitude  of  the  total  heads,  but  are 
not  proportional  thereto.  No  attempt  was  made  to  determine  what  press- 
ure would  give  the  best  efficiency  for  any  particular  head.  The  pressure  used 
was  intrusted  to  a  practical  runner,  and  he  judged  that  when  the  pump  was 
running  regularly  and  well,  the  pressure  then  existing  was  the  proper  one. 
It  is  peculiar  that,  in  the  first  test,  a  pressure  of  19  Ibs.  of  steam  should  pro- 
duce a  greater  number  of  strokes  and  pump  over  50£  more  water  than  26.1 
Ibs..  the  lift  being  the  same,  as  in  the  fourth  experiment. 

Ciias.  E.  Emery  in  discussion  of  Prof.  Wood's  paper  says,  referring  to 
tests  made  by  himself  and  others  at  the  Centennial  Exhibition  in  1876  (see 
Rerjort  of  the  Judges,  Group  xx.),  that  a  vacuum-pump  tested  by  him  in 
1871  gave  a  duty  of  4.7  millions;  one  tested  by  J.  F.  Flagg,  at  the  Cincinnati 
Exposition  in  1875,  gave  a  maximum  duty  of  3.25  millions.  Several  vacuum 
and  small  steam-pumps,  compared  later  on  the  same  basis  were  reported 
to  have  given  duties  of  10  to  11  millions,  the  steam-pumps  doing  no  better 
than  the  vacuum-pumps.  Injectors,  when  used  for  lifting  water  not  re- 
quired to  be  heated,  have  an  efficiency  of  2  to  5  millions;  vacuum-pumps 
vary  generally  between  3  and  10;  small  steam-pumps  between  8  and  15  ; 
larger  steam-pumps,  between  15  and  30,  and  pumping-engines  between  30 
and  140  millions. 

A  very  high  record  of  test  of  a  pulsometer  is  given  in  Eag'g,  Nov.  24, 1893, 
p.  639,  viz.  :  Height  of  suction  11.27  ft.  ;  total  height  of  lift,'  102.6  ft.  ;  hori- 
zontal length  of  delivery-pipe,  118  ft.  ;  quantity  delivered  per  hour,  26,188 
British  gallons.  Weight  of  steam  used  per  H.  P.  per  hour,  92.76  Ibs. ;  work 


614  WATEK-POWER. 

done  per  pound  of  steam  21,345  foot-pounds,  equal  to  a  duty  of  21,345,000 
foot-pounds  pe  -  100  Ibs.  of  coal,  if  10  Ibs  of  steam  were  generated  per 
pound  of  coal. 

Xlie  Jet-pump. — This  machine  works  by  means  of  the  tendency  of  a 
stream  or  jet  of  fluid  to  drive  or  carry  contiguous  particles  of  fluid  along 
with  it.  The  water-jet  pump,  in  its  present  form,  was  invented  by  Prof. 
James  Thomson,  and  first  described  in  1852.  In  some  experiments  on  a 
small  scale  as  to  the  efficiency  of  the  jet-pump,  the  greatest  efficiency  was 
found  to  take  place  when  the  depth  from  which  the  water  was  drawn  by  the 
suction-pipe  was  about  nine  tenths  of  the  height  from  which  the  water  fell 
to  form  the  jet ;  the  flow  up  the  suction-pipe  being  in  that  case  about  one 
fifth  of  that  of  the  jer,  and  the  efficiency,  consequently,  9/10  x  1/5  =  0.18. 
This  is  but  a  low  efficiency;  but  it  is  probable  that  it  may  be  increased  by 
improvements  in  proportions  of  the  machine.  (Rankine,  S.  E.) 

Tlie  Injector  when  used  as  a  pump  has  a  very  low  efficiency.  (See 
Injector-,  under  Steam-boilers.) 

Air-lift  Pump.— The  air-lift  pump  consists  of  a  vertical  water-pipe 
with  its  lower  end  submerged  in  a  well,  and  a  smaller  pipe  delivering  air 
into  it  at  the  bottom.  The  rising  column  in  the  pipe  consists  of  air  mingled 
with  water,  the  air  being  in  bubbles  of  various  sizes,  and  is  therefore  lighter 
£han  a  column  of  water  of  the  same  height;  consequently  the  water  in  the 
pipe  is  raised  above  the  level  of  the  surrounding  water.  This  method  of 
raising  water  was  proposed  as  early  as  1797,  by  Loescher,  of  Freiberg,  and 
was  mentioned  by  Collon  in  lectures  in  Paris  in  1870,  but  its  first  practical 
application  probably  was  by  Werner  Siemens  in  Berlin  in  1885.  Dr.  J.  G. 
Pohle  experimented  on  the  principle  in  California  in  1886,  and  U.  S.  patents 
on  apparatus  involving  it  were  granted  to  Pohle  and  Hill  in  the  same  year. 
A  paper  describing  tests  of  the  air-lift  pump  made  by  Randall,  Browne  and 
Behr  was  read  before  the  Technical  Society  of  the  Pacific  Coast  in  Feb.  1890 

The  diameter  of  the  pump-column  was  3  in.,  of  the  air-pipe  0.9  in.,  and 
of  the  air-discharge  nozzle  %  in.  The  air-pipe  had  four  sharp  bends  and  a 
length  of  35  ft.  plus  the  depth  of  submersion. 

The  water  was  pumped  from  a  closed  pipe-well  (55  ft.  deep  and  10  in.  ir. 
diameter).  The  efficiency  of  the  pump  was  based  on  the  least  work  theo- 
retically  required  to  compress  the  air  and  deliver  it  to  the  receiver.  If  the 
efficiency  of  the  compressor  be  taken  at  70$,  the  efficiency  of  the  pump  and 
compressor  together  would  be  70#  of  the  efficiency  found  for  the  pump 
alone. 

For  a  given  submersion  (h)  and  lift  (//),  the  ratio  of  the  two  being  kept 
within  reasonable  limits,  (// )  being  not  much  greater  than  (h),  the  efficiency 
was  greatest  when  the  pressure  in  the  receiver  did  not  greatly  exceed  the 
head  due  to  the  submersion.  The  smaller  the  ratio  H  -:-  h,  the  higher  wap 
the  efficiency. 

The  pump,  as  erected,  showed  the  following  efficiencies  : 

For  H+h=        0.5  1.0  1.5  2.0 

Efficiency    =        50^  40#  30#  25g 

The  fact  that  there  are  absolutely  no  moving  parts  makes  the  pi«mp 
especially  fitted  for  handling  dirty  or  gritty  water,  sewage,  mine  water, 
and  acid  or  alkali  solutions  in  chemical  or  metallurgical  works. 

In  Newark,  N.  J.,  pumps  of  this  type  are  at  work  having  a  total  capacity 
of  1,000,000  gallons  daily,  lifting  water  from  three  8-in.  artesian  wells.  The 
Newark  Chemical  Works  use  an  air-lift  pump  to  raise  sulphuric  acid  of  1.753° 
gravity.  The  Colorado  Central  Consolidated  Mining  Co.,  in  one  of  its  mines 
at  Georgetown,  Colo.,  lifts  water  in  one  case  250  ft.,  using  a  series  of  lifts. 

For  a  full  account  of  the  theory  of  the  pump,  and  details  of  the  tests 
above  referred  to,  see  Eng'g  News,  June  8,  1893. 

THE:  HYDRAULIC  RAM. 

Efficiency.— The  hydraulic  ram  is  used  where  a  considerable  flow  of 
water  with  a  moderate  fall  is  available,  to  raise  a  small  portion  of  that  flow 
to  a  height  exceeding  that  of  the  fall.  The  following  are  rules  given  by 
Eytelwein  as  the  results  of  his  experiments  (from  Rankine): 

Let  Q  be  the  whole  supply  of  water  in  cubic  feet  per  second,  of  which  q  ia 
lifted  to  the  height  h  above' the  pond,  and  Q  —  q  runs  to  waste  at  the  depth 
H  below  the  pond;  L,  the  length  of  the  supply-pipe,  from  the  pond  to  the 
waste-clack  ;  D,  its  diameter  in  feet;  then 

D-   1/0.630;    L=  H-f  h  +  ^X2feet; 
±± 

Volume  of  air  vessel  =  volume  of  feed  pipe; 


THE  HYDRAULIC  HAM. 


615 


:    =    1.18-0.8  |/i 


—  when  —  does  not  exceed  20. 
JdL  a. 


-  (  1  +  TTTff  )  nearly,  when  — .  does  not  exceed  12. 
\         10./i  '  H 


D'Aubuisson  gives 


=  1.42 -.28 


/•£• 

y  H' 


Clark,  using  five  sixths  of  the  values  given  by  D'Aubuisson's  formula, privets: 
Ratio  of  lift  to  fall.   ...    4      6      8    10    12    14    16    18    20    22    24    26 
Efficiency  per  cent. ...     72    61    52    44    37    31    25    19    14     9      4      0 

Prof.  R.  C.  Carpenter  (Eng'g  Mechanics,  1894)  reports  the  results  of  four 
tests  of  a  ram  constructed  by  Rumsey  &  Co.,  Seneca  Falls.  The  ram  was 
fitted  for  pipe  connection  for  l^-inch  supply  and  ^-inch  discharge.  The 
supply-pipe  used  was  1^  inches  in  diameter,  about  50  feet  long,  with  3  elbows, 
so  that  it  was  equivalent  to  about '05  feet  of  straight  pipe,  so  far  as  resist- 
ance is  concerned.  Each  run  was  made  with  a  different  stroke  for  the  waste,, 
or  clack-valve,  the  supply  and  delivery  head  being  constant;  the  oi.ject  of 
the  experiment  was  to  find  that  stroke  of  clack-valve  which  would  give  the 
highest  efficiency. 


Length  of  stroke  per  cent  

100 

80 

60 

46 

52 

56 

61 

66 

Supply  head   feet  of  water        

5.67 

5.77 

5.58 

5.65 

Delivery  head   feet  of  water 

19.75 

19  75 

19.75 

19.75 

Total  water  pumped  pounds  •. 

297 

296 

301 

297.5 

Total  water  supplied,  pounds  

1615 

1567 

1518 

1455.5 

Efficiency  per  cent                                • 

64  9 

66 

74.9 

70 

The  efficiency,  74.9,  the  highest  realized,  was  obtained  when  the  clack-valve 
travelled  a  distance  equal  to  60$  of  its  full  stroke,  the  full  travel  being  15/16 
of  one  inch. 

Quantity  of  Water  Delivered  by  the  Hydraulic   Ram. 

(Chad wick  Lead  Works.)— From  80  to  100  feet  conveyance,  one  seventh  of 
supply  from  spring  can  be  discharged  at  an  elevation  five  times  as  high  as 
the  fall  to  supply  the  ram;  or,  one  fourteenth  can  be  raided  and  discharged 
say  ten  times  as  high  as  the  fall  applied. 

Water  can  be  conveyed  by  a  ram  3000  feet,  and  elevated  200  feet.  The 
drive-pipe  is  from  25  to  50  feet  long. 

The  following  table  gives  the  capacity  of  several  sizes  of  rams,  the  dimen- 
sions of  the  pipes  to  be  used,  and  the  size  of  the  spring  or  brook  to  which 
they  are  adapted: 


Size  of 
Ram. 

Quantity  of  Water 
Furnished  per 
Min.  by  the  Spring 
or  Brook  to  which 
the  Ram  is 
Adapted. 

Caliber  of 
Pipes. 

Weight  of  Pipe  (Lead),  if  Wrought 
Iron,  then  of  Ordinary  Weight. 

<D 
£ 

P 

Discharge. 

Drive-pipe 
for  head 
or  fall  not 
over  10  ft. 

Discharge- 
pipe  for  not 
over  50  ft. 
rise. 

Discharge- 
pipe  for 
over  50    ft. 
and  not  ex- 
ceeding 
100  ft.  in 
height. 

No.  2 
3 
4 
5 
6 
7 
10 

Gals,  per  min. 
%  to    2 

J*         ! 
6           14 
12           25 
20           40 
25            75 

inch. 

H 

I* 
| 

inch. 

1  4 

¥ 

per  foot. 
2  IDS. 
3    " 
5    " 
8    " 
13    " 
13    " 
21    " 

per  foot. 
10  ozs. 
12    " 
12    " 
lib.  4    " 
2  " 

3   u 

~   K 

per  foot, 
lib. 
1     '  4  ozs. 
1    '  4  ozs 

2    * 
3    ' 
4    ' 

8    * 

616  WATER-POWER. 

HYDRA  ITLir-PRKSSURIi:  TRANSMISSION. 

Water  under  high  pressure  (700  to  2000  Ibs.  per  square  inch  and  upwards) 
affords  a  very  satisfactory  method  of  transmitting  power  to  a  distance, 
especially  for  the  movement  of  heavy  loads  at  small  velocities,  as  by  cranes 
and  elevators.  The  system  consists  usually  of  one  or  more  pumps  capable 
of  developing  the  required  pressure;  accumulators,  which  are  vertical  cylin- 
ders with  heavily-weighted  plungers  passing  through  stuffing-boxes  in  the 
upper  end,  hy  which  a  quantity  of  water  may  be  accumulated  at  the  pres- 
sure to  which  the  plunger  "is  weighted  ;  the  distributing-pipes;  and  the  presses, 
cranes,  or  other  machinery  to  oe  operated. 

The  earliest  important  use  of  hydraulic  pressure  probably  was  in  the 
Bramah  hydraulic  press,  patented  in  1796.  Sir  W.  G.  Armstrong  in  1846  was 
one  of  the  pioneers  in  the  adaptation  of  the  hydraulic  system  to  cranes.  The 
use  of  the  accumulator  by  Armstrong  led  to  the  extended  use  of  hydraulic 
machinery.  Recent  developments  and  applications  of  the  system  are  largely 
due  to  Ralph  Tweddell,  of  London,  and  Sir  Joseph  VVhitvvorth.  Sir  Henry 
Bessemer,  in  his  patent  of  May  13,  1856,  No.  1292,  first  suggested  the  use  of 
hydraulic  pressure  for  compressing  steel  ingots  while  in  the  fiuid  state. 

The  Gross  Amount  ot"  Energy  of  the  water  under  pressure  stored 
in  the  accumulator,  measured  in  foot-pounds,  is  its  volume  in  cubic  feet  X 
its  pressure  in  pounds  per  square  foot.  The  horse-power  of  a  given  quantity 


steadily  flowing  is  H.P.  =        ~  =  .26l8pQ,  in  which  Q  is  the  quantity  flowing 

550 
in  cubic  feet  per  second  and  p  the  pressure  in  pounds  per  square  inch. 

The  loss  of  energy  due  to  velocity  of  flow  in  the  pipe  is  calculated  as  fol- 
lows (R.  G.  Blaine,  Eng^g,  May  22  and  June  5,  1891): 

According  to  D'Arcy,  every  pound  of  water  loses  ——  times  its  kinetic 

energy,  or  energy  due  to  its  velocity,  in   passing  along  a  straight  pipe  L  feet 
in  length  and  D  feet  diameter,  where  A  is  a  variable  coefficient.    For  clean 

cast-iron  pipes  it  may  be  taken  as  A  =  .005  (l  +  r^j),  or  for  diameter  in 
inches  =  d. 

d=     l£       1        2          3  456  7  8  9         10        12 

A  =  .015     .01  .0075  .00667  .00625  .006  .00583  .00571    .00563  .00556  .0055  .00542 

The  loss  of   energy  per   minute  is  60  X  62.36Q  X  —=r-  5-,  and  the  horse- 

power wasted  in  the  pipe  is  W  =  —   '-  —  3      '       ,  in  which  A  varies  with  the 

diameter  as  above,    p  =  pressure  at  entrance  in  pounds  per  square  inch. 
Values  of  .6363A  for  different  diameters  of  pipe  in  inches  are: 
d  =    Yz         1          2          3          4  5          6          7          8          9          10         12 

.00954  .00636  .00477  .00424  .00398  .00382  .00371  .00363  .00358  .00353  .00350  .00345 

Efficiency  of  Hydraulic  Apparatus.—  The  useful  effect  of  a 
direct  hydraulic  plunger  or  ram  is  usually  taken  at  93$.  The  following  is 
given  as  the  efficiency  of  a  rain  with  chain-and-pulley  multiplying  gear 
properly  proportioned  and  well  lubricated: 

Multiplying....  2  to  1    4  to  1    6  to  1    8  to  1    lOtol    12  to  1     14  to  1      16tol 
Efficiency  $....      80          76          72          67  63  59  54  50 

With  large  sheaves,  small  steel  pins,  and  wire  rope  for  multiplying  gear 
the  efficiency  has  been  found  as  high  as  66$  fora  multiplication  of  20  to  1. 

Henry  Adams  gives  the  following  formula  for  effective  pressure  in  cranes 
and  hoists: 

P  =  accumulator  pressure  in  pounds  per  square  inch; 

m  =  ratio  of  multiplying  power; 

E  =  effective  pressure  in  pounds  per  square  inch,  including  all  allowances 
for  friction  ; 

E  =  P(.84  -  .02m). 

J.  E.  Tuit  (Eng^g,  June  15,  1888)  describes  some  experiments  on  the  fric- 
tion of  hydraulic  jacks  from  3*4  to  13%-inch  diameter,  fitted  with  cupped 
leather  packings.  The  friction  loss  varied  from  56$  to  18.8$  according  to 
the  condition  of  the  leather,  the  distribution  of  the  load  on  the  ram,  etc. 
The  friction  increased  considerably  with  eccentric  loads.  With  hemp  pack- 
ing a  plunger,  14  inch  diameter,  showed  a,  friction  loss  of  from  11.4$  to  3.4$T 
the  load  being  central,  and  from  15.0$  lo  7.6$  with  eccentric  load,  the  per- 
centage of  loss  decreasing  in  both  cases  with  increase  of  load. 


HYDRAULIC-PRESSURE  TRANSMISSION".  617 

Thickness  of  Hydraulic  Cylinders.— From  a  table  used  by  Sir 
W.  G.  Armstrong  we  take  the  following,  for  cast-iron  cylinders,  for  an  in- 
terior pressure  of  1000  Ibs,  per  square  inch: 

Diam.  of  cylinder,  inches..      2         4         6         8        10        12       16      20      24 
Thickness,"  inches 0.832  1.146  1.552  1.875  2.222  2.578  3.19  3.69  4.11 

For  any  other  pressure  multiply  by  the  ratio  of  that  pressure  to  1000. 
These  figures  correspond  nearly  to  the  formula  t  =  0.175d  -f-  0.48,  in  which 
t  =  thickness  and  d  —  diameter  in  inches,  up  to  16  inches  diameter,  but  for 
20  inches  diameter  the  addition  0.48  is  reduced  to  0.19  and  at  24  inches  it 
disappears.  For  formulae  for  thick  cylinders  see  page  287,  ante. 

Cast  iron  should  not  be  used  for  pressures  exceeding  2000  Ibs.  per  square 
inch.  For  higher  pressures  steel  castings  or  forged  steel  should  be  used. 
For  working  pressures  of  750  Ibs.  per  square  inch  the  test  pressure  should 
be  2500  Ibs.  per  square  inch,  and  for  1500  Ibs.  the  test  pressure  should  not  be 
less  than  3500  Ibs. 

Speed  of  Hoisting  by  Hydraulic  Pressure.— The  maximum 
allowable  speed  for  warehouse  cranes  is  6  feet  per  second;  for  platform 
cranes  4  feet  per  second;  for  passenger  and  wagon  hoists,  heavy  loads,  2 
feet  per  second.  The  maximum  speed  under  any  circumstances  should 
never  exceed  10  feet  per  second. 

The  Speed  of  Water  Through  Valves  should  never  be  greater 
than  100  feet  per  second. 

Speed  of  Water  Through  Pipes.— Experiments  on  water  at  1600 
Ibs.  pressure  per  square  inch  flowing  into  a  Hanging-machine  ram,  20-inch 
diameter,  through  a  ^-inch  pipe  contracted  at  one  point  to  24-inch,  ffave  a 
velocity  of  114  feet  per  second  in  the  pipe,  and  456  feet  at  the  reduced  sec- 
tion. Through  a  i^-inch  pipe  reduced  to  %-inch  at  one  point  the  velocity 
was  213  feet  per  second  in  the  pipe  and  381  feet  at  the  reduced  section  In  a 
J^-inch  pipe  without  contraction  the  velocity  was  355  feet  per  second. 

For  many  of  the  above  notes  the  author  is  indebted  to  Mr.  John  Platt, 
consulting  engineer,  of  New  York. 

High-pressure  Hydraulic  Presses  in  Iron-works  are  de- 
scribed by  R.  M.  Daelen,  of  Germany,  in  Trans.  A.  I.  M.  E.  1892.  The  fol- 
lowing distinct  arrangements  used  in  different  systems  of  high-pressure 
hydraulic  work  are  discussed  and  illustrated: 

1.  Steam-pump,  with  fly-wheel  and  accumulator. 

2.  Steam  pump,  without  fly-wheel  and  with  accumulator. 

3.  Steam-pump,  without  fly-wheel  and  without  accumulator. 

In  these  three  systems  the  valve-motion  of  the  working  press  is  operated 
in  the  high-pressure  column.  This  is  avoided  in  the  following: 

4.  Single-acting  steam-intensifier  without  accumulator. 

5.  Steam-pump  with  fly-wheel,  without  accumulator  and  with  pipe-circuit. 

6.  Steam-pump  with  fly-wheel,  without  accumulator  and  without  pipe- 
circuit. 

The  disadvantages  of  accumulators  are  thus  stated :  The  weighted  plungers 
which  formerly  served  in  most  cases  as  accumulators,  cause  violent  shocks 
in  the  pipe  line  when  changes  take  place  in  the  movement  of  the  water, 
so  that  in  many  places,  in  order  to  avoid  bursting  from  this  cause,  the  pipes 
are  made  exclusively  of  forged  and  bored  steel.  The  seats  and  cones  of  the 
metallic  valves  are  cut  by  the  water  (at  high  speed),  and  in  such  cases  only 
the  most  careful  maintenance  can  prevent  great  losses  of  power. 

Hydraulic  Power  in  London.— The  general  principle  involved 
is  pumping  water  into  mains  laid  in  the  streets,  from  which  service-pipes 
are  carried  into  the  houses  to  work  lifts  or  three-cylinder  motors  when 
rotatory  power  is  required.  In  some  cases  a  small  Pelton  wheel  has  been 
tried,  working  under  a  pressure  of  over  700  Ibs.  on  the  square  inch.  Over  55 
miles  of  hydraulic  mains  are  at  present  laid  (1892). 

The  reservoir  of  power  consists  of  capacious  accumulators,  loaded  to  a 
pressure  of  800  Ibs.  per  square  inch,  thus  producing  the  same  effect  as  if 
large  supply-tanks  were  placed  at  1700  feet  above  the  street-level.  The 
water  is  taken  from  the  Thames  or  from  wells,  and  all  sediment  is  removed 
therefrom  by  filtration  before  it  reaches  the  main  engine-pumps. 

There  are  over  1750  machines  at  work,  and  the  supply  is  about  6,500,000 
gallons  per  week. 

It  is  essential  that  the  water  used  should  be  clean.  The  storage-tank  ex- 
tends over  the  whole  boiler-house  and  coal-store.  The  tank  is  divided,  and 
a  certain  amount  of  mud  is  deposited  here.  It  then  passes  through  the  sur- 
face condenser  of  the  engines,  and  it  is  turned  into  a  set  of  filters,  eight  in 
number.  The  body  of  the  filter  is  a  cast-iron  cylinder,  containing  a  layer  of 


618  WATER-POWER. 

granular  filtering  material  resting  upon  a  false  bottom;  under  this  is  the  dis- 
tributing arrangement,  affording  passage  for  the  air,  and  under  this  the  real 
bottom  of  the  tank.  The  dirty  water  is  supplied  to  the  filters  from  an  over- 
head tank.  After  passing  through  the  filters  the  clean  effluent  is  pumped 
into  the  clean-water  tank,  from  which  the  pum ping-engines  derive  their 
supply.  The  cleaning  of  the  filters,  which  is  done  at  intervals  of  24  hours,  is 
effected  so  thoroughly  in  situ  that  the  filtering  material  never  requires  to  be 
removed. 

The  engine-house  contains  six  sets  of  triple-expansion  engines.  The 
cylinders  are  15-inch,  22-inch,  36-inch  X  24-inch.  Each  cylinder  drives  a 
single  plunger-pump  with  a  5-inch  ram,  secured  directly  to  the  cross-head, 
the  connecting-rod  being  double  to  clear  the  pump.  The  boiler-pressure  is 
150  Ibs.  on  the  square  inch.  Each  pump  will  deliver  300  gallons  of  water  per 
minute  under  a  pressure  of  800  Ibs.  to  the  square  inch,  the  engines  making 
about  61  revolutions  per  minute.  This  is  a  high  velocity,  considering  the 
heavy  pressure;  but  the  valves  work  silently  and  without  perceptible  shock. 

The  consumption  of  steam  is  14.1  pounds  per  horse  per  hour. 

The  water  delivered  from  the  main  pumps  passes  into  the  accumulators. 
The  rams  are  20  inches  in  diameter,  and  have  a  stroke  of  23  feet.  They  are 
each  loaded  with  110  tons  of  slag,  contained  in  a  wrought-iron  cylindrical 
box  suspended  from  a  cross-head  on  the  top  of  the  ram. 

One  of  the  accumulators  is  loaded  a  little  more  heavily  than  the  other,  so 
that  they  rise  and  fall  successively;  the  more  heavily  loaded  actuates  a  stop- 
valve  on  the  main  steam-pipe.  If  the  engines  supply  more  water  than  is 
wanted,  the  lighter  of  the  two  rams  first  rises  as  far  as  it  can  go ;  the  other 
then  ascends,  and  when  it  has  nearly  reached  the  top,  shuts  off  steam  and 
checks  the  supply  of  water  automatically. 

The  mains  in  the  public  streets  are  so  constructed  and  laid  as  to  be  per- 
fectly trustworthy  and  free  from  leakage. 

Every  pipe  and  valve  used  throughout  the  system  is  tested  to  2500  Ibs.  per 
square  inch  before  being  placed  on  the  ground  and  again  tested  to  a  reduced 
pressure  in  the  trenches  to  insure  the  perfect  tightness  of  the  joints.  The 
jointing  material  used  is  gutta-percha. 

The  average  rate  obtained  by  the  company  is  about  3  shillings  per  thou- 
sa  nd  gallons.  The  principal  use  of  the  power  is  for  intermittent  work  in  cases 
where  direct  pressure  can  be  employed,  as,  for  instance,  passenger  elevators, 
cranes,  presses,  warehouse  hoists,  etc. 

An  important  use  of  the  hydraulic  power  is  its  application  to  the  extin- 
guishing of  fire  by  means  of  Greathead's  injector  hydrant.  By  the  use  of 
these  hydrants  a  continuous  fire-engine  is  available. 

Hydraulic  Riveting-machines.— Hydraulic  riveting  was  intro- 
duced in  England  by  Mr.  R.  H.  Tweddell.  Fixed  riveters  were  first  used  about 
1868.  Portable  riveting-machines  were  introduced  in  1872. 

The  rivetmg  of  the  large  steel  plates  in  the  Forth  Bridge  was  done  by  small 
portable  machines  working  with  a  pressure  of  1000  Ibs.  per  square  inch.  In 
exceptional  cases  3  tons  per  inch  was  used.  (Proc.  Inst.  M.  E.,  May,  1889.) 

An  application  of  hydraulic  pressure  invented  by  Andrew  Higginson,  of 
Liverpool,  dispenses  with  the  necessity  of  accumulators.  It  consists  of  a 
three-throw  pump  driven  by  shafting  or  worked  by  steam,  and  depends 
partially  upon  the  work  accumulated  in  a  heavy  fly-wheel.  The  water  in  its 
passage  from  the  pumps  and  back  to  them  is  in  constant  circulation  at  a 
very  feeble  pressure,  requiring  a  minimum  of  power  to  preserve  the  tube  of 
water  ready  for  action  at  the  desired  moment,  when  by  the  use  ot  a  tap  the 
current  is  stopped  from  going  back  to  the  pumps,  and  is  thrown  upon  the 
piston  of  the  tool  to  be  set  in  motion.  The  water  is  now  confined,  and  the 
driving-belt  or  steam-engine,  supplemented  by  the  momentum  of  the  heavy 
fly-wheel,  is  employed  in  closing  up  the  rivet,  or  bending  or  forging  the  ob- 
ject subjected  to  its  operation. 

Hydraulic  Forging.— In  the  production  of  heavy  forcings  from 
cast  ingots  of  mild  steel  it  is  essential  that  the  mass  of  metal  should  be 
operated  on  as  equally  as  possible  throughout  its  entire  thickness.  When 
employing  a  steam-hammer  for  this  purpose  it  has  been  found  that  the  ex- 
ternal surface  of  the  ingot  absorbs  a  large  proportion  of  the  sudden  impact 
of  the  blow,  and  that  a  comparatively  small  effect  only  is  produced  on  the 
central  portions  of  the  injrot,  owing  to  the  resistance  offered  by  the  inertia 
of  the  mass  to  the  rapid  motion  of  the  falling  hammer — a  disadvantage  that 
is  entirely  overcome  by  the  slow,  though  powerful,  compression  of  the 
hydraulic  forging- press,  which  appears  destined  to  supersede  the  steam- 
hammer  for  the  production  of  massive  steel  forgings, 


HYDRAULIC-PRESSURE  TRANSMISSION.  619 

In  the  Allen  forging-press  the  force-pump  and  the  large  or  main  cylinder 
of  the  press  are  in  direct  and  constant  communication.  There  are  no  inter- 
mediate valves  of  any  kind,  nor  has  the  pump  any  clack-valves,  but  i' 
simply  forces  its  cylinder  full  of  water  direct  into  the  cylinder  of  the  press, 
and  receives  the  same  water,  as  it  were,  back  again  on  the  return  stroke. 
Thus,  when  both  cylinders  and  the  pipe  connecting  them  are  full,  the  large 
ram  of  the  press  rises  and  falls  simultaneously  with  each  stroke  of  tht 
pump,  keeping  up  a  continuous  oscillating  motion,  the  ram,  of  course, 
travelling  the  shorter  distance,  owing  to  the  larger  capacity  of  the  press 
cylinder.  (Journal  Iron  and  Steel  Institute,  1891.  See  also  illustrated  article- 
in  '*  Modern  Mechanism,"  page  668.) 

For  a  very  complete  illustrated  account  of  the  development  of  the  hy- 
draulic forging-press,  see  a  paper  by  R.  H..Tweddell  in  Proc.  Inst.  C.  E.,  vol. 
cxvii.  1893-4. 

Hydraulic  Forging-press.— A  2000-ton  forging-press  erected  at 
the  Couillet  forges  in  Belgium  is  described  in  Eng.  and  M.  Jour.,  Nov.  25, 1893. 

The  press  is  composed  essentially  of  two  parts— the  press  itself  and  the 
compressor.  The  compressor  is  formed  of  a  vertical  steam-cylinder  and  a 
hydraulic  cylinder.  The  piston-rod  of  the  former  forms  the  piston  of  the 
latter.  The  hydraulic  piston  discharges  the  water  into  the  press  proper. 
The  distribution  is  made  by  a  cylindrical  balanced  valve;  as  soon  as  the 
pressure  is  released  the  steam-piston  falls  automatically  under  the  action  of 
gravity.  During  its  descent  the  steam  passes  to  the  other  face  of  the  piston 
to  reheat  the  cylinder,  and  finally  escapes  from  the  upper  end. 

When  steam  enters  under  the  piston  of  the  compressor-cylinder  the  pis- 
ton rises,  and  its  rod  forces  the  water  into  the  press  proper.  The  pressure 
thus  exerted  on  the  piston  of  the  latter  is  transmitted  through  a  cross-head 
to  the  forging  which  is  upon  the  anvil.  To  raise  the  cross-head  two  small 
single-acting  steam-cylinders  are  used,  their  piston-rods  being  connected  to 
the  cross-head ;  steam  acts  only  on  the  pistons  of  these  cylinders  from  below. 
The  admission  of  steam  to  the  cylinders,  which  stand  on  top  of  the  press 
frame,  is  regulated  by  the  same  lever  which  directs  the  motions  of  the  com- 
pressor. The  movement  given  to  the  dies  is  sufficient  for  all  the  ordinary 
purposes  of  forging. 

A  speed  of  30  blows  per  minute  has  been  attained.  A  double  press  on  the 
same  system,  having  two  compressors  and  giving  a  maximum  pressure  of 
6000  tons,  has  been  erected  in  the  Krupp  works,  at  Essen. 

The  A  ikeii  Intensifies  (Iron  Age,  Aug.  1890.)— The  object  of  the 
machine  is  to  increase  the  pressure  obtained  by  the  ordinary  accumulator 
which  is  necessary  to  operate  powerful  hydraulic  machines  requiring  very 
high  pressures,  without  increasing  the  pressure  carried  in  the  accumulator 
and  the  general  hydraulic  system. 

The  Aiken  Intensifier  consists  of  one  outer  stationary  cylinder  and  one 
inner  cylinder  which  moves  in  the  outer  cylinder  and  on  a  fixed  or  stationary 
hollow  plunger.  When  operated  in  connection  with  the  hydraulic  bloom- 
shear  the  method  of  working  is  as  follows:  The  inner  cylinder  having  been 
filled  with  water  and  connected  through  the  hollow  plunger  with  the  hydrau- 
lic cylinder  of  the  shear,  water  at  the  ordinary  accumulator-pressure  is  ad- 
mitted into  the  outer  cylinder,  which  being  four  times  the  sectional  area  of 
the  plunger  gives  a  pressure  in  the  inner  cylinder  and  shear  cylinder  con- 
nected therewith  of  four  times  the  accumulator-pressure— that  is,  if  the  ac- 
cumulator-pressure is  500  Ibs.  per  square  inch  the  pressure  in  the  intensifier 
will  be  2000  Ibs.  per  square  inch. 

Hydraulic  Engine  driving  an  Air-compressor  and  a 
Forging-hamnier.  (Iron  Age,  May  12,  1892.)— The  great  hammer  in 
Terni,  near  Rome,  is  one  of  the  largest  in  existence.  Its  falling  weight 
amounts  to  100  tens,  and  the  foundation  belonging  to  it  consists  of  a  block 
of  cast  iron  of  1000  tons.  The  stroke  is  16  feet  4%  inches;  the  diameter  of 
the  cylinder  6  feet  3*4  inches:  diameter  of  piston-rod  13%  inches;  total  height 
of  the  hammer,  62  feet  4  inches.  The  power  to  work  the  hammer,  as  well  as 
the  two  cranes  of  100  and  150  tons  respectively,  and  other  auxiliary  appli- 
ances belonging  to  it,  is  furnished  by  four  air-compressors  coupled  together 
and  driven  directly  by  water-pressure  engines,  by  means  of  which  the  air  is 
compressed  to  73.5  pounds  per  square  inch.  The  cylinders  of  the  water- 
pressure  engines,  which  are  provided  with  a  bronze  lining,  have  a  13^-inch 
bore.  The  stroke  is  47%  inches,  with  a  pressure  of  water  on  the  piston 
amounting  to  264.6  pounds  per  square  inch.  The  compressors  are  bored  out 
to  31}^  inches  diameter,  and  have  47%-inch  stroke.  Each  of  the  four  cylin- 
ders  requires  a  power  equal  to  280  horse-power.  The  compressed  §it  is  de» 


620  FUEL. 

livered  into  huge  reservoirs,  where  a  uniform  pressure  is  kept  up  by  means 
of  «M  suitable  ivater-cohunn. 

The  Hydraulic  Forging  Plant  at  Bethlehem,  Pa.,  is  de- 
scribed in  a  paper  by  K  W.Davenport,  read  before  the  Society  of  Naval 
Engineers  and  Marine  Architects,  1893.  It  includes  two  hydraulic  forging- 
presses  complete,  with  engines  and  pumps,  one  of  1500  and  one  of  4500  tons* 
capacity,  together  with  two  Whitworth  hydraulic  travelling  forging-cranes 
and  other  necessary  appliances  for  each  press;  and  a  complete  fluid-compres- 
sion plant,  including  a  pi-ess  of  7000  tons  capacity  and  a  125  ton  hydraulic 
travelling  crane  for  serving  it  (the  upper  and  lower  heads  of  this  press 
weighing  respectively  about  135  and  120  tons). 

A  new  forging  press  has  been  designed  by  Mr.  John  Fritz,  for  the  Bethle- 
hem Works,  of  14,000  tons  capacity,  to  be  run  by  engines  and  pumps  of  15,000 
horsepower.  The  plant  is  served  by  four  open-hearth  steel  furnaces  of  a 
united  capacity  of  120  tons  of  steel  per  heat. 

Some  References  on  Hydraulic  Transmission.— Reuleaux's 
"  Constructor  :  "1  "Hydraulic  Motors,  Turbines,  and  Pressure-engines, "  G. 
Bodmer,  London,  1889  ;  Robinson's  ''Hydraulic  Power  and  Hydraulic  Ma- 
chinery," London,  1888  ;  Colyer's  **  Hydraulic  Steam,  and  Hand-power  Lift- 
ing and  Pressing  Machinery,'1'  London,  1881.  See  also  Engineering  (London), 
Aug.  1,  1884,  p.  99,  March  i3,  1885,  p.  262;  May  22  and  June  5,  Ib91,  pp.  6J2, 
665  ;  Feb.  19,  189.',  p.  25  ;  Feb.  10,  1893,  p.  170. 

FUEL. 

Theory  of  Combustion  of  Solid  Fuel,  (From  Rankine,  some- 
what altered.) — The  ingredients  of  every  kind  of  fuel  commonly  used  may 
be  thus  classed:  (1)  Fixed  or  free  carbon,  which  is  left  in  the  form  of  char- 
coal or  coke  after  the  volatile  ingredients  of  the  fuel  have  been  distilled 
away.  These  ingredients  burn  either  wholly  in  the  solid  state  (C  to  CO2),  or 
part  in  the  solid  state  and  part  in  the  gaseous  state  (UO  -f-  O  =  CO2),  the  lat- 
ter part  being  first  dissolved  by  previously  formed  carbonic  acid  by  the  re- 
action CO2  4-  C  =  2(JO.  Carbonic  oxide,  CO,  is  produced  when  the  suppty 
of  air  to  the  fire  is  insufficient. 

(2;  Hydrocarbons,  such  as  olefiant  gas,  pitch,  tar,  naphtha,  etc.,  all  of 
which  must  pass  into  the  gaseous  state  before  being  burned. 

If  mixed  on  their  first  issuing  from  amongst  the  burning  carbon  with  a 
large  quantity  of  hot  air,  these  inflammable  gases  are  completely  burned  with 
a  transparent  blue  flame,  producing  carbonic  acid  and  steam.  When  mixed 
with  cold  air  they  are  apt  to  be  chilled  and  pass  off  unburned.  When 
raised  to  a  red  heat,  or  thereabouts,  before  being  mixed  with  a  sufficient 
quantity  of  air  for  perfect  combustion,  they  disengage  carbon  in  fine  povv 
der,  and  pass  to  the  condition  partly  of  marsh  gas,  and  partly  of  free  hydro- 
gen; and  the  higher  the  temperature,  the  greater  is  the  proportion  of  carbou 
thus  disengaged. 

If  the  disengaged  carbon  is  cooled  below  the  temperature  of  ignition  be- 
fore coming  in  contact  with  oxygen,  it  constitutes,  while  floating  in  the  gas, 
smoke,  and  when  deposited  on  solid  bodies,  soot. 

But  if  the  disengaged  carbon  is  maintained  at  the  temperature  of  ignition, 
and  supplied  with  oxygen  sufficient  for  its  combustion,  it  burns  while  float- 
ing in  the  inflammable  gas,  and  forms  red,  yellow,  or  white  flame.  The  flame 
from  fuel  is  the  larger  the  more  slowly  its  combustion  is  effected.  The 
flame  itself  is  apt  to  be  chilled  by  radiation,  as  into  the  heating  surface  of  a 
steam-boiler,  so  that  the  combustion  is  not  completed,  and  part  of  the  ga;s 
and  smoke  pass  off  unburned. 

(3)  Oxygen  or  hydrogen  either  actually  forming  water,    or  existing  in 
combination  with  the  other  constituents  in  the  proportions  which  form  water. 
Such  quantities  of  oxygen  and  hydrogen  are  to  left  be  out  of  account  in  deter- 
mining the  heat  generated  by  the  combustion.    If  the  quantity  of  water 
actually  or  virtually  present  in  each  pound  of  fuel  is  so  great  as  to  make  its 
latent  heat  of  evaporation  worth  considering,  that  heat  is  to  be  deducted 
from  the  total  heat  of  combustion  of  the  fuel. 

(4)  Nitrogen,  either  free  or  in  combination  with  othsr  constituents.    This 
substance  is  simply  inert. 

(5)  Sulphuret  of  iron,  which  exists  in  coal  and  is  detrimental,  as  tending 
to  cause  spontaneous  combustion. 

(6)  Other  mineral  compounds  of  various  kinds,  which  are  also  inert,  and 
form  the  ash  left  after  complete  combustion  of  the  fuel,  and  also  the  clinker 
or  glassy  material  produced  by  fusion  of  the  a,sh,  which  tends  to  choke  the 
grate. 


FUEL. 


621 


Total  Heat  of  Combustion  of  FuTfeli*-.  (iUHklffilST— The  follow- 
ing table  shows  the  total  heat  of  combustion  with  oxygen  of  one  pound  of 
each  of  the  substances  named  in  it,  in  British  thermal  units,  and  also  in 
Ibs.  of  water  evaporated  from  212°.  It  also  shows  the  weight  of  oxygen  re- 
quired to  combine  with  each  pound  of  the  combustible  and  the  weight  of 
air  necessary  in  order  to  supply  that  oxygen.  The  quantities  of  heat  are 
given  on  the  authority  of  MM.  Favre  and  ttilbermann. 


Combustible. 

Lbs.  Oxy- 
gen per 
Ib.  Com- 
bustible. 

Lb.  Air 

(about). 

Total  Brit- 
ish Heat- 
units. 

Evapora- 
tive Power 
from  212° 
F.,  Ibs. 

Hy  drogen  gas  

8 

36 

62032 

64  2 

Carbon  imperfectly  burned  so  as 
to  make  carbonic  oxide.. 

1H 

6 

4  400 

4  55 

Carbon  perfectly  burned  so  as  to 
make  carbonic  acid  

12 

14  500 

15  0 

Olefiant  gas,  lib  

33/7 

153/7 

21,344 

22.1 

Various  liquid  hydrocarbons,  1  Ib. 

from  21,700 

from  221*3 

Carbonic  oxide,  as  much  as  is  made 
by  the  imperfect  combustion  of 
1  11)  of  carbon,  viz.,  2^j  Ibs  

F 

, 

c 
6 

to    19,000 
10,000 

to    20 
10.45 

The  imperfect  combustion  of  carbon,  making  carbonic  oxide,  produces 
»ess  than  one  third  of  the  heat  which  is  yielded  by  the  complete  combustion. 

The  total  heat  of  combustion  of  any  compound  of  hydrogen  and  carbon 
U  nearly  the  sum  of  the  quantities  of  heat  which  the  constituents  would  pro- 
duce separately  by  their  combustion.  (Marsh-gas  is  an  exception.) 

In  computing  the  total  heat  of  combustion  of  compounds  containing  oxy- 
gen as  well  as  hydrogen  and  carbon,  the  following  principle  is  to  be 
observed  :  When  hydrogen  and  oxygen  exist  in  a  compound  in  the  proper 
proportion  to  form  water  (that  is,  by  weight  one  part  of  hydrogen  to  eight 
of  oxygen),  these  constituents  have  no  effect  on  the  total  heat  of  combus- 
tion. If  hydrogen  exists  in  a  greater  proportion,  only  the  surplus  of  hydro- 
gen above  that  which  is  required  by  the  oxygen  is  to  be  taken  into  account. 

The  following  is  a  general  formula  (Dulong's)  for  the  total  heat  of  combus- 
lion  of  any  compound  of  carbon,  hydrogen,  and  oxygen  : 

Let  C,  H,  and  O  be  the  fractions  of  one  pound  of  the  compound,  which 
consists  respectively  of  carbon,  hydrogen,  and  oxygen,  the  remainder  being 
nitrogen,  ash,  and  other  impurities.  Let  h  be  the  total  heat  of  combustion 
of  one  pound  of  the  compound  in  British  thermal  units.  Then 


h  =  14,500  J  C+4.28(ff-  ~)  [• 


The  following  table  shows  the  composition  of  those  compounds  which  are 
of  importance,  either  as  furnishing  oxygen  for  combustion,  as  entering  into 
tlie  composition,  or  as  being  produced  by  the  combustion  of  fuel  : 


Names. 

Symbol  of 
Chemical 
Composition. 

IM 

111 

I** 

Chemical 
Equivalent 
by  Weight. 

Proportions 
of  Elements 
by  Volume. 

Air  

N  77  +  O  23 

100 

N  79  -f  O  21 

Water  

H2O 

H  2   -f  O  16 

18 

H  2   -f  O 

Ammonia  

NH3 

H3   -f-N  14 

H  3    4-N 

Carbonic  oxide  

CO 

C  12  +  O  16 

28 

C  -f-  O 

COo 

C  12  +  O  32 

44 

C  4-  O2 

Olefiant  gas  

CH2 

C  12-f  H2 

14 

C  4-H2 

Marsh-gas  or  fire-damp  .   
Sulphurous  acid 

CH; 

SO2 

C12  +  H4 

S  32  4-  O  32 

16 
64 

C  -f  H4 

Sulphuretted  hydrogen  

SH2 

S  32  +  H  2 

34 

Sulphuret  of  carbon  

S2C 

S  64  +  C  12 

76 

622 


FUEL; 


Since  each  Ib.  of  C  requires  2^  Ibs.  of  O  to  burn  it  to  CO2 ,  and  air  contains 
23$  of  O,  by  weight.  &%  -4-  0.23  or  11.6  Ibs.  of  air  are  required  to  burn  1  Ib.  of  C. 

Analyses  of  Oases  of  Combustion.— The  following  are  selected 
from  a  large  number  of  analyses  of  gases  from  locomotive  boilers,  to  show 
the  range  of  composition  under  different  circumstances  (P.  H.  Dudley, 
Trans.  A.  I.  M.'E  ,  iv.  250): 


Test. 

C02 

CO 

0 

N 

1 

13.8 

2.5 

2.5 

81.6 

No  smoke  visible. 

2 

11.5 

6 

82  5 

Old  fife,  escaping  gas  white,  engine  working  hard. 

3 

8.5 

8 

83 

Fresh  fire,  much  black  gas,          " 

4 

2.3 

17.2 

80.5 

Old  fire,  damper  closed,  engine  standing  still. 

5 

5.7 

14.7 

79.6 

"      u      smoke  white,  engine  working  hard. 

G 

8.4 

i'.2 

8.4 

82 

New  fire,  engine  not  working  hard. 

7 

12 

I 

4.4 

82.6 

Smoke  black,  engine  not  working  hard. 

8 

3.4 

16.8 

76.8 

dark,  blower  on,  engine  standing  still. 

9 

6 

13.5 

81.5 

"       white,  engine  working  hard. 

In  analyses  on  the  Cleveland  and  Pittsburgh  road,  in  every  instance 
when  the  smoke  was  the  blackest,  there  was  found  the  greatest  percentage 
of  unconsumed  oxygen  in  the  product,  showing  that  something  besides  the 
mere  presence  for  oxygen  is  required  to  effect  the  combustion  of  the  volatile 
carbon  of  fuels. 

J.  C.  Hoadley  (Trans.  A  S.  M.  E.,  vi.  749)  found  as  the  mean  of  a  great 
number  of  analyses  of  flue  gases  from  a  boiler  using  anthracite  coal : 
CO2  ,  13.10  ;    CO,  0.30  ;    O,  11.94  ;    N,  74  66. 

The  loss  of  heat  due  to  burning  C  to  CO  instead  of  to  CO2  was  2.13$.  The 
surplus  oxygen  averaged  113.3$  of  the  O  required  for  the  C  of  the  fuel,  the 
average  for  different  weeks  ranging  from  88.6$  to  137$. 

Analyses  made  to  determine  the  CO  produced  by  excessively  rapid  firing 
gave  results  from  2  54$  to  4.81$  CO  and  5.12  to  8.01$  CO2  ;  the  ratio  of  C  in 
the  CO  to  total  carbon  burned  being  from  43.80$  to  48.55$,  and  the  number  of 
pounds  of  air  supplied  to  the  furnace  per  pound  of  coal  being  from  33.2  to 
19.3  Ibs.  The  loss  due  to  burning  C  to  CO  was  from  27.84$  to  30.86  of  the 
full  power  of  the  coal. 

Temperature  of  the  Fire.  (Rankine,  S.  E.,  p.  283.)— By  temper- 
ature of  the  fire  is  meant  the  temperature  of  the  products  of  combustion  at 
the  instant  that  the  combustion  is  complete.  The  elevation  of  that  temper- 
ature above  the  temperature  at  which  the  air  and  the  fuel  are  supplied  to 
the  furnace  may  be  computed  by  dividing  the  total  heat  of  combustion  of 
one  Ib.  of  fuel  by  the  weight  and  by  the  mean  specific  heat  of  the  whole 
products  of  combustion,  and  of  the  air  employed  for  their  dilution  under 
constant  pressure.  The  specific  heat  under  constant  pressure  of  these  prod 
nets  is  about  as  follows : 

Carbonic-acid  gas,  0.217 ;  steam,  0475;  nitrogen  (probably),  0.245;  air, 
0.238;  ashes,  probably  about  0.200.  Using  these  data,  the  following  results 
are  obtained  for  pure  carbon  and  for  olefiant  gas  burned,  respectively,  first, 
in  just  sufficient  air,  theoretically,  for  their  combustion,  and,  second,  when 
an  equal  amount  of  air  is  supplied  in  addition  for  dilution. 


Fuel. 

Products  undiluted. 

Products  diluted. 

Carbon. 

Olefiant 
Gas. 

Carbon. 

Olefiant 
Gas. 

Total  heat  of  combustion,  per  Ib.  .  . 
Wt  of  products  of  combustion,  Ibs. 
Their  mean  specific  heat  

14,500 
13 
0.237 

3.08 
4580° 

21,300 
16.43 
0.257 
4.22 

5050° 

14,500 
25 
<J.238 
5.94 
2440° 

21,300 
31.86 
0.248 
7.9 
2710° 

Specific  heat  X  weight 

Elevation  of  temperature,  F  

'  [The  above  calculations  are  made  on  the  assumption  that  the  specific 
heats  of  the  gases  are  constant,  but  they  probably  increase  with  the  in- 
crease of  temperature  (see  Specific  Heat),  in  which'  case  the  temperature 
v/rould  be  less  than  those  above  given.  The  temperature  would  be  further 


CLASSIFICATION   OF   FUEL. 


623 


reduced  by  the  heat  rendered  latent  by  the  conversion  into  steam  of  any 
water  present  in  the  fuel.] 
Rise   of  Temperature   in    Combustion  of   Oases.    (Eng^g, 

March  12  and  April  2,  188(5.)— It  is  found  that  the  temperatures  obtained 
by  experiment  fall  short  of  those  obtained  by  calculation.  Three  theo- 
ries have  been  given  to  account  for  this  :  1.  The  cooling  effect  of  the 
sides  of  the  containing  vessel;  2.  The  retardation  of  the  evolution  of  heat 
caused  by  dissociation;  3.  The  increase  of  the  specific  heat  of  the  gases  at 
very  high  temperatures.  The  calculated  temperatures  are  obtainable  only 
on  the  condition  that  the  gases  shall  combine  instantaneously  and  simulta- 
neously throughout  their  whole  mass.  This  condition  is  practically  impos- 
sible in  experiments.  The  gases  formed  at  the  beginning  of  an  explosion 
dilute  the  remaining  combustible  (gases  and  tend  to  retard  or  check  the 
combustion  of  the  remainder. 

CLASSIFICATION    OF    SOLID    FUELS. 

Gruner  classifies  solid  fuels  as  follows  (Eng'g  and  M^g  Jour.,  July,  1874) : 


._                                                  Ratio—     Proportion  of  Coke  or 
Name  of  Fuel.                                                    Charcoal  yielded  by 
or  O  +  N  *.         the  Drv  Pure  Fuei. 

H 

Pure  cellulose  

8 

0  28  (7 

&  0  30 

Wood  (cellulose  and  encasing  matter).  ... 
Peat  and  fossil  fuel  

7 
6  <&  5 

.30  (6 
35  % 

^    .'35 

'O.      40 

Lignite  *f  or  brown  coal 

5 

40  (? 

^    *50 

Bituminous  coals  

4  @  1 

50  (7 

h     90 

Anthracite... 

1  <&  0.75 

*90  6. 

ft.    .92 

The  bituminous  coals  he  divides  into  five  classes  as  below: 


i 

Elementary 

Propor- 

Name of  Type. 

Composition. 

Ratio  ~ 
01P+N*. 

tion  of 
Coke 
yielded 
by  Dis- 
tilla- 

Nature 
and 
Appear, 
ance  of 
Coke. 

a 

H. 

O. 

H 

tion. 

1.  :~jong  flaming  dry  [ 
coaH, 

75@80 

5.5@4.5 

19.5®15 

4@3 

0.50®.  60 

j  Pulveru- 
{     lent. 

2.  Lonr;  flaming   fat  > 

Melted, 

or  coking  coals,  > 

80@85 

5.8®5 

14.2@10 

3@2 

.60®.68 

but 

or  £T.s  coals,         ) 

friable. 

Melted; 

3.  Caking  fat  coals,  ) 
or   blacksmiths1  V. 

84@89 

5  ©4.5 

11  @5.5 

2^1 

.68®.  74 

some- 
what 

coals,                   ) 

com- 

pact. 

4.  Short  flaming  :v.t  J 
or  caking  coals,  > 
coking  coals,       ) 

88©91 

5.5©4.t 

6.5@5.5 

1 

.74@.82 

!  Melted; 
very 
com- 

[    pact. 

5.  Lean    or    anthra-  1 
citic  coals,               f 

90©93 

4.5@4 

5.5©3 

1 

.82®.  90 

j  Ptilveru- 
1     lent. 

*  The  nitrogen  rarely  exceeds  1  per  cent  of  the  weight  of  the  fuel, 
t  Not  including  bituminous  lignites,  which  resemble  petroleums. 

Rankine  gives  the  following:  The  extreme  differences  in  the  chemical 
composition  and  properties  of  different  kinds  of  coal  are  very  great.  The 
proportion  of  fres  carbon  ranges  from  30  to  93  per  cent;  that  of  hydrocar- 
bons of  various  kinds  from  5  to  58  per  cent;  that  of  water,  or  oxygen  and 
hydrogen  in  the  proportions  which  form  water,  from  an  inappreciably 
small  quantity  to  27  per  cent;  that  of  ash,  from  1J^  to  26  per  cent. 

The  numerous  varieties  of  coal  may  be  divided  into  principal  classes  as 
follows:  1,  anthracite  coal;  2,  semi-bituminous  coal;  3,  bituminous  coal; 
4,  long  flaming  or  cannel  coal;  5,  lignite  or  brown  coal. 


624 


FUEL. 


Diminution  of  H  and  O  in  Series  from  Wood  to  A  nthracite. 

(Groves  and  Thorp's  Chemical  Technology,  vol.  i.,  Fuels,  p.  58.) 

Substance.  Carbon.    Hydrogen.    Oxygen. 

Woody  fibre 52.65  5.25  42.10 

Peat  from  Vulcaire 59.57  5.96  34.47 

Lignite  from  Cologne 66.04  5.27  28.69 

Earthy  brown  coal  73.18  5.88  21.14 

Coal  from  Belestat,  secondary 75.06  5.84  19. 10 

Coal  from  Rive  de  Gier 89.29  5.05  5.66 

Anthracite,  Ma3renne,  transition  formation  91.58  3.96  4.46 

Progressive  Change  from  Wood  to  Graphite. 

(J.  S.  Newberry  in  Johnson's  Cyclopedia.) 

Wood  Loss     Li£-  Loss    Bitumi'  T  oss  Anfchra-  T  os«    Graph- 
wooa.  L.OSS.  nite    L.oss.nous  coal  L.OSS.     citef      Loss.      it^ 

Carbon 49.1      18.65   30.45    12.35        18.10       3.57      14.53       1.42      13.11 

Hydrogen...     6.3       3.25     3.05     1.85         1.20       0.93       0.27       0.14       0.13 
Oxygen 44.6      24.40   20.20    18.13         2.07       1.32       0.65       0.65       0.00 

100.0     4630    53.70    32.33        21.37        5.82     15.45        2.21      13.24 

Classification  of  Coals,  as  Anthracite,  Bituminous,  etc.— 

Prof.  Fersifer  Frazer  (/Trans.  A.  I.  M.  E.,  vi,  430)  proposes  a  classifica- 
tion of  coals  according  to  their  "  fuel  ratio,"  that  is,  the  ratio  the  fixed  car- 
bon bears  to  the  volatile  hydrocarbon. 

In  arranging  coals  under  this  classification,  the  accidental  impurities,  such 
as  sulphur,  earthy  matter,  and  moisture,  are  disregarded,  and  the  fuel  con- 
stituents alone  are  considered. 

Carbon  Fixed  Volatile 

Ratio.  Carbon.  Hydrocarbon. 

I.  Hard  dry  anthracite.    100  to  12          100.     to  92.31£          0.     to   7  69# 
II.  Semi -anthracite 12  to  8  92.31to88.89  7. 69  to  11. 11 

III.  Semi-bituminous 8  to   5  88. 89  to  83. 33  11. 11  to  16. 67 

IV.  Bituminous 5  to   0  83.33to   0.  16.67tolOO 

It  appears  to  the  author  that  the  above  classification  does  not  draw  the 
line  at  the  proper  point  between  the  semi -bituminous  and  the  bituminous 
coals,  viz.,  at  a  ratio  of  C  -+•  V.H.C.  =  5,  or  fixed  carbon  83.33#,  volatile  hy- 
drocarbon 16.67$,  since  it  would  throw  many  of  the  steam  coals  of  Clearfield 
and  Somerset  counties,  Penn.,  and  the  Cumberland,  Md.,  and  Pocahontas, 
Va.,  coals,  which  are  practically  of  one  class,  and  properly  rated  as 
semi-bituminous  coals,  into  the  bituminous  class.  The  dividing  line  be- 
tween the  semi -anthracite  and  semi-bituminous  coals,  C  -*•  V.H.C.  =  8, 
would  place  several  coals  known  as  semi-anthracite  in  the  semi-bituminous 
class.  The  following  is  proposed  by  the  author  as  a  better  classification  : 

Carbon  Ratio.  Fixed  Carbon.  Vol.  H.C. 

I.  Hard  dry  anthracite ..     100  to  12  100       to  92. 31^         0       to     7.69$ 

II.  Semi-anthracite 12  to   7  92. 31  to  87. 5  7. 69  to   12.5 

III.  Semi-bituminous 7  to  3  87.5   to  75  12.5   to   25 

IV.  Bituminous 3  to   0  75       to   0  25       to  100 

Rhode  Island  Graphitic  Anthracite.— A  peculiar  graphite  is 
found  at  Cranston,  near  Providence,  R.  I.  It  resembles  both  graphite  and 
anthracite  coal,  and  has  about  the  following  composition  (A.  E.  Hunt,  Trans. 
A.  I.  M.  E.,  xvii.,  678):  Graphitic  carbon,  78$;  volatile  matter,  2.60$;  silica, 
15.06^;  phosphorus,  .045$.  It  burns  with  extreme  difficulty. 

ANALYSES  OF  COAL.S. 

Composition  of  Pennsylvania  Anthracites.  (Trans.  A.  I. 
M.  E.,  xiv.,  706.)— Samples  weighing  100  to  200  Ibs.  were  collected  from  Jots 
of  100  to  200  tons  as  shipped  to  market,  and  reduced  by  proper  methods  to 
laboratory  samples.  Thirty-three  samples  were  analyzed  by  McCreath,  giv- 
ing results  as  follows.  They  show  the  mean  character  of  the  coal  of  the  more 
important  coal-beds  in  the  Northern  field  in  the  vicinity  of  Wilkesbarre,  in 
the  Eastern  Middle  (Lehigh)  field  in  the  vicinity  of  Hazleton,  in  the  Western 


ANALYSES  OF  COALS. 


625 


Middle  field  in  the  vicinity  of  Shenandoah,  and  in  the  Southern  field  between 
Mauch  Chunk  and  Taniaqua. 


Name  of 
Bed. 

Name  of 
Field. 

Water. 

Volatile 
Matter. 

Fixed 
Carbon. 

1 

Sulphur. 

Vol.  Matter. 
Per  cent  of 
total  com- 
bustible. 

Ratio, 
C  -*-  V.H.C. 

Wharton... 

E.  Middle 

3.71 

3.08 

86.40 

6.22 

.58 

3.44 

28.07 

Mammoth.. 

E.  Middle 

4.12 

3.08 

86.38 

5.92 

.49 

3.45 

27.99 

Primrose  .  . 

W.  Middle 

3.54 

3.72 

81.59 

10.65 

.50 

4.36 

21.93 

Mammoth  . 

W.  Middle 

3.16 

3.72 

81.14 

11.08 

.90 

4.38 

21.83 

Primrose  F 

Southern 

3.01 

4.13 

87.98 

4.38 

.50 

4.48 

21.32 

Buck  Mtn.. 

W.  Middle 

3.04 

3.95 

82.66 

9.88 

.46 

4.56 

20.93 

Seven  Foot 

W.  Middle 

3.41 

3.98 

80.87 

11.23 

.51 

4.69 

20.32 

Mammoth  . 

Southern 

3.09 

4.28 

83.81 

8.18 

.64 

4.85 

19.62 

Mammoth  . 

Northern 

3.42 

4.38 

83.27 

8.20 

.73 

5.00 

19.00 

B.  Coal  Bed 

Loyalsock 

1.30 

8.10 

83.34 

6.23 

1.03 

8.86 

10.29 

The  above  analyses  were  made  of  coals  of  all  sizes  (mixed).  When  coal  is 
screened  into  sizes  for  shipment  the  purity  of  the  different  sizes  as  regards 
ash  varies  greatly.  Samples  from  one  mine  gave  results  as  follows: 


Name  of 
Coal. 

Egg 

Stove 

Chestnut 


Buckwheat. . 


Screened  Analyses. 

Through  Over  Fixed 

inches.  inches.  Carbon.  Ash. 

2.5  1.75  88.49  5.66 

1.75  1.25  83.67  10.17 

1.25  .75  80.72  12.67 

.75  .50  79  05  14.66 

.50  .25  76.92  16.62 


Bel-nice  Basin,  Pa.,  Coals. 

Water.    Vol.  H.C.    Fixed  C.    Ash.    Sulphur. 

Sernice   Basin,    Pulllvan   and(°tf          S£6  8252  024 

LycomingCos.;  range  of  8..  ]  ^          ^ 


This  coal  is  on  the  dividing-line  between  the  anthracites  and  semi-anthra- 
</ites,  and  is  similar  to  the  coal  of  the  Lykens  Valley  district. 

More  recent  analyses  (Trans.  A.  I.  M.  E.,  xiv.  721)  give  : 

Water.     Vol.  H.C.    Fixed  Carb.       Ash.         Sulphur. 
Working  seam  .......  065  9.40  83.69  5.34  091 

60ft.  below  seam....  3.67  15.42  71.34  8.97  0.59 

The  first  is  a  semi-anthracite,  the  second  a  semi-bituminous. 

Space  Occupied  by  Anthracite  Coal.    (J.  C.  I.  W.,  vol.  iii.)—  The 
cubic  contents  of  2:240  Ibs.  of  hard  Lehigh  coal  is  a  little  over  36  feet  ;  an 
average  Schuylkill  W.  A.,  37  to  38  feet  ;  Shamokin,  38  to  39  feet;  Lorberry, 
nearly  41. 

According  to  measurements  made  with  Wilkesbarre  anthracite  coal  from 
the  Wyoming  Valley,  it  requires  32.2  cu.  ft.  of  lump,  33.9  cu.  ft.  broken, 
34  5  cu.  ft.  egg,  34.8  cu.  ft.  of  stove,  35.7  cu.  ft.  of  chestnut,  and  36.7  cu.  ft. 
of  pea,  to  make  one  ton  of  coal  of  2240  Ibs.  ;  while  it  requires  28.8  cu.  ft.  of 
lamp,  30.3  cu.  ft.  of  broken,  30.8  cu.  ft.  of  egg,  31.1  cu.  ft.  of  stove,  31.9  cu. 
ft.  of  chestnut,  and  32.8  cu.  ft.  of  pea,  to  make  one  ton  of  2000  Ibs. 

Composition  of  Anthracite  and  Semi-bituminous  Coals. 
(Trans.  A.  I.  M.  E.,  vi.  430.)—  Hard  dry  anthracites,  16  analyses  by  Rogers, 
show  a  range  from  94.10  to  83.47  fixed  carbon,  1.40  to  9.53  volatile  matter, 
and  4.50  to  8.00  ash,  water,  and  impurities.  Of  the  fuel  constituents  alone, 
the  fixed  carbon  ranges  from  98.53  to  89.63,  and  the  volatile  matter  from  1.47 
to  10.37,  the  corresponding  carbon  ratios,  or  C  -H  Vol.  H.C.  being  from  67.02 
to  8.64. 

Semi-anthracites.—  12  analyses  by  Rogers  show  a  range  of  from  90.23  to 
'74.55  fixed  carbon,  7.07  to  13.75  volatile  matter,  and  2.20  to  12.10  water,  ash, 
and  impurities.  Excluding  the  ash,  etc.,  the  range  of  fixed  carbon  is  92.75 
to  84.42,  and  the  volatile  combustible  7.27  to  15.58,  the  corresponding  carbon 
ratio  being  from  12.75  to  5.4U 


626 


FUEL. 


Semi-bituminous  Coals.— 10  analyses  of  Penna.  and  Maryland  coals  give 
fixed  carbon  68.4J  to  84.80,  volatile  matter  11.2  to  17.28,  and  ash,  water,  and 
impurities  4  to  13.99.  The  percentage  of  the  fuel  constituents  is  fixed  carbon 
79.84  to  88.80,  volatile  combustible  11.20  to  20.16,  and  the  carbon  ratio  11.41  to 
3.96. 

American  Semi-bituminous  and  Bituminous  Coals. 

(Selected  chiefly  from  various  papers  in  Trans.  A.  I.  M.  E.) 


Moist- 
ure. 

Vol. 
Hydro- 
arbon. 

Fixed 
Carbon 

Ash. 

Sul- 
phur. 

Penna.  Semi-bituminous  : 

Broad  Top  extremes  of  5 

j    .79 

13.84 

78.46 

6.00 

.91 

1    .78 

17.38 

76.14 

4.81 

.88 

Somerset  Co.,  extremes  of  5  

jl.27 
tl.89 

14.33 
18.51 

77.77 
65.90 

6.63 
10.62 

0.66 
3.08 

1.07 

26.72 

60.77 

9.45 

2.20 

Cambria  Co.,  average  of  7,  | 
lower  bed,  B.            J  " 

0.74 

21.21 

68.94 

7.51 

1.98 

Cambria  Co.,  1,            \ 
upper  bed,  C.    f  " 

1.14 

17.18 

73.42 

6.58 

1.41 

Cambria  Co    South  Fork  1 

15  51 

78  60 

5.84 

Centre  Co.,  1   

0.60 

22.60 

68.71 

5.40 

2^69 

Clearfleld  Co.,  average  of  9,  | 
upper  bed,  C. 
Clearfield  Co.,  average  of  8,  | 
lower  bed,  D.              \'" 

0.70 
0.81 

23.94 
21.10 

69.28 
74.08 

4.62 
3.36 

1.42 
0.42 

10.41 

20.09 

66.69 

2.65 

0.43 

Clearfield  Co.,  range  of  17  anal.. 

]   to 

to 

to 

to 

to 

(1.94 

25.19 

74.02 

7.65 

1.79 

Bituminous  : 

Jefferson  Co.,  average  of  26  — 

1.21 

32.53 

60.99 

3.76 

1.00 

Clarion  Co.,  average  of  7.  ....... 

1.97 

38.60 

54.15 

4.10 

1.19 

A.rmstroncr  Co    1 

1.18 

42.55 

49  69 

4.58 

2  00 

Connellsville  Coal  •. 

1.26 

30  10 

59*61 

8.23 

78 

Coke  from  ConnVille  (Standard) 

.49 

0.01 

87.46 

11.32 

.69 

Youghiogheny  Coal  

1.03 

36.49 

59.05 

2.61 

.81 

Pittsburgh,  Ocean  Mine.  .  . 

.28 

39.09 

57.33 

3.30 

The  percentage  of  volatile  matter  in  the  Kittaning  lower  bed  B  and  the 
Freeport  lower  bed  D  increases  with  great  uniformity  from  east  to  west;  thus' 

Volatile  Matter.  Fixed  Carbon. 

Clearfield  Co,  bed  D 20.09  to  25. 19  68.73  to  74.76 

41        "B 22.56  to  26.13  64.37  to  69.63 

Clarion  Co.,        "  B 35.70  to  42.55  47.51  to  55.44 

"  D  37.15  to  40.80  51.39  to  56.36 

Connellsville  Coal  and  Coke.  (Trans.  A.  I.  M.  E.,  xiii.  832.)  — 
The  Connellsville  coal-field,  in  the  southwestern  part  of  Pennsylvania,. is  a 
strip  about  3  miles  wide  and  60  miles  in  length.  The  mine  workings*  are 
confined  to  the  Pittsburgh  seam,  which  here  has  its  best  development  as  to 
size,  and  its  quality  best  adapted  to  coke-making.  It  generally  affords 
from  7  to  8  feet  of  coal. 

The  following  analyses  by  T.  T.  Morrell  show  about  its  range  of  composi- 
tion : 

Moisture.  Vol.  Mat.     Fixed  C.      Ash.      Sulphur.  Phosph's. 
Herold  Mine  ....  1.26          28.83          60.79  8.44  .67  .013 

Kintz  Mine 0.79  31.91  56.46  9.52  1.32  .02 

In  comparing  the  composition  of  coals  across  the  Appalachian  field,  in  the 
western  section  of  Pennsylvania,  it  will  be  noted  that  the  Connellsvills 
variety  occupies  a  peculiar  position  between  the  rather  dry  semi-bituminous 
coals  eastward  of  it  and  the  fat  bituminous  coals  flanking  it  on  the  west. 

Beneath  the  Connellsville  or  Pittsburgh  coal-bed  occurs  an  interval  of 
from  400  to  600  feet  of  ''barren  measures,"  separating  it  from  the  lower 
productive  coal-measures  of  Western  Pennsylvania.  The  following  tables 


ANALYSES   OF   COALSo 


62? 


show  the  great  similarity  in  composition  in  the  coals  of  these  upper  and 
lower  coal-measures  in  the  same  geographical  belt  or  basin. 


Analyses  from  the  II  i 
We 

Localities.        Moisture. 
Anthracite     .        .1  35 

pper  Coal 
st  \vard  € 

Vol.  Mat. 
3.45 

15.52 
22.35 
31.38 
33.50 
37.66 

-measure: 
•rder. 

Fixed  Garb 

89.06 
74.28 
68.77 
60.30 
61.34 
54.44 

*  (Penna 

Ash. 
5.81 
9.29 
5.96 
7.24 
3.28 
5.86 

.)  in  a 

Sulphur. 
0.30 
0.71 
1.24 
1.09 
0.86 
0.64 

Cumberland,  Md.. 
Salisbury    Pa 

...  0.89 
1.66 

Connellsville,  Pa.. 
Greensburg,  Pa 

l".02 

Ir  win's.  Pa... 

1.41 

Analyses  from  the  :Lower  Coal-measures  In  a  Westward 
Order. 

Localities.        Moisture. 

Anthracite 1.35 

Broad  Top  0.77 

Bennirigton... 1.40 

Johnstown 1.18 

Blair-sville 0.92 

Armstrong  Co 0.96 

Pennsylvania  and  Ohio  Bituminous  Coals.  Variation 
in  Character  of  Coals  of  the  same  Beds  in  different  Dis- 
tricts.— From  50  analyses  in  the  reports  of  the  Pennsylvania  Geological 
Survey,  the  following  are  selected.  They  are  divided  into  different  groups, 
and  the  extreme  analysis  in  each  group  is  given,  ash  and  other  impurities 
being  neglected,  and  the  percentage  in  100  of  combustible  matter  being 
alone  considered. 


Vol.  Mat. 

Fixed  Garb. 

Ash. 

Sulphur. 

3.45 

89.06 

5.81 

0.30 

18.18 

73.34 

6.69 

1.02 

27.23 

61.84 

6.93 

2.60 

16.54 

74.46 

5.96 

1.86 

24.36 

62.22 

7  69 

4.92 

38.20 

52.03 

5.14 

3.66 

No.  of 
Analyses 

Fixed 
Carbon 

Vol. 
H.  C. 

Carbon 
Ratio. 

5 

Jefferson  township,  Greene  Co  
Hopewell  township,  Washington  Co  
\Vaynesburg  coal-bed  lower  bench 

9 

59.72 
53.22 

40.28 
46.78 

1.48 
1.13 

Morgan  township  Greene  Co  

60.69 

39  31 

1  54 

Pleasant  Valley  \Vashington  Co 

54  31 

45  69 

1  19 

Sewickley  coal-bed           

3 

\Vhitely  Creek  Greene  Co 

64  39 

35  61 

80 

Gray's  Bank  Creek,  Greene  Co  
Pittsburgh  coal-bed: 

Upper  bench   \Vashington  Co 

60.35 
J60.87 

39.65 
39.13 

.52 
.65 

Lower  bench,                        **     

5 

I  59.11 
j  63.54 

40.89 
36.46 

.20 
.74 

Main  bench  Greene  Cc  

3 

|  50  .  97 
J61.80 

49.03 
38.20 

.04 
.61 

Frick  &  Co.,  Washington  Co.,  average  . 
Lower  bench   Greene  Co 

1 

|  54.33 
66.44 
57  83 

45  .  67 
33.56 
4  -.2  17 

.19 
1.98 
1  37 

Somerset  Co.,  semi-bituminous  (showing 
decrease  of  vol.  mat.  to  the  eastward). 
Beaver  Co.,  Pa  

\  8 

J79.73 

|  75.47 

20.27 
24.53 

3  93 
3.07 

L)iehl's  Bank  Georgetown 

40.68 

59  32 

0  68 

Bryan's  Bank  Georgetown  

62.57 

37  43 

1  66 

OHIO. 
Pittsburgh  coal-bed  in  Ohio: 
Jefferson  Co    Ohio                  

61  45 

38  55 

59 

Belmont  Co.,  Ohio  
Harrison  Co.,  Ohio  
Pomeroy  Co    Ohio 

j  63.46 
166.14 
J63.46 
J64.93 
(60.92 

36.54 
33.86 
36.54 
35.07 
39.08 

.73 
.95 
1.73 
.85 
.55 

}  62.33 

37.67 

.65 

628 


FUEL. 


Analyses  of  Southern  and  Western  Coals. 


Moisture. 

Vol.  Mat. 

Fixed  C. 

Ash. 

Sul- 
phur. 

OHIO. 
Hocking  Valley  

j            5.00 

32.80 

53.15 

9.05 

0.44 

MARYLAND. 
Cumberland    .                         . 

(            7.40 
J               95 

29.20 
19.13 

60.45 
72.70 

2.95 
6.40 

0.93 
0.78 

VIRGINIA. 
South  of  James  River,  23  anal- 
yses, range 
Average  of  23 

(            1.23 

j  from  0.67 
{     to    2.46 

1.48 

15.47 

27.28 
38.60 
32  24 

73.51 

46.70 
67.83 
58  89 

9.09 

2.00 

15.76 
7  72 

0.70 

0.58 
2.89 
1  45 

North  of  James  River,  eastern 
outcrop, 

Carbonite  or  Natural  Coke  

Western  outcrop,  11  analyses, 
range 
Average  of  11 

j            0.40 
1            1.79 
j             1.57 
1             1.56 
j  from  
1    to      ... 

18.60 
23.96 
9.64 
14.26 
21.33 
30.50 
26  06 

71.00 
59.98 
79.93 
81.61 
54.97 
70.80 
63  75 

10.00 
14.28 
8.86 
2.24 
3.35 
22.60 
10  06 

0,23 

Pocahontas  Flat-top* 
(Castner  &  Curran's  Circular) 
WEST  VIRGINIA  (New  River.) 

Quiunimonr.,t  3  analyses  
Nuttalburgh  t                     

j            0.52 
1            0.62 

from  0.76 
to    0.94 
0.34 

23.90 

18.48 

17.57 
18.19 
29.59 

74.20 
75.22 

75.89 
79.40 
69.00 

1V8B 

5.68 

1.11 
4.92 
1.07 

0.52 
0.28 

0.23 
0.30 

VIRGINIA  and  KENTUCKY. 
Big  Stone  Gap  Field,  t  9  anal- 
yses, range 

KENTUCKY. 
Pulaski  Co.,  3  analyses,  range 

Muhlenberg   Co.,  4   analyses, 
range 
Kentucky  Cannel  Coals,  §  5  an- 
alyses, range 

TENNESSEE. 
Scott  Co.,  Range  of  several.  IT.  . 

Roane  Co    Rock  wood 

1.35 

j  from  0.80 
1     to    2.01 

(from  1.26 
1     to    1.32 
j  from  3.60 
1     to    7.06 
j  from  — 
1    to    .... 

j  from     70 
1     to    1.83 
1.75 

25.35 

31.44 
36.27 

35.15 
39.44 
30.60 
38.70 

40.20H 
60.  30|| 

32.33 

41.29 
26  62 

70.67 

54.80 
63.50 

60.85 
52.48 
58.80 
53.70 
59.80  coke 
33.70  coke 

46.61 
61.66 
60  11 

2.10 

1.73 
8.25 

1.23 

3!  40 
6.50 

8.81 
4.80 

16.94 
1.11 
11  52 

0.08 

0.56 
1.72 

0.40 
1.00 
0.79 
3.16 
0.96 
1.32 

3.37 
0.77 
1  49 

Hamilton  Co    Melville  

2.74 

26  50 

67  08 

3  68 

91 

94 

23  72 

63.94 

11.40 

1  19 

Sewariee  Co    Tracy  City.   .. 

1.60 

29  30 

61  00 

7  80 

Kelly  Co     Whiteside      

1.30 

21  80 

74  20 

2.70 

GEORGIA. 
Dade  Co              .             .... 

1.20 

23  05 

60  50 

15  16 

0  84 

ALABAMA. 
Warren  Field: 
Jefferson  Co.,  Birmingham.. 
"     Black  Creek  .  . 
Tuscaloosa  Co  
Cahaba  Field,     1  Helena  Vein  . 
Bibb  Co   J  Coke  Vein.... 

3.01 
.12 

1.59 
2.00 
1.78 

42.76 
26.11 
38.33 
32.90 
30.60 

48.30 
71.64 
54.64 
53.08 
66.58 

3.21 
2.03 
5.45 
11.34 
1.09 

2.72 

.10 
1.33 
.68 
.04 

*  Analyses  of  Pocahontas  Coal  by  John  Pattinson,  F.C.S.,  1889: 

C.          H.          O.         N.         S.        Ash.    Water.    Coke. 


Vol. 
Mat. 

Lumps...    86.51       4.44        4.95      0.66      0.61        1.54        1.29        78.8       21.2 
Small...    83,13       4.29        5.33      0.66      0.56        4.63        1.40        79.8       20.2 

Calorific  value,  by  Thomson's  Calorimeter:  Lumps  =  15.4  Ibs.  of  water 
evaporated  from  and  at  212°;  small  =  14.7  Ibs. 

t  These  coals  are  coked  in  beehive  ovens,  and  yield  from  63^  to  64#  of  coke. 

JThis  field  covers  about  120  square  miles  in  Virginia,  and  about  30  square 
miles  in  Kentucky. 

§  The  principal  use  of  the  cannel  coals  is  for  enriching  illuminating-gas. 

||  Volatile  matter  including  moisture. 

f  Single  analyses  from  Morgan,  Rhea,  Anderson,  and  Roane  counties  fall 
within  this  range. 


ANALYSES   OF   COALS. 


629 


ALABAMA  COALS.    (W.  B.  Phillips,  Eng.  <&  M.  J.,  June  3, 1893.) 


Name  of 
Seam. 

Location. 

Proximate. 

Ultimate. 

al® 

11 
ogS 

Fixed 
Carbon. 

Carbon. 

Hydrogen. 

Oxygen. 

Nitrogen. 

Sulphur. 

i 

Moisture. 

Wadsworth 
Pratt  
Brookwood 
'Woodstock. 
Underwood 
Pratt  
Milldale.... 

Helena  
Pratt  mines.. 
Brookwood.. 
Blocton  

Pratt  mines.. 
Brookwood.. 
Blue  Creek  .  . 
Coalburg  

34.30 
33.45 
27.80 
34.80 
35.65 
31.55 
30.50 
25.80 
32.55 

30.15 

60.50 
63.20 
58.70 
60.60 
57.30 
64.95 
66.30 
69.90 
65.57 

52.90 

73.23 

75.82 
72.47 
72.75 
70.82 
75.05 
73.96 
72.68 
74.59 

60.37 

7.98 
10.52 
10.38 
8.61 
10.19 
9.91 
10.50 
10.77 
10.58 

10.70 

11.92 
7.51 
1.60 
11.12 
9.95 
8.95 
9.57 
9.83 
9.48 

9.00 

1.07 
1.73 
0.40 
1.48 
1.31 
1.62 
1.62 
1.39 
1.81 

1.26 

0.60 
1.07 
1.65 
1.44 
0.68 
0.97 
1.15 
1.03 
1.32 

1.72 

3.50 
2.00 
11.90 
2.65 
5.25 
2.35 
2.20 
2.80 
1.90 

16.30 

1.70 
1.35 
1.60 
1.95 
1.80 
1.15 
1.00 
1.50 
0.82 

0.65 

Cab  aba 
Field  

Moisture. 

Vol.  Mat. 

Fixed  C. 

Ash. 

Sul- 
phur. 

TEXAS. 

Eagle  Mine                                    .  . 

3  54 

30  84 

50  69 

14.93 

Sabinas  Field  Vein  I  

1.91 

20.04 

62  71 

15  35 

"          "           "    II 

1.37 

16  42 

68  18 

13  02 

"          "           "III    

0.84 

29.35 

50  18 

19  63 

"          "           "  IV 

0  45 

21  6 

45  75 

29  1 

3  15 

INDIANA. 
Block  coal,  average  *  . 

2.10 

37.35 

57.95 

2.60 

"        "     Lafayette 

13.05 

32  34 

48  78 

5  81 

*'        "     Sand  Creekt  

4.50 

91 

00 

4.50 

ILLINOIS.! 
La  Salle        

8.22 

39  40 

43  95 

8  43 

Streator  

7.20 

38.88 

45.30 

8.60 

Danville          .            

11  00 

32  55 

53  00 

3  65 

5.78 

43.70 

45.37 

6.15 

Lincoln                    .              ... 

8  45 

34.99 

44  50 

12  06 

Barclay         „  .  •  

10.80 

27  32 

44  78 

17  10 

6.36 

26.40 

59.84 

7.40 

Du  Quoin         „  

8.86 

23.54 

60  60 

7  00 

Mt.  Carbon  

6.12 

24.68 

66.50 

2.70 

Staunton  .  .  . 

6.27 

57.11 

26.30 

10.32 

*  Indiana  Block  Coal  (J.  S.  Alexander,  Trans.  A.  I.  M.  E.,  iv.  100).— The 
typical  block  coal  of  the  Brazil  (Indiana)  district  differs  in  chemical  com- 
position but  little  from  the  coking  coals  of  Western  Pennsylvania.  The 
physical  difference,  however,  is  quite  marked;  the  latter  has  a  cuboid  struc- 
ture made  up  of  bituminous  particles  lying  against  each  other,  so  that  under 
the  action  of  heat  fusion  throughout  the  mass  readily  takes  place,  while 
block  coal  is  formed  of  alternate  layers  of  rich  bituminous  matter  and  a 
charcoal-like  substance,  which  is  not  only  very  slow  of  combustion,  but  so 
retards  the  transmission  of  heat  that  agglutination  is  prevented,  and  the 
coal  burns  away  layer  by  layer,  retaining  its  form  until  consumed. 

t  Analysis  by  E.  T.  Cox:  C,  72.94;  H,  4.50;  O,  11.77;  N,  1.79;  ash,  4.50; 
moisture,  4.50. 

^  The  Illinois  coals  are  extremely  variable  in  character.  The  above  anal- 
yses are  given  in  D.  L.  Barnes's  paper  on  "  American  Locomotive  Practice," 
Trnns.  A.  S.  C.  E.  1893,  except  the  last,  the  Staunton  coal,  which  is  by  Hunt 
and  Clapp  (Trans.  A.  S.  M.  E.,  v.  266).  The  Staunton  coal  is  remarkable  for 
the  high  percentage  of  volatile  matter,  but  it  is  excelled  in  this  respect  by 


630 


FUEL. 


Moisture. 

Vol.  Mat. 

Fixed  C, 

Ash. 

Sul- 
phur. 

IOWA.  * 
Hiteman         .     .     .          

4  99 

35.27 

25  37 

34  37 

Keb         

9  81 

37.49 

44.7'5 

7  95 

Flaglers  .            -  .         

9  84 

40  16 

37  69 

12  31 

Chisholm     

9.18 

40.42 

39.58 

10  82 

MISSOURI.* 
Brookfield                         

4  34 

40.27 

50  60 

4  79 

Mendota      

9  03 

37.48 

46  24 

7  25 

Hamilton                                . 

5.06 

34  24 

47  69 

13  01 

LingO                                        .     .    .  •    ...... 

7  33 

38  29 

47.24 

7  14 

NEBRASKA.* 

0.21 

27.82 

60.88 

11.09 

WYOMING.* 
Cambria                 •  

4.2 

40.6 

41.5 

13  7 

2.5 

37.4 

37  9 

22  2 

Goose  Creek  

9.7 

40.2 

46.3 

3.8 

13  92 

36.78 

42  03 

7  27 

12.8 

35.0 

47.7 

3  6 

Sheridan                                 

6  04 

42.37 

35  57 

16  02 

COLORADO.}: 
Sunshine    Colo  average  

2.8 

36.3 

37.1 

23  8 

Newcastle      kt          "        

1.7 

37.95 

48.6 

11.6 

El  Moro         tc          " 

1  32 

38.23 

55  86 

3  59 

Crested  Buttes        "        

1  10 

23.20 

72  60 

3  10 

UTAH  (Southern). 
Castledale    

3.43 

42.81 

47.8lt 

9  73 

Cedar  City 

3.50 

43  66 

43.  lit 

5  95 

OREGON. 
Coos  Bay              

15.45 

41.55 

34.95 

8.05 

2.53 

17.27 

44  15 

32  40 

6  18 

1  37 

Yaouina  Bay                   . 

13  03 

46  20 

32.60 

7  10 

1  07 

John  Day  River    

4.55 

40.00 

48.19 

7.26 

.60 

6.54 

34.45 

52.41 

5.95 

.65 

VANCOUVER  ISLAND. 
Comox  Coal  

1.7 

27.17 

68.27 

2.86 

the  Boghead  coal  of  Linlithgowshire,  Scotland,  an  analysis  of  which  by  Dr. 
Penny  is  as  follows:  Proximate — moisture  0.84;  vol.  67.95;  fixed  C,  9.54,  ash, 
21.4;  Ultimate— C,63. 94;  H,  8.86;  O,  4.70;  N,  0.96;  which  is  remarkable  for  the 
high  percentage  of  H. 

*  The  analyses  of  Iowa,  Missouri,  Nebraska,  and  Wyoming  coals  are 
selected  from  a  paper  on  The  Heating  Value  of  Western  Coals,  by  Wm. 
Forsyth,  Mech.  Engr.  of  the  C.,  B.  &  Q.  R.  R.,  Eng'g  News,  Jan.  17,  1895. 

+  Includes  sulphur,  which  is  very  high.  Coke  from  Cedar  City  analyzed  : 
Water  and  volatile  matter,  1.42;  fixed  carbon,  76.70;  ash,  16.61;  sulphur,  5.27. 

$  Colorado  Coals.— The  Colorado  coals  are  of  extremely  variable  com- 
position, ranging  all  the  way  from  lignite  to  anthracite.  G.  C.  Hewitt 
(Trans.  A.  I.  M.  E.,  xvii.  377)  says  :  The  coal  seams,  where  unchanged 
by  heat  and  flexure,  carry  a  lignite  containing  from  5$  to  20$  of  water.  In 
the  south-eastern  corner  of  the  field  the  same  have  been  metamorphosed  so 
that  in  four  miles  the  same  seams  are  an  anthracite,  coking,  and  dry  coal. 
In  the  basin  of  Coal  Creek  the  coals  are  extremely  fat,  and  produce  a  hard, 
bright,  sonorous  coke.  North  of  coal  basin  half  a  mile  of  development 
shows  a  gradual  change  from  a  good  coking  coal  with  patches  of  dry  coal  to 
a  dry  coal  that  will  barely  agglutinate  in  a  beehive  oven.  In  another  half 
mile  the  same  seam  is  dry.  In  this  transition  area,  a  small  cross-fault 
makes  the  coal  fat  for  twenty  or  more  feet  on  either  side.  The  dry  seams 
also  present  wide  chemical  and  physical  changes  in  short  distances.  A  soft 
and  loosely  bedded  coal  has  in  a  hundred  feet  become  compact  and  hard 
without  the  intervention  of  a  fault.  A  couple  of  hundred  feet  has  reduced 
the  water  of  combination  from  12$  to  5$. 

Western  Arkansas  and  Indian  Territory.  (H.  M.  Chance, 
.  I.  M.  E.  1890.)— The  ChocUvw  coal-lielcl  is  a  direct  westward  exten- 


ANALYSES   OF   COALS. 


631 


si  on  of  the  Arkansas  coal-field,  but  its  coals  are  not  like  Arkansas  coals,  ex- 
cept in  the  country  immediately  adjoining  the  Arkansas  line. 

The  western  Arkansas  coals  are  dry  semi-bituminous  or  semi-anthracitic 
coals,  mostly  non -coking,  or  with  quite  feeble  coking  properties,  ranging 
from  14%  to  16$  in  volatile  matter,  the  highest  percentage  yet  found,  accord- 
ing to  Mr.  Winslow's  Arkansas  report,  being  17.655. 

In  the  Mitchell  basin,  about  10  miles  west  from  the  Arkansas  line,  coal 
recently  opened  shows  19$  volatile  matter;  the  May  berry  coal,  about  8  miles 
farther  west,  contains  23$  volatile  matter;  and  the  Bryan  Mine  coal,  about 
the  same  distance  west,  shows  26$  volatile  matter.  About  30  miles  farther 
west,  the  coal  shows  from  38$  to  41^$  volatile  matter,  which  is  also  about 
the  percentage  in  coals  of  the  McAlescer  and  Lehigh  districts. 
Western  Lignites.  (K.  W.  Raymond,  Trans.  A.  I.  M.  E.,  vol.  ii.  1873.) 


C. 

H. 

N. 

0. 

S. 

Mois- 
ture. 

4 

< 

Calorific 
Power, 
calories. 

Mon  te  Diabolo  

59.72 
64.84 
69.84 
64.99 
69.14 
56.24 
55.79 
67.67 
67.58 

5.08 
4.34 
3.90 
3.76 
4.36 
3.38 
3.26 
4.66 
7  4'? 

1.01 
1.29 
1.93 
1.74 
1.25 
0.42 
0.61 
1.58 

15.69 
15.52 
10.99 
15.20 
9.54 
21.82 
19.01 
12.80 
13.42 
14.42 

3.92 

1.60 
0.77 
1.07 
1.03 
0.81 
0.63 
0.92 
0.63 
2.08 

8.94 
9  41 
9.17 
11.56 
8.06 
13.28 
16.52 
3.08 
5.18 
14.68 

5.64 
3.00 
3.40 
1.68 
6.62 
4.05 
4.18 
9.28 
5.77 
3  80 

5757 
5912 
6400 
5738 
6578 
4565 
4610 
6428 
7330 
5602 

Weber  Canon,  Utah  

Echo  Canon  ,  Utah  

Carbon  Station,  Wyo  

Coos  Bay,  Oregon  

Alaska 

Canon  City,  Colo 

Baker  Co..  Ore.  . 

60.72 

4.30 

The  calorific  power  is  calculated  by  Dulong's  formula, 
8080C  +  34462(H  -  ~\ 

N  O  ' 

deducting  the  heat  required  to  vaporize  the  moisture  and  combined  water, 
that  is,  537  calories  for  each  unit  of  water.  1  calorie  =  1.8  British  thermal 
units. 

Analyses  of  Foreign  Coals.    (Selected  from  D.  L.  Barnes's  paper 
on  American  Locomotive  Practice,  A.  S.  C.  E.,  1893.) 


Volatile 
Matter. 

Fixed 
Carbon  . 

Ash. 

Great  Britain  : 
South  Wales 

8.5 
6.2 
17.2 
17.7 
15  05 
17.1 
17.5 
20.4 

21.93 
24.11 
24.35 
40.5 

26.8 
26.9 

15.8 
14.98 
26.5 
6.16 

88.3 
92.3 
80.1 
79.9 
86.8 
63.1 
80.1 
78.6 

70.55 
38.98 
62  25 
57.9 

60.7 
67.6 

64  .3 
82.39 
70.3 
63.4 

3.2 
1.5 

%'A 

1.1 

19.8 
2.4 
1.0 

7.52 
36.91 
13.4 
1.6 

12.5 
5.5 

10.0 
2.04 
14.2 
30.45 

Semi-bit,  coking  coal. 
Boghead  cannel  gas  coal. 
Semi-bit,  steam-coal. 

Lancashire,  Eng  
Derbyshire,    "    
Durham,          "    
Scotland  

Staffordshire,  Eng  
South  America: 
Chili,  Conception  Bay 
"       Chiroqui  
Patagonia  
Brazil  

Canada: 
Nova  Scotia  

Cape  Breton  

Australia  
Australian  lignite  
Sydney,  South  Wales., 
Borneo  
Van  Diemeu's  Land  

An  analysis  of  Fictou,  N.  S.,  coal,  in  Trans.  A.  I.  M.  E.,  xiv.  560,  is:  Vol.. 
29.63;  carbon.  56.98;  ash,  13.39;  and   one  of  Sydney,   Cape  Breton,  coal  is; 
vol.,  34.07;  carbon,  61.  43  5  ash,  4.50. 

632  FUEL. 

Nixon's  Navigation  Welsh  €oal  is  remarkably  pure,  and  con- 
tains not  more  than  3  to  4  per  cent  of  ashes,  giving  88  per  cent  of  hard  and 
lustrous  coke.  The  quantity  of  fixed  carbon  it  contains  would  classify  it 
among  the  dry  coals,  but  on  account  of  its  coke  and  its  intensity  of  com- 
bustion it  belongs  to  the  class  of  fat,  or  long- flaming  coals. 

Chemical  analysis  gave  the  following  results:  Carbon,  90.27;  hydrogen, 
4.39;  sulphur,  .69;  nitrogen,  .49;  oxygen  (difference),  4.16. 

The  analysis  showed  the  following  composition  of  the  volatile  parts:  Car- 
bon, 22.53;  hydrogen,  34.96  ;  O  -f  N  -f  S,  42.51. 

The  heat  of  combustion  was  found  to  be,  as  a  result  of  several  experi- 
ments, 8864  calories  for  the  unit  of  weight.  Calculated  according  to  its 
composition,  the  heat  of  combustion  would  be  8805  calories  =  15,849  British 
thermal  units  per  pound. 

This  coal  is  generally  used  in  trial-trips  of  steam- vessels  in  Great  Britain. 

Sampling  Coal  for  Analysis.— J.  P.  Kimball,  Trans.  A.  I.  M.  E., 
xii.  317,  says  :  The  unsuitable  sampling  of  a  coal-seam,  or  the  improper 
preparation  of  the  sample  in  the  laboratory,  often  gives  rise  to  errors  in  de- 
terminations of  the  ash  so  wide  in  range  as  to  vitiate  the  analysis  for  all 
practical  purposes  ;  every  other  single  determination,  excepting  moisture, 
showing  its  relative  part  of  the  error.  The  determination  of  sulphur  and 
ash  are  especially  liable  to  error,  as  they  are  intimately  associated  in  the 
slates. 

Wm.  Forsyth,  in  his  paper  on  The  Heating  Value  of  Western  Coals  (Eng'g 
Neivs,  Jan.  17, 1895),  says  :  This  trouble  in  getting  a  fairly  average  sample  of 
anthracite  coal  has  compelled  the  Reading  R.  R.  Co.,  in  getting  their  samples, 
to  take  as  much  as  300  Ibs.  for  one  sample,  drawn  direct  from  the  chutes,  as 
it  stands  ready  for  shipment. 

The  directions  for  collecting  samples  of  coal  for  analysis  at  the  C.,  B.  &  Q. 
laboratory  are  as  follows  : 

Two  samples  should  be  taken,  one  marked  "  average,"  the  other  "  select." 
Each  sample  should  contain  about  10  Ibs.,  made  up  of  lumps  about  the  size 
of  an  orange  taken  from  different  parts  of  the  dump  or  car,  and  so  selected 
that  they  shall  represent  as  nearly  as  possible,  first,  the  average  lot;  second, 
the  best  coal. 

An  example  of  the  difference  between  an   "average"  and  a  "select" 
sample,  taken  from  Mr.  Forsytes  paper,  is  the  following  of  an  Illinois  coal: 
Moisture.    Vol.  Mat.    Fixed  Carbon.    Ash. 

Average 1.36  27.69  35.41  35.54 

Select 1.90  34.70  48.23  15.17 

The  theoretical  evaporative  power  of  the  former  was  9.13  Ibs.  of  water 
from  and  at  212°  per  Ib.  of  coal,  and  that  of  the  latter  11.44  Ibs. 

Relative  Value  of  Fine  Sizes  of  Anthracite.— For  burning 
on  a  grate  coal-dust  is  commercially  valueless,  the  finest  commercial  an- 
thracites being  sold  at  the  following  rates  per  ton  at  the  mines,  according 
to  a  recent  address  by  Mr.  Eckley  B.  Coxe  (1893): 

Size.  Range  of  Size.  Price  at  Mines. 

Chestnut 1^  to  %     inch  $2.75 

Pea %to9/16  1.25 

Buckwheat 9/16  to  %  0.75 

Rice %to3/16  0.25 

Barley 3/16  to  2/32  0.10 

But  when  coal  is  reduced  to  a-n  impalpable  dust,  a  method  of  burning  it 
becomes  possible  to  which  even  the  finest  of  these  sizes  is  wholly  una- 
dapted;  the  coal  may  be  blown  in  as  dust,  mixed  with  its  proper  proportion 
of  air,  and  no  grate  at  all  is  then  required. 

Pressed  Fuel.  (E.  F.  Loiseau,  Trans.  A.  I.  M.  E.,  viii.  314.)— Pressed 
fuel  has  been  made  from  anthracite  dust  by  mixing  the  dust  with  ten  per 
cent  of  its  bulk  of  dry  pitch,  which  is  prepared  by  separating  from  tar  at  a 
temperature  of  572°  F.  the  volatile  matter  it  contains.  The  mixture  is  kept 
heated  by  steam  to  212°,  at  which  temperature  the  pitch  acquires  its  ce- 
menting properties,  and  is  passed  between  two  rollers,  on  the  periphery  of 
which  are  milled  out  a  series  of  semi-oval  cavities.  The  lumps  of  the  mix- 
ture, about  the  size  of  an  egg,  drop  out  under  the  rollers  on  an  endless  belt 
which  carries  them  to  a  screen  in  eight  minutes,  which  time  is  sufficient  to 
cool  the  lumps,  and  they  are  then  ready  for  delivery. 

The  enterprise  of  making  the  pressed  fuel  above  described  was  not  com- 
mercially successful,  on  account  of  the  low  price  of  other  coal.  In  France, 
however,  "  briquettes  "  are  regularly  made  of  coal-dust  (bituminous  and 
se  mi-bituminous). 


KELATIVE   VALUE   OF   STEAM   COALS.  633 

RELATIVE  VAL.UE  OF  STEAM  COALS. 

The  heating  value  of  a  coal  may  be  determined,  with  more  or  less  approx- 
imation to  accuracy,  by  three  different  methods. 

1st,  by  chemical  analysis  ;  2d.  by  combustion  in  a  coal  calorimeter  ;  3d, 
by  actual  trial  in  a  steam-boiler.  The  first  two  methods  give  what  may  be 
called  the  theoretical  heating  value,  the  third  gives  the  practical  value. 

The  accuracy  of  the  first  two  methods  depends  on  the  precision  of  the 
method  of  analysis  or  calorimetry  adopted,  and  upon  the  care  and  skill  of 
the  operator.  'The  results  of  the  third  method  are  subject  to  numerous 
sources  of  variation  and  error,  and  may  be  taken  as  approximately  true 
only  for  the  particular  conditions  under  which  the  test  is  made.  Analysis 
and  calorimetry  give  with  considerable  accuracy  the  heating  value  which 
may  be  obtained  under  the  conditions  of  perfect  combustion  and  complete 
absorption  of  the  heat  produced.  A  boiler  test  gives  the  actual  result  under 
conditions  of  more  or  less  imperfect  combustion,  and  of  numerous  and  va- 
riable wastes.  It  may  give  the  highest  practical  heating  value,  if  the  condi- 
tions of  grate  bars,  draft,  extent  of  heating  surface,  method  of  firing,  etc., 
are  the  best  possible  for  the  particular  coal  tested,  and  it  may  give  results 
far  beneath  the  highest  if  these  conditions  are  adverse  or  unsuitable  to  the 
coal. 

The  results  of  boiler  tests  being  so  extremely  variable,  their  use  for  the 
purpose  of  determining  the  relative  steaming  values  of  different  coals  has 
frequently  led  to  false  conclusions.  A  notable  instance  Is  found  in  the 
record  of  Prof.  Johnson's  tests,  made  in  1844,  the  only  extensive  series  of 
tests  of  American  coals  ever  made.  He  reported  the  steaming  value  of  the 
Lehigh  Coal  &  Navigation  Co.'s  coal  to  be  far  the  lowest  of  all  the  anthra- 
cites, a  result  which  is  easily  explained  by  an  examination  of  the  conditions 
under  which  he  made  the  test,  which  were  entirely  unsuited  to  that  coal. 
He  also  reported  a  result  for  Pittsburgh  coal  which  is  far  beneath  that  now 
obtainable  in  every-day  practice,  his  low  result  being  chiefly  due  to  the  use 
of  an  improper  furnace. 

In  a  paper  entitled  Proposed  Apparatus  for  Determining  the  Heating 
Power  of  Different  Coals  (Trans.  A.  I.  M.  E.,  xiv.  727)  the  author  described 
and  illustrated  an  apparatus  designed  to  test  fuel  on  a  large  scale,  avoiding 
the  errors  of  a  stearn-boiler  test.  It  consists  of  a  fire-brick  furnace  enclosed 
In  a  water  casing,  and  two  cylindrical  shells  containing  a  great  number  of 
tubes,  which  are  surrounded  by  cooling  water  and  through  which  the  gases 
of  combustion  pass  while  being  cooled.  No  steam  is  generated  in  the  ap- 
paratus, but  water  is  passed  through  it  and  allowed  to  escape  at  a  tempera- 
ture below  200°  F.  The  product  of  the  weight  of  the  water  passed  through 
the  apparatus  by  its  increase  in  temperature  is  the  measure  of  the  heating 
value  of  the  fuel. 

There  has  been  much  difference  of  opinion  concerning  the  value  of  chemi- 
cal analysis  as  a  means  of  approximating  the  heating  power  of  coal.  It 
was  found  by  Scheurer-KestnerandMeunier-Dollfus,  in  their  extensive  series 
of  tests,  made  in  Europe  in  1868,  that  the  heating  power  as  determined  by 
calorimetric  tests  was  greater  than  that  given  to  chemical  analysis  accord- 
ing to  Dnlong's  law. 

Recent  tests  made  in  Paris  by  M.  Mahler,  however,  show  a  much  closer 
agreement  of  analysis  and  calorimetric  tests.  A  brief  description  of  these 
tests,  translated  from  the  French,  may  be  found  in  an  article  by  the  author 
in  The  Mineral  Industry,  vol.  i.  page  97. 

Dulong's  law  may  be  expressed  by  the  formula, 

Heating  Power  iu  British  Thermal  Units  =  14,500C  +  62,500  (H  -  —  ),* 

in  which  C,  H,  and  O  are  respectively  the  percentage  of  carbon,  hydrogen, 
and  oxygen,  each  divided  by  100.  A  study  of  M.  Mahler's  calorimetric  tests 
shows  that  the  maximum  difference  between  the  results  of  these  tests  and 
the  calculated  heating  power  by  Dulong's  law  in  any  single  case  is  only  a 
little  over  3#,  and  the  results  of  31  tests  show  that  Dulong's  formula  gives  an 
average  of  only  47  thermal  units  less  than  the  calorimetric  tests,  the 
average  total  heating  value  being  over  14,000  thermal  units,  a  difference  of 
less  than  4/10  of  \%. 

*  Mahler  gives  Dulong's  formula  with  Berthelot's  figure  for  the  heating 
value  of  carbon,  in  British  thermal  units, 

Heating  Power  =  14,650C  -f  62,025  (H 

>• 


634 


FUEL. 


Mahler's  calorimetric  apparatus  consists  of  a  strong  steel  vessel  or 
"  bomb  "  immersed  in  water,  proper  precaution  being  taken  to  prevent  radi- 
ation. One  gram  of  the  coal  to  be  tested  is  placed  in  a  platinum  boat  within 
this  bomb,  oxygen  gras  is  introduced  under  a  pressure  of  20  to  25  atmospheres, 
and  the  coal  ignited  explosively  by  an  electric  spark.  Combustion  is  com- 
plete and  instantaneous,  the  heat  is  radiated  into  the  surrounding  water, 
weighing  2200  grams,  and  its  quantity  is  determined  by  the  rise  in  tempera- 
ture of  this  water,  due  corrections  being  made  for  the  heat  capacity  of  the 
apparatus  itself.  The  accuracy  of  the  apparatus  is  remarkable,  duplicate 
tests  giving  results  varying  only  about  2  parts  in  1000. 

The  close  agreement  of  the  results  of  calorimetric  tests  when  properly 
conducted,  and  of  the  heating  power  calculated  from  chemical  analysis,  in- 
dicates that  either  the  chemical  or  the  calorimetric  method  may  be  ac- 
cepted as  correct  enough  for  all  practical  purposes  for  determining  the  total 
heating  power  of  coal.  The  results  obtained  by  either  method  may  be 
taken  as  a  standard  by  which  the  results  of  a  boiler  test  are  to  be  com- 
pared, and  the  difference  between  the  total  heating  power,  and  the  result  of 
the  boiler  test  is  a  measure  of  the  inefficiency  of  the  boiler  under  the  con- 
ditions of  any  particular  test. 

In  practice  with  good  anthracite  coal,  in  a  steam-boiler  properly  propor- 
tioned, and  with  all  conditions  favorable,  it  is  possible  to  obtain  in  the 
sfeeam  80$  of  the  total  beat  of  combustion  of  the  coal.  This  result  was  nearly 
obtained  in  the  tests  at  the  Centennial  Exhibition  in  1876,  in  five  different 
boilers.  An  efficiency  of  70$  to  75$  may  easily  be  obtained  in  regular  prac- 
tice. With  bituminous  coals  it  is  difficult  to  obtain  as  close  an  approach  to 
the  theoretical  maximum  of  economy,  for  the  reason  that  some  of  the  vola^ 
tile  combustible  portion  of  the  coal  escapes  unburned,  the  difficulty  increas- 
ing rapidly  as  the  content  of  volatile  matter  increases  beyond  20$.  With 
most  coals  of  the  Western  States  it  is  with  difficulty  that  as  much  as  60$  or 
65$  of  the  theoretical  efficiency  can  be  obtained  without  the  use  of  gas-pro- 
ducers. 

The  chemical  analysis  heretofore  referred  to  is  the  ultimate  analysis,  ot 
the  percentage  of  carbon,  hydrogen,  and  oxygen  of  the  dry  coal.  It  is  found, 
however,  from  a  study  of  Mahler's  tests  that  the  proximate  analysis,  wlu'ch 
gives  fixed  carbon,  volatile  matter,  moisture,  and  ash,  may  be  relied  on  a? 
giving  a  measure  of  the  heating  value  with  a  limit  of  error  of  only  about  3$. 
After  deducting  the  moisture  and  ash,  and  calculating  the  fixed  carbon  as  a 
percentage  of  the  coal  dry  and  free  from  ash,  the  author  has  constructed  the 
following  table  : 

APPROXIMATE  HEATING  VALUE  OF  COALS. 


Percentage 
F.  C.  in 
Coal  Dry 
and  Free 
from  Ash. 

Heating 
Value 
B.T.U. 
per  Ib. 
Comb'le. 

Equiv.  Water 
Evap.  from 
and  at  212° 
per  Ib. 
Combustible. 

Percentage 
F.  C.  in 
Coal  Dry 
and  Free 
from  Ash. 

Heating 
Value 
B.T.U. 
per  Ib. 
Comb'le. 

Equiv.  Water1 
Evap.  from 
and  at  212° 
per  Ib. 
Combustible. 

100 
97 
94 
90 
87 
80 
72 

14500 
14760 
15120 
15480 
15660 
15840 
15660 

15.00 
15.28 
15.65 
16.03 
16.21 
16.40 
16.21 

68 
63 
60 
57 
54 
51 
50 

15480 
15120 
14580 
14040 
13320 
12600 
12240 

16.03 
15.65 
15.09 
14.53 
13.79 
13.04 
12.67 

Below  50$  the  law  of  decrease  of  heating-power  shown  in  the  table  appar- 
ently does  not  hold,  as  some  cannel  coals  and  lignites  show  much  higher 
heating-power  than  would  be  predicted  from  their  chemical  constitution. 

Ths  use  of  this  table  may  be  shown  as  follows: 

Given  a  coal  containing  moisture  2$,  ash  8$,  fixed  carbon  61$,  and  volatile 
matter  29$.  what  is  its  probable  heating  value  ?  Deducting  moisture  and 
ash  we  find  the  fixed  carbon  is  61/90  or  68$  of  the  total  of  fixed  carbon  and 
volatile  matter.  One  pound  of  the  coal  dry  and  free  from  ash  would,  by  the 
table,  have  a  heating  value  of  15.480  thermal  units,  but  as  the  ash  and  moist- 
ure, having  no  heating  value,  are  10$  of  the  total  weight  of  the  coal,  the 
coal  would  nave  90$  of  the  table  value,  or  13,932  thermal  units.  This  divided 
by  966.  the  latent  heat  of  steam  at  212°  gives  an  equivalent  evaporation  per 
Ib.  of  coal  of  14.42  Ibs. 


RELATIVE  VALUE  OF  STEAM  COALS.  635 

The  heating  value  that  can  be  obtained  in  practice  from  this  coal  would 
depend  upon  the  efficiency  of  the  boiler,  and  this  largely  upon  the  difficulty 
of  thoroughly  burning  its  volatile  combustible  matter  in  the  boiler  furnace. 
If  a  boiler  efficiency  of  65$  cou)d  be  obtained,  then  the  evaporation  per  Ib.  of 
coal  from  and  at  212°  would  be  14.42  x  .65  =  9.37  Ibs. 

With  the  best  anthracite  coal,  in  which  the  combustible  portion  is,  say,  97$ 
fixed  carbon  and  3$  volatile  matter,  the  highest  result  that  can  be  expected 
in  a  boiler-test  with  all  conditions  favorable  is  12.2  Ibs.  of  water  evaporated 
from  and  at  212°  per  Ib.  of  combustible,  which  is  80$  of  15.28  Ibs.  the  theo- 
retical heating-power.  With  the  best  semi-bituminous  coals,  such  as  Cum- 
berland and  Pocahontas,  in  which  the  fixed  carbon  is  80$  of  the  total  com- 
bustible, 12  5  Ibs.,  or  76%  of  the  theoretical  16.4  Ibs.,  may  be  obtained.  For 
Pittsburgh  coal,  with  a  fixed  carbon  ratio  of  68$,  11  Ibs.,  or  69$  of  the  theo- 
retical 16.03  Ibs.,  is  about  the  best  practically  obtainable  with  the  best  boilers. 
With  some  good  Ohio  coals,  with  a  fixed  carbon  ratio  of  60$,  10  Ibs.,  or  66$ 
of  the  theoretical  15.09  Ibs.,  has  been  obtained,  under  favorable  conditions, 
with  a  fire-brick  arch  over  the  furnace.  With  coals  mined  west  of  Ohio, 
with  lower  carbon  ratios,  the  boiler  efficiency  is  not  apt  to  be  as  high  as  60$. 

From  these  figures  a  table  of  probable  maximum  boiler-test  results  from 
coals  of  different  fixed  carbon  ratios  may  be  constructed  as  follows: 

Fixed  carbon  ratio 97  80  68  60  54  50 

Evap.  from  and  at  212°  per  Ib.  combustible,  maximum  in  boiler-tests: 

12.2        12.5        11  10  8.3          7.0 

Boiler  efficiency,  per  cent 80  76  69          66          60          55 

Loss,  chimney,  radiation,  imperfect  combustion,  etc  : 

20  24  31  34  40  45 

The  difference  between  the  loss  of  20$  with  anthracite  and  the  greater 
losses  with  the  other  coals  is  chiefly  due  to  imperfect  combustion  of  the 
bituminous  coals,  the  more  highly  volatile  coals  sending  up  the  chimney  the 
greater  quantity  of  smoke  and  un burned  hydrocarbon  gases.  It  is  a  measure 
of  the  inefficiency  of  the  boiler  furnace  and  of  the  inefficiency  of  heating- 
surface  caused  by  the  deposition  of  soot,  the  latter  being  primarily  caused 
by  the  imperfection  of  the  ordinary  furnace  and  its  unsuitability  to  the 
proper  burning  of  bituminous  coal.  If  in  a  boiler-test  with  an  ordinary  fur- 
nace lower  results  are  obtained  than  those  in  the  above  table,  it  is  an  indica- 
tion of  unfavorable  conditions,  such  as  bad  firing,  wrong  proportions  of 
boiler,  defective  draft,  and  the  like,  which  are  remediable.  Higher  results 
can  be  expected  only  with  gas-producers,  or  other  styles  of  furnace  espe- 
cially designed  for  smokeless  combustion. 

Kind  of  Furnace  Adapted  for  Different  Coals.  (From  the 
author's  paper  on  "The  Evaporative  Power  of  Bituminous  Coals,"  Trans. 
A.  S.  M.  E.,  iv,  257.)— Almost  any  kind  of  a  furnace  will  be  found  well 
adapted  to  burning  anthracite  coals  and  semi-bituminous  coals  containing 
less  than  20$  of  volatile  matter.  Probably  the  best  furnace  for  burning 
those  coals  which  contain  between  20$  and  40$  volatile  matter,  including  the 
Scotch,  English,  Welsh,  Nova  Scotia,  and  the  Pittsburgh  and  Monongahela 
river  coals,  is  a  plain  grate-bar  furnace  with  a  fire-brick  arch  thrown  over 
it,  for  the  purpose  of  keeping  the  combustion-chamber  thoroughly  hot.  The 
best  furnace  for  coals  containing  over  40$  volatile  matter  will  be  a  furnace 
surrounded  by  fire-brick  with  a  large  combustion-chamber,  and  some  spe- 
cial appliance  for  introducing  very  hot  air  to  the  gases  distilled  from  the 
coal,  or,  preferably,  a  separate  gas-producer  and  combustion-chamber,  with 
facilities  for  heating  both  air  arid  gas  before  they  unite  in  the  combustion - 
chamber.  The  character  of  furnace  to  be  especially  avoided  in  burning  all 
bituminous  coals  containing  over  20$  of  volatile  matter  is  the  ordinary  fur- 
nace, in  which  the  boiler  is  set  directly  above  the  grate  bars,  and  in  which  the 
heating-surfaces  of  the  boiler  are  directly  exposed  to  radiation  from  the 
coal  on  the  grate.  The  question  of  admitting  air  above  the  grate  is  still  un- 
settled. The  London  Engineer  recently  said:  "  All  our  experience,  extending 
over  many  years,  goes  to  show  that  when  the  production  of  smoke  is  pre- 
vented by  special  devices  for  admitting  air,  either  there  is  an  increase  in  the 
consumption  of  fuel  or  a  diminution  in  the  production  of  steam.  *  *  *  The 
best  smoke-preventer  yet  devised  is  a  good  fireman." 

I>o\vuward-draiiji,iit  Furnaces.— Recent  experiments  show  that 
with  bituminous  coal  considerable  saving  may  be  made  by  causing  the 
draught  to  go  downwards  from  the  freshly-fired  coal  through  the  hot  coal 
on  the  grate.  Similar  good  results  are  also  obtained  by  the  upward  draught 
by  feeding  the  fresh  coal  under  the  bed  of  hot  coal  instead  of  on  top.  (See 
Boilers.) 


636 


FUEL. 


Calorimetric  Tests  of  American  Coals.— From  a  number  of 
tests  of  American  and  foreign  coals,  made  with  an  oxygen  calorimeter,  by 
Geo.  H.  Barrus  (Trans.  A.  S.  M.  E.,  vol.  xiv.  816),  the  following  are  selected, 
showing  the  range  of  variation: 


Percentage 
of  Ash. 

Total  Heat 
of  Com- 
bustion. 
B.  T.  U. 

Total  Heat 
reduced  to 
Fuel  free 
from  Ash. 

Sem  i-  bituminous. 
George's  Cr'k,  Cumberl'd,  Md.,10  tests 

j     6.1 
1     8.6 
j     3.2 

14,217 

12,874 
14,603 

15,141 
14,085 
15,086 

New  River,  Va.,  6  tests  

1     6.2 
j     3.5 

13,608 
13,922 

14,507 
14,427 

El  '<  Garden  Va  ,  1  test    

)     5.7 

7  8 

13,858 
13,180 

14.696 
14  295 

Welsh,  1  test  

7.7 

13581 

14,714 

Hit  tinii  nous. 
Yougliiogheny,  Pa.,  lump    

5  9 

12,941 

13,752 

10.2 

11,664 

12,988 

Frontenac  Kansas                    

17  7 

10506 

12,765 

(  'ape  Breton  (Caledonia)     

8  7 

12,420 

13602 

Lancashire,  Eng  

6.8 

12,122 

13,006 

Anthracite,  11  tests  

j    10.5 

11,521 

12,873 

1     9.1 

13,189 

14,509 

Evaporative  Power  of  Bituminous  Coals. 

(Tests  with  Babcock  &  Wilcox  Boilers,  Trans.  A.  S.  M.  E.,  iv.  267.) 


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40 

1679 

7.  5 

6.3 

2.07 

11.53 

12.46 

146 

96 

2.  Anthracitescr'sl/5 

Powelton,  Pa., 

ilO^h 

3126 

8.817.6 

4.32 

11.32 

12.42 

272 

448 

Semi-bit.  4/5, 

I 

3.  Pittsbg'h  fine  slack 

4  hrs 

33.7 

1679 

12.321.9 

4.47 

8.12 

9.29 

146 

250 

"    3d  Pool  lump 

10    " 

43.5 

2760 

4.8,27.5 

4.76 

10.47 

11.00 

240 

41P 

4.  Castle  Shannon,  nr 

i 

Pittsb'gh,    %    nut, 

V42^h 

69.1 

4784 

10.5 

27.9 

4.13 

10.00 

11.17 

416 

570 

%  lump, 

) 

5  111  'k  run  of  mine  " 

6  days. 

1196 

1.41 

9  49 

104 

54 

"  Ind.  block,  '*  very 
good  " 

1196 

2.95 

9.47 

104 

111 

6.  Jackson,  O.,  nut  .. 

8  hrs. 

48 

3358 

9.6 

32.1 

4.11 

8.93 

9.  88 

292 

460 

"  Staunton,  111.,  nut.. 

8    " 

60 

3358 

17.7 

25.1 

2.27 

5.09 

6.19 

292 

246 

7.  Renton  screenings. 

5h50m 

21.2 

1564 

13.831.5 

2.95 

6.88 

7.98 

136 

151 

'  Wellington  scr'gs.. 

6h30m 

21.2 

1564 

18.327 

2.93 

7.89 

9.66 

136 

150 

4  Black  Diam.  scr'gs 

5h58m 

21.2 

1564 

19.336.4 

3.11 

6.29 

7.80 

136 

160 

'  Seattle  screenings. 

6  h  24  m 

21.2 

1564 

13.431.3 

2.91 

6.86 

7.92 

136 

150 

'  Wellington  lump.. 

6hl9m 

21.2 

1564 

13.828.2 

3.52 

9.02 

10.46 

136 

171 

'  Cardiff  lump  

6h  47m 

21.2 

1564 

11.726.7 

3.69 

10.07 

11.40 

136 

189 

*         "         " 

7  h  23  m 

21.2 

1564 

19.1!25.6 

3.35 

9.62 

11.89 

136 

174 

*  South  Paine  lump. 

6  h  35  in 

21.2 

1564 

13.9;28.9 

3.53 

8.96 

10.41 

136 

182 

'  Seattle  lump  

6h    5m 

21.2 

1564 

9.5'34.1 

3.57 

7.68 

8.49 

136 

184 

COKE. 


637 


Place  of  Test:  1.  London,  England;  2.  Peacedale,  R.  I.;  3.  Cincinnati,  O. ; 

4.  Pittsburgh,  Pa.;  5.  Chicago,  111.;  6.  Springfield,  O. ;  7.  San  Francisco, 

Cal. 

In  all  the  above  tests  the  furnace  was  supplied  with  a  fire-brick  arch  for 
prevent] in?  the  radiation  of  heat  from  the  coal  directly  to  the  boiler. 

Weathering  of  Coal.  (I.  P.  Kimball,  Trans.  A.  I.  M.  E.,  viii.  204.)— 
The  practical  effect  of  the  weathering  of  coal,  while  sometimes  increasing 
its  absolute  weight,  is  to  diminish  the  quantity  of  carbon  and  disposable 
hydrogen  and  to  increase  the  quantity  of  oxygen  and  of  indisposable  hy- 
drogen. Hence  a  reduction  in  the  calorific  value. 

An  excess  of  pyrites  in  coal  tends  to  produce  rapid  oxidation  and  mechan- 
ical disintegration  of  the  mass,  with  development  of  heat,  loss  of  coking 
power,  and  spontaneous  ignition. 

The  only  appreciable  results  of  the  weathering  of  anthracite  within  the 
ordinary  limits  of  exposure  of  stocked  coal  are  confined  to  the  oxidation  of 
its  accessory  pj-rites.  In  coking  coals,  however,  weathering  reduces  and 
finally  destroys  the  coking  power,  while  the  pyrites  are  converted  from  the 
state  of  bisulphide  into  comparatively  innocuous  sulphates. 

Richters  found  that  at  a  temperature  of  158°  to  180°  Fahr.,  three  coals  lost 
in  fourteen  days  an  average  of  3.6$  of  calorific  power.  (See  also  paper  by 
R.  P.  Rothwell,  Trans.  A.  I.  M.  E.,  iv.  55.) 

COKE. 

Coke  is  the  solid  material  left  after  evaporating  the  volatile  ingredients  of 
coal,  either  by  means  of  partial  combustion  in  furnaces  called  coke  ovens, 
or  by  distillation  in  the  retorts  of  gas-works. 

Coke  made  in  ovens  is  preferred  to  gas  coke  as  fuel.  It  is  of  a  dark-gray 
color,  with  slightly  metallic  lustre,  porous,  brittle,  and  hard. 

The  proportion  of  coke  yielded  by  a  given  weight  of  coal  is  very  different 
for  different  kinds  of  coal,  ranging  from  0.9  to  0.35. 

Being  of  a  porous  texture,  it  readily  attracts  and  retains  water  from  the 
atmosphere,  and  sometimes,  if  it  is  kept  without  proper  shelter,  from  0.15  to 
0.20  of  its  gross  weight  consists  of  moisture. 

Analyses  of  Coke. 
(From  report  of  John  R.  Procter,  Kentucky  Geological  Survey.) 


Where  Made. 

Fixed 
Carbon 

Ash. 

Sul- 
phur. 

Connellsville,  Pa.       (Ave 
Chattanooga,  Tenn. 
Birmingham,  Ala. 
Poca.hontas,  Va. 
New  River,  W.  Va. 
Big  Stone  Gap,  Ky. 

rage  c 

f  3  samples)  

88.96 
80.51 
87.29 
92.53 
92.38 
93.23 

9.74 
16.34 
10.54 
5.74 
7.21 
5.69 

0.810 
1.595 
1.195 
0.597 
0.562 
0.749 

4         "              ... 

4         *«        

3         " 

8         "          
7         **         

Experiments  in  Coking.    CONNELLSVILLE  REGION. 
(John  Fulton,  Amer.  Mfr.,  Feb.  10,  1893.) 


s 

53 

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9 

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Per  cent  of  Yield. 

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6 

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?i 

4 

-< 

c  S 

S 

^0 

o 

c  S 

ES 

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£3 

£" 

h.  m. 

Ib. 

Ib. 

Ib. 

Ib. 

Ib. 

1 

67    00 

12,420 

99 

385 

7.518 

7,903 

00.80 

3  10 

60.53 

63.63 

35.57 

2 

68    00 

1  1  ,090 

90 

359 

6,580 

6,939 

00.81 

3.24 

59.33 

62.57 

36.62 

3 

45    00 

9,120 

77 

272 

5,418 

5.690 

00.84 

2.98 

59.41 

62.39 

36  77 

4 

45    00 

9,020 

74 

349 

5,334 

5,683 

00.82 

3  87 

59.13 

63.00 

36.18 

41,650 

340 

1365 

24,850 

26,215 

00.82 

3.28 

59.66 

62.94 

36.24 

These  results  show,  in  a  general  average,  that  Connellsville  coal  carefully 
coked  in  a  modern  beehive  oven  will  yield  66.17$  of  marketable  coke,  2.30$ 
of  small  coke  or  braize,  and  0.82$  of  ash. 


638  FUEL. 

The  total  average  loss  in  volatile  matter  expelled  from  the  coal  in  coking 
amounts  to  30.71$. 

The  modern  beehive  coke  oven  is  12  feet  in  diameter  and  7  feet  high  at 
crown  of  dome.  It  is  used  in  making  48  and  72  hour  coke. 

In  making  these  tests  the  coal  was  weighed  as  it  was  charged  into  the 
oven;  the  resultant  marketable  coke,  small  coke  or  braize  and  ashes 
weighed  dry  as  they  were  drawn  from  the  oven. 

Coal  Washing.  —  In  making  coke  f  rom  coals  that  are  high  in  ash  and 
sulphur,  it  is  advisable  to  crush  and  wash  the  coal  before  coking  it.  A  coal- 
washing  plant  at  Brookwood,  Ala.,  has  a  capacity  of  50  tons  per  hour.  The 
average  percentage  of  ash  in  the  coal  during  ten  days'  run  varied  from  14$  to 
21$,  in  the  washed  coal  from  4.8$  to  8.1$.  and  in  the  coke  from  6.1$  to  10.5$. 
During  three  months  the  average  reduction  of  ash  was  60.9$.  (Eng.  and 
Milting  Jour.,  March  25,  1893.) 

Recovery  of  Byproducts  in  Coke  Manufacture.—  In  Ger- 
many considerable  progress  has  been  made  in  the  recovery  of  by  products. 
The  Hoffman-Otto  oven  has  been  most  largely  used,  its  principal  feature 
being  that  it  is  connected  with  regenerators.  In  i884  40  ovens  on  this 
S37  stem  were  running,  and  in  1892  the  number  had  increased  to  1209. 

A  Hoffman-Otto  oven  in  Westphalia  takes  a  charge  of  6J4  tons  of  dry  coal 
and  converts  it  into  coke  in  48  hours.  The  product  of  an  oven  annually  is 
1025  tons  in  the  Ruhr  district,  1170  tons  in  Silesia,  and  960  tons  in  the  Saar'dis- 
trict.  The  yield  from  dry  coal  is  75$  to  77$  of  coke,  2.5$  to  3$  of  tar,  and  1.1$ 
to  1.2$  of  sulphate  of  ammonia  in  the  Ruhr  district;  65$  to  70$  of  coke,  4$  to 
4.5$  of  tar,  and  l$to  1.25$  of  sulphate  of  ammonia  in  the  Upper  Silesia  region 
and  68$  to  72$  of  coke,  4$  to  4.3$  of  tar  and  1.8$  to  1  .9$  of  sulphate  of  ammonia 
in  the  Saar  district.  A  group  of  60  Hoffman  ovens,  therefore,  yields  annually 
the  following: 

Poke  Tar  Sulphate 

°         T       n 


. 

Ruhr...  ...............       51,800  1860  780 

UpperSilesia  ..........................       48,000  3000  840 

Saar  .................................       40,500  2400  492 

An  oven  which  has  been  introduced  lately  into  Germany  in  connection 
with  the  recovery  of  by-products  is  the  Sernet-Solvay,  which  works  hotter 
than  the  Hoffman  -Otto,  and  for  this  reason  73$  to  77$  of  gas  coal  can  be 
mixed  with  23$  to  27$  of  coal  low  in  volatile  matter,  and  yet  yield  a  good 
coke.  Mixtures  of  this  kind  yield  a  larger  percentage  of  coke,  but,  on  the 
other  hand,  the  amount  of  gas  is  lessened,  and  therefore  the  yield  of  tar  and 
ammonia  is  not  so  great. 

In  the  manufacture  of  coke  from  soft  coal  in  retort  ovens,  particularly  in 
those  constructed  so  as  to  save  the  b3r-products  formed  in  the  coking  oper- 
ations, the  coke  has  the  disadvantage  of  being  more  porous,  softer,  with 
more  easily  crushed  cell-walls  than  when  the  same  coal  is  coked  in  the 
ordinary  beehive-oven. 

References:  F.  W.  Luerman,  Verein  Deutscher  Eisenhuettenleute  1891, 
Iron  Age,  March  31,  1892  ;  Amer.  Mfr.,  April  28,  1893.  An  excellent  series 
of  articles  on  the  manufacture  of  coke,  by  John  Fulton,  of  Johnstown,  Pa., 
is  published  in  the  Colliery  Engineer,  beginning  in  January,  1893. 

Making  Hard  Coke.—  J.  J.  Fronheiser  and  C.  S  Price,  of  the  Cam- 
bria Iron  Co.,  Johnstown,  Pa.,  have  made  an  improvement  in  coke  manu- 
facture by  which  coke  of  any  degree  of  hardness  may  be  turned  out.  It  is 
accomplished  by  first  grinding  the-coal  to  a  coarse  powder  and  mixing  it 
with  a  trydrate  of  lime  (air  or  water  slacked  caustic  lime)  before  it  is 
charged  into  the  coke-ovens.  The  caustic  lime  or  other  fluxing  material 
used  is  mechanically  combined  with  the  coke,  filling  up  its  cell  walls.  It  has 
been  found  that  about  5$  by  weight  of  caustic  lime  mixed  with  the  fine  coal 
gives  the  best  results.  However,  a  larger  quantity  of  lime  can  be  added  to 
coals  containing  more  than  5$  to  7$  of  ash  (Amer.  Mfr.) 

Generation  of  Steam  from  the  Waste  Heat  and  Gases  of 
Coke-ovens.  (Erskine  Ramsey,  Amer.  Mfr.,  Feb.  1(5,  1894.)—  The  gases 
from  a  number  of  adjoining  ovens  of  the  beehive  type  are  led  into  a  long 
horizontal  flue,  and  thence  to  a  combustion-chamber  under  a  battery  of 
boilers.  Two  plants  are  in  satisfactory  operation  at  Tracy  City,  Tenn.,  and 
two  at  Pratt  Mines.  Ala. 

A  Bushel  of  Coal.  —  The  weight  of  a  bushel  of  coal  in  Indiana  is  70  Ibs., 
in  Penna.  76  Ibs.;  in  Ala.,  Colo.,  Ga.,  111.,  Ohio,  Tenn.,  and  W.  Va.  it  is  80  Ibs. 

A  Bushel  of  Coke  is  almost  uniformly  40  Ibs.,  but  in  exceptional 


WOOD   AS   FUEL.  639 

cases,  when  the  coke  is  very  light,  38,  36,  and  33  Ibs.  are  regarded  as  a  bushel. 
In  others,  from  42  to  50  Ibs.  are  given  as  the  weight  of  a  bushel  ;  in  this  case 
the  coke  would  be  quite  heavy. 

Products  of  tlie  Distillation  of  Coal — S.  P.  Sadler's  Handbook 
of  Industrial  Organic  Chemistry  gives  a  diagram  showing  over  50  chemical 
products  that  are  derived  from  distillation  of  coal.  The  first  derivatives  are 
coal-gas,  gas-liquor,  coal-tar,  and  coke.  From  the  gas-liquor  are  derived 
ammonia  and  sulphate,  chloride  and  carbonate  of  ammonia.  The  coal-tar 
is  split  up  into  oils  lighter  than  water  or  crude  naphtha,  oils  heavier  than 
water — otherwise  dead  oil  or  tar,  commonly  called  creosote, — and  pitch. 
From  the  two  former  are  derived  a  variety  of  chemical  products. 

From  the  coal-tar  there  comes  an  almost  endless  chain  of  known  combina- 
tions. The  greatest  industry  based  upon  their  use  is  the  manufacture  of 
dyes,  and  the  enormous  extent  to  which  this  has  grown  can  be  judged  from 
the  fact  that  there  are  over  GOO  different  coal-tar  colors  in  use,  and  many  more 
which  as  yet  are  too  expensive  for  this  purpose.  Many  medicinal  prepara- 
tions come  from  the  series,  pitch  for  paving  purposes,  and  chemicals  for 
the  photographer,  the  rubber  manufacturers  and  tanners,  as  well  as  for 
preserving  timber  and  cloths. 

The  composition  of  the  hydrocarbons  in  a  soft  coal  is  uncertain  and  quite 
complex;  but  the  ultimate  analysis  of  the  average  coal  shows  that  it  ap- 
proaches quite  nearly  to  the  composition  of  CH4  (marsh-gas).  (W.  H. 
Blauvelt,  Trans.  A.  I.  M.  E.,  xx.  625.) 

WOOD  AS  FUEL,. 

Wood,  when  newly  felled,  contains  a  proportion  of  moisture  which  varies 
very  much  in  different  kinds  and  in  different  specimens,  ranging  between 
30$  and  50$,  and  being  on  an  average  about  40$.  After  8  or  12  months'  ordi- 
nary drying  in  the  air  the  proportion  of  moisture  is  from  20  to  25$.  This 
degree  of  dryness,  or  almost  perfect  dryness  if  required,  can  be  produced 
by  a  few  days'  drying  in  an  oven  supplied  with  air  at  about  240°  F.  When 
coal  or  coke  is  used  as  the  fuel  for  that  oven,  1  Ib.  of  fuel  suffices  to  expel 
about  3  Ibs.  of  moisture  from  the  wood.  This  is  the  result  of  experiments 
on  a  large  scale  by  Mr.  J.  R.  Napier.  If  air- dried  wood  were  used  as 
fuel  for  the  oven,  from  2  to  2%  Ibs.  of  wood  would  probably  be  required  to 
produce  the  same  effect. 

The  specific  gravity  of  different  kinds  of  wood  ranges  from  0.3  to  1.2. 

Perfectly  dry  wood  contains  about  50$  of  carbon,  the  remainder  consisting 
almost  entirely  of  oxygen  and  hydrogen  in  the  proportions  which  form 
water.  The  coniferous  family  contain  a  small  quantity  of  turpentine,  which 
is  a  hydrocarbon.  The  proportion  of  ash  in  wood  is  from  1$  to  5$.  The 
total  heat  of  combustion  of  all  kinds  of  wood,  when  dry,  is  almost  ex- 
actly the  same,  and  is  that  due  to  the  50$  of  carbon. 

The  above  is  from  Rankine;  but  according  to  the  table  by  S.  P.  Sharpless 
in  Jour.  O.  I.  W.,  iv.  36,  the  ash  varies  from  0.03$  to  1.20$  in  American  woods, 
and  the  fuel  value,  instead  of  being  the  same  for  all  woods,  ranges  from 
3667  (for  white  oak)  to  5546  calories  (for  long-leaf  pine)  -  6600  to  9883  British 
thermal  units  for  dry  wood,  the  fuel  value  of  0.50  Ibs.  carbon  being  7272 
B.  T.  U. 

Heating  Value  of  Wood.— The  following  table  is  given  in  several 
books  of  reference,  authority  and  quality  of  coal  referred  to  not  stated. 

The  weight  of  one  cord  of  different  woods  (thoroughly  air-dried)  is  about 
as  follows : 
Hickory  or  hard  maple ....  4500  Ibs.  equal  to  1800  Ibs.  coal.  (Others  give  2000.) 

White  oak 3850    "  "      1540    "      "     (         "  1715.) 

Beech,  red  and  black  oak..  3250    "  "      1300    "      "     (         "  1450.) 

Poplar,  chestnut,  and  elm..  2350    "  "        940    "      "     (         "  1050.) 

The  average  pine 2000    "  800    "        «     (  925.) 

Referring  to  the  figures  in  the  last  column,  it  is  said  : 

From  the  above  it  is  safe  to  assume  that  2^4  Ibs.  of  dry  wood  are  equal  to 
1  Ib.  average  quality  of  soft  coal  and  that  the  full  value  of  the  same  weight 
of  different  woods  is  very  nearly  the  same — that  is,  a  pound  of  hickory  is 
worth  no  more  for  fuel  than  a  pound  of  pine,  assuming  both  to  be  dry.  It 
is  important  that  the  wood  be  dry,  as  each  10$  of  water  or  moisture  in  wood 
will  detract  about  12$  from  its  value  as  fuel. 

Taking  an  average  wood  of  the  analysis  O  51$,  H  6.5$,  O  42.0$,  ash  0.5$, 
perfectly  dry,  its  fuel  value  per  pound,  according  to  Dulong's  formula.  V '  — 


640 


FUEL. 


[l4,500  C  -|-  62,000  (H  -°  )],  is  8170  British  thermal  units.  If  the  wood,  a3 

ordinarily  dried  in  air,  contains  25$  of  moisture,  then  the  heating  value  of  a 
pound  of  such  wood  is  three  quarters  of  8170  =  6127  heat-units,  less  the 
heat  required  to  heat  and  evaporate  the  *4  1°.  °f  water  from  the  atmospheric 
temperature,  and  to  hjat  the  steam  made  from  this  water  to  the  tempera- 
ture of  the  chimney  gases,  say  150  heat-units  per  pound  to  heat  the  water  to 
212°,  966  units  to  evaporate  it  at  that  temperature,  and  100  heat-units  to 
raise  the  temperature  of  the  steam  to  420°  F.,  or  1216  in  all  =  304  for  y±  lb., 
which  subtracted  from  the  6127,  leaves  5824  heat-units  as  the  net  fuel  value 
of  the  wood  per  pound,  or  about  0.4  that  of  a  pound  of  carbon. 

Composition  of  Wood. 

(Analysis  of  Woods,  by  M.  Eugene  Chevandier.) 


Woods. 

Compositior 

. 

Carbon. 

Hydrogen. 

Oxygen. 

Nitrogen. 

Ash. 

Beech 

49  36$ 

6.01$ 

42  69$ 

0  91$ 

1.06$ 

Oak 

49.64 

5.92 

41  16 

1.29 

1.97 

Birch  

50.20 

6.20 

41.62 

1.15 

0.81 

Poplar        .     ... 

49  37 

6  21 

41  60 

0  96 

1  86 

Willow     

49.96 

5.96 

39.56 

0.96 

3.37 

Average  

49.70$ 

6.06$ 

41.  30$ 

1.05* 

1.80$ 

The  following  table,  prepared  by  M.  Violette,  shows  the  proportion  of 
water  expelled  from  wood  at  gradually  increasing  temperatures: 


Temperature. 

Water  Expelled  from  100  Parts  of  Wood. 

Oak. 

Ash. 

Elm. 

Walnut. 

257°  Fahr  

15.26 
17.93 
32.13 
35.80 
44.31 

14.78 
16.19 
21.22 
27.51 
33.38 

15.32 
17.02 
36.94? 
33.38 
40.56 

15.55 
17.43 
21.00 
41.77? 
36.56 

302°  Fahr  

347°  Fahr    

392°  Fahr  

437°  Fahr 

The  wood  operated  upon  had  been  kept  in  store  during  two  years.  When 
wood  which  has  been  strongly  dried  by  means  of  artificial  heat  is  left  ex- 
posed to  the  atmosphere,  it  reabsorbs  about  as  much  water  as  it  contains 
in  its  air-dried  state. 

A  cord  of  wood  =  4  X  4  X  8  =  128  cu.  ft.  About  56$  solid  wood  and  44$ 
interstitial  spaces.  (Marcus  Bull,  Phila.,  1829.  J.  C.  I.  W.,  vol.  i.  p.  293.) 

B.  E.  Fernow  gives  the  per  cent  of  solid  wood  in  a  cord  as  determined  offi- 
cially in  Prussia  (J.  C.  I.  WM  vol.  iii.  p.  20): 

Timber  cords,  74.07$  .=  80  cu.  ft.  per  cord; 
Firewood  cords  (over  6"  diam.),  69.44$  =  75  cu.  ft.  per  cord; 
"  Billet"  cords  (over  3"  diam.),  55.55$  =  60  cu.  ft.  per  cord; 
"  Brush  "  woods  less  than  3"  diam.,  18.52$;  Roots,  37.00$. 

CHARCOAL. 

Charcoal  is  made  by  evaporating  the  volatile  constituents  of  wood  and 
peat,  either  by  a  partial  combustion  of  a  conical  heap  of  the  material  to  be 
charred,  covered  with  a  layer  of  earth,  or  by  the  combustion  of  a  separate 
portion  of  fuel  in  a  furnace,  in  which  are  placed  retorts  containing  the  ma- 
terial to  be  charged. 

According  to  Peclet,  100  parts  by  weight  of  wood  when  charred  in  a  heap 
yield  from  17  to  22  parts  by  weight  of  charcoal,  and  when  charred  in  a 
retort  from  28  to  30  parts. 

This  has  reference  to  the  ordinary  condition  of  the  wood  used  in  charcoal- 
making,  in  which  25  parts  in  100  consist  of  moisture.  Of  the  remaining  75 
parts  the  carbon  amounts  to  one  half,  or  37^$  of  the  gross  weight  of  the 
wood.  Hence  it  appears  that  on  an  average  nearly  half  of  the  carbon  in  the 


CHARCOAL. 


641 


wood  is  lost  during  the  partial  combustion  in  a  heap,  and  about  one  quarter 
during  the  distillation  in  a  retort. 

To  char  100  parts  by  weight  of  wood  in  a  retort,  12^  parts  of  wood  must 
be  burned  in  the  furnace.  Hence  in  this  process  the  whole  expenditure  of 
wood  to  produce  from  28  to  30  parts  of  charcoal  is  112^  parts;  so  that  if  the 
weight  of  charcoal  obtained  is  compared  with  the  whole  weight  of  wood 
expended,  its  amount  is  from  25$  to  27$;  and  the  proportion  lost  is  on  an 
average  11^  -*-  37^  -  0.3,  nearly. 

According  to  Peclet,  good  wood  charcoal  contains  about  0.07  of  its  weight 
of  ash.  The  proportion  of  ash  in  peat  charcoal  is  very  variable,  and  is  es- 
timated on  an  average  at  about  0.18.  (Rankine.) 

Much  information  concerning  charcoal  may  be  found  in  the  Journal  of  the 
Charcoal-iron  Workers'  Assn.,  vols.  i.  to  vi.  From  this  source  the  following 
notes  have  been  taken: 

Yield  of  Charcoal  from  a  Cord  of  Wood.— From  45  to  50 
bushels  to  the  cord  in  the  kiln,  and  from  30  to  35  in  the  ineiler.  Prof.  Egles- 
ton  in  Trans.  A.  I.  M.  E.,  viii.  395,  says  the  yield  from  kilns  in  the  Lake 
Champlain  region  is  often  from  50  to  60  bushels  for  hard  wood  and  50  for 
soft  wood;  the  average  is  about  50  bushels. 

The  apparent  yield  per  cord  depends  largely  upon  whether  the  cord  is  a 
full  cord  of  128  cu.  ft.  or  not. 

In  a  four  months'  test  of  a  kiln  at  Goodrich,  Term.,  Dr.  H.  M.  Pierce  found 
results  as  follows:  Dimensions  of  kiln— inside  diameter  of  base,  28  ft.  8  in.; 
diam.  at  spring  of  arch,  26  ft.  8  in. ;  height  of  walls,  8  ft. ;  rise  of  arch,  5  ft. ; 
capacity,  30  cords.  Highest  yield  of  charcoal  per  cord  of  wood  (measured) 
59.27  bushels,  lowest  50.14  bushels,  average  53.65  bushels. 

No.  of  charges  12,  length  of  each  turn  or  period  from  one  charging  to 
another  11  days.  (J.  C.  I.  W.,  vol.  vi.  p.  26.) 

Results  from  Different  Methods  of  Charcoal-making. 


Yield. 

|| 

3^ 

Coaling  Methods. 

Character  of  Wood  used. 

<8.»s 

.£?>§ 

o|^ 

•£  *  o 

o  o 

O  {_ 

**>  t-l 

rC     C3     2 

&i  ^  « 

s* 

** 

03^3  o 
"OO 

||S 

Odelstjerna's    experiments 

Birch  dried  at  230  F 

35  9 

Mathieu's  retorts,  fuel  ex 
eluded  

(  Air  dry,  av.  good  yel-  ) 
•<     low    pine    weighing  > 
j     abt.  28  Ibs.  per  cu.  ft.  ) 

77.0 
65,8 

28.3 
24.2 

63.4 
54.2 

15.7 
15.7 

Mathieu's  retorts,  fuel   in- 
cluded   

Swedish  ovens,  av.  results 

j  Good  dry  fir  and  pine,  1 
j     mixed. 

81.0 

27.7 

66.7 

13.3 

Swedish  ovens,  av.  results 

j  Poor  wood,  mixed  fir  J 
1     and  pine                       f 

70.0 

25  8 

62.0 

13.3 

Swedish      meiiers     excep- 
tional             

{Fir     and     white-pine  j 
wood  mixed    Av  25  \- 

72.2 

24  7 

59.5 

13.3 

Swedish  meiiers.  av.  results 

Ibs.  oer  cu.  ft.             i 

52  5 

18  3 

43.9 

13.3 

American  kilns,  av.  results  (  Av.   good  yellow  pine  J 
American    meiiers,  av.   re-  |-j     weighing  abt.  25  Ibs.  > 
suits  if     per  cu.  ft.                      j 

54.7 
42.9 

22.0 
17.1 

45.0 

35  0 

17  5 

17.5 

Consumption  of  Charcoal  in  Blast-fiirnaces  per  Ton  of 
Pig  Iron;  average  consumption  according  to  census  of  1880,  1.14  tons 
charcoal  per  ton  of  pig.  The  consumption  at  the  best  furnaces  is  much 
below  this  average.  As  low  as  0  853  ton,  is  recorded  of  the  Morgan  furnace; 
Bay  furnace,  0.858;  Elk  Rapids,  0,884.  (1892.) 

Absorption  of  Water  and  of  Oases  by  Charcoal.  -Svedlius, 
in  his  hand-book  for  charcoal-burners,  prepared  for  the  Swedish  Govern- 
ment, says:  Fresh  charcoal,  also  reheated  charcoal,  contains  scarcely 
any  water  but  when  cooled  it  absorbs  it  very  rapidly,  so  that  after 
twenty-four  hours,  it  may  contain  4$  to  8$  of  water.  After  the  lapse  of  a 
few  weeks  the  moisture  of  charcoal  may  not  increase  perceptibly,  and  may 
be  estimated  at  10$  to  15#,  or  an  average  of  12#.  A  thoroughly  charred 
piece  of  charcoal  ought,  then,  to  contain  about  84  parts  carbon,  12  parts 
water,  3  parts  ash,  and  1  part  hydrogen. 


642 


FUEL. 


M.  Saussure,  operating  with  blocks  of  fine  boxwood  charcoal,  freshly 
burnt,  found  that  by  simply  placing  such  blocks  in  contact  with  certain 
gases  they  absorbed  them  in  the  following  proportion: 


Volumes. 

Ammonia 90.00 

Hydrochloric-acid  gas 85.00 

Sulphurous  acid ...  65.00 

Sulphuretted  hydrogen     55.00 

Nitrous  oxide  (laughing-gas) . .  40.00 
Carbonic  acid . .  35.00 


Volumes. 

Carbonic  oxide 9.42 

Oxygen 9.25 

Nitrogen 6.50 

Carburetted  hydrogen , . .    5.00 

Hydrogen 1.75 


It  is  this  enormous  absorptive  power  that  renders  of  so  much  value  a 
comparatively  slight  sprinkling  of  charcoal  over  dead  animal  matter,  as  a 
preventive  of  the  escape  of  odors  arising  from  decomposition. 

In  a  box  or  case  containing  one  cubic  foot  of  charcoal  may  be  stored 
without  mechanical  compression  a  little  over  nine  cubic  feet  of  oxygen, 
representing  a  mechanical  pressure  of  one  hundred  and  twenty-six  pounds 
to  the  square  inch.  From  the  store  thus  preserved  the  oxygen  can  be 
drawn  by  a  small  hand-pump. 

Composition  of  Charcoal  Produced  at  Various  Tempera- 
tures.   (By  M.  Violette.) 


Temperature  of   Car- 
bonization. 

Composition  of  the  Solid  Product. 

Carbon. 

Hydro- 
gen. 

Oxygen. 

Nitrogen 
and  Loss. 

Ash. 

Cent.       Fahr. 
150°          302° 
200           392 
250           482 
300           592 
350           662 
432           810 
1023          1873 

Per  cent. 
47.51 
51.82 
65.59 
73.24 
76.64 
81.64 
81.97 

Per  cent. 
6.12 
3.99 
4.81 
4.25 
4.14 
4.96 
2.30 

Per  cent. 
46.29 

43.98 
28.97 
21.96 
18.44 
15.24 
14.15 

Per  cent. 
0.08 
0.23 
0.63 
0.57 
0.61 
1.61 
l.GO 

Per  cent. 
47.51 
39.88 
32.98 
24.61 
22.42 
15.40 
15.30 

The  wood  experimented  on  was  that  of  black  alder,  or  alder  buckthorn, 
which  furnishes  a  charcoal  suitable  for  gunpowder.  It  was  previously 
dried  at  150  deg.  C.  =  302  deg.  F. 

MISCELLANEOUS    SOLID    FUELS. 

Dust  Fuel- Dust  Explosions. —Dust  when  mixed  in  air  burns  witi« 
such  extreme  rapidity  as  in  some  cases  to  cause  explosions.  Explosions  of 
flour-mills  have  been  attributed  to  ignition  of  the  dust  in  confined  passages. 
Experiments  in  England  in  1876  on  the  effect  of  coal-dust  in  carrying  flame  in 
mines  showed  that  in  a  dusty  passage  the  flame  from  a  blown-out  shot  may 
travel  50  yards.  Prof.  F.  A.  Abel  (Trans.  A.  I.  M.  E.,  xiii.  260)  says  that  coal- 
dust  in  mines  much  promotes  and  extends  explosions,  and  that  it  may  read- 
ily be  brought  into  operation  as  a  fiercely  burning  agent  which  will  carry 
flame  rapidly  as  far  as  its  mixture  with  air  extends,  and  will  operate  as  an 
explosive  agent  though  the  medium  of  a  very  small  proportion  of  fire-damp 
in  the  air  of  the  mine.  The  explosive  violence  of  the  combustion  of  dust  is 
largely  due  to  the  instantaneous  heating  and  consequent  expansion  of  the 
air.  (See  also  paper  on  "  Coal  Dust  as  an  Explosive  Agent,"  by  Dr.  R.  W. 
Raymond,  Trans.  A.  I.  M.  E.  1894.)  Experiments  made  "in  Germany  in  1893, 
show  that  pulverized  fuel  may  be  burned  without  smoke,  and  with  high 
economy.  The  fuel,  instead  of  being  introduced  into  the  fire-box  in  the 
ordinary  manner,  is  first  reduced  to  a  powder  by  pulverizers  of  any  con- 
struction. In  the  place  of  the  ordinary  boiler  fire-box  there  is  a  combustion 
chamber  in  the  form  of  a  closed  furnace  lined  with  fire-brick  and  provided 
with  an  air-injector  similar  in  construction  to  those  used  in  oil-burning  fur- 
naces. The  nozzle  throws  a  constant  stream  of  the  fuel  into  the  chamber. 
This  nozzle  is  so  located  that  it  scatters  the  powder  throughout  the  whole 


MISCELLANEOUS   SOLID   FUELS.  643 

space  of  the  fire-box.  When  this  powder  is  once  ignited,  and  it  is  veiy 
readily  done  by  first  raising  the  lining  to  a  high  temperature  by  an  open 
fire,  the  combustion  continues  in  an  intense  and  regular  manner  under  the 
action  of  the  current  of  air  which  carries  it  in.  (Mfrs.  Record,  April,  1893.) 

Powdered  fuel  was  used  in  the  Crompton  rotary  puddling-furnace  at 
Woolwich  Arsenal  England,  in  1873.  (Jour.  I.  &  S.  I  ,  i.  1873,  p.  91.) 

Peat  or  Turf,  as  usually  dried  in  the  air,  contains  from  25$  to  30$  of 
water,  which  must  be  allowed  for  in  estimating  its  heat  of  combustion.  This 
water  having  been  evaporated,  the  analysis  of  M.  Regnault  gives,  in  100 
parts  of  perfectly  dry  peat  of  the  best  quality:  C  58$,  H  6$,  O  31$,  Ash  5$. 

In  some  examples  of  peat  the  quantity  of  ash  is  greater,  amounting  to  7$ 
and  sometimes  to  11$. 

The  specific  gravity  of  peat  in  its  ordinary  state  is  about  0.4  or  0.5.  It  can 
be  compressed  by  machinery  to  a  much  greater  density.  (Rankine.) 

Clark  (Steam-engine,  i.  61)  gives  as  the  average  composition  of  dried  Irish 
peat:  C  59$,  H  6$,  O  30$,  N  1.25$,  Ash  4$. 

Applying  Dulong's  formula  to  this  analysis,  we  obtain  for  the  heating  value 
of  perfectly  dry  peat  10,260  heat-units  per  pound,  and  for  air-dried  peat  con- 
taining  25$  of  moisture,  after  making  allowance  for  evaporating  the  water, 
7391  heat-units  per  pound. 

Sawdust  as  Fuel.— The  heating  power  of  sawdust  is  naturally  the 
same  per  pound  as  that  of  the  wood  from  which  it  is  derived,  but  if  allowed 
to  get  wet  it  is  more  like  spent  tan  (which  see  below).  The  conditions  neces- 
sary for  burning  sawdust  are  that  plenty  of  room  should  be  given  it  in  the 
furnace,  and  sufficient  air  supplied  on  the  surface  of  the  mass.  The  same 
applies  to  shavings,  refuse  lumber,  etc.  Sawdust  is  frequently  burned  in 
saw-mills,  etc.,  by  being  blown  into  the  furnace  by  a  fan-blast. 

Horse-manure  has  been  successfully  used  as  fuel  by  the  Cable  Rail- 
way Co.  of  Chicago.  It  was  mixed  with  soft  coal  and  burned  in  an  ordinary 
urnace  provided  with  a  fire-brick  arch. 

Wet  Tan  Bark  as  Fuel.— Tan,  or  oak  bark,  after  having  been  used 
In  the  processes  of  tanning,  is  burned  as  fuel.  The  spent  tan  consists  of  the 
fibrous  portion  of  the  bark.  According  to  M,  Peclet,  five  parts  of  oak  bark 
produce  four  parts  of  dry  tan;  and  the  heating  power  of  perfectly  dry  tan, 
containing  15$  of  ash,  is  6100  English  units;  whilst  that  of  tan  in  an  ordinary 
•state  of  dryness,  containing  30$  of  water,  is  only  4284  English  units.  The 
weight  of  water  evaporated  from  and  at  212°  by  one  pound  of  tan,  equiva- 
lent to  these  heating  powers,  is,  for  perfectly  dry  tan,  5.46  Ibs.,  for  tan  with 
30$  moisture.  3.84  Ibs.  Experiments  by  Prof.  R.  H.  Thurslon  (Jour.  Frank. 
Inst.,  1874)  gave  with  the  Crockett  furnace,  the  wet  tan  containing  59$  of 
water,  an  evaporation  from  and  at  212°  F.  of  4.24  Ibs.  of  water  per  pound 
of  the  wet  tan,  and  with  the  Thompson  furnace  an  evaporation  of  3.19  Ibs. 
per  pound  of  wet  tan  containing  55$  of  water.  The  Thompson  furnace  con- 
sisted of  six  fire-brick  ovens,  each  9  feet  X  4  feet  4  inches,  containing  234 
square  feet  of  grate  in  all,  for  three  boilers  with  a  total  heating  surface  of 
2000  square  feet,  a  ratio  of  heating  to  grate  surface  of  9  to  1.  The  tan  was 
fed  through  holes  in  the  top.  The  Crockett  furnace  was  an  ordinary  fire- 
brick furnace,  6x4  feet,  built  in  front  of  the  boiler,  instead  of  under  it,  the 
ratio  of  heating  surface  to  grate  being  14.6  to  1.  According  to  Prof.  Thurs- 
ton  the  conditions  of  success  in  burning  wet  fuel  are  the  surrounding  of  the 
mass  so  completely  with  heated  surfaces  and  with  burning  fuel  that  it  may 
be  rapidly  dried,  and  then  so  arranging  the  apparatus  that  thorough  com- 
bustion may  be  secured,  and  that  the  rapidity  of  combustion  be  precisely 
equal  to  and  never  exceed  the  rapidity  of  desiccation.  Where  this  rapidity 
of  combustion  is  exceeded  the  dry  portion  is  consumed  completely,  leaving 
an  uncovered  mass  of  fuel  which  refuses  to  take  fire. 

Straw  as  Fuel.  (Eng'g  Mechanics,  Feb.,  1893,  p.  55.)— Experiments  in 
Russia  showed  that  winter-wheat  straw,  dried  at  230°  F.,  had  the  following 
composition:  C,  46.1;  H,  5.6;  N,  0.42:  O,  43.7:  Ash,  4.1.  Heating  value  in 
British  thermal  units:  dry  straw,  6290;  with  6$  water,  5770;  with  10$  water, 
5448.  With  straws  of  other  grains  the  heating  value  of  dry  straw  ranged 
from  5590  for  buckwheat  to  6750  for  flax. 

Clark  (S.  E.,  vol.  1,  p.  62)  gives  the  mean  composition  of  wheat  and  barley 
straw  as  C,  36;  H.  5;  O,  38;  O,  0.50;  Ash,  4.75;  water,  15.75,  the  two  straws 
varying  less  than  1$.  The  heating  value  of  straw  of  this  composition,  accord- 
ing to  Dulong's  formula,  and  deducting  the  heat  lost  in  evaporating  the 
water,  is  5155  heat  units.  Clark  erroneously  gives  it  as  8144  heat  units. 

Bagasse  as  Fuel  in  Sugar  Manufacture.- -Bagasse  is  the  name 
given  to  refuse  sugar-cane,  after  the  juice  lias  been  extracted.  Prof.  L.  A, 


644  FUEL. 

Becuel,  in  a  paper  read  before  the  Louisiana  Sugar  Chemists'  Association,  in 
1892,  says:  "  With  tropical  cane  containing  12.5$  woody  fibre,  a  juice  contain- 
ing 16.13$  solids,  and  83.37$  water,  bagasse  of,  say,  66$  and  72$  mill  extrac- 
tion would  have  the  following  percentage  composition: 

Woody  Combustible  ^rof^ 

Fibre.  Salts.  Water" 

66$  bagasse , 37  10  53 

72%  bagasse 45  9  46 

"Assuming  that  the  woody  fibre  contains  51$  carbon,  the  sugar  and  other 
combustible  matters  an  average  of  42.1$,  and  that  12,906  units  of  heat  are 
generated  for  every  ponnd  of  carbon  consumed,  the  66$  bagasse  is  capable 
of  generating  297,834  heat  units  as  against  345,200,  or  a  difference  of  47,366 
units  in  favor  of  the  72$  bagasse. 

"Assuming  the  temperature  of  the  waste  gases  to  be  450°  F.,  that  of  the 
surrounding  atmosphere  and  water  in  the  bagasse  at  86°  F.,  and  the  quan- 
tity of  air  necessary  for  the  combustion  of  one  pound  of  carbon  at  24  Ibs., 
the  lost  heat  will  be  as  follows:  In  the  waste  gases,  heating  air  from  86°  to 
450°  F.,  and  in  vaporizing  the  moisture,  etc.,  the  66$  bagasse  will  require 
112,546  heat  units,  and  116,150  for  the  72$  bagasse. 

"  Subtracting  these  quantities  from  the  above,  we  find  that  the  66$  bagasse 
will  produce  185,288  available  heat  units,  or  nearly  38$  less  than  the  72$ 
bagasse,  which  gives  299,050  units.  Accordingly,  one  ton  of  cane  of  2000  Ibs. 
at  66$  mill  extraction  will  produce  680  Ibs.  bagasse,  equal  to  125,995,840  avail- 
able heat  units,  while  the  same  cane  at  72$  extraction  will  produce  560  Ibs. 
bagasse,  equal  to  167,468,000  units. 

"A  similar  calculation  for  the  case  of  Louisiana  cane  containing  10$  woody 
fibre,  and  16$  total  solids  in  the  juice,  assuming  75$  mill  extraction,  shows 
that  bagasse  from  one  ton  of  cane  contains  157,395,640  heat  units,  from 
which  56,146,500  have  to  be  deducted. 

"  This  would  make  such  bagasse  worth  on  an  average  nearly  92  Ibs.  coal 
per  ton  of  cane  ground.  Under  fairly  good  conditions,  1  Ib.  coal  will  evap- 
orate 7^  Ibs.  water,  while  the  best  boiler  plants  evaporate  10  Ibs.  Therefore, 
the  bagasse  from  1  ton  of  cane  at  75$  mill  extraction  should  evaporate  from 
689  Ihs.  to  919  Ibs.  of  water.  The  juice  extracted  from  such  cane  would  un- 
der these  conditions  contain  1260  Ibs.  of  water.  If  we  assume  that  tlio 
water  added  during  the  process  of  manufacture  is  10$  (by  weight)  of  the 
juice  made,  the  total  water  handled  is  1410  Ibs.  From  the  juice  represented 
in  this  case,  the  commercial  massecuite  would  be  about  15$  of  the  weight  of 
the  original  mill  juice,  or  say  225  Ibs.  Said  mill  juice  1500  Ibs.,  plus  10$, 
equals  1650 Ibs.  liquor  handled;  and  1650  Ibs..  minus  225  Ibs.,  equals  1425  Ibs., 
the  quantity  of  water  to  be  evaporated  during  the  process  of  manufacture. 
To  effect  a  7^-lb.  evaporation  requires  190  Ibs.  of  coal,  and  142^  Ibs.  for  a  10- 
Ib.  evaporation. 

"To  reduce  1650  Ibs.  of  juice  to  syrup  of,  say,  27°  Baume,  requires  the  evap- 
oration of  1770  Ibs  of  water,  leaving  480  Ibs.  of  syrup.  If  this  work  be  ac- 
complished in  the  open  air,  it  will  require  about  156  Ibs.  of  coal  at  7*4  Ibs. 
boiler  evaporation,  and  117  at  10  Ibs.  evaporation. 

•'  With  a  double  effect  the  fuel  required  would  be  from  59  to  78  Ibs.,  and 
with  a  triple  effect,  from  36  to  52  Ibs. 

"To  reduce  the  above  480  Ibs.  of  syrup  to  the  consistency  of  commercial 
massecuite  means  the  further  evaporation  of  255  Ibs.  of  water,  requiring 
the  expenditure  of  34  Ibs.  coal  at  7^  Ibs.  boiler  evaporation,  and  25J/£  Ibs. 
with  a  10-lb.  evaporation.  Hence,  to  manufacture  one  ton  of  cane  into  sugar 
and  molasses,  it  will  take  from  145  to  190  Ibs.  additional  coal  to  do  the  work 
by  the  open  evaporator  process;  from  85  to  112  Ibs.  with  a  double  effect,  and 
only  7^j  Ibs.  evaporation  in  the  boilers,  while  with  10  Ibs.  boiler  evaporation 
the  bagasse  alone  is  capable  of  furnishing  8$  more  heat  than  is  actually  re- 
quired to  do  the  work.  With  triple-effect  evaporation  depending  on  the  ex- 
cellence of  the  boiler  plant,  the  1425  Ibs.  of  water  to  be  evaporated  from  the 
juice  will  require  between  62  and  86  Ibs.  of  coal.  These  values  show  that 
from  6  to  30  Ibs.  of  coal  can  be  spared  from  the  value  of  the  bagasse  to  run 
engines,  grind  cane,  etc. 

"It  accordingly  appears,"  says  Prof.  Becuel,  "that  with  the  best  boiler 
plants,  those  taking  up  all  the  available  heat  generated,  by  using  this  heat 
economically  the  bagasse  can  be  made  to  supply  all  the  fuel  required  by  oui 
sugar-houses." 


PETROLEUM. 


645 


PETROLEUM. 

Products  of  the  Distillation  of  Crude  Petroleum. 

Crude  American  petroleum  of  sp.  gr.  0.800  may  be  split  up  by  fractional 
distillation  as  follows  (Robinson's  Gas  and  Petroleum  Engines): 


Temp,  of 
Distillation 
Fahr. 

Distillate. 

Percent- 
ages. 

Specific 
Gravity. 

Flashing 
Point. 
Deg.  F. 

113° 

Rhigolene.     / 

traces 

590  to  625 

113  to  140° 
HO  to  158° 
158  to  248° 
248° 
to 

Chymogerie.  j    * 
Gasolene  (petroleum  spirit).  .  . 
Benzine,  naphtha  C,  benzolene. 
(  Benzine,  uaphtha  B  
A  

1.5 
10. 
2.5 

2. 

.636  to  .657 
.680  to  .700 
.714  to  .718 
.725  to  .737 

"*ii'v 

32 

347° 

(  Polishing  oils  

338°  and  ) 

Kerosene  (lamp-oil).       .  . 

50. 

802  to  820 

100  to  122 

upwards,  f 
482° 

Lubricating  oil  

15 

850  to  915 

230 

Paraffine  wax  

2. 

Residue  and  Loss  

16. 

Lima  Petroleum,  produced  at  Lima,  Ohio,  is  of  a  dark  green  color, 
very  fluid,  and  marks  48°  Baum6  at  15°  C.  (sp.  gr.,  0.792). 

The  distillation  in  fifty  parts,  each  part  representing  2%  by  volume,  gave 
the  following  results : 


Per 

Sp. 

Per 

Sp. 

Per 

Sp. 

Per 

Sp. 

Per 

Sp. 

Per 

Sp. 

cent. 

Gr. 

cent. 

Gr. 

cent. 

Gr. 

cent. 

Gr. 

cent. 

Gr. 

cent. 

Gr. 

2 

0.680 

18 

0.720 

34 

0.764 

50 

0.802 

68 

0.820 

88 

0.815 

4 

.683 

20 

.728 

36 

.768 

52) 

70 

.825 

90 

.815 

6 

.685 

22 

.730 

38 

.772 

tot 

.806 

72 

.830 

S" 

8 

.690 

24 

.735 

40 

.778 

58  J 

73 

.830 

921 

3 

10 

.694 

26 

.740 

42 

.782 

60 

.800 

76 

.810 

toV 

3 

12 

.698 

28 

.742 

44 

.788 

62 

.804 

78 

.820 

100  \ 

2 

14 

.700 

30 

.746 

46 

.792 

64 

.808 

82 

.818 

0) 

16 

.706 

32 

.760 

48 

.800 

66 

.812 

86 

.816 

« 

RETURNS. 

16  per  cent  naphtha,  70°  Baume.  6  per  cent  paraffine  oil. 

68  burning  oil.  10        "         residuum. 

The  distillation  started  at  23°  C.,  this  being  due  to  the  large  amount  of 
naphtha  present,  and  when  60$  was  reached,  at  a  temperature  of  310°  C., 
the  hydrocarbons  remaining  in  the  retort  were  dissociated,  then  gases 
escaped,  lighter  distillates  were  obtained,  and,  as  usual  in  such  cases,  the 
temperature  decreased  from  310°  C.  down  gradually  to  200°  C.,  until  75$  of 
oil  was  obtained,  and  from  this  point  the  temperature  remained  constant 
until  the  end  of  the  distillation.  Therefore  these  hydrocarbons  in  statu 
mnriendi  absorbed  much  heat.  (Jour.  Am.  Chem.  Soc.) 

Value  of  Petroleum  as  Fuel.— Thos.  Urquhart,  of  Russia  (Proc. 
Inst.  M.  E.,  Jan.  1889),  gives  the  following  table  of  the  theoretical  evapora- 
tive power  of  petroleum  in  comparison  with  that  of  coal,  as  determined  by 
Messrs.  Favre  &  Silbermann: 


Fuel. 

Specific 
Gravity 
at 
32°  F., 
Water 
=  1.000. 

Chem.  Comp. 

Heating- 
power, 
British 
Thermal 
Units. 

Theoret. 
Evap.,  Ibs. 
Water  per 
Ib.  Fuel, 
from  and 
at  212°  F. 

C. 

H. 

O. 

Penna.  heavy  crude  oil  
Caucasian  light  crude  oil.  . 
"         heavy    **      "  .. 
Petroleum  refuse  
Good  English  Coal,  Mean 
of  98  Samples  

S.  G. 
0.886 
0.884 
0.938 
0.928 

1.380 

84.9 
86.3 
86.6 

87.1 

80.0 

p.  c. 
13.7 
13.6 
12.3 

11.7 

5.0 

p.  c. 

1.4 
0.1 
1.1 
1.2 

8.0 

Units. 
20.736 

22,027 
20,138    • 
19,832 

14,112 

Ibs. 

21.48 
22.79 
20.85 
20.53 

14.61 

646  FUEL. 

In  experiments  on  Russian  railways  with  petroleum  as  fuel  Mr.  Urquhart 
obtained  an  actual  efficiency  equal  to  82%  of  the  theoretical  beating-value 
The  petroleum  is  fed  to  the  furnace  by  means  of  a  spray-injector  driven  by 
steam.  An  induced  current  of  airiscariied  in  around  the  injector-nozzle, 
and  additional  air  is  supplied  at  the  bottom  of  the  furnace. 

Oil  vs.  Coal  as  Fuel.  (Iron  Age,  Nov.  2.  1893.)— Test  by  the  Twin 
City  Rapid  Transit  Company  of  Minneapolis  and  St.  Paul.  This  test  showed 


price  of  coal  was  $3  85  per  ton  of  2000  Ibs.  With  the  same  coal  at  $2.00  per 
ton,  the  coal  was  37%  more  economical,  and  with  the  coal  at  $4.85  per  ton, 
the  coal  was  20$  more  expensive  than  the  oil.  These  results  include  the 
difference  in  the  cost  of  handling  the  coal,  ashes,  and  oil. 

In  1892  there  were  reported  to  the  Engineers1  Club  of  Philadelphia  some 
comparative  figures,  from  tests  undertaken  to  ascertain  the  relative  value 
of  coal,  petroleum,  and  gas. 

Lbs.  Water,  from 
and  at  212°  F. 

]  Ib.  anthracite  coal  evaporated 9. 70 

1  Ib.  bituminous  coal 10.14 

1  Ib.  fuel  oil,  30°  gravity 16.48 

1  cubic  foot  gas,  20  C.  P 1.28 

The  gas  used  was  that  obtained  in  the  distillation  of  petroleum,  having 
about  the  same  fuel-value  as  natural  or  coal-gas  of  equal  candle-power. 

Taking  the  efficiency  of  bituminous  coal  as  a  basis,  the  calorific  energy  of 
petroleum  is  more  than  60$  greater  than  that  of  coal;  whereas,  theoretically, 
petroleum  exceeds  coal  only  about  45$ — the  one  containing  14,500  heat-units^ 
and  the  other  21,000. 

Crude  Petroleum  vs.  Indiana  Block  Coal  for  Steam1 
raising  at  the  South  Chicago  Steel  Works.  (E.  C.  Potter, 
Trans.  A.  I.  M.  E.,  xvii,  807.)— With  coal.  14  tubular  boilers  16  ft.  X  5  ft.  re- 
quired  25  men  to  operate  them :  with  fuel  oil,  6  men  were  required,  a  saving 
of  19  men  at  $2  per  day,  or  $38  per  day. 

For  one  week's  work  2731  barrels  of  oil  were  used,  against  848  tons  of  coal 
required  for  the  same  work,  showing  3. 22  barrels  of  oil  to  be  equivalent  to  1 
ton  of  coal.  With  oil  at  60  cents  per  barrel  and  coal  at  $2.15  per  ton,  the  rel- 
ative cost  of  oil  to  coal  is  as  $1.93  to  $2.15.  No  evaporation  tests  were 
made. 

Petroleum  as  a  Metallurgical  Fuel.— C.  E.  Felton  (Trans.  A.  1 
M.  E..  xvii.  809)  reports  a  series  of  trials  with  oil  as  fuel  in  steel-heating  anc 
open-hearth  steel-furnaces,  and  in  raising  steam  with  results  as  follows:  1. 
In  a  run  of  six  weeks  the  consumption  of  oil,  partly  refined  (the  paraffine 
and  some  of  the  naphtha  being  removed),  in  heating  14-inch  ingots  in  Siemen  s 
furnaces  was  about  6^  gallons  per  ton  of  blooms.  2.  In  melting  in  a  30-ton 
open  h«arth  furnace  48  gallons  of  oil  were  used  per  ton  of  ingots.  3.  In  a 
six  weeks1  trial  with  Lima  oil  from  47  to  54  gallons  of  oil  were  required  p  ?i' 
ton  of  ingots.  4.  In  a  six  months'  trial  with  Siemens  heating-furnaces  the 
consumption  of  Lima  oil  was  6  gallons  per  ton  of  ingots.  Under  the  most 
favorable  circumstances,  charging  hot  ingots  and  running  full  capacity,  /^ 
to  5  gallons  per  ton  were  required.  5.  In  raising  steam  in  two  100-H.P. 
tubular  boilers,  the  feed- water  being  supplied  at  160°  F.,  the  average  evap- 
oration was  about  12  pounds  of  water  per  pound  of  oil,  the  best  12  hours' 
work  being  16  pounds. 

In  all  of  the  trials  the  oil  was  vaporized  in  the  Archer  producer,  an  apparat- 
us for  mixing  the  oil  and  superheated  steam,  and  heating  the  mixture  to  a 
high  temperature.  From  0.5  Ib.  to  0.75  Ib.  of  pea-coal  was  used  per  gallon 
of  oil  in  the  producer  itself. 

FUEL  GAS. 

The  following  notes  are  extracted  from  a  paper  by  W.  J.  Taylor  on  "The 
Energy  of  Fuel  "  (Trans.  A.  I.  M.  E.,  xviii.  205): 

Carbon  Gas. — In  the  old  Siemens  producer,  practically,  all  the  heat  of 
primary  combustion— that  is,  the  burning  of  solid  carbon  to  carbon  monox- 
ide, or  about  30$  of  the  total  carbon  energy — was  lost,  as  little  or  no  steam 
was  used  in  the  producer,  and  nearly  all  the  sensible  heat  of  the  gas  was 
dissipated  in  its  passage  from  the  producer  to  the  furnace,  which  was  usu- 
ally placed  at  a  considerable  distance. 

Modern  practice  has  improved  on  this  plan,  by  introducing  steam  with  the 


FUEL   (IAS.  647 

air  blown  into  the  producer,  and  by  utilizing  the  sensible  heat  of  the  gas  in 
the  combustion-furnace.  It  ought  to  be  possible  to  oxidize  one  out  of  every 
four  Ibs.  of  carbon  with  oxygen  derived  from  water-vapor.  The  thermic 
reactions  in  this  operation  are  as  follows: 

Heat-units. 
4  Ibs.  C  burned  to  CO  (3  Ibs.  gasified  with  air  and  1  Ib.  with  water) 

develop 17,600 

1.5  Ibs.  of  water  (which  furnish  1.33  Ibs.  of  oxygen  to  combine  with  1 

Ib.  of  carbon)  absorb  by  dissociation 10,333 

The  gas,  consisting  of  9.333  Ibs.  CO,  0.167  Ib.  H,  and  13.39  Ibs.  N,  heated 

600°,  absorbs 3,748 

Leaving  for  radiation  and  loss  3,519 


?7,600 

The  steam  which  is  blown  into  a  producer  with  the  air  is  almost  all  con- 
densed into  finely-divided  water  before  entering  the  fuel,  and  consequently 
is  considered  as  water  in  these  calculations. 

The  1.5  Ibs.  of  water  liberates  .1671b.  of  hydrogen,  which  is  delivered  to 
the  gas,  and  yields  in  combustion  the  same  heat  that  it  absorbs  in  the  pro- 
ducer by  dissociation.  According  to  this  calculation,  therefore,  60*  of  the 
heat  of  primary  combustion  is  theoretically  recovered  by  the  dissociation  of 
steam,  and,  even  if  all  the  sensible  heat  of  the  gas  be  counted,  with  radia- 
tion and  other  minor  items,  as  loss,  yet  the  gas  must  carry  4  X  14,500  — 
(3748  +  3519)  =  50,733  heat-units,  or  87*  of  the  calorific  energy  of  the  carbon. 
This  estimate  shows  a  loss  in  conversion  of  13*,  without  crediting  the  gas 
with  its  sensible  heat,  or  charging  it  with  the  heat  required  for  generating 
the  necessary  steam,  or  taking  into  account  the  loss  due  to  oxidizing  some 
of  the  carbon  to  CO2.  In  good  producer-practice  the  proportion  of  CO2  in 
the  gas  represents  from  4%  to  7%  of  the  C  burned  to  CO2,  but  the  extra  heat 
of  this  combustion  should  be  largely  recovered  in  the  dissociation  of  more 
water-vapor,  and  therefore  does  not  represent  as  much  loss  as  it  would  indi- 
cate. As  a  conveyer  of  energy,  this  gas  has  the  advantage  of  carrying  4.46 
Ibs.  less  nitrogen  than  would  be  present  if  the  fourth  pound  of  coal  bad 
been  gasified  with  air;  and  in  practical  working  the  use  of  steam  reduces 
the  amount  of  clinkering  in  the  producer. 

Anthracite  Gas. — In  anthracite  coal  there  is  a  volatile  combustible 
varying  in  quantity  from  1.5*  to  over  7*.  The  amount  of  energy  derived 
from  the  coal  is  shown  in  the  following  theoretical  gasification  made  with 
coal  of  assumed  composition:  Carbon,  85*;  vol.  HC,  5*;  ash,  10*:  80  Ibs.  car- 
bon assumed  to  be  burned  to  CO;  5  Ibs.  carbon  burned  to  CO2;  three  fourths 
of  the  necessary  oxygen  derived  from  air,  and  one  fourth  from  water. 

, Products. — , 

Process.  Pounds.    Cubic  Feet.    Anal,  by  Vol. 

80  Ibs.  C  burned  to CO    186.66  2529.24  33.4 

5  Ibs.  C  burned  to  CO2      18.33  157.64  2.0 

5  Ibs.  vol.  HC  (distilled) 5.00  116.60  1.6 

120  Ibs.  oxygen  are  required,  of  which 

301bs.  from  H2O  liberate H        3.75  712.50  9.4 

90  Ibs.  from  air  are  associatied  with  N    301 .05          4064.17  53.6 


514.79  7580.15  100.0 


Energy  in  the  above  gas  obtained  from  100  Ibs.  anthracite: 

186.66  Ibs.  CO 807,304  heat-units. 

5.00    "    CH4 117,500 

3.75    "        H 232,500          " 


1,157,304 

Total  energy  in  gas  per  Ib 2,248          " 

"  100  Ibs.  of  coal..  1,349,500 

Efficiency  of  the  conversion 86*. 

The  sum  of  CO  and  H  exceeds  the  results  obtained  in  practice.  The  sen- 
sible heat  of  the  gas  will  probably  account  for  this  discrepancy,  and,  there- 
fore, it  is  safe  to  assume  the  possibility  of  delivering  at  least  82*  of  the 
energy  of  the  anthracite. 

Bituminous  Gas. — A  theoretical  gasification  of  100  Ibs.  of  coal,  con- 
taining 55*  of  carbon  and  32*  of  volatile  combustible  (which  is  above  the 
average  of  Pittsburgh  coal),  is  made  in  the  following  table.  It  is  assumed 
that  50  Ibs.  of  C  are  burned  to  CO  and  5  Ibs.  to  CO2;  one  fourth  of  the  O  is 


648  FUEL. 

derived  from  steam  and  three  fourths  from  air;  the  heat  value  of  the 
volatile  combustible  is  taken  at  20,000  heat-units  to  the  pound.  In  comput- 
ing volumetric  proportions  all  the  volatile  hydrocarbons,  fixed  as  well  as 
condensing,  are  classed  as  marsh-gas,  since  it  is  only  by  some  such  tenta- 
tive assumption  that  even  an  approximate  idea  of  the  volumetric  composi- 
tion can  be  formed.  The  energy,  however,  is  calculated  from  weight: 

, Products. v 

Process.                                       Pounds.  Cubic  Feet.  Anal,  by  Vol. 

50  Ibs.  C  burned  to CO    116.66  1580.7  27.8 

5  Ibs.  C  burned  to COo      18.33  157.6  2.7 

32  Ibs.  vol.  HC  (distilled) 32.00  746.2  13.2 

80  Ibs.  O  are  required,  of  which  20  Ibs., 

derived  from  H2O,  liberate H        2.5  475.0  8.3 

60   Ibs.  O,  derived  from  air,  are  asso- 
ciated with N    200.70  2709.4  47.8 

370.19  5668.9  99.8 

Energy  in  116.66  Ibs.  CO 504,554  heat-units. 

41     32.00  Ibs.  vol.  HC....     640,000 
44        *4      2.50  Ibs.  H 155,000 

1,299,554          " 

Energy  in  coal 1,437,500          " 

Per  cent  of  energy  delivered  in  gas 90.0 

Heat-units  in  1  Ib.  of  gas. 3,484 

"Water-gas.— Water-gas  is  made  in  an  intermittent  process,  by  blowing 
up  the  fuel-bed  of  the  producer  to  a  high  state  of  incandescence  (and  in 
some  cases  utilizing  the  resulting  gas,  which  is  a  lean  producer-gas),  then 
shutting  off  the  air  and  forcing  steam  through  the  fuel,  which  dissociates 
the  water  into  its  elements  of  oxygen  and  hydrogen,  the  former  combining 
with  the  carbon  of  the  coal,  and  the  latter  being  liberated. 

This  gas  can  never  play  a  very  important  part  in  the  industrial  field,  owing 
to  the  large  loss  of  energy  entailed  in  its  production,  yet  there  are  places 
and  special  purposes  where  it  is  desirable,  even  at  a  irreat  excess  in  cost  per 
unit  of  heat  over  producer-gas;  for  instance,  in  small  high-temperature  fur- 
naces, where  much  regeneration  is  impracticable,  or  where  the  "  blow-up  " 
gas  can  be  used  for  other  purposes  instead  of  being  wasted. 

The  reactions  and  energy  required  in  the  production  of  1000  feet  of  water- 
gas,  composed,  theoretically,  of  equal  volumes  of  CO  and  H,  are  as  follows: 

500  cubic  feet  of  H  weigh 2.635  Ibs. 

500  cubic  feet  of  CO  weigh 36.89     " 

Total  weight  of  1000  cubic  feet 39.525  Ibs. 

Now,  as  CO  is  composed  of  12  parts  C  to  16  of  O,  the  weight  of  C  in  36.89 
Ibs.  is  15.81  Ibs.  and  of  O  21.08  Ibs.  When  this  oxygen  is  derived  from  water 
it  liberates,  as  above,  2.635  Ibs.  of  hydrogen.  The  heat  developed  and  ab- 
sorbed in  these  reactions  (roughly,  as  we  will  not  take  into  account  the  en- 
ergy required  to  elevate  the  coal  from  the  temperature  of  the  atmosphere 
to  say  1800°)  is  as  follows: 

Heat-units. 
2.635  Ibs.  H  absorb  in  dissociation  from  water  2.635  X  62,000..  =  163,370 

15.81  Ibs.  C  burned  to  CO  develops  15.81  X  4400 =    69,564 

Excess  of  heat- absorption  over  heat-development =    93,806 

If  this  excess  could  be  made  up  from  C  burnt  to  CO2  without  loss  by  radi- 
ation, we  would  only  have  to  burn  an  additional  4.83  Ibs.  C  to  supply  this 
heat,  and  we  could  then  make  1000  feet  of  water-gas  from  20.64  Ibs.  of  car- 
bon (equal  24  Ibs.  of  85$  coal).  This  would  be  the  perfection  of  gas-making, 
as  the  gas  would  contain  really  the  same  energy  as  the  coal;  but  instead,  we 
require  in  practice  more  than  double  this  amount  of  coal,  and  do  not  deliver 
more  than  50$  of  the  energy  of  the  fuel  in  the  gas,  because  the  supporting 
heat  is  obtained  in  an  indirect  way  and  with  imperfect  combustion.  Besides 
this,  it  is  not  often  that  the  sum  of  the  CO  and  H  exceed  90$,  the  balance  be- 
ing CO2  and  N.  But  water-gas  should  be  made  with  much  less  loss  of  en- 
ergy by  burning  the  "blow-up"'  (producer)  gras  in  brick  regenerators,  the 
stored -up  heat  of  which  can  be  returned  to  the  producer  by  the  air  used  in 
blowing-up. 

The  following  table  shows  what  may  be  considered  average  volumetric 


FUEL  GAS. 


649 


analyses,  and  the  weight  and  energy  of  1000  cubic  feet,  of  the  four  types  of 
gases  used  for  heating  and  illuminating  purposes: 


Natural 
Gas. 

Coal- 
gas. 

Water- 
gas. 

Produc 

;er-gas. 

CO  

0  50 

6  0 

45  0 

Anthra. 

27  0 

Bitu. 

27  0 

H 

2  18 

46  0 

45  0 

12  0 

12  0 

CH4  

92  6 

40  0 

2  0 

1  2 

2  5 

C.H4  

0.31 

4.0 

0  4 

cbo 

0  26 

0  5 

4  0 

2  5 

2  5 

N 

3  61 

1  5 

2  0 

57  0 

56  2 

o 

0  34 

0  5 

0  5 

0  3 

0  3 

Vapor               

1  5 

1  5 

Pounds  in  1000  cubic  feet 

#45  6 

32  0 

45  6 

65  6 

65  9 

Heat  units  in  1000  cubic  feet  

1,100,000 

735,000 

322,000 

137,455 

156,917 

Natural  Gas  in  Ohio  and  Indiana. 

(Eng.  and  M.  «/.,  April  21,  1894.) 


Description. 

Ohio. 

Indiana. 

Fos- 
toria. 

Findlay 

St 
Mary's. 

Muncie. 

Ander- 
son. 

Koko- 
mo. 

Mar- 
ion. 

Hydrogen  

1.89 
92.84 
.20 
.55 
.20 
.35 
3.82 
.15 

1.64 
93.35 
.35 
.41 
.25 
.39 
3.41 
.20 

1.94 
93.85 
.20 
.44 
.23 
.35 
2.98 
.21 

2.35 
92.67 
.25 
.45 
.25 
.35 
3.53 
.15 

1.86 
93.07 
.47 
.73 
.26 
.42 
3.02 
.15 

1.42 
94.16 
.30 
.55 
.29 
.30 
2.80 
.18 

1.20 
93.57 
.15 
.60 
.30 
.55 
3.42 
.20 

Marsh-gas 

Olefian  t  gas  

Carbon  monoxide.. 
Carbon  dioxide  
Oxygen  
Nitrogen  

Hydrogen  sulphide 

Approximately  30,000  cubic  feet  of  gas  have  the  heating  power  of  one 
ton  of  coal. 

Producer-gas  from  One  Ton  of  Coal. 

(W.  H.  Blauvelt,  Trans.  A.  I.  M.  E.,  xviii.  614.) 


Analysis  by  Vol. 

Per 

Cent. 

Cubic  Feet. 

Lbs. 

Equal  to  — 

CO 

25.3 
9.2 
3.1 
0.8 
3.4 
58.2 

33,213.84 
12,077.76 
4,069.68 
1,050.24 
4,463.52 
76,404.96 

2451.20 
63.56 
174.66 
77.78 
519.02 
5659.63 

1050.51  Ibs 
63.56     ' 
174.66     ' 
77.78     ' 
141.54     ' 
7350.17     ' 

C  +1400.  7  Ibs.  O. 
H. 
CH4. 
C2H4. 
C  +  377.  44  Ibs.  0. 
Air. 

H  
CH4  

S??4  
\^\j  

N  (by  difference. 

100.0 

131,280.00 

8945.85 

Calculated  upon  this  basis,  the  131,280  ft,  of  gas  from  the  ton  of  coal  con- 
tained 20,311,162  B.T.U.,  or  155  B.T.U.  per  cubic  ft.,  or  2270  B.T.U.  per  Ib. 

The  composition  of  the  coal  from  which  this  gas  was  made  was  as  follows: 
Water,  1.26$;  volatile  matter,  36.22$;  fixed  carbon,  57.98$;  sulphur,  0.70$; 
ash,  3.78$.  One  ton  contains  1159.6  Ibs.  carbon  and  724.4  Ibs.  volatile  com- 
bustible, the  energy  of  which  is  31,302,200  B.T.U.  Hence,  in  the  processes  of 
gasification  and  purification  there  was  a  loss  of  35.2$  of  the  energy  of  the 
coal. 

The  composition  of  the  hydrocarbons  in  a  soft  coal  is  uncertain  and  quite 
complex;  but  the  ultimate  analysis  of  the  average  coal  shows  that  it  ap- 
proaches quite  nearly  to  the  composition  of  CH4  (marsh-gas). 

Mr.  Blauvelt  emphasizes  the  following  points  as  highly  important  in  soft- 
coal  producer-practice; 


A  min  

C02. 
3.6 

0. 
0.4 

W 

CO. 

20  0 

H. 
5.3 

A  max  
A  average  .  .  . 
B  min  
B  max  
B  average  .  .  . 

5.6 
,     4.84 
4.6 
,     6.0 
5.3 

0.4 
0.4 
0.4 
0.8 
0.54 

0.4 
0.34 
0.2 
0.4 
0.36 

24.8 
22.1 
20.8 
24.0 
22.74 

8.5 

6.8 
6.9 
9.8 
8.37 

650  FUEL. 

First.  That  a  large  percentage  of  the  energy  of  the  coal  is  lost  when  the 
gas  is  made  in  the  ordinary  low  producer  and  cooled  to  the  temperature  of 
the  air  before  being  used.  To  prevent  these  sources  of  loss,  the  producer 
should  be  placed  so  as  to  lose  as  little  as  possible  of  the  sensible  heat  of  the 
gas,  and  prevent  condensation  of  the  hydrocarbon  vapors.  A  high  fuel-bed 
should  be  carried,  keeping  the  producer  cool  on  top,  thereby  preventing  the 
breaking-down  of  the  hydrocarbons  and  the  deposit  of  soot,  as  well  as  keep- 
ing the  carbonic  acid  low. 

Second.  That  a  producer  should  be  blown  with  as  much  steam  mixed  with 
the  air  as  will  maintain  incandescence.  This  reduces  the  percentage  of 
nitrogen  and  increases  the  hydrogen,  thereby  greatly  enriching  the  gas. 
The  temperature  of  the  producer  is  kept  down,"  diminishing  the  loss  of  heat 
by  radiation  through  the  walls,  and  in  s  largre  measure  preventing  clinkers 

The  Combustion  of  Producer-gas.  (H.  H.  Campbell,  Trans. 
A.  I.  M.  E.,  xix.  128.) — The  combustion  of  the  components  of  ordinary  pro- 
ducer-gas may  be  represented  by  the  following  formulae: 

C2H4  +  GO  =  2C02  +  2HaO;        2H  +  O  =  HaO; 
CH4  4-  40  =    C02  +  2H20 ;        CO  -f  O  =  CO2. 

AVERAGE  COMPOSITION  BY  VOLUME  OF  PRODUCER-GAS:  A,  MADE  WITH  OPEN 
GRATES,  NO  STEAM  IN  BLAST;  B,  OPEN  GRATES,  STEAM-JET  IN  BLAST.  10 
SAMPLES  OF  EACH. 

CH4.  N. 

3.0  58? 

5.2  644 

3.74  61  78 

2.2  57.2 

3.4  620 

2.56  60.13 

The  coal  used  contained  carbon  82%,  hydrogen  4.7$. 
The  following  are  analyses  of  products  of  combustion  : 

CO2.          O.  CO.         CH4.          H.          N. 

Minimum 15.2  0.2        trace.      trace.       trace.     80.1 

Maximum 17.2  1.6  2.0  0.6  2.0       83.6 

Average 16.3  0.8  0.4  0.1  0.2       82.2 

Use  of  Steam  in  Producers  and  in  Boiler-furnaces.  (R. 
W.  Raymond,  Trans.  A.  I.  M.  E.,  xx.  635.) — No  possible  use  of  steam  can 
cause  a  gain  of  heat.  If  steam  be  introduced  into  a  bed  of  incandescent 
carbon  it  is  decomposed  into  hvdrogen  and  oxygen. 

The  heat  absorbed  by  the  reduction  of  one  pound  of  steam  to  hydrogen  is 
much  greater  in  amount  than  the  heat  generated  by  the  union  of  the 
oxygen  thus  set  free  with  carbon,  forming  either  carbonic  oxide  or  carbonic 
acid.  Consequently,  the  effect  of  steam  alone  upon  a  bed  of  incandescent 
fuel  is  to  chill  it.  In  every  water-gas  apparatus,  designed  to  produce  by 
means  of  the  decomposition  of  steam  a  fuel -gas  relatively  free  from  nitro- 
gen, the  loss  of  heat  in  the  producer  must  be  compensated  by  some  reheat- 
ing device. 

This  loss  may  be  recovered  if  the  hydrogen  of  the  steam  is  subsequently 
burned,  to  form  steam  again.  Such  a  combustion  of  the  hydrogen  is  con- 
templated, in  the  case  of  fuel-gas,  as  secured  in  the  subsequent  use  of  that 
gas.  Assuming  the  oxidation  of  H  to  be  complete,  the  use  of  steam  will 
cause  neither  gain  nor  loss  of  heat,  but  a  simple  transference,  the  heat 
absorbed  by  steam  decomposition  being  restored  by  hydrogen  combustion. 
In  practice,  it  may  be  doubted  whether  this  restoration  is  ever  complete. 
But  it  is  certain  that  an  excess  of  steam  would  defeat  the  reaction  alto- 
gether, and  that  there  must  be  a  certain  proportion  of  steam,  which  per- 
mits the  realization  of  important  advantages,  without  too  great  a  net  loss  in 
heat. 

The  advantage  to  be  secured  (in  boiler  furnaces  using  small  sizes  of 
anthracite)  consists  principally  in  the  transfer  of  heat  from  the  lower  side 
of  the  fire,  where  it  is  not  wanted,  to  the  upper  side,  where  it  is  wanted. 
The  decomposition  of  the  steam  below  cools  the  fuel  and  the  grate-bars, 
whereas  a  blast  of  air  alone  would  produce,  at  that  point,  intense  combus- 
tion (forming  at  first  CO2),  to  the  injury  of  the  grate,  the  fusion  of  part  of 
the  fuel,  etc. 

The  proportion  of  steam  most  economical  is  not  easily  determined.  The 
temperature  of  the  steam  itself,  the  nature  of  the  fuel  mixture,  and  the  use 
pr  non,-use  of  auxiliary  air- supply,  introduced  into  the  gases  above  or 


ILLTJMLN'ATIKG-GAS. 


651 


beyond   the   fire-bed,    are   factors   affecting    the   problem.     (See   Trans. 

^a^'AnaWseVby  Volume  and  by  Weight.-To  convert  an  an- 
alv^is  of  a  mixed  gas  uy  volume  into  analysis  by  weight:  Multiply  the . per- 
centage of  each  constituent  gas  by  the  density  of  that  gas  (see  p.  166).  Divide 
each  oroduct  by  the  sum  of  the  products  to  obtain  the  percentages  by  weight. 
Gas-fuel  tor  Small  Furnaces.-E.  P.  Reichhelm  (Am  Mack., 
Tan  10  1895)  discusses  the  use  of  gaseous  fuel  for  forge  fires,  for  drop- 
forking  in  annealing-ovens  and  furnaces  for  melting  brass  and  copper,  for 
case-hardening,  muffle-furnaces,  and  kilns.  Under  ordinary  conditions,  m 
such  furnaces  he  estimates  that  the  loss  by  draught,  radiation  and  the 
heating  of  space  not  occupied  by  work  is,  with  coal,  80^,  with  petroleum  70*, 
and  w\fh  gas  above  the  grade  of  producer-gas  25*.  He  gives  the  following 
table  of  comparative  cost  of  fuels,  as  used  in  these  furnaces  : 


Kind  of  Gas. 

ti       <J1 
0>  C  3 

w~  • 

<Mi§£ 

£ 

fe 

~£S*>  . 
Sgass 

&s|2 

6§§fi£ 

Average  Cost 
per  1,000  Ft. 

Cost  of  1,000,- 
000  Heat- 
units  Ob- 
tained in  Fur- 
naces. 

Natural  gas  
Coil  £?as  20  candle-power 

1,000,000 
675;000 
646,000 
690,000 
313,000 
377,000 
185.  (MX 
150,0(K 
306.36.' 

750,000 
506,250 
484,500 
517,500 
234,750 
282,750 
138,750 
112,500 
229,774 

••$r.25 
1.00 
.90 
.40 
.45 
.20 
.15 
.15 

$2.46 
2.06 
1.73 
1.70 
1.59 
1.44 
1.33 
.65 
.73 
.73 

Carburetted  water  gas                   

Water-gas  from  bituminous  coal  
Water-gas  and  producer-gas  mixed.  . 
Producer-gas                  

Naphtha-gas,  fuel  2)4  gals,  per  1000  ft. 

Coal,  $4  per  ton,  per  1  ,000,000  heat-units  utilized  
Crude  petroleum,  3  cts.  per  gal.,  per  1,000,000  heat-units  

Mr.  Reichhelm  gives  the  following  figures  from  practice  in  melting  brass 
with  coal  and  with  naphtha  converted  into  gas:    1800  Ibs.  of  metal  require 

w lull  uoa/i  a/tiu.  vrivu  uaputruoi  ^WUT^HCHJ  iuws  p,**0-      *-w^>   ««^»».  •»-.  -   -~~ay- — 

1080  Ibs.  of  coal,  at  $4.65  per  ton,  equal  to  $2.51,  or,  say,  15  cents  per  100  Ibs. 
Mr.  T.'s  report :  2500  Ibs.  of  metal  require  47  gals,  of  naphtha,  at  6  cents  per 
gal.,  equal  to  $2.82,  or,  say,  11*4  cents  per  100  Ibs. 


ILLUMINATING-GAS. 

Coal-gas  is  made  by  distilling  bituminous  coal  in  retorts.  The  retort 
is  usually  a  long  horizontal  semi-cylindrical  or  o  shaped  chamber,  holding 
from  160  to  300  Ibs.  of  coal.  The  retorts  are  set  in  4l benches"  of  from 
3  to  9,  heated  by  one  fire,  which  is  generally  of  coke.  The  vapors  distilled 
from  the  coal  are  converted  into  a  fixed  gas  by  passing  through  the  retort, 
which  is  heated  almost  to  whiteness. 

The  gas  passes  out  of  the  retort  through  an  "  ascension-pipe  "  into  a  long 
horizontal  pipe  called  the  hydraulic  main,  where  it  deposits  a  portion  of 
the  tar  it  contains:  thence  it  goes  into  a  condenser,  a  series  of  iron  tubes 
surrounded  by  cold  water,  where  it  is  freed  from  condensable  vapors,  as 
ammonia-water,  then  into  a  washer,  where  it  is  exposed  to  jets  of  water, 
and  into  a  scrubber,  a  large  chamber  partially  filled  with  trays  made  of 
wood  or  iron,  containing  coke,  fragments  of  brick  or  paving-stones,  which 
are  wet  with  a  spray  of  water.  By  the  washer  and  scrubber  the  gas  is  freed 
from  the  last  portion  of  tar  and  ammonia  and  from  some  of  the  sulphur 
compounds.  The  gas  is  then  finally  purified  from  sulphur  compounds  by 
passing  it  through  lime  or  oxide  of  iron.  The  gas  is  drawn  from  the  hy- 
draulic main  and  forced  through  the  washer,  scrubber,  etc.,  by  an  exhauster 
or  gas- pump. 

The  kind  of  coal  used  is  generally  caking  bituminous,  but  as  usually  this 
coal  is  deficient  in  gases  of  high  illuminating  power,  there  is  added  to  it  a 
portion  of  cannel  coal  or  other  enricher. 

The  following  table,  abridged  from  one  in  Johnson's  Cyclopedia,  snows; 
the  analysis,  candle  power,  etc.,  of  some  gas-coals  and  enrichers: 


652 


ILLUMINATING-GAS. 


Gas-coals,  etc. 

t* 

"cl 

"o 

Fixed  Carb. 

i 

4 

1 

|. 

P 

Coke  per 
ton  of  2240 
Ibs. 

Gas  purified 
by  1  bush,  of 
lime,incu.ft., 

Ibs. 

bush. 

Pittsburgh,  Pa  
Westmoreland,  Pa  
Sterling  O        

36.76 
36.00 
37.50 
40.00 
43.00 
46.00 
53.50 

51.93 
58.00 
56.90 
53.30 
40.00 
41.00 
44.50 

7.07 
6.00 
5.60 
6.70 
17.00 
13.00 
2.00 

10,642 
10,528 
10,765 
9,800 
13,200 
15,000 

ie!62 

18.81 
20.41 
34.98 

42.79 
28.70 

i544 
1480 
1540 
1320 
1380 
1056 

40 
36 
36 
32 
32 
44 

6420 
3993 
2494 
280t; 
4510 

Despard    W  Va     

Darlington  O  

Petonia  W  Va 

Grahamite,  W.  Va  

The  products  of  the  distillation  of  100  Ibs.  of  average  gas-coal  are  about  as 
follows.  They  vary  according  to  the  quality  of  coal  and  the  temperature  of 
distillation. 

Coke,  64  to  65  Ibs.;  tar,  6.5  to  7.5  Ibs.;  ammonia  liquor,  10  to  12  Ibs.;  puri- 
fied gas,  15  to  12  Ibs.;  impurities  and  loss,  4.5$  to 3.5$. 

The  composition  of  the  gas  by  volume  ranges  about  as  follows:  Hydro- 
gen, 38$  to 48$;  carbonic  oxide,  2$  to  14$;  marsh-gas  (Methane,  CH4),  43$  to 
31$;  heavy  hydrocarbons  (C«H2n,  ethylene,  propyleue,  benzole  vapor,  etc.), 
7.5$  to  4.5$;  nitrogen,  1$  to  3$. 

In  the  burning  of  the  gas  the  nitrogen  is  inert;  the  hydrogen  and  carbonic 
oxide  give  heat  but  no  light.  The  luminosity  of  the  flame  is  due  to  the  de- 
composition by  heat  of  the  heavy  hydrocarbons. into  lighter  hydrocarbons 
and  carbon,  the  latter  being  separated  in  a  state  of  extreme  subdivision. 
By  the  heat  of  the  flame  this  separated  carbon  is  heated  to  intense  white- 
ness, and  the  illuminating  effect  of  the  flame  is  due  to  the  light  of  incandes- 
cence  of  the  particles  of  carbon. 

The  attainment  of  the  highest  degree  of  luminosity  of  the  flame  depends 
upon  the  proper  adjustment  of  the  proportion  of  the  heavy  hydrocarbons 
(with  due  regard  to  their  individual  character)  to  the  nature  of  the  diluent 
mixed  therewith. 

Investigations  of  Percy  F.  Frankland  show  that  mixtures  of  ethylene  and 
hydrogen  cease  to  have  any  luminous  effect  when  the  proportion  of  ethy- 
lene does  not  exceed  10$  of  the  whole.  Mixtures  of  ethylene  and  carbonic 
oxide  cease  to  have  any  luminous  effect  when  the  proportion  of  the  former 
does  not  exceed  20$,  while  all  mixtures  of  ethylene  and  marsh-gas  have  more 
or  less  luminous  effect.  The  luminosity  of  a  mixture  of  10$  ethylene  and  90$ 
marsh-gas  being  equal  to  about  18  candles,  and  that  of  one  of  20$  ethylene 
and  80$  marsh-gas  about  25  candles.  The  illuminating  effect  of  marsh -ga.s 
alone,  when  burned  in  an  argand  burner,  is  by  no  means  inconsiderable. 

For  further  description,  see  the  Treatises  on  Gas  by  King.  Richards,  and 
Husrhes;  also  Appleton's  Cyc.  Mech.,  vol.  i.  p.  900. 

"Water-gas.— Water-gas  is  obtained  by  passing  steam  through  a  bed  of 
coal,  coke,  or  charcoal  heated  to  redness  or  beyond.  The  steam  is  decom- 
posed, its  hydrogen  being  liberated  and  its  oxygen  burning  the  carbon  of 
the  fuel,  producing  carbonic-oxide  eas.  The  chemical  reaction  is,  C  +  HaO 
=  CO  +  2H,  or  2C  +  2H2O  =  04-  CO2  -f  4H,  followed  by  a,  splitting  up  ot 
the  CO2,  making  2CO  -f  4H.  By  weight  the  normal  gas  CO  -f-  2H  is  com- 
posed of  C  +  O  4-  H  =  28  parts  CO  and  2  parts  H,  or  93.33$  CO  and  6.67$  H ; 

12  +  16  +    2 

by  volume  it  is  composed  of  equal  parts  of  carbonic  oxide  and  hydrogen. 
Water-gas  produced  as  above  described  has  great  heating-power,  but  no 
illuminating-power.  It  may,  however,  be  used  for  lighting  by  causing  it  to 
heat  to  whiteness  some  solid  substance,  as  is  done  in  the  Welsbach  incan- 
descent light. 

An  illuminating-gas  is  made  from  water-gas  by  adding  to  it  hydrocarbon 
gases  or  vapors,  which  are  usually  obtained  from  petroleum  or  some  of  its 
products.  A  history  of  the  development  of  modern  illuminating  water-gas 
processes,  together  with  a  description  of^the  most  recent  forms  of  apparatus, 
is  given  by  Alex.  C.  Humphreys,  in  a  paper  on  "  Water-gas  in  the  Unite  I 
States,"  rea'd  before  the  Mechanical  Section  of  the  British  Association  fcr 
Advancement  of  Science,  in  1889.  After  describing  many  earlier  patents,  be 
states  that  success  in  the  manufacture  of  water-gas  may  be  said  to  dat  e 


ANALYSES  OF  WATER-GAS  AHD  COAL-GAS  COMPARED.  653 


from  1874,  when  the  process  of  T.  S.  C.  Lowe  was  introduced.  All  the  later 
most  successful  processes  are  the  modifications  of  Lowe's,  the  essential 
features  of  which  were  "  an  apparatus  consisting  of  a  generator  and  super- 
heater internally  fired;  the  superheater  being  heated  by  the  secondary 
combustion  from  the  generator,  the  heat  so  stored  up  in  the  loose  brick  of 
the  superheater  being  used,  in  the  second  part  of  the  process,  in  the  fixing 
or  rendering  permanent  of  the  hydrocarbon  gases;  the  second  part  of  the 
process  consisting  in  the  passing  of  steam  through  the  generator  fire,  and 
the  admission  of  oil  or  hydrocarbon  at  some  point  between  the  fire  of  the 
generator  and  the  loose  filling  of  the  superheater.'1 

The  water-gas  process  thus  has  two  peiiods:  first  the  v' blow,"  during 
which  air  is  blown  through  the  bed  coal  in  the  generator,  and  the  partially 
burned  gaseous  products  are  completely  burned  in  the  superheater,  giving 
up  a  great  portion  of  their  heat  to  the  fire-brick  work  contained  in  it,  and 
then  pass  out  to  a  chimney;  second,  the  "  run  "  during  which  the  air  blast 
is  stopped,  the  opening  to  the  chimney  closed,  and  steam  is  blown  through 
the  incandescent  bed  of  fuel.  The  resulting  water-gas  passing  into  the  car- 
buretting  chamber  in  the  base  of  the  superheater  is  there  charged  with  hy- 
drocarbon vapors,  or  spray  (such  as  naphtha  and  other  distillates  or  crude 
oil)  and  passes  through  the  superheater,  where  the  hydrocarbon  vapors  be- 
come converted  into  fixed  illuminating  gases."  From  the  superheater  the 
combined  gases  are  passed,  as  in  the  coal-gas  process,  through  washers, 
scrubbers,  etc.,  to  the  gas-holder.  In  this  case,  however,  there  is  no  am- 
monia to  be  removed. 

The  specific  gravity  of  water-gas  increases  with  the  increase  of  the  heavy 
hydrocarbons  which  give  it  illuminating  power.   The  following  figures,  taken 
from  different  authorities,  are  given  by  F.  H.  Shelton  in  a  paper  on  Water- 
gas,  read  before  the  Ohio  Gas  Light  Association,  in  1894; 
(Handle-power  ...  19.5      20.    22.5  24.        25.4   26.3    28.3    29.6    .30  to  31.9 

8p.gr.  (Air  =  1)..  .571    .630    .589     .60  to  .67    .64    .602     .70      .65    .65  to    .71 

Analyses  of  Water-gas  and  Coal-gas  Compared. 

The  following  analyses  are  taken  from  a  report  of  Dr.  Gideon  E.  Moore 
on  the  Granger  Water-gas,  1885: 


Composition  by  Volume. 

Composition  by  Weight. 

Water-gas. 

Coal-gas. 
Heidel- 
berg. 

Water-gas. 

Coal- 
gas. 

Wor- 
cester. 

Lake. 

Wor- 
cester. 

Lake. 

Nitrogen  

2.64 
0.14 
0.06 
11.29 
0.00 
1.53 
28.26 
18.88 
37.20 

100.00 

3.85 
0.30 
0.01 
12.80 
0.00 
2.63 
23.58 
20.95 
35.88 

2.15 
3.01 
0.65 
2.55 
1.21 
1.33 
8.88 
34.02 
46.20 

0.04402 
0.00365 
0.00114 
0.18759 

0.06175 
0.00753 
0.00018 
0.20454 

0.04559 
0.09992 
0.01569 
0.05389 
0.03834 
0.07825 
0.18758 
0.41087 
0.06987 

1.00000 

Carbonic  acid  
Oxygen  
Ethyleue  

Propylene  
Benzole  vapor  
Carbonic  oxide... 
Marsh-  gas  

0.07077 
0.46934 
0.17928 
0.04421 

0.11700 
0.37664 
0.19133 
0.04103 

Hydrogen  

100.00 

100.00 

1.00000 

1.00000 

Density  :  Theory. 
Practice  . 

0.5825 
0.5915 

0.6057 
0.6018 

0.4580 

B.  T.  U.  from  1  cu. 
ft.:  Water  liquid. 
"      vapor. 

650.1 
597.0 

688.7 
646.6 

642.0 
577.0 

Flame-temp  

5311.  2°F. 

5281.  1°F. 

5202.  9°F. 

A  v.  candle-power. 

22.06 

26.31 

The  heating  values  (B.  T.  U.)  of  the  gases  are  calculated  from  the  analysis 
by  weight,  by  using  the  multipliers  given  below  (computed  from  results  of. 


654 


ILLTTMIKATIKG-GAS. 


J.  Thomsen),  and  multiplying  the  result  by  the  weight  of  1  cu.  ft.  of  the  gas 
at  62°  F.,  and  atmospheric  pressure. 

The  flame  temperatures  (theoretical)  are  calculated  on  the  assumption  or 
complete  combustion  of  the  gases  in  air,  without  excess  of  air. 

The  candle-power  was  determined  by  photometric  tests,  using  a  pressure 
of  U-in  water-column,  a  candle  consumption  of  120  grains  of  spermaceti 
per  hour  and  a  meter  rate  of  5  cu.  ft.  per  hour,  the  result  being  corrected 
for  a  temperature  of  62°  F.  and  a  barometric  pressure  of  30  in.  It  appears 
that  the  candle-power  may  be  regulated  at  the  pleasure  of  the  person  in 
charge  of  the  apparatus,  the  range  of  candle-power  being  from  20  to  29 
caudles,  according  to  the  manipulation  employed. 

Calorific  Equivalents  of  Constituents  of  Illuminating- 
gas. 

Heat-units  from  1  Ib.  Heat-units  from  1  Ib. 

Water        Water  Water       Water 

Liquid.       Vapor.  Liquid.      Vapor. 

Ethylene 21,524.4       20,134.8    Carbonic  oxide. .    4,395.6       4.395.6 

Propylene 21,222.0       19,834.2    Marsh-gas 24,021.0      21,592.8 

Benzole  vapor...,  18,954.0        17,817.0    Hydrogen 61,524.0      51,804.0 


(Proc.  Am.  Gaslight ,  „ 0  ._      _._ 

The  results  refer  to  1000  cu.  ft.  of  unpurified  carburetted  gas,  reduced  to 
60°  F.  The  total  anthracite  charged  per  1000  cu.  ft.  of  gas  was  33.4  Ibs.,  ash 
and  unconsumed  coal  removed  9.9  Ibs.,  leaving  total  combustible  consumed 
23.5  Ibs.,  which  is  taken  to  have  a  fuel-value  of  14500  B.  T.  U.  per  pound,  or 
a  total  of  340,750  heat- units. 


Composi- 
tion by 
Volume. 

Weight 
per 
100  cu.  ft. 

Composi- 
tion by 
Weight. 

Specific 
Heat. 

rCOa  +  HaS.. 
I  C«Ho 

3.8 
14  6 

.465842 
1  139968 

.09647 
23607 

.02088 
.08720 

cb    .'.'.'...'. 

I.    Carburetted         J  CH4  .**! 

28.0 
17.0 

2.1868 
.75854 

.45285 
.15710 

.11226 
.09314 

Water-gas  '  H 

35  6 

1991404 

04124 

.14041 

1  0 

078596 

.01627 

00397 

I 

100.0 

4.8288924 

1.00000 

.45786 

fCOo 

3  5 

429065 

1019 

02205 

ICO  
II.    Uncarburetted   J  H 

43.4 
51  8 

3.389540 
289821 

.8051 
0688 

.19958 
23424 

gas.  I  N 

1  3 

102175 

0242 

00591 

1 

100.0 

4.210601 

1.0000 

.46178 

f  COa  

17  4 

2  133066 

2464 

05342 

III.    Blast  products  |  O 

3  2 

2856096 

0329 

00718 

escaping  from  •{  N  

79.4 

6.2405224 

.7207 

.17585 

100.0 

8.6591980 

1.0000  . 

.23645 

rcoa  

9  7 

1  189123 

1436 

031075 

17  8 

1  390180 

1680 

041647 

IV.    Generator          J  .^   

72  5 

5  698210 

6884 

1G7970 

blast-  gases.  1         

I 

100.0 

8.277513 

1.0000 

.24069-3 

xue  utJitt  energy  aosoroea  Dy  tne  apparatus  is  23.5  X  14,500  =  340,750  heat- 
units  =  A.  Its  disposition  is  as  follows  : 

P,  the  energy  of  the  CO  produced; 

C,  the  energy  absorbed  in  the  decomposition  of  the  steam; 

A  the  difference  between  the  sensible  heat  of  the  escaping  illuminating- 
gases  and  that  of  the  entering  oil; 

E,  the  heat  carried  off  by  the  escaping  blast  products; 

F,  the  heat  lost  by  radiation  from  the  shells; 


EFFICIENCY  OF  A  WATER-GAS  PLAKT.  655 

G,  the  heat  carried  away  from  the  shells  by  convection  (air-currents) ; 

H,  the  heat  rendered  latent  in  the  gasification  of  the  oil; 

/,  the  sensible  heat  in  the  ash  and  unconsumed  coal  recovered  from  the 

gCThe  heat  equation  is  A  =  B+C+D+E+  F+  G  -f  H+  I\  A  being 

280 
known.    A  comparison  of  the  CO  in  Tables  I  and  II  show  that— r. ,  or  64.5£ 

of  the  volume  of  carburetted  gas  is  pure  water-gas,  distributed  thus  :  CO«  , 
2.3#;  CO,  28.0£;  H,  33.4#;  N,  0.8#;  =  64.5#.  1  Ib.  of  CO  at  60°  F.  =  13.531  cu. 
ft.  CO  per  1000  cu.  ft.  of  gas  =  280  H-  13.531  =  20.694  Ibs.  Energy  of  the  CO 
-  20.694  X  4395.6  =  91,043  heat-units,  =  B.  1  Ib.  of  H  at  60°  F.  =  189.2  cu. 
ft.  H  per  M  of  gas  =  3:34  -*• 189.2  =  1.7653  Ibs.  Energy  of  the  H  per  Ib. 
(according  to  Thomson,  considering  the  steam  generated  by  its  combustion 
to  be  condensed  to  water  at  75°  F.)  =  61,524  B.  T.  U.  In  Mr.  Glasgow's  ex- 
periments the  steam  entered  the  generator  at  331°  F. ;  the  heat  required  to 
raise  the  product  of  combustion  of  1  Ib.  of  H,  viz.,  8.98  Ibs.  H2O,  from  water 
at  75°  to  steam  at  331°  must  therefore  be  deducted  from  Thomsen's  figure,  or 
61,524  -  (8.98  X  1140.2)  =  51,285  B.  T.  U.  per  Ib.  of  H.  Energy  of  the  H,  then, 
is  1.7653  X  51,285  =  90,533  heat-units,  =  C.  The  heat  lost  due  to  the  sensible 
heat  in  the  illuminating-gases,  their  temperature  being  1450°  F.,  and  that  of 
the  entering  oil  235°  F.,  is  48.29  (weight)  X  .45786  sp.  heat  X  1215  (rise  of  tem- 
perature) =  26,864  heat-units  =  D. 

(The  specific  heat  of  the  entering  oil  is  approximately  that  of  the  issuing 
gas.) 

The  heat  carried  off  in  1000  cu.  ft.  of  the  escaping  blast  products  is  86.592 
(weight)  X  .23645  (sp.  heat)  X  1474°  (rise  of  temp.)  =  30,180  heat-units:  the 
temperature  of  the  escaping  blast  gases  being  1550°  F.,  and  that  of  the 
entering  air  76°  F.  But  the  amount  of  the  blast  gases,  by  registra- 
tion of  an  anemometer,  checked  by  a  calculation  from  the  analyses  of  the 
blast  gases,  was  2457  cubic  feet  for  every  1000  cubic  feet  of  carburetted  gas 
made.  Hence  the  heat  carried  off  per  M.  of  carburetted  gas  is  30,180  X 
2.457  =  74,152  heat-units  =  E. 

Experiments  made  by  a  radiometer  covering  four  square  feet  of  the  shell 
of  the  apparatus  gave  figures  for  the  amount  of  heat  lost  by  radiation 
=  12,454  heat-units  =  F,  and  by  convection  =  15,696  heat-units  =  G. 

The  heat  rendered  latent  by  the  gasefication  of  the  oil  was  found  by  taking 
the  difference  between  all  the  heat  fed  into  the  carburetter  and  super- 
heater and  the  total  heat  dissipated  therefrom  to  be  12,841  heat-units  =  H. 
The  sensible  heat  in  the  ash  and  unconsumed  coal  is  9.9  Ibs.  X  1500°  X  .25 
(sp.  ht.)  =  3712  heat-units  =  L 

The  sum  of  all  the  items  B  +  C  +  D  +  E+ F-\-  G  +  H+I=  327,295  heat- 
units,  which  substracted  from  the  heat  energy  of  the  combustible  consumed, 
340,750  heat-units,  leaves  13,455  heat-units,  or  4  percent,  unaccounted  for. 

Of  the  total  heat  energy  of  the  coal  consumed,  or  340,750  heat-units,  the 
energy  wasted  is  the  sum  of  items  D,  E,  F,  G,  and  7,  amounting  to  132,878 
heat-units,  or  39  per  cent;  the  remainder,  or  207,872  heat-units,  or  61  per 
cent,  being  utilized.  The  efficiency  of  the  apparatus  as  a  heat  machine  is 
therefore  61  per  cent. 

Five  gallons,  or  35  Ibs.  of  crude  petroleum  were  fed  into  the  carburetter 
per  1000  cu.  ft.  of  gas  made;  deducting  5  Ibs.  of  tar  recovered,  leaves  30  Ibs. 
X  20,000  =  600,000  heat-units  as  the  net  heating  value  of  the  petroleum  used. 
Adding  this  to  the  heating  value  of  the  coal,  340,750  B.  T.  U.,  gives  940,750 
heat-units,  of  which  there  is  found  as  heat  energy  in  the  carburetted  gas,  as 
in  the  table  below,  764,050  heat  units,  or  81  per  cent,  which  is  the  commer- 
cial efficiency  of  the  apparatus,  i.e.,  the  ratio  of  the  energy  contained  in 
the  finished  product  to  the  total  energy  of  the  coal  and  oil  consumed. 


The  heating  power  per  M.  cu.  ft.  of 


C0a       38.0 


the  carburetted  gas  is 


CO2    35.0 


C3H6*  146.0  X  .117220  X  21222.0  =  363200  CO    434.0  X  .078100  X    4395.6  =  148991 
CO       280.0  X  .078100  X    4395.6  =    96120  H      518.0  X  .005594  X  61524.0  =  178277 
CH4     170.0  X  .044620  X  24021.0  =  182210  N         13.0 
H         356.0  X  .005594  X  61524.0  =  122520 
N  10.0 


1000.0  764050 


The  heating  power  per  M.  of  the 


uncarburetted  gas  is 


1000.0  327268 


*  The  heating  value  of  the  illuminants  CnH2n  is  assumed  to  equal  that 
of  C3Ha. 


656  ILLUMlSTATItfG-GAS. 

The  candle-power  of  the  gas  is  31,  or  6.2  candle-power  per  gallon  of  oil 
used.  The  calculated  specific  gravity  is  .6355,  air  being  1. 

For  description  of  the  operation  of  a  modern  carburetted  water-gas 
Dlant  see  paper  by  J.  Stelfox,  Eng^g,  July  20,  1894,  p.  89. 

Space  required  for  a  Waier-gas  Plant.— Mr.  Shelton,  taking 
15  modern  plants  of  the  form  requiring  the  most  floor-space,  figures  the 
average  floor-space  required  per  1000  cubic  feet  of  daily  capacity  as  follows: 

Water-gas  Plants  of  Capacity  Require  an  Area  of  Floor-space  for 

in  24  hours  of  each  1000  cu.  ft.  of  about 

100,000  cubic  feet 4  square  feet. 

200,000    "         "    3.5    *' 

400,000    "         "    2.75  " 

600,000    "         "    2  to  2.5  sq.  ft. 

7  to  10  million  cubic  feet 1.25  to  1.5  sq.  ft. 

These  figures  include  scrubbing  and  condensing  rooms,  but  not  boiler  and 
engine  rooms.  In  coal-gas  plants  of  the  most  modern  and  compact  forms  one 
with  16  benches  of  9  retorts  each,  with  a  capacity  of  1,500,000  cubic  feet  per 
24  hours,  will  require  4.8  sq.  ft.  of  space  per  1000  cu.  ft.  of  gas,  and  one  of  6 
benches  of  6  retorts  each,  with  300,000  cu.  ft.  capacity  per  24  hours  will  re- 
quire 6  sq.  ft.  of  space  per  1000  cu.  ft.  The  storage-room  required  for  the 
gas-making  materials  is:  for  coal-gas,  1  cubic  foot  of  room  for  every  232 
cubic  feet  of  gas  made;  for  water-gas  made  from  coke,  1  cubic  foot  of  room 
for  every  373  cu.  ft.  of  gas  made;  and  for  water-gas  made  from  anthracite, 
1  cu.  ft.  of  room  for  every  645  cu.  ft.  of  gas  made. 

The  comparison  is  still  more  in  favor  of  water-gas  if  the  case  is  considered 
of  a  water-gas  plant  added  as  an  auxiliary  to  an  existing  coal-gas  plant; 
for,  instead  of  requiring  further  space  for  storage  of  coke,  part  or  that 
already  required  for  storage  of  coke  produced  and  not  at  once  sold  can  be 
•cut  off,  by  reason  of  the  water-gas  plant  creating  a  constant  demand  for 
more  or  less  of  the  coke  so  produced. 

Mr.  Shelton  gives  a  calculation  showing  that  a  water-gas  of  .625  sp.  gr. 
would  require  gas-mains  eight  per  cent  greater  in  diameter  than  the  same 
quantity  coal-gas  of  .425  sp.  gr.  if  the  same  pressure  is  maintained  at  the 
holder.  The  same  quantity  may  be  carried  in  pipes  of  the  same  diameter 
if  the  pressure  is  increased  in  proportion  to  the  specific  gravity.  With  the 
same  pressure  the  increase  of  candle-power  about  balances  the  decrease  of 
flow.  With  five  feet  of  coal-gas,  giving,  say,  eighteen  candle-power,  1  cubic 
foot  equals  3.6  candle-power;  with  water-gas  of  23  candle-power,  1  cubic 
foot  equals  4.6  candle-power,  and  4  cubic  feet  gives  18.4  candle-power,  or 
more  than  is  given  by  5  cubic  feet  of  coal-gas.  Water-gas  may  be  made 
from  oven-coke  or  gas-house  coke  as  well  as  from  anthracite  coal.  A  water- 
gas  plant  may  be  conveniently  run  in  connection  with  a  coal-gas  plant,  the 
surplus  retort  coke  of  the  latter  being  used  as  the  fuel  of  the  former. 

In  coal-gas  making  it  is  impracticable  to  enrich  the  gas  to  over  twenty 
candle-power  without  causing  too  great  a  tendency  to  smoke,  but  water-gas 
of  as  high  as  thirty  candle-power  is  quite  common.  A  mixture  of  coal-gas 
and  water-gas  of  a  higher  C.P.  than  20  can  be  advantageously  distributed. 

Fuel-value  of,  Illuminating-gas.— E.  G.  Love  (School  of  Mines 
Qtly,  January,  1892)  describes  F.  W.  Hartley's  calorimeter  for  determining 
the  calorific  power  of  gases,  and  gives  results  obtained  in  tests  of  the  car- 
buretted water-gas  made  by  the  municipal  branch  of  the  Consolidated  Co. 
of  New  York.  The  tests  were  made  from  time  to  time  during  the  past  two 
years,  and  the  figures  give  the  heat-units  per  cubic  foot  at  60*  F.  and  30 
inches  pressure:  715,  692, 725,  732,  691,  738, 735,  703,  734,  730,  731, 727.  Average, 
721  heat  units.  Similar  tests  of  mixtures  of  coal-  and  water-gases  made  by 
other  branches  of  the  same  company  give  694,  715,  684,  692,  727,  665,  695,  and 
686  heat-units  per  foot,  or  an  average  of  694.7.  The  average  of  all  these 
tests  was  710.5  heat-units,  and  this  we  may  fairly  take  as  representing  the 
calorific  power  of  the  illuminating  gas  of  New  York.  One  thousand  feet  of 
this  gas,  costing  $1.25,  would  therefore  yield  710,500  heat-units,  which  would 
be  equivalent  to  568,400  heat-units  for  $1.00. 

The  common  coal-gas  of  London,  with  an  illuminating  power  of  16  to  17 
candles,  has  a  calorific  power  of  about  668  units  per  foot,  and  costs  from  60 
to  70  cents  per  thousand. 

The  product  obtained  by  decomposing  steam  by  incandescent  carbon,  as 
SOflfofH  m  Motav  Process,  consists  of  about  40£  of  CO,  and  a  little  over 


FLOW  OF   GAS  IK   PIPES. 


65? 


This  mixture  would  have  a  heating-power  of  about  300  units  per  cubic  foot, 
and  if  sold  at  50  cents  per  1000  cubic  feet  would  furnish  600,000  units  for  $1.00, 
as  compared  with  568,400  units  for  $1.00  from  illuminating  gas  at  $1 .25  per  1000 
cubic  feet.  This  illuminating-gas  if  sold  at  $1.15  per  thousand  would  there- 
fore be  a  more  economical  heating  agent  than  the  fuel-gas  mentioned,  at  50 
cents  per  thousand,  and  be  much  more  advantageous  than  the  latter,  in  that 
one  main,  service,  and  meter  could  be  used  to  furnish  gas  for  both  lighting 
and  heating. 

A  large  number  of  fuel-gases  tested  by  Mr.  Love  gave  from  184  to  470  heat- 
units  per  foot,  with  an  average  of  309  units. 

Taking  the  cost  of  heat  from  illuminating-gas  at  the  lowest  figure  given 
by  Mr.  Love,  viz.,  $1.00  for  600,000  heat-units,  it  is  a  very  expensive  fuel,  equal 
to  coal  at  $40  per  ton  of  2000  Ibs.,  the  coal  having  a  calorific  power  of  only 
12,000  heat-units  per  pound,  or  about  83$  of  that  of  pure  carbon: 

600,000  :  (12,000  X  2000) ::  $1  :  $40. 

FLOW  OF  GAS  IN  PIPES. 

The  rate  of  flow  of  gases  of  different  densities,  the  diameter  of  pipes  re- 
quired, etc.,  are  given  in  King's  Treatise  on  Coal  Gas,  vol.  ii.  374,  as  follows: 


If  d  =.  diameter  of  pipe  in  inches, 
Q  =  quantity  of  gas  in  cu.  ft.  per 

hour, 

I  =  length  of  pipe  in  yards, 
h  =  pressure  in  inches  of  water, 
a  =  specific  gravity  of  gas,  air  be- 
ing 1, 


d  - 


^-=1350 


Molesworth  gives  Q  =  lOOO^/  — 


J.  P.  Gill,  Am.  Gas-light  Jour.  1894,  gives  Q  =  1291  A/  — - 


This  formula  is  said  to  be  based  on  experimental  data,  and  to  make  allow- 
ance for  obstructions  by  tar,  water,  and  other  bodies  tending  to  check  the 
flow  of  gas  through  the  pipe. 

A  set  of  tables  in  Appleton's  Cyc.  Mech.  for  flow  of  gas  in  2,  6,  and  12  in. 
pipes  is  calculated  on  the  supposition  that  the  quantity  delivered  varies 
as  the  square  of  the  diameter  instead  of  as  d2  X  Vd,  or  ^d6. 

These  tables  give  a  flow  in  large  pipes  much  less  than  that  calculated  by 
the  formulae  above  given,  as  is  shown  by  the  following  example.  Length  of 
pipe  100  yds.,  specific  gravity  of  gas  .042,  pressure  1-in.  water-column. 

2 -in.  Pipe.     6-in.  Pipe.      12-in.  Pipe. 
1178  18,368  103,912 


Q  =  1291 


Table  in  App.  Cyc 


13,606 

16,327 
11,657 


76,972 

93,845 
46,628 


An  experiment  made  by  Mr.  Clegg,  in  London,  with  a  4-in.  pipe,  6  miles 
long,  pressure  3  in.  of  water,  specific  gravity  of  gas  .398,  gave  a  discharge 
into  the  atmosphere  of  852  cu.  ft.  per  hour,  after  a  correction  of  33  cu.  ft. 
was  made  for  leakage. 

Substituting  this  value,  852  cu.  ft.,  for  Q  in  the  formula  Q  =  C  \/d*h  -5-  sl, 
we  find  C,  the  coefficient,  =  997,  which  corresponds  nearly  with  the  formula 
given  by  Molesworth. 


658 


ILLUMIKATIKG-&AS. 


Services  for  Lamps.   (Moles worth.) 


Lamps. 
g 

Ft.  from 
Main. 
40 

Require 
Pipe-bore. 

Lamps. 
15  

Ft.  from 
Main. 
130 

Require 
Pipe-bore. 
1  in. 

4 

40 

y%  in. 

20  

..  150 

1*4  in. 

g 

50 

%  in. 

25  

180 

1^  in. 

10... 

..  100 

3£in. 

30  .... 

200 

igin! 

(In  cold  climates  no  service  less  than  %  in.  should  be  used.) 

maximum  Supply  of  Gas  through  Pipes  in  cu.  ft.  per 
Hour,  Specific  Gravity  being  taken  at  .45,  calculated 
from  the  Formula  Q  —  100O  Vd^h  -*-  si.  (Molesworth.) 

LENGTH  OF  PIPE  =  10  YARDS. 


Pressure  by  the  Water-gauge  in  Inches. 


Inches. 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

1.0 

1  4 
2 

13 
26 
73 
149 
260 
411 
843 

18 
37 
103 
211 
368 
581 
1192 

22 
46 
126 
253 
451 
711 
1460 

26 
53 
145 
298 
521 
821 
1686 

29 
59 
162 
333 

582 
918 
1886 

31 
64 

187 
365 
638 
1006 
2066 

34 
70 
192 
394 
689 
1082 
2231 

36 
74 

205 
422 
737 
1162 
2385 

38 
79 
218 
447 
781 
1232 
2530 

41 
83 
230 
471 
823 
1299 
2667 

LENGTH  OP  PIPE  =  100  YARDS. 


Pressure  by  the  Water-gauge  in  Inches. 


.1 

.2 

.3 

A 

.5 

.75 

1.0 

1.25 

1.5 

2 

2.5 

^ 

8 

12 

14 

17 

19 

23 

26 

29 

32 

36 

42 

H 

23 

32 

42 

46 

51 

63 

73 

81 

89 

103 

115 

\ 

47 

67 

82 

94 

105 

129 

149 

167 

183 

211 

236 

i/>4 

82 

116 

143 

165 

184 

225 

260 

291 

319 

368 

412 

i^» 

130 

184 

225 

260 

290 

356 

411 

459 

503 

581 

649 

o 

267 

377 

462 

533 

596 

730 

843 

943 

1033 

1193 

133?, 

2H 

466 

659 

807 

932 

1042 

1276 

1473 

1647 

1804 

2083 

232V 

3 

735 

1039 

1270 

1470 

1643 

2012 

2323 

2598 

2846 

3286 

36?  * 

3H 

1080 
1508 

1528 
2133 

1871 
2613 

2161 
3017 

2416 
3373 

2958 
4131 

3416 

4770 

3820 
5333 

4184 

5842 

4831 
6746 

5402 

7542 

LENGTH  OF  PIPE  =  1000  YARDS. 


ft 
f 

5 
6 

Pressure  by  the  Water-gauge  in  Inches. 

.5 

.75 

1.0 

1.5 

2.0 

2.5 

3.0 

33 
92 

189 
329 
520 
1067 
1863 
2939 

41 
113 
231 
403 
636 
1306 
2282 
3600 

47 
130 

267 
466 
735 
1508 
2635 
4157 

58 
159 
327 
571 
900 
1847 
3227 
5091 

67 
184 
377 
659 
1039 
2133 
3727 
5879 

75 

205 
422 
737 
1162 
2385 
4167 
6573 

82 
226 
462 
807 
1273 
2613 
4564 
7200 

STEAM. 


659 


LENGTH  OP  PIPE  =  5000  YARDS. 


Diameter 
of  Pipe 
in 
Inches. 

Pressure  by  the  Water-gauge  in  Inches. 

1.0 

1.5 

2.0 

2.5 

3.0 

2 
3 
4 
5 
6 
7 
8 
9 
10 
12 

119 
329 
675 
1179 
1859 
2733 
3816 
5123 
6667 
10516 

146 
402 
826 
1443 
2277 
3347 
4674 
6274 
8165 
12880 

169 
465 
955 
1667 
2629 
3865 
5397 
7245 
9428 
14872 

189 
520 
1067 
1863 
2939 
4321 
6034 
8100 
10541 
16628 

207 

569 
1168 
2041 
3220 
4734 
6610 
8873 
11547 
18215 

Mr.  A.  C.  Humphreys  says  his  experience  goes  to  show  that  these  tables 
give  too  small  a  flow,  but  it  is  difficult  to  accurately  check  the  tables,  on  ac- 
count of  the  extra  friction  introduced  by  rough  pipes,  bends,  etc.  For 
bends,  one  rule  is  to  allow  1/42  of  an  inch  pressure  for  each  right-angle  bend. 

Where  there  is  apt  to  be  trouble  from  frost  it  is  well  to  use  no  service  of 
less  diameter  than  %  in.,  no  matter  how  short  it  may  be.  In  extremely  cold 
climates  this  is  now  often  increased  to  1  in.,  even  fora  single  lamp.  The  best 
practice  in  the  U.  S.  now  condemns  any  service  less  than  %  in. 

STEAM. 


The  Temperature  of  Steam  in  contact  with  water  depends  upon 
the  pressure  under  which  it  is  generated.  At  the  ordinary  atmospheric 
pressure  (14.7  Ibs.  per  sq.  in.)  its  temperature  is  212°  F.  As  the  pressure  is 
increased,  as  by  the  steam  being  generated  in  a  closed  vessel,  its  tempera- 
ture, and  that  of  the  water  in  its  presence,  increases. 

Saturated  Steam  is  steam  of  the  temperature  due  to  its  pressure- 
not  superheated 

Superheated  Steam  is  steam  heated  to  a  temperature  above  that  due 
to  its  pressure. 

Dry  Steam  is  steam  which  contains  no  moisture.  It  may  be  either 
saturated  or  superheated. 

"Wet  Steam  is  steam  containing  intermingled  moisture,  mist,  or  spray. 
It  has  the  same  temperature  as  dry  saturated  steam  of  the  same  pressure. 

Water  introduced  into  the  presence  of  superheated  steam  will  flash  into 
vapor  until  the  temperature  of  the  steam  is  reduced  to  that  due  its  pres- 
sure. Water  in  the  presence  of  saturated  steam  has  the  same  temperature 
as  the  steam.  Should  cold  water  be  introduced,  lowering  the  temperature 
of  the  whole  mass,  some  of  the  steam  will  be  condensed,  reducing  the  press- 
ure and  temperature  of  the  remainder,  until  an  equilibrium  is  established. 

Temperature  and  Pressure  of  Saturated  Steam.— The  re- 
lation between  the  temperature  and  the  pressure  of  steam,  according  to 
Regnault's  experiments,  is  expressed  by  the  formula  (Buchanan's,  as  given 
2938.16 


by  Clark)  t  -  - 


•  —  371.85,  in  which  p  is  the  pressure  in  pounds 


"6.1993544  -  log  p 

per  square  inch  and  t  the  temperature  of  the  steam  in  Fahrenheit  degrees. 
It  applies  with  accuracy  between  120°  F.  and  446°  F.,  corresponding  to  pres- 
sures of  from  1.68  Ibs.  to  445  Ibs.  per  square  inch.  (For  other  formulae  see 
Wood's  and  Peabody's  Thermodynamics.) 

Total  Heat  of  Saturated  Steam  (above  32°  F.).— According  to 
Regnault's  experiments,  the  formula  for  total  heat  of  steam  is  H  =  1091.7  + 
.305(*  -  32°),  in  which  t  is  temperature  Fahr.,  and  H  the  heat-units.  (Ran- 
kine  and  many  others;  Clark  gives  1091.16  instead  of  1091.7.) 

Latent  Heat  of  Steam.— The  formula  for  latent  heat  of  steam,  as 
given  by  Rankine  and  others,  is  L  -  1091.7  —  .695(£  -  32°).  Clausius's  for- 
mula, in  Fahrenheit  units,  as  given  by  Clark,  is  L  =  1092.6  -  .708(*  —  32°). 


660  STEAM. 

The  total  heat  in  steam  (above  32°)  includes  three  elements: 

1st.  The  heat  required  to  raise  the  temperature  of  the  water  to  the  tem- 
perature of  the  steam. 

2d.  The  heat  required  to  evaporate  the  water  at  that  temperature,  called 
internal  latent  heat. 

3d  The  latent  heat  of  volume,  or  the  external  work  done  by  the  steam  in 
making  room  for  itself  against  the  pressure  of  the  superincumbent  atmos- 
phere (or  surrounding  steam  if  inclosed  in  a  vessel). 

The  sum  of  the  last  two  elements  is  called  the  latent  heat  of  steam.  In 
Buel's  tables  (Weisbach,  vol.  ii.,  Dubois's  translation)  the  two  elements  are 
given  separately. 

Latent  Heat  of  Volume  of  Saturated  Steam.  (External 
Work.)— The  following  formulas  are  sufficiently  accurate  for  occasional  use 
within  the  given  ranges  of  pressure  (Clark,  S.  E.): 

From  14.7  Ibs.  to  50  Ibs.  total  pressure  per  square  inch. . .  55.900  -f  .0772*. 
From  50  Ibs.  to  200  Ibs.  total  pressure  per  square  inch....  59.191  -f  .0655*. 

Heat  required  to  Generate  1  Ib.  of  Steam  from  water  at  32°  F. 

Heat-units. 

Sensible  heat,  to  raise  the  water  from  32°  to  212°  =  ....  180.9 

Latent  heat,  1,  of  the  formation  of  steam  at  212°  = . . . .  894.0 
2,  of  expansion  against  the  atmospheric 
pressure,  2116.4  Ibs.  per  sq.  **,.  X26.36  cu.  ft. 
=  55,786  foot-pounds -f- 778  = 71.7      965.7 

Total  heat  above  32°  F 1146.6 

The  Heat  Unit,  or  British  Thermal  Unit.— The  definition  of 
the  heat-unit  used  in  this  work  is  that  of  Rankine,  accepted  by  most  modern 
writers,  viz.,  the  quantity  of  heat  required  to  raise  the  temperature  of  1  Ib. 
of  water  1°  F.  at  or  near  its  temperature  of  maximum  density  (39.1°  F.). 
Peabody's  definition,  the  heat  required  to  raise  a  pound  of  water  from  62° 
to  6rJ°  F.  is  not  generally  accepted.  (See  Thurston,  Trans.  A.  S.  M.  E., 
xiii.  351.) 

Specific  Heat  of  Saturated  Steam.— The  specific  heat  of  satu- 
rated steam  is  .305,  that  of  water  being  1 ;  or  it  is  1.281,  if  that  of  air  be  1. 
The  expression  .305  for  specific  heat  is  taken  in  a  compound  sense,  relating 
to  changes  both  of  volume  and  of  pressure  which  takes  place  in  the  eleva- 
tion of  temperature  of  saturated  steam.  (Clark,  S.  E.) 

This  statement  by  Clark  is  not  strictly  accurate.  When  the  temperature 
of  saturated  steam  is  elevated,  water  being  present  and  the  steam  remain- 
ing saturated,  water  is  evaporated.  To  raise  the  temperature  of  1  Ib.  of 
water  1°  F.  requires  1  thermal  unit,  and  to  evaporate  it  at  1°  F.  higher  would 
require  0.695  less  thermal  unit,  the  latent  heat  of  saturated  steam  decreas- 
ing 0.695  B.T.U.  for  each  increase  of  temperature  of  1°  F.  Hence  0.305  is 
the  specific  heat  of  water  and  its  saturated  vapor  combined. 

When  a  unit  weight  of  saturated  steam  is  increased  in  temperature  and  in 
pressure,  the  volume  decreasing  so  as  to  just  keep  it  saturated,  the  specific 
heat  is  negative,  and  decreases  as  temperature  increases.  (See  Wood, 
Therm.,  p.  147;  Peahody,  Therm.,  p.  93.) 

Density  and  Volume  of  Saturated  Steam.— The  density  of 
steam  is  expressed  by  the  weight  of  a  given  volume,  say  one  cubic  foot;  and 
the  volume  is  expressed  by  the  number  of  cubic  feet  in  one  pound  of  steam. 

Mr.  Brownlee's  expression  for  the  density  of  saturated  steam  in  terms  of 

the  pressure  is  D  =  J^,,  or  log  D  =  .941  p  -  2.519,  in  which  D  is  the  den- 
sity, and  p  the  pressure  in  pounds  per  square  inch.    In  this  expression,  p'94* 
is  the  equivalent  of  p  raised  to  the  16/17  power,  as  employed  by  Raukine. 
The  volume  v  being  the  reciprocal  of  the  density, 

330.36 
v  =  — ^,  or  log  v  =  2.519  —  .941  log  p. 

Relative  Volume  of  Steam.-The  relative  volume  of  saturated 
steam  is  expressed  by  the  number  of  volumes  of  steam  produced  from  one 


STEAM.  661 

volume  of  water,  the  volume  of  water  being  measured  at  the  temperature 
39°  F.  The  relative  volume  is  found  by  multiplying  the  volume  in  cu.  ft.  of 
one  Ib.  of  steam  by  the  weight  of  a  cu.  ft.  of  water  at  39*  F.,  or  62.425  Ibs. 

Gaseous  Steam.— When  saturated  steam  is  superheated,  or  sur- 
charged with  heat,  it  advances  from  the  condition  of  saturation  into  that  of 
gaseity.  The  gaseous  state  is  only  arrived  at  by  considerably  elevating  the 
temperature,  supposing  the  pressure  remains  the  same.  Steam  thus  suffi- 
ciently superheated  is  known  as  gaseous  steam  or  steam  gas. 

Total  Heat  of"  Gaseous  Steam.— Regnault  found  that  the  total 
heat  of  gaseous  steam  increased,  like  that  of  saturated  steam,  uniformly 
with  the  temperature,  and  at  the  rate  of  .475  thermal  units  per  pound  for 
each  degree  of  temperature,  under  a  constant  pressure. 

The  general  formula  for  the  total  heat  of  gaseous  steam  produced  from 
1  pound  of  water  at  32°  F.  is  H  =  1074.6  -h  .475*.  [This  formula  is  for  vapor 
generated  at  32°.  It  is  not  true  if  generated  at  212°,  or  at  any  other  tempera- 
ture than  32°.  (Prof.  Wood.)] 

The  Specific  Heat  of  Gaseous  Steam  is  .475,  under  constant 
pressure,  as  found  by  Reguault.  It  is  identical  with  the  coefficient  of  in- 
crease of  total  heat  for  each  degree  of  temperature.  [This  is  at  atmospheric 
pressure  and  212°  temperature.  He  found  it  not  true  for  any  other  pressure. 
Theory  indicates  that  it would  be  less  at  higher  temperatures.  (Prof.  Wood.)] 

The  Specific  Density  of  Gaseous  Steam  is  .622,  that  of  air  being 
1.  That  is  to  say,  the  weight  of  a  cubic  foot  of  gaseous  steam  is  about  five 
eighths  of  that  of  a  cubic  foot  of  air,  of  the  same  pressure  and  temperature. 

The  density  or  weight  of  a  cubic  foot  of  gaseous  steam  is  expressible  by 
the  same  formula  as  that  of  air,  except  that  the  multiplier  or  coefficient  is 
less  in  proportion  to  the  less  specific  density.  Thus, 

_  2.7074p  X  .622  _  1.684p 
J  +  461        "  £+461' 

in  which  D'  is  the  weight  of  a  cubic  foot  of  gaseous  steam,  p  the  total  pres- 
sure per  square  inch,  and  t  the  temperature  Fahrenheit. 

Superheated  Steam.—  The  above  remarks  concerning  gaseous  steam 
are  taken  from  Clark's  Steam-engine.  Wood  gives  for  the  total  heat  (above 
32°)  of  superheated  steam  H  =  1091.7  -f  OA8(t  -  32°). 

The  following  is  abridged  from  Peabody  (Therrn.,  p.  115,  etc.). 

When  far  removed  from  the  temperature  of  saturation,  superheated  steam 
follows  the  laws  of  perfect  gases  very  nearly,  but  near  the  temperature  of 
saturation  the  departure  from  those  laws  is  too  great  to  allow  of  calculations 
by  them  for  engineering  purposes. 

The  specific  heat  at  constant  pressure,  Cp,  from  the  mean  of  three  experi- 
ments by  Regnault,  is  0.4805. 

Values  of  the  ratio  of  Op  to  specific  heat  at  constant  volume: 

Pressure »,  pounds  per  square  inch..        5         50        100       200       300 
Ratio  Cp  -5-  Cv  =  k  =      1.335  1.332    1.330    1.324    1.316 

Zeuner  takes  k  as  a  constant  =  1.333. 

SPECIFIC  HEAT  AT  CONSTANT  VOLUME,  SUPERHEATED  STEAM. 

Pressure,  pounds  per  square  inch 5       50        100       200       300 

Specific  heat  Cv 0.351.348     .346      .344      .341 

It  is  quite  as  reasonable  to  assume  that  Cv  is  a  constant  as  to  suppose  that 
Cp  is  constant,  as  has  been  assumed.  If  we  take  Cv  to  be  constant,  then  Cp 
will  appear  as  a  variable. 

If  p  =  pressure  in  Ibs.  per  sq.  ft.,  v  =  volume  in  cubic  feet,  and  T  = 
temperature  in  degrees  Fahrenheit  -f  460.7,  then  pv  =  93.5!F—  971pi. 

Total  heat  of  superheated  steam,  H  =  0.4805(2"  -  10.38pi)  4-  857.2. 

The  Rationalization  of  Regnault's  Experiments  on 
Steam.  (J.  McFarlaue  Gray.  Proc.  Insr.  M.  E  ,  July,  Ib89.)— The  formulas 
constructed  by  Regnault  are  strictly  empirical,  and  were  based  entirely  on 
his  experiments.  They  are  therefore  not  valid  beyond  the  range  of  temper- 
atures and  pressures  observed 

Mr.  Gray  has  made  a  most  elaborate  calculation,  based  not  on  experiments 
but  on  fundamental  principles  of  thermodynamics,  from  which  he  deduces 
formulae  for  the  pressure  and  total  heat  of  steam,  and  presents  tables  calcu- 


662 


STEAK. 


Temperature. 

Pounds  per 

Temperature. 

Pounds  per 

C. 

Fahr. 

sq.  in. 

C. 

Fahr 

sq.  in. 

230 

446 

406.9 

340 

644 

2156.2 

240 

464 

488.9 

360 

680 

2742.5 

250 

482 

579.9 

380 

716 

3448.1 

260 

500 

691.6 

400 

752 

4300.2 

280 

536 

940.0 

415 

779 

5017.1 

300 

572  * 

1261.8 

427 

800.6 

5659.9 

320 

608 

1661.9 

These  pressures  are  higher  than  those  obtained  by  Regnault's  formula, 
which  gives  for  415°  C.  only  4067.1  Ibs.  per  square  inch. 

Table  of  the  Properties  of  Saturated  Steam.— In  the  table 
of  properties  of  saturated  steam  on  the  following  pages  the  figure*  for  tem- 
perature, total  heat,  and  latent  heat  are  taken,  up  to  210  Ibs.  absolute  pres- 
sure, from  the  tables  in  Porter's  Steam-engine  Indicator,  which  tables  have 
been  widely  accepted  as  standard  by  American  engineers.  The  figures  for 
total  heat,  given  in  the  original  as  from  0°  F.,  have  been  changed  to  heat 
above  32°  F.  The  figures  for  weight  per  cubic  foot  and  for  cubic  feet  per 
pound  have  been  taken  from  Dwelshauvers-Dery's  table,  Trans.  A.  S.  M.  E., 
vol.  xi.,  as  being  probably  more  accurate  than  those  of  Porter.  The  figures 
for  relative  volume  are  from  Buel's  table,  in  Dubois's  translation  of  Weis- 
bach,  vol.  ii.  They  agree  quite  closely  with  the  relative  volumes  calculated 
from  weights  as  given  by  Dery.  From  211  to  219  Ibs.  the  figures  for  temper- 
ature, total  heat,  and  latent  heat  are  from  Dery's  table;  and  from  220  to  1000 
Ibs.  all  the  figures  are  from  Duel's  table.  The  figures  have  not  been  carried 
out  to  as  many  decimal  places  as  they  are  in  most  of  the  tables  given  by  the 
different  authorities:  but  any  figure  beyond  the  fourth  significant  figure  is 
unnecessary  in  practice,  and  beyond  the  limit  of  error  of  the  observations 
and  of  the  formulae  from  which  the  figures  were  derived. 

Weight  of  1  Cubic  Foot  of  Steam  in  Decimals  of  a  Pound. 
Comparison  of  Different  Authorities. 


_*  Absolute 
ooooo£-*  Pressure, 
LS  Ibs.  per  sq.  in 

Weight  of  1  cubic  foot 
according  to— 

Absolute 
Pressure, 
Ibs.  persq.  in. 

Weight  of  1  cubic  foot 
according  to— 

Por- 
ter. 

Clark 

Duel. 

Dery. 

Pea- 
body. 

Por- 
ter. 

Clark 

Buel. 

Dery. 

Pea- 

body 

.2695 
.3113 
.3530 
.3945 
.4359 
.4772 
.5186 

.0030 
.03797 
.0511 
.0994 
.1457 
.19015 
.23302 

.003 
.0380 
.0507 
.0974 
.1425 
.186,) 
.2307 

.00303 
.03793 
.0507 
.0972 
.1424 
.1866 
.2303 

.00299 

.'0507 
.0972 
.1422 
.1862 
.2296 

.00299 
.0376 
.0502 
.0964 
.1409 
.1843 
.2271 

120 
140 
160 
180 
200 
220 
240 

.27428 
.31386 
.35209 
.38895 
.42496 

.2738 
.3162 
.3590 
.4009 
.4431 
.4842 
.5248 

.2735 
.3163 
.3589 
.4012 
.4433 
.4852 
.5270 

.2724 
.3147 
.3567 
.3983 
.4400 

There  are  considerable  differences  between  the  figures  of  weight  and  vol- 
ume of  steam  as  given  by  different  authorities.  Porter's  figures  are  based 
on  the  experiments  of  Fairbairn  and  Tate.  The  figures  given  by  the  other 
authorities  are  derived  from  theoretical  formulae  which  are  believed  to  give 
more  reliable  results  than  the  experiments.  The  figures  for  temperature, 
total  heat,  and  latent  heat  as  given  by  different  authorities  show  a  practical 
agreement,  all  being  derived  from  Regnault's  experiments.  See  Peabody's 
Tables  of  Saturated  Steam;  also  Jacobus,  Trans.  A.  S.  M,  E.,  vol,  xij.,  593, 


STEAM. 


663 


Properties  of  Saturated  Steam. 


is 

!$•?: 

^ 

Total 
above 

Heat 
32°  F. 

*»     .2 

.5  c|  || 

«| 

N 

lit 

ssg 

Absolute  Pi 
ure,  Ibs.  p 
square  inc 

II 
|1 

In  the 
Water 
h 
Heat- 
units. 

In  the 
Steam 
H 
Heat- 
units. 

fill 

1*1 

•«;>'S 

Volume.  0 
in  lib.  of  Si 

Weight  of  1 
ft.  Steam 

29.74 

.089 

32 

0 

1091.7 

1091.7 

208080 

3333.3 

.00030 

29.67 

.122 

40 

8. 

1094.1 

1086.1 

154330 

2472.2 

.00040 

29.56 

.176 

50 

18. 

1097.2 

1079.2 

107630 

1724.1 

.00058 

29.40 

.254 

60 

28.01 

1100.2 

1072.2 

76370 

1223.4 

.00082 

29.19 

.359 

70 

38.02 

1103.3 

1065.3 

54660 

875.61 

.00115 

28.90 

.502 

80 

48.04 

1106.3 

1058.3 

39690 

635.80 

.00158 

28.51 

.692 

90 

58.06 

1109.4 

1051.3 

29290 

469.20 

.00213 

28.00 

.943 

100 

68.08 

1112.4 

1044.4 

21830 

349.70 

.00286 

27.88 

1 

102.1 

70.09 

1113.1 

1043.0 

20623 

334.23 

.00299 

25.85 

2 

126.3 

94.44 

1120.5 

1026.0 

10730 

173.23 

.00577 

23.83 

3 

141.8 

109.9 

1125.1 

1015.3 

7325 

117.98 

.00848 

21.78 

4 

153.1 

121.4 

1128.6 

1007.2 

5588 

89.80 

.01112 

19.74 

5 

162.3 

130.7 

1131.4 

1000.7 

4530 

72.50 

.01373 

17.70 

6 

170.1 

138.6 

1133.8 

995.2 

3816 

61.10 

.01631 

15.67 

7 

176.9 

145.4 

1135.9 

990.5 

3302 

53.00 

.01887 

13.63 

8 

182.9 

151.5 

1137.7 

986.2 

2912 

46.60 

.02140 

11.60 

9 

188.3 

156  9 

1139.4 

982.4 

2607 

41.82 

.02391 

9.56 

10 

193.2 

161.9 

1140.9 

979.0 

2361 

37.80 

.02641 

7.52 

11 

197.8 

166.5 

1142.3 

975.8 

2159 

34.61 

.02889 

5.49 

12 

202.0 

170.7 

1143.5 

972.8 

1990 

31.90 

.03136 

3.45 

13 

205.9 

174.7 

1144.7 

970.0 

1846 

29.58 

.03381 

1.41 

14 

209.6 

178.4 

1145.9 

967.4 

1721 

27.59 

.03625 

Gauge 

Pressure 
Ibs.  per 

14.7 

212 

180.9 

1146.6 

965.7 

1646 

26.36 

.03794 

sq.  in. 

0.304 

15 

213.0 

181.9 

1146.9 

965.0 

1614 

25.87 

.03868 

1.3 

16 

216.3 

185.3 

1147.9 

962.7 

1519 

24.33 

.04110 

2.3 

17 

219.4 

188.4 

1148.9 

960.5 

1434 

22.98 

.04352 

3.3 

18 

222.4 

191.4 

1149  8 

958.3 

1359 

21  78 

.04592 

4.3 

19 

225.2 

194.3 

1150.6 

956.3 

1292 

20^70 

.04831 

5.3 

20 

227.9 

197.0 

1151.5 

954.4 

1231 

19.72 

.05070 

6.3 

21 

230.5 

199.7 

1152.2 

952.6 

1176 

18.84 

.05308 

7.3 

22 

233.0 

202.2 

1153.0 

950.8 

1126 

18.03 

.05545 

8.3 

23 

235.4 

204.7 

7 

949.1 

1080 

17.30 

.05782 

9.3 

24 

237.8 

207.0 

1154^5 

947.4 

1038 

16.62 

.06018 

10.3 

25 

240.0 

209.3 

1155.1 

945.8 

998.4 

15.99 

.06253 

11.3 

26 

242.2 

211.5 

.8 

944.3 

962.3 

15.42 

.06487 

12.3 

27 

244.3 

213.7 

1156.4 

942.8 

928.8 

14.88 

.06721 

13.3 

28 

246.3 

215.7 

1157.1 

941.3 

897.6 

14.38 

.06955 

14.3 

29 

248.3 

217.8 

.7 

939.9 

868.5 

13.91 

.07188 

15.3 

30 

250.2 

219.7 

1158.3 

938.9 

841.3 

13.48 

.07420 

16.3 

31 

252.1 

221.6 

.8 

937.2 

815  8 

13.07 

.07652 

17.3 

32 

254.0 

223.5 

1159.4 

935.9 

791.8 

12.68 

.07884 

18.3 

33 

255.7 

225  3 

.9 

934.6 

769.2 

12.32 

.08115 

19.3 

34 

257.5 

227.1 

1160.5 

933.4 

748.0 

11.98 

.08346 

20.3 

35 

259.2 

228.8 

1161.0 

932.2 

727.9 

11.66 

.08576 

21.3 

36 

260.8 

230.5 

1161.5 

931.0 

708.8 

11.36 

.08806 

22.3 

37 

262.5 

232.1 

1162.0 

929.8 

690.8 

11.07 

.09035 

664 


STEAM. 


Properties  of  Saturated  Steam. 


„ 

Total  Heat 

2n   . 

«l 

Gauge  Pressure 
Ibs.  per  sq.  in 

Absolute  Press- 
ure, Ibs.  per 
square  inch. 

®-s 
5% 
gg 

P 
P 

above  32°  F. 

Latent  Heat  L 
=  H-h. 
Heat-  units. 

Relative  Volurr 
Vol.  of  Wate 
at  39°  F.  =  1 

Volume.  Cu.  1 
in  1  Ib.  of  Stea 

Weight  of  1  cu 
ft.  Steam,  Ib 

In  the 
Water 
h 
Heat- 
units. 

In  the 
Steam 
H 
Heat- 
units. 

23.3 

38 

261.0 

233.8 

1162.5 

928.7 

673.7 

10.79 

.09264 

24.3 

39 

265.6 

235.4 

.9 

927.6 

657.5 

10.53 

.09493 

25.3 

40 

267.1 

236.9 

1163.4 

926.5 

642.0 

10.28 

.09721 

26.3 

41 

268.6 

238.5 

.9 

925.4 

627.3 

10.05 

.09949 

27.3 

42 

270.1 

240.0 

1164.3 

924.4 

613.3 

9.83 

.1018 

28.3 

43 

271.5 

241.4 

.7 

923.3 

599.9 

9.61 

.1040 

29.3 

44 

272.9 

242.9 

1165.2 

922.3 

587.0 

9.41 

.1063 

30.3 

45 

274.3 

244.3 

.6 

921.3 

574.7 

9.21 

.1086 

31.3 

46 

27'5.7 

245.7 

1166.0 

920.4 

563.0 

9.02 

.1108 

32.3 

47 

277.0 

247.0 

.4 

919.4 

551.7 

8.84 

.1131 

33.3 

48 

278.3 

248.4 

.8 

918.5 

540.9 

8.67 

.1153 

34.3 

49 

279.6 

249.7 

1167.2 

917.5 

530.5 

8.50 

.1176 

35.3 

50 

280.9 

251.0 

.6 

916.6 

520.5 

8.34 

.1198 

36.3 

51 

282.1 

252.2 

1168.0 

915.7 

510.9 

8.19 

.1221 

37.3 

52 

283.3 

253.5 

.4 

914.9 

501.7 

8.04 

.1243 

38.3 

53 

284.5 

254.7 

.7 

914.0 

492.8 

7.90 

.1266 

39.3 

54 

285.7 

256.0 

1169.1 

913.1 

484.2 

7.76 

.1288 

40.3 

55 

286.9 

257.2 

.4 

912.3 

475.9 

7.63 

.1311 

41.3 

56 

288.1 

258.3 

.8 

911.5 

467.9 

7.50 

.1333 

42.3 

57 

289.1 

259.5 

1170.1 

910.6 

460.2 

7.38 

.1355 

43.3 

58 

290.3 

260.7 

.5 

909.8 

452.7 

7.26 

.1377 

44.3 

59 

291.4 

261.8 

.8 

909.0 

445.5 

7.14 

.1400 

45.3 

60 

292.5 

262.9 

1171.2 

908.2 

438.5 

7.03 

.1422 

46.3 

61 

293.6 

264.0 

.5 

907.5 

431.7 

6.92 

.1444 

47.3 

62 

294.7 

265.1 

.8 

906.7 

425.2 

6.82 

.1466 

48.3 

63 

295.7 

266.2 

1172.1 

905.9 

418.8 

6.72 

.1488 

49.3 

64 

296.8 

267.2 

.4 

905.2 

412.6 

6.62 

.1511 

50.3 

65 

297.8 

268.3 

.8 

904.5 

406.6 

6.53 

.1533 

51.3 

66 

298.8 

269.3 

1173.1 

903  7 

400.8 

6.43 

.1555 

52.3 

67 

299.8 

270.4 

.4 

903.0 

395.2 

6.34 

.157? 

53.3 

68 

300.8 

271.4 

.7 

902.3 

389.8 

6.25 

.1599 

54.3 

69 

301.8 

272.4 

1174.0 

901.6 

384.5 

6.17 

.1621 

55.3 

70 

302.7 

273.4 

.3 

900.9 

379.3 

6.09 

.1643 

56.3 

71 

303.7 

274.4 

.6 

900.2 

374.3 

6.01 

.1665 

57.3 

72 

304.6 

275.3 

.8 

899.5 

369.4 

5.93 

.1687 

58.3 

73 

305.6 

276.3 

1175.1 

898.9 

364.6 

5.85 

.1709 

59.3 

74 

306.5 

277.2 

.4 

898.2 

360.0 

5.78 

.1731 

60.3 

75 

307.4 

278.2 

.7 

897.5 

355.5 

5.71 

.17'53 

61.3 

76 

308.3 

279.1 

1176.0 

896.9 

351.1 

5.63 

.1775 

62.3 

77 

309.2 

280.0 

.2 

896.2 

346.8 

5.57 

.1797 

63.3 

78 

310.1 

280.9 

.5 

895.6 

342.6 

5.50 

.1819 

64.3 

79 

310.9 

281.8 

1176.8 

895.0 

338.5 

5.43 

.1840 

65.3 

80 

311.8 

282.7 

1177.0 

894.3 

334.5 

5.37 

.1862 

66.3 

81 

312.7 

283.6 

.3 

893.7 

330.6 

5.31 

.1884 

67.3 

82 

313.5 

284.5 

.6 

893.1 

326.8 

5.25 

.1906 

68.3 

83 

314.4 

285.3 

.8 

892.5 

323.1 

5.18 

.1928 

69.3 

84 

315.2 

286.2 

1178.1 

.891.9 

319.5 

5.13 

.1950 

70.3 

85 

316.0 

287.0 

.3 

891.3 

315.9 

5.07 

.1971 

STEAM. 


665 


Properties  of  Saturated  Steam. 


, 

Total 

Heat 

§fa 

d  ** 

I'S- 

111 

g£jj 

above 

32°  F. 

-^          CC 

=  17 

si 

S3  rj 
OS 

t£ 

*»~ 

3  "<3 

In  the 

In  the 

it| 

>t* 

°2 

if 

P4 

~3'"H  o3 

0)  •-> 

Water 

Steam 

>    °O5 

*y 

Slcc 

•3«3 

&& 

h 

H 

C  ^  0) 

Ts'TJco 

s 

"§^ 

§1 

os  •=  O4 
&  3  cc 

s^ 

Heat- 

Heat- 

tg  llffl 

~p>  ^ 

*o  fl 

gd 

o 

H 

units. 

units. 

3 

tf 

J>~ 

te 

71.3 

86 

316.8 

287.9 

1178.6 

890.7 

312.5 

5.02 

.1993 

72.3 

87 

317.7 

288.7 

.8 

890.1 

309.1 

4.96 

.2015 

73.3 

88 

318.5 

289.5 

1179.1 

889.5 

305.8 

4.91 

.2036 

t  74.3 

89 

319.3 

290.4 

.3 

888.9 

302.5 

4.86 

.2058 

75.3 

90 

320.0 

291.2 

.6 

888.4 

299.4 

4.81 

.2080 

76.3 

91 

320.8 

292.0 

.8 

887.8 

296.3 

4.76 

.2102 

77.3 

92 

321.6 

292.8 

1180.0 

887.2 

293.2 

4.71 

.2123 

78.3 

93 

322.4 

293.6 

.3 

886.7 

290.2 

4.66 

.2145 

79.3 

94 

323.1 

294.4 

.5 

886.1 

287.3 

4.62 

.2166 

80.3 

95 

323.9 

295.1 

.7 

885.6 

284.5 

4.57 

.2188 

81.3 

96 

324.6 

295.9 

1181.0 

885.0 

281.7 

4.53 

.2210 

82.3 

97 

325.4 

296.7 

.2 

884.5 

279.0 

4.48 

.2231 

83.3 

98 

326.1 

297.4 

.4 

884.0 

276  .  3 

4.44 

.2253 

84  3 

99 

326.8 

298.2 

.6 

883.4 

273:7 

4.40 

.2274 

85.3 

100 

327.6 

298.9 

.8 

882.9 

271.1 

4.36 

.2296 

86.3 

101 

328.3 

299  7 

1182.1 

882.4 

268.5 

4.32 

.2317 

87.3 

102 

3-^9.0 

300.4 

.3 

881.9 

266.0 

4.28 

.2339 

88.3 

103 

329.7 

301.1 

.5 

881.4 

263.6 

4.24 

.2360 

89.3 

104 

330.4 

301.9 

.7 

880.8 

261.2 

4.20 

.2382 

90.3 

105 

331.1 

302.6 

.9 

880.3 

258.9 

4.16 

.2403 

91.3 

106 

331.8 

303.3 

1183.1 

879.8 

256.6 

4.12 

.2425 

92.3 

107 

332.5 

304.0 

.4 

879.3 

254.3 

4.09 

.2446 

93.3 

108 

333.2 

304.7 

.6 

878.8 

252.1 

4.05 

.2467 

94.3 

109 

333.9 

305.4 

.8 

878.3 

249.9 

4.02 

.2489 

95.3 

110 

334.5 

306.1 

1184.0 

877.9 

247.8 

3.98 

.2510 

96.3 

111 

335.2 

306.8 

2 

877.4 

245.7 

3.95 

.2531 

97.3 

112 

335.9 

307.5 

.4 

876.9 

243.6 

3.92 

.2553 

98.3 

113 

336.5 

308.2 

.6 

876.4 

241.6 

3.88 

.2574 

99.3 

114 

337.2 

308.8 

.8 

875.9 

239.6 

3.85 

.2596 

100.3 

115 

337.8 

309.5 

1185.0 

875.5 

237.6 

3.82 

.2617 

101.3 

116 

338.5 

310.2 

.2 

875.0 

235.7 

3.79 

.2638 

102.3 

117 

339.1 

310.8 

.4 

874.5 

233.8 

3.76  - 

.2660 

103.3 

118 

339.7 

311.5 

.6 

874.1 

231.9 

3.73 

.2681 

104.3 

119 

340.4 

312.1 

.8 

873.6 

230.1 

3.70 

.2703 

105.3 

120 

341.0 

312,8 

.9 

873.2 

228.3 

3.67 

.2724 

106.3 

121 

341.6 

313.4 

1186.1 

872.7 

226.5 

3.G4 

.2745 

107.3 

122 

342.2 

314.1 

.3 

872.3 

224.7 

3.62 

.2766 

108.3 

123 

342.9 

314.7 

.5 

871.8 

223.0 

3.59 

.2788 

109.3 

124 

343.5 

315.3 

.7 

871.4 

221.3 

3.56 

.2809 

110.3 

125 

344.1 

316  0 

.9 

870.9 

219.6 

3.53 

.2830 

111.3 

126 

344.7 

316.6 

1187.1 

870.5 

218.0 

3.51 

.2851 

112.3 

127 

345.3 

317.2 

.3 

870.0 

216.4 

3.48 

.2872 

113.3 

128 

345.9 

317.8 

.4 

869.6 

214.8 

3.46 

.2894 

114.3 

129 

346.5 

318.4 

.6 

869.2 

213.2 

3.43 

.2915 

115.3 

130 

347.1 

319.1 

.8 

868.7 

211.6 

3.41 

.2936 

116.8 

131 

347.6 

319.7 

1188.0 

868.3 

210.1 

3.38 

.2957 

117.3 

132 

348.2 

320.3 

.2 

867.9 

208.6 

3.36 

.2978 

118.3 

133 

348.8 

320.8 

.3 

867.5 

207.1 

3.33 

.3000 

119.3 

134 

349.4 

321.5 

.5 

867.0 

205.7 

3.31 

.3021 

666 


STEAM. 


Properties  of  Saturated  Steam. 


Total  Heat 

V<£ 

£  S 

£« 

*5  JH     « 

above  32°  F. 

•q 

Is- 

c3 

3    • 

3— 
£fc 

2S.-S 

fc  ..S 

||g 

11 

3  .S 

S 

fi- 
ts1! 

6'  £ 
02 

«M 

If 

In  the 
Water 

In  the 
Steam 

&* 

"3  <C  3 

P*4 

h 

H 

cffl  S3 

I™  0) 

|°fe 

C;2 

t£GQ 

£r? 

Heat- 

Heat- 

luw 

<OTH 

**  *i 

o5 

5 

£ 

units. 

units. 

5 

$>% 

£.s 

£«" 

120.3 

135 

350.0 

322.1 

1188.7 

866.6 

204.2 

3.29 

.3042 

121.3 

136 

350.5 

322.6 

.9 

866.2 

202.8 

3.27 

.8063 

122.3 

137 

351.1 

323.2 

1189.0 

865.8 

201  4 

3.24 

.3084 

123.3 

138 

351.8 

323.8 

.2 

865.4 

200.0 

3.22 

.3105 

124.3 

139 

352.2 

324.4 

.4 

865.0 

198.7 

3.20 

.3126 

125.3 

140 

352.8 

325.0 

.5 

864.6 

197.3 

3.18 

.3147 

126.3 

141 

353.3 

325.5 

.7 

864.2 

196.0 

3.16 

.3169 

127.3 

142 

353.9 

326.1 

.9 

863.8 

194.7 

3.14 

.3190 

128  3 

143 

354.4 

326.7 

1190.0 

863.4 

193.4 

3.11 

.3211 

129.3 

144 

355.0 

327.2 

.2 

863.0 

192.2 

3.09 

.3232 

130.3 

145 

355.5 

327.8 

.4 

862.6 

190.9 

3.07 

.3253 

131.3 

146 

356.0 

328.4 

.5 

862.2 

189.7 

3.05 

.3274 

132.3 

147 

356.6 

328.9 

.7 

861.8 

185.5 

3.04 

.3295 

133.3 

148 

357.1 

329.5 

.9 

861.4 

187.3 

3.02 

.3316 

134.3 

149 

357.6 

330.0 

1191.0 

861.0 

186.1 

3.00 

.3337 

135.3 

150 

358.2 

330.6 

.2 

860.6 

184.9 

2.98 

.3358 

136.3 

151 

358.7 

331.1 

.3 

860.2 

183.7 

2.96 

.3379 

137.3 

152 

359.2 

331.6 

.5 

859.9 

182.6 

2.94 

.3400 

138.3 

153 

359.7 

332.2 

.7 

859.5 

181.5 

2.92 

.3421 

139.3 

154 

360.2 

332.7 

.8 

859.1 

180.4 

2.91 

.3443 

140.3 

155 

360.7 

,'{33.2 

1192.0 

858.7 

179.2 

2.89 

.3463 

141.3 

156 

361.3 

333.8 

.1 

858.4 

178.1 

2.87 

.3483 

142.3 

157 

361.8 

334.3 

.3 

858.0 

177.0 

2.85 

.3504 

143.3 

158 

362.3 

334.8 

.4 

857.6 

175.0 

2.84 

.3525 

144.3 

159 

362.8 

335.3 

.6 

857.2 

174.9 

2.82 

.3546 

145.3 

160 

363.3 

335.9 

.7 

856.9 

173.9 

2.80 

.3567 

146.3 

161 

363.8 

336.4 

.9 

856.5 

172.0 

2.79 

.3588 

147.3 

162 

364.3 

336.9 

1193.0 

856.1 

171.9 

2.77 

.3609 

148.3 

163 

364.8 

337.4 

.2 

855.8 

171.0 

2.76 

.3630 

149.3 

164 

365.3 

337.9 

.3 

855.4 

170.0 

2.74 

.3650 

150.3 

165 

365.7 

338.4 

.5 

855.1 

169.0 

2.72 

.3671 

151.3 

166 

366.2 

338.9 

.6 

854.7 

168.1 

2.71 

.3692 

152.3 

167 

366.7 

339.4 

.8 

854.4 

167.1 

2.69 

.371'i 

153.3 

168 

367.2 

339.9 

.9 

854.0 

166.2 

2.68 

.37?i 

154.3 

169 

367.7 

340.4 

1194.1 

853.6 

165.3 

2.66 

.37M 

155.3 

170 

368.2 

340.9 

.2 

853.3 

164.3 

2.65 

.3775 

156.3 

171 

368.6 

341.4 

.4 

852.9 

163.4 

2.63 

.3796 

157.3 

172 

369.1 

341.9 

.5 

852.6 

162.5 

2.62 

.3817 

158.3 

173 

369.6 

342.4 

.7 

852.3 

161.6 

2.61 

.3838 

159.3 

174 

370.0 

342.9 

.8 

851.9 

160.7 

2.59 

.3858 

160.3 

175 

370.5 

343.4 

.9 

851.6 

159.8 

2.58 

.3879 

161.3 

176 

371.0 

343.9 

1195.1 

851  .2 

158.9 

2.56 

.3900 

162.3 

177 

371.4 

344.3 

.2 

850.9 

158.1 

2.55 

.3921 

163.3 

178 

371.9 

344.8 

.4 

850.5 

157.2 

2.54 

.3942 

164.3 

179 

372.4 

345.3 

.5 

850.2 

156.4 

2.52 

.3962 

165.3 

180 

372.8 

345.8 

.7 

849.9 

155.6 

2.51 

.3983 

166.3 

181 

373.3 

346.3 

.8 

849.5 

154.8 

2  50 

.4004 

167.3 

182 

373.7 

346.7 

.9 

849.2 

154.0 

2.48 

.4025 

168.3 

183 

374.2 

347.2      1196.1 

848.9 

153.2 

2.47 

.4046 

STEAM. 


667 


Properties  of  Saturated  Steam. 


„ 

Total 

Heat 

OJ-M 

4*    S 

£  d 

CG   I* 

above 

32°  F. 

t^ 

£  ._, 

*tH   gj 

3     • 

0>    a  rf 

-W         O3 

w  6- 

£     o 

oS    .£ 

O  "£g    . 

CD  03 
PH£ 
&a 

III 

s'i 

•~  3 

II 

In  the 
Water 
h 

In  the 
Steam 
H 

»1! 

1*8 

>  &~ 

Eg". 
55  .fa 

."o 

O>     ' 

=  1 
S.2 

bCCO 

3  en 
oSXJ 

o? 

S-c't 

<j  5  M 

SIS 

Jl* 

Heat- 
units. 

Heat- 
units. 

4-J    II  hH 

.IIS 

^"oo 

&>* 

"o  a 

il 

169.3 

184 

374.6 

347.7 

1196.2 

848.5 

152.4 

2.46 

.4066 

170.3 

185 

375.1 

348.1 

.3 

848.2 

151  .6 

2.45 

.4087 

171.3 

186 

375.5 

348.6 

.5 

847.9 

150.8 

2.43 

.4108 

172.3 

187 

375.9 

349.1 

.6 

847.6 

150.0 

2.42 

.4129 

173.3 

188 

376.4 

349.5 

.7 

847.2 

149.2 

2.41 

.4150 

174.3 

189 

376.9 

350.0 

.9 

846.9 

148.5 

2.40 

.4170 

175.3 

190 

377.3 

350.4 

1197.0 

846.6 

147.8 

2.39 

.4191 

176.3 

191 

377.7 

350.9 

.1 

846.3 

147.0 

2.37 

.4212 

177.3 

192 

378.2 

351.3 

.3 

845.9 

146.3 

2.36 

.4233 

178.3 

193 

378.6 

351.8 

.4 

845.6 

145.6 

2.35" 

.4254 

179.3 

194 

379.0 

352.2 

.5 

845.3 

144.9 

2.34 

.4275 

180.3 

195 

379.5 

352.7 

.7 

845.0 

144.2 

2.33 

.4296 

181.3 

196 

380.0 

353.1 

.8 

844.7 

143.5 

2.32 

.4317 

182.3 

197 

380.3 

353.6 

.9 

844.4 

142.8 

2.31 

.4337 

183.3 

198 

380.7 

354.0 

1198.1 

844.1 

142.1 

2.29 

.4358 

184.3 

199 

381.2 

354.4 

.2 

843.7 

141.4 

2.28 

.4379 

185.3 

200 

381.6 

354.9 

.3 

843.4 

140.8 

2.27 

.4400 

186.3 

201 

382.0 

355.3 

.4 

843.1 

140.1 

2.26 

.4420 

187.3 

202 

382.4 

355.8 

.6 

842.8 

139.5 

2.25 

.4441 

188.3 

203 

38-'.  8 

356.2 

.7 

842.5 

138.8 

2  24 

.4462 

189.3 

204 

383.2 

356.6 

.8 

842.2 

138.1 

2.23 

.4482 

190.3 

205 

383.7 

357.1 

1199.0 

841.9 

137.5 

2.22 

.4503 

191.3 

206 

384.1 

357.5 

.1 

841.6 

136.9 

2.21 

.4523 

192.3 

207 

384.5 

357.9 

.2 

841.3 

136.3 

2.20 

.4544 

193.3 

208 

384.9 

358.3 

.3 

841  0 

135.7 

2.19 

.4564 

194.3 

209 

385.3 

358.8 

.5 

840.7 

135.1 

2.18 

.4585 

195.3 

210 

385.7 

359.2 

.6 

840.4 

134.5 

2.17 

.4605 

196.3 

211 

386.1 

359.6 

.7 

840.1 

133.9 

2.16 

.4626 

197.3 

212 

386.5 

360.0 

.8 

839.8 

133.3 

2.15 

.4646 

198.3 

213 

386.9 

360.4 

.9 

839.5 

132.7 

2.14 

.4667 

199.3 

214 

387.3 

360.9 

1200.1 

839.2 

132.1 

2.13 

.4687 

200.3 

215 

387.7 

361.3 

.2 

838.9 

131.5 

2.12 

.4707 

201.3 

216 

388  1 

361.7 

.3 

838.6 

130.9 

2.12 

.4728 

202.3 

217 

388.5 

362.1 

.4 

838.3 

130.3 

2.11 

.4748 

203.3 

218 

388.9 

362.5 

.6 

838.1 

129.7 

2.10 

.4768 

204.3 

219 

389.3 

362.9 

.7 

837.8 

129.2 

2.09 

.4788 

205.3 

220 

389.7 

362'.  2* 

1200.8 

838.6* 

128.7 

2.06 

.4852 

215.3 

230 

393.6 

366.2 

1202.0 

835.8 

123.3 

1.98 

.5061 

225.3 

240 

397.3 

370.0 

1203.1 

833.1 

118.5 

1.90 

.5270 

235.3 

250 

400.9 

373.8 

1204.2 

830.5 

114.0 

1.83 

.5478 

245.3 

260 

404.4 

377.4 

1205.3 

827.9 

109.8 

1.76 

.5686 

255.3 

270 

407.8 

380.9 

1206.3 

825.4 

105.9 

1.70 

.5894 

265.3 

280 

411.0 

384.3 

1207.3 

823.0 

102.3 

1.64 

.6101 

275.3 

290 

414.2 

387.7 

1208.3 

820.6 

99.0 

1.585 

.6308 

285.3 

300 

417.4 

390.9 

1209.2 

818.3 

95.8 

1.535 

.6515 

335.3 

350 

432.0 

406.3 

1213.7 

807.5 

82.7 

1.325 

.7545 

*  The  discrepancies  at  205.3  Ibs.  gauge  are  due  to  the  change  from  Dery's 
to  Duel's  figures. 


668 


STEAM. 


Properties  of  Saturated  Steam. 


, 

Total  Heat 

^4J 

... 

Is 

1®   • 

<D 

above  32°  F. 

+3          03 

S  c8 

3  - 

<w—  • 

§£ 

tfl      • 

£0 

3  '53 

ej  ^5 

O  -t->  ^_. 

5a 

7-1   r5" 

£   W 

&  »'2 

IP 

In  the 

In  the 

£7.1 

^  i  II 

•  3 

'o  § 

8c& 

3*| 

S  <D 
§£ 

Water 
| 

Steam 
H 

si 

3  "^ 

11 

p  Cfi 

j§  ^  CT1 

Sis 

Heat- 

Heat- 

"S  ii  ffl 

r-H    O  ^ 

•MQU 

"55  ^ 

o~ 

<!<  3» 

gfe 

units. 

units. 

^ 

£>CO 

>*% 

^«M 

385.3 

400 

444.9 

419.8 

1217.7 

797.9 

72.8 

1.167 

.8572 

435.3 

450 

456.6 

432.2 

1221.3 

789.1 

j 

65.1 

1.042 

.9595 

485.3 

500 

467.4 

443.5 

1224.5 

781.0 

58.8 

.942 

1.062 

535.3 

550 

477.5 

454.1 

1227.6 

773.5 

53.6 

.859 

1.164 

585.3 

600 

486.9 

464.2 

1230.5 

766.3 

49.3 

.790 

1.266 

635.3 

650 

495.7 

473.6 

1233.2 

759.6 

45.6 

.731 

1.368 

685.3 

700 

504.1 

482.4 

1235.7 

753.3 

42.4 

.680 

1.470 

735.3 

750 

512.1 

490.9 

1238.0 

747.2 

39.6 

.636 

1.572 

785.3 

800 

519.6 

498.9 

1240.3 

741.4 

37.1 

.597 

1.674 

835.3 

850 

526.8 

506.7 

1242.5 

735.8 

34.9 

.563 

1.776 

885.3 

900 

533.7 

514.0 

1244.7 

730.6 

33.0 

.532 

1.878 

935.3 

950 

540.3 

521.3 

1246.7 

725.4 

31.4 

.505 

1.980 

985.3 

1000 

546.8 

528.3 

1248.7 

720.3 

30.0 

.480 

2.082 

FL.OW  OF  STEAM. 

Flow  of  Steam  through  a  Nozzle.  (From  Clark  on  the  Steam- 
engine.)— The  flow  of  steam  of  a  greater  pressure  into  an  atmosphere  of  a 
less  pressure  increases  as  the  difference  of  pressure  is  increased,  until  the 
external  pressure  becomes  only  58$  of  the  absolute  pressure  in  the  boiler. 
The  flow  of  steam  is  neither  increased  nor  diminished  by  the  fall  of  the  ex- 
ternal pressure  below  58#,  or  about  4/7ths  of  the  inside  pressure,  even  to  th« 
extent  of  a  perfect  vacuum.  In  flowing  through  a  nozzle  of  the  best  form, 
the  steam  expands  to  the  external  pressure,  and  to  the  volume  due  to  this 
pressure,  so  long  as  it  is  not  less  than  58#  of  the  internal  pressure.  For  an 
external  pressure  of  58$,  and  for  lower  percentages,  the  ratio  of  expansion 
is  1  to  1.624.  The  following  table  is  selected  from  Mr.  Brownlee's  data  exem- 
plifying the  rates  of  discharge  under  a  constant  internal  pressure,  into 
various  external  pressures: 

0 11  tf low  of  Steam ;  from  a  Given  Initial  Pressure  Into 
Various  L«ower  Pressures. 

Absolute  initial  pressure  in  boiler,  75  Ibs.  per  sq.  in. 


Absolute 
Pressure  in 
Boiler  per 
square 
inch. 

External 
Pressure 
per  square 
inch. 

Ratio  of 
Expansion 
in 

Nozzle. 

Velocity  of 
Outflow 
at  Constant 
Density. 

Actual 

Velocity  of 
Outflow 
Expanded. 

Discharge 
per  square 
inch  of 
Orifice  per 
minute. 

Ibs. 

Ibs. 

ratio. 

feet  per  sec. 

feet  p.  sec. 

Ibs. 

75 

74 

1.012 

227.5 

230 

16.68 

75 

72 

1.037 

386.7 

401 

28.35 

75 

70 

1.063 

490 

521 

35.93 

75 

65 

1.136 

660 

749 

48.38 

75 

61.62 

1.198 

736 

876 

53.97 

75 

60 

1.219 

765 

933 

56.12 

75 

50 

1.434 

873 

1252 

64 

75 

45 

1.575 

890 

1401 

65.24 

(        4Q  4«       ) 

75 

)            <*O  .  4O         ( 

I  58  p.  cent  j 

1.624 

890.6 

1446.5 

65.3 

75 

15 

1.624 

890.6 

1446.5 

65.3 

75 

0 

1.624 

890.6 

1446.5 

65.3 

FLOW   OF   STEAM. 


669 


When  steam  of  varying  initial  pressures  is  discharged  into  the  atmos- 
phere—the atmospheric  pressure  being  not  more  than  58#  of  the  initial 
pressure — the  velocity  of  outflow  at  constant  density,  that  is,  supposing  the 
initial  density  to  be  maintained,  is  given  by  the  formula  V  =  3.5953  yh. 

V  =  the  velocity  of  outflow  in  feet  per  minute,  as  for  steam  of  the  initial 
density ; 

h  =  the  height  in  feet  of  a  column  of  steam  of  the  given  absolute  initial 
pressure  of  uniform  density,  the  weight  of  which  is  equal  to  the  pres- 
sure on  the  unit  of  base. 

The  lowest  initial  pressure  to  which  the  formula  applies,  when  the  steam 
is  discharged  into  the  atmosphere  at  14.7  Ibs.  per  square  inch,  is  (14.7  X 
100/58  —)  25.37  Ibs.  per  square  inch.  Examples  of  the  application  of  the 
formula  are  given  in  the  table  below. 

From  the  contents  of  this  table  it  appears  that  the  velocity  of  outflow  into 
the  atmosphere,  of  steam  above  25  Ibs.  per  square  inch  absolute  pressure, 
or  10  Ibs.  effective,  increases  very  slowly  with  the  pressure,  obviously  be- 
cause the  density,  and  the  weight  to  be  moved,  increase  with  the  pressure. 
An  average  of  900  feet  per  second  may,  for  approximate  calculations,  be 
taken  for  the  velocity  of  outflow  as  for  constant  density,  that  is,  taking  the 
volume  of  the  steam  at  the  initial  volume. 

Outflow  of  Steam  into  the  Atmosphere.— External  pressure 
per  square  inch  14.7  Ibs.  absolute.  Ratio  of  expansion  in  nozzle,  1.624. 


•S%* 

tH   0).2 
*5<D 

5  |a  3 

Jn"  O1 
P-l  05 


Ibs. 

25.37 

30 

40 

50 

60 

70 

75 


"*£ 

**2 


feet 

p. sec. 

863 

867 
874 
880 
885 
889 
891 


!*•§ 


feet 
per  sec. 
1401 
1408 
1419 
1429 
1437 
1444 
1447 


33| 


Ibs. 

22.81 
26.84 
35.18 
44.06 
52  59 
61.07 
65.30 


t.  g 


- 

12  «* 


H.P. 

45.6 
53.7 
70.4 
88.1 
105.2 
122.1 
130.6 


c3  h  . 

!&•§ 


Ibs. 

90 
100 
115 
135 
155 
165 
215 


*S  fc  g 

0  o.g 
" 


feet 
p.  sec. 
895 
898 
902 
906 
910 
912 
919 


feet 
per  sec. 
1454 
1459 
1466 
1472 
1478 
1481 
1493 


-  t.  o 

5  §5  s 


Ibs. 

77.94 
86.34 
98.76 
115.61 
132.21 
140.46 
181.58 


S|9!5 


H.P. 

155.9 
172.7 
197.5 
231.2 
J.J64.4 
280.9 
363.2 


Napier's  Approximate  Rule.  —Flow  in  pounds  per  second  =  ab- 
solute pressure  x  area  in  square  inches  -i-  70.  This  rule  gives  results  which 
closely  correspond  with  those  in  the  above  table,  as  shown  below. 

Abs.  press.,  Ibs.  p.  sq.  in.  25.37     40       60       75  100        135         165        215 
Discharge  per  min.,  by 

table.  Ibs 22.8135.1852.5965.30  86.34  115.61  140.46  181.58 

By  Napier's  rule 21.74  34.29  51.43  64.29  .85.71  115.71  141.43  184.29 

Prof.  Peabody,  in  Trans.  A.  S.  M.  E.,  xi,  187,  reports  a  series  of  experi- 
ments on  flow  of  steam  through  tubes  J4  inch  in  diameter,  and  J4,  ^,  and  1^ 
inch  long,  with  rounded  entrances,  in  which  the  results  agreed  closely  with 
Napier's  formula,  the  greatest  difference  being  an  excess  of  the  experimental 
over  the  calculated  result  of  3.2$.  An  equation  derived  from  the  theory  of 
thermodynamics  is  given  by  Prof.  Peabody,  but  it  does  not  agree  with  the 
experimental  results  as  well  as  Napier's  rule,  the  excess  of  the  actual  flow 
being  6.61 

•     Flow  of  Steam  in  Pipes.— A  formula  commonly  used  for  velocity 
of  flow  of  steam  in  pipes  is  the  same  as  Downing's  for  the  flow  of  water  in 

smooth  cast-iron  pipes,  viz.,  V  =  50  A/  —  D,  in  which  V  =  velocity  in  feet 

per  second,  L  =  length  and  D  —  diameter  of  pipe  in  feet,  H  =  height  in 
feet  of  a  column  of  steam,  of  the  pressure  of  the  steam  at  the  entrance, 


670  STEAM. 


which  would  produce  a  pressure  equal  to  the  difference  of  pressures  at  the 
two  ends  of  the  pipe.  (For  derivation  of  the  coefficient  50,  see  Briggs  on 
"Warming  Buildings  by  Steam,"  Proc.  Inst.  C.  E.  1882.) 

It  Q  =  quantity  in  cubic  feet  per  minute,  d  =  diameter  in  inches,  L  and  H 
being  in  feet,  the  formula  reduces  to 


(These  formulae  are  applicable  to  air  and  other  gases  as  well  as  steam.) 

If  »,  =  pressure  in  pounds  per  square  inch  of  the  steam  (or  gas)  at  the  en- 
trance to  the  pipe,  p2  =  the  pressure  at  the  exit,  then  144(pi  —  p2)  =  differ- 
ence in  pressure  per  square  foot.  Let  w  =  density  or  weight  per  cubic  foot 
of  steam  at  the  pressure  plt  then  the  height  of  column  equivalent  to  the 
difference  in  pressures 


and    Q  =  60  X  .7854  X  60D^/144(p'  f 
\  wL 


If  W  =  weight  of  steam  flowing  in  pounds  per  minute  =  Qw,  and  d  is 
taken  in  inches,  L  being  in  feet, 


=  56.68, 


Lw 

d  .  ""-  - 


.  0.199 

\  w(pl  -p2 


Velocity  in  feet  per  minute  =  F  =  Q  H-  -7854^  =  10892 A/(Pl  v^d- 

For  a  velocity  of  6000  feet  per  minute,  d  =  $- —     — - ;  pl  —  p.2  =  — -. 

dlPi  —  Pz) 

For  a  velocity  of  6000  feet  per  minute,  a  steam-pressure  of  100  Ibs.  gauge, 

or  w  =.264,  and  a  length  of  100  feet,  d  =  — — — ;  p1  -  p2  =  ^r-    That  is,  a 

Pi  —  P%  '•* 

pipe  1  inch  diameter,  100  feet  long,  carrying  steam  of  100  Ibs.  gauge-pressure 
at  6000  feet  velocity  per  minute,  would  have  a  loss  of  pressure  of  8.8  Ibs.  per 
sq aare  inch,  while  steam  travelling  at  the  same  velocity  in  a  pipe  8.8  inches 
diameter  would  lose  only  1  Ib.  pressure. 
G.  H.  Babcock,  in  "Steam,"  gives  the  formula 


In  earlier  editions  of  "  Steam  "  the  coefficient  is  given  as  300,— evidently  an 
error,— and  this  value  has  been  reprinted  in  Clark's  Pocket-Book  (1892  edi- 
tion). It  is  apparently  derived  from  one  of  the  numerous  formulae  for  flow 
of  water  in  pipes,  the  multiplier  of  L  in  the  denominator  being  used  for  an 
expression  of  the  increased  resistance  of  small  pipes.  Putting  this  formula 

in  the  form  W  =  cju  -  —j-— — » in  which  c  will  vary  with  the  diameter 
of  the  pipe,  we  have, 

For  diameter,  inches 1  2  3  4  6  9  12 

Value  of  c 40.7       52.1         58.8         63         088       73.7        79.3 

instead  of  the  constant  value  56.68,  given  with  the  simpler  formula. 
One  of  the  most  widely  accepted  formulae  for  flow  of  water  is  D'Arcy's, 

V  =  c/4/ jrp in  which  c  has  values  ranging  from  65  for  a  J^-inch  pipe  up  to 


FLOW  OF   STEAM. 


671 


111.5  for  24-inch.    Using  D'Arcy's  coefficients,  and  modifying  his  formula  tc 
make  it  apply  to  steam,  to  the  form 


Q  = 


(Pi    ~ 


wL 


or    W  =  < 


we  obtain, 

For  diameter,  inches . . . .  y>  1  2  3        4        5  6 

Value  of  c 36.8  45.3  52.7  56.1  57.8  58.4  59.5 

For  diameter,  inches....  9  10  12  14  16       18  20       22 

Value  of  c 61.2  61.8  62.1  62.3  62.6  62.7  62.9    63.2 


7 
60.1 


8 
60.7 

24 
63.2 


In  the  absence  of  direct  experiments  these  coefficients  are  probably  as 
accurate  as  any  that  may  be  derived  from  formulae  for  flow  of  water. 

Loss  of  pressure  in  Ibs.  per  sq.  in.  =  pl  —  p.2  =      ™5  . 


of  Pressure  due  to  Radiation  as  well  as  Friction.— 

E.  A.  Rudiger  (Mechanics^  June  30,  1883)  gives  the  following  formulae  and 
tables  for  flow  of  steam  in  pipes.  He  takes  into  consideration  the  losses  in 
pressure  due  both  to  radiation  and  to  friction. 

Loss  of  power,  expressed  in  heat-units  due  to  friction,  Hf  =        :  .  . 


Loss  due  to  radiation, 


Hr  =  0.2Q2rld. 


In  which  Wis  the  weight  in  Ibs.  of  steam  delivered  per  hour, /the  coeffi- 
cient of  friction  of  the  pipe,  I  the  length  of  the  pipe  in  feet,  p  the  absolute 
terminal  pressure,  d  the  diameter  of  the  pipe  in  inches,  and  r  the  coefficient 
»f  radiation.  /  is  taken  as  from  .0165  to  .0175,  and  r  varies  as  follows  : 

TABLE  OF  VALUES  FOR  r. 


Absolute  Pressure. 


ripe  uovermg. 

40  Ibs. 

65  Ibs. 

90  Ibs. 

115  Ibs. 

yjncovered  P'P®                  •   

437 

555 

620 

684 

Jt'-inch  cement  composition  

146 

178 

193 

209 

ft          asbestos         "                 • 

157 

192 

202 

222 

2          asbestos  flock  

1    150 

185 

197 

210 

100 

122 

145 

151 

2           mineral  wool 

61 

76 

85 

93 

2           hair  felt  

48 

58 

66 

73 

The  appended  table  shows  the  loss  due  to  friction  and  radiation  in  a  steam- 
pipe  where  the  quantity  of  steam  to  be  delivered  is  1000  Ibs.  per  hour,  I  = 
1000  feet,  the  pipe  being  so  protected  that  loss  by  radiation  r  =  64,  and  the 
absolute  terminal  pressure  being  90  Ibs.: 


Diameter 
of  Pipe, 
inches. 

Loss  by 
Friction, 
Hf. 

Loss  by 
Radia- 
tion, 
Hr. 

Total 
Loss, 
L. 

Diam. 
of  Pipe, 
inches. 

Loss  by 
Friction, 
Hf. 

Loss  by 
Radia- 
tion, 
Hr. 

Total 
Loss. 
L. 

1 

1J4 
lj? 

1% 

2 

g 

197,531 
64,727 
26,012 
12,035 
6,173 
2,023 
813 

16,76^ 
20,960 
25,152 
29,344 
33,536 
41,920 
50,304 

214,300 
85,687 
51,164 
41,379 
39,709 
43,943 
51,117 

3^ 
4 
5 
6 

7 
8 

376 
193 
63 
25 
12 
6 

58,688 
67,072 
83,840 
100.608 
117,376 
134,144 

59,064 
67,265 
83,903 
100,623 
117,388 
134,150 

672 


STEAM. 


If  the  pipes  are  carrying  steam  with  minimum  loss,  then  for  same  r,  t, 
and  p,  the  loss  of  pressure  L  for  pipes  of  different  diameters  varies  in- 
versely as  the  diameters. 

The  general  equation  for  the  loss  of  pressure  for  the  minimal  loss  from 
friction  and  radiation  is 

0.0007023    drip 

-~w~ 

The  loss  of  pressure  for  pipes  of  1  inch  diameter  for  different  absolute 
terminal  pressures  when  steam  is  flowing  with  minimal  loss  is  expressed  by 

the  formula  L  =  Cl^i*,  in  which  the  coefficient  C  has  the  following  values: 

For  651bs.  abs.  term,  pressure C  =  0.00089337 

"    75   "      "        **  " 0.00093684 

"    90    "      «•        "  "         0.00099573 

"  100   "      *«        "  "         0.00103132 

"  115   "      "        "  "         0.00108051 

In  order  to  find  the  loss  of  pressure  for  any  other  diameter,  divide  the  loss 
of  pressure  in  a  1-inch  pipe  for  the  given  terminal  pressure  by  the  given 
diameter,  and  the  quotient  will  be  the  loss  of  pressure  for  that  diameter. 

The  following  is  a  general  summary  of  the  results  of  Mr.  Rudiger's  inves- 
tigation : 

The  flow  of  steam  in  a  pipe  is  determined  in  the  same  manner  as  the  flow 
of  water,  the  formula  for  the  flow  of  steam  being  modified  only  by  substi- 
tuting the  equivalent  loss  of  pressure,  divided  by  the  density  of  the  steam, 
for  the  loss  of  head. 

The  losses  in  the  flow  of  steam  are  two  in  number— the  loss  due  to  the 
friction  of  flow  and  that  due  to  radiation  from  the  sides  of  the  pipe.  The 
sum  of  these  is  a  minimum  when  the  equivalent  of  the  loss  due  to  fric- 
tion of  flow  is  equal  to  one  fifth  of  the  loss  of  heat  by  radiation.  For  a 
greater  or  less  loss  of  pressure— i.e.,  for  a  less  or  greater  diameter  of  pipe 
— the  total  loss  increases  very  rapidly. 

For  delivering  a  given  quantity  of  steam  at  a  given  terminal  pressure, 
with  minimal  total  loss,  the  better  the  non-conducting  material  employed, 
the  larger  the  diameter  of  the  steam -pipe  to  be  used. 

The  most  economical  loss  of  pressure  for  a  pipe  of  given  diameter  is  equal 
to  the  most  economical  loss  of  pressure  in  a  pipe  of  1  inch  diameter  for  same 
conditions,  divided  by  the  diameter  of  the  given  pipe  in  inches. 

The  following  table  gives  the  capacity  of  pipes  of  different  diameters,  to 
deliver  steam  at  different  terminal  pressures  through  a  pipe  one  half  mile 
long  for  loss  of  pressure  of  10  Ibs.,  and  a  mean  value  of  /  =  0.0175.  Let  Vf 
denote  the  number  of  pounds  of  steam  delivered  per  hour  : 


Diameter 
of  Pipe, 
inches. 

Abs.  Term.  Pressure. 

Diameter 
of  Pipe, 

Abs.  Term.  Pressure. 

65  Ibs. 

80  Ibs. 

100  Ibs. 

inches. 

65  Ibs. 

80  Ibs. 

100  Ibs. 

1  

W 

102 
179 
282 
415 
579 
1,011 
1,595 
2,346 
3,275 

W 

113 
198 
312 
459 
641 
1,121 
1,768 
2,599 
3.629 

W 
125 

219 
346 

508 
710 
1.240 
1,956 

2,875 
4,042 

4U 

W 

4,397 
5,721 
9,U24 
13,268 
18,526 
24,870 
32,364 
41,081 
51,049 

W 

4,872 
6,339 
10,000 
14,701 
20,528 
27,556 
35,860 
45,507 
56,564 

W 

5,390 
7,013 
11,063 
16,265 
22,71  1 
30,488 
39,675 
50,349 
62,581 

5 

\V 

6 

134 

7 

2  

g 

%y2  .  .  .  ,  

9 

3 

10 

f*-::::::::: 

11  
12  

Resistance  to  Flow  by  Bends,  Valves,  etc.  (From  Briggs  on 
Warming  Buildings  by  Steam.)— The  resistance  at  the  entrance  to  a  tube 
when  no  special  bell-mouth  is  given  consists  of  two  parts.  The  head  v*  -*-  2g 

is  expended  in  giving  the  velocity  of  flow;  and  the  head  0.505^- in  over- 


FLOW   OF   STEAM.  673 

coming  the  resistance  of  the  mouth  of  the  tube.    Hence  the  whole  loss  of 

V** 

head  at  the  entrance  is  1.505  —  .    This  resistance  is  equal  to  the  resistance 

of  a  straight  tube  of  a  length  equal  to  about  60  times  its  diameter. 

The  loss  at  each  sharp  right-angled  elbow  is  the  same  as  in  flowing 
through  a  length  of  straight  tube  equal  to  about  40  times  its  diameter.  For 
a  globe  steam  stop-valve  the  resistance  is  taken  to  be  1%  times  that  of  the 
right-angled  elbow. 

Sizes  of  Steam-pipes  for  Stationary  Engines.— Authorities 
on  the  steam-engine  generally  agree  that  steam-pipes  supplying  engines 
should  be  of  such  size  that  the  mean  velocity  of  steam  in  them  does  not 
exceed  6000  feet  per  minute,  in  order  that  the  loss  of  pressure  due  to  friction 
may  not  be  excessive.  The  velocity  is  calculated  on  the  assumption  that  the 
cylinder  is  filled  at  each  stroke.  In  very  long  pipes.  100  feet  and  upward,  it 
is  welJ  to  make  them  larger  than  this  rule  would  give,  and  to  place  a  large 
steam  receiver  on  the  pipe  near  the  engine,  especially  when  the  engine  cuts 
off  early  in  the  stroke. 

An  article  in  Power,  May,  1893,  on  proper  area  of  supply-pipes  for  engines 
gives  a  table  showing  the  practice  of  leading  builders.  To  facilitate  com- 
parison, all  the  engines  have  been  rated  in  horse-power  at  40  pounds  mean 
effective  pressure.  The  table  contains  all  the  varieties  of  simple  engines, 
from  the  slide-valve  to  the  Corliss,  and  it  appears  that  there  is  no  general 
difference  in  the  sizes  of  pipe  used  in  the  different  types. 

The  averages  selected  from  this  table  are  as  follows: 

Diam.  of  pipe,  in 2  2^  3  3^  4  4^  5  6  7  8  9  10 

Av.H.P.of  engines....  25    39      56    77    100    126    156    225    306    400    506  625 

Calculated,formula  (1)  23    36      51    70      91    116    143    206    278    366    463  571 

formula  (2)  24  37.5    54    73     96    121    150    216    294    384    486  600 

Formula  (1)  is:  1  H  P.  requires  .1375  sq.  in.  of  steam-pipe  area. 

Formula  (2)  is:  Horse-power  =  6d2.  d  =  diam.  of  pipe  in  inches. 

The  factor  .1375  in  formula  (1)  is  thus  derived:  Assume  that  the  linear 
velocity  of  steam  in  the  pipe  should  not  exceed  6000  feet  per  minute,  then 
pipe  area  =  cyl.  area  X  piston-speed  -s-  6000  (a).  Assume  that  the  av.  mean 
effective  pressure  is  40  Ibs.  per  sq.  in.,  then  cyl.  area  X  piston-speed  X  40  -r- 
33,000  =  horse-power  (6).  Dividing  (a)  by  (b)  and  cancelling,  we  have  pipe 
area -j-  H.P.  =  .1375  sq.  in.  If  we  use  8000  ft.  per  min.  as  the  allowable 
velocity,  then  the  factor. 1375  becomes  .1031;  that  is,  pipe  area -f- H.P.  = 
.1031,  or  pipe  area  X  .97  =  horse-power.  This,  however,  gives  areas  of  pipe 
smaller  than  are  used  in  the  most  recent  practice.  A  formula  which  gives 
results  closely  agreeing  with  practice,  as  shown  in  the  above  table  is 

Horse-power  =  6d2,    or    pipe  diameter  =  i/  :~&  =  .408  1/H.P. 

DIAMETERS  OP  CYLINDERS  CORRESPONDING  TO  VARIOUS  SIZES  OP  STEAM- 
PIPES  BASED  ON  PISTON-SPEED  OF  ENGINE  OP  600  FT.  PER  MINUTE,  AND 
ALLOWABLE  MEAN  VELOCITY  OP  STEAM  IN  PIPE  OP  4000,  6000,  AND  8000 
FT.  PER  MlN.  (STEAM  ASSUMED  TO  BE  ADMITTED  DURING  FtTLL  STROKE.) 

Diam.  of  pipe,  Inches ...      2  2^       3       3^       4  4^       5         6 

Vel.  4000 5.2  6.5   7.7   9.0  10.3  11.6  12.9  15.5 

"  6000 6.3  7.9  9.5  11.1  12.6  14.2  15.8  19. 

"  8000. 7.3  9.1  10.9  12.8  14.6  16.4  18.3  21.9 

Horse-power,  approx 20  31  45  62  80  100  125        180 

Diam.  of  pipe,  inches 7  8  9  10  11  12  13       14 

Vel.  4000 18.1  20.7  23.2  25.8  28.4  31.0  33.6  36.1 

"  6000 22.1  25.3  28.5  31.6  34.8  37.9  41.1  44.3 

"  8000 25.6  29.2  32.9  36.5  40.2  43.8  47.5  51.1 

Horse-power,  approx 245  320  406  500  606  718  845  981 

Area  of  cylinder  X  piston-speed 

Formula.    Area  of  pipe  =  —  — •. 

mean  velocity  of  steam  in  pipe 

For  piston-speed  of  600  ft.  per  min.  and  velocity  in  pipe  of  4000,  6000,  and 
8000  ft.  per  min.  area  of  pipe  =  respectively  .15,  .10,  and  .075  X  area  of  cyl- 
inder. Diam.  of  pipe  =  respectively  .3873,  .3162,  and  .2739  X  diam.  of  cylin- 
der. Reciprocals  of  these  figures  are  2.582,  3.162,  and  3.651. 

The  first  line  in  the  above  table  may  be  used  for  proportioning  exhaust- 


674 


STEAM. 


pipes,  in  which  a  velocity  not  exceeding  4000  ft.  per  minute  is  advisable. 
The  last  line,  approx.  H.P.  of  engine,  is  based  on  the  velocity  of  6000  ft.  per 
min.  in  the  pipe,  using  the  corresponding  diameter  of  piston,  and  taking 
H.P.  =  ^(diam.  of  piston  in  inches)2- 

Sizes  of  Steam-pipes  for  Marine  Engines.—  In  marine-engine 
practice  the  steam  -pipes  are  generally  not  as  large  P-S  in  stationary  practice 
for  the  same  sizes  of  cylinder.  Seaton  gives  the  following  rules: 

Main  Steam-pipes  should  be  of  such  size  that  the  mean  velocity  of  flow 
does  not  exceed  8000  ft.  per  min. 

In  large  engines,  1000  to  2000  H.P.,  cutting  off  at  less  than  half  stroke,  the 
steam-pipe  may  be  designed  for  a  mean  velocity  of  9000  ft.,  and  10,000  ft. 
for  still  larger  engines. 

In  small  engines  and  engines  cutting  later  than  half  stroke,  a  velocity  of 
less  than  8000  ft.  per  minute  is  desirable. 

Taking  8100  ft.  per  min.  as  the  mean  velocity,  S  speed  of  piston  in  feet  per 
min.,  and  D  the  diameter  of  the  cyl., 


Diam.  of  main  steam-pipe  cjtf          = 


Stop  and  Throttle  Valves  should  have  a  greater  area  of  passages  than  the 
area  of  the  main  steam-pipe,  on  account  of  the  friction  through  the  cir- 
cuitous passages.  The  shape  of  the  passages  should  be  designed  so  as  to 
avoid  abrupt  changes  of  direction  and  of  velocity  of  flow  as  far  as  possible. 

Area  of  Steam  Ports  and  Passages  = 

Area  of  piston  X  speed  of  piston  in  ft.  per  min.  _  (Diam.)2  X  speed 
6000  7639 

Opening  of  Port  to  Steam.—  To  avoid  wire-drawing  during  admission  the 
area  of  opening  to  steam  should  be  such  that  the  mean  velocity  of  flow  does 
not  exceed  10,000  ft.  per  min.  To  avoid  excessive  clearance  the  width  of 
port  should  be  as  short  as  possible,  the  necessary  area  being  obtained  by 
length  (measured  at  right  angles  to  the  line  of  travel  of  the  valve).  In 

Sractice  this  length  is  usually  0.6  to  0.8  of  the  diameter  of  the  cylinder,  but 
i  long-stroke  engines  it  may  equal  or  even  exceed  the  diameter. 

Exhaust  Passages  and  Pipes.  —  The  area  should  be  such  that  the  mean 
velocity  of  the  steam  should  not  exceed  6000  ft.  per  min.,  and  the  area 
should  be  greater  if  the  length  of  the  exhaust-pipe  is  comparatively  long. 
The  area  of  passages  from  cylinders  to  receivers  should  be  such  that  the 
velocity  will  not  exceed  5000  ft.  per  min. 

The  following  table  is  computed  on  the  basis  of  a  mean  velocity  of  flow 
of  8000  ft.  per  min.  for  the  main  steam-pipe,  10.000  for  opening  to  steam, 
and  6000  for  exhaust.  A  =  area  of  piston,  D  its  diameter. 

STEAM  AND  EXHAUST  OPENINGS. 


Piston- 
speed, 
ft.  per  min. 

Diam.  of 
Steam-pipe 

Area  of 
Steam-pipe 
•*-A. 

Diam.  of 
Exhaust 

-5-  D. 

Area  of 
Exhaust 

-f-  A. 

Opening 
to  Steam 
~*-A. 

300 
400 
500 
600 
700 
800 
900 
1000 

0.194 
0.224 
0.250 
0.274 
0.296 
0.316 
0.335 
0.353 

0.0375 
0.0500 
0.0625 
0.0750 
0.0875 
0.1000 
0.1125 
0.1250 

0.223 
0.258 
0.288 
0.316 
0.341 
0.365 
0.387 
0.400 

0.0500 
0.0667 
0.0833 
0.1000 
0.1167 
0.1333 
0.1500 
0.1667 

0.03 
0  04 
0.05 
0.06 
0.07 
0.08 
0.09 
0.10 

STEAM  FIFES. 

Bursting-tests  of  Copper  Steam-pipes.  (From  Report  of  Chief 
Engineer  Melville,  U.  S.  N.,  for  1892.)— Some  tests  were  made  at  the  New 
York  Navy  Yard  which  show  the  unreliability  of  brazed  seams  in  cop- 
per pipes.  Each  pipe  was  8  in.  diameter  inside  and  3  ft.  1%  in  .  long. 
Both  ends  were  closed  by  ribbed  heads  and  the  pipe  was  subjected  to  a  hot- 
water  pressure,  the  temperature  being  maintained  constant  at  371*  F.  Three 


STEAM-PIPES.  675 

of  the  pipes  were  made  of  No.  4  sheet  copper  ("  Stubbs  "  gauge)  and  the 
fourth  was  made  of  No.  3  sheet. 
The  following  were  the  results,  in  Ibs.  per  sq.  in.,  of  bursting-pressure: 

Pipe  number  .............  .....  1  2  3            4            4' 

Actual  bursting-strength  ________  835  785  950  1225  1275 

Calculated"              "         .....  1336  1336  1569  1568  1568 

Difference  .......................  501  551  619         343  293 

The  theoretical  bursting-pressure  of  the  pipes  was  calculated  by  using  the 
figures  obtained  in  the  tests  for  the  strength  of  copper  sheet  with  a  brazed 
oint  at  350°  F.  Pipes  1  and  2  are  considered  as  having  been  annealed. 


fig 
joi 


. 

The  tests  of  specimens  cut  from  the  ruptured  pipes  show  the  injurious 
ction  of  heat  upon  copper  sheets;  and  that,  while  a  white  heat  does  not 
change  the  character  of  the  metal,  a  heat  of  only  slightly  greater  degree 


causes  it  to  lose  the  fibrous  nature  that  it  has  acquired  in  rolling,  and  a 
serious  reduction  in  its  tensile  strength  and  ductility  results. 

All  the  brazing  was  done  by  expert  workmen,  and  their  failure  to  make  a 
pipe-joint  without  burning  the  metal  at  some  point  makes  it  probable  that, 
with  copper  of  this  or  greater  thickness,  it  is  seldom  accomplished. 

That  it  is  possible  to  make  a  joint  without  thus  injuring  the  metal  was 
proven  in  the  cases  of  many  of  the  specimens,  both  of  those  cut  from  the 
pipes  and  those  made  separately,  which  broke  with  a  fibrous  fracture. 

Rule  tor  Thickness  of  Copper  Steam-pipes.  (U.  S.  Super- 
vising Inspectors  of  Steam  Vessels.)  —  Multiply  the  working  steam-pressure 
in  Ibs.  per  sq.  in.  allowed  the  boiler  by  the  diameter  of  the  pipe  in  inches, 
then  divide  the  product  by  the  constant  whole  number  8000,  and  add  .0625  to 
the  quotient;  the  sum  will  give  the  thickness  of  material  required. 

EXAMPLE.—  Let  175  Ibs.  =  working  steam-pressure  per  sq.  in.  allowed  the 

boiler,  5  in.  =  diameter  of  the  pipe;  then    '**     -f  .0625  =  .1718  -f  inch. 

oOUU 

thickness  required. 

Reinforcing:  Steam-pipes.  (Eng.,  Aug.  11,  1893.)—  In  the  Italian 
Kavy  copper  pipes  above  8  in.  diarn.  are  reinforced  by  wrapping  them  with 
a  cll»se  spiral  of  copper  or  Delta-metal  wire.  Two  or  three  independent 
spirals  are  used  for  safety  in  case  one  wire  breaks.  They  are  wound  at  a 
tension  of  about  1V<>  tons  per  sq.  in. 

Wire-wound  Steam-pipes.—  The  system  instituted  by  the  British 
Admiralty  of  winding  all  steam  -pipes  over  8  in.  in  diameter  with  3/16-in. 
copper  wire,  thereby  about  doubling  the  bursting-pressure,  has  within  re- 
cent years  been  adopted  on  many  merchant  steamers  using  high-pressure 
steam,  says  the  London  Engineer.  The  results  of  some  of  the  Admiralty 
tests  showed  that  a  wire  pipe  stood  just  about  the  pressure  it  ought  to  have 
stood  when  unwired,  had  the  copper  not  been  injured  in  the  brazing. 

Riveted  Steel  Steam-pipes  have  recently  been  used  for  high 
pressures.  See  paper  OM  A  Method  of  Manufacture  of  Large  Steam-pipes, 
by  Chas.  H.  Manning,  Trans.  A.  S.  M.  EM  vol.  xv. 

Valves  in  Steam-pipes.—  Should  a  globe-valve  on  a  steam-pipe  have 
the  steam-pressure  on  top  or  underneath  the  valve  is  a  disputed  question. 
With  the  steam-pressure  on  top,  the  stuffing-box  around  the  valve-stem  can- 
not be  repacked  without  shutting  off  steam  from  the  whole  line  of  pipe;  on 
the  other  hand,  if  the  steam  -pressure  is  on  the  bottom  of  the  valve  it  all  has 
to  be  sustained  by  the  screw-thread  on  the  valve-stem,  and  there  is  danger 
of  stripping  the  thread. 

A  correspondent  of  the  American  Machinist,  1892,  says  that  it  is  a  very 
uncommon  thing  in  the  ordinary  globe-valve  to  have  the  thread  give  out, 
but  by  water-hammer  and  merciless  screwing  the  seat  will  be  crushed  down 
quite'  frequently.  Therefore  with  plants  where  only  one  boiler  is  used  he 
advises  placing  the  valve  with  the  boiler-pressure  underneath  it.  On  plants 
where  several  boilers  are  connected  to  one  main  steam-pipe  he  would  re- 
verse the  position  of  the  valve,  then  when  one  of  the  valves  needs  repacking 
the  valve  can  be  closed  and  the  pressure  in  the  boiler  whose  pipe  it  controls 
can  be  reduced  to  atmospheric  by  lifting  the  safety-valve.  The  repacking 
can  then  be  done  without  interfering  with  the  operation  of  the  other  boilers 
of  the  plant. 

He  proposes  also  the  following  other  rules  for  locating  valves:  Place 
valves'  with  the  stems  horizontal  to  avoid  the  formation  of  a  water-pocket. 
Never  put  the  junction-valve  close  to  the  boiler  if  the  main  pipe  is  above 
the  boiler,  but  put  it  on  the  highest  point  of  the  junction  -pipe.  If  the  other 


676  STEAM. 

plan  is  followed,  the  pipe  fills  with  water  whenever  this  boiler  is  stopped 
and  the  others  are  running,  and  breakage  of  the  pipe  may  cause  serious  re- 
sults. Never  let  a  junction-pipe  run  into  the  bottom  of  the  main  pipe,  but 
into  the  side  or  top.  Always  use  an  angle-valve  where  convenient,  as  there 
is  more  room  in  them.  Never  use  a  gate  valve  under  high  pressure  unless  a 
by-pass  is  used  with  it.  Never  open  a  blow-off  valve  on  a  boiler  a  little  and 
then  shut  it;  it  is  sure  to  catch  the  sediment  and  ruin  the  valve;  throw  it 
well  open  before  closing.  Never  use  a  globe-valve  on  an  indicator-pipe.  For 
water,  always  use  gate  or  angle  valves  or  stop-cocks  to  obtain  a  clear  pas- 
sage. Buy  if  possible  valves  with  renewable  disks.  Lastly,  never  let  a  man 
go  inside  a  boiler  to  work,  especially  if  he  is  to  hammer  on  it,  unless  you 
break  the  joint  between  the  boiler  and  the  valve  and  put  a  plate  of  steel 
between  the  flanges. 

Flanges  for  Steam-nozzles  and  Steam-pipe,  used  with  the 
Gill  Water-tube  Boiler,  Phila.,  1892. 

Size  of  pipe 3456789 

Outside  diameter  of  flange,  inches..  9       10       11        12       13       14       15 

Pilch-circle  for  bolts,  diam.,      "     ..  7         8         9        10        11        12        13 

Outside  diam.  of  gaskets,          "    ..  5^      6^      7^      8^      9}^    1(%    11^ 

Inside  diam.  of  gaskets,  "     . .  3^      4^      (g$      6^1      7%      8^      9^ 

Number  of  bolts 5         6         7         8         9        10        11 

Size  of  pipe 10  11  12  13  14  15  16 

Outside  diameter  of  flange,  inches..  16  17  18  19  20  21  22 

Pitch-circle  for  bolts,  diam.,     "     ..  14  15  16  17  18  19  20 

Outside  diam.  of  gaskets,  "     ..  12^  13^  14^  15^  16^  17^  18^ 

Inside  diam.  of  gaskets,  "     ..  10^  11^  12J4  13V6  14J^  15J4  16^ 

Number  of  bolts 12  13  14  15  16  17  18 

All  holes  drilled  15/16  in.,  with  a  jig  accurately  laid  out. 

All  bolts  to  be  %  in.  diam.  by  3^  in.  long  under  the  head. 

All  bolts  to  have  square  heads  and  hexagon  nuts. 

The  *4  Steam  I^oop"  is  a  system  of  piping  by  which  water  of  con- 
densation in  steam-pipes  is  automatically  returned  to  the  boiler.  In  its 
simplest  form  it  consists  of  three  pipes,  which  are  called  the  riser,  the  hori- 
zontal, and  the  drop-leg.  When  the  steam-loop  is  used  for  returning  to  the 
boiler  the  water  of  condensation  and  entrainment  from  the  steam-pipe 
through  which  the  steam  flows  to  the  cylinder  of  an  engine,  the  riser  is  gen- 
erally attached  to  a  separator;  this  riser  empties  at  a  suitable  height  into 
the  horizontal,  and  from  thence  the  water  of  condensation  is  led  into  the 
drop-leg,  which  is  connected  to  the  boiler,  into  which  the  water  of  condensa 
tion  is  fed  as  soon  as  the  hydrostatic  pressure  in  drop-leg  in  connection  witl> 
the  steam-pressure  in  the  pipes  is  sufficient  to  overcome  the  boiler-pressure. 
The  action  of  the  device  depends  on  the  following  principles:  Difference  of 
pressure  may  be  balanced  by  a  water-column;  vapors  or  liquids  tend  to  flow 
to  the  point  of  lowest  pressure;  rate  of  flow  depends  on  difference  of  pres- 
sure and  mass;  decrease  of  static  pressure  in  a  steam-pipe  or  chamber  is 
proportional  to  rate  of  condensation;  in  a  steam-current  water  will  be  car- 
ried or  swept  along  rapidly  by  friction.  (Illustrated  in  Modern  Mechanism, 
p.  807.) 

Loss  from  an  Uncovered  Steam-pipe.  (Bjorling  on  Pumping- 
engines.) — The  amount  of  loss  by  condensation  in  a  steam-pipe  carried  down 
a  deep  mine-shaft  has  been  ascertained  by  actuai  practice  at  the  Clay  Cross 
Colliery,  near  Chesterfield,  where  there  is  a  pipe  7J4  in.  internal  diam'..  1100 
ft.  long.  The  loss  of  steam  by  condensation  was  ascertained  by  direct 
measurement  of  the  water  deposited  in  a  receiver,  and  was  found  to  be 
equivalent  to  about  1  Ib.  of  coal  per  I.H.P.  per  hour  for  every  100  ft.  of 
steam-pipe;  but  there  is  no  doubt  that  if  the  pipes  had  been  in  the  upcast 
shaft,  and  well  covered  with  a  good  non-conducting  material,  the  loss  would 
have  been  less.  (For  Steam-pipe  Coverings,  see  p.  469,  ante.) 


THE   HORSE-POWER  OF   A   STEAM-BOILER.  67? 


THE   STEAM-BOILEB,. 

Tlie  Horse-power  of  a  Steam-boiler.— The  term  horsepower 
has  two  meanings  in  engineering  :  First,  an  absolute  unit  or  measure  of  the 
rate  of  work,  that  is,  of  the  work  done  in  a  certain  definite  period  of  time, 
by  a  source  of  energy,  as  a  steam-boiler,  a  waterfall,  a  current  of  air  or 
water,  or  by  a  prime  mover,  as  a  steam-engine,  a  water-wheel,  or  a  wind- 
mill. The  value  of  this  unit,  whenever  it  can  be  expressed  in  foot-pounds 
of  energy,  as  in  the  case  of  steam-engines,  water-wheels,  and  waterfalls,  is 
33,000  foot-pounds  per  minute.  In  the  case  of  boilers,  where  the  work  done, 
the  conversion  of  water  into  steam,  cannot  be  expressed  in  foot-pounds  of 
available  energy,  the  usual  value  given  to  the  term  horse-power  is  the  evap- 
oration of  30  ^bs.  of  water  of  a  temperature  of  100°  F.  into  steam  at  70  Ibs. 
pressure  above  the  atmosphere.  Both  of  these  units  are  arbitrary ;  the  first, 
33,000  foot-pounds  per  minute,  first  adopted  by  James  Watt,  being  considered 
equivalent  to  the  power  exerted  by  a  good  London  draught-horse,  and  the 
30  Ibs.  of  water  evaporated  per  hour  being  considered  to  be  the  steam  re- 
quirement per  indicated  horse-power  of  an  average  engine. 

The  second  definition  of  the  term  horse-power  is  an  approximate  measure 
of  the  size,  capacity,  value,  or  "  rating  "  of  a  boiler,  engine,  water-wheel,  or 
other  source  or  conveyer  of  energy,  by  which  measure  it  may  be  described, 
bought  and  sold,  advertised,  etc.  No  definite  value  can  be  given  to  this 
measure,  which  varies  largely  with  local  custom  or  individual  opinion  of 
makers  and  users  of  machinery.  The  nearest  approach  to  uniformity  which 
can  be  arrived  at  in  the  term  k' horse  power,"  used  in  this  sense,  is  to  say 
that  a  boileivengine,  water-wheel,  or  other  machine,  "  rated1'  at  a  certain 
horse-power,  should  be  capable  of  steadily  developing  that  horse-power  for 
a  long  period  of  time  under  ordinary  conditions  of  use  and  practice,  leaving 
to  local  custom,  to  the  judgment  of  the  buyer  and  seller,  to  written  contracts 
of  purchase  and  sale,  or  to  legal  decisions  upon  such  contracts,  the  interpre- 
tation of  what  is  meant  by  the  term  "  ordinary  conditions  of  use  and 
practice.'1  (Trans.  A.  S.  M.  E.,  vol.  vii.  p.  226.) 

The  committee  of  the  A.  S.  M.  E.  on  Trials  of  Steam-boilers  in  1884  (Trans., 
vol.  vi.  p.  265)  discussed  the  question  of  the  horse-power  of  boilers  as  follows: 

The  Committee  of  Judges  of  the  Centennial  Exhibition,  to  whom  the  trials 
of  competing  boilers  at  that  exhibition  were  intrusted,  met  with  this  same 
problem,  and  finally  agreed  to  solve  it,  at  least  so  far  as  the  work  of  that 
committee  was  concerned,  by  the  adoption  of  the  unit,  30  Ibs.  of  water  evap- 
orated into  dry  steam  per  hour  from  feed-water  at  100°  F.,  and  under  a 
pressure  of  70  Ibs.  per  square  inch  above  the  atmosphere,  these  conditions 
being  considered  by  them  to  represent  fairly  average  practice.  The  quan- 
tity of  heat  demanded  to  evaporate  a  pound  of  water  under  these  conditions 
is  1110.2  British  thermal  units,  or  1.1496  units  of  evaporation.  The  unit  of 
power  proposed  is  thus  equivalent  to  the  development  of  33,305  heat  units 
per  hour,  or  34.488  units  of  evaporation.  .  .  . 

Your  committee,  after  due  consideration,  has  determined  to  accept  the 
Centennial  Standard,  the  first  above  mentioned,  and  to  recommend  that  in 
all  standard  trials  the  commercial  horse-power  be  taken  as  an  evaporation 
of  30  Ibs.  of  water  per  hour  from  a  feed-water  temperature  of  100°  F.  into 
steam  at  70  Ibs.  gauge  pressure,  which  shall  be  considered  to  be  equal  to  34^ 
units  of  evaporation,  that  is,  to  34^  Ibs.  of  water  evaporated  from  a  feed- 
water  temperature  of  212°  F.  into  steam  at  the  same  temperature.  This 
standard  is  equal  to  33,305  thermal  units  per  hour. 

It  is  the  opinion  of  this  committee  that  a  boiler  rated  at  any  stated  number 
of  horse-powers  should  be  capable  of  developing  that  power  with  easy  firing, 
moderate  draught,  and  ordinary  fuel,  while  exhibiting  good  economy  ;  and 
further,  that  the  boiler  should  be  capable  of  developing  at  least  one  third 
more  than  its  rated  power  to  meet  emergencies  at  times  when  maximum 
economy  is  not  the  most  important  object  to  be  attained. 

Unit  of  Evaporation.— It  is  the  custom  to  reduce  results  of  boiler- 
tests  to  the  common  standard  of  weight  of  water  evaporated  by  the  unit 
weight  of  the  combustible  portion  of  the  fuel,  the  evaporation  being  consid- 
ered to  have  taken  place  at  mean  atmospheric  pressure,  and  at  the  temper- 
ature due  that  pressure,  the  feed-water  being  also  assumed  to  have  been 
supplied  at  that  temperature.  This  is,  in  technical  language,  said  to  be  the 
equivalent  evaporation  from  and  at  the  boiling-point  at  atmospheric  pres- 
rnre,  or  "from  and  at  212°  F."  This  unit  of  evaporation,  or  one  pound  of 


678  THE  STEAM-BOILER. 

water  evaporated  from  and  at  212°,  is  equivalent  to  965.7  British  thermal 
units. 

Measures  for  Comparing  the  Duty  of  Boilers.— The  meas- 
ure of  the  efficiency  of  a  boiler  is  the  number  of  pounds  of  water  evaporated 
per  pound  of  combustible,  the  evaporation  being  reduced  to  the  standard  of 
"  from  and  at  212° ;"  that  is,  the  equivalent  evaporation  from  feed-water  at  a 
temperature  of  212°  F.  into  steam  at  the  same  temperature. 

The  measure  of  the  capacity  of  a  boiler  is  the  amount  of  "boiler  horse- 
power "  developed,  a  horse-power  being  defined  as  the  evaporation  of  30  Ibs. 
of  water  per  hour  from  100°  F.  into  steam  at  70  Ibs.  pressure,  or  34^  Ibs.  per 
hour  from  and  at  212°. 

The  measure  of  relative  rapidity  of  steaming  of  boilers  is  the  number  of 
pounds  of  water  evaporated  per  hour  per  square  foot  of  water-heating  sur- 
face. 

The  measure  of  relative  rapidity  of  combustion  of  fuel  in  boiler-furnaces 
is  the  number  of  pounds  of  coal  burned  per  hour  per  square  foot  of  grate- 
surface. 

STEAM-BOILER  PROPORTIONS. 

Proportions  of  Orate  and  Heating  Surface  required  for 
a.  given  Horse-power. — The  term  horse-power  here  means  capacity 
10  evaporate  30  Ibs.  of  water  from  100°  F.,  temperature  of  feed-water,  to 
steam  of  70  Ibs.,  gauge-pressure  =  34.5  Ibs.  from  and  at  212°  F. 

Average  proportions  for  maximum  economy  for  land  boilers  fired  with 
good  anthracite  coal: 

Heating  surface  per  horse-power 11.5  sq.  ft. 

Grate  1/3      " 

Ratio  of  heating  to  grate  surface 34.5     4t 

Water  evap'd  from  and  at  212°  per  sq.  ft.  H.S.  per  hour    3     Ibs. 

Combustible  burned  per  H. P.  per  hour 3      ** 

Coal  with  1/6  refuse,  Ibs.  per  H.P.  per  hour 3.6   " 

Combustible  burned  per  sq.  ft.  grate  per  hour 9 

Coal  with  1/6  refuse,  Ibs.  per  sq.  ft.  grate  pe-*  hour 10.8   '• 

Water  evap'd  from  and  at  212°  per  Ib.  combustible. . .  11.5   " 

"   coal  (1/6  refuse)    9.6   " 

The  rate  of  evaporation  is  most  conveniently  expressed  in  pounds  evapo- 
rated from  and  at  212°  per  sq.  ft.  of  water-heating  surface  per  hour,  and  the 
rate  of  combustion  in  pounds  of  coal  per  sq.  ft.  of  grate-surface  per  hour. 

Heating-surface. — For  maximum  economy  with  any  kind  of  fuel  a 
boiler  should  be  proportioned  so  that  at  least  one  square' foot  of  heating- 
surface  should  be  given  for  every  3  Ibs.  of  water  to  be  evaporated  from  and 
at  212°  F.  per  hour.  Still  more  liberal  proportions  are  required  if  a  portion 
of  the  heating-surface  has  its  efficiency  reduced  by:  1.  Tendency  of  the 
heated  gases  to  short-circuit,  that  is,  to  select  passages  of  least  resistance 
and  flow  through  them  with  high  velocity,  to  the  neglect  of  other  passages. 
2.  Deposition  of  soot  from  smoky  fuel.  3.  Incrustation.  If  the  heating-sur- 
faces are  clean,  and  the  heated  gases  pass  over  it  uniformly,  little  if  any 
increase  in  economy  can  be  obtained  by  increasing  the  heating-surface  be- 
yond the  proportion  of  1  sq.  ft.  to  every  3  Ibs.  of  water  to  be  evaporated,  and 
with  all  conditions  favorable  but  little  decrease  of  economy  will  take  place 
if  the  proportion  is  1  sq.  ft.  to  every  4  Ibs.  evaporated;  but  in  order  to  pro- 
vide for  driving  of  the  boiler  beyond  its  rated  capacity,  and  for  possible 
decrease  of  efficiency  due  to  the  causes  above  named,  it  is  better  to  adopt  1 
sq.  ft.  to  3  lus.  evaporation  per  hour  as  the  minimum  standard  proportion. 

Where  economy  may  be  sacrificed  to  capacity,  as  where  fuel  is  very  cheap, 
it  is  customary  to  proportion  the  heating-surface  much  less  liberally.  The 
following  table  shows  approximately  the  relative  results  that  may  be  ex- 
pected with  different  rates  of  evaporation,  with  anthracite  coal. 

Lbs.  water  evapor'd  from  and  at  212°  per  sq.  ft.  heating-surface  per  hour: 
2  2.5  3  3.5  4  5  6  7  8  9  10 

Sq.  ft.  heating-surface  required  per  horse-power: 
17.3      13.8        11.5         9.8         8.6          6.8          5.8          4.9          4.3          3.8           3.5 

Ratio  of  heating  to  grate  surface  if  1/3  sq.  ft.  of  G.  S.  is  required  per  H.P.: 
52  41.4  34.5  29.4  25.8  20.4  17.4  13.7  12.9  11.4  10.5 

Probable  relative  economy: 
100      100         100          95  90  85  80  75  70  65  60 

Probable  temperature  of  chimney  gases,  degrees  F.: 
450      450          450        518         585         652         720          787         855         922         990 


STEAM-BOILER  PROPORTIOHS.  679 

The  relative  economy  will  vary  not  only  with  the  amount  of  heating-sur- 
face per  horse-power,  but  with  the  efficiency  of  that  heating-surface  as 
regards  its  capacity  for  transfer  of  heat  from  the  heated  gases  to  the  water, 
which  will  depend  on  its  freedom  from  soot  and  incrustation,  and  upon  the 
circulation  of  the  water  and  the  heated  gases. 

With  bituminous  coal  the  efficiency  will  largely  depend  upon  the  thorough- 
ness with  which  the  combustion  is  effected  in  the  furnace. 

The  efficiency  with  any  kind  of  fuel  will  greatly  depend  upon  the  amount 
of  air  supplied  to  the  furnace  in  excess  of  that  required  to  support  com- 
bustion. With  strong  draught  and  thin  fires  this  excess  may  be  very  great, 
causing  a  serious  loss  of  economy. 

Measurement  of*  Heating-surface,— Authorities  are  not  agreed 
as  to  the  methods  of  measuring  the  heating -surf  ace  of  steam-boilers.  The 
usual  rule  is  to  consider  as  heating-surface  all  the  surfaces  that  are  sur- 
rounded by  water  on  one  side  and  by  flame  or  heated  gases  on  the  other,  but 
there  is  a  difference  of  opinion  as  to  whether  tubular  heating-surface  should 
be  figured  from  the  inside  or  from  the  outside  diameter.  Some  writers  say, 
measure  the  heating-surface  always  on  the  smaller  side — the  fire  side  of  the 
tube  in  a  horizontal  return  tubular  boiler  and  the  water  side  in  a  water-tube 
boiler.  Others  would  deduct  from  the  heating-surface  thus  measured  an 
allowance  for  portions  supposed  to  be  ineffective  on  account  of  being  cov- 
ered by  dust,  or  being  out  of  the  direct  current  of  the  gases. 

For  the  sake  of  uniformity,  however,  it  would  appear  to  be  the  best  metho/i 
to  consider  all  surfaces  as  heating-surfaces  which  transmit  heat  from  the 
flame  or  gases  to  the  water,  making  no  allowance  for  different  degrees  Of 
effectiveness;  also,  to  use  the  external  instead  of  the  internal  diameter 
of  tubes,  for  greater  convenience  in  calculation,  the  external  diameter  of 
boiler-tubes  usually  being  made  in  even  inches  or  half  inches.  There  would 
seem  to  be  no  good  reason  for  considering  the  smaller  surface  in  a  tube  as 
the  heating-surface,  for  the  transmission  of  heat  through  plates  that  are 
ribbed  or  corrugated  on  one  side  does  not  appear  to  be  proportional  to  the 
smaller  surface,  but  rather  to  the  larger.  Thus  the  Serve  ribbed  tube  trans- 
mits more  heat  to  the  water  per  foot  of  length  than  a  plain  tube  of  «ame 
external  diameter,  and  a  ribbed  steam-radiator  radiates  more  heat  than  a 
plain  radiator  having  the  same  internal  or  smaller  surface. 

RULE  for  finding  the  heating-surface  of  vertical  tubular  boilers :  Multiply 
the  circumference  of  the  fire-box  (in  inches)  by  its  height  above  the  grate  ; 
multiply  the  combined  circumference  of  all  the  tubes  by  their  length,  and 
to  these  two  products  add  the  area  of  the  lower  tube-sheet ;  from  this  sum 
subtract  the  area  of  all  the  tubes,  and  divide  by  144 :  the  quotient  is  the 
number  of  square  feet  of  heating-surface. 

RULE  for  finding  the  heating-surface  of  horizontal  tubular  boilers:  Take 
the  dimensions  in  inches.  Multiply  two  thirds  of  the  circumference  of  the 
shell  by  its  length;  multiply  the  sum  of  the  circumferences  of  all  the  tubes 
by  their  common  length;  to  the  sum  of  these  products  add  two  thirds  of  the 
area  of  both  tube-sheets;  from  this  sum  subtract  twice  the  combined  area  of 
all  the  tubes;  divide  the  remainder  by  144  to  obtain  the  result  in  square  feet. 

RULE  for  finding  the  square  feet  of  heating -surf  ace  in  tubes :  Multiply  the 
number  of  tubes  bv  the  diameter  of  a  tube  in  inches,  by  its  length  in  feet, 
and  by  .2618. 

Horse-power,  Builder's  Rating.  Heating-surface  per 
Horse-power.— It  is  a  general  practice  among  builders  to  furnish  about 
12  square  feet  of  heating-surface  per  horse-power,  but  as  the  practice  is  not 
uniform,  bids  and  contracts  should  always  specify  the  amount  of  heating  - 
surface  to  be  furnished.  Not  less  than  one  third  square  foot  of  grate-surface 
should  be  furnished  per  horse-power. 

Engineering  News,  July  5,  1894,  gives  the  following  rough-and-ready  rule 
for  finding  approximately  the  commercial  horse-power  of  tubular  or  water- 
tube  boilers  :  Number  of  tubes  X  their  length  in  feet  X  their  nominal 
diameter  in  inches  -e-  50  =  nLd  -*-  50.  The  number  of  square  feet  of  surface 

in  the  tubes  isn-^-~  =  9-^-,  and  the  horse-power  at  12  square  feet  of  surface 

I'-v  O.O£ 

of  tubes  per  horse-power,  not  counting  the  shell,  =  nLd  -*-  45.8.  If  15  square 
feet  of  surface  of  tubes  be  taken,  it  is  nLd  -*-  57.3.  Making  allowance  for 
the  heating-surface  in  the  shell  will  reduce  the  divisor  to  about  50. 

Horse-power  of  Marine  and  Locomotive  Boilers.— The 
term  horse-power  is  not  generally  used  in  connection  with  boilers  in  marine 
practice,  or  with  locomotives.  The  boilers  are  designed  to  suit  the  engines, 
and  are  rated  by  extent  of  grate  and  heating-surface  only. 


680 


THE   STEAM-BOILER. 


Grate-surface.— The  amount  of  grate-surface  required  per  horse 
power,  and  the  proper  ratio  of  heatings-surface  to  grate-surface  are  ex- 
tremely variable,  depending  chiefly  upon  the  character  of  the  coal  and  upon 
the  rate  of  draught.  With  good  coal,  low  in  ash,  approximately  equal  results 
may  be  obtained  with  large  grate-surface  and  light  draught  and  with  small 
grate-surface  and  strong  draught,  the  total  amount  of  coal  burned  per  hour 
being  the  same  in  both  cases.  With  good  bituminous  coal,  like  Pittsburgh, 
low  in  ash,  the  best  results  apparently  are  obtained  with  strong  draught 
and  high  rates  of  combustion,  provided  the  grate-surfaces  are  cut  down  so 
that  the  total  coal  burned  per  hour  is  not  too  great  for  the  capacity  of  the 
heating-surface  to  absorb  the  heat  produced. 

With  coals  high  in  ash,  especially  if  the  ash  is  easily  fusible,  tending  to 
choke  the  grates,  large  grate-surface  and  a  slow  rate  of  combustion  are 
required,  unless  means,  such  as  shaking  grates,  are  provided  to  get  rid  of 
the  ash  as  fast  as  it  is  made. 

The  amount  of  grate-surface  required  per  horse-power  under  various  con- 
ditions may  be  estimated  from  the  following  table  : 


h 

0)^ 

•£  fl 

TO   jg             - 

£«*>£    • 

rfgS   Ug 

^  9 

SwS 

r/   ^   ** 

Pounds  of  Coal  burned  per  square  foot 
of  Grate  per  hour. 

3  £3  £8 

3&S, 

8 

10  |  12 

15 

20  |  25 

30 

35 

40 

Sq.  Ft.  Grate  per  H.  P. 

Good  coal 

i  10 

3.45 

.43 

.35 

.28 

.23 

.17 

.14 

.11 

.10 

.09 

and  boiler, 

'1      9 

3.83 

.48 

.38 

.32 

.25 

.19 

.15 

.13 

.11 

.10 

Fair  coal    or 
boiler, 

(     8.61 

1  ? 

4. 
4.31 
4.93 

.50 
.54 
.62 

.40 
.43 
.49 

.33 
.36 
.41 

.26 
.29 
.33 

.20 
.22 
.24 

.16 
.17 
.20 

.13 

.14 
.17 

.12 

.13 
.14 

.10' 
.11 
.12 

Poor  coal  or 
boiler, 

i     6.9 

1     6 
i      5 

5. 
5.75 
6.9 

.63 
.72 

.86 

.50 
.58 
.69 

.42 

.48 
58 

.34 

.38 
.46 

.25 
.29 
.35 

.20 
.23 
.28 

.17 
.19 
.23 

.15 
17 
.22 

.13 
.14 

.17 

Lignite  and 
poor  boiler, 

[     3.45 

10. 

1.25 

1.00 

.83 

.67 

.50 

.40 

.33 

.29 

.25. 

In  designing  a  boiler  for  a  given  set  of  conditions,  the  grate-surface  should 
be  made  as  liberal  as  possible,  say  sufficient  for  a  rate  of  combustion  of  10 
Ibs.  per  square  foot  of  grate  for  anthracite,  and  15  Ibs.  per  square  foot  for 
bituminous  coal,  and  in  practice  a  portion  of  the  grate-surface  may  be 
bricked  over  if  it  is  found  that  the  draught,  fuel,  or  other  conditions  render 
it  advisable. 

Proportions  of  Areas  of  Flues  and  other  Gas-passages. 
—Rules  are  usually  given  making  the  area  of  gas-passages  bear  a  certain 
ratio  to  the  area  of  the  grate-surface;  thus  a  common  rule  for  horizontal 
tubular  boilers  is  to  make  the  area  over  the  bridge  wall  1/7  of  the  grate- 
surface,  the  flue  area  1/8,  and  the  chimney  area  1/9. 

For  average  conditions  with  anthracite  coal  and  moderate  draught,  say  a 
rate  of  combustion  of  12  Ibs.  coal  per  square  foot  of  grate  per  hour,  and  a  rat  io 
of  heating  to  grate  surface  of  30  to  1,  this  rule  is  as  good  as  any,  but  it  is  evi- 
dent that  if  the  draught  were  increased  so  as  to  cause  a  rate  .of  combustion 
of  24  Ibs.,  requiring  the  grate-surface  to  be  cut  down  to  a  ratio  of  60  to  1,  the 
areas  of  gas-passages  should  not  be  reduced  much,  because  the  grate-sur- 
face is  reduced.  The  coal  burned  being  the  same  under  the  changed  condi- 
tions, and  there  being  no  reason  why  the  gases  should  travel  at  a  higher 
velocity,  the  actual  areas  of  the  passages  should  remain  as  before,  but  the 
ratio  of  the  area  to  the  grate-surface  would  in  that  case  be  doubled. 

Mr.  Barrus  states  that  the  highest  efficiency  with  anthracite  coal  is 
obtained  when  the  tube  area  is  1/9  to  1/10  of  the  grate-surface,  and  with 
bituminous  coal  when  it  is  1/6  to  1/7,  for  the  conditions  of  medium  rates  of 
combustion,  such  as  10  to  12  Ibs.  per  square  foot  of  grate  per  hour,  and  12 
square  feet  of  hearing- surf  ace  allowed  to  the  horse-power. 

The  tube  area  should  be  made  large  enough  not  to  choke  the  draught,  and 
so  lessen  the  capacity  of  the  boiler;  if  made  too  large  the  gases  are  apt  to 
select  the  passages  of  least  resistance  and  escape  from  them  at  a  high 
velocity  and  high  temperature. 

This  condition  is  very  commonly  found  in  horizontal  tubular  boilers  where 


PERFORMANCE    OF    BOILERS. 


681 


the  gases  go  chiefly  through  the  upper  rows  of  tubes;  sometimes  also  in 
vertical  tubular  boilers,  where  the  gases  are  apt  to  pass  most  rapidly 
through  the  tubes  nearest  to  the  centre. 

Air-passages  through  Grate-bars.—  The  usual  practice  is,  air- 
opening  =  30^  to  50$  of  area  of  the  grate  ;  the  larger  the  better,  to  avoid 
stoppage  of  the  air-supply  by  clinker;  but  with  coal  free  from  clinker  much 
smaller  air-space  may  be  used  without  detriment.  See  paper  by  F.  A. 
Scheffler,  Trans.  A.  S.  M.  E.,  vol.  xv.  p.  503. 


PERFORMANCE  OF 

Clark  (Steam-engine,  vol.  i.  p.  327)  gives  the  following  formulas  for  the 
relation  of  coal  and  water  consumed  in  steam-boilers  per  square  foot  of 
grate-area  per  hour,  and  the  ratio  of  the  heating-surface  to  the  area  of  the 
fire-grate.     Water  taken  as  evaporated  from  and  at  212°  F. 
Stationary  boilers  ......................  .  ................  w  =  .0222r2  -f-    9.56c 

Marine  boilers  ....................  .......................  w  =    .016r2  -f-  10.25c 

Portable-engine  boilers  ........................  .  .........  w  =    .008r2  4-   8.6c 

Locomotive  boilers  (coal-burning)  .......  ................  iv  =    .009ra  f    9.7c 

Locomotive  boilers  (coke-burning)  .....................  w  =  ,0178r2  -j-    7,94c 

In  which  w  =  weight  of  water  in  pounds  per  square  foot  of  grate  per  hour; 
c  =  pounds  of  fuel  per  square  foot  of  grate  per  hour; 
r  —  ratio  of  heating  to  grate  surface. 

There  are  minimum  rates  of  consumption  of  fuel  below  which  these 
formulas  are  not  applicable.  The  limit  varies  for  each  kind  of  boiler,  and  it 
varies  with  the  surface-ratio.  It  is  imposed  by  the  fact  that  the  maximum 
evaporative  power  of  fuel  is  a  fixed  quantity,  and  is  naturally  at  that  point 
where  the  reduction  of  the  rate  of  combustion  for  a  given  ratio  procures  the 
absorption  into  the  boiler  of  the  whole  of  the  proportion  of  the  heat  which 
is  available  for  evaporation.  In  the  combustion  of  good  coal  the  limit  of 
evaporative  efficiency  rnay  be  taken  as  measured  by  12^  Ibs.  of  water  from 
and  at  212°  F.  ;  and  in  that  of  good  coke  by  12  Ibs.  of  water  from  and  at 
212°  F.  Based  on  these  formulae  Clark  gives  the  following  table  : 
Evaporative  Performance  of  Steam-boilers  for  increasing 
Rates  of  Combustion  and  different  Surface-ratios. 
For  best  coal;  surface-ratio  30. 


Kind  of 
Boiler. 

Water  from  and  at 
212°  F.  per  hour. 

Fuel  per  Square  Foot  of  Grate  per  hour, 
in  pounds. 

5 

10 

15 

20 

30 

40 

50 

Stationary. 
Marine. 
Portable. 
Locomotive. 

Per  sq.  ft.  of  grate 
Per  Ib.  of  coal.  
Per  sq.  ft.  of  grate 
Per  Ib.  of  coal  
Per  sq.  ft.  of  grate 
Per  Ib.  of  coal  
Per  sq.  ft.  of  grate 
Per  Ib.  of  coal  

Ibs. 
62.5* 
12.5 
62.5* 
12.5 
50 
10 
57 
11.4 

Ibs. 
116 
11.56 
117 
11.69 
93 
9.3 
105 
10.5 

Ibs. 
163 
10.89 
168 
11.25 
136 
9.01 
154 
10.26 

Ibs. 
211 
10.56 
219 
10.95 
179 
8.95 
202 
10.10 

Ibs. 
307 
10.23 
322 
10.69 
265 
8.83 
299 
9.97 

Ibs. 
402 
10.06 
424 
10.61 
351 
8.77 
396 
9.90 

Ibs. 
498 
9.96 
527 
10.54 
437 
8.74 
493 
9.86 

Surface-ratio  50. 


5 

10 

15 

20 

30 

40 

50 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Stationary. 

Per  sq.  ft.  of  grate 

62.5* 

125* 

187.5* 

247 

342 

438 

534 

Per  Ib.  of  coal  

12.5 

12.5 

12.5 

12.33 

11.41 

10.95 

10.67 

Marine. 

Per  sq.  ft.  of  grate 

62.5* 

125* 

187.5* 

245 

348 

450 

552 

" 

Per  Ib.  of  coal  

12.5 

12.5 

12.5 

12.25 

11.58 

11.25 

11.05 

Portable. 

Per  sq.  ft.  of  grate 

62.5* 

106 

149 

192 

278 

364 

450 

14 

Per  Ib.  of  coal  

12.5 

10.6 

9.93 

9.6 

9.27 

9.10 

9.00 

Locomotive. 

Per  sq.  ft.  of  grate 

62.5* 

120 

168 

217 

314 

411 

508 

44 

Per  Ib.  of  coal  

12.5 

11.95 

11.  aO 

10.85 

10  45 

10.26 

10.15 

*  These  quantities  fall  below  the 
explained  in  the  text. 


scope  of  the  formulae  for  the  water,  as 


682 


THE   STEAM-BOILER. 


Surface  ratio  75. 


30 

40 

50 

60 

76 

90 

100 

Locomotive. 

Per  sq.  ft.  of  grate. 
Per  Ib.  of  coal  

Ibs. 
342 
11.39 

Ibs. 
439 
10.97 

Ibs. 
536 
10.71 

Ibs. 
633 
10.65 

Ibs. 

778 
10.37 

Ibs. 
927 
10.26 

Ibs, 
102C 
10.20 

General  Conditions  which  secure  Economy  of  Steam- 
tooilers. — In  general,  the  highest  results  are  produced  where  the  tempera- 
ture of  the  escaping  gases  is  the  least.  An  examination  of  this  question  is 
made  by  Mr.  G.  H.  Barrus  in  his  book  on  "  Boiler  Tests,"  by  selecting  those 
tests  made  by  him,  six  in  number,  in  which  the  temperature  exceeds  the 
average,  that  is,  375°  F.,  and  comparing  with  five  tests  in  which  the  temper- 
ature is  less  than  375°.  The  boilers  are  all  of  the  common  horizontal  type, 
and  all  use  anthracite  coal  of  either  egg  or  broken  size.  The  average  flue 
temperatures  in  the  two  series  was  444°  and  343°  respectively,  and  the  dif- 
ference was  101°.  The  average  evaporations  are  10.40  Ibs.  and  11.02  Ibs.  re- 
spectively, and  the  lowest  result  corresponds  to  the  case  of  the  highest  flue 
temperature.  In  these  tests  it  appears,  therefore,  that  a  reduction  of  101° 
in  the  temperature  of  the  waste  gases  secured  an  increase  in  the  evaporation 
of  6#.  This  result  corresponds  quite  closely  to  the  effect  of  lowering  the 
temperature  of  the  gases  by  means  of  a  flue-heater  where  a  reduction  of 
107°  was  attended  by  an  increase  of  1%  in  the  evaporation  per  pound  of  coal. 

A  similar  comparison  was  made  on  horizontal  tubular  boilers  using  Cum- 
berland coal.  The  average  flue  temperature  in  four  tests  is  450°  and  the 
average  evaporation  is  11.34  Ibs.  Six  boilers  have  temperatures  below  415°, 
the  average  of  which  is  383°,  and  these  give  an  average  evaporation  of  11.75 
Ibs.  With  67°  less  temperature  of  the  escaping  gases  the  evaporation  is 
higher  by  about  4#. 

The  wasteful  effect  of  a  high  flue  temperature  is  exhibited  by  other  boilers 
than  those  of  the  horizontal  tubular  class.  This  source  of  waste  was  shown 
to  be  the  main  cause  of  the  low  economy  produced  in  those  vertical  boilers 
which  are  deficient  in  heating-surface. 

Relation  between  the  Heating-surface  and  Grate-surface  to  obtain  the 
Highest  Efficiency.— A  comparison  of  three  tests  of  horizontal  tubular 
boilers  with  anthracite  coal,  the  ratio  of  heating- surf  ace  to  grate-surface 
being  36. 4  to  1,  with  three  other  tests  of  similar  boilers,  in  which  the  ratio 
was  48  to  1,  showed  practically  no  difference  in  the  results.  The  evidence 
shows  that  a  ratio  of  36  to  1  provides  a  sufficient  quantity  of  heating-surface 
to  secure  the  full  efficiency  of  anthracite  coal  where  the  rate  of  combustion 
is  not  more  than  12  Ibs.  per  sq.  ft.  of  grate  per  hour. 

In  tests  with  bituminous  coal  an  increase  in  the  ratio  from  36.8  to  42.8  se- 
cured a  small  improvement  in  the  evaporation  per  pound  of  coal,  and  a  high 
temperature  of  the  escaping  gases  indicated  that  a  still  further  increase 
would  be  beneficial.  Among  the  high  results  produced  on  common  horizon- 
tal tubular  boilers  using  bituminous  coal,  the  highest  occurs  where  the  ratio 
is  53.1  to  1.  This  boiler  gave  an  evaporation  of  12.47  Ibs.  A  double-deck 
boiler  furnishes  another  example  of  high  performance,  an  evaporation  of 
12.42  Ibs.  having  been  obtained  with  bituminous  coal,  and  in  this  case  the 
ratio  is  65  to  1.  These  examples  indicate  that  a  much  larger  amount  of 
beating-surface  is  required  for  obtaining  the  full  efficiency  of  bituminous 
coal  than  for  boilers  using  anthracite  coal.  The  temperature  of  the  escap- 
ing gases  in  the  same  boiler  is  invariably  higher  when  bituminous  coal  is 
used  than  when  anthracite  coal  is  used.  The  deposit,  of  soot  on  the  surfaces 
when  bituminous  coal  is  used  interferes  with  the  full  efficiency  of  the  sur- 
face, and  an  increased  area  is  demanded  as  an  offset  to  the  loss  which  this 
deposit  occasions.  It  would  seem,  then,  that  if  a  ratio  of  36  to  1  is  sufficient 
for  anthracite  coal,  from  45  to  50  should  be  provided  when  bituminous  coal 
is  burned,  especially  in  cases  where  the  rate  of  combustion  is  above  10  or  12 
Ibs.  per  sq.  ft.  of  grate  per  hour. 

The  number  of  tubes  controls  the  ratio  between  the  area  of  grate-surface 
and  area  of  tube -opening.  A  certain  minimum  amount  of  tube-opening  is 
required  for  efficient  work. 

The  best  results  obtained  with  anthracite  coal  in  the  common  horizontal 
boiler  are  in  cases  where  the  ratio  of  area  of  grate-surface  to  area  of  tube- 
opening  is  larger  than  9  to  1.  The  conclusion  is  drawn  that  the  highest  effi- 
ciency with  anthracite  coal  is  obtained  when  tb,e  tube-opening  is  from  1/9  to 
J/10  of  the  grate-surface. 


.       PERFORMANCE   OF   BOILERS.  683 

When  bituminous  coal  is  burned  the  requirements  appear  to  be  different. 
The  effect  of  a  large  tube-opening  does  not  seem  to  make  the  extra  tubes 
inefficient  when  bituminous  coal  is  used.  The  highest  result  on  any  boiler  of 
the  horizontal  tubular  class,  fired  with  bituminous  coal,  was  obtained  where 
the  tube-opening  was  the  largest.  This  gave  an  evaporation  of  12.47  Ibs.,  the 
ratio  of  grate-surface  to  tube- opening  being  5.4  to  1.  The  next  highest  re- 
sult was  12.42  Ibs.,  the  ratio  being  5.2  to  1.  Three  high  results,  averaging 
12.01  Ibs.,  were  obtained  when  the  average  ratio  was  7.1  to  1.  Without  going 
to  extremes,  the  ratio  to  be  desired  when  bituminous  coal  is  used  is  that 
which  gives  a  tube-opening  having  an  area  of  from  1/6  to  1/7  of  the  grate- 
surface.  This  applies  to  medium  rates  of  combustion  of,  say,  10  to  12  Ibs.  per 
sq.  ft.  of  grate  per  hour,  12  sq.  ft.  of  water-heating  surface  being  allowed  per 
horse-power. 

A  comparison  of  results  obtained  from  different  types  of  boilers  leads  to 
the  general  conclusion  that  the  economy  with  winch  different  types  of 
boilers  operate  depends  much  more  upon  their  proportions  and  the  condi- 
tions under  which  they  work,  than  upon  their  type  ;  and,  moreover,  that 
when  these  proportions  are  suitably  carried  out,  arid  when  the  conditions 
are  favorable,  the  various  types  of  boilers  give  substantially  the  same  eco- 
nomic result. 

Efficiency  of  a  Steam-boiler.— The  efficiency  of  a  boiler  is  the 
percentage  of  the  total  heat  generated  by  the  combustion  of  the  fuel 
which  is  utilized  in  heating  the  water  and  in  raising  steam.  With  anthracite 
coal  the  heating- value  of  the  combustible  portion  is  very  nearly  14,500 
B.  T.  U.  per  lb.,  equal  to  an  evaporation  from  and  at  212°  of  14,500  -=-  966 
=  15  Ibs.  of  water.  A  boiler  which  when  tested  with  anthracite  coal  shows 
an  evaporation  of  12  Ibs.  of  water  per  lb.  of  combustible,  has  an  efficiency  of 
12  -f- 15  =  80#,  a  figure  which  is  approximated,  but  scarcely  ever  quite 
reached,  in  the  best  practice.  With  bituminous  coal  it  is  necessary  to  have 
a  determination  of  its  heating-power  made  by  a  coal  calorimeter  before  the 
efficiency  of  the  boiler  using  it  can  be  determined,  but  a  close  estimate  may 
be  made  from  the  chemical  analysis  of  the  coal.  (See  Coal.) 

The  difference  between  the  efficiency  obtained  by  test  and  100#  is  the  sum 
of  the  numerous  wastes  of  heat,  the  chief  of  which  is  the  necessary  loss  due 
to  the  temperature  of  the  chimney-gases.  If  we  have  an  analysis  and  a 
calorimetric  determination  of  the  heating-power  of  the  coal  (properly  sam- 
pled), and  an  average  analysis  of  the  chimney-gases,  the  amounts  of  the 
several  loses  may  be  determined  with  approximate  accuracy  by  the  method 
described  below. 

Data  given  : 

1.  ANALYSIS  OF  THE  COAL.  2.    ANALYSIS  OP  THE  DRY  CHIMNEY- 
Cumberland  Semi-bituminous.  GASES,  BY  WEIGHT. 

Carbon 80.55  C.         O.          N. 

Hydrogen 4.50  CO2   =    13.6    =    3.71       9.89       

Oxygen 2.70  CO     =       .2    =      .09         .11       

Nitrogen 1.08  O        =    11.2    =    ....     11.20       

Moisture 2.92  N        =    75.0    =    75.00 

Ash 8.25 

100.0  3.80    21.20      75.00 

100.00 

Heating-value  of  the  coal  by  Dulong's  formula,  14,243  heat-units. 
The  gases  being  collected  over  water,  the  moisture  in  them  is  net  deter- 
mined. 

3.  Ash  and  refuse  as  determined  by  boiler-test,  10.25,  or  2%  more  than  that 
found  by  analysis,  the  difference  representing  carbon  in  the  ashes  obtained 
in  the  boiler-test. 

4.  Temperature  of  external  atmosphere,  60°  F. 

5.  Relative  humidity  of  air,  60£,  corresponding  (see  air  tables)  to  .007  lb.  of 
vapor  in  each  lb.  of  air. 

6.  Temperature  of  chimney-gases,  560°  F. 
Calculated  results  : 

The  carbon  in  the  chimney-gases  being  3.8#  of  their  weight,  the  total 
weight  of  dry  gases  per  lb.  of  carbon  burned  is  100  -f-  3.8  =  26.32  Ibs.  Since 
the  carbon  burned  is  80.55  -  2  =  78. 55$  of  the  weight  of  the  coal,  the  weight 
of  the  dry  gases  per  lb.  of  coal  is  26.32  X  78.55  -*-  100  =  20.67  Ibs. 

Each  pound  of  coal  furnishes  to  the  dry  chimney -gases  .7855  lb.  C,  .0108N, 

and  (2.70  -  i~)  •*- 100  =  .0214  lb.  O;  a  total  of  .8177,  say  .83  lb.   This  sub- 


684  THE   STEAM-BOILER. 

tracted  from  20.6?  Ibs.  leaves  19.85  Ibs.  as  the  quantity  of  dry  air  (not  includ- 
ing moisture)  which  enters  the  furnace  per  pound  of  coal,  not  counting  the 
air  required  to  burn  the  available  hydrogen,  that  is,  the  hydrogen  minus  one 
eighth  of  the  oxygen  chemically  combined  in  the  coal.  Each  Ib.  of  coal 
burned  contained  .045  Ib.  H,  which  requires  .045  X  8  —  .36  Ib.  O  for  its  com- 
bustion. Of  this,  .027  Ib.  is  furnished  by  the  coal  itself,  leaving  .333  Ib.  to 
come  from  the  air.  The  quantity  of  air  needed  to  supply  this  oxygen  (air 
containing  23#  by  weight  of  oxygen)  is  .333  -*-  .23  =  1.45  Ib.,  which  added  to 
the  19.85  Ibs.  already  found  gives  21.30  Ibs.  as  the  quantity  of  dry  air  sup- 
plied to  the  furnace  per  Ib.  of  coal  burned. 

The  air  carried  in  as  vapor  is  .0071  Ib.  for  each  Ib.  of  dry  air,  or  21.3  X  .0071 
=  0.15  Ih.  for  each  Ib.  of  coal.  Each  Ib.  of  coal  contained  .029  Ib.  of  mois- 
ture, which  was  evaporated  and  carried  into  the  chimney -gases.  The  .045  Ib. 
of  H  per  Ib.  of  coal  when  burned  formed  .045  X  9  =  .405  Ib.  of  HaO. 

From  the  analysis  of  the  chimney-gas  it  appears  that  .09  -f-  3.80  =  2.3?#  of 
the  carbon  in  the  coal  was  burned  to  CO  instead  of  to  CO2. 

We  now  have  the  data  for  calculating  the  various  loses  of  heat  as  follows, 
for  each  pound  of  coal  burned  : 

TT     f  Per  cent  of 

unite  Heat-value 

lts'  of  the  Coal. 

21.3  Ibs.  dry  air  X  (560°  -  60°)  X  sp.  heat  .238  =    2534.7  17.80 

.15  Ib.  vapor  in  air  X  (560°  -  60°)  x  sp.  heat  .48        =        36.0  0.25 

.029  Ib.  moisture  in  coal  heated  from  60°  to  212°        -          4.4  0.03 

evaporated  from  and  at  212°;  .029  X  966         =        28.0  0.20 

"        steam  (heated  from  21 2°  to  560°)  X  348  X  .48   =          4.8  0.03 

. 405  Ib.  H2O  from  H  in  coal  X  (152  4- 966  4-348  X  4S1  =      520.4  3.65 

.0237  Ib.  C  burned  to  CO;  loss  by  incomplete  com- 
bustion, .0237  X  (14544  -  4451)  =      239.2  1.68 
.02  Ib  coal  lost  in  ashes;  .02  X  14544                             =      290.9             2.04 
Radiation  and  unaccounted  for,  by  difference              =      569.7             4.00 


4228.1  29  68 

Utilized  in   making  steam,  equivalent  evaporation 

10.37  Ibs.  from  and  at  212°  per  Ib.  of  coal  =  10,014  9  70.32 


14,243.0          100.00 

The  heat  lost  by  radiation  from  the  boiler  and  furnace  is  not  easily  deter- 
mined directly,  especially  if  the  boiler  is  enclosed  in  brickwork,  or  is  pro- 
tected by  non-conducting  covering.  It  is  customary  to  estimate  the  heat 
lost  by  radiation  by  difference,  that  is,  to  charge  radiation  with  all  the  heat 
lost  which  is  not  otherwise  accounted  for. 

One  method  of  determining  the  loss  by  radiation  is  to  block  off  a  portion 
of  the  grate-surface  and  build  a  small  fire  on  the  remainder,  and  drive  this 
fire  with  just  enough  draught  to  keep  up  the  steam-pressure  and  supply  the 
heat  lost  by  radiation  without  allowing  any  steam  to  be  discharged,  weigh- 
ing the  coal  consumed  for  this  purpose  during  a  test  of  several  hours'  dura- 
tion. 

Estimates  of  radiation  by  difference  are  apt  to  be  greatly  in  error,  as  in 
this  difference  are  accumulated  all  the  errors  of  the  analyses  of  the  coal 
and  of  the  gases.  An  average  value  of  the  heat  lost  by  radiation  from  a 
boiler  set  in  brickwork  is  about  4  percent.  When  several  boilers  are  in  a 
battery  and  enclosed  in  a  boiler-house  the  loss  by  radiation  may  be  very 
much  less,  since  much  of  the  heat  radiated  from  the  boiler  is  returned  to  it 
in  the  air  supplied  to  the  furnace,  which  is  taken  from  the  boiler-room. 

An  important  source  of  error  in  making  a  "heat  balance"  such  as  the 
one  above  given,  especially  when  highly  bituminous  coal  is  used,  may  be 
due  to  the  non-combustion  of  part  of  the  hydrocarbon  gases  distilled  from 
the  coal  immediately  after  firing,  when  the  temperature  of  the  furnace  may 
be  reduced  below  the  point  of  ignition  of  the  gases.  Each  pound  of  hydro- 
gen which  escapes  burning  is  equivalent  to  a  loss  of  heat  in  the  furnace  of 
62,500  heat-units. 

In  analyzing  the  chimney  gases  by  the  usual  method  the  percentages  of 
the  constituent  gases  are  obtained  by  volume  instead  of  by  weight.  To 
reduce  percentages  by  volume  to  percentages  by  weight,  multiply  the  per- 
centage by  volume  of  each  gas  by  its  specific  gravity  as  compared  with  air, 
and  djvide  each  product  by  the  sum  of  the  products. 


TESTS  OF   STEAM-BOILER. 


C85 


The  pounds  of  air  required  to  burn  a  pound  of  carbon  may  be  obtained 
directly  from  the  analysis  by  volume  by  the  following  formula: 
Lbs.  of  air  required  to  burn  f  _  1  j  2(CO2  -f  O)  +  CO  > 
one  pound  of  carbon          f      3)         CO2  -f  CO        j 

In  which  O,  COa,  and  CO  are  the  per  cents,  by  volume,  of  the  several  con* 
stitueuts  of  the  flue  gases. 

Lbs.  of  air  per  pound  I      j  Lbs.  of  air  per  pound  J  v  j  Per  cent  of  carbon 
of  coal  }     *     of  carbon  \      1     in  coal. 

To  reduce  to  volume  at  temperature  of  32°  F.  make  use  of  the  formula 
V0  =  12.387  X  Ibs.  of  air  per  pound  of  coal. 

TESTS  OF  STEAM-BOILERS. 

Boiler-tests  at  (lie  Centennial  Exhibition,  Philadel- 
phia, 1876.— (See  Reports  and  Awards  Group  XX,  International  Exhibi- 
tion. Fliila.,  1876;  also,  Clark  on  the  Steam-engine,  vol.  i,  page  253.) 

Competitive  tests  were  made  of  fourteen  boilers,  using  good  anthracite 
coal,  one  boiler,  the  Galloway,  being  tested  with  both  anthracite  and  semi- 
bituminous  coal.  Two  tests  were  made  with  each  boiler :  one  called  the 
capacity  trial,  to  determine  the  economy  and  capacity  at  a  rapid  rate  of 
driving;  and  the  other  called  the  economy  trial,  to  determine  the  economy 
when  driven  at  a  rate  supposed  to  be  near  that  of  maximum  economy  and 
rated  capacity.  The  following  table  gives  the  principal  results  obtained  in 
the  economy  trial,  together  with  the  capacity  and  economy  figures  of  the 
capacity  trial  for  comparison. • 


Economy  Tests. 

Capacity 
Tests. 

3«>| 

<u 

2  *-' 

c3  ^ 

02  « 

£> 

CO 

3 

0   - 

73  8  g 

x 

1 

li 

0   0) 

.2  *- 

r& 

TH  p. 

~ 

Name 
of 

il 

HH 

G 

So? 

SK 

|Ss 

P 

E 

•4-, 

O 

i 

Boiler. 

II 

rc'f 

^ 

**"!  *j 

^  8  ° 

£ 

cc 

G° 

u 

sJ 

30 

G  * 

3 

§^ 

§•  .w* 

3 

.5 

1 

1 

§*&  • 

*o 

P  0) 

G 
§ 

0)  «j 

*d|, 

eg 

I 

* 

5 

1 

9- 

| 

*l| 

§£ 

1o 

O 

5 

•££ 

«l5o 

o> 

eg 

"o 

1 

o 

j> 

S*iJ 

« 

O 

PH 

^S 

^®?«M 

H 

^ 

cc 

K 

W 

^ 

Ibs. 

p.ct 

Ibs. 

Ibs. 

deg 

Jg 

deg 

H.P. 

H.P. 

Ibs. 

Root          

34.6 

9.1 

10  4 

2.25 

12.094 

393 

41.4 

119.8 

148.6 

10.441 

Firmenich  

64.3 

12.0 

10.4 

1.68 

11.988 

32.6 

57.8 

68.4 

11.064 

Lowe  . 

30.6 

6.8 

11.3!1.87 

11.923 

333 

47.0 

69.3 

11.163 

Smith    ...           .     . 

45.8 

13.1 

11.1  2.42 

11.906 

411 

i.3 

99  8 

125  0 

11  925 

Babcock  &  Wilcox 

37.7 

10.0 

11.0i2.43 

11.822 

296 

2.7 

135.6 

186.6 

10.330 

Galloway  

23.7 

9.6 

11.113.63 

11  583 

303 

'lA 

103.3 

133.8 

11.216 

Do.    semi-bit,  coal 

23.7 

7.9 

8.8,3.20 

12.125 

325 

6!s 

90.9 

125.1 

11.609 

Andrews 

15.6 

8.0 

10.3  2.32 

11.039 

71  [7 

42.6 

58.7 

9.745 

Harrison  

27.3 

12.4 

8.5  2.75 

10.930 

517 

6.9 

82^4 

108^4 

9^889 

Wiegand 

30.7 

12  3 

9.5  3.30 

10.834 

524 

20.5 

147.5 

162.8 

9  145 

Anderson  

17.5 

9.7 

9.32.64 

10.618 

417 

15.7 

98.0 

132.8 

9.  '568 

Kelly   

20.9 

10.8 

9.03.82 

10.312 

5.6 

81.0 

99.9 

8.397 

Exeter  

33.5 

11.4  1.38 

10.041 

430 

4.2 

72.1 

108.0 

9.974 

Pierce  

14  0 

s!o 

11  04.44 

10  021 

374 

5.2 

51.7 

67  8 

9.865 

Rogers  &  Black  .  .  . 

19.0 

8.6 

9.93.43 

9.613 

572 

2.1 

45.7 

67.2 

9.429 

Averages  

....  2.77 

11.123 

85.0 

110.8 

10.251 

The  comparison  of  the  economj'  and  capacity  trials  shows  that  an  average 
increase  in  capacity  of  30  per  cent  was  attended  by  a  decrease  in  economy 
of  8  per  cent,  but  the  relation  of  economy  to  rate  of  driving  varied  greatly 
in  the  different  boilers.  In  the  Kelly  boiler  an  increase  in  capacity  of  22  per 
cent  was  attended  by  a  decrease  in  economy  of  over  18  per  cent,  while  the 
Smith  boiler  with  an  increase  of  25  per  cent  in  capacity  showed  a  slight 
Increase  in  economy. 


686 


THE   STEAM-BOILER. 


One  of  the  most  important  lessons  gained  from  the  above  tests  is  that 
there  is  no  necessary  relation  between  the  type  of  a  boiler  and  economy.  Of 
the  five  boilers  that  gave  the  best  results,  the  total  range  of  variation  be- 
tween the  highest  and  lowest  of  the  five  being  only  2.3$,  three  were  water- 
tube  boilers,  one  was  a  horizontal  tubular  boiler,  and  the  fifth  was  a  com- 
bination of  the  two  types.   The  next  boiler  on  the  list,  the  Galloway,  was  an 
internally  fired  boiler,  all  of  the  others  being  externally  fired.   The  following 
is  a  brief  description  of  the  principal  constructive  features  of  the  fourteen 
boilers: 

•DM*  j  4-in.  water-  tubes,  inclined  20°  to  horizontal  ;  reversed 

Koofc  ...................  1     draught. 

Firmenich  .............    3-  in.  water-tubes,  nearly  vertical;  reversed  draught. 

Lowe  ..................    Cylindrical  shell,  multitubular  flue. 

c    .,,  j  Cylindrical  shell,  multitubular  flue—  water-tubes  in 

Smith  ..................  1     side  flues. 

Babcock&Wilcox....|3^^  inclined  15°  to  horizontal;  re- 

Galloway  ............      Cylindrical  shell,  furnace-tubes  and  water-tubes. 

Andrews  ......  .......     Square  fire-box  and  double  return  multitubular  flues. 

TTO  .,.;0^.  j  8  slabs  of  cast-iron  spheres,  8  in.  in  diameter;  re- 

Hamson  ..............  1     versed  draught. 

w*»  on/1  J  4-in.  water  tubes,  vertic 

viegana  ..............  -j     tubes 

Anderson  ..............    3-in.  flue-tubes,  nearly  horizontal  ;  return  circulation. 

T7v»iiv  j  3-in.  water-tubes,  slightly  inclined;  each  divided  by 

Ae  y  ..................  j     internal  diaphragm  to  promote  circulation. 

Exeter  ................    27  hollow  rectangular  cast-iron  slabs. 

Pierce  ...............    Rotating  horizontal  cylinder,  with  flue-tubes. 

Rogers  &  Black  .......     Vertical  cylindrical  boiler,  with  external  water-tubes. 

Tests  of  T  ii  bill  ous  Boilers,—  The  following  tables  are  given  by  S. 
H.  Leonard,  Asst.  Engr.  U.  S.  N.,  in  Jour.  Am.  Soc.  Naval  Enyrs.  1890.  The 
tests  were  made  at  d  inherent  times  by  boards  of  U.  S.  Naval  Engineers,  ex- 
cept tiietestofthelocornotiye-tprp^ 


. 
ubes,  vertical,  with  internal  circulating 


£J 

Evaporation 

. 

from  and  at 

Weights,  Ibs. 

0 

| 

gV 

212°  F. 

t-  S 

a 

£ 

*  8 

9 

*"* 

^  ^ 

3 

w 

bo 

W 

®  *c 

u  53 

OJ 

Type. 

IP, 

«£ 

>.-S 

PH* 

n.  « 

"S^ 

3"g 

£ 

o 
O 

il 

ss 

~r/2 

f| 
111 

W 
b 

s| 

5| 

£^ 
& 

&. 

6 

I 

r 

Jr   . 

Pi 

& 

r 

«s 

5 

CO 

Belleville.. 

12.8 

10.42 

5.2 

6.4 

E  40,670 
S  42,770 

204 

53.2 

10.1 

Nat'l. 

111 

Herreshoff 

j     9.3 
1    25.8 

10.23 

8.68 

3.1 

8 

9.1 
23.8 

E    2,945 
S    3,050 

96 
35 

14.8 

4.8 
1.3 

Jet. 
Jet. 

120 
195 

Towne  

»    4.3 
j    24.5 

18.4 

6  .  77 

2.7 
8.2 

10 

30.4 

E    1,380 
S    1,640 

172 

56 

21.8 

8.1 
2.6 

Nat'l. 
1.14 

148 
152 

Ward  

J     7.9 
*    15.5 

10.77 
10.01 

1.7 
3.2 

5.8 
11 

E    1,682 

154 
82 

13.2 

4^07 

Nat1!. 
Jet. 

0 
17 

(    62.5 

7.01 

10 

34.2 

26 

1.3 

Jet. 

161 

Scotch  

J    24.8 
1    38 

9.98 
9.06 

8.6 

12.8 

11 
16.3 

E  18,900 
S  30,000 

120 

80 

41.2 

4.7 
3.1 

2.08 
4.01 

77 
78 

Locom'tive 

j    98.3 

17.1 

30.5 

oon  47.7 

qi      O 

1.8 

3.13 

125 

torpedo, 

1  120.8 

20.05 

36.2 

b  d4,9JO 

33.3 

1.2 

4.95 

128 

Ward  

55.04 

8.44 

9.47 

32.1 

E  26,533 

26 

12.3 

1.3 

2 

160 

Thorny- 
croft.  (U. 
S.S.Cush- 

1- 

E  20.160 
S  24,640 

*31 

10.3 

3 

245 

ing.) 

J 

*  Approximate. 
Per  cent  moisture  in  steam:  Belleville,  6.31;  Herreshoff  (first  test),  3 

jotch,  1st,  3.44;  2d,  4.29;  Ward,  11.6;  others  not  given. 

TESTS   OF   STEAM-BOILERS. 


687 


DIMENSIONS  OP  THE  BOILERS. 


No. 

1 

2 

3 

4 

5 

6 

to 

8 

Length,  ft.  and  in.. 
Width,    "     ^ 
Height,"      "    ".. 
Space,  cu.  ft  
Grate-  area,  sq.  ft.  . 
Heating  -surf  ace, 
sq.  ft  

7   0 
11    0 
645.5 
34.1? 

804 

3    8 
4    0 
69.6 
9 

205 

2   6 
3    3 
20   3 
4.25 

75 

1    7 
7   2 
42.7 
3.68 

146 

9'  0" 
9    0 

572  .*5 
31.16 

727 

16'  8 
6    4 
7    6 
630.3 
28 

1116 

10'  3"* 
4    6  t 
11    8 
729.3 
66.5 

2490 

10'  0"± 
7   Ot 
8   0$ 
560$ 
38.3 

2375 

Ratio  H.S.  •+-  G  .  .  .  . 

23.5 

22 

17.6 

39.5 

23.3 

39.8 

37.4 

62 

boiler  was  limited  to  80  Ibs.  pressure  of  steam. 

The  following  approximation  is  made  from  the  large  table,  on  the  assump- 
tion that  the  evaporation  varies  directly  as  the  combustion,  and  25  Ibs.  of 
coal  per  square  foot  of  grate  per  hour  used  as  the  unit. 


Type  of  Boiler. 

Com 
bustion. 

Evapora- 
tion per 
cu.  ft.  of 
Space. 

Weight 
iSlJP. 

Weight 
per  sq.  ft. 
Heating- 
surface. 

Weight 
per  Ib. 
Water 
Evapo- 
rated. 

Belleville  

0.50 

0  50 

2.02 

2.10 

2  50 

Herreshoff  

1.00 

0.95 

0.72 

0.60 

0.90 

Towne    

1.00 

1.20 

1  12 

0  87 

1.30 

Scotch 

1.00 

0  44 

2  40 

1  64 

2  30 

Locomotive          

3.90 

0.31 

3.70 

1  25 

3.50 

Ward  .. 

2.20 

0.58 

1.27 

0.50 

1.53 

The  Belleville  boiler  has  no  practical  advantage  over  the  Scotch  either  in 
space  occupied  or  weight.    All  the  other  tubulous  boilers  given  greatly 
exceed  the  Scotch  in  these  advantages  of  weight  and  space. 
Some  High  Rates  of  Evaporation.— Eng'g,  May  9,  1884,  p.  415. 

Locomotive.  Torpedo-boat. 

Water  evap.  per  sq.  ft.  H.S.  per  hour 12.57        13.73  12.54       20.74 

"    Ib.  fuel  from  and  at  21 2°.      8.22         8.94  8.37         7.04 

Thermal  units  transf'd  per  sq.  ft.  of  H.S.  12,142      13,263  12,113      20,034 

Efficiency 586         .637  .542        .468 

It  is  doubtful  if  these  figures  were  corrected  for  priming. 
Economy  Effected  by  Heating  the  Air  Supplied  to 
Holler-furnaces.  (Clark,  S.  E.)— Meunier  and  Scheurer-Kestner  ob- 
tained about  1%  greater  evaporative  efficiency  in  summer  than  in  winter, 
from  the  same  boilers  under  like  conditions,— an  excess  which  had  been  ex- 
plained by  the  difference  of  loss  by  radiation  and  conduction.  But  Mr. 
Poupardin,  surmising  that  the  gain  might  be  due  in  some  degree  also  to  the 
greater  temperature  of  the  air  in  summer,  made  comparative  trials  with 
two  groups  of  three  boilers,  each  working  one  week  with  the  heated  air, 
and  the  next  week  with  cold  air.  The  following  were  the  several  efficien- 
cies: 

FIRST  TRIALS:  THREE  BOILERS;  RONCHAMP  COAL. 

Water  per  Ib.  of    Water  per  Ib.  of 
Coal.  Combustible. 

With  heated  air  (128°  F.)  7.77  Ibs.  8.95  Ibs. 

With  cold  air  (t>9°.8) 7.33   "  8.63  " 

Difference  in  favor  of  heated  air 0.44  "  0.32  " 

SECOND  TRIALS:  SAME  COAL;  THREE  OTHER  BOILERS. 

With  heated  air  (120°.4  F.) 8.70  Ibs.  10.08  Ibs. 

With  cold  air  (75°. 2) 8.09  "  9.34  " 

Difference  in  favor  of  heated  air 0.61  "  0.64  " 


688 


THE   STEAM-BOILER. 


These  results  show  economies  in  favor  of  heating  the  air  of  6#  and  7^j£. 
Mr.  Poupardin  believes  that  the  gain  iu  efficiency  is  due  chiefly  to  tlie 
better  combustion  of  the  gases  with  heated  air.    It  was  observed  that  with 
heated  air  the  flames  were  much  shorter  and  whiter,  and  that  there  was 
notably  less  smoke  from  the  chimney. 

An  extensive  series  of  experiments  was  made  by  J.  C.  Hoadley  (Trans. 
A.  S.  M.  E.,  vol.  vi.,  676)  on  a  "Warm-blast  Apparatus,"  for  utilizing  the 
heat  of  the  waste  gases  iu  heating  the  air  supplied  to  the  furnace.  The  ap- 
paratus, as  applied  to  an  ordinary  horizontal  tubular  boiler  60  in.  diameter, 
21  feet  long, with  65  3^-inch  tubes,  consisted  of  240  2-inch  tubes,  18  feet  long, 
through  which  the  hot  gases  passed  while  the  air  circulated  around  them. 
The  net  saving  of  fuel  effected  by  the  warm  blast  was  from  10.7$  to  15.5$  of 
the  fuel  used  with  cold  blast.  The  comparative  temperatures  averaged  as 
follows,  in  degrees  F. : 

Cold-blast    Warm-blast 
Boiler.  Boiler. 

Inheatoffire 2493  2793 

At  bridge  wall 1340  1600 

In  smoke  box 373  375 

Air  admitted  to  furnace 32  332  300 

Steam  and  water  in  boiler 300  300  0 

Gases  escaping  to  chimney 373  162  211 

External  air 32  32  0 

With  anthracite  coal  the  evaporation  from  and  at  212°  per  Ib.  combustible 
was,  for  the  cold-blast  boiler,  days  10.85  Ibs.,  days  and  nights  10.51 ;  and  for 
the  warm-blast  boiler,  days  11.83,  days  and  nights  11.03. 

Results  of  Tests  of  Heine  Water-tube  Boilers  with 
Different  Coals. 

(Communicated  by  E.  D.  Meier,  C.E.,  1894.) 


Difference. 


300 
260 


1 

2 

3 

4 

5 

6 

7 

8 

•eg 

.f 

_f 

§3 

2d.Pool, 

5 

S'S 

>    . 

.a 

a 

Kind  of  Coal. 

11 

i* 

W    1 

Youghiogh- 
eny. 

fa 

J£ 

O  '2 

is 

If 

1s' 

3  02 
O 

1 

e§ 
O 

o 

5 

1 

Per  cent  ash        .      ... 

5  1 

4.89 

11  6 

16  1 

11  5 

PI.  8 

12.8 

Heating-surface,  sq.  ft.. 

2900 

2040 

2040 

2300 

1260 

3730 

1168 

2770 

Grate-surface,  sq.  ft  

54 

44.8 

44.8 

50 

21 

73.3 

27.9 

50 

Ratio  H.S.  to  G.S  

53.7 

45.5 

45.5 

46 

60 

50.9 

41.9 

55.4 

Coal  per  sq.  ft.  G.per  hr. 

24.7 

23.5 

22.7 

35 

33.7 

26.2 

27.7 

36 

Water  persq.  ft.  H.S.per 

hr.  from  and  at  212°.  ... 

5.03 

5.14 

5.24 

5.56 

4.26 

4.28 

4.86 

5.08 

Water  evap.  from  and  at 

212°  per  Ib.  coal  

10.91 

9.94 

10.51 

7.31 

7.59 

8.33 

7.36 

7.81 

Per  Ib.  combustible  

11.50 

10.48 

8.27 

9.05 

9.41 

9.41 

8.96 

Temp,  of  chimney  gases 
Calorific  value  of  fuel.  .  . 

530° 
13,800 

12,936 

"400 
12,936 

567 

10,487 

571 

11,785 

11,610 

609 
9,739 

707 
10,359 

Efficiency  of  boiler  per  c. 

77.0 

74.3 

78.5 

67.2 

625 

69.3 

78.0 

?3.6 

Tests  Nos.  7  and  8  were  made  with  the  Hawley  Down-draught  Fun.ace, 
the  others  with  ordinary  furnaces. 

These  tests  confirm  the  statement  already  made  as  to  the  difficulty  of 
obtaining,  with  ordinary  grate-furnaces,  as  high  a  percentage  of  the  calo- 
rific value  of  the  fuel  with  the  Western  as  with  the  Eastern  coals. 

Test  No  3,  78.5$  efficiency,  is  remarkably  good  for  Pittsburgh  (Youghiogh- 
eny)  coal.  If  the  Washington  coal  had  given  equal  efficiency,  the  saving  of 

fuel  would  be      "  ~    ~'°  =  20.2$.    The  results  of  tests  Nos.  7  and  8  indicate 

7o.5 

that  the  downward-draught  furnace  is  well  adapted  for  burning  Illinois 
coals. 


BOILERS   USIKG   WASTE   GASES.  689 

Maximum  Boiler   Efficiency  with   Cumberland   Coal.— 

About  12.5  Ibs.  of  water  per  Ib.  combustible  from  and  at  212°  is  about  the 
highest  evaporation  that  can  be  obtained  from  the  best  steam  fuels  in  the 
United  States,  such  as  Cumberland,  Pocahontas,  and  Clearfield.  In  excep- 
tional cases  13  Ibs.  has  been  reached,  and  one  test  is  on  record  (F.  W.  Dean, 
Eng'g  News,  Feb.  1,  1894)  giving  13.23  Ibs.  The  boiler  was  internally  fired, 
of  the  Belpaire  type,  82  inches  diameter,  31  feet  long,  with  160  3-inch  tubes 
1'J^  feet  long.  Heating-surf  ace,  1998  square  feet;  gral:e-surface,45  square  feet, 
reduced  during  the  test  to  30^  square  feet.  Double  furnace,  with  fire-brick 
arches  and  a  long  combustion -chamber.  Feed-water  heater  in  smoke-box. 
The  following  are  the  principal  results  : 

1st  Test.  2d  Test. 

Dry  coal  burned  per  sq.  ft.  of  grate  per  hour,  Ibs 8.85  16.06 

Water  evap.  per  sq.  ft.  of  heating-surface  per  hour,  Ibs    1.63  3.00 
Water  evap.  from  and  at  212°  per  Ib.  combustible,  in- 
cluding feed-water  heater 13.17  13.23 

Water  evaporated,  excluding  feed-water  heater 12.88  12.90 

Temperature  of  gases  after  leaving  heater,  F 360°  463° 

BOILERS    USING   WASTE  OASES. 

Proportioning  Boilers  for  Blast-Furnaces.— (F.  W.  Gordon, 
Trans.  A.  I.  M.  E.,  vol.  xii.,  1883.) 

Mr.  Gordon's  recommendation  forproponioning  boilers  Avhen  properly  set 
for  burning  blast-furnace  gas  is,  for  coke  practice,  30  sq.  ft.  of  heating-sur- 
face per  ton  of  iron  per  24  hours,  which  the  furnace  is  expected  to  make, 
calculating  the  heating-surface  thus  :  For  double-flued  boilers,  all  shell- 
surface  exposed  to  the  gases,  and  half  the  flue-surface;  for  the  French  type, 
all  the  exposed  surface  of  the  upper  boiler  and  half  the  lower  boiler- 
surface;  for  cylindrical  boilers,  not  more  than  60  ft.  long,  all  the  heating- 
surface. 

To  the  above  must  be  added  a  battery  for  relay  in  case  of  cleaning,  repairs, 
etc.,  and  more  than  one  battery  extra  in  large  plants,  when  the  water  carries 
much  lime. 

For  anthracite  practice  add  50$  to  above  calculations.  For  charcoal  prac- 
tice deduct  20%. 

In  a  letter  to  the  author  in  May,  1894,  Mr.  Gordon  says  that  the  blast- 
furnace practice  at  the  time  when  his  article  (from  which  the  above  extract 
is  taken)  was  written  was  very  different  from  that  existing  at  the  present 
time;  besides,  more  economical  engines  are  being  introduced,  so  that  less 
than  30  sq.  ft.  of  boiler-surface  per  ton  of  iron  made  in  24  hours  may  now  be 
adopted.  He  says  further:  Blast-furnace  gases  are  seldom  used  for  other 
than  furnace  requirements,  which  of  course  is  throwing  away  good  fuel.  In 
this  case  a  furnace  in  an  ordinary  good  condition,  and  a  condition  where  it 
can  take  its  maximum  of  blast,  \vhich  is  in  the  neighborhood  of  200  to  225 
cubic  ft.,  atmospheric  measurement,  per  sq.  ft.  of  sectional  area  of  hearth, 
will  generate  the  necessary  H.P.  with  very  small  heating-surface,  owing  to 
the  high  heat  of  the  escaping  gases  from  the  boilers,  which  frequently  is 
1000  degrees. 

A  furnace  making  200  tons  of  iron  a  day  will  consume  about  900  H.P.  in 
blowing  the  engine.  About  a  pound  of  fuel  is  required  in  the  furnace  per 
pound  of  pig  metal. 

In  practice  it  requires  70  cu.  ft.  of  air-piston  displacement  per  Ib.  of  fuel 
consumed,  or  22,400  cu.  ft.  per  minute  for  200  tons  of  metal  in  1400  working 
minutes  per  day,  at,  say,  10  Ibs.  discharge-pressure.  This  is  equal  to  9*4  Ibs. 
M.E.P.  on  the  steam-piston  of  equal  area  to  the  blast-piston,  or  900 1. H.P.  To 
this  add  20$  for  hoisting,  pumping  and  other  purposes  for  which  steam  is  em- 
ployed around  blast-furnaces,  and  we  have  1100  H.P.,  or  say  5^  H.P.  per 
ton  of  iron  per  day.  Dividing  this  into  30  gives  approximately  5^  sq.  ft.  of 
heating-surface  of  boiler  per  H.P. 

Water- tube  Boilers  using  Blast* furnace  Gases.— D.  S. 
Jacobus  (Trans.  A.  I.  M.  E.,  xvii.  50)  reports  a  test  of  a  water  tube  boiler  using 
blast-furnace  gas  as  fuel.  The  heating-surface  was  2535  sq.  ft.  It  developed 
328  H.P.  (Centennial  standard),  or  5.01  Ibs.  of  water  from  and  at  212°  per 
sq.  ft.  of  heating-surface  per  hour.  Some  of  the  principal  data  obtained 
were  as  follows:  Calorific  value  of  1  Ib.  of  the  gas,  1413  B  T.U.,  including 
the  effect  of  its  initial  temperature,  which  was  650°  F.  Amount  of  air  used 
to  burn  1  Ib.  of  the  gas  =  0.9  Ib.  Chimney  draught,  1^  in.  of  water.  Area  of 
gas  inlet,  300  sq.  in.;  of  air  inlet,  100  sq.  in.  Temperature  of  the  chimney 


690 


THE   STEAM-BOILER. 


gases,  775°  F.  Efficiency  of  the  boiler  calculated  from  the  tempera tureS 
and  analyses  of  the  gases  at  exit  and  entrance,  61$.  The  average  analyses 
were  as  follows,  hydrocarbons  being  included  in  the  nitrogen  : 


By  Weight. 

By  Volume. 

At  Entrance. 

At  Exit. 

At  Entrance. 

At  Exit. 

COn.. 

10.69 
.11 
26.71 
62.48 
2.92 
11.45 
14.37 

26.37 
3.05 
1.78 
68.80 
7.19 
.76 
7.95 

7.08 
.10 
27.80 
65.02 

18.64 
2.96 
1.98 
76.42 

o     .             

CO                     

C  in  CO.  

C  in  CO  

Total  C  

Steam-boilers  Fired  with  Waste  Oases  from  Puddling 
and  Heating  Furnaces.— The  Iron  Age,  April  6, 1893,  contains  a  report 
of  a  number  of  tests  of  steam-boilers  utilizing  the  waste  heat  from  pud- 
dling and  heating  furnaces  iu  rolling-mills.  The  following  principal  data  are 
selected:  In  Nos.  1,  2,  and  4  the  boiler  is  a  Babcock  &  Wilcox  water-tube 
boiler,  and  in  No.  3  it  is  a  plain  cylinder  boiler,  42  in.  diam.  and  26  ft.  long. 
No.  4  boiler  was  connected  with  a  heating-furnace,  the  others  with  puddling 
furnaces. 


No.  1. 

No.  2. 

No.  3. 

No.  4. 

1026 

1196 

143 

1380 

19.9 

13  6 

13.6 

16.7 

52 

87.2 

10.5 

82.8 

3358 

2159 

1812 

3055 

3.3 

1.8 

12.7 

2.2 

5.9 

6.24 

3.76 

6.34 

7.20 

4.31 

8.34 

Heating-surface,  sq.  ft 

Grate-surface,  sq.  ft 

Ratio  H.S.  to  G. S 

Water  evap.  per  hour,  Ibs 

"  "  per  sq.  ft.  H.S.  per  hr.,  Ibs ... 
"  per  Ib.  coal  from  and  at  212°. 

**       "         **     '•  comb.  *'      "     "    " 

In  No.  2,  1 .38  Ibs.  of  iron  were  puddled  per  Ib.  of  coal. 
In  No.  3,  1.14  Ibs.  of  iron  were  puddled  per  Ib.  of  coal. 
No.  3  shows  that  an  insufficient  amount  of  heating-surface  was  provided 
for  the  amount  of  waste  heat  available. 

RULES  FOR  CONDUCTING  BOILER-TESTS. 

The  Committee  of  the  A.  S.  M.  E.  on  Boiler-tests,  consisting  of  Win.  Kent 
(chairman),  J.  C.  Hoadley,  R.  H.  Thurston.  Chas.  E.  Emery,  and  Chas.  T. 
Porter,  recommended  the  following  code  of  rules  for  boiler-tests  (Trans., 
vol.  vi.  p.  256): 

PRELIMINARIES  TO  A  TEST. 

I.  In  preparing  for  and  conducting  trials  of   steam-boilers  the  specific 
object  of  the  proposed  trial  should  be  clearly  defined  and  steadily  kept  in 
view. 

II.  Measure  and  record  the  dimensions,  position,  etc.,  of  grate  and  heat- 
ing surfaces,  flues  and  chimneys,  proportion  of  air-space  in  the  grate-sur- 
face, kind  of  draught,  natural  or  forced. 

III.  Put  the  boiler  in  good  condition.    Have  heating-surface  clean  inside 
and  out,  grate-bars  and  sides  of  furnace  free  from  clinkers,  dust  and  ashes 
removed  from  back  connections,  leaks  in  masonry  stopped,  and  all  obstruc- 
tions to  draught  removed.  See  that  the  damper  will  open  to  full  extent,  and 
that  it  may  be  closed  when  desired.     Test  for  leaks  in  masonry  by  firing  a 
little  smoky  fuel  and  immediately  closing  damper.    The  smoke  will  then 
escape  through  the  leaks. 

IV.  Have  an  understanding  with  the  parties  in  whose  interest  the  test  is 
to  be  made  as  to  the  character  of  the  coal  to  be  used.    The  coal  must  be  dry. 
or,  if  wet,  a  sample  must  be  dried  carefully  and  a  determination  of  the 
amount  of  moisture  in  the  coal  made,  and  the  calculation  of  the  results  of 
the  test  corrected  accordingly.   Wherever  possible,  the  test  should  be  made 
with  standard  coal  of  a  known  quality.     For  that  portion  of  the  country 
east  of  the  Alleghany  Mountains  good  anthracite  egg  coal   or  Cumberland 
semi-bituminous  coal  may  be  taken  as  the  standard  for  making  tests.   West 


EULES   FOR  CONDUCTING    BOILER-TEsTS.  691 

of  the  Alleghany  Mountains  and  east  of  the  Missouri  River,  Pittsburgh  lump 
coal  may  be  used.* 

V.  In  all  important  tests  a  sample  of  coal  should  be  selected  for  chemical 
analysis. 

VI.  Establish  the  correctness  of  all  apparatus  used  in  the  test  for  weighing 
and  measuring.    These  are:    1.  Scales  for  weighing  coal,  ashes,  and  water. 
2.  Tanks,  or  water-meters  for  measuring  water.     Water-meters,  as  a  rule, 
should  only  be  used  as  a  check  on  other  measurements     For  accurate  work 
the  water  should  be  weighed  or  measured  in  a  tank.    3.  Thermometers  and 
pyrometers  for  taking  temperatures  of  air,  steam,  feed-water,  waste  gases, 
etc.    4.  Pressure-gauges,  draught-gauges,  etc. 

VII.  Before  beginning  a  test,  the  boiler  and  chimney  should  be  thoroughly 
heated  to  their  usual  working  temperature.    If  the  boiler  is  new,  it  should 
be  in  continuous  use  at  least  a  week  before  testing,  so  as  to  dry  the  mortar 
thoroughly  and  heat  the  walls. 

VIII.  Before  beginning  a  test,  the  boiler  and  connections  should  be  free 
from  leaks,  and  all  water  connections,  including  blow  and  extra  feed  pipes, 
should  be  disconnected  or  stopped  with  blank  flanges,  except  the  particular 
pipe  through  which  water  is  to  be  fed  to  the  boiler  during  the  trial.    In  lo- 
cations where  the  reliability  of  the  power  is  so  important  that  an  extra  feed- 
pipe must  be  kept  in  position,  and  in   general  when  for  any  other  reason 
water-pipes  other  than  the  feed-pipes  cannot  be  dibC  mnected,  such  pipes 
may  be  drilled  so  as  to  leave  openings  in  their  lower  sides,  which  should  be 
kept  open  throughout  the  test  as  a  means  of  detecting  leaks,  or  accidental 
or  unauthorized  opening  of  valves.    During  the  test  the  blow-off  pipe  should 
remain  exposed. 

If  an  injector  is  used  it  must  receive  steam  directly  from  the  boiler  being 
tested,  and  not  from  a  steam-pipe  or  from  any  other  boiler. 

See  that  the  steam-pipe  is  so  arranged  that  water  of  condensation  cannot 
run  back  into  the  boiler.  If  the  steam-pipe  has  such  an  inclination  that  the 
water  of  condensation  from  any  portion  of  the  steam-pipe  system  may  rnn 
back  into  the  boiler,  it  must  be  trapped  so  as  to  prevent  this  water  getting 
into  the  boiler  without  being  measured. 

STARTING  AND  STOPPING  A  TEST. 

A  test  should  last  at  least  ten  hours  of  continuous  running,  and  twenty- 
four  hours  whenever  practicable.  The  conditions  of  the  boiler  and  furnace 
in  all  respects  should  be,  as  nearly  as  possible,  the  same  at  the  end  as  at 
the  beginning  of  the  test.  The  steam-pressure  should  be  the  same,  the 
water-level  the  same,  the  fire  upon  the  grates  should  be  the  same  in  quan- 
tity and  condition,  and  the  walls,  flues,  etc.,  should  be  of  the  same  tempera- 
ture. To  secure  as  near  an  approximation  to  exact  uniformity  as  possible 
in  conditions  of  the  fire  and  in  temperatures  of  the  walls  and  flues,  the 
following  method  of  starting  and  stopping  a  test  should  be  adopted  : 

X.  Standard  Method.— Steam  being  raised  to  the  working  pressure,  re- 
move rapidly  all  the  fire  from  the  grate,  close  the  damper,  clean  the  ash-pit, 
and  as  quickly  as  possible  start  a  new  fire  with  weighed  wood  and  coal, 
noting  the  time  of  starting  the  test  and  the  height  of  the  water-level  while 
the  water  is  in  a  quiescent  state,  just  before  lighting  the  fire. 

At  the  end  of  the  test  remove  the  whole  fire,  clean  the  grates  and  ash-pit, 
and  note  the  water-level  when  the  water  is  in  a  quiescent  state  ;  record  the 
time  of  hauling  the  fire  as  the  end  of  the  test.  The  water-level  should  be 
as  nearly  as  possible  the  same  as  at  the  beginning  of  the  test.  If  it  is  not 
the  same,  a  correction  should  be  made  by  computation,  and  not  by  operat- 
ing pump  after  test  is  completed.  It  will  generally  be  necessary  to  regulate 
the  discharge  of  steam  from  the  boiler  tested  by  means  of  the  stop-valve 
for  a  time  while  fires  are  being  hauled  at  the  beginning  and  at  the  end  of 
the  test,  in  order  to  keep  the  steam-pressure  in  the  boiler  at  those  times  up 
to  the  average  during  the  test. 

XI.  Alternate  Method.— Instead  of  the  Standard  Method  above  described, 
the  following  may  be  employed  where  local  conditions  render  it  necessary  : 

At  the  regular  time  for  slicing  and  cleaning  fires  have  them  burned  rather 
low,  as  is  usual  before  cleaning,  and  then  thoroughly  cleaned  ;  note  the 
amount  of  coal  left  on  the  grate  as  nearly  as  it  can  be  estimated  ;  note  the 

*  These  coals  are  selected  because  they  are  about  the  only  coals  which 
contain  the  essentials  of  excellence  of  quality,  adaptability  to  various  kinds 
of  furnaces,  grates,  boilers,  and  methods  of  firing,  and  wide  distribution  and 
general  accessibility  in  the  markets. 


692  THE   STEAM-BOILER. 

pressure  of  steam  and  the  height  of  the  water-level— which  should  be  at  the 
medium  height  to  be  carried  throughout  the  test— at  the  same  time  ;  and 
note  this  time  as  the  time  of  starting  the  test.  Fresh  coal,  which  has  been 
weighed,  should  now  be  fired.  The  ash-pits  should  be  thoroughly  cleaned 
at  once  after  starting.  Before  the  end  of  the  test  the  fires  should  be  burned 
low,  just  as  before  the  start,  and  the  fires  cleaned  in  such  a  manner  as  to 
leave  the  same  amount  of  fire,  and  in  the  same  condition,  on  the  grates  as  at 
the  start.  The  water-level  and  steam-pressure  should  be  brought  to  the 
same  point  as  at  the  start,  and  the  time  of  the  ending  of  the  test  should  be 
noted  just  before  fresh  coal  is  fired. 

DURING  THE  TEST. 

XII.  Keep  the  Conditions  Uniform.— The  boiler  should  be  run  continu- 
ously, without  stopping  for  meal-times  or  for  rise  or  fall  of  pressure  of 
steam  due  to  change  of  demand  for  steam.    The  draught  being  adjusted  to 
the  rate  of  evaporation  or  combustion  desired  before  the  test  is  begun,  it 
should  be  retained  constant  during  the  test  by  means  of  the  damper. 

If  the  boiler  is  not  connected  to  the  same  steam-pipe  with  other  boilers, 
an  extra  outlet  for  steam  with  valve  in  same  should  be  provided,  so  that  in 
case  the  pressure  should  rise  to  that  at  which  the  safety-valve  is  set  it  may 
be  reduced  to  the  desired  point  by  opening  the  extra  outlet,  without  check- 
ing the  fires. 

If  the  boiler  is  connected  to  a  main  steam-pipe  with  other  boilers,  the 
safety-valve  on  the  boiler  being  tested  should  be  set  a  few  pounds  higher 
than  those  of  the  other  boilers,  so  that  in  case  of  a  rise  in  pressure  the 
other  boilers  may  blow  off,  and  the  pressure  be  reduced  by  closing  their 
dampers,  allowing  the  damper  of  the  boiler  being  tested  to  remain  open, 
and  firing  as  usual. 

All  the  conditions  should  be  kept  as  nearly  uniform  as  possible,  such  as 
force  of  draught,  pressure  of  steam,  and  height  of  water.  The  time  of 
cleaning  the  fires  will  depend  upon  the  character  of  the  fuel,  the  rapidity  of 
combustion,  and  the  kind  of  grates.  When  very  good  coal  is  used,  and  the 
combustion  not  too  rapid,  a  ten-hour  test  may  be  run  without  any  cleaning 
of  the  grates,  other  than  just  before  the  beginning  and  just  before  the  end 
of  the  test.  But  in  case  the  grates  have  to  be  cleaned  during  the  test,  the 
intervals  between  one  cleaning  and  another  should  be  uniform. 

XIII.  Keeping  the  Records. — The  coal  should  be  weighed  and  delivered  to 
the  firemen  in  equal  portions,  each  sufficient  for  about  one  hour's  run,  and 
a  fresh  portion  should  not  be  delivered  until  the  previous  one  has  all  been 
fired.    The  time  required  to  consume  each  portion  should  be  noted,  the 
time  being  recorded  at  the  instant  of  firing  the  first  of  each  new  portion.  It 
is  desirable  that  at  the  same  time  the  amount  of  water  fed  into  the  boiler 
should  be  accurately  noted  and  recorded,  including  the  height  of  the  water 
in  the  boiler  and  the  average  pressure  of  steam  and  temperature  of  feed 
during  the  time.    By  thus  recording  the  amount  of  water  evaporated  by 
successive  portions  of  coal,  the  record  of  the  test  may  be  divided  into 
several  divisions,  if  desired,  at  the  end  of  the  test,  to  discover  the  degree 
of  uniformity  of  combustion,  evaporation,  and  economy  at  different  stages 
of  the  test. 

XIV.  Priming  Tests. — In  all  tests  in  which  accuracy  of  results  is  impor- 
tant, calorimeter  tests  should  be  made  of  the  percentage  of  moisture  in  the 
steam,  or  of  the  degree  of  superheating.    At  least  ten  such  tests  should  be 
made  during  the  trial  of  the  boiler,  or  so  many  as  to  reduce  the  probable 
average  error  to  less  than  one  per  cent,  and  the  final  records  of  the  boile"- 
test  corrected  according  to  the  average  results  of  the  calorimeter  tests. 

On  account  of  the  difficulty  of  securing  accuracy  in  these  tests,  the  great- 
est care  should  be  taken  in  the  measurements  of  weights  and  temperatures. 
The  thermometers  should  be  accurate  within  a  tenth  of  a  degree,  and  the 
scales  on  which  the  water  is  weighed  to  within  one  hundredth  of  a  pound. 

ANALYSES  OF  GASES.— -MEASUREMENT  OF  AIR-SUPPLY,  ETC. 

XV.  In  tests  for  purposes  of  scientific  research,  in  which  the  determina- 
tion of  all  the  variables  entering  into  the  test  is  desired,  certain  observations 
should  be  made  which  are  in  general  not  necessary  in  tests  for  commercial 
purposes.    These  are  the  measurement  of  the  air-supply,  the  determination 
of  its  contained  moisture,  the  measurement,  and  analysis  of  the  flue  gases, 
the  determination  of  the  amount  of  heat  lost  by  radiation,  of  the  amount  of 
infiltration  of  air  through  the  setting,  the  direct  determination  by  calorim- 
eter experiments  of  the  absolute  heating  value  of  the  fuel,  and  (by  conden- 


RULES    FOR   CONDUCTING    BOILER-TESTS. 


693 


sation  of  all  the  steam  made  by  the  boiler)  of  the  total  heat  imparted  to  the 
water. 

The  analysis  of  the  flue-gases  is  an  especially  valuable  method  of  deter- 
mining the  relative  value  of  different  methods  of  firing,  or  of  different  kinds 
of  furnaces.  In  making  these  analyses  great  care  should  be  taken  to  pro- 
cure average  samples— since  the  composition  is  apt  to  vary  at  different 
points  of  the  flue,  and  the  analyses  should  be  intrusted  only  to  a  thoroughly 
competent  chemist,  who  is  provided  with  complete  and  accurate  apparatus. 

As  the  determinations  of  the  other  variables  mentioned  above  are  not 
likely  to  be  undertaken  except  by  engineers  of  high  scientific  attainments, 
and  as  apparatus  for  making  them  is  likely  to  be  improved  in  the  course  of 
scientific  research,  it  is  not  deemed  advisable  to  include  in  this  code  any 
specific  directions  for  making  the  n. 

RECORD  OP  THE  TEST. 

XVI.  A  "log  "of  the  test  should  be  kept  on  properly  prepared  blanks, 
containing  headings  as  follows: 


Time. 

Pressures. 

Temperatures. 

Fuel. 

Feed- 
water. 

Barome- 
ter. 

g  to 

P 

Draught- 
gauge. 

External 
Air. 

Boiler- 
room. 

£ 

Feed- 
water. 

Steam. 

1 

t/5 

3 

oJ 

£ 

EH 

6*5 

«3  ^ 

3s 

REPORTING  THE  TRIAL. 

XVII.  The  final  results  should  be  recorded  upon  a  properly  prepared 
blank,  and  should  include  as  many  of  the  following  items  as  are  adapted  for 
the  specific  object  for  which  the  trial  is  made.  The  items  marked  with  a  * 
may  be  omitted  for  ordinary  trials,  but  are  desirable  for  comparison  with 
siniilar  data  from  other  sources. 

Results  of  the  trials  of  a 

Boiler  at 

To  determine 


1.  Date  of  trial  

2.  Duration  of  trial  

hours 

DIMENSIONS  AND  PROPORTIONS. 

Leave  space  for  complete  description. 
3.  Grate-surf  ace  wide  long  area  
4   Water-heating  surface 

sq.  ft. 

Sq    ft 

5    Superheating  surface                       

sq  ft" 

6.  Ratio  of  water-heating  surface  to  grate-sur- 
face     .     .                              .         

AVERAGE  PRESSURES. 

7.  Steam-pressure  in  boiler,  by  gauge  
*8.  Absolute  steam-pressure  

Ibs. 
Ibs. 

*9    Atmospheric  pressure  per  barometer    . 

in 

10    Force  of  draught  in  inches  of  water  

in 

AVERAGE  TEMPERATURES. 

deg. 

*12.  Of  fire-room  

deg. 

•M3    Of  steam..          

deer. 

14.  Of  escaping  gases  

deg. 

15.  Of  feed-water  

cleg. 

*  See  reference  in  paragraph  preceding  table. 


694 


THE    STEAM-BOILER. 


16.  Total  amount  of  coal  consumed  t Ibs. 

17.  Moisture  in  coal per  cent, 

18.  Dry  coal  consumed Ibs. 

19.  Total  refuse,  dry pounds  = per  cent 

20.  Total  combustible  (dry  weight  of  coal,  Item 

18;  less  refuse.  Item  19) Ibs. 

*21.  Dry  coal  consumed  per  hour Ibs. 

*22.  Combustible  consumed  per  hour. Ibs. 

RESULTS  OF  CALORIMETRIC  TESTS. 

23.  Quality  of  steam,  dry  steam  being  taken  as 

unity 

24.  Percentage  of  moisture  in  steam per  cent. 

25.  Number  of  degrees  superheated deg. 

WATER. 

26.  Total  weight  of  water  pumped  into  boiler  and 

apparently  evaporated^ Ibs. 

27.  Water   actually   evaporated,   corrected   for 

quality  of  steam  § Ibs. 

28.  Equivalent  water  evaporated  into  dry  stean 

from  and  at  212°  F.  § Ibs. 

*29.  Equivalent  total  heat  derived  from  fuel  in 

British  thermal  units §.. B.T.U 

30.  Equivalent  water  evaporated  into  dry  steam 

from  and  at  212°  F.  per  hour Ibs. 

ECONOMIC  EVAPORATION. 

31.  Water  actually  evaporated  per  pound  of  dry 

coal,  from  actual  pressure  and  tempera- 
ture §   Ibs 


*  See  reference  in  paragraph  preceding  table. 

t  Including  equivalent  of  wood  used  in  lighting  fire.  1  pound  of  wood 
equals  0.4  pound  coal.  Not  including  unburnt  coal  withdrawn  from  fire  at 
end  of  test. 

i  Corrected  for  inequality  of  water-level  and  of  steam-pressure  at  begin- 
ning and  end  of  test. 

§  The  following  shows  how  some  of  the  items  in  the  above  table  are 
derived  from  others: 

Item  27  =  Item  26  X  Item  23. 

Item  28  =  Item  27  X  Factor  of  evaporation. 

Factor  of  evaporation  =  —   -  „  ,  H  and  h  being  respectively  the  total  heat- 

yoo.  i 

units  in  steam  of  the  average  observed  pressure  and  in  water  of  the  average 
observed  temperature  of  feed,  as  obtained  from  tables  of  the  properties  of 
steam  and  water. 

.Item  29  =  Item  27  X  (H  -  h). 
Item  31  =  Item  27  -*-  Item  18. 

Item  32  =  Item  28  H-  Item  18,  or  =  Item  31  X  factor  of  evaporation. 
Item  33  =  Item  28  -s-  Item  20,  or  =  Item  32  H-  (per  cent  100  -  Item  19). 
Items  36  to  38.     First  term  =  Item  22  X  6/5. 
Items  40  to  42.     First  term  =  Item  30  X  0.8698. 


Item  43  =  Item  29  x  0.00003,  or  = 


*° 


Item  45  = 


34^ 

Difference  of  Items  43  and  44 
Item  44  ' 


-. 


RULES   FOR   CONDUCTING    BOILER-TESTS. 


695 


32    Equivalent  water  evaporated  per  pound  of 
dry  coal  from  and  at  ^12°  F  § 

Ibs. 
Ibs. 

Ibs. 

Ibs. 
Ibs. 
Ibs. 
Ibs. 

Ibs. 
Ibs. 
Ibs. 
Ibs. 

H.P. 

H.P. 
per  cent 

33.  Equivalent  water  evaporated  per  pound  of 
combustible  from  and  at  212°  F  § 

COMMERCIAL  EVAPORATION. 

*34.  Equivalent  water  evaporated  per  pound  of 
dry  coal  with  one  sixth  refuse,  at  70  pounds 
gauge-pressure,  from  temperature  of  100° 
F   —  Item  33  X  0  7249      

RATE   OF  COMBUSTION. 

35,  Dry  coal  actually  burned  per  square  foot  of 
grate-surface  per  hour 

(                                        \  Per  sq.  ft.  of  grate- 
*ofi     1     Consumption  of  dry  |      surface  
^7    j  coal   per  hour.      Coal  !  Persq.  ft.  of  water- 
JCQ     1  assumed      with      one  f     heating  surface.. 
db->  |  sixth  refuse.§                  I  Per  sq.  ft.  of  least 
[                                        J     area  for  draught. 

RATE  OP  EVAPORATION. 

39.  Water  evaporated  from  and  at  212°  F.  per 
sq  ft  of  heating-surface  per  hour  . 

[     Water     evaporated")  P-  %£  «  *?» 

'$.  Jgs±?  3%^Hsa2#2£ 

*43.    !  into  steam  of  70  Ibs.    p^SDK^t^i 
[gauge-pressure.  §         \  ^S^g^ 

COMMERCIAL  HORSE-POWER. 

43.  On  basis  of  thirty  pounds  of  water  per  hour 
evaporated   from   temperature  of  100°  F 
into  steam   of    70  pounds  gauge-pressure 
(=  34^  Ibs.  from  and  at  212°)  §  
44.  Horse-power,  builders'  rating,  at  square 
feet  per  horse-power  

45.  Per  cent  developed  above,  or  below,  rating§ 

Factors  of  Evaporation.— The  table  on  the  following  pages  was 
originally  published  by  the  author  in  Trans.  A.  S.  M.  E.,  vol.  vi.,  1884,  under 
the  title,  Tables  for  Facilitating  Calculations  of  Boiler-tests.  The  table 
gives  the  factors  for  every  3°  of  temperature  of  feed-water  from  32°  to  212° 
F.,  and  for  every  two  pounds  pressure  of  steam  within  the  limits  of  ordinary 
working  steam-pressures. 

The  difference  in  the  factor  corresponding  to  a  difference  of  3°  tempera- 
ture of  feed  is  always  either  .0031  or  .0032.  For  interpolation  to  find  a  factor 
for  a  feed-water  temperature  between  32°  and  212°,  not  given  in  the  table, 
take  the  factor  for  the  nearest  temperature  and  add  or  subtract,  as  the  case 
may  be,  .0010  if  the  difference  is  .0031,  and  .0011  if  the  difference  is  .0032.  As 
in  nearly  all  cases  a  factor  of  evaporation  to  three  decimal  places  is  accu- 
rate enough,  any  error  which  may  be  made  in  the  fourth  decimal  place  by 
interpolation  is  of  no  practical  importance. 

The  tables  used  in  calculating  these  factors  of  evaporation  are  those  given 
in  Charles  T.  Porter's  Treatise  on  the  Richards'  Steam-engine  Indicator. 

The  formula  is  Factor  =       ~    ,  in  which  H  is  the  total  heat  of  steam  at  the 
9o5.  t 

observed  pressure,  and  h  the  total  heat  of  feed-water  of  the  observed 
temperature. 


696 


THE    STEAM-BOILER. 


Lbs. 
O*oge-  pressures.  .  .0  -t- 
Absolute  pressures    15 

10  + 
25 

20  + 
35 

30  + 
45 

40  + 
55 

45  + 
60 

50  + 
65 

52  + 
67 

54  + 
69 

g,t 

Feed-water 
T«nperature 

FACTORS  OF  EVAPORATION. 

212°  F. 

1.0003  1.0088 

1.01491.0197 

1  .  0237  1  .  0254  1  .  0271  1  .  0277  1  1  .  0283  .  1  .  0290 

209 

35 

1.0120 

80 

1.0228 

68!        86  11.0302  1.0309 

1.0315 

1.0321 

206 

66 

51 

1.0212 

60 

99  1.0317 

34         40 

46 

52 

203 

98 

83 

43 

91 

1.0331 

49 

65         72 

78 

84 

200 

1.0129 

1.0214 

75 

1.0323 

62 

80 

97  1.0403 

1.0409 

1.0415 

197 

60 

4C 

1.0306 

54 

941.0412 

1.0428         34 

41 

47 

194 

92 

77 

38 

85 

1.0425 

43 

60 

66 

7' 

78 

191 

1.0223 

1.0308 

69 

1.0417 

57 

74 

91 

97 

1.0503 

1.0510 

188 

55 

41 

1.0400 

48 

88 

1.0506 

1.05221.0528 

35 

41 

185 

86 

71 

32 

80 

1.0519 

37 

54 

60 

66 

72 

182 

1.0317 

1.0403 

63 

1.0511 

51 

68 

85 

91 

98 

1.0604 

179 

49 

34 

95 

42 

82 

1.0600 

1.0616 

1.0623i  1.06^9 

35 

176 

80 

65 

1.0526 

74 

1.0613 

31 

48         54 

60 

66 

173 

1.0411 

97 

57 

1.0605 

45 

63 

79         85 

92 

98 

170 

43 

1.0528 

89 

36 

76 

94 

1.0710;  1.0717 

1.0723 

1.0729 

167 

7^ 

59 

1.0620 

68 

1.0707 

1.0725 

42!        48 

54 

60 

164 

1.0505 

91 

51 

99 

39 

56 

73         80 

86 

92 

161 

37 

1.0622 

82 

1.0730 

70 

88 

1.08041.0811 

1.0817 

1.0823 

158 

68 

53 

1.0714 

62 

1.0801 

1.0819 

36         42 

48 

54 

155 

99 

84 

45 

93 

33 

50 

67         73 

80 

86 

152 

1.0631 

1.0716 

76 

1.0824 

64 

82 

98  !  1.0905 

1.0911 

1.0911' 

149 

62 

47 

1.0808 

55 

95 

1.0913 

1.0930 

36 

42 

48 

146 

93 

78 

39 

87 

1.0926 

44 

61 

67 

7< 

79 

143 

1.0724 

1.0810 

70 

1.0918 

58 

75 

92 

98 

1.1005 

1.1011 

140 

56 

41 

1.0901 

49 

89 

1.1007 

1.1023 

1.1030 

36 

4M 

137 

87 

72 

33 

80 

1.1020 

38 

55 

61 

67 

7i< 

134 

1.0818 

1.0903 

64 

1.1012 

51 

69 

86 

92 

98 

1.1104 

131 

49 

34 

95 

43 

83 

1.1100 

1.1117 

1.1123 

1.1130 

36 

128 

81 

66 

1.1026 

74 

1.1114 

32 

48 

55 

61 

67' 

125 

1.0912 

97 

57 

1.1105 

45 

63 

79 

86 

92 

9P 

122 

43 

1.1028 

89 

36 

76 

94 

1.1211 

1.1217 

1.1223 

1.122^ 

119 

74 

59 

1.1120 

68 

1.1207 

1.1225 

42 

48 

54 

60 

116 

1.1005 

90 

51 

99 

39 

56 

73 

79 

86 

9't 

113 

36 

1.1122 

82 

1.1230 

70 

88 

1.1304 

1.1310 

1.1317 

1  132»{ 

110 

68 

53 

1.12131        61 

1.1301 

1.1319 

35 

48 

54 

107 

99 

84 

451        92 

32 

50 

66 

73 

79 

8fi 

104 

1.1130 

1.1215 

76  1  .  1323 

63 

81 

98 

1.1404 

1.1410 

1.1416 

101 

61 

46 

1.1307         55 

94 

1.1412 

1.1429 

35 

41 

4( 

98 

92 

77 

38 

86 

1.1426 

43 

60 

66 

73 

79 

95 

1.1223 

1.1309 

69 

1.1417 

57 

75 

91 

97 

1.1504 

1.1510 

92 

55 

40 

1.1400 

48 

88 

1.1506 

1.1522 

1.1529 

35 

41 

89 

86 

71 

31 

79 

1.1519 

37 

53 

60 

66 

72 

86 

1.1317 

1.1402 

63 

1.1510 

50 

68 

84 

91 

97 

1.1603 

83 

48 

33 

94 

41 

81 

99 

1.1616 

1  .  1622 

1.1628 

34 

80 

79 

64 

1.1525 

73 

1.1612 

1.1630 

47 

53 

59 

65 

77 

1.1410 

95 

56 

1.1604 

44 

61 

78 

84 

90 

96 

74 

41 

1.1526 

87 

35 

75 

92 

1.1709 

1.1715 

1  1722 

1.1728 

71 

72 

58 

1.1618 

66 

1.1706 

1.1723 

40 

46 

53 

59 

68 

1.1504 

89 

49 

97 

37 

55 

71 

78 

84 

90 

65 

35 

1.1620 

80 

1.1728 

68 

86 

1  .  1802 

1.1809 

1.1815 

1.1821 

62 

66 

51 

1.1711 

59 

99 

1.1817 

33 

40 

46 

52 

59 

97 

82 

43 

90 

1.1830 

48 

64 

71 

77' 

83 

56 

1.1628 

1.1713 

74 

1.1821 

61 

79 

96 

1.1902 

1.1908 

1  1914 

53 

59 

44 

1.1805 

52 

92 

1.1910 

1.1927 

33 

39 

45 

50 

90 

75 

36 

84 

1.1923 

41 

58 

64 

70 

76 

47 

1.1721 

1.1806 

67 

1.1915 

54 

72 

89 

95 

1.2001 

1.2007 

44 

52 

37 

98 

46 

'86 

1.2003 

.20201.2026 

32 

39 

41 

83 

68 

1.1929 

77 

1.2017 

34 

51  i        57 

64 

70 

38 

1.1814 

1.1900 

60 

1.2008 

48 

65 

82         88 

95 

1.2101 

35 

45 

31 

91 

39 

79 

96 

1.21131.211911.2126 

32 

32 

70 

62 

1.2022 

70 

1.2110 

1.2128 

44         51  i        57 

63 

FACTORS  OF   EVAPOKATIOH". 


697 


Gauge-press.,  Ibs.  58  -f 
Abaolute  Pressures..  73. 

ff* 

62  -f 
77 

64  + 
79 

66  + 
81 

68  + 
83 

70  + 
85 

72  + 
87 

74  + 
89 

76  -t- 
91 

Feed  water 
Temp. 

FACTORS  OF  EVAPORATION. 

| 

212°  F. 

1  .0295 

1.0301 

1.0307 

1  .0312 

1.0318 

1.0323!  1.0329 

1.0334 

1.0339 

1.0344 

209 

1.0327 

33 

38 

44 

49 

55         (50 

65 

70 

75 

206 

58 

64 

7d 

75 

81 

86 

91 

97 

1.0402 

1.0407 

203 

90 

96 

1.0401 

1.0407 

1.0412 

1.0418|1.0423 

1.0428 

33 

38 

200 

1.0421 

1.0427 

223 

38 

44 

49 

54 

59 

65 

69 

197 

53 

58 

64 

70 

75 

80 

86 

91 

96 

1.0501 

194 

84 

90 

96 

1.0501 

1.0507 

1.0512 

1.0517 

1.0522 

1.0527 

32 

191 

1.0515 

1.0521 

1.0527 

33 

38 

43 

49 

54 

59 

64 

188 

47 

53 

58 

64 

69 

75 

80 

85 

90 

95 

185 

78 

84 

90 

95 

1.0601 

1.0606 

1.0611 

1.0616 

1.0622 

1.0626 

182 

1.0610 

1.0615 

1.0621 

1.0627 

32 

37 

43 

48 

53 

58 

179 

41 

47 

52 

58 

63 

69 

74 

79 

84 

89 

176 

72 

78 

84 

89 

95 

1.0700 

1.0705 

1.0711 

1.0716 

1.0721 

173 

1.0704 

1  .0709 

1.0715 

1.0721 

1.0726 

32 

37 

42 

47 

52 

170 

35 

41 

46 

52 

57 

63 

68 

73 

78 

83 

167 

6? 

72!        78 

83 

89 

94 

99 

1.0805  1.0810 

1.0815 

164 

<  4 

1.08031.08091.08!5 

1.0820 

1.0825 

1  .0831 

36         41 

46 

161 

1.08.29 

35 

40         46 

51 

57 

62 

67         72 

77 

158 

60 

66 

72         77 

83 

88 

93 

981  0904  1.0908 

155 

92 

97 

1.09031.0909 

1.0914 

1.0919 

1.0925 

1.0930         35  1        40 

152 

1.0923 

1.0929 

34 

40 

45 

51 

56 

61         66         71 

149 

54 

60 

66 

71 

77 

82 

87 

92         971.1002 

146 

85 

91 

971.1002 

1.1008 

1.1013 

1.1018 

1.10241.1029         34 

143 

1.1017 

1.1022 

1.1028!        34 

39 

44 

50 

55         60         65 

140 

48 

54 

59         65 

70 

76 

81 

86         91         96 

137 

79 

85 

91 

96 

1.1102 

1.1107 

1.1112 

1.1117;i.  112211.  1127 

134 

1.1110 

1.1116  1.11221.1127 

33 

38 

43 

49         54         59 

131 

42 

47!        53!        59 

64 

69 

75 

80         85  i        90 

128 

73 

79  !        84 

90 

95 

1.1201 

1.1206 

1.1211  1.12161.1221 

125 

1.1204 

1.1210  1.1215 

1.1221 

1.1226 

32 

37 

42!        47 

52 

122 

35 

41         47 

52 

58 

63 

68 

73;        78 

83 

119 

66 

72  i        78 

83 

89 

94 

99 

1.13051.1310 

1.1315 

116 

98 

1.1303  1.1309 

1.1315 

1.1320 

1.1325 

1.1331 

36         41 

46 

113 

1.1329 

34         40 

46 

51 

57 

62 

67         72 

77 

110 

60 

66         71 

77 

82 

88 

93 

981.1403 

1.1408 

107 

91 

97  1.1403 

1.1408 

1.1414 

1.1419 

1.1424 

1.1429         34 

39 

104 

1.1422 

1.1428         34         39 

45 

50 

55 

60  i        65 

70 

101 

53 

59  1        65         70 

76 

81 

86 

92  1        97|1.1502 

98 

85 

90  !        961.1502 

1.1507 

1.1512 

1.1518 

1.152311.1528         33 

95 

1.1516 

1.1521 

1.1527|        33 

38 

43 

49 

54 

59!        64 

92 

47 

53 

58 

64 

69 

75 

80 

85 

90         95 

89 

78 

84 

89 

95 

1.1600 

1.1606 

1.1611 

1.  161611.  1621!1.  1626 

86 

1  1609 

1.1615 

1.1621 

1.1626 

32 

37 

42 

47 

52         57 

83 

40 

46 

52 

57 

63 

68 

73 

78         83i        t8 

80 

71 

77 

83 

88 

94 

99 

1.1704 

1.1710  1.1715  1.1720 

77 

1.1702 

1  1708 

1.1714 

1.1719 

1.1725 

1.1730 

35 

41 

46         51 

74 

34 

39 

45 

51 

56 

61 

67 

72         77 

82 

71 

65 

70!        76 

& 

87 

92 

98 

1.1803  1.18081.1813 

68 

96 

1  1802 

1.1807 

1.1813 

1.1818 

1.1824 

1.1829 

34         39  i        44 

65 

1.1827 

33         38         4^ 

49 

55 

60 

65  i         70         75 

62 

58 

64         69 

75 

80 

86 

91 

96  1.1901  |l.l906 

59 

89 

95il.l901 

1.1906 

1.1912 

1.1917 

1.1922 

1.1927 

32 

37 

56 

1.1920 

1.1926J        32 

37 

43 

'    48 

53 

58 

63 

68 

53 

51 

57 

63 

68 

74 

79 

84 

89 

94 

99 

50 

82 

88 

94 

99 

1.2005 

1.2010 

1.2015 

1.2021 

1.2026 

1.2031 

47 

1.2013 

1.2019 

1.2025 

1.2030 

36 

41 

46 

52 

57 

62 

44 

44 

50 

56 

61 

67 

72 

78 

.       83 

88 

93 

41 

76 

81 

87 

93 

98 

1.2103 

1.2109 

1.2114 

1.21191.2124 

38 

1.2107 

1.2112 

1.2118 

1.2124 

1.2129 

34 

40 

45 

50|        55 

35 

38 

43 

49 

55 

60 

65 

71 

76 

81 

86 

32                    69 

75         80         86 

91 

97 

1.2202 

1.22071.2212  1.221 

698 


THE   STEAM-BOILER. 


Gauge-pressures 
lbs.,78  + 
Absolute 
Pressures,  93 

80  + 
95 

82  + 
97 

84  + 
99 

86  + 
101 

88  + 
103 

90  + 
105 

92  + 
107 

94  + 
109 

96  + 
111 

98  f- 
113 

FACTORS  OF  EVAPORATION. 


212 
209 

1.034  9  11.0353 

80         85 

1  .  0358 
90 

1.  0303  '1.  0307  il  0372 
94  !         9911.0403 

1.0376 
1  0408 

1  .0381 
1.0412 

1.0385,1.0389 
1.0416  1.0421 

1.0393 
1.0425 

206 

1.0411 

1.0416 

1.0421 

1.0426 

1.0430)        35 

39 

43 

48 

52 

56 

203 

43 

48 

52 

57 

621        60 

71 

75 

79 

83 

88 

200 

74 

79 

84 

89         93 

9^ 

1  .0502 

1.0506 

1.0511 

1.0515 

1.0519 

197 

1.0506 

1.0511 

1.0515 

1.05201.0525 

1.0521.' 

33 

38 

42 

46 

50 

194 

37 

42 

47 

51 

56 

60 

65 

69 

73 

78 

82 

191 

69 

73 

78 

83 

87 

92 

96 

1.0601 

1.0605 

1  0609 

1.0613 

188 

1.0600 

1.0605 

1  0610 

1.0614 

1  .0619 

1.0623 

1.0628 

32 

36 

40 

45 

185 

31 

36 

41 

46 

50 

55 

59 

63 

68 

72 

76 

182 

63 

68 

72 

77 

81 

86 

90 

95 

99 

1  .0703 

1.0707 

179 

94 

99 

1  0704 

1.0708 

1.0713 

1.0717 

1.0722 

1.0726 

1.0730 

35 

39 

176 

1.0725 

1.0730 

35 

40 

44 

49 

53 

57 

62 

66 

70 

173 

57 

62 

66 

?! 

75 

80 

84 

89 

93 

97 

1.0801 

170 

88 

93 

98 

1  .Cd02 

1.0807 

1.0811 

1  .0810 

1.0820 

1.0824 

1.0829 

33 

167 

1.0819 

1.0884 

1.0829 

34 

38 

43 

47 

51 

56 

60 

64 

164 

51 

56 

60 

65 

69 

74 

78 

83 

87 

91 

95 

161 

82 

87  1        92 

96 

1  .0901 

1  .0905 

1.0910 

1.0914 

1.0918 

1.0923 

1.0927 

158 

1  .0913 

1.0918 

1.0923 

1.0927 

32 

37 

41 

45 

50 

54 

58 

155 

45 

49 

54 

59 

63 

68 

72 

77 

81 

85 

89 

152 

76 

81 

85 

90 

95 

99 

1.1004 

1.1008 

1.1012 

1.1016 

1.1021 

149 

1.1007 

1.1012 

1.1017 

1.1021 

1.1026 

1.1030 

35 

39 

43 

48 

52 

146 

38 

43 

48 

53 

57 

62 

66 

70 

75 

79 

83 

143 

70 

74 

79 

84 

88 

93 

97 

1.1102 

1.1106 

1.1110 

1.1114 

140 

1.1101 

1.1106 

1.1110 

1.1115 

1.1120 

1.1124 

1.1129 

33 

37 

41 

40 

137 

32 

37 

42 

46 

51 

55 

60 

64 

68 

73 

77 

134 

63 

68 

73 

78 

82 

87 

91 

95 

1.1200 

1.1204 

1.1208 

131 

95 

99 

1.1204 

1.1209 

1.1213 

1.1218 

1.1222 

1.1227 

31 

35 

39 

128 

r.  1226 

1,1231 

35 

40 

45 

49 

53 

58 

62 

66 

71 

125 

57 

62 

67 

71 

76 

80 

85 

89 

93 

98 

1.1302 

122 

88 

93 

98 

1.1302 

1  .  1307 

1.1311 

1.1316 

1.1320 

1.1325 

1  .  1329 

33 

119 

1  .  1320 

1.1324 

1.1329 

34 

38 

43 

47 

51 

56 

60 

01 

116 

51 

55 

60 

65 

69 

74 

78 

83 

87 

91 

95 

113 

82 

87 

91 

96 

1.1401 

1.1405 

1.1409 

1.1414 

1.1418 

1.1422 

1.1420 

110 

1.1413 

1.1418 

1.1422 

1.1427 

32 

30 

41 

45 

49 

53 

58 

107 

44 

49 

54 

58 

63 

67 

72 

76 

80 

85 

89 

104 

75 

80 

85 

89 

94 

99 

1.1503 

1.1507 

1.1512 

1.1516 

1.1520 

101 

1.1506 

1.1511 

1.1516 

1.1521 

1.1525 

1.1530 

34 

38 

43 

47 

51 

98 

38 

42 

47 

52 

56 

61 

65 

70 

74 

78 

82 

95 

69 

74 

78 

83 

87 

92 

96 

1.1601 

1.1605 

1.1609 

1.1613 

92 

1.1600 

1.1605 

1.1609 

1.1614 

1.1619 

1.1623 

1.1628 

32 

36 

40 

45 

89 

31 

36 

41 

45 

50 

54 

59 

63 

67 

72 

76 

86 

fi2 

67 

72 

76 

81 

85 

90 

94 

98 

1.1703 

1.1707 

83 

93 

98 

1.1703 

1.1707 

1.1712 

1.1717 

1.1721 

1.1725 

1.1730 

34 

38 

80 

1.1724 

1.1729 

34 

39 

43 

48 

52 

56 

61 

05 

69 

77 

56         60 

65 

70 

74 

79 

83 

88]        92 

961.1800 

74 

87|        91 

96 

1.1801 

1.1805 

1.1810 

1.1814 

1.1819,1.1823 

1.1827 

31 

71 

1.1818J1.1823 

1.1827 

32 

36 

41 

45 

.  50 

54 

58 

02 

68 

49         54 

58 

63 

68 

72 

77 

81 

85 

89 

94 

65 

80        85 

89         94 

99:1.1903 

1.1908 

1.1912 

1.1916 

1  19201.1925 

62 

1.1911  1.1916 

1  ipj>l 

1.1925 

1.1930 

34 

39 

43 

47 

52 

50 

59 

42 

47* 

52 

50 

61 

65 

70 

74 

78 

83 

87 

56 

73 

tS 

83 

87 

92 

96 

1.2001 

1.2005 

1.2010 

1.2014 

1.2018 

53 

1.2004 

1  f*009 

1.2014 

1.2018 

1  2023 

1.2028 

32 

36 

41 

45 

49 

50 

35 

40 

45 

50 

54 

59 

63 

67 

72 

76 

80 

47 

66 

71 

76 

81 

85 

90 

94 

98 

1.2103 

1.2107 

1.2111 

44 

981.2102 

1.2107 

1.2112 

1.2116 

1.2121 

1.2125 

1.2130 

34 

38 

42 

41 

1.2129 

33 

38 

43 

47 

52 

56 

61 

65 

69 

73 

38 

60 

64 

69 

74 

78 

83 

87 

92 

96 

1.2200 

1.2204 

35 

91 

96 

1.2200 

1.2205 

1.2209 

1.2214 

1.2218 

1.2223 

1.2227 

31 

35 

82 

1.2222 

1.2227 

31 

36 

41 

45 

49 

54 

58 

62 

67 

FACTORS   OF   EVAPORATION. 


699 


Gauge-pressures 
Ibs.  100  4- 
Absulute  Press. 
Ibs.  115. 

105  + 
120 

110  +  1  115  + 
125      1  130 

120  + 
135 

125  + 
140 

130  + 
145 

135  + 
160 

140  + 
155 

145  + 
160 

150  + 
165 

Fe^e^riter                                             FACTORS  OF  EVAPORATION. 

212° 

1.0397 

1.0407)1.0417 

1.0427 

1.0436 

1.0445 

1.0453 

1.0462  1.0470 

1.04781.0486 

209 

1.0429 

39         49 

58 

67 

76 

85 

93  '1.0501 

1.0509 

1.0517 

206 

60 

70         80 

89 

99  i  1.0508 

1.0516 

1.0525i        33 

41 

48 

203 

92 

1.0502 

1.0511 

1.0521 

1.0530 

39 

48 

56 

64 

72 

80 

200 

1.0523 

33 

43 

52 

62 

70 

79 

87 

961.0604 

1.0611 

19? 

55 

65 

74 

84 

93 

1  .0602 

1.0610 

1.0619 

1.0627 

35 

43 

194 

86 

96 

1.0606 

1.0615 

1.0624 

33 

42 

50 

58 

66 

74 

191 

1.0617 

1.0627 

37 

47 

56 

65 

73 

82 

90 

98 

1.0706 

188 

49 

59 

69 

78 

87 

96 

1.0705 

1.0713 

1.0721 

1.0729 

3? 

185 

80 

90 

1.0700 

1.0709 

1.0719 

1.072? 

36 

44 

53 

61 

68 

182 

1.0712 

1.0722 

31 

41 

50 

59 

67 

76 

84 

92 

1.0800 

179 

43 

53 

63 

72 

81 

90 

99 

1.0807 

1.0815 

1.0823 

31 

176 

74 

84 

94 

1.0803 

1.0813 

1.0821 

1.0830 

39 

47 

55 

62 

173 

1.0806 

1.0816 

1.0825 

35 

44 

53 

61 

70 

78 

86 

94 

170 

37 

47 

57 

66 

75 

84 

93 

1.0901 

1.0909 

1.0917 

1.0925 

167 

68 

78 

88 

97 

1.0907 

1.0915 

1.0924 

32 

41 

49 

56 

1(54 

1.0900 

1.0910 

1.0919 

1.0929 

38 

47 

55 

64 

72 

80 

88 

161 

31 

41 

51 

60 

69 

78 

87 

95 

1  .  1003 

1.1011 

1.1019 

158 

62 

72 

82 

91 

1.1000 

1.1009 

1.1018 

1.1026 

35 

43 

50 

155 

03 

1.1003 

1.1013 

1.1023 

32 

41 

49 

58 

66 

74 

82 

152 

1.1025 

35 

44 

54 

63 

72 

81 

89 

9? 

1.1105 

1.1113 

149 

56 

66 

76 

85 

94 

1.1103 

1.1112 

1.1120 

1.1128 

36 

44 

146 

87 

97 

1.1107 

1.1116 

1.1126 

34 

43 

51 

60 

68 

75 

i43 

1.1118 

1.1129 

38 

48 

57 

66 

74 

83 

91 

99 

1.1207 

140 

50 

60 

70 

79 

88 

9? 

1  .  1206 

1.1214 

1..1222 

1.1230 

38 

137 

81 

91 

1.1201 

1.1210 

1.1219 

1.1228 

3? 

45 

53 

61 

69 

134 

1.1212 

1.1222 

32 

41 

51 

59 

68 

76 

85 

93 

1.1300 

131 

43 

53 

63 

73 

82 

91 

99 

1.130.8 

1.1316 

1.1324 

32 

128 

75 

85 

94 

1.1304 

1.1313 

1.1322 

1.1331 

39 

47 

55 

63 

125 

1.1306 

1.1316 

1.1326 

35 

44 

53 

62 

70 

78 

86 

94 

122 

37 

47 

57 

66 

75 

84 

93 

1.1401 

1.1409 

1.1417 

1.1425 

119 

68 

78 

88 

97 

1.1407 

1.1415 

1.1424 

32 

41 

49 

56 

116 

99 

1.1409 

1.1419 

1.1429 

38 

47 

55 

64 

72 

80 

88 

113 

1.1431 

41 

50 

60 

69 

78 

86 

95 

1.1503 

1.1511 

1.1519 

110 

62 

72 

82 

9.1 

1.1500 

1.1509 

1.1518 

1.1516 

34 

42 

50 

107 

93 

1.1503 

1.1513 

1.1522 

31 

40 

49 

57 

65 

73 

81 

104 

1.1524 

34 

44 

53 

62 

71 

80 

88 

97 

1.1605 

1.1612 

101 

55 

65 

75 

84 

94 

1.1602 

1.1611 

1.1620 

1.1628 

36 

43 

98 

86 

96 

1.1606 

1.1616 

1.1625 

34 

42 

51 

59 

67 

75 

95 

1.1618 

1.1628 

37 

47 

56 

65 

73 

82 

90 

98 

1.1706 

92 

49 

50 

68 

78 

87 

96 

1.1705 

1.1713 

1.1721 

1.1729 

37 

89 

80 

90 

1.1700 

1.1709 

1.1718 

1.1727 

36 

44 

52 

60 

68 

86 

1.1711 

1.1721 

31 

40 

49 

58 

67 

75 

83 

91 

99 

83 

42 

52 

62 

71 

80 

89 

98 

1.1806 

1.1815 

1.1823 

1.1830 

80 

73 

83 

93 

1.1802 

1.1812 

1.1820 

1.1829 

37 

46 

54 

61 

77 

1.1804 

1.18.14 

1.1824 

34 

43 

52 

60 

69 

77 

85 

93 

74 

35 

45 

55 

65 

74 

83 

91 

1.1900 

1.1908 

1.1916 

1.1924 

71 

67 

77 

86 

96 

1.1905 

1.1914 

1.1922 

31 

39 

4? 

55 

68 

98 

1.1908 

1.1917 

1.1927 

36 

45 

54 

62 

70 

78 

86 

65 

1.1929 

39 

49 

58 

6£ 

76 

85 

93 

1.2001 

1.2009 

1.2017 

S2 

60 

70 

80 

89 

981.2007 

1.2016 

1.2024 

32 

40 

48 

59 

91 

1.2001 

1.2011 

1.2020 

1.2029         38 

47 

55 

63 

71 

79 

56 

1.2022 

32 

42 

51 

60         69 

78 

86 

94 

1.2102 

1.2110 

53 

53 

63 

73 

82 

91 

1.2100 

1.1209 

1.2117 

1.2126 

34 

41 

50 

84 

94 

1.2104 

1.2113 

1.2123 

31 

40 

48 

5? 

65 

72 

47 

1.2115 

1.2125 

35 

44 

54 

63 

71 

80 

88 

96 

1.2203 

44 

46 

56 

66 

76 

85 

94 

1.2202 

1.2211 

1.2219 

1  .2227 

35 

41 

77 

87 

97 

1.2207 

1.2216 

1.2225 

33 

42 

50 

58 

66 

38 

1.2208 

1.2219 

1.2228 

38 

47 

56 

64 

73 

81 

89 

97 

35 

40 

50 

59 

69  i        78         87 

95 

1.2304  1.2312 

1.2320 

1.2328 

32 

71 

81 

901.23001.2309  1.2318 

1.2326 

35         43 

51 

59 

700  THE   STEAM-BOILER. 

STRENGTH   OF   STEAM-HOIL.ERS.    VARIOUS   RUIZES 
FOR  CONSTRUCTION. 

There  is  a  great  lack  of  uniformity  in  the  rules  prescribed  by  differ- 
ent writers  and  by  legislation  governing  the  construction  of  steam-boilers 
In  the  United  States,  boilers  for  merchant  vessels  must  be  constructed  ac- 
cording to  the  rules  and  regulations  prescribed  by  the  Board  of  Supervising 
Inspectors  of  Steam  Vessels;  in  the  U.  S.  Navy,  according  to  rules  of  the 
Navy  Department,  and  in  some  cases  according  to  special  acts  of  Congress. 
On  land,  in  some  places,  as  in  Philadelphia,  the  construction  of  boilers  is 
governed  by  local  laws;  but  generally  there  are  no  laws  upon  the  subject, 
and  boilers  are  constructed  according  to  the  idea  of  individual  engineers  and 
boiler-makers.  In  Europe  the  construction  is  generally  regulated  by  strin- 
gent inspection  laws.  The  rules  of  the  U.  8.  Supervising  Inspectors  of 
Steam-  vessels,  the  British  Lloyd's  and  Board  of  Trade,  the  French  Bureau 
Veritas,  and  the  German  Lloyd's  are  ably  reviewed  in  a  paper  by  Nelson 
Foley,  M.  Inst.  Naval  Architects,  etc.,  read  at  the  Chicago  Engineering  Con- 
gress, Division  of  Marine  and  Naval  Engineering.  From  this  paper  the  fol- 
lowing notes  are  taken,  chiefly  with  reference  to  the  U.  S.  and  British  rules: 

(Abbreviations.  —  T.  S.,  for  tensile  strength;  El.,  elongation;  Contr.,  con- 
traction of  area.) 

Hydraulic  Tests.—  Board  of  Trade,  Lloyd's,  and  Bureau  Veritas.— 
Twice  the  working  pressure. 

United  States  Statutes.—  One  and  a  half  times  the  working:  pressure. 

Mr.  Foley  proposes  that  the  proof  pressure  should  be  1^  times  the  work- 
ing pressure  +  one  atmosphere. 

Established  Nominal  Factors  of  Safety.  -Board  of  Trade.— 
4.5  for  a  boiler  of  moderate  length  and  of  the  nest  construction  and  work- 
manship. 

Lloyd's.  —  Not  very  apparent,  but  appears  to  lie  between  4  and  5. 

United  States  Statutes.—  Indefinite,  because  the  strength  of  the  joint  is 
not  considered,  except  by  the  broad  distinction  between  single  and  double 
riveting. 

Bureau  Veritas:  4.4. 

German  Lloyd's:  5  to  4.65.  according  to  the  thickness  of  the  plates. 

Material  for  Riveting?.—  Board  of  Trade.—  Tensile  strength  of 
rivet  bars  between  26  and  30  tons,  el.  in  10"  not  less  than  25£,  and  contr.  of 
area  not  less  than  50$. 

Lloyd's.—  T.  S.,  26  to  30  tons;  el.  not  less  than  20#  in  8".  The  material 
must  'stand  bending  to  a  curve,  the  inner  radius  of  which  is  not  greater  than 
iy2  times  the  thickness  of  the  plate,  after  having  been  uniformly  heated  ttf- 
a  low  cherry-red,  and  quenched  in  water  at  82°  F. 

United  States  Statutes.  —  No  special  provision. 

Rules  Connected  with  Riveting.—  Board  of  Trade.—  The  shear- 
ing  resistance  of  the  rivet  steel  to  be  taken  at  23  tons  per  square  inch,  5  to 
be  used  for  the  factor  of  safety  independently  of  any  addition  to  this  factor 
for  the  plating.  Rivets  in  double  shear  to  have  only  1.75  times  the  single 
section  taken  in  the  calculation  instead  of  2.  The  diameter  must  not  be  less 
than  the  thickness  of  the  plate  and  the  pitch  never  greater  than  8*4".  The 
thickness  of  double  butt-straps  (each)  not  to  be  less  than  %  the  thickness  of 
the  plate;  single  butt-straps  not  less  than  9/8. 

Distance  from  centre  of  rivet  to  edge  of  hole  =  diameter  of  rivet  X  l^j. 

Distance  between  rows  of  rivets 


=  2  X  diam.  of  rivet  or  =  [(diam.  X  4)  -f  1]  H-  2,  if  chain,  and 

. 


4/[(  pitch  X  H)  +  (diam.  x"4)]  X  (pitch  -f  diani.  X  4)        . 
~~~ 


Diagonal  pitch  =  (pitch  X  6  -f  diam.  X  4)  -T-  10. 

Lloyd's.—  Rivets  in  double  shear  to  have  only  1.75  times  the  single  section 
taken  in  the  calculation  instead  of  2.  The  shearing  strength  of  rivet  steel  to 
be  taken  at  85^  of  the  T.  S.  of  the  material  of  shell  plates.  In  any  case 
where  the  strength  of  the  longitudinal  joint  is  satisfactorily  shown  by  ex- 
periment to  be  greater  than  given  by  the  formula,  the  actual  strength  may 
be  taken  in  the  calculation. 

United  States  Statutes—  No  rules. 

Material  for  Cyindrical  Shells  Subject  to  Internal  Pres- 
sure.— Board  of  Trade.—  T.  8.  between  27  and  32  tons.  In  the  normal  con- 
dition, el.  not  less  than  18#  in  10",  but  should  be  about  25$  ;  if  annealed,  not 


STRENGTH   OF   STEAM-BOILERS.  701 

less  than  20$.  Strips  2"  wide  should  stand  bending  until  the  sides  are 
parallel  at  a  distance  from  each  other  of  not  more  than  three  times  the 
plate's  thickness.  * 

Lloyd's.— T.  S.  between  the  limits  of  26  and  30  tons  per  square  inch.  El. 
not  less  than  20$  in  8".  Test  strips  heated  to  a  low  cherry-red  and  plunged 
into  water  at  82°  F.  must  stand  bending  to  a  curve,  the  inner  radius  of 
which  is  not  greater  than  1^  times  the  plate's  thickness. 

U.  S.  Statutes.— Plates  of  W  thick  and  under  shall  show  a  contr.  of  not 
less  than  50$:  when  over  y^'  and  up  to  %",  not  less  than  45$  ;  when  over 
%"i  n°t  less  than  40$. 

Mr.  Foley's  comments  :  The  Board  of  Trade  rules  seem  to  indicate  a  steel 
of  too  high  T.  S.  when  a  lower  and  more  ductile  one  can  be  got  :  the  lower 
tensile  limit  should  be  reduced,  and  the  bending  test  might  with  advantage 
be  made  after  tempering,  and  made  to  a  smaller  radius.  Lloyd's  rule  for 
quality  seems  more  satisfactory,  but  the  temper  test  is  not  severe.  The 
United  States  Statutes  are  not  sufficiently  stringent  to  insure  an  entirely 
satisfactory  material. 

Mr.  Foley  suggests  a  material  which  would  meet  the  following  :  25  tons 
lower  limit  in  tension  ;  25$  in  8"  minimum  elongation  ;  radius  for  bending 
test  after  tempering  =  the  plate's  thickness. 

Shell-plate  Formulse.-#oa?-c/  of  Trade :  P  =      X D  * F . 

D  —  diameter  of  boiler  in  inches  ; 
P  —  working-pressure  in  Ibs.  per  square  inch  ; 
t  =  thickness  in  inches  ; 

B  —  percentage  of  strength  of  joint  compared  to  solid  plate  ; 
T  —  tensile  strength  allowed  for  the  material  in  Ibs.  per  square  inch  ; 
F  —  a  factor  of  safety,  being  4.5,  with  certain  additions  depending  on 
method  of  construction. 

C  X  (t  -  2)  X  B 
Lloyd's  :  P  = — — . 

t  =  thickness  of  plate  in  sixteenths  ;  B  and  D  as  before;  C  =  a  constant 
depending  on  the  kind  of  joint. 

When  longitudinal  seams  have  double  butt-straps,  C  =  20.  When  longi- 
tudinal seams  have  double  butt-straps  of  unequal  width,  only  covering  on 
one  side  the  red  need  section  of  plate  at  the  outer  line  of  rivets,  C  =  19.5. 

When  the  longitudinal  seams  are  lap-jointed,  C  =  18.5. 

U.  IS.  Statutes.— Using  same  notation  as  for  Board  of  Trade, 

t  X  2  X  T 
P  =   r-£ — _ _  for  single-riveting  ;  add  20$  for  double -riveting  ; 

J-J  X  6 
where  T  is  the  lowest  T.  S.  stamped  on  any  plate. 

Mr.  Foley  criticises  the  rule  of  the  United  States  Statutes  as  follows  :  The 
rule  ignores  the  riveting,  except  that  it  distinguishes  between  single  and 
double,  giving  the  latter  20$  advantage:  the  circumferential  riveting  or 
class  of  seam  is  altogether  ignored.  The  rule  takes  no  account  of  workman- 
ship or  method  adopted  of  constructing  the  joints.  The  factor,  one  sixth, 
simply  covers  the  actual  nominal  factor  of  safety  as  well  as  the  loss  of 
strength  at  the  joint,  no  matter  what  its  percentage  ;  we  may  therefore 
dismiss  it  as  unsatisfactory. 

C(t  +  1  )2 

Rules  for  Flat  Plates.—  Board  of  Trade  ;  P=  —$-—£-  • 

•P  =  wot  king  pressure  in  Ibs.  per  square  inch; 
S=  surface  supported  in  square  inches; 
t  =  thickness  in  sixteenths  of  an  inch; 
C  =  a  constant  as  per  following  table: 

C  =  125  for  plates  not  exposed  to  heat  or  flame,  the  stays  fitted  with  nuts 
and  washers,  the  latter  at  least  three  times  the  diameter  of  the  stay 
and  %  the  thickness  of  the  plate; 
C  =  187.5  for  the  same  condition,  but  the  washers  %  the  pitch  of  stays  in 

diameter,  and  thickness  not  less  than  plate; 

C  =  200  for  the  same  condition,  but  doubling  plates  in  place  of  washers,  the 
width  of  which  is  %  the  pitch  and  thickness  the  same  as  the  plate; 


702  THE    STEAM-BOILER. 

C  =  67.5  for  the.  same  condition,  but  stays  fitted  with  nuts  only; 

C  =  100  when  exposed  to  heat  or  flame,  and  water  in  contact  with  the  plates, 

and  stays  screwed  into  the  plates  and  fitted  with  nuts; 
C  =  66  for  the  same  condition,  but  stays  with  riveted  heads. 

C  X  t 
U.  S.  Statutes.—  Using  same  notation  as  for  Board  of  Trade.    P  =  -  —  » 

where  p  =  greatest  pitch  in  inches,  P  and  t  as  above; 

C  =  112  for  plates  7/16"  thick  and  under,  fitted  with  screw  stay-bolts 

and  nuts,  or  plain  bolt  fitted  with  single  nut  and  socket,  or 

riveted  head  and  socket; 

C  =  120  for  plates  above  7/1  6",  under  the  same  conditions; 
C  —•  140  for  flat  surfaces  where  the  stays  are  fitted  with  nuts  inside 

and  outside: 
C  =  200  for  flat  surfaces  under  the  same  condition,  but  with  the  addi- 

tion of  a  washer  riveted  to  the  plate  at  least  ^£  plate's  thick- 

ness, and  of  a  diameter  equal  to  2/5  pitch. 

N.B.—  Plates  fitted  with  double  angle-irons  and  riveted  to  plate,  with  leaf 
at  least%  the  thickness  of  plate  and  depth  at  least  14  of  pitch,  would  be 
allowed  the  same  pressure  as  determined  by  formula  for  plate  with  washer 
riveted  on. 

N.B.—  No  brace  or  stay-bolt  used  in  marine  boilers  to  have  a  greater  pitch 
than  10*4"  on  fire-boxes  and  back  connections. 

Certain  experiments  were  carried  out  by  the  Board  of  Trade  which  showed 
that  the  resistance  to  bulging  does  not  vary  as  the  square  of  the  plate's 
thickness.  There  seems  also  good  reason  to  believe  that  it  is  not  inversely 
as  the  square  of  the  greatest  pitch.  Bearing  in  mind,  says  Mr.  Foley,  that 
mathematicians  have  signally  failed  to  give  us  true  theoretical  foundations 
for  calculating  the  resistance  of  bodies  subject  to  the  simplest  forms  of 
stresses,  we  therefore  cannot  expect  much  from  their  assistance  in  the 
matter  of  flat  plates. 

The  Board  of  Trade  rules  for  flat  surfaces,  being  based  on  actual  experi- 
ment, are  especially  worthy  of  respect;  sound  judgment  appears  also  to 
have  been  used  in  framing  them. 

Furnace  Formulae.—  BOARD  OP  TRADE.—  Long  Furnaces.— 

C  X  /2 
P=  —  -  --  =r,  but  not  where  L  is  shorter  than  (11.  5£  —  1),  at  which  length 

(L  -\-  1)  X  D 
the  rule  for  short  furnaces  comes  into  play. 

P  =  working-pressure  in  pounds  per  square  inch;  t  =  thickness  in  inches; 
D  =  outside  diameter  in  inches;  L  —  length  of  furnace  in  feet  up  to  10  ft.; 
C  =  a  constant,  as  per  following  table,  for  drilled  holes  : 

C  =  99,000  for  welded    or    butt-jointed  with    single    straps,  double- 

riveted; 

C  =  88,000  for  butts  with  single  straps,  single-riveted; 
C  =  99,000  for  butts  with  double  straps,  single-riveted. 

Provided  always  that  the  pressure  so  found  does  not  exceed  that  given  by 
the  following  formulae,  which  apply  also  to  short  furnaces  : 

C1  x  t 
P  =  —  —  —  for  all  the  patent  furnaces  named; 


C1  V  t  /          7"  X  1  *•* 


*•*  "\ 

~t  )  wnen  with  Adarnson  rings. 
*f 


—          r  < 

o  X  "\         of..)  X 

C-    8,800  for  plain  furnaces; 

C  =  14,000  for  Fox;  minimum  thickness  5/16",  greatest  %";  plain  part 

not  to  exceed  6"  in  length; 
C  =  13,500  for  Morison:  minimum  thickness  5/16",  greatest  %'';  plain 

part  not  to  exceed  6"  in  length  : 
C  =  14,000  for  Purves-Brown;  limits  of  thickness  7/16"  and  %";  plain 

part  9"  in  length; 
C  =    8,800  for  Adamson  rings;  radius  of  'flange  next  fire  1>£". 

U.  S.  STATUTES.—  Long  Furnaces.—  Same  notation. 

P  =  —  '—  --  FT™»  but  L  not  to  exceed  8  ft. 
L  X  O 

N.B.  —  If  rings  of  wrought  iron  are  fit£ed  and  riveted  on  properly  around 
and  to  the  flue  in  such  a  manner  that  the  tenaile  stress  on  the  rivets  shall 


STRENGTH   OF   STEAM-BOILERS.  703 

not  exceed  6000  Ibs.  per  sq.  in.,  the  distance  between  the  rings  shall  be  taken 
as  the  length  of  the  flue  in  the  formulae. 
Short    Furnaces,    Plain    and   Patent.— P,    as   before,    when    not   8  ft. 

89,600  X  J2 
long=      LXD     ; 
P  =  L*-£  when 

C  —  14,000  for  Fox  corrugations  where  D  —  mean  diameter; 
C  =  14.000  for  Purves-Brown    where  D  =  diameter  of  flue; 
C  =  5677  for  plain  flues  over  16"  diameter  and  less  than  40",  when 
not  over  3  ft.  lengths. 

Mr.  Foley  comments  on  the  rules  for  long  furnaces  as  follows:  The  Board 
of  Trade  general  formula,  where  the  length  is  a  f  tic  tor,  has  a  very  limited 
range  indeed,  viz.,  10  ft.  as  the  extreme  length,  and  135  thicknesses  —  12", 

(7x  £2 
as  the  short  limit.     The  original  formula,  P  =  - — - ,  is  that  of  Sir  W. 

Fairbairn,  and  was,  I  believe,  never  intended  by  him  to  apply  to  short  fur- 
naces. On  the  very  face  of  it,  it  is  apparent,  on  the  other  hand,  that  if  it  is 
true  for  moderately  long  furnaces,  it  cannot  be  so  for  very  long  ones.  We 
are  therefore  driven  to  the  conclusion  that  any  formula  which  includes 
simple  L  as  a  factor  must  be  founded  on  a  wrong  basis. 

With  Mr.  Traill's  form  of  the  formula,  namely,  substituting  (L  -f  1)  for  L, 
the  results  appear  sufficiently  satisfactory  for  practical  purposes,  and  in- 
deed, as  far  as  can  be  judged,  tally  with  the  results  obtained  from  experi- 
ment as  nearly  as  could  be  expected.  The  experiments  to  which  I  refer 
were  six  in  number,  and  of  great  variety  of  length  to  diameter;  the  actual 
factors  of  safety  ranged  from  4.4  to  6.2,  the  mean  being  4.78,  or  practically 
5.  It  seems  tome,  therefore,  that,  within  the  limits  prescribed,  the  Board  of 
Trade  formula  may  be  accepted  as  suitable  for  our  requirements. 

The  United  States  Statutes  give  Fairbairn's  rule  pure  and  simple,  except 
that  the  extreme  limit  of  length  to  which  it  applies  is  fixed  at  8  feet.  As 
far  as  can  be  seen,  no  limit  for  the  shortest  length  is  prescribed,  but  the 
rules  to  me  are  by  no  means  clear,  flues  and  furnaces  being  mixed  or  not 
well  distinguished. 

Material  for  Stays.— The  qualities  of  material  prescribed  are  as 
follows: 

Board  of  Trade.— The  tensile  strength  to  lie  between  the  limits  of  27  and 
32  tons  per  square  inch,  and  to  have  an  elongation  of  not  less  than  20$  in 
10".  Steel  stays  which  have  been  welded  or  worked  in  the  fire  should  not 
be  used. 

Lloyd's.— 26  to  30  ton  steel,  with  elongation  not  less  than  20$  in  8". 

U.  8.  Statutes.— The  only  condition  is  that  the  reduction  of  area  must  not 
be  less  than  40$  if  the  test  bar  is  over  %"  diameter. 

Loads  allowed  on  Stays.—  Board  of  Trade.— 9000  Ibs.  per  square 
inch  is  allowed  on  the  net  section,  provided  the  tensile  strength  ranges  from 
27  to  32  tons.  Steel  stays  are  not  to  be  welded  or  worked  in  the  fire. 

Lloyd's.— For  screwed  and  other  stays,  not  exceeding  1^"  diameter  effec- 
tive, 8000  Ibs.  per  square  inch  is  allowed;  for  stays  above  1^",  9000  Ibs.  No 
stays  are  to  be  welded. 

U.  S.  Statutes. — Braces  and  stays  shall  not  be  subjected  to  a  greater  stress 
than  6000  Ibs.  per  square  inch. 

[Rankine,  S.  E.,  p.  459,  says:  "The  iron  of  the  stays  ought  not  to  be  ex- 
posed to  a  greater  working  tension  than  3000  Ibs.  on  the  square  inch,  in 
order  to  provide  against  their  being  weakened  by  corrosion.  This  amounts 
to  making  the  factor  of  safety  for  the  working  pressure  about  20."  It  is 
evident,  however,  that  an  allowance  in  the  factor  of  safety  for  corrosion  may 
reasonably  be  decreased  with  increase  of  diameter.  W.  K.] 

/~i  -y   .-72  y   f- 

(   Girders.—  Board  of  Trade.    P=         *       *  P  =  working  pres- 

(  VY  —  IP)*-)  X  -Li 

sure  in  Ibs.  per  sq.  in.;  W  =  width  of  flame-box  in  inches;  L  —  length  of 
girder  in  inches;  p  —  pitch  of  bolts  in  inches;  D  =  distance  between  girders 
from  centre  to  centre  in  inches;  d  =  depth  of  girder  in  inches;  t  =  thick- 
ness of  sum  of  same  in  inches;  C  =  a  constant  =  6600  for  1  bolt,  9900  for  2 
or  3  bolts,  and  11,220  for  4  bolts. 

Lloyd's.—  The  same  formula  and  constants,  except  that  C  =  11,000  for  4  or 
5  bolts,  11,550  for  6  or  7,  and  11,880  for  8  or  more. 

U.  8.  Statutes.— The  matter  appears  to  be  left  to  the  designers. 


704  THE   STEAM-BOILER. 

Tube-Flates.-/?oarrf   of   Trade.     P  =  t<D  ~£'.     D  =  least 

horizontal  distance  between  centres  of  tubes  in  inches;  d  —  inside  diameter 
of  ordinary  tubes;  t  —  thickness  of  tube-plate  in  inches;  W  —  extreme 
width  of  combustion-box  in  inches  f rom  front  tube-plate  to  back  of  fire- 
box, or  distance  between  combustion-box  tube-plates  when  the  boiler  is 
double-ended  and  the  box  common  to  both  ends. 

The  crushing  stress  on  tube-plates  caused  by  the  pressure  on  the  flame- 
box  top  is  to  be  limited  to  10,000  Jbs.  per  square  inch. 

Material  for  Tubes.  -Mr.  Foley  proposes  the  following:  If  iron,  the 
quality  to  be  such  as  to  give  at  least  22  tons  per  square  inch  as  the  minimum 
tensile  strength,  with  an  elongation  of  not  less  than  15$  in  8".  If  steel,  the 
elongation  to  be  not  less  than  26%  in  8"  for  the  material  before  being  rolled 
into  strips;  and  after  tempering,  the  test  bar  to  stand  completely  closing 
together.  Provided  the  steel  welds  well,  there  does  not  seem  to  be  any  ob- 
ject in  providing  tensile  limits. 

The  ends  should  be  annealed  after  manufacture,  and  stay-tube  ends  should 
be  annealed  before  screwing. 

Holding-power  of  Boiler-tubes.— Experiments  made  in  Wash- 
ington Navy  Yard  show  that  wii  h  2*4  in-  brass  tubes  in  no  case  was  the  holding- 
power  less,  roughly  speaking,  than  6000  Ibs.,  while  the  average  was  upwards 
of  20,000  Ibs.  It  was  further  shown  that  with  these  tubes  nuts  were  snper- 
fluous,  quite  as  good  results  being  obtained  with  tubes  simply  expanded  into 
the  tube-plate  and  fitted  with  a  ferrule.  When  nuts  were  fitted  it  was  shown 
that  they  drew  off  without  injuring  the  threads. 

In  Messrs.  Yarrow's  experiments  on  iron  and  steel  tubes  of  2"  to  2*4" 
diameter  the  first  5  tubes  gave  way  on  an  average  of  23,740  Ibs.,  which  would 
appear  to  be  about  %  the  ultimate  strength  of  the  tubes  themselves.  In  all 
these  cases  the  hole  through  the  tube-plate  was  parallel  with  a  sharp  edge 
to  it,  and  a  ferrule  was  driven  into  the  tube. 

Tests  of  the  next  5  tubes  were  made  under  the  same  conditions  as  the  first 
5,  with  the  exception  that  in  this  case  the  ferrule  was  omitted,  the  tubes  be- 
ing simply  expanded  into  the  plates.  The  mean  pull  required  was  15,270  Ibs., 
or  considerably  less  than  half  the  ultimate  strength  of  the  tubes. 

Effect  of  beading  the  tubes,  the  holes  through  the  plate  being  parallel  and 
ferrules  omitted.  The  mean  of  the  first  3,  which  are  tubes  of  the  same 
kind,  gives  26,876  Ibs.  as  their  holding-power,  under  these  conditions,  as  com- 
pared with  23,740  Ibs.  for  the  tubes  fitted  with  ferrules  only.  This  high 
figure  is,  however,  mainly  due  to  an  exceptional  case  where  the  holding- 
power  is  greater  than  the  average  strength  of  the  tubes  themselves. 

It  is  disadvantageous  to  cone  the  hole  through  the  tube-plate  unless  its 
sharp  edge  is  removed,  as  the  results  are  much  worse  than  those  obtained 
with  parallel  holes,  the  mean  pull  being  but  U5.031  Ibs.,  the  experiments  be- 
ing made  with  tubes  expanded  and  fer ruled  but  not  beaded  over. 

In  experiments  on  tubes  expanded  into  tapered  holes,  beaded  over  and 
fitted  with  ferrules,  the  net  result  is  that  the  holding-power  is,  for  the  size 
experimented  on,  about  %  of  the  tensile  strength  of  the  tube,  the  mean  pull 
being  28,797  Ibs. 

With  tubes  expanded  into  tapered  holes  and  simply  beaded  over,  better 
results  were  obtained  than  with  ferrules;  in  these  cases,  however,  the  sharp 
edge  of  the  hole  was  rounded  off,  which  appears  in  general  to  have  a  good 
effect. 

In  one  particular  the  experiments  are  incomplete,  as  it  is  impossible  to 
reproduce  on  a  machine  the  racking  the  tubes  get  by  the  expansion  of  a 
boiler  as  it  is  heated  up  and  cooled  down  again,  and  it  is  quite  possible, 
therefore,  that  the  fastening  giving  the  best  results  on  the  testing-machine 
may  not  prove  so  efficient  in  practice. 

N.B.— It  should  be  noted  that  the  experiments  were  all  made  under  the 
cold  condition,  so  that  reference  should  be  made  with  caution,  the  circum- 
stances in  practice  being  very  different,  especially  when  there  is  scale  on 
the  tube-plates,  or  when  the  tube -plates  are  thick  and  subject  to  intense 
heat. 

Iron  versus  Steel  Boiler-tubes.  (Foley.)  — Mr.  Blechynden 
prefers  iron  tubes  to  those  of  steel,  but  how  far  he  would  go  in  attributing 
the  leaky-tube  defect  to  the  use  of  steel  tubes  we  are  not  aware.  It  appeal's, 
however,  that  the  results  of  his  experiments  would  warrant  him  in  going  a 
considerable  distance  in  this  direction.  The  test  consisted  of  heating  and 
cooling  two  tubes,  one  of  wrought  iron  and  the  other  of  steel.  Both  tubes 
were  2%  in.  in  diameter  and  .16  in.  thickness  of  metal.  The  tubes  were 


e 
...     parts  of  boiler  which  are  subject  to 
I     tensile  strain  a  test  piece  prepared 
in  form  according  to  the  following 


STRENGTH    OF   STEAM-BOILERS.  705 

put  in  the  same  furnace,  made  red-hot,  and  then  dipped  in  water.    The 
length  was  gauged  at  a  temperature  of  46°  F. 
This  operation  was  twice  repeated,  with  results  as  follows  : 

Steel.  Iron. 

Original  length  ................................     55.495  in.  55.495  in. 

Heated  to  186°  F.;  increase  .........  ..........  052"  .048  " 

Coefficient  of  expansion  per  degree  F  .........  0000067  .0000062 

Heated  red-hot  and  dipped  in  water;  decrease       .00?  in.  .003  in. 

Second  heating  and  cooling,  decrease  .........  031  in.  .004  in. 

Third  heating  and  cooling,  decrease  ..........  017  in.  .006  in. 

Total  contraction  ........................  055  in.  .013  in. 

Mr.  A.  C.  Kirk  writes  :  That  overheating  of  tube  ends  is  the  cause  of  the 
leakage  of  the  tubes  in  boilers  is  proved  by  the  fact  that  the  ferrules  at 
present  used  by  the  Admiralty  prevent  it.  These  act  by  shielding  the  tube 
ends  from  the  action  of  the  flame,  and  consequently  reducing  evaporation, 
and  so  allowing  free  access  of  the  water  to  keep  them  cool. 

Although  many  causes  contribute,  there  seems  no  doubt  that  thick  tube- 
plates  must  bear  a  share  of  causing  the  mischief. 

Rules  for  Construction  of  Boilers   in  Merchant  Vessels 
in  the  United  States. 

(Extracts  from  General  Rules  and  Regulations  of  the  Board  of  Supervising 

Inspectors  of  Steam  -vessels  (as  amended  1893  and  1894).) 
Tensile  Strength  of  Plate.    (Section  3.)—  To  ascertain  the  tensile 

strength  and  other  qualities  of  iron  plate  there  shall  be  taken  from  each 

sheet  to  be  used  in  shell  or  other 
parts  of  boiler  which  are  subject  to 
tensile  strain  a  test  piece  prepared 
in  form  according  to  the  following 
diagram,  viz.:  10  inches  in  length,  2 
inches  in  width,  cut  out  in  the 
centre  in  the  manner  indicated. 
To  ascertain  the  tensile  strength 

and  other  qualities  of  steel  plate,  there  shall  be  taken  from  each  sheet  to  be 

used  in  shell  or  other  parts  of  boiler  which  are  subject  to  tensile  strain,  a  test- 

piece  prepared  in  form  according 

to  the  following  diagram,  the  length 

of  straight  part  in  centre  yawing-  as 

called  for  by  different  thickness  of 

material,  as  follows: 
The  straight  portion  shall  be  in 

,] 

ai 
inch.    This  rule  to  take  effect  on  and  after  July  1,  _____ 

Provided,  that  where  contracts  for  boilers  for  ocean-going  steamers  re- 
quire a  test  of  material  in  compliance  with  the  British  Board  of  Trade. 
British  Lloyd's,  or  Bureau  Veritas  rules  for  testing,  the  inspectors  shall 
make  the  tests  in  compliance  with  the  following  rules: 

Steel  plates  shall  in  all  cases  to  have  an  ultimate  elongation  not  less  than  20% 
in  a  length  of  8  inches.  It  is  to  be  capable  of  being  bent  to  a  curve  of  which 
the  inner  radius  is  not  greater  than  one  and  a  half  times  the  thickness  of 
the  plates  after  having  been  heated  uniformly  to  a  low  cherry-red,  and 
quenched  in  water  of  82°  F. 

[Prior  to  1894  the  shape  of  test-piece  for  steel  was  the  same  as  that  for  iron, 
viz.,  the  grooved  shape.  This  shape  has  been  condemned  by  authorities  on 
strength  of  materials  for  over  twenty  years.  It  always  gives  results  which 
are  too  high,  the  error  sometimes  amounting  to  25  per  cent.  See  pages  242, 
243,  ante;  also,  Strength  of  Materials,  W.  Kent,  Van  N.  Science  Series  No.  41, 
and  Beardslee  on  Wrought-iron  and  Chain  Cables.] 

Ductility.  (Section  6.)—  To  ascertain  the  ductility  and  other  lawful 
qualities,  iron  of  45,000  Ibs.  tensile  strength  shall  show  a  contraction  of  area 
of  15  per  cent,  and  each  additional  1000  Ibs.  tensile  strength  shall  show  1 
per  cent  additional  contraction  of  area,  up  to  and  including  55,000  tensile 
strength.  Iron  of  55,000  tensile  strength  and  upwards,  showing  25  per  cent 
reduction  of  area,  shall  be  deemed  to  have  the  lawful  ductility.  All  steel 
plate  of  y%  inch  thickness  and  under  shall  show  a  contraction  of  area  of  not 
less  than  50  per  cent.  Steel  plate  over  ^  inch  in  thickness,  up  to  %  inch  in 


... 
I 
I 
I 
| 
.  —  ->j 


706 


THE    STEAM-BOILER. 


thickness,  shall  show  a  reduction  of  not  less  than  45  per  cent.  All  steel  plate 
over  §4  inch  thickness  shall  show  a  reduction  of  not  less  than  40  per  cent. 

Bumped  Heads  of  Boilers.  (Section' 17  as  amended  ~  1894.)  — 
Pressure  Allowed  on  Bumped  Heads.— Multiply  the  thickness  of  the  plate 
by  one  sixth  of  the  tensile  strength,  and  divide  by  six  tenths  of  the  radius  to 
which  head  is  bumped,  which  will  give  the  pressure  per  square  inch  of 
steam  allowed. 

Pressure  Allowable  for  Concaved  Heads  of  Boilers—  Multiply  the  pressure 
per  square  inch  allowable  for  bumped  heads  attached  to  boilers  or  drums 
convexly,  by  the  constant  .6,  and  the  product  will  give  the  pressure  per 
square  inch' allowable  in  concaved  heads. 

Tlie  pressure  on  unstayed  flat-Reads  on  steam-drums  or  shells 
of  boilers,  when  flanged  and  made  of  wrought  iron  or  steel  or  of  cast  steel, 
shall  be  determined  by  the  following  rule: 

The  thickness  of  plate  in  inches  multiplied  by  one  sixth  of  its  tensile 
strength  in  pounds,  which  product  divided  by  the  area  of  the  head  in  square 
inches  multiplied  by  .09  will  give  pressure  per  square  inch  allowed.  The 
material  used  in  the  construction  of  flat-heads  when  tensile  strength  has 
not  been  officially  determined  shall  be  deemed  to  have  a  tensile  strength  of 
45,000  Ibs. 

Table  of  Pressures  allowable  on  Steam-boilers  made  of 
Riveted  Iron  or  Steel  Plates. 

(Abstract  from  a  table  published  in  Rules  and  Regulations  of  the  U.  S. 

Board  of  Supervising  Inspectors  of  Steam-vessels.) 

Plates  Y±  inch  thick.  For  other  thicknesses,  multiply  by  the  ratio  of  the 
thickness  to  J4  inch. 


°  «> 

50,000  Tensile 
Strength. 

55.000  Tensile 
Strength. 

60.000  Tensile 
Strength. 

65.000  Tensile 
Strength. 

70,000  Tensile 
Strength. 

«.y 

2 

•5 

2 

7j 

oi 

JM 

"3 

<D 

,3 

8 

13 

e.s 

a 

^o 

3 

05 

<2 

S 

en 

3.1 

3 
CG 

ij 

"*m 

£ 

t~3 

2 

Vt^rt 

£ 

v^ 

2 

t'B 

S 

v.^ 

fa 

OH 

§ 

PH 

?t 

PH 

PH 

c^ 

36 

115.74 

138.88 

127.31 

152.77 

138.88 

166.65 

150.46 

180.55 

162.03 

194.43 

38 

109.64 

131.56 

120.61 

144.73 

131.57 

157.88 

142.54 

171.04 

153.5 

184.20 

40 

104.16 

124.99 

114.58 

137.49 

125 

150 

135.41 

162.49 

145.83 

174.99 

42 

99.2 

119.04 

109.12 

130.94 

119.04 

142  81 

128.96 

154.75 

138.88 

166.65 

44 

94.69 

113.62 

104.16 

124.99 

113.63 

136.35 

123.1 

147.72 

132.56 

159.07 

46 

90.57 

108.08 

99.63 

119.55 

108.69 

130.42 

117.75 

141.3 

126.8 

152.16 

48 

86.8 

104.16 

95.48 

114.57 

104.16 

121.99 

112.84 

135.4 

121.52 

145.82 

54 

77.16 

92.59 

84.87 

101.84 

92.59 

111.10 

100.3 

120.36 

108.02 

129.62 

60 

69.44 

83.32 

76  38 

91.65 

83.33 

99.99 

90.27 

108.32 

97.22 

116.66 

66 

63.13 

75  .  75 

69.44 

83.32 

75.75 

90.90 

82.07 

98.48 

88.37 

106.04 

72 

57.87 

69.44 

63.65 

76.38 

69  44 

83.32 

75.22 

90.26 

81.01 

97.21 

78 

53.41 

64.09 

58.76 

70.5 

64.4 

76.92 

69.44 

83.32 

74.78 

89.73 

84 

49.6 

59.52 

54.56 

65.47 

59.52 

71.42 

64.48 

77.37 

69.44 

83.32 

90 

46.29 

55.44 

50.92 

61.1 

55.55 

66.66 

60.18 

72  21 

64.81 

77  77 

96 

43.4 

52.08 

47.74 

57.28 

52.08 

62.49 

56.42 

67.67 

60.76 

72.91 

The  figures  under  the  columns  headed  "  pressure"  are  for  single-riveted 
boilers.  Those  under  the  columns  headed  "  20$  Additional1'  are  for  double- 
riveted. 

U.  S.  RULE  FOR  ALLOWABLE  PRESSURES. 

The  pressure  of  any  dimension  of  boilers  not  found  in  the  table  annexed 
to  these  rules  must  be  ascertained  by  the  following  rule: 

Multiply  one  sixth  of  the  lowest 'tensile  strength  found  stamped  on  any 
plate  in  the  cylindrical  shell  by  the  thickness  (expressed  in  inches  or  parts 
of  an  inch)  of  the  thinnest  plate  in  the  same  cylindrical  shell,  and  divide  by 
the  radius  or  half  diameter  (also  expressed  in  inches),  the  quotient  will  be 
the  pressure  allowable  per  square  inch  of  surface  for  single-riveting,  to 
which  add  twenty  per  centum  for  double-riveting. 

The  author  desires  to  express  his  condemnation  of  the  above  rule,  and  of 
the  tables  derived  from  it,  as  giving  too  low  a  factor  of  safety.  (See  also 
criticism  by  Mr.  Foley,  page  701,  ante.) 


STRENGTH    OF    STEAM-BOIL  EKiS. 


;or 


If  r*&  =  bursting-pressure,  t  =  thickness,   T  —  tensile  strength,  c  —  coef- 
ficient of  strength  of  riveted  joint,  that  is,  ratio  of  strength  of  the  joint  to 

that  of  the  solid  plate,  d  =  diameter,  P&  =  -—  -  ',  or  if  c  be  taken  for  double- 

1  4tT 

riveting  at  0.7,  then  Pb  =  —  =  —  . 
a 


By  the  U.  S.  rule  the  allowable  pressure  Pa 


X  1.20  = 


0  4/T7 


whence 


, 

Pb  =  3.5Pa;  that  is,  the  factor  of  safety  is  only  3.5,  provided  the  "tensile 
strength  found  stamped  in  the  plate  "  is  the  real  tensile  strength  of  the 
material.  But  in  the  case  of  iron  plates,  since  the  stamped  T.S.  is  obtained 
from  a  grooved  specimen,  it  may  be  greatly  in  excess  of  the  real  T.S.,  which 
would  make  the  factor  of  safety  still  lower.  According  to  the  table,  a  boiler 
40  in.  diam.,  %  in-  thick,  made  of  iron  stamped  60,000  T.S.,  would  be  licensed 
to  carry  150  Ibs.  pressure  if  double-riveted.  If  the  real  T.S.  is  only  50,000  Ibs. 
the  calculated  bursting-strength  would  be 


P  = 


2tTc       2  X  50,000  X  .25  X  .70 


d 


40 


and  the  factor  of  safety  only  437.5  -*-  150  =  2.91  ! 
The  author"1  s  formula  for  safe  working-pressure  of  externally  -fired  boilers 

with  longitudinal  seams  double-riveted,  is  P=  •—  —  ;  t  =  37;  P  =  gauge- 


— 

pressure  in  Ibs.  per  sq.  in.;  t  =  thickness  and  d  =  diam.  in  inches. 

2tTc 
This  is  derived  from  the  formula  P  =  —  -,  taking  c  at  0.7  and  /  =  5  for 

steel  of  50,000  Ibs.  T.S.,  or  6  for  60,000  Ibs.  T.S.;  the  factor  of  safety  being 
increased  in  the  ratio  of  the  T.S.,  since  with  the  higher  T.S.  there  is  greater 
danger  of  cracking  at  the  rivet-holes  from  the  effect  of  punching  and  rivet- 
ing and  of  expansion  and  contraction  caused  by  variations  of  temperature. 
For  external  shells  of  internally-fired  boilers,  these  shells  not  being  exposed 
to  the  fire,  with  rivet-holes  drilled  or  reamed  after  punching,  a  lower  factor 

le. 

would  give  a  factor  of 


of  safety  and  steel  of  a  higher  T.S.  may  be  allowable. 
If  the  T.S.  is  60,000,  a  working  pressure  P  = 


safety  of  5.25. 

The  following  table  gives  safe  working  pressures  for  different  diameters 
of  shell  and  thicknesses  of  plate  calculated  from  the  author's  formula. 

Safe  Working  Pressures  in  Cylindrical  Shells  of  Boilers, 
Tanks,  Pipes,  etc.,  in  Pounds  per  Square  Inch. 


Longitudinal  seams  double-riveted. 
(Calculated  from  formula  P=  14,000  X  thickness  - 


-  diameter.) 


W    O  _£H 

III 

Diameter  in  Inches. 

24 

30 

36 

38 

40 

42 

44 

46 

48 

50 

52 

1 

36.5 

29.2 

24.3 

23.0 

21.9 

20.8 

19.9 

19.0 

18.2 

17.5 

16  8 

2 

72.9 

58.3 

48.6 

46.1 

43.8 

41.7 

39.8 

38.0 

36.5 

25.0 

33.7 

3 

109.4 

87.5 

72.9 

69.1 

65.6 

62.5 

59.7 

57.1 

54.7 

52.5 

50.5 

4 

145.8!  116.7 

97.2 

92.1 

87.5 

83.3 

79.5 

76.1 

72  9 

70.0 

67.3 

5 

182.3 

145.8 

121.5 

115.1 

109.4 

104.2 

99.4 

95.1 

9l!l 

87.5 

84.1 

6 

218.7 

175.0 

145.8 

138.2 

131.3 

125.0 

119.3 

114.1 

109.4 

105.0 

101.0 

255.2 

204.1 

170.1 

161.2 

153.1 

145.9 

139.2 

133.2 

127.6 

122.5 

117.8 

8 

291.7 

233.3 

194.4 

184.2 

175.0 

166.7 

159.1 

152.2 

145.8 

140.0 

134.6 

9 

328.1 

262.5 

218.§ 

207.2 

196.9 

187.5 

179.0 

171.2 

164.1 

157.5 

151.4 

10 

364.6 

291.7 

243.1 

230.3 

218.8 

208.3 

198.9 

190.2 

182.3 

175.0 

168.3 

11 

401.0 

320.8 

267.4 

253.3 

240.6 

229.2 

218.7 

209.2 

200.5 

192.5 

185.1 

12 

437.5 

350.0 

291.7 

276.3 

262.5 

250.0 

238.6 

228.3 

218.7 

210.0 

201.9 

13 

473.9 

379.2 

316.0 

299.3 

284.4 

270.9 

258.5 

247.3 

337.0 

227.5 

218.8 

14 

410.4 

408.3 

340.3 

322.4 

306.3 

291.7 

278.4 

266.3 

255.2 

245.0 

235.6 

15 

546.9 

437.5 

364.6 

345.4 

328.1 

312.5 

298.3 

285.3 

273.4 

266.5 

252.4 

16 

583.3 

466.7 

388.  9'  3(58.4 

350.0 

333.3 

318.2 

304.4 

291.7 

280.0 

269.2 

708 


THE   STEAM-BOILER. 


Ill 

Diameter  in  Inches. 

y  Si—  i 

iiS 

54 

60 

66 

72 

78 

84 

90 

96 

102 

108 

114 

.120 

1 

16.2 

14.6 

13.3 

12.2 

11.2 

10.4 

9.7 

9.1 

8.6 

8.1 

7.r 

7.3 

2 

32.4 

29.2 

26.5 

24.3 

22.4 

20.8 

19.4 

18.2 

17.2 

16.2 

15  4 

14.6 

3 

48.6 

43.7 

39.8 

36.5 

33.7 

31.3 

29.2 

27.3 

25.7 

24.3 

23  0 

21.9 

4 

64.8 

58.3 

53.0 

48.6 

44.9 

41.7 

38.9 

36.5 

34.3 

32.4 

30.7 

29.2 

5 

81.0 

72.9 

66.3 

60.8 

56.1 

52.1 

48.6 

45.6 

42.9 

40.5 

38.4 

36.5 

6 

97.2 

87.5 

79.5 

72.9 

67.3 

62.5 

58.3 

54.7 

51.5 

48.6 

46.1 

43.8 

7 

113.4 

102.1 

92.8 

85.1 

78.5 

72.9 

68.1 

63.8 

60.0 

56.7 

53.7 

51.0 

8 

129.6 

116.7 

106.1 

97.2 

89.7 

83.3 

77.8 

72.9 

68.6 

64.8 

61.4 

58.3 

9 

145.8 

131.2 

119.3 

109.4 

101.0 

93.8 

87.5 

82.0 

77.2 

72.9 

69.1 

65.6 

10 

162.0 

145.8 

132.6 

121.5 

112.2 

104.2 

97.2 

91.1 

85.8 

81.0 

7'6.8 

72.9 

11 

178.2 

160.4 

145.8 

133.7 

123.4 

114.6 

106.9 

100.3 

94.4 

89.1 

84.4 

80.2 

12 

194  4 

175.0 

159.1 

145.8    134.6 

125.0 

116.7 

109.4 

102.9 

97.2 

92.1 

87  5 

13 

210.7 

189.6 

172.4 

158.01  145.8 

135.4 

126.4 

118.5 

111.5 

105.3 

99.8 

94.8 

14 

226.9 

204.2 

185.6 

170.1 

157.1 

H5.8 

136.1 

127.6 

120.1 

113.4 

107.5 

102.1 

15 

243.1 

218.7 

198.9 

182.3 

168.3 

156.3 

145.8 

136.7 

128.7 

121.5 

115.1 

109.4 

16 

259.3 

233.3 

212.  ll  194.4 

179.5 

166.7 

155.6 

145.8 

137.3 

129.6 

122.8 

116.7 

Rules  governing  Inspection  of  Boilers  in  Philadelphia. 

In  estimating  the  strength  of  the  longitudinal  seams  in  the  cylindrical 
shells  of  boilers  the  inspector  shall  apply  two  formulae,  A  and  B  : 

j  Pitch  of  rivets  —  diameter  of  holes  punched  to  receive  the  rivets 
A>  1  ~~  pitch  of  rivets 

percentage  of  strength  of  the  sheet  at  the  sejim. 

(  Area  of  hole  filled  by  rivet  X  No.  of  rows  of  rivets  in  seam  X  shear- 
•<  ing  strength  of  rivet  _ 

'    '      pitch  of  rivets  X  thickness  of  sheet  X  tensile  strength  of  sheet 

percentage  of  strength  of  the  rivets  in  the  seam. 

Take  the  lowest  of  the  percentages  as  found  by  formulae  A  and  B  and 
apply  that  percentage  as  the  "  strength  of  the  seam  "  in  the  following 
formula  C,  which  determines  the  strength  of  the  longitudinal  seams: 

(  Thickness  of  sheet  in  parts  of  inch  X  strength  of  seam  as  obtained 
*    •<     by  formula  A  or  B  X  ultimate  strength  of  iron  stamped  on  plates     _ 
''    I          internal  radius  of  boiler  in  inches  X  5  as  a  factor  of  safety 

safe  working  pressure. 

TABLE  OF  PROPORTIONS  AND  SAFE  WORKING  PRESSURES  WITH  FORMULAE  A 

AND  C,   @  50,000  LBS.,  T.S. 


Diameter  of  rivet  

%" 

11/16 

H 

13/16 

% 

Din  meter  of  rivet-hole.  . 

11/16" 

% 

13/16 

% 

15/16 

Pitch  of  rivets  

2" 

2  1/J6 

% 

2  3/16 

2^4 

Strength  of  seam,  %,.  ... 
Thickness  of  plate  

.656 
U" 

.636 
5/16 

.62 

% 

.60 

7/16 

.58 

y* 

Diameter  of  boiler,  in  ... 

Safe  Working  Pressure  with  Longitudinal  Seams, 
Single-riveted. 

24 

137 

165 

193 

220 

242 

30 

109 

132 

154 

176 

194 

32 

102 

124 

144 

165 

182 

84 

96 

117 

136 

155 

171 

36 

91 

110 

129 

147 

161 

38 

86 

104 

122 

139 

153 

40 

82 

99 

116 

132 

145 

44 

74 

91 

105 

120 

132 

48 

68 

83 

96 

110 

121 

54 

60 

73 

86 

98 

107 

60 

55 

66 

77 

88 

97 

STRENGTH   OP   STEAM-BOILERS. 


Diameter  of  rivet. 

w 

11/16 

H 

13/16 

% 

Diameter  of  rivet-hole.  .  . 

11/16" 

& 

13/16 

15/16 

Pitch  of  rivets 

3" 

3U 

31A 

31^ 

Strength  of  seam,  %  

.77 

.76 

75 

.74 

.73 

Thickness  of  plate  

\SL 

5/16 

% 

7/16 

H 

Diameter  of  boiler,  in  ... 

Safe  Working  Pressure  with  Longitudinal  Seams, 
Double-riveted. 

24 

160 

198 

235 

269 

305 

30 

127 

158 

188 

215 

243 

32 

119 

148 

176 

202 

228 

34 

112 

140 

166 

190 

215 

36 

106 

132 

156 

179 

203 

38 

101 

125 

148 

170 

192 

40 

96 

119 

141 

161 

183 

44 

87 

108 

128 

147 

166 

48 

79 

99 

118 

135 

152 

54 

70 

88 

104 

120 

135 

60 

64 

79 

94 

108 

122 

Flues  and  Tubes  for  Steam-boilers.— (From  Rules  of  U.  S. 
Supervising  Inspectors.  Steam -pressures  per  square  inch  allowable  on 
riveted  and  lap- welded  flues  made  in  sections.  Extract  from  table  in  Rules 
of  U.  S.  Supervising  Inspectors.) 

T  =  least  thickness  of  material  allowable,  D  =  greatest  diameter  in  inches, 
P  =  allowable  pressure.  For  thickness  greater  than  T  with  same  diameter 
P  is  increased  in  the  ratio  of  the  thickness. 

D  =  in.  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23 
T=  in.  .18  .20  .21  .21  .22  .22  .23  .24  .25  .26  .27  .28  .29  30  .31  .32  .33 
P  =  lbs.  189184179174  172  158  152  147  143  139  136134131129126125122 
D  =  in.  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
T=  in.  .34  .35  .36  .37  .38  .39  .40  .41  .42  .43  .44  .45  .46  .47  .48  .49  .50 
P=  Ibs.  121  120  119  117  116  115  115  114  112  112  110  110  109  109  108  108  107 

For  diameters  not  over  10  inches  the  greatest  length  of  section  allowable 
is  5  feet;  for  diameters  10  to  23  inches,  3  feet;  for  diameters  23  to  40  inches,  30 
inches.  If  lengths  of  sections  are  greater  than  these  lengths,  the  allowable 
pressure  is  reduced  proportionately. 

TheU.  S.  rule  for  corrugated  flues,  as  amended  in  1894,  is  as  follows:  Rule 
II,  Section  14.  The  strength  of  all  corrugated  flues,  when  used  for  furnaces 
or  steam  chimneys  (corrugation  not  less  than  1^  inches  deep  and  notexceed- 
ing  8  inches  from  centres  of  corrugation),  and  provided  that  the  plain  parts 
at  the  ends  do  not  exceed  6  inches  in  length,  and  the  plates  are  not  less  than 
5/16  inch  thick,  when  new,  corrugated,  and  practically  true  circles,  to  be 
calculated  from  the  following  formula: 


14,000 
D 


X  T  =  pressure. 


T  =  thickness,  in  inches;  D  =  mean  diameter  in  inches. 

Ribbed  Flues.— The  same  formula  is  given  for  ribbed  flues,  with  rib 
projections  not  less  than  1%  inches  deep  and  not  more  than  9  inches 
apart. 

Flat  Stayed  Surfaces  in  Steam-boilers.— Rule  II.,  Section  6,  of 
the  rules  of  the  U.  S.  Supervising  Inspectors  provides  as  follows: 

No  braces  or  stays  hereafter  employed  in  the  construction  of  boilers 
shall  be  allowed  a  greater  strain  than  6000  Ibs.  per  square  inch  of 
section. 

Clark,  in  his  treatise  on  the  Steam-engine,  also  in  his  Pocket-book,  gives 
the  following  formula:  p  =  40?£,s  -r-  d,  in  which  p  is  the  internal  pressure  in 
pounds  per  square  inch  that  will  strain  the  plates  to  their  elastic  limit,  t  is 
the  thickness  of  the  plate  in  inches,  d  is  the  distance  between  two  rows  of 
stay-bolts  in  the  clear,  and  s  is  the  tensile  stress  in  the  plate  in  tons  of 
2240  Ibs.  per  square  inch,  at  the  elastic  limit.  Substituting  values  of  s 
for  iron,  steel,  and  copper,  12,  14,  and  8  tons  respectively,  we  have  the 
following  : 


710 


THE   STEAM-BOILER. 


FORMULA  FOR  ULTIMATE  ELASTIC  STRENGTH  OF  FLAT  STAYED  SURFACES. 


Iron. 

Steel. 

Copper. 

Pressure 

p  —  5000- 

o  —   5700  - 

p  -  3300  f 

Thickness  of  Dlate 

,       p  X  d 

d 
p  X  d 

d 
.pxd 

Pitch  of  bolts 

~    5000 
_  5000£ 

5700 
d_5700f 

~     3300 

3300£ 
o  — 

P 

P 

P 

' PP'P 


For  Diameter  of  tUe  Stay-bolts,  Clark  gives  d'  =  .00244  / 

iu  which  d'  =  diameter  of  screwed  bolt  at  bottom  of  thread,  P  =  longitudi- 
nal and  P'  transverse  pitch  of  Btay-boltfe  between  centres,  p  =  internal 
pressure  in  Ibs.  per  sq.  in.  that  will  strain  the  plate  to  its  elastic  limit,  s  = 
elastic  strength  of  the  stay-bolts  in  Ibs.  per  sq.  in.  Taking  s  =  12,  14,  and  8 
tons,  respectively  for  iron,  steel,  and  copper,  we  have 

For  iron,        d'  =  .00069  tfPJFp'or  if  P  =  P',  d!  =  .00069P  Vp\ 
For  steel,      d'  =  .00004  VPP'p,     "        "        d'  =  .00004 P  \/p\ 
For  copper,  d'  =  .00084  |/PP'p,      "         "         d1  -  .00084P  \'p. 
In  using  these  formulae  a  large  factor  of  safety  should  be  taken  to  allow 
for  reduction  of  size  by  corrosion.    Thurston's  Manual  of  Steam-boilers,  p. 
144,  recommends  that   the  factor  be  as  large  as  15  or  20.     The  Hartford 
Steam  Boiler  Insp.  &  Ins.  Co.  recommends  not  less  than  10. 

Strength  of  Stays.— A.  F.  Yarrow  (Engr.,  March  20,  1891)  gives  the 
following  results  of  experiments  to  ascertain  the  strength  of  water-space 
stays  : 


Description. 

Length 
between 
Plates. 

Diameter  of  Stay  over 
Threads. 

Ulti- 
mate 

Stress. 

Hollow  stays  screwed  into  j 
plates  and  hole  expanded  | 
Solid    stays    screwed    into  j 
plates  and  riveted  over.     | 

4.  75  in. 

4.04  in. 
4.  80  in. 
4.  80  in. 

1  in.  (hole  7/16  in.  and  5/16  in, 
lin.<>.le  9/16  in.  and  7/16  in. 
%in. 
%in. 

Ibs. 
25,457 
20,992 

22,008 
22,070 

The  above  are  taken  as  a  fair  average  of  numerous  tests. 
Stay-bolts  in  Curved  Surfaces,  as  in  Water-legs  of  Verti- 
cal Boilers.— The  rules  of  the  U.  S.  Supervising  Inspectors  provide  as 


stayed  wun  DOILS  as  provided  oy  §  o  or  ±uiie  11,  tor  nac  suriaces;  ana  me 
thickness  of  material  required  for  the  shells  of  such  furnaces  shall  be  de- 
termined by  the  distance  between  the  centres  of  the  stay-bolts  in  the  fur- 
nace and  not  in  the  shell  of  the  boiler;  and  the  steam-pressure  allowable 
shall  be  determined  by  the  distance  from  centre  of  stay-bolts  in  the  furnace 
and  the  diameter  of  such  stay-bolts  at  the  bottom  of  the  thread. 
The  Hartford  Steam-boiler  Insp.  &  Ins.  Co.  approves  the  above  rule  (The 


._.,.,  __  -----------  LUG  ruiea  UL  uue  u.  o.  oupej.  vusiug  .uispcciui  s. 

Fusible-plugs.  —  Fusible-plugs  should  be  put  in  that  portion  of  the 
heating-surface  which  first  becomes  exposed  from  lack  of  water.  The  rules 
of  the  U.  S.  Supervising  Inspectors  specify  Banca  tin  for  the  purpose.  Its 
melting-point  is  about  445°  F.  The  rule  says:  All  steamers  shall  have 


. 

inserted  in  their  boilers  plugs  of  Banca  tin,  at  least  ^  in.  in  diameter  at  the 
the  internal  opening,   in  the  following  manner,  to  wit: 


smallest  end  of  the 


icuiciLci^    uciui o   me    lire  iiiic    nuu   nut    less   IIUMI  •*  i  ^.  n1    LIJ  LUC  iui  wwu 

end  of  the  boiler.    All  fire-box  boilers  shall  have  one  plug  inserted  iu  the 
crown  of  the  back  connection,  or  in  the  highest  fire-surface  of  the  boiler. 


IMPROVED  METHODS  OF  FEEDIKG  COAL.     Til 

All  upright  tubular  boilers  used  for  marine  purposes  shall  have  a  fusible 
plug  inserted  in  one  of  the  tubes  at  a  point  at  least  2  in.  below  the  lower 
gauge-cock,  and  said  plug  may  be  placed  in  the  upper  head  sheet  when 
deemed  advisable  by  thejlocal  inspectors. 

Steam-domes.— Steam  domes  or  drums  were  formerly  almost  univer- 
sally used  on  horizontal  boilers,  but  their  use  is  now  generally  discontinued, 
as  they  are  considered  a  useless  appendage  to  a  steam-boiler,  and  unless 
properly  designed  and  constructed  are  an  element  of  weakness. 

Height  of  Furnace.— Recent  practice  in  the  United  States  makes 
the  height  of  furnace  much  greater  than  it  was  formerly.  With  large  sizes 
of  anthracite  there  is  no  serious  objection  to  having  the  furnace  as  low  as  12 
to  18  in.,  measured  from  the  surface  of  the  grate  to  the  nearest  portion  of 
the  heating-surface  of  the  boiler,  but  with  coal  containing  much  volatile 
matter  and  moisture  a  much  greater  distance  is  desirable.  With  very  vola- 
tile coals  the  distance  may  be  as  great  as  4  or  5  ft.  Ranldne  (S.  E.,  p.  457) 
says:  The  clear  height  of  the  "  crown  "  or  roof  of  the  furnace  above  the  grate- 
bars  is  seldom  less  than  about  18  in.,  and  often  considerably  more.  In  the 
fire-boxes  of  locomotives  it  is  on  an  average  about  4  ft.  The  height  of  18  in. 
is  suitable  where  the  crown  of  the  furnace  is  a  brick  arch.  Where  the  crown 
of  the  furnace,  on  the  other  hand,  forms  part  of  the  heating-surface  of  the 
boiler,  a  greater  height  is  desirable  in  every  case  in  which  it  can  be 
obtained;  for  the  temperature  of  the  boiler-plates,  being  much  lower  than 
that  of  the  flame,  tends  to  check  the  combustion  of  the  inflammable  gases 
which  rise  from  the  fuel.  Asa  general  principle  a  high  furnace  is  favorable 
to  complete  combustion. 

IMPROVED  METHODS  OF  FEEDING  COAL, 

Mechanical  Stokers.    (William  R.  Roney,  Trans.  A.  S.  M.  E.,  vol. 

xii.)— Mechanical  stokers  have  been  used  in  England  to  a  limited  extent 
since  1785.  In  that  year  one  was  patented  by  James  Watt.  It  was  a  simple 
device  to  push  the  coal,  after  it  was  coked  at  the  front  end  of  the  grate, 
back  towards  the  bridge.  It  was  worked  intermittently  by  levers,  and  was 
designed  primarily  to  prevent  smoke  from  bituminous  coal.  (See  D.  K. 
Clark's  Treatise  on  the  Steam-engine.) 

After  the  year  1840  many  styles  of  mechanical  stokers  were  patented  in 
England,  but  nearly  all  were  variations  and  modifications  of  the  two  forms 
of  stokers  patented  by  John  Jukes  in  1841,  and  by  E.  Henderson  in  1843. 

The  Jukes  stoker  consisted  of  longitudinal  fire-bars,  connected  by  links, 
so  as  to  form  an  endless  chain,  similar  to  the  familiar  treadmill  horse-power. 
The  small  coal  was  delivered  from  a  hopper  on  the  front  of  the  boiler,  on  to 
the  grate,  which  slowly  moving  from  front  to  rear,  gradually  advanced  the 
fuel  into  the  furnace  and  discharged  the  ash  and  clinker  at  the  back. 

The  Henderson  stoker  consists  primarily  of  two  horizontal  fans  revolving 
on  vertical  spindles,  which  scatter  the  coal  over  the  fire. 

Numerous  faults  in  mechanical  construction  and  in  operation  have  limited 
the  use  of  these  and  other  mechanical  stokers.  The  first  American  stoker 
was  the  Murphy  stoker,  brought  out  in  1878.  It  consists  of  two  coal  maga- 
zines placed  in  the  side  walls  of  the  boiler  furnace,  and  extending  back  from 
the  boiler  front  6  or  7  feet.  In  the  bottom  of  these  magazines  are  rectangu- 
lar iron  boxes,  which  are  moved  from  side  to  side  by  means  of  a  rack  and 
pinion,  and  serve  to  push  the  coal  upon  the  grates,  which  incline  at  an  angle 
of  about  35°  from  the  inner  edge  of  the  coal  magazines,  forming  a  V-shaped 
receptacle  for  the  burning  coal.  The  grates  are  composed  of  narrow  parallel 
bars,  so  arranged  that  each  alternate  bar  lifts  about  an  inch  at  the  lower 
end,  while  at  the  bottom  of  the  V,  and  filling  the  space  between  the  ends  of 
the  prate-bars,  is  placed  a  cast-iron  toothed  bar,  arranged  to  be  turned  by  a 
crank.  The  purpose  of  this  bar  is  to  grind  the  clinker  coming  in  contact 
with  it.  Over  this  V-shaped  receptacle  is  sprung  a  fire-brick  arch. 

In  the  Roney  mechanical  stoker  the  fuel  to  be  burned  is  dumped  into  a 
hopper  on  the  boiler  front.  Set  in  the  lower  part  of  the  hopper  is  a  "  pusher" 
to  which  is  attached  the  "  feed-plate  "  forming  the  bottom  of  the  hopper. 
The  "  pusher,"  by  a  vibratory  motion,  carrying  with  it  the  "feed-plate," 
gradually  forces  the  fuel  over  the  *'  dead-plate  "  and  on  the  grate.  The 
grate-bars,  in  their  normal  condition  form  a  series  of  steps,  to  the  top  step 
of  which  coal  is  fed  from  the  "  dead-plate."  Each  bar  rests  in  a  concave 
seat  in  the  bearer,  and  is  capable  of  a  rocking  motion  through  an  adjustable 
angle.  All  the  grate-bars  are  coupled  together  by  a  "rocker- bar."  A  vari- 
able back-and-forth  motion  being  given  to  the  "  rocker-bar,"  through  a  con- 


712  THE   STEAM-BOILER. 

necting-rod,  the  grate-bars  rock  in  unison,  now  forming  a  series  of  steps, 
and  now  approximating  to  an  inclined  plane,  with  the  grates  partly  over- 
lapping, like  shingles  on  a  roof.  When  the  grate-bars  rock  forward  the  fire 
will  tend  to  work  down  in  a  body.  But  before  the  coal  can  move  too  far 
the  bars  rock  back  to  the  stepped  position,  checking  the  downward  motion, 
breaking  up  the  cake  over  the  whole  surface,  and  admitting  a  free  volume 
of  air  through  the  fire.  The  rocking  motion  is  slow,  being  from  7  to  10 
strokes  per  minute,  according  to  the  kind  of  coal.  This  alternate  starting 
and  checking  motion  is  continuous,  and  finally  lauds  the  cinder  and  ash  on 
the  dumping-grate  below. 

Mr.  Honey  gives  the  following  record  of  six  tests  to  determine  the  com- 
parative economy  of  the  Roney  mechanical  stoker  and  hand-firing  on  return 
tubular  boilers,  60  inches  X  20  feet,  burning  Cumberland  coal  with  natural 
draught.  Rating  of  boiler  at  12.5  square  feet,  105  H.  P. 

Three  tests,  hand-firing.    Three  tests,  Stoker. 

6SI83S%£T}  ^  ">•«  »•«>     >'-89  ™  ™ 

H. P.  developed  above  rating,  %       5.8      13.5         68  54.6      66.7      84.3 

Results  of  comparative  tests  like  the  above  should  -be  used  with  caution- 
in  drawing  generalizations.  It  by  no  means  follows  from  these  results  that 
a  stoker  will  always  show  such  comparative  excellence,  for  in  this  cas-e  the 
results  of  hand-firing  are  much  below  what  may  be  obtained  under  favor- 
able circumstances  from  hand-firing  with  good  Cumberland  coal. 

Tlie  Hawley  Down-draught  Furnace.— A  foot  or  more  above 
the  ordinary  grate  there  is  carried  a  second  grate  composed  of  a  series  of 
water- tubes,  opening  at  both  ends  into  steel  drums  or  headers,  through  which 
water  is  circulated.  The  coal  is  fed  on  this  second  grate,  and  as  it  is  par- 
tially consumed  falls  through  it  upon  the  lower  grate,  where  the  combustion 
is  completed  in  the  ordinary  manner.  The  draught  through  the  coal  on  the 
upper  grate  is  downward  through  the  coal  and  the  grate.  The  volatile  gases 
are  therefore  carried  down  through  the  bed  of  coal,  where  they  are  thor- 
oughly heated,  and  are  burned  in  the  space  beneath,  where  they  meet  the 
excess  of  hot  air  drawn  through  the  fire  on  the  lower  grate.  In  tests  in 
Chicago,  f  rom  30  to  45  Ibs.  of  coal  were  burned  per  square  foot  of  grate  upon 
this  system,  with  good  economical  results.  (See  catalogue  of  the  Hawley 
Down  Draught  Furnace  Co.,  Chicago,  1894.) 

Under-feed  Stokers.— Results  similar  to  those  that  may  be  obtained; 
with  downward  draught  are  obtained  by  feeding  the  coal  at  the  bottom  of  the 
bed,  pushing  upward  the  coal  already  on  the  bed  which  has  had  its  volatile 
matter  distiilea  from  it.  The  volatile  matter  of  the  freshly  fired  coal  them 
has  to  pass  through  a  body  of  ignited  coke.  (See  circular  of  the  Jones  Un- 
der-feed Stoker,  Fraser  &  Chalmers,  Chicago,  1894.) 

SMOK£  PREVENTION. 

A  committee  of  experts  was  appointed  in  St.  Louis  in  1891  to  report  on  the 
sm,oke  problem.  A  summary  of  its  report  is  given  in  the  Iron  Age.  of  April 
7,  189£  It  describes  the  different  means  that  have  been  tried  to  prevent 
smoke,  such  as  gas-fuel,  steam-jets,  fire-brick  arches  and  checker-work, 
hollow  walls  for  preheating  air,  coking  arches  or  chambers,  double  combus- 
tion furnaces,  and  automatic  stokers.  All  of  these  means  have  been  more  or 
less  effective  in  diminishing  smoke,  their  effectiveness  depending  largely 
upon  the  skill  with  which  they  are  operated  ;  but  none  is  entirely  satisfac- 
tory. Fuel-gas  is  objectionable  chiefly  on  account  of  its  expense.  The 
average  quality  of  fuel-gas  made  from  a  trial  run  of  several  car-loads  of 
Illinois  coal,  in  a  well-designed  fuel-gas  plant,  showed  a  calorific  value  of 
243,391  heat-units  per  1000  cubic  feet.  This  is  equivalent  to  5052.8  heat  units 
per  Ib.  of  coal,  whereas  by  direct  calorimeter  test  an  average  sample  of  the 
coal  gave  11,172  heat-units.  One  Ib.  of  the  coal  showed  a  theoretical  evap- 
oration of  11.56  Ibs.  water,  while  the  gas  from  1  Ib.  showed  a  theoretical 
evaporation  of  5.23  Ibs.  48.17  Ibs.  of  coal  were  required  to  furnish  1000  cubic 
feet  of  the  gas.  In  39  tests  the  smoke-preventing  furnaces  showed  only  7-l<£ 
of  the  capacity  of  the  common  furnaces,  reduced  the  work  of  the  boilers 
28#,  and  required  about  2$  more  fuel  to  do  the  same  work.  In  one  case  with 
steam-jets  the  fuel  consumption  was  increased  12#  for  the  same  work. 

Prof.  O.  H.  Landreth,  in  a  report  to  the  State  Board  of  Health  of  Tennes- 
see (Engineering  News,  June  8,  1893),  writes  as  follows  on  the  subject  of 
smoke  prevention: 


SMOKE    PKEVEXTION.  713 

As  pertains  to  steam-boilers,  the  object  must  be  attained  by  one  or  more 
of  the  following  agencies  : 

1.  Proper  design  and  setting  of  the  boiler-plant.    This  implies  proper  grate 
area,  sufficient  draught,  the  necessary  air-space  between  grate-bars  and 
through  furnace,  and  ample  combustion-room  under  boilers. 

2.  That  system  of  firing  that  is  best  adapted  to  each  particular  furnace  to 
secure  the  perfect  combustion  of  bituminous  coal.    This  may  be  either:  (a) 
"coke-firing,'1  or  charging  all  coal  into  the  front  of  the  furnace  until  par- 
tially coked,  then  pushing  back  and  spreading;  or  (b)  "alternate  side-fir- 
ing"; or  (c)  "spreading,1"  by  which  the  coal  is  spread  over  the  whole  grate 
area  in  thin,  uniform  layers  at  each  charging. 

3.  The  admission  of  air  through  the  furnace-door,  bridge-wall,  or  side  walls. 

4.  Steam-jets  and  other  artificial  means  for  thoroughly  mixingjthe  air  and 
combustible  gases. 

5.  Preventing  the  cooling  of  the  furnace  and  boilers  by  the  inrush  of  cold 
air  when  the  furnace-doors  are  opened  for  charging  coal  and  handling  the 
fire. 

6.  Establishing  a  gradation  of  the  several  steps  of  combustion  so  that  the 
coal  rnay  be  charged,  dried,  and  warmed  at  the  coolest  part  of  the  furnace, 
and  then  moved  by  successive  steps  to  the  hottest  place,  where  the  final 
combustion  of  the  coked  coal  is  completed,  and  compelling  the   distilled 
combustible  gases  to  pass  through  this  hottest  part  of  the  fire. 

7.  Preventing  the  cooling  by  radiation  of  the  unburned  combustible  gases 
until  perfect  mixing  and  combustion  have  been  accomplished. 

8.  Varying  the  supply  of  air  to  suit  the  periodic  variation  in  demand. 

9.  The  substitution  of  a  continuous  uniform  feeding  of  coal  instead  of 
intermittent  charging. 

10.  Down-draught  burning  or  causing  the  air  to  enter  above  the  grate  and 
pass  down  through  the  coal,  carrying  the  distilled  products  down  to  the  high 
temperature  plane  at  the  bottom  of  the  fire. 

The  number  of  smoke-prevention  devices  which  have  been  invented  is 
legion.  A  brief  classification  is  : 

(a)  Mechanical  stokers.    They  effect  a  material  saving  in  the  labor  of 
firing,  and  are  efficient  smoke-preventers  when  not  pushed  above  their 
capacity,  and  when  the  coal  does  not  cake  badly.    They  are  rarely  suscepti- 
ble to  the  sudden  changes  in  the  rate  of  firing  frequently  demanded  in 
service. 

(b)  Air-flues  in  side  walls,  bridge-wall,  and  grate-bars,  through  which  air 
when  passing  is  heated.    The  results  are  always  beneficial,  but  the  flues  are 
difficult  to  keep  clean  and  in  order. 

(c)  Coking  arches,  or  spaces  in  front  of  the  furnace  arched  over,  in  which 
the  fresh  coal  is  coked,  both  to  prevent  cooling  of  the  distilled  gases,  and  to 
force  them  to  pass  through  the  hottest  part  of  the  furnace  just  beyond  the 
arch.    The  results  are  good  for  normal  conditions,  but  ineffective  when  the 
fires  are  forced.    The  arches  also  are  easily  burned  out  and  injured  by 
working  the  fire. 

(d)  Dead-plates,  or  a  portion  of  the  grate  next  the  furnace-doors,  reserved 
for  warming  and  coking  the  coal  before  it  is  spread  over  the  grate.    These 
give  good  results  when  the  furnace  is  not  forced  above  its  normal  capacity. 
This  embodies  the  method  of  "coke-firing"  mentioned  before. 

(e)  Down-draught  furnaces,  or  furnaces  in  which  the  air  is  supplied  to  the 
coal  above  the  grate,  and  the  products  of  combustion  are  taken  away  from 
beneath  the  grate,  thus  causing  a  downward  draught  through  the  coal,  carry- 
ing the  distilled  gases  down  to  the  highly  heated  incandescent  coal  at  the 
bottom  of  the  layer  of  coal  on  the  grate.    This  is  the  most  perfect  manner 
of  producing  combustion,  and  is  absolutely  smokeless. 

(/)  Steam-jets  to  draw  air  in  or  inject  air  into  the  furnace  above  the  grate, 
and  also  to  mix  the  air  and  the  combustible  gases  together.  A  very  efficient 
smoke-preventer,  but  one  liable  to  be  wasteful  of  fuel  by  inducing  too  rapid 
a  draught. 

(g)  Baffle-plates  placed  in  the  furnace  above  the  fire  to  aid  in  mixing  the 
combustible  gases  with  the  air. 

(7i)  Double  furnaces,  of  which  there  are  two  different  styles;  the  first  of 
which  places  the  second  grate  below  the  first  grate;  the  coal  is  coked  on  the 
first  grate,  during  which  process  the  distilled  gases  are  made  to  pass  over 
the  second  grate,  where  they  are  ignited  and  burned;  the  coke  from  the  first 
grate  is  dropped  onto  the  second  grate:  a  very  efficient  and  economical 
smoke-preventer,  but  rather  complicated  to  construct  and  maintain.  In  the 
second  form  the  products  of  combustion  from  the  first  furnace  pass  through 


714  THE   STEAM-BOILER. 

the  grate  and  fire  of  the  second,  each  furnace  being  charged  with  fresh  fuel 
when  needed,  the  latter  generally  with  a  smokeless  coal  or  coke :  an  irra. 
tional  and  unpromising  method. 

Mr.  C.  F.  White,  Consulting  Engineer  to  the  Chicago  Society  for  the  Pre- 
vention of  Smoke,  writes  under  date  of  May  4,  1893  : 

The  experience  had  in  Chicago  has  shown  plainly  that  it  is  perfectly  easy 
to  equip  steam-boilers  with  furnaces  which  shall  burn  ordinary  soft  coal  in 
such  a  manner  that  the  making  of  smoke  dense  enough  to  obstruct  the  vision 
shall  be  confined  to  one  or  two  intervals  of  perhaps  a  couple  of  minutes' 
duration  in  the  ordinary  day  of  10  hours. 

Gas-fired  Steam-boilers.— Converting  coal  into  gas  in  a  separate 
producer,  before  burning  it  under  the  steam-boiler,  is  an  ideal  method  of 
smoke-prevention,  but  its  expense  has  hitherto  prevented  its  general  intro- 
duction. A  series  of  articles  on  the  subject,  illustrating  a  great  number  of 
devices,  by  F.  J.  Rowan,  is  published  in  the  Colliery  Engineer,  1889-90.  See 
also  Clark  on  the  Steam-engine. 

FORCED  COMBUSTION  IN  STEAM-BOILERS. 

For  the  purpose  of  increasing  the  amount  of  steam  that  can  be  generated 
by  a  boiler  of  a  given  size,  forced  draught  is  of  great  importance.  It  is 
universally  used  in  the  locomotive,  the  draught  being  obtained  by  a  steam- 
jet  in  the  smoke-stack.  It  is  now  largely  used  in  ocean  steamers,  especially 
in  ships  of  war,  and  to  a  small  extent  in  stationary  boilers.  Economy  of  fuel 
is  generally  not  attained  by  its  use,  its  advantages  being  confined  to  the 
securing  of  increased  capacity  from  a  boiler  of  a  given  bulk,  weight,  or  cost. 
The  subject  of  forced  draught  is  well  treated  in  a  paper  by  James  Howden, 
entitled,  "Forced  Combustion  in  Steam-boilers"  (Section  G,  Engineering 
Congress  at  Chicago,  in  1893),  from  which  we  abstract  the  following : 

Edwin  A.  Stevens  at  Bordentown,  N.  J.,  in  1827,  in  the  steamer  "North 
America,"  fitted  the  boilers  with  closed  ash-pits,  into  which  the  air  of  com- 
bustion was  forced  by  a  fan.  In  1828  Ericsson  fitted  in  a  similar  manner  the 
steamer  "  Victory,'1  commanded  by  Sir  John  Ross. 

Messrs.  E.  A.  and  R.  L.  Stevens  continued  the  use  of  forced  draught  for 
a  considerable  period,  during  which  they  tried  three  different  modes  of  using 
the  fan  for  promoting  combustion:  1,  blowing  direct  into  a  closed  ash-pit; 
2,  exhausting  the  base  of  the  funnel  by  the  suction  of  the  fan;  3,  forcing  air 
into  an  air-tight  boiler-room  or  stroke-hold.  Each  of  these  three  methods 
was  attended  with  serious  difficulties. 

In  the  use  of  the  closed  ash-pit  the  blast-pressure  would  frequently  force 
the  gases  of  combustion,  in  the  shape  of  a  serrated  flame,  from  the  joint 
around  the  furnace  doors  in  so  great  a  quantity  as  to  affect  both  the  effi- 
ciency and  health  of  the  firemen. 

The  chief  defect  of  the  second  plan  was  the  great  size  of  the  fan  required 
to  produce  the  necessary  exhaustion.  The  size  of  fan  required  grows  in  a 
rapidly  increasing  ratio  as  the  combustion  increases,  both  on  account  of  the 
greater  air-supply  and  the  higher  exit  temperature  enlarging  the  volume  of 
the  waste  gases. 

The  third  method,  that  of  forcing  cold  air  by  the  fan  into  an  air-tight 
boiler-room — the  present  closed  stoke-hold  system — though  it  overcame  the 
difficulties  in  working  belonging  to  the  two  forms  first  tried,  has  serious 
defects  of  its  own,  as  it  cannot  be  worked,  even  with  modern  high-class 
boiler-construction,  much,  if  at  all,  above  the  power  of  a  good  chimney 
draught,  in  most  boilers,  without  damaging  them. 

In  1875  John  I.  Thornycroft  &  Co.,  of  London,  began  the  construction  of 
torpedo-boats  with  boilers  of  the  locomotive  type,  in  which  a  high  rate  of 
combustion  was  attained  by  means  of  the  air-tight  boiler-room,  into  which 
air  was  forced  by  means  of  a  fan. 

In  1882  H.B.M.  ships  "  Satellite  "  and  "  Conqueror  "  were  fitted  with  this 
system,  the  former  being  a  small  ship  of  1500  I.H.P.,  and  the  latter  an  iron- 
clad of  4500  I.H.P.  On  the  trials  with  forced  draught,  which  lasted  from  two 
to  three  hours  each,  the  highest  rates  of  combustion  gave  16.9  I.H.P.  per 
square  foot  of  fire-grate  in  the  ki  Satellite,"  and  13.41  I.H.P.  in  the  "  Con- 
queror." 

None  of  the  short  trials  at  these  rates  of  combustion  were  made  without 
injury  to  the  seams  and  tubes  of  the  boilers,  but  the  system  was  adopted, 
and  it  has  been  continued  in  the  British  Navy  to  this  day  (1893). 

In  Mr.  Howden's  opinion  no  advantage  arising  from  increased  combustion 
over  natural-draught  rates  is  derived  fropi  using  forced  draught  in  a  closed 
ash-pit  sufficient  to  compensate  the  disadvantages  arising  from  difficulties 


FUEL   ECONOMIZERS.  715 

in  working,  there  being  either  excessive  smoke  from  bituminous  coal  or 
reduced  evaporative  economy. 

In  1880  Mr.  Howden  designed  an  arrangement  intended  to  overcome  the 
defects  of  both  the  closed  ash-pit  and  closed  stoke-hold  systems. 

An  air-tight  reservoir  or  chamber  is  placed  on  the  front  end  of  the  boiler 
and  surrounding  the  furnaces.  This  reservoir,  which  projects  from  8  to  10 
inches  from  the  end  of  the  boiler,  receives  the  air  under  pressure,  which  is 
passed  by  the  valves  into  the  ash-pits  and  over  the  fires  in  proportions 
suited  to  the  kind  of  fuel  used  and  the  rate  of  combustion  required.  The 
air  nsed  above  the  fires  is  admitted  to  a  space  between  the  outer  and  iuner 
furnace-doors,  the  inner  having  perforations  and  an  air-distributing  box 
through  which  the  air  passes  under  pressure. 

By  means  of  the  balance  of  air-pressure  above  and  below  the  fires  all 
tendency  for  the  fire  to  blow  out  at  the  furnace-door  is  removed. 

By  regulating  the  admission  of  the  air  by  the  valves  above  and  below  the 
fires,  the  highest  rate  of  combustion  possible  by  the  air-pressure  used  can 
be  effected,  and  in  same  manner  the  rate  of  combustion  can  be  reduced  to 
far  below  that  of  natural  draught,  while  complete  and  economical  combus- 
tion at  all  rates  is  secured. 

A  feature  of  the  system  is  the  combination  of  the  heating  of  the  air  of 
combustion  by  the  waste  gases  with  the  controlled  and  regulated  admission 
of  air  to  the  furnaces.  This  arrangement  is  effected  most  conveniently  by- 
passing the  hot  fire- gases  after  they  leave  the  boiler  through  stacks  of 
vertical  tubes  enclosed  in  the  uptake,  their  lower  ends  being  immediately 
above  the  smoke-box  doors. 

Installations  on  Howden's  system  have  hitherto  been  arranged  for  a  rate 
of  combustion  to  give  at  full  sea-power  an  average  of  from  18  to  22  I.H.P. 
per  square  foot  of  fire-grate  with  fire-bars  from  5'  0"  to  5'  6"  in  length. 

It  is  believed  that  with  suitable  arrangement  of  proportions  even  SO 
I.H.P.  per  square  foot  can  be  obtained. 

For  an  account  of  recent  uses  of  exhaust- fans  for  increasing  draught,  see 
paper  by  W.  R.  Roney,  Trans.  A.  S.  M.  E.,  vol.  xv. 

FUEL.   ECONOMIZERS. 

Green's  Fuel  Economizer.— Clark  gives  the  following  average  re- 
sults of  comparative  trials  of  three  boilers  at  Wigan  used  with  and  without 
economizers  : 

Without  With 

Economizers.    Economizers. 

Coal  per  square  foot  of  gi;ate  per  hour 21 . 6  21 .4 

Water  at  1 00°  evaporated  per  hour 73 . 55  79 . 32 

Water  at  212°  per  pound  of  coal 9.60  10.56 

Showing  that  in  burning  equal  quantities  of  coal  per  hour  the  rapidity  of 
evaporation  is  increased  9.3$  and  the  efficiency  of  evaporation  10%  by  the 
addition  of  the  economizer. 

The  average  temperatures  of  the  gases  and  of  the  feed-water  before  and 
after  passing  the  economizer  were  as  follows: 

With  6-ft.  grate.         With  4-ft.  grate. 
Before.   After.  Before.  After. 

Average  temperature  of  gases 649  340  501          312 

Average  temperature  of  feed-water.        47  157  41          137 

Taking  averages  of  the  two  grates,  to  raise  the  temperature  of  the  feed- 
water  100°  the  gases  were  cooled  down  250°. 
Performance  of  a  Green  Economizer  with  a  Smoky  Coal. 

— The  action  of  Green's  Economizer  was  tested  by  M.  W.  Grosseteste  for  a 
period  of  three  weeks.  The  apparatus  consists  of  four  ranges  of  vertical 
pipes,  6^  feet  high,  3%  inches  in  diameter  outside,  nine  pipes  in  each  range, 
connected  at  top  and  bottom  by  horizontal  pipes.  The  water  enters  all  the 
tubes  from  below,  and  leaves  them  from  above.  The  system  of  pipes  is  en- 
veloped in  a  brick  casing,  into  which  the  gaseous  products  of  combustion 
are  introduced  from  above,  and  which  they  leave  from  below.  The  pipes 
are  cleared  of  soot  externally  by  automatic  scrapers.  The  capacity  for 
water  is  24  cubic  feet,  and  the  total  external  heating-surface  is  290  square 
feet.  The  apparatus  is  placed  in  connection  with  a  boiler  having  355  square 
feet  of  surface. 

This  apparatus  had  been  at  work  for  seven  weeks  continuously  without 
tiaving  been  cleaned,  and  had  accumulated  a  J^-inch  coating  of  soot  and 


716 


THE    STEAM-BOILER. 


ash,  when  its  performance,  in  the  same  condition,  was  observed  for  one 
week.  During  the  second  week  it  was  cleaned  twice  every  day;  but  during 
the  third  week,  after  having  been  cleaned  on  Monday  morning,  it  was 
worked  continuously  without  further  cleaning.  A  smoke-making  coal  was 
used.  The  consumption  was  maintained  sensibly  constant  from  day  to  day, 

GREEN'S  ECONOMIZER.— RESULTS  OP   EXPERIMENTS   ON   ITS   EFFICIENCY  AS 

AFFECTED   BY   THE   STATE   OF   THE    SURFACE.      (W,  GrOSSCtCSte.) 


TIME 
(February  and  March). 

Temperature  of  Feed- 
water. 

Temperature  of  Gas- 
eous Products. 

Enter- 
ing 
Feed- 
heater. 

Leav- 
ing 
Feed- 
heater. 

Differ- 
ence. 

Enter- 
ing 
Feed- 
heater. 

Leav- 
ing 
Feed- 
heater. 

Differ- 
ence. 

1st  Week  

Fahr. 
73.5° 
77.0 
73.4 
73.4 
79.0 
80.6 
80.6 
79.0 

Fahr. 
161.5° 
230  0 
196.0 
181.4 
178.0 
170.6 
169  0 
172.4 

Fahr. 

88.0° 
153.0 
122.6 
108.0 
99.0 
90.0 
88.4 
93.4 

Fahr. 

849° 
882 
831 
871 

952 
889 
901 

Fahr. 

261° 
297 
284 
309 

329 
338 
351 

Fahr. 

588° 
585 
547 
562 

623 
551 
550 

2d  Week 

3d  Week  —  Monday  

Tuesday  

Wednesday  
Thursday  
Friday  

Saturday  

1st  Week.  2d  Week.  3d  Week. 

Coal  consumed  per  hour 214  Ibs.      216  Ibs.      213  Ibs. 

Water  evaporated  from  32°  F.  per  hour. .  1424  1525  1428 

Water  per  pound  of  coal 6.65  7.06  6.70 

It  is  apparent  that  there  is  a  great  advantage  in  cleaning  the  pipes  daily 
—the  elevation  of  temperature  having  been  increased  by  it  from  88°  to  153°. 
In  the  third  week,  without  cleaning,  the  elevation  of  temperature  relapsed 
in  three  days  to  the  level  of  the  first  week;  even  on  the  first  day  it  was 
quickly  reduced  by  as  much  as  half  the  extent  of  relapse.  By  cleaning  the 
pipes  daily  an  increased  elevation  of  temperature  of  65°  F.,  was  obtained, 
whilst  a  gain  of  6%  was  effected  in  the  evaporative  efficiency. 

INCRUSTATION  AND  CORROSION. 

Incrustation  and  Scale.— Incrustation  (as  distinguished  from 
mere  sediments  due  to  dirty  water,  which  are  easily  blown  out.  or  gathered 
up,  by  means  of  sediment  collectors)  is  due  to  the  presence  of  salts  in  the 
feed-water  (carbonates  and  sulphates  of  lime  and  magnesia  for  the  most 
part),  which  are  precipitated  when  the  water  is  heated,  and  form  hard  de- 
posits upon  the  boiler-plates.  (See  Impurities  in  Water,  p.  551,  ante.) 

Where  the  quantity  of  these  salts  is  not  very  large  (12  grains  per  gallon, 
say)  scale  preventives  may  be  found  effective.  The  chemical  preventives 
either  form  with  the  salts  other  salts  soluble  in  hot  wafer;  or  precipitate 
them  in  the  form  of  soft  mud,  which  does  not  adhere  to  the  plates,  and  can 
be  washed  out  from  time  to  time.  The  selection  of  the  chemical  must  de- 
pend upon  the  composition  of  the  water,  and  it  should  be  introduced  regu- 
larly with  the  feed. 

EXAMPLES.— Sulphate-of -lime  scale  prevented  by  carbonate  of  soda:  The 
sulphate  of  soda  produced  is  soluble  in  water;  and  the  carbonate  of  lime 
falls  down  in  grains,  does  not  adhere  to  the  plates,  and  may  therefore  be 
blown  out  or  gathered  into  sediment- collectors.  The  chemical  reaction  is: 

Sulphate  of  lime  -f-  Carbonate  of  soda  =  Sulphate  of  soda  -f  Carbonate  of  lime 
CaSO«  NA2COa  NA2SO4  CaCO3 

Sodium  phosphate  will  decompose  the  sulphates  of  lime  and  magnesia: 
Sulphate  of  lime  -f  Sodium  phosphate  =  Calcium  phos.  -f  Sulphate  of  soda. 

CaSO4  Na2HPO4  CaHPO4  Na2SO4 

Sul.  of  magnesia -f- Sodium  phosphate  =  Phosphate  of  magnesia  -f  Sul. of  soda. 

MgHPO4 


INCRUSTATION   AND   CORROSION.  717 

Where  the  quantity  of  salts  is  large,  scale  preventives  are  not  of  much 
use.  Some  other  source  of  supply  must  be  sought,  or  the  bad  water  purified 
before  it  is  allowed  to  enter  the  boilers.  The  damage  done  to  boilers  by  un* 
suitable  water  is  enormous. 

Pure  water  may  be  obtained  by  collecting:  rain,  or  condensing  steam  by 
means  of  surface  condensers.  The  water  thus  obtained  should  be  mixed 
with  a  little  bad  water,  or  treated  with  a  little  alkali,  as  undiluted,  pure 
water  corrodes  iron;  or,  after  each  periodic  cleaning,  the  bad  may  be  used 
for  a  day  or  two  to  put  a  skin  upon  the  plates. 

Carbonate  of  lime  and  magnesia  may  be  precipitated  either  by  heating  the 
water  or  by  mixing  milk  of  lime  (Porter  Clark  process)  with  it,  the  water 
being  then  filtered. 

Corrosion  may  be  produced  by  the  use  of  pure  water,  or  by  the  presence 
of  acids  in  the  water,  caused  perhaps  in  the  engine-cylinder  by  the  action  of 
high-pressure  steam  upon  the  grease,  resulting  in  the  production  of  fatty 
acids.  Acid  water  may  be  neutralized  by  the  addition  of  lime. 

Amount  of  Sediment  which  may  collect  in  a  100-H.P.  steam-boiler, 
evaporating  3000  Ibs.  of  water  per  hour,  the  water  containing  different 
amounts  of  impurity  in  solution,  provided  that  no  water  is  blown  off: 

Grains  of  solid  impurities  per  gallon: 

5         10         20         30  40         50  60         70       80         90         100 

Equivalent  parts  per  100,000: 

8.57    17.14    34.28    51.42    68.56    85.71    102.85      120    137.1    154.3    171.4 
Sediment  deposited  in  1  hour,  pounds: 

2.57      5.14    10.28    15.42    20.56    25.71      30.85        36      41.1      46.3      51.4 
In  one  day  of  10  hours,  pounds: 

25.7      51.4    102.8    154.2    205.6    257.1      308.5      360        411        463        514 
In  one  week  of  6  days,  pounds: 
154.3    308.5    617.0    925.5      1?34      1543        1851      2160      2468      2776      3085 

If  a  100-H.P.  boiler  has  1200  sq.  ft.  heating-surface,  one  week's  running 
without  blowing  off,  with  water  containing  100  grains  of  solid  matter  per 
gallon  in  solution,  would  m,ake  a  scale  nearly  1/5  in.  thick,  if  evenly  depos- 
ited all  over  the  heating-surface,  assuming  the  scale  to  have  a  sp.  gr.  of 
2.5  =  156  Ibs.  percu.  ft.;  1/5  X  1200  X  156  X  1/12  =  3120  Ibs. 

Boiler-scale  Compounds.— The  Bavarian  Steam-boiler  Inspection 
Assn.  in  1885  reported  as  follows: 

Generally  the  unusual  substances  in  water  can  be  retained  in  soluble  form 
or  precipitated  as  mud  by  adding  caustic  soda  or  lime.  This  is  especially 
desirable  when  the  boilers  have  small  interior  spaces. 

It  is  necessary  to  have  a  chemical  analysis  of  the  water  in  order  to  fully 
determine  the  kind  and  quantity  of  the  preparation  to  be  used  for  the 
above  purpose. 

All  secret  compounds  for  removing  boiler-scale  should  be  avoided.  (A  list 
of  27  such  compounds  manufacturea  and  sold  by  German  firms  is  then  given 
which  have  been  analyzed  by  the  association.) 

Such  secret  preparations  are  either  nonsensical  or  fraudulent,  or  contain 
either  one  of  the  two  substances  recommended  by  the  association  for  re- 
moving scale,  generally  soda,  which  is  colored  to  conceal  its  presence,  and 
sometimes  adulterated  with  useless  or  even  injurious  matter. 

These  additions  as  well  as  giving  the  compound  some  strange,  fanciful 
name,  are  meant  simply  to  deceive  the  boiler  owner  and  conceal  from  him 
the  fact  that  he  is  buying  colored  soda  or  similar  substances,  for  which  he  is 
paying  an  exorbitant  price. 

The  Chicago,  Milwaukee  &  St.  P.  R.  R.  uses  for  the  prevention  of  scale  in 
locomotive-boilers  an  alkaline  compound  consisting  of  3750  gals,  of  water, 
2600  Ibs.  of  70%  caustic  soda,  and  1600  Ibs.  of  58$  soda-ash.  Between  Milwau- 
kee and  Madison  the  water-supply  contains  from  1  to  4^  Ibs.  of  incrusting 
solids  per  1000  gals.,  principally  calcium  carbonate  and  sulphate  and  mag- 
nesium sulphate.  The  amount  of  compound  necessary  to  prevent  the  in- 
crustation is  1^  to  7  pints  per  1000  gals',  of  water.  This  is  really  only  one 
fourth  of  the  quantity  needed  for  chemical  combination,  but  the  action  of 
the  compound  is  regenerative.  The  soda-ash  (sodium  carbonate)  extracts 
carbonic  acid  from  the  carbonates  of  lime  and  magnesia  and  precipitates 
them  in  a  granular  form.  The  bicarbonate  of  soda  thus  formed,  however, 
loses  its  carbonic  acid  by  the  heat,  and  is  again  changed  to  the  active  car- 
bonate form.  Theoretically  this  action  might  continue  indefinitely;  but  on 


718  THE  STEAM-BOILEfc. 

account  of  the  loss  by  blowing  off  and  the  presence  of  other  impurities  in 
the  water,  it  is  found  that  the  soda-ash  will  precipitate  only  about  four 
times  the  theoretical  quantity.  Scaling  is  entirely  prevented.  One  engine 
made  122,000  miles,  and  inspection  of  the  boiler  showed  that  it  was  as  clean 
as  when  new.  This  compound  precipitates  the  impurities  in  a  granular 
form,  and  careful  attention  must  be  paid  to  washing  out  the  precipitate. 
The  practice  is  to  change  the  water  every  600  miles  and  wash  put  the  boiler 
every  1200  miles,  using  the  blow-off  cocks  also  whenever  there  is  any  indica- 
tion of  foaming,  which  seems  to  be  caused  by  the  precipitate  in  the  water, 
but  not  by  the  alkali  itself.  (Eng'g  News,  Dec.  5,  1891.) 
.  Kerosene  and  other  Petroleum  Oils  ;  Foaming.— Kerosene 
has  recently  been  highly  recommended  as  a  scale  preventive.  See  paper 
by  L.  F.  Lyne  (Trans.  A.  S.  M.  E.,  ix.  247).  The  Am.  Mach.<  May  22,  1890, 
says:  Kerosene  used  in  moderate  quantities  will  not  make  the  boiler  foam; 
it  is  recommended  and  used  for  loosening  the  scale  and  for  preventing  the 
formation  of  scale.  Neither  will  a  small  quantity  of  common  oil  always 
cause  foaming;  it  is  sometimes  injected  into  small  vertical  boilers  to  pre- 
vent priming,  and  is  supposed  to  have  the  same  effect  on  the  disturbed  sur- 
face of  the  water  that  oil  has  when  poured  on  the  rough  sea.  Yet  oil  in  boilers 
will  not  have  the  same  effect,  and  give  the  desired  results  in  all  cases.  The 
presence  of  oil  in  combination  with  other  impurities  increases  the  tendency 
of  many  boilers  to  foam,as  the  oil  with  the  impurities  impedes  the  free  escape 
of  steam  from  the  water  surface.  The  use  of  common  oil  not  only  tends  to 
cause  foaming,  but  is  dangerous  otherwise.  The  grease  appears  to  combine 
with  the  impurities  of  the  water,  and  when  the  boiler  is  at  rest  this  com- 
pound sinks  to  the  plates  and  clings  to  them  in  a  loose,  spongy  mass,  pre- 
venting the  water  from  coming  in  contact  with  the  plates,  and  thereby  pro- 
ducing overheating,  which  may  lead  to  an  explosion.  Foaming  may  also 
be  caused  by  forcing  the  fire,  or  by  taking  the  steam  from  a  point  over  the 
furnace  or  where  the  ebullition  is  violent;  the  greasy  and  dirty  state  of  new 
boilers  is  another  good  cause  for  foaming.  Kerosene  should  be  used  at  first 
in  small  quantities,  the  effect  carefully  noted,  and  the  quantity  increased  if 
necessary  for  obtaining  the  desired  results. 

R.  C.  Carpenter  (Trans.  A.  S.  M.  E.,  vol.  xi.)  says:  The  boilers  of  the  State 
Agricultural  College  at  Lansing,  Mich.,  were  badly  incrusted  with  a  hard 
scale.  It  was  fully  three  eighths  of  an  inch  thick  in  many  places.  The  first 
application  of  the  oil  was  made  while  the  boilers  were  being  but  little  used, 
by  inserting  a  gallon  of  oil,  filling  with  water,  heating  to  the  boiling-point 
and  allowing  the  water  to  stand  in  the  boiler  two  or  three  weeks  before 
removal.  By  this  method  fully  one  half  the  scale  was  removed  during  the 
warm  season  and  before  the  boilers  were  needed  for  heavy  firing.  The  oil 
was  then  added  in  small  quantities  when  the  boiler  was  in  actual  use.  For 
boilers  4  ft.  in  diam.  and  12  ft.  long  the  best  results  were  obtained  by  the 
use  of  2  qts.  for  each  boiler  per  week,  and  for  each  boiler  5  ft.  in  diam.  3  qts. 
per  week.  The  water  used  in  the  boilers  has  the  following  analysis: 

t 

CaCO3  (carbonate  calcium) 206  parts  in  1,000,000. 

MgCOs  (carbonate  magnesium) 78      "       " 

F2CO3  (carbonate  iron) 22      "       "          " 

Traces  of  sulphates  and  chlorides  of  potash  and  soda. 

Total  solid  parts,  825  to  1,000,000. 

Taiinate  of  Soda  Compound.— T.  T.  Parker  writes  to  Am.  Mach.: 
Should  you  find  kerosene  not  doing  any  good,  try  this  recipe:  50  Ibs.  sal-soda, 
35  Ibs.  japonica;  put  the  ingredients  in  a  50-gal.  barrel,  fill  half  full  of  water, 
and  run  a  steam  hose  into  it  until  it  dissolves  and  boils.  Remove  the  hose, 
fill  up  with  water,  and  allow  to  settle.  Use  one  quart  per  day  of  ten  hours 
for  a40-H.P.  boiler,  and,  if  possible,  introduce  it  as  you  do  cylinder  oil  to 
your  engine.  Barr  recommends  tannate  of  soda  as  a  remedy  for  scale  com- 
posed of  sulphate  and  carbonate  of  lime.  As  the  japonira  yields  the  taunic 
acid,  I  think  the  resultant  equivalent  to  the  tannate  of  soda. 

Petroleum  Oils  heavier  than  kerosene  have  been  used  with  good  re- 
sults. Crude  oil  should  never  be  used.  The  more  volatile  oils  it  contains 
make  explosive  gases,  and  its  tarry  constituents  are  apt  to  form  a  spongy 
incrustation. 

Removal  of  Hard  Scale.— When  boilers  are  coated  with  a  hard 
scale  difficult  to  remove  the  addition  of  y±  Ib.  caustic  soda  per  horse-power, 
and  steaming  for  some  hours,  according  to  the  thickness  of  the  scale,  just 
before  cleaning,  will  greatly  facilitate  that  operation,  rendering  the  scale 


IXCRUSTATIOtf   AHD   COftROSlOX.  tl§ 

soft,  and  loose.  This  should  be  done,  if  possible,  when  the  boilers  are  not 
otherwise  in  use.  (Steam.) 

Corrosion  In  Marine  Boilers.  (Proc.  Inst.  M.  E.,  Aug.  1884).— The 
investigations  of  the  Committee  on  Boilers  served  to  show  that  the  internal 
corrosion  of  boilers  is  greatly  due  to  the  combined  action  of  air  and  sea- 
water  when  under  steam,  and  when  not  under  steam  to  the  combined  action 
of  air  and  moisture  upon  the  unprotected  surfaces  of  the  metal.  There  are 
other  deleterious  influences  at  work,  such  as  the  corrosive  action  of  fatty 
acids,  the  galvanic  action  of  copper  and  brass,  and  the  inequalities  of  tem- 
perature; these  latter,  however,  are  considered  to  be  of  minor  importance. 

Of  the  several  methods  recommended  for  protecting  the  internal  surfaces 
of  boilers,  the  three  found  most  effectual  are:  First,  the  formation  of  a 
thin  layer  of  hard  scale,  deposited  by  working  the  boiler  with  sea-water; 
second,  the  coating  of  the  surfaces  with  a  thin  wash  of  Portland  cement, 
particularly  wherever  there  are  signs  of  decay ;  third,  the  use  of  zinc  slabs 
suspended  in  tne  water  and  steam  spaces. 

As  to  general  treatment  for  the  preservation  of  boilers  in  store  or  when 
laid  up  in  the  reserve,  either  of  the  two  following  methods  is  adopted,  as 
may  be  found  most  suitable  in  particular  cases.  First,  the  boilers  are 
dried  as  much  as  possible  by  airing-stoves,  after  which  2  to  3  cwt.  of  quirk- 
lime,  according  to  the  size  of  the  boiler,  is  placed  on  suitable  trays  at  the 
bottom  of  the  boiler  and  on  the  tubes.  The  boiler  is  then  closed  and  made 
as  air-tight  as  possible.  Periodical  inspection  is  made  every  six  months, 
when  if  the  lime  be  found  slacked  it  is  renewed.  Second,  the  other 
method  is  to  fill  the  boilers  up  with  sea  or  fresh  water,  having  added  soda 
to  it  in  the  proportion  of  1  Ib.  of  soda  to  every  100  or  120  Ibs.  of  water.  The 
sufficiency  of  the  saturation  can  be  tested  by  introducing  a  piece  of  clean 
new  iron  and  leaving  it  in  the  boiler  for  ten  or  twelve  hours;  if  it  shows 
signs  of  rusting,  more  soda  should  be  added.  It  is  essential  that  the  boilers 
be  entirely  filled,  to  the  complete  exclusion  of  air. 

Great  care  is  taken  to  prevent  sudden  changes  of  temperature  in  boilers. 
Directions  are  given  that  steam  shall  not  be  raised  rapidly,  and  that  care 
shall  be  taken  to  prevent  a  rush  of  cold  air  through  the  tubes  by  too  sud- 
denly opening  the  smoke-box  doors.  The  practice  of  empt3'ing  boilers  by 
blowing  out  is  also  prohibited,  except  in  cases  of  extreme  urgency.  As  a 
rule  the  water  is  allowed  to  remain  until  it  becomes  cool  before  the  boilers 
are  emptied. 

Mineral  oil  has  for  many  years  been  exclusively  used  for  internal  lubrica- 
tion of  engines,  with  the  view  of  avoiding  the  effects  of  fatty  acid,  as  this  oil 
does  not  readily  decompose  and  possesses  no  acid  properties. 

Of  all  the  preservative  methods  adopted  in  the  British  service,  the  use  of 
zinc  properly  distributed  and  fixed  has  been  found  the  most  effectual  in 
saving  the  iron  and  steel  surfaces  from  corrosion,  and  also  in  neutralizing 
by  its  own  deterioration  the  hurtful  influences  met  with  in  water  as  ordina- 
rily supplied  to  boilers.  The  zinc  slabs  now  used  in  the  navy  boilers  are  12 
in.  long,  6  in.  wide,  and  ^  inch  thick^  this  size  being  found  convenient  for 
general  application.  The  amount  ot  zinc  used  in  new  boilers  at  present  is 
one  slab  of  the  above  size  for  every  20  I.H.P.,  or  about  one  square  foot  of 
zinc  surface  to  two  square  feet  of  grate  surface.  Rolled  zinc  is  found  the 
most  suitable  for  the  purpose.  To  make  the  zinc  properly  efficient  as  a 
protector  especial  care  must  be  taken  to  insure  perfect  metallic  contact 
between  the  slabs  and  the  stays  or  plates  to  which  they  are  attached.  The 
slabs  should  be  placed  in  such  positions  that  all  the  surfaces  in  the  boiler 
shall  be  protected.  Each  slab  should  be  periodically  examined  to  see  that 
its  connection  remains  perfect,  and  to  renew  any  that  may  have  decayed ; 
this  examination  is  usually  made  at  intervals  not  exceeding  three  months. 
Under  ordinary  circumstances  of  working  these  zinc  slabs  may  be  expected 
to  last  in  fit  condition  from  sixty  to  ninety  days,  immersed  in  hot  sea- water; 
but  in  new  boilers  they  at  first  decay  more  rapidly.  The  slabs  are  generally 
secured  by  means  of  iron  straps  2  in.  wide  and  %  inch  thick,  and  long 
enough  to  reach  the  nearest  stay,  to  which  the  strap  is  firmly  attached  by 
screw-bolts. 

To  promote  the  proper  care  of  boilers  when  not  in  use  the  following  order 
has  been  issued  to  the  French  Navy  by  the  Government:  On  board  all  ships 
in  the  reserve,  as  well  as  those  which  are  laid  up,  the  boilers  will  be  com- 
pletely filled  with  fresh  water.  In  the  case  of  large  boilers  with  large  tubes 
there  will  be  added  to  the  water  a  certain  amounts  of  milk  of  lime,  or  a 
solution  of  soda  may  be  used  instead.  In  the  case  of  tubulous  boilers  with 
small  tubes  milk  of  lime  or  soda  may  be  added,  but  the  solution  will  not  be 


720  THE   STEAM-BOILER. 

so  strong  as  in  the  case  of  the  larger  tube,  so  as  to  avoid  any  danger  of 
contracting  the  effective  area  by  deposit  from  the  solution;  but  the  strength 
of  the  solution  will  be  just  sufficient  to  neutralize  any  acidity  of  the  water. 
(Iron  Age,  Nov.  2,  1893.) 

IJse  of  Zinc.— Zinc  is  often  used  in  boilers  to  prevent  the  corrosive 
action  of  water  on  the  metal.  The  action  appears  to  be  an  electrical  one, 
the  iron  being  one  pole  of  the  battery  and  the  zinc  being  the  other.  The 
hydrogen  goes  to  the  iron  shell  and  escapes  as  a  gas  into  the  steam.  The 
oxygen  goes  to  the  zinc. 

On  account  of  this  action  it  is  generally  believed  that  zinc  will  always 
prevent  corrosion,  and  that  it  cannot  be  harmful  to  the  boiler  or  tank. 
Some  experiences  go  to  disprove  this  belief,  and  in  numerous  cases  zinc  has 
not  only  been  of  no  use,  but  has  even  been  harmful.  In  one  case  a  tubular 
boiler  had  been  troubled  with  a  deposit  of  scale  consisting  chiefly  of  or- 
ganic matter  and  lime,  and  zinc  was  tried  as  a  preventive.  The  beneficial 
action  of  the  zinc  was  so  obvious  that  its  continued  use  was  advised,  with 
frequent  opening  of  the  boiler  and  cleaning  out  of  detached  scale  until  all 
the  old  scale  should  be  removed  and  the  boiler  become  clean.  Eight  or  ten 
mouths  later  the  water-supply  was  changed,  it  being  now  obtained  from 
another  stream  supposed  to  be  free  from  lime  and  to  contain  only  organic 
matter.  Two  or  three  months  after  its  introduction  the  tubes  and  shell 
were  found  to  be  coated  with  an  obstinate  adhesive  scale,  and  composed  of 
zinc  oxide  and  the  organic  matter  or  sediment  of  the  water  used.  The 
deposit  had  become  so  heavy  in  places  as  to  cause  overheating  and  bulging 
of  the  plates  over  the  fire.  (The  Locomotive.} 

Effect  of  Deposit  oil  Flues.  (Rankine.)— An  external  crust  of  a 
carbonaceous  kind  is  often  deposited  from  the  flame  and  smoke  of  the  fur- 
naces in  the  flues  and  tubes,  and  if  allowed  to  accumulate  seriously  impairs 
the  economy  of  fuel.  It  is  removed  from  time  to  time  by  means  of  scrapers 
and  wire  brushes.  The  accumulation  of  this  crust  is  the  probable  cause  of 
the  fact  that  in  some  steamships  the  consumption  of  coal  per  indicated 
horse-power  per  hour  goes  on  gradually  increasing  untii  it  reaches  one  and 
a  half  times  its  original  amount,  and  sometimes  more. 

Dangerous  Steam-boilers  discovered  by  Inspection.- 
The  Hartford  Steam-boiler  Inspection  and  Insurance  Co.  reports  that  its 
inspectors  during  1893  examined  163,328  boilers,  inspected  66,698  boilers, 
both  internally  and  externally,  subjected  7861  to  hydrostatic  pressure,  and 
found  597  unsafe  for  further  use.  The  whole  number  of  defects  reported 
was  122,893,  of  which  12,390  were  considered  dangerous.  A  summary  is 
given  below.  (The  Locomotive,  Feb.  1894.) 

SUMMARY,  BY  DEFECTS,  FOR  THE  YEAR  1893. 


NatureofDefects.  ™g(Prous. 
Deposit  of  sediment  9,774  548 
Incrustation  and  scale  ...  1  8,369  865 
Internal  grooving  1,249  148 
Internal  corrosion  6,252  397 
External  corrosion  8,600  536 

Nature  of  Defects.        ^^  e 
Leakage  around  tubes.  .  .21.211 
Leakage  at  seams  5,424 
Water-gauges  defective.  3,670 
Blow  outs  defective  1,620 
Deficiency  of  water  204 
Safety-valves  overloaded     723 
Safety-valves  defective..      942 
Pressure-gauges  def'tive  5,953 
Boilers  without  pressure- 
gauges  115 

Dan- 
erous. 
2,909 

482 
660 
425 
107 
203 
300 
552 

115 
4 

Deftive  braces  and  stays  1,966  485 
Settings  defective  3,094  352 
Furnaces  out  of  shape.  .  .  4,575  254 
Fractured  plates  3  532  640 

Burned  plates  2,762  325 

Blistered  plates  3331  164 

Unclassified  defects  75f. 

Defective  rivets  17  415  1  569 

Defective  heads.  .  ..  1.357  350 

Total...                       ...122.893 

12.390 

The  above-named  company  publishes  annually  a  classified  list  of  boiler- 
explosions,  compiled  chiefly  from  newspaper  reports,  showing  that  from 
200  to  300  explosions  take  place  in  the  United  States  every  year,  killing  from 
200  to  300  persons,  and  injuring  from  300  to  450.  The  lists  are  not  pretended 
to  be  complete,  and  may  include  only  a  fraction  of  the  actual  number  of 
explosions. 

Steam-boilers  as  Magazines  of  Explosive  Energy.— Prof. 

R.   H.   Thurston  (Trans.  A.  S.  M.  E..  vol.  vi.),  in    a  paper  with  the  above 

title,  presents  calculations  showing  the  stored  energy  in  the  hot  water  and 

>am  of  various  boilers.      Concerning  the  plain    tubular    boiler  of   the 

>  and  dimensions  adopted  as  a  standard  by  the  Hartford  Steam-boiler 


SAFET  Y-  V  ALV  ES.  72  1 

Insurance  Co.,  he  says:  It  is  60  inches  in  diameter,  containing  66  3-inch 
tubes,  and  is  15  feet  long.  It  has  850  feet  of  heating  and  30  feet  of  grate 
surface;  is  rated  at  60  horse-power,  but  isoftener  driven  up  to  75;  weighs 
9500  pounds,  and  contains  nearly  its  own  weight  of  water,  but  only  21 
pounds  of  steam  when  under  a  pressure  of  75  pounds  per  square  inch, 
which  is  below  its  safe  allowance.  It  stores  52,000,000  foot-pounds  of  en- 
ergy, of  which  but  4  per  cent  is  in  the  steam,  and  this  is  enough  to  drive 
the  boiler  just  about  one  mile  into  the  air,  with  an  initial  velocity  of  nearly 
600  feet  per  second. 

SAFETY-VALVES. 

Calculation  of  "Weight,  etc.,  for  l,ever  Safety-valves, 

Let  W  —  weight  of  ball  at  end  of  lever,  in  pounds; 
w  —  weight  of  lever  itself,  in  pounds; 
V  =  weight  of  valve  and  spindle,  in  pounds; 
L  =  distance  between  fulcrum  and  centre  of  ball,  in  inches; 
I  =        "  "  valve,  in  inches; 

g  =        "  "  gravity  of  lever,  in  in.; 

A  =  area  of  valve,  in  square  inches; 
P  =  pressure  of  steam,  in  Ibs.  per  sq.  in.,  at  wrhich  valve  wrill  open. 

Then    PA  X  I  =  WxL  +  wXg+Vxl', 

WL  +  wg  -f-  VI 
whence    P  =  -     ,,      —  ; 
Al 


L 
PAl  -  u'g  -  VI 


EXAMPLE.—  Diameter  of  valve,  4";  distance  from  fulcrum  to  centre  of  ball, 
86";  to  centre  of  valve,  4";  to  centre  of  gravity  of  lever,  15^";  weight  of 
valve  and  spindle,  3  Ibs.;  weight  of  lever,  7  Ibs.;  required  the  weight  of  ball 
to  make  the  blowing-off  pressure  80  Ibs.  per  sq.  in.;  area  of  4"  valve  =  12.566 
sq.  in.  Then 

PAl  -wg-  VI        80  X  12.566  X4-7Xl5^-3X4 


=  = 

L  36 

The  following  rules  governing  the  proportions  of  lever-  valves  are  given  by 
the  U.  S.  Supervisors.  The  distance  from  the  fulcrum  to  the  valve-stem 
must  in  no  case  be  less  than  the  diameter  of  the  valve-opening;  the  length 
of  the  lever  must  not  be  more  than  ten  times  the  distance  from  the  fulcrum 
to  the  valve-stem;  the  width  of  the  bearings  of  the  fulcrum  must  not  be 
less  than  three  quarters  of  an  inch  ;  the  length  of  the  fulcrum-link  must  not 
be  less  than  four  inches;  the  lever  and  fulcrum-link  must  be  made  of 
wrought  iron  or  steel,  and  the  knife-edged  fulcrum  points  and  the  bearings 
for  these  points  must  be  made  of  steel  and  hardened;  the  valve  must  be 
guided  by  its  spindle,  both  above  and  below  the  ground  seat  and  above  the 
lever,  through  supports  either  made  of  composition  (gun-metal)  or  bushed 
with  it;  and  the  spindle  must  fit  loosely  in  the  bearings  or  supports. 

Rules  for  Area  of  Safety-valves. 

(Rule  of  U.  S.  Supervising  Inspectors  of  Steam-  vessels  (as  amended  1894).) 

Lever  safety-valves  to  be  attached  to  marine  boilers  shall  have  an  area  of 

not  less  than  1  sq.  in.  to  2  sq.  ft.  of  the  grate  surface  in  the  boiler,  and  the 

seats  of  all  such  safety-valves  shall  have  an  angle  of  inclination  of  45°  to  the 

centre  line  of  their  axes. 

Spring-loaded  safety-valves  shall  be  required  to  have  an  area  of  not  less 
than  1  sq.  in.  to  3  sq.  ft.  of  grate  surface  of  the  boiler,  except  as  hereinafter 
otherwise  provided  for  water-tube  or  coil  and  sectional  boilers,  and  each 
spring-  loaded  valve  shall  be  supplied  with  a  lever  that  will  raise  the  valve 
from  its  seat  a  distance  of  not  less  than  that  equal  to  one  eighth  the  diam- 
eter of  the  valve-opening,  and  the  seats  of  all  such  safety-valves  shall  have 
an  angle  of  inclination  to  the  centre  line  of  their  axes  of  45°.  All  spring- 
loaded  safety-valves  for  water-tube  or  coil  and  sectional  boilers  required  to 


722  THE   STEAM-BOILER. 

carry  a  steam-pressure  exceeding  175  Ibs.  per  square  inch  shall  be  required 
to  have  an  area  of  not  less  than  1  sq.  in.  to  6  sq.  ft.  of  the  grate  surlace  <>f 
the  boiler.  Nothing  herein  shall  be  construed  so  as  to  prohibit  the  use  of 
two  safety-valves  on  one  water- tube  or  coil  and  sectional  boiler,  provided 
the  combined  area  of  such  valves  is  equal  to  that  required  by  rule  for  one 
such  valve. 

Rule  in  Philadelphia  Ordinances :  Bureau  of  Steam- 
engine  and  Boiler  Inspection.— Every  boiler  when  fired  sepa- 
rately, and  every  set  or  series  of  boilers  when  placed  over  one  fire,  shall 
have  attached  thereto,  without  the  interposition  of  any  other  valve,  two  or 
more  safety-valves,  the  aggregate  area  of  which  shall  have  such  relations  to 
the  area  of  the  grate  and  the  pressure  within  the  boiler  as  is  expressed  in 
schedule  A. 

SCHEDULE  A.— Least  aggregate  area  of  "safety-valve  (being  the  least  sec- 
tional area  for  the  discharge  of  steam)  to  be  placed  upon  all  stationary  boil- 
ers with  natural  or  chimney  draught  [see  note  a]. 
_     22.5G 
~~  P-f  8.62' 

in  which  A  is  area  of  combined  safety-valves  in  inches;  G  is  area  of  grate  in 
square  feet;  2*  is  pressure  of  steam  in  pounds  per  square  inch  to  be  carried 
in  the  boiler  above  the  atmosphere. 

The  following  table  gives  the  results  of  the  formula  for  one  square  foot  of 
grate,  as  applied  to  boilers  used  at  different  pressures: 

Pressures  per  square  inch : 

10        20        30        40        50        60        70        80        90        "^        110        150 

Area  corresponding  to  one  square  foot  of  grate: 
1.21    0.79    0.58    0.46    0.38    0.33    0.29    0.25    0.23     0.21     0.19      0.17 

[Note  a.]  Where  boilers  have  a  forced  or  artificial  draught,  the  inspector 
must  estimate  the  area  of  grate  at  the  rate  of  one  square  foot  of  grate- sur- 
face for  each  16  Ibs.  of  fuel"  burned  on  the  average  per  hour. 

Comparison  of  Various  Rules  for  Area  of  Iiever  Safety- 
valves.  (From  an  article  by  the  author  in  Ann'riatn  Macinnixt,  May  vl. 
1894,  with  some  alterations  and  additions.)— Assume  the  case  of  a  boiler 
rated  at  100  horse-power;  40  sq.  ft.  grate;  1200  sq.  ft.  heating-surface;  using 
400  Ibs.  of  coal  per  hour,  or  10  Ibs.  per  sq.  ft.  of  grate  per  hour,  and  evapora- 
ting  3600  Ibs.  of  water,  or  3  Ibs.  per  sq.  ft.  of  heating-surface  per  hour; 
steam-pressure  by  gauge,  100  Ibs.  What  size  of  safety-valve,  of  the  lever 
type,  should  be  required  ? 

A  compilation  of  various  rules  for  finding  the  area  of  the  safety-vale  disk, 
from  T/ie  Locomotive  of  July,  1892,  is  given  in  abridged  form  below,  to- 
gether with  the  area  calculated  by  each  rule  for  the  above  example. 

Disk  Area  in  sq.  in. 

U.  S.  Supervisors,  heating-surface  in  sq.  f  t.  -=-  25  * 48 

English  Board  of  Trade,  grate-surface  in  sq.  f t.  -*-  2 20 

Molesworth,  four  fifths  of  grate-surface  in  sq.  ft 32 

Thurston,  4  times  coal  burned  per  hour  x  (gauge  pressure  -j-  10) 14.5 

1  (5  x  heating-surface) 

Thurston,  -  —-' 27.3 

2  gauge  pressure  -4-10 

Rankine,  .006  X  water  evaporated  per  hour 210 

Committee  of  U.  S.  Supervisors,  .005  X  water  evaporated  per  hour 18 

Suppose  that,  other  data  remaining  the  same,  the  draught  were  increased 
so  as  to  burn  13^  Ibs.  coal  per  square  foot  of  grate  per  hour,  and  the  grate- 
surface  cut  down  to  30  sq.  ft.  to  correspond,  making  the  coal  burned  per 
hour  400  Ibs.,  and  the  water  evaporated  3600  Ibs.,  the  same  as  before:  then 
the  English  Board  of  Trade  rule  and  Molesworth's  rule  would  give  an  area, 
of  disk  of  only  15  and  24  sq.  in.,  respective ry,  showing  the  absurditj"  of  mak- 
ing the  area  of  grate  the  basis  of  the  calculation  of  disk  area. 

Another  rule  by  Prof.  Thurston  is  given  in  American  Machinist,  Dec.  1877, 
viz.: 

Disk  area  =  ^  max-  wt-  of  water  evap.  per  hour 

gauge  pressure  -f  10 
This  gives  for  the  example  considered  16.4  sq.  in. 

*  The  edition  of  1893  of  the  Rules  of  the  Supervisors  does  not  contain  this 
but  gives  the  rule  grate-surface  H-  2. 


SAFETY-VALVES,  723 

One  rule  by  Rankine  is  1/150  to  1/180  of  the  number  of  pounds  of  water 
evaporated  per  hour,  equals  for  the  above  case  27  to  20  sq.  in.  A  communi- 
tion  in  Power,  July,  1890.  gives  two  other  rules: 

1st.  1  sq.  iu.  disk  area  for  3  sq.  ft.  grate,  which  would  give  13.3  sq.  in. 

2d.  %  sq.  in.  disk  area  for  1  sq.  ft.  grate,  which  would  give  30  sq.  in.;  but 
if  the  grate-surface  were  reduced  to  30  sq.  ft.  on  account  of  increased 
draught,  these  rules  would  make  the  disk  area  only  10  and  22.5  sq.  in., 
respectively. 

The  Philadelphia  rule  for  100  Ibs.  gauge  pressure  gives  a  disk  area  of  0.21 
sq.  in.  for  each  sq.  ft.  of  grate  area,  which  would  give  an  area  of  8.4  sq.  in. 
for  40  sq.  ft.  grate,  and  only  6.3  sq.  in.  if  the  grate  is  reduced  to  30  sq.  ft. 

According  to  the  rule  this  aggregate  area  would  have  to  be  divided  between 
two  valves.  But  if  the  boiler  was  driven  by  forced  draught,  then  the  in- 
spector ''must  estimate  the  area  of  grate  at  1  sq.  ft.  for  each  16  Ibs.  of  fuel 
burned  per  hour/' 

Under  this  condition  the  actual  grate-surface  might  be  cut  down  to  400  -5- 
16  =  25  sq.  ft.,  and  by  the  rule  the  combined  area  of  the  two  safety-valves 
would  be  only  25  X  0.21  =  5.25  sq.  in. 

Nystrom's  Pocket-book,  edition  of  1891,  gives  %  sq.  in.  for  1  sq.  ft.  grate; 
also  quoting  from  Weisbach,  vol.  ii,  1/3000  of  the  heating-surface.  This  in 
the  case  considered  is  1200/3000  =  .4  sq.  ft.  or  57.6  sq.  in. 

We  thus  have  rules  which  give  for  the  area  of  safety-valve  of  the  same  100- 
horse-power  boiler  results  ranging  all  the  way  from  5.25  to  57.6  sq.  in. 

All  of  the  rules  above  quoted  give  the  area  of  the  disk  of  the  valve  as  the 
thing  to  be  ascertained,  and  it  is  this  area  which  is  supposed  to  bear  some 
direct  ratio  to  the  grate-surface,  to  the  heating-surface,  to  the  water  evap- 
orated, etc.  It  is  difficult  to  see  wh}r  this  area  has  been  considered  even 
approximately  proportional  to  these  quantities,  for  with  small  lifts  the  area 
of  actual  opening  bears  a  direct  ratio,  not  to  tne  area  of  disk,  but  to  the 
circumference. 

Thus  for  various  diameters  of  valve  : 

Diameter 1         2  3  4  6  7 

Area 785      3.14      7.07      12.57        JJ.64        28.27      38.48 

Circumference 3.14        6.28      9.42      12.57       15.71         18.85      21.99 

Circum.  X  lift  of  0.1  in 31          .63        .94        1.26         1.57          1.89        2.20 

Ratio  to  area 4  .2         .13         .1  .08  .067        .057 

The  apertures,  therefore,  are  therefore  directly  proportional  to  the  diam- 
eter or  to  the  circumference,  but  their  relation  to  the  area  is  a  varying  one. 

If  the  lift  =  14  diameter,  then  the  opening  would  be  equal  to  the  area  of 
the  disk,  for  circumference  X  Y±  diameter  =  area,  but  such  a  lift  is  far 
beyond  the  actual  lift  of  an  ordinary  safety-valve. 

A  correct  rule  for  size  of  safety-valves  should  make  the  product  of  the 
diameter  and  the  lift  proportional  to  the  weight  of  steam  to  be  discharged. 

A  "logical"  method  for  calculating  the  size  of  safety-valve  is  given  in 
The  Locomotive,  July,  1892,  based  on  the  assumption  that  the  actual  opening 
should  be  sufficient  to  discharge  all  the  steam  generated  by  the  boiler. 
Napier's  rule  for  flow  of  steam  is  taken,  viz.,  flow  through  aperture  of  one 
sq.  in.  in  Ibs.  per  second  =  absolute  pressure  ^-  70,  or  in  Ibs.  per  hour  =  51.43 
X  absolute  pressure. 

If  the  angle  of  the  seat  is  45°,  as  specified  in  the  rules  of  the  U.  S.  Super- 
visors, the  area  of  opening  in  sq.  in.  =  circumference  of  the  disk  X  the  lift 
X  .71,  .71  being  the  cosine  of  45°;  or  diameter  of  disk  X  lift  X  2.23. 

A.  G.  Brown  in  his  book  on  The  Indicator  and  its  Practical  Working 
(London,  1894)  gives  the  following  as  the  lift  of  the  ordinary  lever  safety- 
valve  for  100  Ibs.  gauge-pressure: 

Diam.  of  valve..       2       2>£        3       3%       4        4^        5         6     inches. 
Rise  of  valve 0583  .0523  .0507  .0492  .0478  .0462  .0446  .0430  inch. 

The  lift  decreases  with  increase  of  steam -pressure;  thus  fora  4-inch  valve: 
Abs.  pressure,  Ibs.  45  65  85  105  115  135  155  175  195  215 
Gauge-press.,  Ibs..  30  50  7u  90  100  120  140  160  180  200 
Rise,  inch 1034  .0775  .06^0  .0517  .0478  .0413  .0365  .0327  .0296  .0270 

The  effective  area  of  opening  Mr.  Brown  takes  at  70£  of  the  rise  multiplied 
by  the  circumference. 

An  approximate  formula  corresponding  to  Mr.  Brown's  figures  for  diam- 
eters between  2^>  and  6  in.  and  gauge-pressures  between  70  and  200  Ibs.  is 

Lift  =  (.0603  -  0031d)  X  n  -— ,  in  which  d  =  diam.  of  valve  in  in. 

•    abs.  pressure 


724 


THE   STEAM-BOILER. 


If  we  combine  this  formula  with  the  formulas 

Flowinlbs.  per  hour  =  area  of  opening  in  sq.  in.X  51.43X  abs.  pressure,  and 

Area  —  diameter  of  valve  X  lift  X  2.28,  we  obtain  the  following,  which  the 
author  suggests  as  probably  a  more  correct  formula  for  the  discharging 
capacity  of  the  ordinary  lever  safety-valve  than  either  of  those  above  given. 

Flow  in  Ibs.  per  hour  =  d(.0603  -  .0031d)  X  115  X  2.28  x  51.43  =  d(795  —  41d). 

From  which  we  obtain  : 

Diameter,  inches....     1       1^       2       2%       3       3^       4         5         6         7 
Flow,  Ibs.  per  hour..  754    1100    1426    1733    2016    2282    2524    2950    3294    3556 

Horse-power 25       37       47       58        67        76        84       98       110      119 

the  horse-power  being  taken  as  an  evaporation  of  30  Ibs.  of  water  per  hour. 

If  we  solve  the  example,  above  given,  of  the  boiler  evaporating  3600  Ibs.  of 
water  per  hour  by  this  table,  we  find  it  requires  one  7-inch  valve,  or  a  2^- 
and  a  3-inch  valve  combined.  The  7-inch  valve  has  an  area  of  38.5  sq.  in., 
and  the  two  smaller  valves  taken  together  have  an  area  of  only  12  sq.  in.; 
another  evidence  of  the  absurdity  of  considering  the  area  of  disk  as  the 
factor  which  determined  the  capacity  of  the  valve. 

It  is  customary  in  practice  not  to  use  safety-valves  of  greater  diameter 
than  4  in.  If  a  greater  diameter  is  called  for  by  the  rule  that  is  adopted, 
then  two  or  more  valves  are  used  instead  of  one. 

Spring-loaded  Safety-valves.— Instead  of  weights,  springs  are 
sometimes  employed  to  hold  down  safety-valves.  The  calculations  are 
similar  to  those  for  lever  safety-valves,  the  tension  of  the  spring  correspond- 
ing to  a  given  rise  being  first  found  by  experiment  (see  Springs,  page  347). 

The  rules  of  the  IT.  S.  Supervisors  allow  an  area  of  1  sq.  in.  of  the  valve 
to  3  sq.  ft.  of  grate,  in  the  case  of  spring-loaded  valves,  except  in  water-tube, 
coil,  or  sectional  boilers,  in  which  1  sq.  in.  to  6  sq.  ft.  of  grate  is  allowed. 

Spring-loaded  safety-valves  are  usually  of  the  reactionary  or  "  pop  "  type, 
in  which  the  escape  of  the  steam  is  opposed  by  a  lip  above  the  valve-seat, 
against  which  the  escaping  steam  reacts,  causing  the  valve  to  lift  higher 
than  the  ordinary  valve. 

A.  GK  Brown  gives  the  following  for  the  rise,  effective  area,  and  quantity 
of  steam  discharged  per  hour  by  valves  of  the  "pop  "  or  Richardson  type. 
The  effective  is  taken  at  only  50$  of  the  actual  area  due  to  the  rise,  on  account 
of  the  obstruction  which  the  lip  of  the  valve  offers  to  the  escape  of  steam. 


Dia.  value,  in 

1 

Ifcj 

2 

2^ 

3 

31^ 

4 

4^ 

5 

6 

Lift,  inches. 

.125 

.150 

.175 

200 

.225 

.250 

.275 

.300 

.325 

.375 

Area,  sq.  in. 

.196 

.354 

.550 

.785 

1.061 

1.375 

1.728 

2.121 

2.553 

3.535 

Gauge-pres,, 

Steam  discharged  per  hour,  Ibs. 

30  Ibs. 

474 

856 

1330 

1897 

2563 

3325 

4178 

5128 

6173 

8578 

50 

669 

1209 

1878 

2680 

3620 

4695 

5901 

7242 

8718 

12070 

70 

861 

1556 

2417 

3450 

4660 

6144 

7596 

9324 

11220 

15535 

90 

1050 

1897 

2947 

4207 

5680 

7370 

9260 

11305 

13685 

18945 

100 

1144 

2065 

3208 

4580 

6185 

8322 

10080 

12375 

14895 

20625 

120 

1332 

2405 

3736 

5332 

7202 

9342 

11735 

14410 

17340 

24015 

140 

1516 

2738 

4254 

6070 

8200 

10635 

13365 

16405 

19745 

27340 

160 

1696 

3064 

4760 

6794 

9175 

11900 

14955 

18355 

22095 

30595 

180 

1883 

3400 

5283 

7540 

10180 

13250 

16595 

20370 

24520 

33950 

200 

2062 

3724 

5786 

8258 

11150 

14465 

18175 

22310 

26855 

37185 

If  we  take  30  Ibs.  of  steam  per  hour,  at  100  Ibs.  gauge-pressure  =  1  H.P., 
we  have  from  the  above  table: 

Diameter,  inches...    1     1^     2      2^      3      3^      4      4^      5       6 

Horse-power 38    69    107    153    206    277    336    412    496    687 

A  safety-valve  should  be  capable  of  discharging  a  much  greater  quantity 
of  steam  than  that  corresponding  to  the  rated  horse-power  of  a  boiler,  since 
i\,  boiler  having  ample  grate  surface  and  strong  draught  may  generate  more 
than  double  the  quantity  of  steam  its  rating  calls  for. 

The  Consolidated  Safety-valve  Co.'s  circular  gives  the  following  rated 
capacity  of  its  nickel-seat  "  pop  "  safety-valves: 

Size,  in  1      1W    1U      2     S*£      8        3^       4        4^       5        5^ 

Boiler  I  from     8       10      20      35      60       75       100      125      150      175      200 
H.P.  "j       to    10      15      30      50      75      100      125      150      175      200      275 
The  figures  in  the  lower  line  from  2  inch  to  5  inch,  inclusive,  correspond  to 
*ormula  H.P.  =  50(diameter  -  1  inch). 


THE   INJECTOR. 


725 


THE    INJECTOR. 

Equation  of  the  Injector, 

Let  S  be  the  number  of  pounds  of  steam  used ; 

W  the  number  of  pounds  of  water  lifted  and  forced  into  the  boiler; 
h  the  height  in  feet  of  a  column  of  water,  equivalent  to  the  absolute 

pressure  in  the  boiler; 

h0  the  height  in  feet  the  water  is  lifted  to  the  injector; 
ti  the  temperature  of  the  water  before  it  enters  the  injector; 
£2  the  temperature  of  the  water  after  leaving  the  injector; 
H  the  total  heat  above  32°  F.  in  one  pound  of  steam  in  the  boiler,  in 

heat-units; 

L  the  lost  work  in  friction  and  the  equivalent  lost  work  due  to  radia- 
tion and  lost  heat; 

778  the  mechanical  equivalent  of  heat. 
Then 

S[H  -  ff,  -  32°)]  =  W,  -  *,)  +  {W+S}k  +  ] 

i  to 

An  equivalent  formula,  neglecting  Wh0  -f  L  as  small,  is 


or    S  = 


-(t^  -  32°)d  -  .1851p' 
in   which  d  —  weight  of  1  cu.  ft.  of  water  at  temperature  fa;  p  —  absolute 
pressure  of  steam,  Ibs.  per  sq.  in. 

The  rule  for  finding  the  proper  sectional  area  for  the  narrowest  part  of 
the-  nozzles  is  given  as  follows  by  Rankine,  S.  E.  p.  477: 

cubic  feet  per  hour  gross  feed- water 

Area  in  square  inches  =  — -  — 

800  y  pressure  in  atmospheres 

An  important  condition  which  must  be  fulfilled  in  order  that  the  injector 
will  work  is  that  the  supply  of  water  must  be  sufficient  to  condense  the 
steam.  As  the  temperature  of  the  supply  or  feed -water  is  higher,  the 
amount  of  water  required  for  condensing  purposes  will  be  greater. 

The  table  below  gives  the  calculated  value  of  the  maximum  ratio  of  water 
to  the  steam,  and  the  values  obtained  on  actual  trial,  also  the  highest  admis- 
sible temperature  of  the  feed- water  as  shown  by  theory  and  the  highest 
actually  found  by  trial  with  several  injectors. 


Gauge- 
pres- 
sure, 
pounds 
per 
sq.  in. 

MAXIMUM  RATIO  WATER 
TO  STEAM. 

Gauge- 
pres- 
sure, 
pounds 
per 
sq.  in. 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
120 
150 

MAXIMUM  TEMPERATURE  OF 
FEED-WATER. 

Calculated 
from 
Theory. 

36.5 
25.6 
20.9 
17.87 
16.2 
14.7 
13.7 
12.9 
12.1 
11.5 

Actual  Expe- 
riment. 

Theoretical. 

Experrtal  Results. 

<D 

d^    ' 

C  ^  O 
•r  pfl  GO 

H&~ 

-3 

<D 

*$•• 

B.5& 

EHJT 

'O 

H. 

p. 

M. 

S. 

132° 
134 
134 
132 
131 
130 
130 
131 
132* 
132* 
134* 
121* 

H. 

30.9 
22.5 
19,0 
15.8 
13.3 
11.2 
12.3 
11.4 

P. 

19"!9 
17.2 
15.0 
14.0 
11.2 
11.7 
11.2 

M. 

21  .5 
19.0 

15.86 
13.3 
12.6 
12.9 

10 
20 
30 
40 
50 
60 
70 
80 
90 
100 

142°' 
132 
126 
120 
114 
109 
105 
99 
95 
87 
77 

"173° 
162 
156 
150 
143 
139 
134 
129 
125 
117 
107 

i35° 
*i40' 

120° 
113' 

130° 
125 

i23 
123 
122 

iii* 

141* 

115 
118 

Temperature  of  delivery  above  212°.    Waste-valve  closed. 
H.  Hancock  inspirator;  P,  Park  injector;  M,  Metropolitan  injector;  S,  Sel- 
lers 1876  injector, 


726  THE    STEAM-BOILER. 

Efficiency  of  the  Injector.— Experiments  at  Cornell  University, 
described  by  Prof.  R.  C.  Carpenter,  in  Cassier^s  Magazine,  Feb.  1892,  show 
that,  the  injector,  when  considered  merely  as  a  pump,  has  an  exceedingly 
low  efficiency,  the  duty  ranging  from  161,000  to  2,752.000  under  different  cir- 
cumstances of  steam  and  delivery  pressure.  Small  direct-acting  pumps, 
such  as  are  used  for  feeding  boilers,  show  a  duty  of  from  4  to  8 
million  IDS  ,  and  the  best  pumping-engines  from  100  to  140  million.  When 
used  for  feeding  water  into  a  boiler,  however,  the  injector  has  a  thermal 
efficiency  of  100$,  less  the  trifling  loss  due  to  radiation,  since  all  the  heat  re- 
jected passes  into  the  water  which  is  carried  into  the  boiler. 

The  loss  of  work  in  the  injector  due  to  friction  reappears  as  heat  which  is 
carried  into  the  boiler,  and  the  heat  which  is  converted  into  useful  work  in 
the  injector  appears  in  the  boiler  as  stored-up  energy. 

Although  the  injector  thus  has  a  perfect  efficiency  as  a  boiler-feeder,  it  is 
nevertheless  not  the  most  economical  means  for  feeding  a  boiler,  since  it 
can  draw  only  cold  or  moderately  warm  water,  while  a  pump  can  feed 
water  which  has  been  heated  by  exhaust  steam  which  would  otherwise  be 
wasted. 

Performance  of  Injectors.— In  Am.  Mach.,  April  13,  1893,  are  a 
number  of  letters  from  different  manufacturers  of  injectors  in  reply  to  the 
question:  "  What  is  the  best  performance  of  the  injector  in  raising  or  lifting 
water  to  any  height  ?"  Some  of  the  replies  are  tabulated  below. 

W.  Sellers  &  Co.— 25.51  Ibs.  water  delivered  to  boiler  per  Ib.  of  steam;  tem- 
perature of  water,  64°;  steam  pressure,  65  Ibs. 

Schaeffer  &  Budenberg— 1  gal.  water  delivered  to  boile-  for  0.4  to  0.8  Ib. 
steam. 

Injector  will  lift  by  suction  water  of 

140°  F.          136°  to  133°      122°  to  180°       113°  to  107° 
If  boiler  pressure  is.  30  to  60  Ibs.     60  to  90  Ibs.     90  to  120  Ibs.     120  to  150  Ibs. 

If  the  water  is  not  over  80°  F.,  the  injector  will  force  against  a  pressure  75 
Ibs.  higher  than  that  of  the  steam. 
Hancock  Inspirator  Co.: 

Lift  in  feet 22  22  22  11 

Boiler  pressure,  absolute,  Ibs 75 . 8  54 . 1  95 . 5  75 . 4 

Temperature  of  suction 34.9°          35.4°          47.3°          53.2° 

Temperature  of  delivery 134°  117.4°        173.7°        131.1 

Water  fed  per  Ib.  of  steam,  Ibs...     11.02         13.67          8.18         13.3 

The  theory  of  the  injector  is  discussed  in  Wood's.  Peabody's,  and  Ront- 
geii's  treatises  on  Thermodynamics.  See  also  "  Theory  and  Practice  of  the 
Injector,1'  by  Strickland  L.  Kneass,  New  York,  1895. 

Boiler-feeding  Pumps.— Since  the  direct-acting  pump,  commonly 
used  for  feeding  boilers,  has  a  very  low  efficiency,  or  less  than  one  tenth 
that  of  a  good  engine,  it  is  generally*  better  to  vise  a  pump  driven  by  belt 
from  the  main  engine  or  driving  shaft.  The  mechanical  work  needed  to  feed 
a  boiler  may  be  estimated  as  follows:  If  the  combination  of  boiler  and  en- 
gine is  such  that  half  a  cubic  foot,  say  32  Ibs.  of  water,  is  needed  per  horse- 
power, and  the  boiler-pressure  is  100  Ibs.  per  sq.  in.,  then  the  work  of  feed- 
ing the  quantity  of  water  is  100  Ibs.  X  144  sq.  in.  x  ^  ft.-lbs.  per  hour  —  120 
ft.-lbs.  per  min.  =  120/33,000  =  .0036  H.P.,  or  less  than  4/10  of  \%  of  the 
power  exerted  by  the  engine.  If  a  direct-acting  pump,  which  discharges  its 
exhaust  steam  into  the  atmosphere,  is  used  for  feeding,  and  it  has  only  1/10 
the  efficiency  of  the  main  engine,  then  the  steam  used  by  the  pump  will  be 
equal  to  nearly  4$  of  that  generated  by  the  boiler. 

The  following  table  by  Prof.  D.  S.  Jacobus  gives  the  relative  efficiency  of 
steam  and  power  pumps  and  injector,  with  and  without  heater,  as  used 
upon  a  boiler  with  80  Ibs.  gauge-pressure,  the  pump  having  a  duty  of 
10,000,000  ft.-lbs.  per  100  Ibs.  of  coal  when  no  heater  is  used ;  the  injector 
heating  the  water  from  60°  to  150°  F. 

Direct-acting  pump  feeding  water  at  60°,  without  a  heater 1 .000 

Injector  feeding  water  at  150°,  without  a  heater 985 

Injector  feeding  water  through  a  heater  in  which  it  is  heated  from 

150°  to  200° .938 

Direct-acting  pump  feeding  water  through  a  heater,  in  which  it  is 

heated  from  60°  to  200° 879 

Geared  pump,  run  from  the  engine,  feeding  water  through  a  heater, 

in  which  it  is  heated  from  60°  to  200° , . .  . , ,863 


FEE  D  -W ATE  R    H  K AT  E RS. 


727 


FEED-HEATER  HEATERS. 

Percentage  of  Saving  for  Each  Degree  of  Increase  in  Tem^ 
perature  of  Feed-water  Heated  by  Waste  Steam. 


Pressure  of  Steam  in  Boiler,  Ibs.  per  sq.  in.  above 

Initial 
Temp. 

Atmosphere. 

Initial 

of 
Feed. 

0 

20 

40 

60 

80 

100 

120 

140 

100 

180 

200 

lemp. 

32° 

.0872 

.0861 

.0855 

.0851 

.0847 

.0844 

.0841 

.0839 

.0837 

.0835 

.0833 

32 

40 

.0878 

.0867 

.0861 

.0856 

.0853 

.0850 

.0847 

.0845 

.0843 

.0841 

.0839 

40 

50 

.0886 

.0875 

.0868 

.0864 

.0860 

.0857  .0854 

.0852 

.0850 

.0848 

.0846 

50 

GO 

.0894 

.0883 

.0876 

.0872 

.0867 

.0864  .0862 

.0859 

.0856 

.0855 

.0853 

60 

70 

.0902 

.0890 

.0884 

.0879 

.0875 

.0872  1.0869  .  0867 

.0864 

.0862 

.0860 

70 

80 

.0910 

.0898 

.0891 

.0887 

.0883 

.0879  ,.0877 

.0874 

.0872 

.0870 

.0868 

80 

90 

.0919 

.0907 

.0900 

.0895 

.0888 

.0887J.0884 

.0883 

.0879 

.0877 

.0875 

90 

100 

.0927 

.0915 

.0908 

.0903 

.0899 

.0895  .0892 

.0890 

.0887 

.0885 

.0883 

100 

110   .0936 

.0923 

.0916 

.0911 

.0907 

.  0903  !.  0900 

.0898 

.0895 

.0893 

.0891 

110 

120  j.0945 

.0932 

.0925 

.0919 

.0915 

.09111.0908 

.0906 

.0903 

.0901 

.0899 

120 

130 

.0954 

.0941 

.0934 

.0928 

.0924 

.0920 

.0917 

.0914 

.0912 

.0909 

.0907 

130 

140 

.0963 

.0950 

.0943 

.0937 

.0932 

.0929 

.0925 

.0923 

.0920 

.0918 

.0916 

140 

150 

.0973 

.0959 

.0951 

.0946 

.0941 

.0937 

.0934 

.0931 

.0929 

.0926 

.0924 

150 

160 

0982 

0968 

.0961 

0955 

0950 

0946 

.0943 

.0940 

.0937 

.0935 

0933 

160 

170 

.0992 

.0978 

.0970 

.0964 

.0959 

.0955 

.0952 

.0949 

.0946 

.0944 

.0941 

170 

180 

.1002 

.0988 

.0981 

.0973 

.0969 

.0965 

.0961 

.0958 

.0955 

.0953 

.0951 

180 

190 

.1012 

.0998 

.0989 

.0983 

.0978 

.0974 

.0971 

.0968 

.0964 

.0962 

.0960 

190 

200 

.1022 

.1008 

.0999 

.0993 

.0988 

.0984 

.0980 

.0977 

.0974 

.0972 

.0969 

200 

210 

.1033 

.1018 

.1009 

.1003 

.0998 

.0994 

.0990 

.0987 

.0984 

.0981 

.0979 

210 

220 

.1029 

.1019 

.1013 

.1008 

.1004 

.1000 

.0997 

.0994 

.0991 

.0989 

220 

230 

.1039 

.1031 

.1024 

.1018 

.1012 

.1010 

.1007 

.1003 

.1001 

.0999 

230 

240 

.1050 

.1041 

.1034 

.1029 

.1024 

.1020 

.1017 

.1014 

.1011 

.1009 

240 

250 

.1062 

.1052 

.1045 

.1040 

.1035 

.1031 

.1027 

.1025 

.1022 

.1019 

250 

An  approximate  rule  for  the  conditions  of  ordinary  practice  is  a  saving 
of  \%  is  made  by  each  increase  of  11°  in  the  temperature  of  the  feed-water. 
This  corresponds  to  .0909$  per  degree. 

The  calculation  of  saving  is  made  as  follows:  Boiler-pressure,  100  Ibs. 
gauge;  total  heat  in  steam  above  32°  =  1185  B.T.U.  Feed-water,  original 
Temperature  60°,  final  temperature  209°  F.  Increase  in  heat-units,  150. 
Heat-units  above  32°  in  feed-water  of  original  temperature  =  28.  Heat- 
units  in  steam  above  that  in  cold  feed-water,  1185  -  28  =  1157.  Saving  by  the 
teed- water  heater  =  150/1157  =  12.96$.  The  same  result  is  obtained  by  the 
use  of  the  table.  Increase  in  temperature  150°  X  tabular  figure  .0864  = 
12.96$.  Let  total  heat  of  lib.  of  steam  at  the  boiler-pressure  =  H;  total 
heat  of  1  Ib.  of  feed-water  before  entering  the  heater  =  /<,,  and  after  pass- 
ing through  the  heater  =  7i2;  then  the  saving  made  by  the  heater  is  *  ~  ,  *. 

ri  —  /11 

Strains  Caused  by  Cold  Feed-water.— A  calculation  is  made 
in  The  Locomotive  of  March,  1893.  of  the  possible  strains  caused  in  the  sec- 
tion of  the  shell  of  a  boiler  by  cooling  it  by  the  injection  of  cold  feed-water. 
Assuming  the  plate  to  be  cooled  200°  F.,  and  the  coefficient  of  expansion  of 
steel  to  be  .0000067  per  degree,  a  strip  10  in.  long  would  contract  .013  in.,  if  it 
were  free  to  contract.  To  resist  this  contraction,  assuming  that  the  strip  is 
firmly  held  at  the  ends  and  that  the  modulus  of  elasticity  is  29,000,000,  would 
require  a  force  of  37,700  Ibs.  per  sq.  in.  Of  course  this  amount  of  strain  can- 
not actually  take  place,  since  the  strip  is  not  firmly  held  at  the  ends,  but  is 
allowed  to  contract  to  some  extent  by  the  elasticity  of  the  surrounding 
metal.  But,  says  The  Locomotive,  we  may  feel  pretty  confident  that  in  the 
case  considered  a  longitudinal  strain  of  somewhere  in  the  neighborhood  of 
8000  or  10,000  Ibs.  per  sq.  in.  may  be  produced  by  the  feed -water  striking 
directly  upon  the  plates;  and  this,  in  addition  to  the  normal  strain  pro- 
duced by  the  steam-pressure,  is  quite  enough  to  tax  the  girth-seams  beyond 
their  elastic  limit,  if  the  feed-pipe  discharges  anywhere  near  them.  Hence 
it  is  not  surprising  that  the  girth-seams  develop  leaks  and  cracks  in  99 
cases  out  of  every  100  in  which  the  feed  discharges  directly  upon  the  fire- 
sheets, 


THE    STEAM-BOILER. 


STEAM    SEPARATORS. 

If  moist  steam  flowing  at  a  high  velocity  in  a  pipe  has  its  direction  sud- 
denly changed,  the  particles  of  water  are  by  their  momentum  projected  in 
their  original  direction  against  the  bend  in  the  pipe  or  wall  of  the  chamber 
n  which  the  change  of  direction  takes  place.  By  making  proper  provision 
for  drawing  off  the  water  thus  separated  the  steam  may  be  dried  to  a 
greater  or  less  extent. 

For  long  steam-pipes  a  large  drum  should  be  provided  near  the  engine 
for  trapping  the  water  condensed  in  the  pipe.  A  drum  3  feet  diameter,  15 
feet  high,  has  given  good  results  in  separating  the  water  of  condensation  of 
a  steam-pipe  10  inches  diameter  and  800  feet  long. 

Efficiency  of  Steam  Separators.— Prof.  R.  C.  Carpenter,  in  1891, 
made  a  series  of  tests  of  six  steam  separators,  furnishing  them  with  steam 
containing  different  percentages  of  moisture,  and  testing  the  quality  of 
steam  before  entering  and  after  passing  the  separator.  A  condensed  table 
of  the  principal  results  is  given  below. 


Make  of 
Separator. 

Test  with  Steam  of  about  10$  of 
Moisture. 

Tests  with  Varying  Moisture. 

Quality  of 
Steam 
before. 

Quality  of 
Steam 
after. 

Efficiency 
per  cent. 

Quality  of 
Steam 
before. 

Quality  of 
Steam 
after. 

Av'ge 
Effi- 
ciency. 

B 
A 
D 

C 
E 

F 

87.0^ 
90.1 
89.6 
90.6 
88.4 
88.9 

98.  8# 
98.0. 
95.8 
93.7 
90.2 
92.1 

90.8 
80.0 
59.6 
33.0 
15.5 
28.8 

66.1  to  97.5$ 
51.9  "  98 
72.2  "  96.1 
67.1  "  96.8 
68.6  "  98.1 
70.4  "  97.7 

97.8  to  99$ 
97.9       99.1 
95.5       98.2 
93.7       98.4 
79.3       98.5 
84.1       97.9 

87.6 
76.4 
71.7 
63.4 
36.9 
28.4 

Conclusions  from  the  tests  were:  1.  That  no  relation  existed  between  the 
volume  of  the  several  separators  and  their  efficiency. 

2.  No  marked  decrease  in  pressure  was  shown  by  any  of  the  separators, 
the  most  being  1.7  Ibs.  in  E. 

3.  Although  changed  direction,  reduced  velocity,  and  perhaps  centrifugal 
force  are  necessary  for  good  separation,  still  some  means  must  be  provided 
to  lead  the  water  out  of  the  current  of  the  steam. 

The  high  efficiency  obtained  from  B  and  A  was  largely  due  to  this  feature. 
In  B  the  interior  surfaces  are  corrugated  and  thus  catch  the  water  thrown 
out  of  the  stearn  and  readily  lead  it  to  the  bottom. 

In  A,  as  soon  as  the  water  falls  or  is  precipitated  from  the  steam,  it  comes 
in  contact  with  the  perforated  diaphragm  through  which  it  runs  into  the 
space  below,  where  it  is  not  subjected  to  the  action  of  the  steam. 

In  D,  the  next  in  efficiency,  this  is  accomplished  by  means  of  a  >-shaped 
diaphragm  which  throws  the  water  back  into  the  corners  out  of  the  current 
of  steam. 

DETERMINATION    OF    THE    MOISTURE    IN   STEAM- 
STEAM   CALORIMETERS. 

In  all  boiler  tests  it  is  important  to  ascertain  the  quality  of  the  steam, 
i.e.,  1st,  whether  the  steam  is  "saturated"  or  contains  the  quantity 
of  heat  due  to  the  pressure  according  to  standard  experiments;  2d,  whether 
the  quantity  of  heat  is  deficient,  so  that  the  steam  is  wet;  and  3d,  whether 
the  heat  is  in  excess  and  the  steam  superheated.  The  best  method  of  ascer- 
taining the  quality  of  the  steam  is  undoubtedly  that  employed  by  a  com- 
mittee which  tested  the  boilers  at  the  American  Institute  Exhibition  of 
1871-2,  of  which  Prof.  Thurston  was  chairman,  i.e.,  condensing  all  the  water 
evaporated  by  the  boiler  by  means  of  a  surface  condenser,  weighing  the 
condensing  water,  and  taking  its  temperature  as  it  enters  and  as  it  leaves 
the  condenser;  but  this  plan  cannot  always  be  adopted. 

A  substitute  for  this  method  is  the  barrel  calorimeter,  which  with  careful 
operation  and  fairly  accurate  instruments  may  generally  be  relied  on  to 
give  results  within  two  per  cent  -of  accuracy  (that  is,  a  sample  of  steam 
which  gives  the  apparent  result  of  2#  of  moisture  may  contain  anywhere  be 
tween  0  and  4$).  This  calorimeter  is  described  as  follows:  A  sample  of  the 
steam  is  taken  by  inserting  a  perforated  ^-inch  pipe  into  and  through  the 
main  pipe  near  the  boiler,  and  led  by  a  hose,  thoroughly  felted,  to  a  barrel, 
holding  preferably  400  Ibs.  of  water,  which  is  set  upon  a  platform  scale  and. 


DETERMINATION   01*  THE   MOISTURE   IK   STEAM.   729 

provided  with  a  cock  or  valve  for  allowing  the  water  to  flow  to  waste,  and 
with  a  small  propeller  for  stirring  the  water. 

To  operate  the  calorimeter  the  barrel  is  filled  with  water,  the  weight  and 
temperature  ascertained,  steam  blown  through  the  hose  outside  the  barrel 
until  the  pipe  is  thoroughly  wanned,  when  the  hose  is  suddenly  thrust  into 
the  water,  and  the  propeller  operated  until  the  temperature  of  the  water  is 
increased  to  the  desired  point,  say  about  110°  usually.  The  hose  is  then 
withdrawn  quickly,  the  temperature  noted,  and  the  weight  again  taken. 

An  error  of  1/10  of  a  pound  in  weighing  the  condensed  steam,  or  an  error 
of  y%  degree  in  the  temperature,  will  cause  an  error  of  over  1%  in  the  calcu- 
lated percentage  of  moisture.  See  Trans.  A.  S.  M.  E..  vi.  293. 

The  calculation  of  the  percentage  of  moisture  is  made  as  below: 


Q  =  quality  of  the  steam,  dry  saturated  steam  being  unity. 

H  =  total  heat  of  1  Ib.  of  steam  at  the  observed  pressure. 

T  =      u        "     '•      "      kt  water  at  the  temperature  of  steam  of  the  ob- 
served pressure. 

Ji  —      "        "     "     "      "  condensing  water,  original. 

/,,  =      "        "     "      "      "  "      final. 

W  —  weight  of  condensing  water,  corrected  for  water-equivalent  of  the 
apparatus. 

w  =  weight  of  the  steam  condensed. 

Percentage  of  moisture  =  1  —  Q. 

If  Q  is  greater  than  unity,  the  steam  is  superheated,  and  the  degrees  of 
superheating  =  2.0833  (H  -  T)  (Q  -  1). 

Difficulty  of  Obtaining  a  Correct  Sample.—  Recent  experiments 
by  Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  xvi.  1017,  show  that  it  is  practi- 
cally impossible  to  obtain  a  true  average  sample  of  the  steam  flowing  in  a 
pipe.  For  accurate  determinations  all  the  steam  made  by  the  boiler  should 
be  passed  through  a  separator,  the  water  separated  should  be  weighed,  and 
a  calorimeter  test  made  of  the  steam  just  after  it  has  passed  the  separator. 
Coil  Calorimeters.—  Instead  of  the  open  barrel  in  which  the  steam 
is  condensed,  a  coil  acting  as  a  surface-condenser  may  be  used,  which  is 
placed  in  the  barrel,  the  water  in  coil  and  barrel  being  weighed  separately. 
For  description  of  an  apparatus  of  this  kind  designed  by  the  author,  which 
he  has  found  to  give  results  with  a  probable  error  not  exceeding  ^  per  cent 
of  moisture,  see  Trans.  A.  S.  M.  E.,  vi.  294.  This  calorimeter  may  be  used 
continuously,  if  desired,  instead  of  intermittently.  In  this  case  a  continu- 
ous flow  of  condensing  water  into  and  out  of  the  barrel  must  be  established, 
and  the  temperature  of  inflow  and  outflow  and  of  the  condensed  steam 
read  at  short  intervals  of  time. 

Throttling  Calorimeter.—  For  percentages  of  moisture  not  ex- 
ceeding 3  per  cent  the  throttling  calorimeter  is  most  useful  and  convenient 
and  remarkably  accurate.  In  this  instrument  the  steam  which  reaches  it 
in  a  i^-inch  pipe  is  throttled  by  an  orifice  1/16  inch  diameter,  opening  into  a 
chamber  which  has  an  outlet  to  the  atmosphere.  The  steam  in  this  cham- 
ber has  its  pressure  reduced  nearly  or  quite  to  the  pressure  of  the  atmos- 
phere. but  the  total  hear,  in  the  steam  before  throttling  causes  the  steam  in 
the  chamber  to  be  superheated  more  or  less  according  to  whether  the 
steam  before  throttling  was  dry  or  contained  moisture.  The  only  observa- 
tions required  are  those  of  the  temperature  and  pressure  of  the  steam  on 
each  side  of  the  orifice. 

The  author's  formula  for  reducing  the  observations  of  the  throttling 
calorimeter  is  as  follows  (Experiments  on  Throttling  Calorimeters,  Am. 

Mack.,  Aug.  4,  1892)  :    w  =  100  X  H  ~  h  ~^(T  ~—  ),  in  wm'ch  w  =  percent- 

age of  moisture  in  the  steam;  H  =  total  heat,  and  L  =  latent  heat  of  steam 
in  the  main  pipe;  h  =  total  heat  due  the  pressure  in  the  discharge  side  of 
the  calorimeter,  =  1146.6  at  atmospheric  pressure:  K  =  specific  heat  of  su- 
perheated steam;  T=  temperature  of  the  throttled  and  superheated  steam 
in  the  calorimeter;  t=  temperature  due  the  pressure  in  the  calorimeter, 
=  t21S°  at  atmospheric  pressure. 

Taking  K  at  0.48  and  the  pressure  in  the  discharge  side  of  the  calorimeter 
as  atmospheric  pressure,  the  formula  becomes 

w  -  10o      H~  1146'6  - 


From  this  formula  the  following  table  is  calculated  : 


730  THE   STEAM-BOILER. 

MOISTURE  IN  STEAM— DETERMINATIONS  BY  THROTTLING  CALORIMETER. 


o> 

& 

5  beg," 

-^ 

l>,q&H 

So 
« 

Q 

Gauge-pressures. 

5 

10 

20 

30 

40 

50 

60 

70 

75 

80 

85 

90 

Per  Cent  of  Moisture  in  Steam. 

0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 

Dif.p.dey 

0.51 
0.01 

0.90 
0.39 

1.54 
1.02 
.51 
.00 

2.06 
1.54 
1.02 
.50 

2.50 
1.97 
1.45 
.92 
.39 

2.90 
2.36 
1.83 
1.30 
.77 
.24 

3.24 

2.71 
2  17 
1.'64 
1.10 
.57 
.03 

3.56 
3.02 

2.48 
1.94 
1.40 
.87 
.33 

3.71 
3.17 
2.63 
2.09 
1.55 
1.01 
.47 

3.86 
3  32 

2^23 
1.69 
1.15 
.60 
.06 

.0542 

3.99 
3.45 
2.90 
2.35 
1.80 
1.26 

!l7 

4.13 
3.58 
3.03 
2.49 
1.91 
1.40 
.85 
.31 

.0503 

.0515 

.0521 

.052(5 

.0507 

.0531 

.0535  .0539 

.0541 

.0544 

.0546 

Degree  of  Super- 
heating 
T  -212°. 

Gauge-pressures. 

100 

110 

120 

130 

140 

150 

160 

170 

180 

190 

200 

250 

Per  Cent  of  Moisture  in  Steam. 

0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 
80° 
90° 
100° 
110° 

4.39 
3.84 
3.29 
2.74 
2.19 
1.64 
1.09 
.55 
.00 

4.63 
4.08 
3.52 
2.97 
2.42 
1.87 
1.32 
.77 
.22 

4.85 
4.29 
3.74 
3.18 
2.63 
2.08 
1.52 
.97 
.42 

5.08 
4.52 
3.96 
3.41 
2.85 
2.29 
1.74 
1.18 
.63 
.07 

5.29 
4.73 
4.17 
3.61 
3.05 
2.49 
1.93 
1.88 
.82 
.26 

5.49 
4.93 
4.37 
3.80 
3.24 
2.68 
2.12 
1.56 
1.00 
.44 

5.68 
5.12 
4.56 
3.99 
3.43 
2.87 
2.30 
1.74 
1.18 
.61 
.05 

5.87 
5.30 
4.74 
4.17 
3.61 
3.04 
2.48 
1.91 
1.34 
.78 
.21 

6.05 
5.48 
4.91 
4.34 
3.78 
3.21 
2.64 
2.07 
1.50 
.94 
.37 

6.22 
5.65 
5.08 
4.51 
3.94 
3.37 
2.80 
2.23 
1.66 
1.09 
.52 

6.39 
5.82 
5.25 
4.67 
4.10 
3.53 
2.96 
2.38 
1.81 
1.24 
.67 
.10 

7.16 
6.58 
6.00 
5.41 
4.83 
4.25 
3.67 
3.09 
2.51 
1.93 
1.34 
.76 

Dif.p.deg 

.0549 

.0551 

.0554 

.0556 

.0559 

.0561 

.0564 

.0566 

.0568 

.0570 

.0572 

.0581 

Separating  Calorimeters. — For  percentages  of  moisture  beyond 
tiie  range  of  the  throttling  calorimeter  the  separating  calorimeter  is  used, 
which  is  simply  a  steam  separator  on  a  small  scale.  An  improved  form  of 
this  calorimeter  is  described  by  Prof.  Carpenter  in  Power,  Feb.  1893. 

For  fuller  information  on  various  kinds  of  calorimeters,  see  papers  by 
Prof.  Peabody,  Prof.  Carpenter,  and  Mr.  Barrus  in  Trans.  A.  S.  M.  E.,  vols. 
x,  xi.  xii,  1889  to  1891;  Appendix  to  Report  of  Corn,  on  Boiler  Tests, 
A.  S.  M.  E.,  vol.  vi,  1884;  Circular  of  Schaeffer  &  Budenberg,  N.  Y.,  ''Calo- 
rimeters. Throttling  and  Separating,"  1894. 

Identification  of  Dry  Strain  by  Appearance  of  a  Jet. — 
Prof.  Denton  (Trans.  A  S.  M.  E.,  vol.  x.)  found  lhat  jets  of  steam  show  un- 
mistakable change  of  appearance  to  the  eye  when  steam  varies  less  than  \% 
from  the  condition  of  saturation  either  in  the  direction  of  wetness  or  super- 
heating. 

If  a  jet  of  steam  flow  from  a  boiler  into  the  atmosphere  under  circumstances 
such  that  very  little  loss  of  heat  occurs  through  radiation,  etc.,  and  the  jet 
be  transparent  close  to  the  orifice,  or  be  even  a  grayish-white  color,  the 
steam  may  be  assumed  to  be  so  nearly  dry  that  no  portable  condensing 
calorimeter  will  be  capable  of  measuring  the  amount  of  water  in  the  steam. 
If  the  jet  be  strongly  white,  the  amount  of  water  may  be  roughly  judged  up 
to  about  2$,  but  beyond  this  a  calorimeter  only  can  determine  the  exact 
amount  of  moisture. 


CHIMNEYS. 


731 


A  Common  brass  pet-cock  may  be  used  as  an  orifice,  but  it  should,  if  possi- 
ble, be  set  into  the  steam-drurn  of  the  boiler  and  never  be  placed  further 
away  from  the  latter  than  4  feet,  and  then  only  when  the  intermediate  reser- 
voir or  pipe  is  well  covered. 

Usual  A  in  on  nt  of  Moisture  in  Steam  Escaping  from  a 
Boiler. — In  the  common  forms  of  horizontal  tubular  land  boilers  and 
water-tube  boilers  with  ample  horizontal  drums,  and  supplied  with  water 
free  from  substances  likely  to  cause  foaming,  the  moisture  in  the  steam 
does  not  generally  exceed  2%  unless  the  boiler  is  overdriven  or  the  water- 
level  is  carried  too  high. 

CHIMNEYS. 

Chimney  Draught  Theory.— The  commonly  accepted  theory  of 
chimney  draught,  based  on  Peclet's  and  Rankine's  hypotheses  (see  Rankine, 
S.  E.),  is  discussed  by  Prof.  De  Volson  Wood  in  Trans.  A.  S.  M.  E.,  vol.  xi. 

Peclet  represented  the  law  of  draught  by  the  formula 


in  which  h  is  the  "  head,1'  defined  as  such  a  height  of  hot  gases  as,  if  added 
to  the  column  of  gases  in  the  chimney,  would  produce  the 
same  pressure  at  the  furnace  as  a  column  of  outside  air,  of  the 
same  area  of  base,  and  a  height  equal  to  that  of  the  chimney; 

u  is  the  required  velocity  of  gases  in  the  chimney; 

G  a  constant  to  represent  the  resistance  to  the  passage  of  air 
through  the  coal ; 

I  the  length  of  the  flues  and  chimney; 

m  the  mean  hydraulic  depth  or  the  area  of  a  cross-section  divi- 
ded by  the  perimeter; 

/  a  constant  depending  upon  the  nature  of  the  surfaces  over  which 
the  gases  pass,  whether  smooth,  or  sooty  and  rough. 

Rankine's  formula  (Steam  Engine,  p.  288),  derived  by  giving  certain  values 
to  the  constants  (so-called)  in  Peclet's  formula,  is 


I°(  0.084) 
T 


H  -  H= 


in  which  H  =  the  height  of  the  chimney  in  feet; 

TO  —  493°  F.,  absolute  (temperature  of  melting  ice); 

T!  =  absolute  temperature  of  the  gases  in  the  chimney; 

T2  =  absolute  temperature  of  the  external  air. 

Prof.  Wood  derives  from  this  a  still  more  complex  formula  which  gives 
the  height  of  chimney  required  for  burning  a  given  quantity  of  coal  per 
second,  and  from  it  he  calculates  the  following  table,  showing  the  height  of 
chimney  required  to  burn  respectively  24,  20,  and  16  Ibs.  of  coal  per  square 
foot  of  grate  per  hour,  for  the  several  temperatures  of  the  chimney  gases 
given. 


Outside  Air. 

T2 

Chimney  Gas. 

Coal  per  sq.  ft.  of  grate  per  hour.  Ibs. 

1 
TI 
Absolute. 

Temp. 
Fahr. 

24 

20 

16 

Height  H,  feet. 

520° 
absolute  or 
59°  F. 

700 

800 
1000 
1100 
1200 
1400 
1600 
2000 

239 
339 

539 
639 

739 
939 
113!) 
1539 

250.9 
172.4 
149.1 

148.8 
152.0 
159.9 
168.8 
206.5 

157.6 

115.8 
100.0 
98.9 
100.9 
105.7 
111.0 
132.2 

67.8 
55.7 
48.7 
48.2 
49.1 
51.2 
53.5 
63.0 

732 


CHIMNEYS. 


Rankine's  formula  gives  a  maximum  draught  when  r  =  2  1/12V2,  or  622°  F., 
when  the  outside  temperature  is  60°.  Prof.  Wood  says:  "  This  result  is  not 
a  fixed  value,  but  departures  from  theory  in  practice  do  not  affect  the  result 
largely.  There  is,  then,  in  a  properly  constructed  chimney,  properly  work- 
ing, a  temperature  giving  a  maximum  draught,*  and  that  temperature  is  not 
far  from  the  value  given  by  Rankine,  although  in  special  cases  it  may  be  50° 
or  75°  more  or  less.1' 

All  attempts  to  base  a  practical  formula  for  chimneys  upon  the  theoret- 
ical formula  of  Peclet  and  Rankine  have  failed  on  account  of  the  impos- 
sibility of  assigning  correct  values  to  the  so-called  *4  constants  "  G  and  f. 
(See  Trans.  A.  S.  M.  E.,  xi.  984.) 

Force  or  Intensity  of  Draught.— The  force  of  the  draught  is  equal 
to  the  difference  between  the  weight  of  the  column  of  hot  gases  inside  of  the 
chimney  and  the  weight  of  a  column  of  the  external  air  of  the  same  height. 
It  is  measured  by  a  draught-gauge,  usually  a  U-tube  partly  filled  with  water, 
one  leg  connected  by  a  pipe  to  the  interior  of  the  flue,  and  the  other  open  to 
the  external  air. 

If  D  is  the  density  of  the  air  outside,  d  the  density  of  the  hot  gas  inside, 
in  Ibs.  per  cubic  foot,  h  the  height  of  the  chimney  in  feet,  and  .192  the  factor 
for  converting  pressure  in  Ibs.  per  sq.  ft.  into  inches  of  water  column,  then 
the  formula  for  the  force  of  draught  expressed  in  inches  of  water  is, 
F=  .192/t(D-  d). 

The  density  varies  with  the  absolute  temperature  (see  Rankine). 

d  =  —  0.084;    D  =  0.0807  — , 
T!  T2 

where  TO  is  the  absolute  temperature  at  32°  F.,  =  493.,  rt  the  absolute  tem- 
perature of  the  chimney  gases  and  r2  that  of  the  external  air.  Substituting 
these  values  the  formula  for  force  of  draught  becomes 

F=  .18»(«L»  _  ILil)  =  rf!*  _  ZJ«). 

\      T2  T!      /  V    T2  fi  / 

To  find  the  maximum  intensity  of  draught  for  any  given  chimney,  tho 
heated  column  being  600°  F.,  and  the  external  air  60°,  multiply  the  height 
above  grate  in  feet  by  .0073,  and  the  product  is  the  draught  in  inches  of  water. 
Height  of  Water  Column  Due  to  Unbalanced  Pressure  in 
Chimney  1OO  Feet  High.  (The  Locomotive,  18h4.) 


Temperature  of  the  External  Air—  Barometer,  14.7  Ibs.  per  sq.  in. 


s^.s 

H  6 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

200 

.453 

.419 

-.384 

.353 

.321 

.292 

.263 

.234 

.209 

.182 

.157 

220 

.488 

.453 

.419 

.388 

.355 

.326 

.298 

.269 

.244 

.217 

.192 

240 

.520 

.488 

.451 

.421 

.388 

.359 

.330 

.301 

.276 

.250 

.225 

260 

.555 

.528 

.484 

.453 

.420 

.392 

.363 

.334 

.309 

.282 

.257 

280 

.584 

.549 

.515 

.482 

.451 

.422 

.394 

.365 

.340 

.313 

.288 

300 

.611 

.576 

.541 

.511 

.478 

.449 

.420 

.392 

.367 

.340 

.315 

320 

.637 

.603 

.568 

.538 

.505 

.476 

.447 

.419 

.394 

.367 

.342 

340 

.662 

.638 

.593 

.563 

.530 

.501 

.472 

.443 

.419 

.392 

.367 

300 

.687 

!653 

.618 

.588 

.555 

.526 

.497 

.468 

.444 

.417 

.392 

380 

.710 

.676 

.641 

.611 

.578 

.549 

.520 

.492 

.467 

.440 

.415 

400 

.732 

.697 

.662 

.632 

.598 

.570 

.541 

.513 

.488 

.461 

.436 

420 

753 

.718 

.684 

.653 

.620 

.591 

.563 

.534 

.509 

.482 

.457 

440 

.774 

.739 

.705 

.674 

.641 

.612 

.584 

.555 

.530 

.503 

.478 

400 

.793 

.758 

.724 

.694 

.660 

.632 

.603 

.574 

.549 

.522 

.497 

480 

.810 

.776 

.741 

.710 

.678 

.649 

.620 

.£91 

.566 

.540 

.515 

500 

.829 

.791 

.760 

.730 

.697 

.669 

.689 

.610 

.586 

.559 

.534 

*  Much  confusion  to  students  of  the  theory  of  chimneys  has  resulted  from 
their  understanding  the  words  maximum  draught  to  mean  maximum  inten- 
sity or  pressure  of  draught,  as  measured  by  a  draught-gauge.  It  here  means 
maximum  quantity  or  weight  of  gases  passed  up  the  chimney.  The  maxi- 
mum intensity  is  found  only  with  maximum  temperature,  but  after  the 
temperature  reaches  about  622°  F.  the  density  of  the  gas  decreases  more 
rapidly  than  its  velocity  increases,  so  that  the  weight  is  a  maximum  about 
622°  F.,  as  shown  by  Rankine.— W.  K. 


CHIMNEYS. 


For  any  other  height  of  chimney  than  100  ft.  the  height  of  water- coin  inn 
is  found  by  simple  proportion,  the  height  of  water  column  being  directly 
proportioned  to  the  height  of  chimney. 

The  calculations  have  been  made  for  a  chimney  100  ft.  hijrh.  with  various 
temperatures  outside  and  inside  of  the  flue,  and  on  the  supposition  that  the 
temperature  of  the  chimney  is  uniform  from  top  to  bottom.  This  is  the 
basis  on  which  all  calculations  respecting  the  draught-power  of  chimneys 
have  been  made  by  Rankine  and  other  writers,  but  it  is  very  far  from  the 
truth  in  most  cases.  The  difference  will  be  shown  by  comparing  the  read- 
ing of  the  draught-gauge  with  the  table  given.  In  one  case  a  chimney  122  ft. 
high  showed  a  temperature  at  the  base  of  320°,  and  at  the  top  of  230°. 

Box,  in  his  **  Treatise  on  Heat,'1  gives  the  following  table  : 

DRAUGHT  POWERS  OF  CHIMNEYS,  ETC.,  WITH  THE  INTERNAL  AIR  AT  552°,  AND 
THE  EXTERNAL  AIR  AT  62°,  AND  WITH  THE  DAMPER  NEARLY  CLOSED. 


Height  of 
Chimney  in 
feet. 

Draught 
Power  in  ins. 
of  water. 

Theoretical  Velocity 
in  feet  per  second. 

Height  of 
Chimney  in 
feet.  ' 

Draught 
Power  in  ins. 
of  water. 

Theoretical  Velocity 
in  feet  per  second. 

Cold  Air 
Entering. 

Hot  Air 
at  Exit. 

Cold  Air 
Entering. 

Hot  Air 
at  Exit. 

10 
20 
30 
40 
50 
60 
70 

.073 
.146 
.219 
.292 
.365 
.438 
.511 

17.8 
25.3 
31.0 
35.7 
40.0 
43.8 
47.3 

35.6 
50.6 
62.0 
71.4 
80.0 
87.6 
94.6 

80 
90 
100 
120 
150 
175 
200 

.585 
.657 
.730 
.876 
1.095 
1.877 
1.460 

50.6 
53.7 
56,5 
62.0 
69.3 
74.3 
80.0 

101.2 
107.4 
113.0 
124.0 
138.6 
149.6 
160.0 

Rate    of    Combustion    Due    to    Height    of    Chimney.— 

Trowbridge's  "Heat  and  Heat  Engines'"  gives  the  following  table  showing 
the  heights  of  chimney  for  producing  certain  rates  of  combustion  per  sq. 
ft.  of  section  of  the  chimney.  It  may  be  approximately  true  for  anthracite 
in  moderate  and  large  sizes',  but  greater  heights  than  are  given  in  the  table 
are  needed  to  secure  the  given  rates  of  combustion  with  small  sizes  of 
anthracite,  and  for  bituminous  coal  smaller  heights  will  suffice  if  the  coal 
is  reasonably  free  from  ash— 5%  or  less. 


Lbs.  of  Coal 

Lbs.  of  Coal 

Lbs.  of  Coal 

Burned  per 

Lbs.  of  Coal 

Burned  per 

Burned  per 

Sq.  Ft.  of 

Burned  per 

Sq.  Ft.  of 

Heights 
in 

Hour  per 
Sq.  Ft. 

Grate,  the 
Ratio  of 

Heights 
in 

Hour  per 
Sq.  Ft. 

Grate,  the 
Ratio  of 

feet. 

of  Section 

Grate  to  Sec- 

feet. 

of  Section 

Grate  to  Sec- 

of 

tion  of 

of 

tion  of 

Chimney. 

Chimney  be- 

Chimney. 

Chimney  be- 

ing 8  to  1. 

ing  8  to  1. 

20 

60 

7.5 

70 

126 

15.8 

25 

68 

8.5 

75 

131 

16  4 

30 

76 

9.5 

80 

135 

16.9 

35 

84 

10.5 

85 

139 

17.4 

40 

93 

11.6 

90 

144 

18.0 

45 

99 

12.4 

95 

148 

18.5 

50 

105 

13.1 

100 

152 

19  0 

55 

111 

13.8 

105 

156 

19.5 

60 

116 

14.5 

110 

160 

20  0 

65 

121 

15.1 

Thurston's  rule  for  rate  of  combustion  effected  by  a  given  fteight  of  chim- 
ney (Trans.  A.  S.  M.  E.,  xi.  991)  is:  Subtract  1  from  twice  the  square  root  of 
the  height,  and  the  result  is  the  rate  of  combustion  in  pounds  per  square  foot 
of  grate  per  hour,  for  anthracite.  Or  rate  =  2  \'Ji  —  },  in  which  h  is  the 
height  in  feet.  This  rule  gives  the  following: 


h  =    50 
-  1  =  13.14 


60 
14.49 


70 
15.73 


80         90      100 
16.89    17.97    19 


110       125       150       175       200 
19.97    21.36    23.49    25.45    27.28 


The  results  agree  closely  with  Trowbridge's  table  given  above.    In  prac- 


CHIMNEYS. 


tice  the  high  rates  of  combustion  for  high  chimneys  given  by  the  formula 
are  not  generally  obtained,  for  the  reason  that  with  high  chimneys  there  are 
usually  long  horizontal  flues,  serving  many  boilers,  and  the  friction  and  the 
interference  of  currents  from  the  several  boilers  are  apt  to  cause  the  inten- 
sity of  draught  in  the  branch  flues  leading  to  each  boiler  to  be  much  less 
than  that  at  the  base  of  the  chimney.  The  draught  of  each  boiler  is  also 
usually  restricted  by  a  damper  and  by  bends  in  the  gas-passages.  In  a  bat- 
tery of  several  boilers  connected  to  a  chimney  150  ft.  high,  the  author  found 
a  draught  of  %-inch  water-column  at  the  boiler  nearest  the  chimney,  and 
only  ^-inch  at  the  boiler  farthest  away.  The  first  boiler  was  wasting  fuel 
from  too  high  temperature  of  the  chimney-gases,  900°,  having  too  large  a 
grate-surface  for  the  draught,  and  the  last  boiler  was  working  below  its 
rated  capacity  and  with  poor  economy,  on  account  of  insufficient  draught. 

The  effect  of  changing  the  length  of  the  flue  leading  into  a  chimney  60  ft. 
high  and  2  ft.  9  in.  square  is  given  in  the  following  table,  from  Box  on 
"  Heat"  : 


Length  of  Flue  in 
feet. 

Horse-power. 

Length  of  Flue  in 
feet. 

Horse-power. 

50 
100 
200 
400 
600 

107.6 
100.0 
85.3 
70.8 
02.5 

800 
1,000 
1,500 
2,000 
3,000 

56.1 
.51.4 
43.3 
38.2 
31.7 

The  temperature  of  the  gases  in  this  chimney  was  assumed  to  be  552°  F., 
and  that  of  the  atmosphere  62°. 

Iliiih  Chimneys  not  Necessary.— Chimneys  above  150  ft.  in  height 
are  very  costly,  and  their  increased  cost  is  rarely  justified  by  increased  ef- 
ficiency. In  recent  practice  it  has  become  somewhat  common  to  build  two  or 
more  smaller  chimneys  instead  of  one  large  one.  A  notable  example  is  the 
Spreckels  Sugar  Refinery  in  Philadelphia,  where  three  separate  chimneys  are 
used  for  one  boiler-plant  of  7500  H.P.  The  three  chimneys  are  said  to  have 
cost  several  thousand  dollars  less  than  a  single  chimney  of  their  combined 
capacity  would  have  cost.  Very  tall  chimneys  have  been  characterized  by 
one  writer  as  "  monuments  to  the  folly  of  their  builders.11 

Heights  of  Chimney  required  for  Different  Fuels.— The 
minimum  height  necessary  varies  with  the  fuel,  wood  requiring  the  least, 
then  good  bituminous  coal,  and  fine  sizes  of  anthracite  the  greatest.  It 
also  varies  with  the  character  of  the  boiler — the  smaller  and  more  circuitous 
the  gas-passages  the  higher  the  stack  required;  also  with  the  number  of 
boilers,  a  single  boiler  requiring  less  height  than  several  that  discharge 
into  a  horizontal  flue.  No  general  rule  can  be  given. 

SIZE  OF  <  HI  ?IM;YS. 

The  formula  given  below,  and  the  table  calculated  therefrom  for  chimneys 
up  to  96  in.  diameter  and  200  ft.  high,  were  first  published  by  the  author 
in  1884  (Trans.  A.  S.  M.  E.  vi.,  81).  They  have  met  with  much  approval 
since  that  date  by  engineers  who  have  used  them,  and  have  been  frequently 
published  in  boiler-makers1  catalogues  and  elsewhere.  The  table  is  now 
extended  to  cover  chimne}rs  up  to  12  ft.  diameter  and  300  ft.  high.  The  sizes 
corresponding  to  the  given  commercial  horse-powers  are  believed  to  be 
ample  for  all  cases  in  which  the  draught  areas  through  the  boiler-flues  and 
connections  are  sufficient,  say  not  less  than  20$  greater  than  the  area  of  the 
chimney,  and  in  which  the  draught  between  the  boilers  and  chimney  is  not 
checked  by  long  horizontal  passages  and  right-angled  bends. 

Note  that  the  figures  in  the  table  correspond  to  a  coal  consumption  of  5  Ibs. 
of  coal  per  horse-power  per  hour.  This  liberal  allowance  is  made  to  cover 
the  contingencies  of  poor  coal  being  used,  and  of  the  boilers  being  driven 
beyond  their  rated  capacity.  In  large  plants,  with  economical  boilers  and 
engines,  good  fuel  and  other  favorable  conditions,  which  will  reduce  the 
maximum  rate  of  coal  consumption  at  any  one  time  to  less  than  5  Ibs.  per 
H.  P.  per  hour,  the  figures  in  the  table  may  be  multiplied  by  the  ratio  of  5  to 
the  maximum  expected  coal  consumption  per  H.P.  per  hour.  Thus,  with 
conditions  which  make  the  maximum  coal  consumption  only  2.5  Ibs.  per 
hour,  the  chimney  300  ft.  high  X  12  ft.  diameter  should  be  sufficient  for  6155 
X  2  =  12,310  horse-power.  The  formula  is  based  on  the  following  data  : 


SIZE    OF    CHIMNEYS. 


735 


J^a?^  "w 
gdCM   .S 

>    S    SSM     ^ 

F§s  + 

W         *C  |l^ 


S|^!§ 


SS    S^l^§ 


S8SS    £ 


ei§i  igi 


43  *     ^S 

|J»4i# 

H        ii 


t^t^oooo 
• 


a 

I 


2cr 


736  CHIMNEYS. 

1.  The  draxight  power  of  the  chimney  varies  as  the  square  root  of  the 
height. 

2.  The  retarding  of  the  ascending  gases  by  friction  may  be  considered  as 
equivalent  to  a  diminution  of  the  area  of  the  chimney,  or  to  a  lining  of  the 
chimney  by  a  layer  of  gas  which  has  no  velocity.    The   thickness  of  this 
lining  is  assumed  to  be  2  inches  for  all  chimneys,  or  the  diminution  of  area 
equal  to  the  perimeter  x  2  inches  (neglecting  the  overlapping  of  the  corners 
of  the  lining).    Let  D  —  diameter  in  feet,  A  —  area,  and  E  =  effective  area 
in  square  feet. 

o  r\  9         __ 

For  square  chimneys,  E  =  D*  —  —  =  A  -  -  \/A. 

1-4  O 

For  round  chirneys,      E  =  ?  (/)«  -  8^)  =  A  -  0.591  |/Z 


simplifying  calculations,  the  coefficient  of   \/A  may  be  taken  as  0.6 
th  square  and  round  chimneys,  and  the  formula  becomes 


For  r___. 

for  both  squai 


E  =  A  -  0.6  V'A. 


3.  The  power  varies  directly  as  this  effective  area  E. 

4.  A  chimney  should  be  proportioned  so  as  to  be  capable  of  giving  sufficient 
draught  to  cause  the  boiler  to  develop  much  more  than  its  rated  power,  in 
case  of  emergencies,  or  to  cause  the  combustion  of  5  Ibs.  of  fuel  per  rated 
horse-power  of  boiler  per  hour. 

5.  The  power  of  the  chimney  varying  directly  as  the  effective  area,  E,  and 
as  the  square  root  of  the  height,  Jf,  the  formula  for  horse-power  of  boiler  for 
a  given  size  of  chimney  will  take  the  form  H.P.  —  CE  \/H,  in  which  C  is  a 
constant,   the  average  value  of  which,   obtained  by  plotting  the  results 
obtained  from  numerous  examples  in  practice,  the  author  finds  to  be  3.33. 

The  formula  for  horse-power  then  is 

H.P.  =  3.33#  yH,    or    H.P.  =  3.33(4  -  .6  VA)  \/H. 

If  the  horse-power  of  boiler  is  given,  to  find  the  size  of  chimney,  the  height 
being  assumed, 


For  round  chimneys,  diameter  of  chimney  =  diam.  of  E  +  4". 

For  square  chimneys,  side  of  chimney  =  ^ E  -f  4". 

If  effective  area  E  is  taken  in  square  feet,  the  diameter  in  inches  is  d  = 
13.54  VE4-4",  and  the  side  of  a  square  chimney  in  inches  is  s  —  12  VE-}-  4". 

x  r\   o   TT     T>    \  2 

If  horse-power  is  given  and  area  assumed,  the  height  II  =  (    '    „' —  )  . 

In  proportioning  chimneys  the  height  is  generally  first  assumed,  with  due 
consideration  to  the  heights  of  surrounding  buildings  or  hills  near  to  the 
proposed  chimney,  the  length  of  horizontal  flues,  the  character  of  coal  to  be 
used,  etc.,  and  then  the  diameter  required  for  the  assumed  height  and 
horse-power  is  calculated  by  the  formula  or  taken  from  the  table. 

The  Protection  of  Tall  Chimney-shafts  from  Lightning. 
— C.  Molyneux  and  J.  M.  Wood  (Industries,  March  28,  1890)  recommend  for 
tall  chimneys  the  use  of  a  coronal  or  heavy  band  at  the  top  of  the  chimney, 
with  copper  points  1  ft.  in  height  at  intervals  of  2  ft.  throughout  the  circum- 
ference. The  points  should  be  gilded  to  prevent  oxidation.  The  most  ap- 
proved form  of  conductor  is  a  copper  tape  about  %  in.  by  ^  in.  thick, 
weighing  6  ozs.  per  ft.  If  iron  is  used  it  should  weigh  not  less  than  2*4  Ibs. 
per  ft.  There  must  be  no  insulation,  and  the  copper  tape  should  be  fastened 
to  the  chimney  with  holdfasts  of  the  same  material,  to  prevent  voltaic 
action.  An  allowance  for  expansion  and  contraction  should  be  made,  say  1 
in.  in  40  ft.  Slight  bends  in  the  tape,  not  too  abrupt,  answer  the  purpose. 
For  an  earth  terminal  a  plate  of  metal  at  least  3  ft.  sq.  and  1/16  in.  thick 
should  be  buried  as  deep  as  possible  in  a  damp  spot.  The  plate  should  be  of 
the  same  metal  as  the  conductor,  to  which  it  should  be  soldered.  The  best 
earth  terminal  is  water,  and  when  a  deep  well  or  other  large  body  of  water 
is  at  hand,  the  conductor  should  be  carried  down  into  it.  Right-angled 
bends  in  the  conductor  should  be  avoided.  No  bend  in  it  should  be  over  30°, 


SIZE   OF   CHBOTEYS. 


737 


Some  Tall  Brick  Chimneys. 


+Z 

1 

1 

Internal  Diam. 

Outside 
Diameter. 

Capacity  by  the 
Author's 
Formula. 

« 

d 

e 

H.  P. 

Pounds 
Coal 
per 
hour. 

1.  Hallsbriickner  Hiitte,  Sax. 
2.  Townsend's.  Glasgow..   .. 
3.  Ten  n  ant's,  Glasgow  
4.  Dobson  &  Barlow,  Bolton, 
Eng           

460 
454 
435 

367^ 
350 

335 

282'9" 

250 
250 
238 
214 

200 

150 

15.7' 
'"i3'"6"" 

13'  2" 
11 

11 
12 

10 
10 
14 

8 

9 

50"  x  120" 

33' 
32 

40 

33'10" 
30 

28'  6" 

16' 

21 
14 

each 

13,221 
9,795 

8,245 
5,558 

5,435 
5,980 

3,839 
3,839 
7,515 

2,248 

2,771 
1,541 

66,105 
48,975 

41,225 
27,790 

27,175 
29,900 

19,195 
19,195 
37,575 
11,240 

13,855 
7,705 

5.  Fall  River  Iron  Co.,  Boston 
6.  Clark  Thread  Co.,  Newark, 
N  J 

7.  Merrimac  Mills,  Low'l,Mass 
8.  Washington     Mills,     Law- 
rence Mass      

9.  Amoskeag  Mills,  Manches- 
ter N  H 

10.  Narragansett    E.    L.    Co., 
Providence,  R.  I  

11.  Lower  Pacific  Mills,  Law- 
rence Mass  

12.  Passaic  Print  Works,  Pas- 
saic  N  J                     .  . 

13.  Edison  Sta,B'klyn,Twoe'ch 

NOTES  ON  THE  ABOVE  CHIMNEYS.—!.  This  chimney  is  situated  near 
Freiberg,  on  the  right  bank  of  the  Mulde,  at  an  elevation  of  219  feet  above 
that  of  the  foundry  works,  so  that  its  total  height  above  the  sea  will  be  711% 
feet.  The  works  are  situated  on  the  bank  of  the  river,  and  the  furnace- 
gases  are  conveyed  across  the  river  to  the  chimney  on  a  bridge,  through  a 
pipe  3227  feet  in  length.  It  is  built  throughout  of  brick,  and  will  cost  about 
$40,000.— M/r.  and  Bldr. 

2.  Owing  to  the  fact  that  it  was  struck  by  lightning,  and  somewhat 
damaged,  as  a  precautionary  measure  a  copper  extension  subsequently  was 
added  to  it,  making  its  entire  height  488  feet. 

1,  2,  3,  and  4  were  built  of  these  great  heights  to  remove  deleterious 
gases  from  the  neighborhood,  as  well  as  for  draught  for  boilers. 

5.  The  structure   rests  on  a  solid  granite  foundation,  55  X  30  feet,  and 
16  feet  deep.    In  its  construction  there  were  used  1,700,000  bricks,  2000  tons 
of  stone,  2000  barrels  of  mortar,  1000  loads  of  sand,  1000  barrels  of  Portland 
cement,  and  the  estimated  cost  is  $40.000.    It  is  arranged  for  two  flues,  9 
feet  6  inches  by  6  feet,  connecting  with  40  boilers,  which  are  to  be  run  in 
connection  with  four  triple-expansion  engines  of  1350  horse-power  each. 

6.  It  has  a  uniform  batter  of   2.85    inches  to  every   10  feet.     Designed 
for  21   boilers  of  200  H.   P.  each.    It  is  surmounted  by  a  cast-iron  cop- 
ing which  weighs    six   tons,    and    is    composed    of    thirty-two    sections, 
which  are  bolted  together  by  inside  flanges,  so  as  to  present  a  smooth 
exterior.     The    foundation    is    in    concrete,    composed    of   crushed   lime- 
stone 6  parts,  sand  3  parts,  and  Portlan  1  cement  1  part.    It  is  40  feet 
square  and  5  feet  deep.    Two   qualities   of   brick  were  used;    the  outer 
portions  were  of  the  first  quality  North  River,  and  the  1  acking  up  was  of 
good  quality  New  Jersey  brick.     Every  twenty  feet  in  vertical  measurement 
an  iron  ring,  4  inches  wide  and  %  to  ^  inch  thick,  placed  edgewise,  \vas 
built  into  the  walls  about  8  inches  from  the  outer  circle.     As  the  chimney 
starts  from  the  base  it  is  double.    The  outer  wall  is  5  feet  2  inches  in   thick- 
ness, and  inside  of  this  is  a  second  wall  20  inches  thick  and  spaced  off  about 
20  inches  from  main  wall.    From  the  interior  surface  of  the  main  wall  eight 
buttresses    are  carried,  nearly  touching    this  inner  or  main  flue  wall    in 
order  to  keep  it,  in  line  should  it  tend  to  sag.    The  interior  wall,  starting 
with  the  thickness  described,  is  gradually  reduced  until  a  height  of  about 
90  feet  is  reached,  when  it  is  diminished  to  8  inches.    At  165  feet  it  ceases, 


738  CHIMNEYS. 

and  the  rest  of  the  chimney  is  without  lining.    The  total  weight  of  the  chim- 
ney and  foundation  is  5000  tons.    It  was  completed  in  September,  1888. 

7.  Connected  to  12  boilers,  with  1200  square  feet  of  grate-surface.    Draught- 
gauge  1  9/16  inches. 

8.  Connected  to  8  boilers,  6'  8"  diameter  X  18  feet.     Grate-surface  448 
square  feet. 

9.  Connected  to  64  Blanning  vertical  boilers,  total  grate  surface  1810  sq.  ft. 
Designed  to  burn  18,000  Ibs.  anthracite  per  hour. 

10.  Designed  for  12,000  H. P.  of  engines;  (compound  condensing). 

11.  Grate-surface  434  square  feet;  H.P.  of  boilers  (Galloway)  about  2500. 
13.  Eight  boilers  (water-tube)  each  450  H.P. ;  12  engines,  each  300  H.P.    Plant 

designed  for  36,000  incandescent  lights.    For  the  first  60  feet  the  exterior 
wall  is  28  inches  thick,  then  24  inches  for  20  feet,  20  inches  for  30  feet,  16 
inches  for  20  feet,  and  12  inches  for  20  feet.    The  interior  wall  is  9  inches 
thick  of  fire-brick  for  50  feet,  and  then  8  inches  thick  of  red  brick  for  the 
next  30  feet.    Illustrated  in  Iron  Age,  January  2,  1890. 
A  number  of  the  above  chimneys  are  illustrated  in  Power,  Dec.,  1890. 
Chimney  at  Knoxville,  Tenn.,  illustrated  in  Eng'gNews,  Nov.  2, 1893. 
6  feet  diameter,  120  feet  high,  double  wall: 

Exterior  wall,  height      20  feet,    30  feet,  30  feet,  40  feet; 

"  "     thickness  21^  in. ,17 in. ,   13  in,,  &/»  in.; 

Interior  wall,  height      85     ft.,  35  ft.,    29ft.,  21  ft.; 
44      thickness  13^  in.,  8^  in.,  4  in.,  0. 

Exterior  diameter,  15'  6"  at  bottom ;  batter.  7/16  inch  in  12  inches  from  bot- 
tom to  8  feet  from  top.  Interior  diameter  of  inside  wall,  6  feet  uniform  to 
top  of  interior  wall.  Space  between  \yalls,  16  inches  at  bottom,  diminishing 
to  0  at  top  of  interior  wall.  The  interior  wall  is  of  red  brick  except  a  lining 
of  4  inches  of  fire-brick  for  20  feet  from  bottom. 

Stability  of  Chimneys.—  Chimneys  must  be  designed  to  resist  the 
maximum  force  of  the  wind  in  the  locality  in  which  they  are  built,  (see 
Weak  Chimneys,  below).  A  general  rule  for  diameter  of  base,  of  brick 
chimneys,  approved  by  many  years  of  practice  in  England  and  the  United 
States,  is  to  make  the  diameter  of  the  base  one  tenth  of  the  height.  If  th/a 
chimney  is  square  or  rectangular,  make  the  diameter  of  the  inscribed  circle 
of  the  base  one  tenth  of  the  height.  The  "  batter  "  or  taper  of  a  chimney- 
should  be  from  1/16  to  J4  inch  to  the  foot  on  each  side.  The  brickwork 
should  be  one  brick  (8  or  9  inches)  thick  for  the  first  25  feec  from  the  top,  in- 
creasing y%  brick  (4  or  4^  inches)  for  each  25  feet  from  the  top  down  wards. 
If  the  inside  diameter  exceed  5  feet,  the  top  length  should  be  l^j  bricks;  arid 
if  under  3  feet,  it  may  be  ^  brick  for  ten  feet. 

(From  The  Locomotive,  1884  and  1886.)  For  chimneys  of  four  feet  in  diani- 
eter  and  one  hundred  feet  high,  and  upwards,  the  best  form  is  circular,with 
a  straight  batter  on  the  outside.  A  circular  chimney  of  this  size,  in  addition 
to  being  cheaper  than  any  other  form,  is  lighter,  stronger,  and  looks  much 
better  and  more  shapely. 

Chimneys  of  any  considerable  height  are  not  built  up  of  uniform  thickness 
from  top  to  bottom,  nor  with  a  uniformly  varying  thickness  of  wall,  but  the 
wall,  heaviest  of  course  at  the  base,  is  reduced  by  a  series  of  steps. 

Where  practicable  t  he  load  on  a  chimney  foundation  should  not  exceed  two 
tons  per  square  foot  in  compact  sand,  gravel,  or  loam.  Where  a  solid  rock- 
bottom  is  available  for  foundation,  the  load  may  be  greatly  increased.  If 
the  rock  is  sloping,  all  unsound  portions  should  be  removed,  and  the  face 
dressed  to  a  series  of  horizontal  steps,  so  that  there  shall  be  no  tendency  to 
slide  after  the  structure  is  finished. 

All  boiler-chimneys  of  any  considerable  size  should  consist  of  an  outer 
stack  of  sufficient  strength  to  give  stability  to  the  structure,  and  an  inner 
stack  or  core  independent  of  the  outer  one.  This  core  is  by  many  engineers 
extended  up  to  a  height  of  but  50  or  60  feet  from  the  base  of  the  chimney, 
but  the  better  practice  is  to  run  it  up  the  whole  height  of  the  chimney;  it 
may  be  stopped  off,  say,  a  couple  feet  below  the  top,  and  the  outer  shell  con- 
tracted to  the  area  of  the  core,  but  the  better  way  is  to  run  it  up  to  about  8 
or  12  inches  of  the  top  and  not  contract  the  outer  shell.  But  under  no  cir- 
cumstances should  the  core  at  its  upper  end  be  built  into  or  connected  with 
the  outer  stack.  This  has  been  done  in  several  instances  by  bricklayers,  and 
the  result  has  been  the  expansion  of  the  inner  core  which  lifted  the  top  of 
the  outer  stack  squarely  up  and  crecked  the  brickwork. 

For  a  height  of  100  feet  we  would  make  the  outer  shell  in  three  steps,  the 
first  20  feet  high,  16  inches  thick,  the  second  30  feet  high,  12  inches  thick,  the 


SIZE   OF   CHIMHEYS.  739 

third  50  feet  high  and  8  inches  thick.  These  are  the  minimum  thicknesses 
admissible  for  chimneys  of  this  height,  and  the  batter  should  be  not  less 
than  1  in  36  to  give  stability.  The  core  should  also  be  built  in  three  steps 
each  of  which  maybe  about  one  third  the  height  of  the  chimney,  the  lowest 
12  inches,  the  middle  8  inches,  and  the  upper  step  4  inches  thick.  This  will 
insure  a  good  sound  core.  The  top  of  a  chimney  may  be  protected  by  a 
cast-iron  cap;  or  perhaps  a  cheaper  and  equally  good  plan  is  to  la}7  the 
ornamental  part  in  some  good  cement,  and  plaster  the  top  with  the  same 
material. 

Weak  Chimneys.— James  B.  Francis,  in  a  report  to  the  Lawrence 
Mfg.  Co.  in  1873  (Eng'g  News,  Aug.  28,  1880),  gives  some  calculations  con- 
cerning the  probable  effects  of  wind  on  that  company's  chimney  as  then 
constructed.  Its  outer  shell  is  octagonal.  The  inner  shell  is  cylindrical, 
with  an  air-space  between  it  and  the  outer  shell;  the  two  shells  not  being 
bonded  together,  except  at  the  openings  at  the  base,  but  with  projections  in 
the  brickwork,  at  intervals  of  about  20  ft.  in  height,  to  afford  lateral  sup- 
port by  contact  of  the  two  shells.  The  principal  dimensions  of  the  chimney 
are  as  follows : 

Height  above  the  surface  of  the  ground 211  ft. 

Diameter  of  the  inscribed  circle  of  the  octagon  near  the  ground .  15  " 
Diameter  of  the  inscribed  circle  of  the  octagon  near  the  top ...     10  ft.  \y%  in. 

Thickness  of  the  outer  shell  near  the  base,  6  bricks,  or . 23^  in. 

Thickness  of  the  outer  shell  near  the  top,  3  bricks,  or 11^  " 

Thickness  of  the  inner  shell  near  the  base,  4  bricks,  or 15      " 

Thickness  of  the  inner  shell  near  the  top,  1  brick,  or  3M  " 

One  tenth  of  the  height  for  the  diameter  of  the  base  is  the  rule  commonly 
adopted.  The  diameter  of  the  inscribed  circle  of  the  base  of  the  Lawrence 
Manufacturing  Company's  chimney  being  15  ft.,  it  is  evidently  much  less 
than  is  usual  in  a  chimney  of  that  height. 

Soon  after  the  chimney  was  built,  and  before  the  mortar  had  hardened,  it 
*.vas  found  that  the  top  had  swayed  over  about  29  in.  toward  the  east.  This 
was  evidently  due  to  a  strong  westerly  wind  which  occurred  at  that  time. 
It  was  soon  brought  back  to  the  perpendicular  by  sawing  into  som-e  of  the 
joints,  and  other  means. 

The  stability  of  the  chimney  to  resist  the  force  of  the  wind  depends  mainly 
on  the  weight  of  its  outer  shell,  and  the  width  of  its  base.  The  cohesion  of 
the  mortar  may  add  considerably  to  its  strength;  but  it  is  too  uncertain  to 
be  relied  upon.  The  inner  shell  will  add  a  little  to  the  stability,  but  it  may 
be  cracked  by  the  heat,  and  its  beneficial  effect,  if  any,  is  too  uncertain  to 
be  taken  into  account. 

The  effect  of  the  joint  action  of  the  vertical  pressure  due  to  the  weight  of 
the  chimney,  and  the  horizontal  pressure  due  to  the  force  of  the  wind  is  to 
yhift  the  centre  of  pressure  at  the  base  of  the  chimney,  from  the  axis  to- 
ward one  side,  the  extent  of  the  shifting  depending  on  the  relative  magni- 
tude of  the  two  forces.  If  the  centre  of  pressure  it  brought  too  near  the 
»5ide  of  the  chimney,  it  will  crush  the  brickwork  on  that  side,  and  the  chim- 
ney will  fall.  A  line  drawn  through  the  centre  of  pressure,  perpendicular  to 
the  direction  of  the  wind,  must  leave  an  area  of  brickwork  between  it  and 
the  side  of  the  chimney,  sufficient  to  support  half  the  weight  of  the  chim- 
ney; the  other  half  of  the  weight  being  supported  by  the  brickwork  on  the 
windward  side,  of  the  line. 

Different  experimenters  on  the  strength  of  brickwork  give  very  different 
results.  Kirkaldy  found  the  weights  which  caused  several  kinds  of  bricks, 
Jaid  in  hydraulic  lime  mortar  .and  in  Roman  and  Portland  cements,  to  fail 
slightly,' to  vary  from  19  to  60  tons  (of  2000  Ibs.)  per  sq.  ft.  If  we  take  in  this 
case  25  tons  per  sq.  ft.,  as  the  weight  that  would  cause  it  to  begin  to  fail,  we 
shall  not  err  greatly.  To  support  half  the  weight  of  the  outer"  shell  of  the 
chimney,  or  823  tons,  at  this  rate,  requires  an  area  of  12.88  sq.  ft.  of  brick- 
work. From  these  data  and  the  drawings  of  the  chimney,  Mr.  Francis  cal- 
culates that  the  area  of  12.88  sq.  ft.  is  contained  in  a  portion  of  the  chimney 
extending  2.428  ft.  from  one  of  its  octagonal  sides,  and  that  the  limit  to 
which  the  centre  of  pressure  may  be  shifted  is  therefore  5.072  ft.  from  the 
axis.  If  shifted  beyond  this,  he  says,  on  the  assumption  of  the  strength 
of  the  brickwork,  it  will  crush  and  the  chimney  will  fall. 

Calculating  that  the  wind-pressure  can  affect  only  the  upper  141  ft.  of  the 
chimney,  the  lower  70  ft.  being  protected  by  buildings,  he  calculates  that  a 
wind-pressure  of  44.02  Ibs.  per  sq.  ft.  would  blow  the  chimney  down. 

Rankine,  in  a  paper  printed  in  the  transactions  of  the  Institution  of  Engi- 


740 


CHIMNEYS. 


neers,  in  Scotland,  for  1867-68,  says:  "  It  had  previously  been  ascertained 
by  observation  of  the  success  and  failure  of  actual  chimneys,  and  especially 
of  those  which  respectively  stood  and  fell  during  the  violent  storms  of  1856, 
that,  in  order  that  a  round  chimney  may  be  sufficiently  stable,  its  weight 
should  be  such  that  a  pressure  of  wind,  of  about  55  Ibs.  per  sq.  ft.  of  a  plane 
surface,  directly  facing  the  wind,  or  27%  Ibs.  per  sq.  ft.  of  the  plane  projec- 
tion of  a  cylindrical  surface,  .  .  .  shall  not  cause  the  resultant  pressure 
at  any  bed- joint  to  deviate  from  the  axis  of  the  chimney  by  more  than  one 
quarter  of  the  outside  diameter  at  that  joint," 

According  to  Rankine's  rule,  the  Lawrence  Mfg.  Co.'s  chimney  is  adapted 
to  a  maximum  pressure  of  wind  on  a  plane  acting  on  the  whole  height  of 
18.80  Ibs.  per  sq.  ft.,  or  of  a  pressure  of  21. 70  Ibs.  per  sq.  ft.  acting  on  the 
uppermost  141  ft.  of  the  chimney. 

Steel  Chimneys  are  largely  coming  into  use,  especially  for  tall  chim- 
neys of  iron-works,  from  150  to  300  feet  in  height.  The  advantages  claimed 
are  :  greater  strength  and  safety;  smaller  space  required;  smaller  cost,  by 
30  to  50  per  cent,  as  compared  with  brick  chimneys;  avoidance  of  infiltra- 
tion of  air  and  consequent  checking  of  the  draught,  common  in  brick  chim- 
neys. They  are  usually  made  cylindrical  in  shape,  with  a  wide  curved  flare 
for  10  to  25  feet  at  the  bottom.  A  heavy  cast-iron  base-plate  is  provided,  to 
•vyhich  the  chimney  is  riveted,  and  the  plate  is  secured  to  a  massive  founda- 
tion by  holding-down  bolts.  No  guys  are  used.  F.  W.  Gordon,  of  the  Phila. 
Engineering  Works,  gives  the  following  method  of  calculating  their  resist- 
ance to  wind  pressure  (Power,  Oct.  1893)  : 

In  tests  by  Sir  William  Fairbairn  we  find  four  experiments  to  determine 
the  strength  of  thin  hollow  tubes.  In  the  table  will  be  found  their  elements, 
with  their  breaking  strain.  These  tubes  were  placed  upon  hollow  blocks, 
and  the  weights  suspended  at  the  centre  from  a  block  fitted  to  the  inside  of 
the  tube. 


Clear 
Span, 
ft.  in. 

Thick- 
ness Iron, 
in. 

Outside 
Diame- 
ter, in. 

Sectional 
Area, 
in. 

Breaking 
Weight, 
Ibs. 

Breaking  W't, 
Ibs.,  by  Clarke's 
Formula, 
Constant  1.2. 

I. 
II. 
III. 

IV. 

17 
15    7^ 
23    5 
23    5 

.037 
.113 
.0631 
.119 

12 
12.4 
17.68 
18.18 

1.3901 
4.3669 
3.487 
6.74 

2,704 
11,440 
6,400 
14,240 

2,627 
9,184 
7,302 
13,910 

Edwin  Clarke  has  formulated  a  rule  from  experiments  conducted  by  him 
during  his  investigations  into  the  use  of  iron  and  steel  for  hollow  tub^ 
bridges,  which  is  as  follows  : 

Center  break-  {  _Area  of  material  in  sq.in.  X  Mean  depth  in  in.  X  Constant 
ing  ioad,in  tons.  \  ~  Clear  span  in  feet. 

When  the  constant  used  is  1.2,  the  calculation  for  the  tubes  experimented 
upon  by  Mr.  Fairbairn  are  given  in  the  last  column  of  the  table.  D.  K 
Clark's  "Rules,  Tables,  and  Data,"  page  513,  gives  a  rule  for  hollow  tube^ 
as  follows  :  W—  3.14D2T/S  -t-L.  W—  breaking  weight  in  pounds  in  centre; 
D—  extreme  diameter  in  inches;  T=  thickness  in  inches;  L  =  length  be- 
tween supports  in  inches;  S  =  ultimate  tensile  strength  in  pounds  per-  sq.  in. 

Taking  S,  the  strength  of  a  square  inch  of  a  riveted  joint,  at  35,000  Ibs. 
per.  sq.  in.,  this  rule  figures  as  follows  for  the  different  examples  experi- 
mented upon  by  Mr.  Fairbairn  :  I,  2870;  II.  10,190;  III,  7700;  IV,  15.320. 

This  shows  a  close  approximation  to  the  breaking  weight  obtained  by 
experiments  and  that  derived  from  Edwin  Clarke's  and  D.  K.  Clark's  rules. 
We  therefore  assume  that  this  system  of  calculation  is  practically  correct, 
and  that  it  is  eminently  safe  when  a  large  factor  of  safety  is  provided,  and 
from  the  fact  that  a  chimney  may  be  standing  for  many  years  without 
receiving  anything  like  the  strain  taken  as  the  basis  of  the  calculation,  viz., 
fifty  pounds  per  square  foot.  Wind  pressure  at  fifty  pounds  per  square  foot 
may  be  assumed  to  be  travelling  in  a  horizontal  direction,  "and  be  of  the 
same  velocity  from  the  top  to  the  bottom  of  the  stack.  This  is  the  extreme 
assumption.  If,  however,  the  chimney  is  round,  its  effective  area  would  be 
only  half  of  its  diameter  plane.  We  assume  that  the  entire  force  may  iv 
concentrated  in  the  centre  of  the  height  of  the  section  of  the  chimney 
under  consideration. 


SIZE  OF   CHLMKEYS. 


741 


Taking  as  an  example  a  125-foot  iron  chimney  at  Poughkeepsie,  N.  Y.,  the 
B  verage  diameter  of  which  is  90  inches,  the  effective  surface  in  square  feet 
upon  which  the  force  of  the  wind  may  play  will  therefore  be  7*4  times  125 
divided  by  2,  which  multiplied  by  50  gives  a  total  wind  force  of  23,437 
pounds.  The  resistance  of  the  chimney  to  breaking  across  the  top  of  the 
foundation  would  be  3  14  X  1682  (that  is,  diameter  of  base)  X  .25  x  35.000  + 
(750  X  4)  =  258,486,  or  10.6  times  the  entire  force  of  the  wind.  We  multiply 
(.he  half  height  above  the  joint  in  inches,  750,  by  4,  because  the  chimney  is 
considered  a  fixed  beam  with  a  load  suspended  on  one  end.  In  calculating 
Its  strength  half  way  up,  we  have  a  beam  of  the  same  character.  It  is  a 
fixed  beam  at  a  line  'half  way  up  the  chimney,  where  it  is  90  inches  in  diam- 
eter and  .187  inch  thick.  Taking  the  diametrical  section  above  this  line, 
and  the  force  as  concentrated  in  the  centre  of  it,  or  half  way  up  from  the 
point  under  consideration,  its  breaking  strength  is:  3.14  X  902  x  .187  X  35,000 
-T-  (381  X  4)  =  109,220;  and  the  force  of  the  wind  to  tear  it  apart  through  its 
cross-section,  7J4  x  6^  X  50-^-2  =  11,352,  or  a  little  more  than  one  tenth  of 
the  strength  of  the  stack. 

The  Babcock  &  Wilcox  Co.'s  book  4t  Steam"  illustrates  a  steel  chimney 
at  the  works  of  the  Maryland  Steel  Co.,  Sparrow's  Point,  Md.  It  is  225  ft. 
in  height  above  the  base,  with  internal  brick  lining  13'  9"  uniform  inside 
diameter.  The  shell  is  25  ft.  diam.  at  the  base,  tapering  in  a  curve  to  17  ft. 
25  ft.  above  the  base,  thence  tapering  almost  imperceptibly  to  14'  8"  at  the 
top.  The  upper  40  feet  is  of  W-inch  plates,  the  next  four  sections  of  40  ft. 
each  are  respectively  9/32,  5/16,  11/32,  and  %  inch. 

Sizes  of  Foundations  for  Steel  Chimneys. 

(Selected  from  circular  of  Phila.  Engineering  Works.) 
HALF-LINED  CHIMNEYS. 


Diameter,  clear,  feet  .........      3456  7          9 

Height,  feet.  .................     100        100        150        150          150        150 

Least  diameter  foundation..  15'9"    16'4"    20'4  '    21'10"    22'7"    23'8" 
Least  depth  foundation  ......      6'         6'          9'          8'  9'         10' 

Height,  feet  ......................       125       200         200         250        275 

Least  diameter  foundation  .......     18'5"    23'8"       25'  29'8"    33'G" 

Least  depth  foundation..  ........        7'         10'         10'  12'         12' 

Weight  of  Sheet-iron  Smoke-stacks  per  Foot. 

(Porter  Mfg.  Co.) 


11 

150 

24'8' 

10' 

300 


Diam., 
inches. 

Thick- 
ness 
W.  G. 

Weight 
•per  ft. 

Diam., 
inches. 

Thick- 
ness 
W.  G. 

Weight 
per  ft. 

Diam. 
inches. 

Thick- 
ness 
W.  G. 

Weight 
per  ft, 

18.33 
20.00 
21.66 
23.33 
25.00 
26.66 

10 
12 
14 
16 
20 
22 
24 

No.416 

u 

n 

7.20 
8.66 
9.58 
11.68 
13.75 
15.00 
16.25 

26 
28 
30 
10 
12 
14 
16 

No.^16 
No.^14 

17.50 
18.75 
20.00 
9.40 
11.11 
13.69 
15.00 

20 
22 
24 
26 
28 
30 

No.  14 

Sheet-iron  Chimneys.    (Columbus  Machine  Co.) 


Diameter 
Chimney, 
inches. 

Length 
Chimney, 
feet. 

Thick- 
ness 
Iron, 
B.  W.  G. 

Weight, 
Ibs. 

Diameter 
Chimney, 
inches. 

Length 
Chimney, 
feet. 

Thick- 
ness 
Iron, 
B.  W.  G 

Weight, 
Ibs. 

10 

20 

No.   16 

160 

30 

40  - 

ISo.    15 

960 

15 

20 

"      16 

240 

32 

40 

4      15 

1.020 

20 

20 

"      16         320 

34 

40 

'      14 

1,170 

22 

20 

"      10         350 

36 

40 

'      14 

1.240 

24 

40 

"      16         760 

38 

40 

k      12 

1,HOO 

26 

40 

"      16 

826 

40 

40 

'      12 

1,890 

28 

40 

"      15  i       900 

742 


THE   STEAM-EKGIKE. 


THE  STEAM-ENGINE. 

Expansion  of  Steam.    Isothermal  and  Adiabatic.— Accord 

ing  10  Mariotte's  law,  the  volume  of  a  perfect  gas,  the  temperature  being 

kept  constant,  varies  inversely  as  its  pressure,  or  p  x  - ;  pv  =  a  constant. 

The  curve  constructed  from  this  formula  is  called  the  isothermal  curve,  or 
curve  of  equal  temperatures,  and  is  a  common  or  rectangular  hyperbola. 
The  relation  of  the  pressure  and  volume  of  saturated  steam,  as  deduced 
from  Regnault's  experiments,  and  as  given  in  Steam  tables,  is  approxi- 
mately, according  to  Rankine  (S.  E.,  p.  403),  for  pressures  not  exceeding  120 

Ibs.,  p  oc  -— ,  orp  <x  v~  il,  or  pv  ~  is  —.  pv  ~~  lt0625  =  a  constant.    Zeuner  has 

found  that  the  exponent  1.0646  gives  a  closer  approximation. 

When  steam  expands  in  a  closed  cylinder,  as  in  an  engine,  according  to 

Rankine  (S.  E.,  p.  385),  the  approximate  law  of  the  expansion  is  p  <x  — — ,  or 

pocv"1^0,  0rjpv  ~^  =  a  constant.  The  curve  constructed  from  this  for- 
mula is  called  the  adiabatic  curve,  or  curve  of  no  transmission  of  heat. 

Peabody  Therm.,  p.  112)  says:  "It  is  probable  that  this  equation  was 
obtained  by  comparing  the  expansion  lines  on  a  large  number  of  indicator- 
diagrams.  .  .  .  There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection, . . .  and  the  action  of  a  lagged  steam- 
engine  cylinder  is  far  from  being  adiabatic.  .  .  .  For  general  purposes  the 
hyperbola  is  the  best  curve  for  comparison  with  the  expansion  curve  of  an 
indicator- card.  .  .  ."  Wolff  and  Denton,  Trans.  A.  S.  M.  E.,  ii.  175,  say  ; 
41  From  a  number  of  cards  examined  from  a  variety  of  steam-engines  in  cur 
rent  use,  we  find  that  the  actual  expansion  line  varies  between  the  10/J 
adiabatic  curve  and  the  Mariotte  curve." 

Prof.  Thurston  (A.  S.  M.  E  ,  ii.  203),  says  he  doubts  if  the  exponent  evei ' 
becomes  the  same  in  any  two  engines,  or  even  in  the  same  engines  at  dif 
ferent  times  of  the  day  and  under  varying:  conditions  of  the  day. 

Expansion  of  Steam  according:  to  Mariotte's  Law  and 
to  the  Adiabatic  Law.  (Trans.  A.  s.  M.  E.,  ii.  156.)— Mariotte's  law 

pv  —P^V!  ;  values  calculated  from  formula  —  =  — (1  4  hyp  log  R),  in  whicl 

R  =  i?2-f-  v,,  PI  =  absolute  initial  pressure,  Pm  =  absolute  mean  pressure. 
v1  =  initial  volume  of  steam  in  cylinder  at  pressure  PI,  vz=  final  volume  ol 
steam  at  final  pressure.  Adiabatic  law:  pv1?  =  Piv^s]  values  calculated 
from  formula.-—  =  WR  ~  l  ~-  9R  ~~  V- 


Ratio  of 
Expan- 

Ratio of  Mean 
to  Initial 
Pressure. 

Ratio 
of 
Expan- 

Ratio of  Mean 
to  Initial 
Pressure. 

Ratio 
of 
Expan- 

Ratio of  Mean 
to  Initial 
Pressure. 

sion  R. 

Mar. 

Adiab. 

sion  R. 

Mar. 

Adiab. 

sion  R. 

Mar. 

Adiab. 

1.00 

1.000 

1.000 

3.7 

.624 

.600 

6. 

.465 

.438 

1.25 

.978 

.976 

3.8 

.614 

.590 

6.25 

.453 

.425 

1.50 

.937 

.931 

3.9 

.605 

.580 

6.5 

.442 

.413 

1.75 

.891 

.881 

4. 

.597 

.571 

6.75 

.431 

.403 

2. 

.847 

.834 

4.1 

.588 

.562 

7 

.421 

.393 

2  2 

.813 

.798 

4.2 

.580 

.554 

7^25 

.411 

.383 

2^4 

.781 

.765 

4.3 

.572 

.546 

75 

.402 

.374 

2.5 

.766 

.748 

4.4 

.564 

.538 

7.75 

.393 

.365 

2.6 

.752 

.733  . 

4.5 

.556 

.530 

8. 

.385 

.357 

2.8 

.725 

.704 

4.6 

.549 

.523 

8.25 

.377 

.349 

3. 

.700 

.678 

4.7 

.542 

.516 

8.5 

.369 

.342 

3.1 

.688 

.666 

4.8 

.535 

.509 

8.75 

.362 

.335 

3.2 

.676 

.654 

4.9 

.528 

.502 

9. 

.355 

.328 

3.3 

.665 

.642 

5.05 

.522 

.495 

9.25 

.349 

.321 

3.4 

.654 

.630 

5  2 

.506 

.479 

9.5 

.342 

.315 

3.5 

.644 

.620 

5.5 

.492 

.464 

9.75 

.  336 

.309 

3.6 

.634 

.610 

5.75 

.478 

.450 

10. 

340 

.303 

AKD  TERMINAL  ABSOLUTE   PRESSURES.     743 


Mean  Pressure  of  Expanded  Steam.— For  calculations  of 
engines  it  is  generally  assumed  that  steam  expands  according  to  Marietta's 
law,  the  curve  of  the  expansion  line  being  a  hyperbola.  The  mean  pressure, 
measured  above  vacuum,  is  then  obtained  from  the  formula 

1  +  hyp  log  K 
Pm  -Pi -^ •, 

in  which  F^t  is  the  absolute  mean  pressure,  p,  the  absolute  initial  pressure 
taken  as  uniform  up  to  the  point  of  cut-off,  and  R  the  ratio  of  expansion.  If 
I  =  length  of  stroke  to  the  cut-off,  L  =  total  stroke, 

pj+pj  hyp  logy                           L                     1  + hyp  log  12 
Pm  =  —     — g : ;     and  if  R  =  j,    Pm  =  Pi ^ . 

Mean  and  Terminal  Absolute  Pressures.— JXEariotte'8 
Law,— The  values  in  the  following  table  are  based  on  Mariotte's  law, 
except  those  in  tb'S  last  column,  which  give  the  mean  pressure  of  superheated 
steam,  which,  according  to  Rankine,  expands  in  a  cylinder  according  to 
the  law  p  v,  v  ~~  T!.  These  latter  values  are  calculated  from  the  formula 

_J?  =    <  ~   — L.    R~™  may  be  found  by  extracting  the  square  root  of  — 

p^  11  K 

fbur  timei.  From  the  mean  absolute  pressures  given  deduct  the  mean  back 
pressure  (absolute)  to  obtain  the  mean  effective  pressure. 


Rate 
of 
Expan- 
sion. 

Cut- 
off. 

Ratio  of 
Mean  to 
Initial 
Pressure. 

Ratio  of 
Mean  to 
Terminal 
Pressura. 

Ratio  of 
Terminal 
to  Mean 
Pressure. 

Ratio  of 
Initial 
to  Mean 
Pressure. 

Ratio  of 
Mean  to 
Initial 
Dry  Steam. 

30 

°8 

0.033 
0  036 

0.1467 
0  1547 

4.40 
4  33 

0.227 
0  231 

6.82 
6.46 

0.136 

26 

0  038 

0.1638 

4  26 

0.235 

6.11 

24 

0  042 

0.1741 

4.18 

0.239 

5.75 

22 

0  045 

0  1860 

4  09 

0  244 

5  38 

80 

18 

0.050 
0  055 

0.1998 
0  2161 

4.00 
3  89 

0.250 
0  256 

5.00 
4  63 

0.186 

16 

0  062 

0  2358 

3  77 

0.265 

4  24 

15 

0  066 

0  2472 

3  71 

0  269 

4  05 

14 

0  071 

0  2599 

3  64 

0  275 

3  85 

13.33 
13 

0.075 
0  077 

0.7690 

0  2742 

3.59 
3  56 

0.279 
0  280 

3.72 
3.65 

0.254 

12 

0  083 

0  2904 

3  48 

0  287 

3  44 

ll 

0  091 

0  3089 

3  40 

0  294 

3  24 

10 
9 

0.100 
0  111 

0.3303 
0  3552 

3.30 
3  20 

0.303 
0  312 

3.03 
2.81 

0.314 

8 

0.125 
0  143 

0.3849 
0.4210 

3.08 
2.95 

0.321 
0  339 

2.60 
2.37 

0.370 

6.66 
6.00 

0.150 
0  166 

0.4347 
0  4653 

2.90 
2  79 

0.345 
0  360 

2.30 
2  15 

0.417 

5  71 

0  175 

0  4807 

2  74 

0  364 

2  08 

6.  CO 
4.44 

0.200 
0.225 

0.5218 
0  5608 

2.61 

2  50 

0.383 
0.400 

1.92 

1.78 

0.506 

4  DO 
3  63 

0.250 
0  275 

0.5965 
0  6308 

2.39 
2  29 

0.419 
0  437 

1.68 
1  58 

0.582 

fi.33 

3  00 

0.300 
0  333 

0.6615 
0  6995 

2.20 
2  10 

0.454 
0  476 

1.51 
1  43 

0.648 

2.86 
2  66 

0.350 
0  375 

0.7171 
0  7440 

2.05 
98 

0.488 
0  505 

1.39 
1  34 

0.707 

2.50 
2.22 
2.00 
1.82 
1.66 
1  60 

0.400 
0.450 
0.500 
0.550 
0  600 
0  625 

0.7664 
0.8095 
0.8465 
0.8786 
0.9066 
0  9187 

.91 

.80 
.69 
.60 
.51 

1  47 

0.523 
0.556 
0.591 
0.626 
0.662 
0  680 

1.31 
1.24 
1.18 
1.14 
1.10 
1  09 

0.756 
0.800 
0.840 

8.874 
0.900 

1.54 

1.48 

0.650 
0.675 

0.9292 
0.9405 

1.43 
1.39 

0.699 
0.718 

1.07 
1.06 

0.926 

744 


THE   STEAM-EHGINE. 


Calculation  of  Mean  Effective  Pressure,  Clearance  and 
Compression  Considered.— In  the  above  tables  no  account  is  taken 

of  clearance,  which  in  actual 
steam-engines  modifies  the  ratio 
of  expansion  and  the  mean  pres- 
sure ;  nor  of  compression  and 
back-pressure,  which  diminish 
the  mean  effective  pressure.  In 
the  following  calculation  these 
elements  are  considered. 

L  =  length  of  stroke,  I  —  length 
before  cut-off,  x  =  length  of  com- 
pression part  of  stroke,  c  =  clear- 
ance, pl  =  initial  pressure,  pb  = 
back  pressure,  pc  =  pressure  of 
clearance  steam  at  end  of  com- 
pression. All  pressures  are  abso- 
lute, that  is,  measured  from  a 
perfect  vacuum. 


Area  of  ABCD  =  Pl(Z  +  c)(l  +  hyp  log  j^j 


C  =  pcc(l  +  hyp  log  £±£)  =  pb(x  +  c)(l  +  hyp  log 


D  =  (Pi  -  Pc)c  =  pxc  -  pb(x  +  c). 
Area  of  A  =  ABCD  -  (B  +  C  -f  D) 


-  [pb(L  -  x)  +  pb(x  +  c)(l  +  hyp  log  £±£)  +  Pic  -  pb(x  +  c)  J 


-  pb[(L  -  x}  +  (a;  -f  c)  hyp  log 


-  ptc. 


area  of  A 


Mean  effective  pressure  = 

I 

EXAMPLE.—  Let  L  —  1,  I  =  0.25,  x  =  0.25,  c  =  O.I,  PI  =  60  Ibs.,  pb  =  2  Ibs. 
Area  A  =  60(.25  -{-  .l)(l  4-  hyp  log  -^-) 

-2[(l-.25)-f  .35  hyplog^y-j  -  60  X  .1 

=  21(1  -f  1.145)  -  2[.75  -f  35  X  1.253]  -  6 

=  45.045  -  2.377  -  6  =  36.668  =  mean  effective  pressure. 

The  actual  indicator-diagram  generally  shows  a  mean  pressure  consider- 
ably less  than  that  due  to  the  initial  pressure  and  the  rate  of  expansion.  The 
causes  of  loss  of  pressure  are:  1.  Friction  in  the  stop-valves  and  steam- 
pipes.  2.  Friction  or  wire-drawing  of  the  steam  during  admission  and  cut- 
off, due  chiefly  to  defective  valve-gear  and  contracted  steam-passages. 
3.  Liquefaction  during  expansion.  4.  Exhausting  before  the  engine  has 
completed  its  stroke.  5.  Compression  due  to  early  closure  of  exhaust. 
6.  Friction  in  the  exhaust-ports,  passages,  and  pipes. 

Re-evaporation  during  expansion  of  the  steam  condensed  during  admis- 
sion, and  valve-leakage  after  cut-off,  tend  to  elevate  the  expansion  line  of 
the  diagram  and  increase  the  mean  pressure. 

If  the  theoretical  mean  pressure  be  calculated  from  the  initial  pressure 
and  the  rate  of  expansion  on  the  supposition  that  the  expansion  curve  fol- 


EXPANSION   OF    STEAM.  745 

lows  Mariotte's  law,  pv  =  a  constant,  and  the  necessary  corrections  are 
made  for  clearance  and  compression,  the  expected  mean  pressure  in  practice 
may  be  found  by  multiplying  the  calculated  results  by  the  factor  in  the 
following  table,  according  to  Seaton. 

Particulars  of  Engine.  Factor. 

Expansive  engine,  special  valve-gear,  or  with  a  separate 
cut-off  valve,  cylinder  jacketed 0.94 

Expansive  engine  having  large  ports,  etc.,  and  good  or- 
dinary valves,  cylinders  jacketed 0.9  to  0.92 

Expansive  engines  with  the  ordinary  valves  and  gear  as 
in  general  practice,  and  unjacketed  0.8  to  0.85 

Compound  engines,  with  expansion  valve  to  h.p.  cylin- 
der; cylinders  jacketed,  and  with  large  ports,  etc 0.9  to  0.92 

Compound  engines,  with  ordinary  slide-valves,  cylinders 
jacketed,  and  good  ports,  etc 0.8  to  0.85 

Compound  engines  as  in  general  practice  in  the  merchant 
service,  with  early  cut-off  in  both  cylinders,  without 
jackets  and  expansion-valves  0.7  to  0.8 

Fast-running  engines  of  the  type  and  design  usually  fitted 
in  war-ships  0.6  to  0.8 

If  no  correction  be  made  for  clearance  and  compression,  and  the  engine 
is  in  accordance  with  general  modern  practice,  the  theoretical  mean  pres^ 
sure  may  be  multiplied  by  0.96,  and  the  product  by  the  proper  factor  in  the 
table,  to  obtain  the  expected  mean  pressure. 

Given  the  Initial  Pressure  and  the  Average  Pressure,  to 
Find  the  Ratio  of  expansion  and  the  Period  of  Admis- 
sion. 

P  =  initial  absolute  pressure  in  Ibs.  per  sq.  in. ; 

p  =  average  total  pressure  during  stroke  in  Ibs.  per  sq.  in.; 

L  =  length  of  stroke  in  inches; 

I  —  period  of  admission  measured  from  beginning  of  stroke; 

c  =  clearance  in  inches; 

K  =  actual  ratio  of  expansion  =      "^ (1) 

P(l  +  hyp  log  R) 


P  = 


R 


To  find  average  pressure  p,  taking  account  of  clearance, 
p  =  P(*  +  c)  -f  Pd  +  c)  hyp  log  R  -  PC 

whence  pL  +  PC  =  P(l  +  c)(l  -f-  hyp  log  B)  ; 


p  =  P(*  +  c)  -f  Pd  +  c)  hyp  log  R  -  PC 


Given  p  and  P,  to  find  R  and  I  (by  trial  and  error).  —  There  being  two  un- 
known quantities  R  and  I,  assume  one  of  them,  viz.,  the  period  of  admission 
I,  substitute  it  in  equation  (3)  and  solve  for  R.  Substitute  this  value  of  R  in 

the  formula  (1),  or  I  =  •     „  ?  -  c,  obtained  from  formula  (1),  and  find  I    If 

K 

the  result  is  greated  than  the  assumed  value  of  /,  then  the  assumed  value  of 
the  period  of  admission  is  too  long;  if  less,  the  assumed  value  is  too  short. 
Assume  a  new  value  of  /,  substitute  it  in  formula  (3)  as  before,  and  continue 
by  this  method  of  trial  and  error  till  the  required  values  of  R  and  I  are 
obtained. 
EXAMPLE.—  P  =  70,  p  =  42.78,  L  =  60",  c  =  3'-,  to  find  1.  Assume  I  —  21  in. 


1.653-1 


hyp  log  R  =s  ,653,    whence    R  =  1.9 


746  THE    STEAM-ENGINE. 


3- 

~ 


_--- 
R  ~   192 

which  is  greater  than  the  assumed  value,  21  inches. 
Now  assume  I  =  15  inches  : 


hyp  log  R  =     '     .,   ,   .  --  1  =  1.204,  whence   K  =  3.5; 
lo  -J-  o 

Z  =  —  ^  --  c  =  —  —  —  3  =  18  —  3  =  15  inches,  the  value  assumed. 
-ft  3.5 

Therefore  R  =  3.5,  and  I  =  15  inches. 

Period  of  Admission  Required  for  a  Given  Actual  Ratio  of  Expansion: 
I  =  —  =  --  c,  in  inches  .........    (4) 

K 

In  percentage  of  stroke,  I  =  100+P-ct  .clearance  _       ^  clearance.    .    (5) 

XV 


__  P 

Terminal  pressure  =  ^-f^f  ^  =  =-  ..............    (6) 

-L/  "J"  C  ZS 

Pressure  at  any  othei\Point  of  the  Expansion.—  "Let  L±  =  length  of  stroke 
up  to  the  given  point. 

p/j  I  r\ 
Pressure  at  the  given  point  =  "1    "V    .............    (7) 


WORK  OF  STEAM  IN  A  SINGLE!  CYLINDER. 

To  facilitate  calculations  of  steam  expanded  in  cylinders  the  table  on  the 
next  page  is  abridged  from  Clark  on  the  Steam-engine.  The  actual  ratios 
of  expansion,  column  1,  range  from  1.0  to  8.0,  for  which  the  hyperbolic 
logarithms  are  given  in  column  2.  The  3d  column  contains  the  periods  of 
admission  relative  to  the  actual  ratios  of  expansion,  as  percentages  of  the 
stroke,  calculated  by  formula  (5)  above.  The  4th  column  gives  the  values 
of  the  mean  pressures  relative  to  the  initial  pressures,  the  latter  being  taken 
as  1,  calculated  by  formula  (2).  In  the  calculation  of  columns  3  and  4,  clear- 
ance is  taken  into  account,  and  its  amount  is  assumed  at  "t%  of  the  stroke. 
The  final  pressures,  in  the  5th  column,  are  such  as  would  be  arrived  at  by 
the  continued  expansion  of  the  whole  of  the  steam  to  the  end  of  the  stroke, 
the  initial  pressure  being  equal  to  1.  They  are  the  reciprocals  of  the  ratios 
of  expansion,  column  1.  The  6th  column  contains  the  relative  total  per- 
formances of  equal  weights  of  steam  worked  with  the  several  actual  ratios 
of  expansion;  the  total  performance,  when  steam  is  admitted  for  the  whole 
of  the  stroke,  without  expansion,  being  equal  to  1.  They  are  obtained  by 
dividing  the  figures  in  column  4  by  those  in  column  5. 

The  pressures  have  been  calculated  on  the  supposition  that  the  pressure  of 
steam,  during  its  admission  into  the  cylinder,  is  uniform  up  to  the  point  of 
cutting  off,  and  that  the  expansion  is  continued  regularly  to  the  end  of  the 
stroke.  The  relative  performances  have  been  calculated  without  any  allow- 
ance for  the  effect  of  compressive  action. 

The  calculations  have  been  made  for  periods  of  admission  ranging  from 
lOOjC,  or  the  whole  of  the  stroke,  to  6.4&  or  1/16  of  the  stroke.  And  though, 
nominally,  the  expansion  is  16  times  in  the  last  instance,  it  is  actually  only 
8  times,  as  given  in  the  first  column.  The  great  difference  between  the 
nominal  and  the  actual  ratios  of  expansion  is  caused  by  the  clearance, 
which  is  equal  to  1%  of  the  stroke,  and  causes  the  nominal  volume  of  steam 
admitted,  namely,  6.4g,  to  be  augmented  to  6.4  -f  7  =  13.  4$  of  the  stroke,  or, 
say,  double,  for  expansion.  When  the  steam  is  cut  off  at  1/9,  the  actual 
expansion  is  only  6  times;  when  cut  off  at  1/5,  the  expansion  is  4  times; 
when  cut  off  at  JJ£,  the  expansion  is  %%  times;  and  to  effect  an  actual  expan- 
sion to  twice  the  initial  volume,  the  steam  is  cut  off  at  46U#  of  the  stroke, 
not  a,t  half  -stroke, 


WORK   OF  STEAM 


A   SINGLE   CYLINDER. 


747 


Expansive  Working  of  Steam— Actual  Ratio*  of  Expan- 
sion, with  the  Relative  Periods  oi  Admission,  Press- 
ores,  and  Performance. 

Steam-pressure  100  Ibs.  absolute.    Clearance  attach  end  of  the  cylinder  1% 
of  the  stroke. 

(SINGLE  CYLINDER.) 


1 

2 

3 

4 

5 

6 

7 

8 

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I 

.0000 

100 

1.000 

1.000 

1.000 

58,273 

34.0 

4.05 

1.1 

.0953 

90.3 

.996 

.909 

1.096 

63,850 

31.0 

4.45 

1.18 

.1698 

83.3 

.986 

.847 

1.164 

67,836 

29.2 

4.78 

1.23 

.2070 

80 

.980 

.813 

1.206 

70,246 

28.2 

4.98 

1.3 

.2624 

75.3 

.969 

.769 

1.261 

73,513 

26.9 

5.26 

1.39 

.3293 

70 

.953 

.719 

1.325 

77,242 

25.6 

5.63 

1.45 

.3716 

66.8 

.942 

.690 

1.365 

79,555 

24.9 

5.87 

1.54 

.4317 

62.5 

.925 

.649 

1.425 

83,055 

23.8 

6.23 

1.6 

.4700 

59.9 

.913 

.625 

1.461 

85,125 

23.3 

6.47 

1.75 

.5595 

54.1 

.883 

.571 

1.546 

90,115 

22.0 

7.08 

1.88 

.6314 

50 

.860 

.532 

1.616 

94,200 

21.0 

7.61 

2 

.8931 

46.5 

.836 

.5 

1.672 

97,432 

20.3 

8.09 

2.28 

.8241 

40 

.787 

.439 

1.793 

104,466 

19.0 

9.23 

2.4 

.8755 

37.6 

.766 

.417 

1.837 

107,050 

18.5 

9.71 

2.65 

.9745 

33.3 

.726 

.377 

1.925 

112,220 

17.7 

10.72 

2.9 

.065 

29.9 

.692 

.345 

2.006 

116,885 

16.9 

11.74 

3.2 

.163 

26.4 

.652 

.313 

2.083 

121,386 

16.3 

12.95 

3.35 

.209 

25 

.637 

.298 

2.129 

124,066 

16.0 

13.56 

3.6 

.281 

22.7 

.608 

.278 

2.187 

127,450 

15.5 

14.57 

3.8 

.335 

21.2 

.589 

.263 

-2.240 

130,533 

15.2 

15.38 

4 

.386 

19.7 

.569 

.250 

2.278 

132.770 

14.9 

16.19 

4.2 

.435 

18.5 

.551 

.238 

2.315 

134.900 

14.7 

17.00 

4.5 

.504 

16.8 

.526 

.222 

2.370 

138,130 

14.34 

18.21 

4.8 

.569 

15.3 

.503 

.208 

2.418 

140,920 

14.05 

19.43 

5 

.609 

14.4 

.488 

.200 

2.440 

142,180 

13.92 

20.23 

5.2 

.649 

13.6 

.476 

.193 

2.466 

143,720 

13.78 

21.04 

5.5 

.705 

12.5 

.457 

.182 

2.511 

146,325 

13.53 

22.25 

5.8 

.758 

11.4 

.438 

.172 

2.547 

148,390 

13.34 

23.47 

5.9 

.775 

11.1 

.432 

.169 

2.556 

148,940 

13.29 

23.87 

6.2 

.825 

10.3 

.419 

.161 

2.585 

150,630 

13.14 

25.09 

6.3 

.841 

10 

.413 

.159 

2.597 

151,370 

13.08 

25.49 

6.6 

1.887 

9.2 

.398 

.152 

2.619 

152,595 

12.98 

26.71 

7 

1.946 

8.3 

.381 

.143 

2.664 

155,200 

12.75 

28.33 

7.3 

'  1.988 

7.7 

.369 

.137 

2.693 

156,960 

12.61 

29.54 

7.6 

2.028 

7.1 

.357 

.132 

2.711 

157,975 

12.53 

30.76 

7.8 

2.054 

6.7 

.348 

.128 

2.719 

158,414 

12.50 

31.57 

8 

2.079 

6.4 

.342 

.125 

2.736 

159,433 

11.83 

32.38 

ASSUMPTIONS  OP  THE  TABLE.—  That  the  initial  pressure  is  uniform;  that 
the  expansion  is  complete  to  the  end  of  the  stroke;  that  the  pressure  in  ex- 
pansion varies  inversely  as  the  volume;  that  there  is  no  back-pressure  of 
exhaust  or  of  compression,  and  that  clearance  is  7$  of  the  stroke  at  each 
end  of  the  cylinder.  No  allowance  has  been  made  for  loss  of  steam  by  cyl- 
inder-condensation or  leakage. 

Volume  of  1  Ib.  of  steam  of  100  Ibs.  pressure  per  sq.  in.,  or  14,400 

Ibs.  per  sq,  ft 4.33  cu.  ft. 

Product  of  initial  pressure  and  volume ....... . .62,352  f  t.-lbs. 


748 


THE   STEAM-ENGINE. 


Though  a  uniform  clearance  of  ?#  at  each  end  of  the  stroke  has  been 
assumed  as  an  average  proportion  for  the  purpose  of  compiling  the  table, 
the  clearance  of  cylinders  with  ordinary  slides  varies  considerably — say 
from  5%  to  10$.  (With  Corliss  engines  it  is  sometimes  as  low  as  2%.}  With 
the  clearance,  7#,  that  has  been  assumed,  the  table  gives  approximate  re- 
sults sufficient  for  most  practical  purposes,  and  more  trustworthy  than  re- 
sults deduced  by  calculations  based  on  simple  tables  of  hyperbolic  loga- 
rithms, where  clearance  is  neglected. 

Weight  of  steam  of  100  Ibs.  total  initial  pressure  admitted  for  one  stroke, 
per  cubic  foot  of  net  capacity  of  the  cylinder,  in  decimals  of  a  pound  = 
reciprocal  of  figures  in  column  9. 

Total  actual  work  done  by  steam  of  100  Ibs.  total  initial  pressure  in  one 
stroke  per  cubic  foot  of  net  capacity  of  cylinder,  in  foot-pounds  =  figures 
in  column  7  -s-  figures  in  column  9. 

RULE  1 :  To  find  the  net  capacity  Of  cylinder  for  a  given  weight  of  steam 
admitted  for  one  stroke,  and  a  given  actual  ratio  of  expansion.  (Column  9 
of  table.)— Multiply  the  volume  of  1  Ib.  of  steam  of  the  given  pressure  by  the 
given  weight  in  pounds,  and  by  the  actual  ratio  of  expansion.  Multiply  the 
product  by  100,  and  divide  by  100  plus  the  percentage  of  clearance.  The 
quotient  is  the  net  capacity  of  the  cylinder.  . 

RULE  2:  To  find  the  net  capacity  of  cylinder  for  the  performance  of  a 
given  amount  of  total  actual  work  in  one  stroke,  with  a  given  initial  press- 
ure and  actual  ratio  of  expansion.— Divide  the  given  work  by  the  total 
actual  work  done  by  1  Ib.  of  steam  of  the  same  pressure,  and  with  the  same 
actual  ratio  of  expansion;  the  quotient  is  the  weight  of  steam  necessary  to 
do  the  given  work,  for  which  the  net  capacity  is  found  by  Rule  1  preceding. 

NOTE. — 1.  Conversely,  the  weight  of  steam  admitted  per  cubic  foot  of  net 
capacity  for  one  stroke  is  the  reciprocal  of  the  cylinder-capacity  per  pound 
of  steam,  as  obtained  by  Rule  1. 

2.  The  total  actual  work  done  per  cubic  foot  of  net  capacity  for  one  stroke 
is  the  reciprocal  of  the  cylinder-capacity  per  foot-pound  of  work  done,  ay 
obtained  by  Rule  2. 

3.  The  total  actual  work  clone  per  square  inch  of  piston  per  foot  of  the 
stroke  is  l/144th  part  of  the  work  done  per  cubic  foot. 

4.  The  resistance  of  back  pressure  of  exhaust  and  of  compression  are  to 
be  added  to  the  net  work  required  to  be  done,  to  find  the  total  actual  work. 

APPENDIX  TO  ABOVE  TABLE— MULTIPLIERS  FOR  NET  CYLINDER-CAPACITY,  AND 
TOTAL  ACTUAL  WORK  DONE. 

(For  steam  of  other  pressures  than  100  Ibs.  per  square  inch.) 


Total  Pres- 
sures per 
square  inch. 

Multipliers. 

Total  Pres- 
sures per 
square  inch. 

Multipliers. 

For  Col.  7 
Total  Work 
by  1  Ib  of 
Steam. 

For  Col.  9. 
Capacity 
of 
Cylinder. 

For  Col.  7. 
Total  Work 
by  1  Ib.  of 
Steam. 

For  Col.  9. 
Capacity 
of 
Cylinder. 

Ibs. 
65 
70 
75 
80 
85 
90 
95 

.975 
.981 
.986 
.988 
.991 
.995 
.998 

1.50 
1.40 
1.31 
1.24 
1.17 
1.11 
1.05 

Ibs. 
100 
110 
120 
ISO 
140 
150 
160 

1.000 
1.009 
1.011 
1.015 
1.022 
1.025 
1.031 

1.00 
.917 
.843 
.781 
.730 
.683 
.644 

The  figures  in  the  second  column  of  this  table  are  derived  by  multiplying 
the  total  pressure  per  square  foot  of  any  given  steam  by  the  volume  in 
cubic  feet  of  1  Ib.  of  such  steam,  and  dividing  the  product  by  62,352,  which 
is  the  product  in  foot-pounds  for  steam  of  100  Ibs.  pressure.  The  quotient 
is  the  multiplier  for  the  given  pressure. 

The  figures  in  the  third  column  are  the  quotients  of  the  figures  in  the 
second  column  divided  by  the  ratio  of  the  pressure  of  the  given  steam  to  100 
Ibs. 

Measures  tor  Comparing  tlie  Duty  of  Engines.— Capacity  is 
measured  in  horse-powers,  expressed  by  the  initials,  H.P. :  1  H.P.  =  33,00tf 
ft. -Ibs.  per  minute,  =  550  ft.-lbs.  per  second,  =  1,980,000  ft.-lbs.  per  hour 


WORK   OF  STEAM  1ST  A  SIKGLE   CYLINDER.        749 

1  ft.-lb.  =  a  pressure  of  1  Ib.  exerted  through  a  space  of  1  ft.  Economy  is 
measured,  1,  in  pounds  of  coal  per  horse-power  per  hour;  2,  in  pounds  of 
steam  per  horse-power  per  hour.  The  second  of  these  measures  is  the  more 
accurate  and  scientific,  since  the  engine  uces  steam  and  not  coal,  and  it  is 
indepndent  of  the  economy  of  the  boiler. 

In  gas-engine  tests  the  common  measure  is  the  number  of  cubic  feet 
of  gas  (measured  at  atmospheric  pressure)  per  horse-power,  but  as  all  gas 
is  not  of  the  same  quality,  it  is  necessary  for  comparison  of  tests  to  give  the 
analysis  of  the  gas.  When  the  gas  for  one  engine  is  made  in  one  gas-pro- 
ducer, then  the  number  of  pounds  of  coal  used  in  the  producer  per  hour  per 
horse-power  of  the  engine  is  the  proper  measure  of  economy. 

Economy,  or  duty  of  an  engine,  is  also  measured  in  the  number  of  foot- 
pounds of  work  done  per  pound  of  fuel.  As  1  horse-power  is  equal  to  1,980,- 

000  ft.-lbs.  of  work  in  an  hour,  a  duty  of  1  Ib.  of  coal  per  H.P.  per  hour 
would  be  equal  to  1,980,000  ft.-lbs.  per  Ib.  of  fuel;  2  Ibs.  per  H.P.  per  hour 
equals  990,000  ft.-lbs.  per  Ib.  of  fuel,  etc. 

The  duty  of  pumping-engines  is  commonly  expressed  by  the  number  of 
foot-pounds  of  work  done  per  100  Ibs.  of  coal. 

When  the  duty  of  a  pumping-engine  is  thus  given,  the  equivalent  number 
of  pounds  of  fuel  consumed  per  horse-power  per  hour  is  found  by  dividing 
198  by  the  number  of  millions  of  foot-pounds  of  duty.  Thus  a  pumping- 
engine  giving  a  duty  of  99  millions  is  equivalent  to  198/99  =  2  Ibs.  of  fuel  per 
horse- power  per  hour. 

Efficiency  Measured  in  Thermal  Units  per  minute.— 
Some  writers  express  the  efficiency  of  an  engine  in  terms  of  the  number  of 
thermal  units  used  by  the  engine  per  minute  for  each  indicated  horse-power, 
instead  of  by  the  number  of  pounds  of  steam  used  per  hour. 

The  heat  chargeable  to  an  engine  per  pound  of  steam  is  the  difference  be- 
tween the  total  heat  in  a  pound  of  steam  at  the  boiler-pressure  and  that  in 
fti  pound  of  the  feed  water  entering  the  boiler.  In  the  case  of  condensing 
engines,  suppose  we  have  a  temperature  in  the  hot-well  of  101°  F.,  corre- 
sponding to  a  vacuum  of  28  in.  of  mercury,  or  an  absolute  pressure  of  1  Ib. 
per  sq.  in.  above  a  perfect  vacuum  :  we  may  feed  the  water  into  the  boiler 
at  that  temperature.  In  the  case  of  anon-condensing-engine,  by  using  a  ppr- 

1  ion  of  the  exhaust  steam  in  a  good  feed-water  heater,  at  a  pressure  a  trifle 
above   the  atmosphere   (due   to  the  resistance  of    the  exhaust  passages 
through  the  heater),  we  may  obtain  feed-water  at  212°.   One  pound  of  steam 
used  by  the  engine  then  would  be  equivalent  to  thermal  units  as  follows: 
f/ressure  of  steam  by  gauge: 

50  75  100  125  150  175  200 

fotal  heat  in  steam  above  32°  : 

1172.8      1179.6      1185.0      1189.5      1193.5      1197.0      1200.2 

Subtracting  69.1  and  180.9  heat-units,  respectively,  the  heat  above  32°  in 
feed-water  of  101°  and  212°  F.,  we  bave— 

Heat  given  by  boiler: 

Feed  at  101° 1103.7      1110.5      1115.fr      1120.4      1124.4      1127.9      1131.1 

Feed  at  212° 991.9        998.7      1004.1      1008.6      1012.6      1016.1      1019.3 

Thermal  units  per  minute  used  by  an  engine  for  each  pound  of  steam  used 
per  indicated  horse-power  per  hour: 

Feed  at  101° 18.40        18.51        18.60        18.67        1S.V4        18.80       18.85 

Feed  at  212° 16.53        16.65        16.74        16.81        16.88        16.94        16.99 

EXAMPLES.— A  triple-expansion  engine,  condensing,  with  steam  at  175 Ibs., 
gauge  and  vacuum  28  in.,  uses  13  Ibs.  of  water  per  I.H.P.  per  hour,  and  a 
high -speed  non -condensing  engine,  with  steam  at  100  Ibs.  gauge,  uses  30 
Ibs.  How  many  thermal  units  per  minute  does  each  consume  ? 

Ans.— 13  X  18.80  =  244.4,  and  30  X  16.74  =  502.2  thermal  units  per  minute. 

A  perfect  engine  converting  ail  the  heat-energy  of  the  steam  into  work 
would  require  33,000  ft.-lbs,  -*-  778  =  42.4164  thermal  units  per  minute  per 
indicated  horse-power.  This  figure,  42.4164,  therefore,  divided  by  the  num- 
ber of  thermal  units  per  minute  per  I.H.P.  consumed  by  an  engine,  gives  its 
efficiency  as  compared  with  an  ideally  perfect  engine.  In  the  examples 
above.  42.4164  divided  by  244.4  and  by  502.2  gives  17,35$  and  8.45#  efficiency, 
respectively. 

Total  Work  Done  by  One  Pound  of  Steam  Expanded  in 
a  Single  Cylinder.  (Column  7  of  table.)— If  1  pound  of  water  be  con- 
verted into  steam  of  atmospheric  pressure  =  2116.8  Ibs.  per  sq.  ft.,  it  occu- 
pies a  volume  equal  to  26.36  cu.  ft.  The  work  done  is  equal  to  2116.8  Ibs, 


750 


STEAM-ESTGttfE. 


X  26.36  ft.  =  55,788  ft.  -Ibs.  The  heat  equivalent  of  this  work  is  (55,788  -4-  778 
=)71.7  units.  This  is  the  work  of  1  Ib.  of  steam  of  one  atmosphere  acting 
on  a  piston  without  expansion. 

The  gross  work  thus  done  on  a  piston  by  1  Ib.  of  steam  generated  at  total 
pressures  varying  from  15  Ibs.  to  100  Ibs.  per  sq.  in.  varies  in  round  numbers 
from  56,000  to  62,000  ft.-lbs.,  equivalent  to  from  72  to  80  units  of  heat. 

This  work  of  1  Ib.  of  steam  without  expansion  is  reduced  by  clearance 
according  to  the  proportion  it  bears  to  the  net  capacity  of  the  cylinder.  If 
the  clearance  be  7f0  of  the  stroke,  the  work  of  a  given  weight  of  steam  with- 
out expansion,  admitted  for  the  whole  of  the  stroke,  is  reduced  in  the  ratio 
of  107  to  100. 

Having  determined  by  this  ratio  the  quantity  of  work  of  1  Ib.  of  steam  with- 
out expansion,  as  reduced  by  clearance,  the  work  of  the  same  weight  of  stea  m 
for  various  ratios  of  expansion  may  be  found  by  multiplying  it  by  the  relative 
performance  of  equal  weights  of  steam,  given  in  the  6th  column  of  the  table. 

Quantity  of  Steam  Consumed  per  Horse-power  of  Total 
"Work  per  Hour.  (Column  8  of  table.)—  The  measure  of  a  horse-power 
is  the  performance  of  33,000  ft.-lbs.  per  minute,  or  1,980,000  ft.-lbs.  per  hour. 
This  work,  divided  by  the  work  of  1  Ib.  of  steam,  gives  the  weight  of  steam 
required  per  horse-power  per  hour.  For  example,  the  total  actual  work 
done  in  the  cylinder  by  1  Ib.  of  100  Ibs.  steam,  without  expansion  and  with 


1%  of  clearance,  is  58,273  ft.-lbs.  ;  and  j~~  =  34  Ibs.  of  steam,  is  the  weight 
of  steam  consumed  for  the  total  work  done  in  the  cylinder  per  horse-power 
per  hour.  For  any  shorter  period  of  admission  with  expansion  the  weight 
of  steam  per  horse-power  is  less,  as  the  total  work  of  1  Ib.  of  steam  is  more, 
and  may  be  found  by  dividing  1,980,000  ft.-lbs.  by  the  respective  total  work 
done;  or  by  dividing  34  Ibs.  by  the  ratio  of  performance,  column  6  in  the 
table. 

ACTUAL     EXPANSIONS. 

With  Different   Clearances  and   Cut-offs. 

Computed  by  A.  F.  Nagle. 


Per  Cent  of  Clearance. 

Cut- 

off. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

.01 

100.00 

50.5 

34.0 

25.75 

20.8 

17.5 

15.14 

13.38 

12.00 

10.9 

10 

.02 

50.00 

33.67 

25.50 

20.60 

17.83 

15.00 

13.25 

11.89 

10.80 

9.91 

8.17 

.03 

33.33 

25.25 

20.40 

17.16 

14.86 

13.12 

11.78 

10.70 

9.82 

9.08 

8.46 

.04 

25.00 

20.20 

17.00 

14.71 

13.00 

11.66 

10.60 

9.73 

9.00 

8.39 

7.86 

.05 

20.00 

16.83 

14.57 

12.87 

11.55 

10.50 

9.64 

8.92 

8.31 

7.79 

7.33 

.06 

16.67 

14.43 

12.75 

11.44 

10.40 

9.55 

8.83 

8.23 

7.71 

7  27 

6.88 

.07 

14.28 

12.62 

11.33 

10.30 

9.46 

8.75 

8.15 

7.64 

7.20 

6^81 

6.47 

.08 

12.50 

11.22 

10.2 

9.36 

8.67 

8.08 

7.57 

7.13 

6.75 

6.41 

6.11 

.09 

11.11 

10.10 

9.27 

8.58 

8.00 

7.50 

7.07 

6.69 

6.35 

6.0(5 

5.79 

.10 

10.00 

9.18 

8.50 

7.92 

7.43 

7.00 

6.62 

6.30 

6.00 

5.74 

5.50 

.11 

9.09 

8.42 

7.84 

7.36 

6.93 

6.56 

6.24 

5.94 

5.68 

5.45 

5.24 

.12 

8.33 

7  78 

7.29 

6.86 

6.50 

6.18 

5.89 

5.63 

5.40 

5.19 

5.00 

.14 

7.14 

6>3 

6.37 

6.06 

5.78 

5.53 

5.30 

5.10 

4.91 

4.74 

4.58 

.16 

6.25 

5.94 

5.67 

5.42 

5.20 

5.00 

4.82 

4.65 

4.50 

4.36 

4  23 

.20 

5.00 

4.81 

4.64 

4.48 

4.33 

4.20 

4.08 

3.96 

3.86 

3.76 

3.67 

.25 

4.00 

3.88 

3.77 

3.68 

3.58 

3.50 

3.42 

3.34 

3.27 

3.21 

8.14 

.30 

3.33 

3.26 

3.19 

3.12 

3.06 

3.00 

2.94 

2.90 

2.84 

2.80 

2.75 

.40 

2.50 

2.46 

2.43 

2.40 

2.36 

2.33 

2.30 

2.28 

2.25 

2  22 

2.20 

.50 

2.00 

1.98 

1.96 

1.94 

1.92 

1.90 

1.89 

1.88 

1.86 

1.85 

1.83 

.60 

1.67 

1.66 

1.65 

1.64 

1.63 

.615 

1.606 

1.597 

1.588 

1.580 

1.571 

.70 

1.43 

1.42 

1.42 

1.41 

1.41 

.400 

1.395 

1.390 

1.385 

1.380 

1.375 

.80 

1.25 

1.25 

1.244 

1.241 

1.238 

.235 

1.233 

1.230 

1.227 

1.224 

1.222 

.90 

1.111 

1.11 

1.109 

1.108 

1.106 

.105 

1.104 

1.103 

1.102 

1,101 

1.100 

1.00 

l.OC 

1.00 

1.000 

1.000 

1.000 

.000 

1.000 

1.000 

1.000 

1.000 

1.000 

I 

WO&K   OF   STEAM   Iff   A   SIffGLft   CYLINDER.        751 

Relative  Efficiency  of  1  Ib.  of  Steam  with  and  without 
Clearance;  back  pressure  and  compression  not  considered. 

Mean  total  pressure  op-  ^  +  c)  +  *«  +  4*»  "*•  *  ~  fc. 


LetP=l;  £=100;  Z  =  25;  c  =  7. 

38  +  32  hyp,  log.  ^-7 

*=  -         "Too—  -w-     ~  =  •637' 

If  the  clearance  be  added  to  the  stroke,  so  that  clearance  becomes  zero, 
the  same  quantity  of  steam  being  used,  admission  I  being  then  =  I  -f-  c  = 
32,  and  stroke  L  -f  c  =  107. 


=  -707' 


That  is,  if  the  clearance  be  reduced  to  0,  the  amount  of  the  clearance  7 
being  added  to  both  the  admission  and  the  stroke,  the  same  quantity  of 
steam  will  do  more  work  than  when  the  clearance  is  7  in  the  ratio  707  :  637, 
or  \\%  more. 

Back  Pressure  Considered.—  If  back  pressure  =  .10  of  P,  this 
amount  has  to  be  subtracted  from  p  andpj  giving  p  =  .537,  pt  =  .607,  the 
work  of  a  given  quantity  of  steam  used  without  clearance  being  greater 
than  when  clearance  is  7  per  cent  in  the  ratio  of  607  :  537,  or  13%  more. 

Effect  of  Compression.—  By  early  closure  of  the  exhaust,  so  that  a 
portion  of  the  exhaust-steam  is  compressed  into  the  clearance-space,  much 
of  the  loss  due  to  clearance  may  be  avoided.  If  expansion  is  continued 
down  to  the  back  pressure,  if  the  back  pressure  is  uniform  throughout  the 
exhaust-stroke,  and  if  compression  begins  at  such  point  that  the  exhaust- 
steam  remaining  in  the  cylinder  is  compressed  to  the  initial  pressure  at  the 
end  of  the  back  stroke,  then  the  work  of  compression  of  the  exhaust-steam 
equals  the  work  done  during  expansion  by  the  clearance-steam.  The  clear- 
ance-space being  filled  by  the  exhaust-steam  thus  compressed,  no  new  steam 
is  required  to  fill  the  clearance-space  for  the  next  forward  stroke,  and  the 
work  and  efficiency  of  the  steam  used  in  the  cylinder  are  just  the  same  as  if 
there  were  no  clearance  and  no  compression.  When,  however,  there  is  a 
drop  in  pressure  from  the  final  pressure  of  the  expansion,  or  the  terminal 
pressure,  to  the  exhaust  or  back  pressure  (the  usual  case),  the  work  of  com- 
pression to  the  initial  pressure  is  greater  than  the  work  done  by  the  expan- 
sion of  the  clearance-steam,  so  that  a  loss  of  efficiency  results.  In  this 
case  a  greater  efficiency  can  be  attained  by  inclosing  for  compression  a  less 

Suantity  of  steam  than  that  needed  to  fill  the  clearance-space  with  steam  of 
le  initial  pressure.  (See  Clark,  S.  E.,  p.  399,  et  seq.;  also  F.  H.  Ball,  Trans. 
A.  S.  M.  E.,  xiv.  1067.)  It  is  shown  by  Clark  that  a  somewhat  greater  effi- 
ciency is  thus  attained  whether  or  not  the  pressure  of  the  steam  be  carried 
down  by  expansion  to  the  back  exhaust-pressure.  As  a  result  of  calcula- 
tions to  determine  the  most  efficient  periods  of  compression  for  various 
percentages  of  back  pressure,  and  for  various  periods  of  admission,  he  gives 
the  table  on  the  next  page  : 

Clearance  in  I>ow-  and  High-speed  Engines.  (Harris 
Tabor,  Am.  Mach.,  Sept.  17,  1891.)  —  The  construction  of  the  high-speed 
engine  is  such,  with  its  relatively  short  stroke,  that  the  clearance  must  be 
much  larger  than  in  the  releasing-valve  type.  The  short-stroke  engine  is, 
of  necessity,  an  engine  with  large  clearance,  which  is  aggravated  when  a 
variable  compression  is  a  feature.  Conversely,  the  releasing-  valve  gear  is, 
from  necessity,  an  engine  of  slow  rotative  speed,  where  great  power  is 
obtainable  from  long  stroke,  and  small  clearance  is  a  feature  in  its  construc- 
tion. In  one  case  the  clearance  will  vary  from  8#  to  V&%  of  the  piston-dis- 
placement, and  in  the  other  from  2%  to  3#.  In  the  case  of  an  engine  with  a 
clearance  equalling  10$  of  the  piston-displacement  the  waste  room  becomes 
enormous  when  considered  in  connection  with  an  early  cut-off.  The  system  of 
compounding  reduces  the  waste  due  to  clearance  in  proportion  as  the  steam 
is  expanded  to  a  lower  pressure.  The  farther  expansion  is  carried  through 
a  train  of  cylinders  the  greater  will  be  the  reduction  of  waste  due  to  clear- 
ance. This  is  shown  from  the  fact  that  the  high-speed  engine,  expanding 


752 


THE   STEAM-ENGINE. 


steam  much  less  than  the  Corliss,  will  show  a  greater  gain  when  changed 
from  simple  to  compound  than  its  rival  under  similar  conditions. 

COMPRESSION  OP  STEAM  IN  THE  CYLINDER. 
Best  Periods  of  Compression;  Clearance  7  per  cent. 


Cut-off  in 
Percent- 
ages of 
the 
Stroke. 

Total  Back  Pressure,  in  percentages  of  the  total  initial  pressure. 

2^ 

5 

10 

15 

20 

25 

30 

35 

Periods  of  Compression,  in  parts  of  the  stroke. 

10* 

15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 

65# 
58 
52 
47 
42 
39 
36 
33 
30 
27 
24 
22 
19 
17 

57# 
52 
47 
42 
39 
35 
32 
30 
27 
24 
22 
20 
17 
16 

44% 
40 
37 
34 
32 
29 
27 
25 
23 
21 
19 
17 
16 
14 

32# 
29 
27 
26 
25 
23 
21 
20 
18 
17 
15 
15 
14 
13 

23£ 
22 
21 
20 
19 
18 
17 
16 
15 
14 
14 
14 
12 

Yl% 
16 
15 
14 
14 
13 
13 
12 
12 
12 
11 

14* 
13 
13 
12 
12 
11 
11 
10 
10 
9 

12* 
11 
11 
10 
10 
9 
9 
8 
8 
8 

NOTES  TO  TABLE.— 1.  For  periods  of   admission,  or  percentages  of  back 

Eressure,  other  than  those  given,  the  periods  of  compression  may  be  readily 
)und  by  interpolation. 

2.  For  any  other  clearance,  the  values  of  the  tabulated  periods  of  com- 
pression are  to  be  altered  in  the  ratio  of  7  to  the  given  percentage  of 
clearance. 

Cylinder-condensation  may  have  considerable  effect  upon  the  best  point 
of  compression,  but  it  has  not  yet  (1893)  been  determined  by  experiment. 
(Trans.  A.  S.  M.  E..  xiv.  1078.) 

Cylinder-condensation.— Rankine,  S.  E.,  p.  421,  says  :  Conduction 
of  heat  to  arid  from  the  metal  of  the  cylinder,  or  to  and  from  liquid  water 
contained  in  the  cylinder,  has  the  effect  of  lowering  the  pressure  at  the  be- 
ginning and  raising  it  at  the  end  of  the  stroke,  the  lowering  effect  being  on 
the  whole  greater  than  the  raising  effect.  In  some  experiments  the  quantity 
of  steam  wasted  through  alternate  liquefaction  and  evaporation  in  the 
cylinder  has  been  found  to  be  greater  than  the  quantity  wnich  performed 
the  work. 

Percentage  of  Loss  by  Cylinder-condensation,  taken  at 
Cut-off.  (From  circular  of  the  Ashcroft  Mfg.  Co.  on  the  Tabor 
Indicator,  1889.) 


Percentage  of 
Stroke  completed 
at  Cut-off. 

Percent,  of  Feed  -water  accounted 
for  by  the  Indicator  diagram. 

Percent,  of  Feed-water  Consump- 
tion due  to  Cylinder-condensat'n. 

Simple 
Engines. 

Compound 
Engines, 
h.p.  cyl. 

Triple-ex- 
pansion 
Engines, 
b.p.  cyl. 

Simple 
Engines. 

Compound 
Engines, 
h.p.  cyl. 

Triple-ex- 
pansion 
Engines, 
h.p.  cyl. 

5 
10 
15 
20 
30 
40 
50 

58 
66 
71 

74 
78 
82 
86 

42 
34 
29 
26 
22 
18 
14 

74 
76 

78 
82 
85 
88 

26 
24 
22 
18 
15 
1£ 

78 
80 
84 

87 
90 

22 

20 
16 
13 
10 

WORK  OF  STEAM  IK  A  SINGLE  CYLINDEB.        753 


Theoretical  Compared  with  Actual  Water-consump- 
tion, Single-cylinder  Automatic  Cut-off  Engines.  (From 
the  catalogue  of  the  Buckeye  Engine  Co.) — The  following  table  has  been 
prepared  on  the  basis  of  the  pressures  that  result  in  practice  with  a  con- 
stant boiler- pressure  of  80  Ibs.  and  different  points  of  cut-off,  with  Buckeye 
engines  and  others  with  similar  clearance.  Fractions  are  omitted,  except 
in  the  percentage  column,  as  the  degree  of  accuracy  their  use  would  seem 
to  imply  is  not  attained  or  aimed  at. 


Cut-off  Part 
of  Stroke. 

Mean 
Effective 
Pressure. 

Total 
Terminal 
Pressure. 

Indicated 
Rate, 
Ibs.  Water, 
perl.H.P. 
per  hour. 

Assumed. 

Act'l  Rate. 

Per  ct.  Loss. 

.10 

18 

11 

20 

32 

58 

.15 

.27 

15 

19 

27 

41 

.20 

35 

20 

19 

25 

31.5 

.25 

42 

25 

20 

25 

25 

.30 

48 

30 

20 

24 

21.8 

.35 

53 

35 

21 

25 

19 

.40 

57 

38 

22 

26 

16.7 

.45 

61 

43 

23 

27 

15 

.50 

64 

48 

24 

27 

13.6 

It  will  be  seen  that  while  the  best  indicated  economy  is  when  the  cut-off 
is  about  at  .15  or  .20  of  the  stroke,  giving  about  30  Ibs.  M.E.P.,  and  a  termi- 
nal 3  or  4  Ibs.  above  atmosphere,  when  we  come  to  add  the  percentages  due 
to  a  constant  amount  of  unindicated  loss,  as  per  sixth  column,  the  most  eco- 
nomical point  of  cut-off  is  found  to  be  about  .30  of  the  stroke,  giving  48  Ibs. 
M.E.P.  and  30  Ibs.  terminal  pressure.  This  showing  agrees  substantially 
with  modern  experience  under  automatic  cut-off  regulation. 

Experiments  on  Cylinder-condensation,— Experiments  by 
fvlajor  Thos.  English  (Eng'y,  Oct.  7,  1887,  p.  386)  with  an  engine  10  X  14  in., 
jacketed  in  the  sides  but  not  on  the  ends,  indicate  that  the  net  initial  con- 
densation (or  excess  of  condensation  over  re-evaporation)  by  the  clearance 
surface  varies  directly  as  the  initial  density  of  the  steam,  and  inversely  as 
the  square  root  of  the  number  of  revolutions  per  unit  of  time.  The  mean 
results  gave  for  the  net  initial  condensation  by  clearance-space  per  sq.  ft.  of 
surface  at  one  rev.  per  second  6.06  thermal  units  in  the  engine  when  run 
non-condensing  and  5.75  units  when  condensing. 

G.  R.  Bodmer  (Eng^g,  March  4,  1892,  p.  299)  says  :  Within  the  ordinary 
limits  of  expansion  desirable  in  one  cylinder  the  expansion  ratio  has  prac- 
tically no  influence  on  the  amount  of  condensation  per  stroke,  which  for 
simple  engines  can  be  expressed  by  the  following  formula  for  the  weight 
of  water  condensed  [per  minute,  probably;  the  original  does  not  state]  : 

S(T-t) 
W  =  C^   s/— ,  where  T  denotes  the  mean  admission  temperature,  t  the 


mean  exhaust  temperature,  S  clearance-surface  (square  feet),  N  the  num- 
ber of  revolutions  per  second,  L  latent  heat  of  steam  at  the  mean  admission 
temperature,  and  C  a  constant  for  any  given  type  of  engine. 

Mr.  Bodmer  found  from  experimental  data  that  for  high-pressure  non- 
jacketed  engines  C  =  about  0.11,  for  condensing  non- jacketed  engines  0.085 
to  0.11,  for  condensing  jacketed  engines  0.085  to  0.053.  The  figures  for  jack- 
eted engines  apply  to  those  jacketed  in  the  usual  way,  and  not  at  the  ends. 

C  varies  for  different  engines  of  the  same  class,  but  is  practically  con- 
stant for  any  given  engine.  For  simple  high-pressure  non -jacketed  engines 
it  was  found  to  range  from  0.1  to  0.112. 

Applying  Mr.  Bodrner'a  formula  to  the  case  of  a  Corliss  non-jacketed  non- 
condensing  engine,  4-ft.  stroke,  24  in.  diam.,  60  revs,  per  min.,  initial  pres- 
sure 90  Ibs.  gauge,  exhaust  pressure  2  Ibs.,  we  have  T  -  t  —  112°,  N  =  1, 
L  =  880,  S  =  7  sq.  ft.;  and,  taking  C  =  .112  and  W  =  Ibs.  water  condensed 

per  minute,  W  —  ' — ~  =  .09  Ib.  per  minute,  or  5.4  Ibs.  per  hour.    If 

the  steam  used  per  I.H.P.  per  hour  according  to  the  diagram  is  20  Ibs.,  the 
actual  water  consumption  is  25.4  Ibs.,  corresponding  to  a  cylinder  condensa- 
tion of  27#. 


THE  STEAM-EKGINE, 


INDICATOR-DIAGRAM   OF   A    SINGLE-CYLINDER 
ENGINE. 

Definitions.  —The  Atmospheric  Line,  AB,  is  a  line  drawn  by  the  pencil 
of  the  indicator  when  the  connections  with  the  engine  are  closed  and  both 
sides  of  the  piston  are  open  to  the  atmosphere. 


FIG.  138. 

Tlie  Vacuum  Line,  OX,  is  a  reference  line  usually  drawn  about  14  7/14 
pounds  by  scale  below  the  atmospheric  line. 

The  Clearance  Line,  OY,  is  a  reference  line  drawn  at  a  distance  from  th<^ 
end  of  the  diagram  equal  to  the  same  per  cent  of  its  length  as  the  clearance 
and  waste  room  is  of  the  piston-displacement. 

The  Line  of  Boiler -pressure,  JK,  is  drawn  parallel  to  the  atmospheric 
line,  and  at  a  distance  from  it  by  scale  equal  to  the  boiler-pressure  shown 
by  the  gauge. 

The  Admission  Line,  CD,  shows  the  rise  of  pressure  due  to  the  admission 
of  steam  to  the  cylinder  by  opening  the  steam-valve. 

The  Steam  Line,  DE,  is  drawn  when  the  steam- valve  is  open  and  steam  is 
being  admitted  to  the  cylinder. 

The  Point  of  Cut-off,  E,  is  the  point  where  the  admission  of  steam  is 
stopped  by  the  closing  of  the  valve.  It  is  often  difficult  to  determine  the 
exact  point  at  which  the  cut-off  takes  place.  It  is  usually  located  where  thf 
outline  of  the  diagram  changes  its  curvature  from  convex  to  concave. 

The  Expansion  Curve,  EF,  shows  the  fall  in  pressure  as  the  steam  in  the 
cylinder  expands  doing  work. 

The  Point  of  Release,  F,  shows  when  the  exhaust-valve  opens. 

The  Exhaust  Line,  FG,  represents  the  change  in  pressure  *hat  takes 
place  when  the  exhaust- valve  opens. 

The  Back-pressure  Line,  GH,  shows  the  pressure  against  which  the  piston 
acts  during  its  return  stroke. 

The  Point  of  Exhaust  Closure,  H,  is  the  point  where  the  exhau«»*-valve 
closes.  It  cannot  be  located  definitely,  as  the  change  in  pressure  is  at  first 
due  to  the  gradual  closing  of  the  valve. 

The  Compression  Curve,  HC,  shows  the  rise  in  pressure  due  to  the  com- 
pression of  the  steam  remaining  in  the  cylinder  after  the  exhaust-valve  has 
closed. 

The  Mean  Height  of  the  Diagram  equals  its  area  divided  by  its  lengt)  . 

The  Mean  Effective  Pressure  is  the  mean  net  pressure  urging  the  piston 
forward  =  the  mean  height  X  the  scale  of  the  indicator-spring. 

To  find  the  Mean  Effective  Pressure  from  the  Diagram. — Divide  Che 
length,  LB,  into  a  number,  say  10,  equal  parts,  setting  off  half  a  part  at  L, 
half  a  part  at  B,  and  nine  other  parts  between;  erect  ordinates  perpendicu- 
lar to  the  atmospheric  line  at  the  points  of  division  of  LB,  cutting  the  dia- 
gram; add  together  the  lengths  of  these  ordinates  intercepted  between  the 
tipper  and  lower  lines  of  the  diagram  and  divide  by  their  number.  This* 


INDICATED   HORSE-POWER  OF   EKGINES.  755 

gives  the  mean  height,  which  multiplied  by  the  scale  of  the  indicator-spring 
gives  the  M.E.P.  Or  find  the  area  by  a  planimeter,  or  other  means  (see 
Mensuration,  p.  55),  and  divide  by  the  length  LB  to  obtain  the  mean  height. 

The  Initial  Pressure  is  the  pressure  acting  on  the  piston  at  the  beginning 
of  the  stroke. 

The  Terminal  Pressure  is  the  pressure  above  the  line  of  perfect  vacuum 
that  would  exist  at  the  end  of  the  stroke  if  the  steam  had  not  been  released 
earlier.  It  is  found  by  continuing  the  expansion-curve  to  the  end  of  the 
diagram. 

INDICATED  HORSE-POWER  OF  ENGINES.   SINGLE- 
CYLINDER. 

Indicated  Horse-power  I.H.P.= 

in  which  P  =  mean  effective  pressure  in  Ibs.  per  sq.  in. ;  L  =  length  of  stroke 
in  feet;  a  =  area  of  piston  in  square  inches.  For  accuracy,  one  half  of  the 
sectional  area  of  the  piston-rod  must  be  subtracted  from  the  area  of  the 
piston  if  the  rod  passes  through  one  head,  or  the  whole  area  of  the  rod  if  it 
passes  through  both  heads;  n  =  No.  of  single  strokes  per  min.  =  2  X  No.  of 
revolutions. 

PaS 
I.H.P.  =  33  OOQ,  in  which  S  =  piston  speed  in  feet  per  minute. 

I.H.P.  =  ~?~  =  ^j^7  =  .0000238PZ,d2n  =  .0000238Pd*S, 

In  which  d  =  diam.  of  cyl.  in  inches.  (The  figures  238  are  exa^t,  since 
7854  -H  33  =  23.8  exactly.)  If  product  of  piston-speed  X  mean  effective 
pressure  =  42,017,  then  the  horse-power  would  equal  the  square  of  the 
diameter  in  inches. 

Handy  Rule  for  Estimating  tlie  Horse-power  of*  a 
Single-cylinder  Engine.— Square  the  diameter  and  divide  by  2.  This  is 
correct  whenever  the  product  of  the  mean  effective  pressure  and  the  piston- 
speed  =  l£  of  42,017,  or,  say,  21,000,  viz.,  when  M.E.P.  =  30  and  8=  700; 
when  M.E.P.  =35  and  6'=  600;  when  M.E.P.  =  38.2  and  8  =  550;  and  when 
M.E.P.  =  42  and  S  =  500.  These  conditions  correspond  to  those  of  ordinary 
practice  with  both  Corliss  engines  and  shaft-erovernor  high-speed  engines. 

Given  Horse-power,  Mean  Effective  Pressure,  and 
Piston-speed,  to  find  Size  of  Cylinder.— 


Brake  Horse-power  is  the  actual  horse-power  of  the  engine  as 
measured  at  the  fly-wheel  by  a  friction-brake  or  dynamometer.  It  is  the 
indicated  horse-Dower  minus  the  friction  of  the  engine. 

Table  for  Roughly  Approximating  tlie  Horse-power  of 
a.  Compound  Engine  from  tlie  Diameter  of  its  Low- 
pressure  Cylinder. —The  indicated  horse-power  of  an  engine  being 
Psd'2 

'       ,  in  which  P  =  mean  effective  pressure  per  sq.  in.,  s  =  piston-speed  in 

ft.  per  min.,  and  d  =  diam.  of  cylinder  in  inches;  if  s  =  600  ft.  per  min.t 
which  is  approximately  the  speed  of  modern  stationary  engines,  and  P  =  35 
Ibs.,  which  is  an  approximately  average  figure  for  the  M.E.P.  of  single- 
cylinder  engines,  and  of  compound  engines  referred  to  the  low-pressure 
cylinder,  then  I.H.P.  =  J^cZ2;  hence  the  rough-and-ready  rule  for  horse-power 
given  above:  Square  the  diameter  in  inches  and  divide  by  2.  This  applies  to 
triple  and  quadruple  expansion  engines  as  well  as  to  single  cylinder  and 
compound.  For  most  economical  loading,  the  M.E  P.  referred  to  the  low- 
pressure  cylinder  of  compound  engines  is  usually  not  greater  than  that  of 
simple  engines;  for  the  greater  economy  is  obtained  by  a  greater  number  of 
expansions  of  steam  of  higher  pressures,  and  the  greater  the  number  of 
expansions  for  a  given  initial  pressure  the  lower  the  mean  effective  pressure. 
The  following  table  gives  approximately  the  figures  of  mean  total  and  effec- 


tive  pressures  for  the  different  types  of  engines,  together  with  the  factor  by 
which  the  square  of  the  diameter  'is  to  be  multiplied  to  obtain  the  horse- 
power at  most  economical  loading,  for  a  piston-speed  of  000  ft.  per  minute. 


Type  of  Engine. 

Initial  Abso- 
lute Steam- 
pressure. 

Number  of 
Expan- 
sions. 

Terminal 
Absolute 
Press.,  Ibs. 

Ratio  Mean 
Total  to 
Initial 
Pressure. 

Mean  Total 
Pressure, 
Ibs. 

Total  Back 
Pressure, 
Mean,  Ibs. 

Mean  Effec- 
tive Pres- 
sure, Ibs. 

£  H 

ifs 

O  a;  f-c 

S&fc. 

PH 

II  X 

ill 

K&' 

Non-condensing. 


Single  Cylinder. 
Compound. 

100 
120 

5. 

20 

16 

.522 

.402 

52.2 

48.2 

15.5 
15  5 

36.7 

32  7 

600 

.524 
467 

Triple  
Quadruple  

160 
•200 

10. 
12.5 

16 
16 

.330 

.282 

52.8 
56.4 

15.5 
15.5 

37.3 
40.9 

« 

.538 

.584 

Condensing  Engines. 


Single  Cylinder. 
Compound  
Triple      

100 
120 
160 

10. 
15. 
20. 

10 
8 
8 

.330 
.247 
.200 

33.0 
29.6 
32.0 

2 

2 
2 

31.0 
27.6 
30.0 

600 

.443 
.390 
.429 

Quadruple  

200 

25. 

8 

.169 

33.8 

2 

31.8 

14 

.454 

For  any  other  piston-speed  than  600  ft.  per  min.,  multiply  the  figures  in 
the  last  column  by  the  ratio  of  the  piston-speed  to  600  ft. 

Nominal  Horse-power.— The  term  "nominal  horse-power"  origi- 
nated in  the  time  of  Walt,  and  was  used  to  express  approximately  the  power 
of  an  engine  as  calculated  from  its  diameter,  estimating  the  mean  pressure 
in  the  cylinder  at  7  Ibs.  above  the  atmosphere.  It  has  long  been  obsolete  in 
America,  and  is  nearly  obsolete  in  England. 

Horse-power  Constant  of  a  given  Engine  for  a  Fixed 
Speed  =  product  of  its  area  of  piston  in  square  inches,  length  of  stroke  in 

feet,  and  number  of  single  strokes  per  minute  divided  by  33,000,  or  •—-— 

oo,000 

—  C.  The  product  of  the  mean  effective  pressure  as  found  by  the  diagram 
and  this  constant  is  the  indicated  horse-power. 

Horse-power  Constant  of  a  given  Engine  for  Varying 
Speeds  —  product  of  its  area  of  piston  and  length  of  stroke  divided  by 
33.000.  This  multiplied  by  the  mean  effective  pressure  and  by  the  number 
of  sinsrle  strokes  per  minute  is  the  indicated  horse-power. 

Horse-power  Constant  of  any  Engine  of  a  given  Diam- 
eter of  Cylinder,  whatever  the  length  of  stroke  =  area  of  piston -t- 33,000 
=  square  of  the  diameter  of  piston  in  inches  X  .0000238.  A  table  of  constants 
derived  from  this  formula  is  given  below. 

The  constant  multiplied  by  the  piston-speed  in  feet  per  minute  and  by 
the  M.E.P.  gives  the  I.H.P. 

Errors  of  Indicators.— The  most  common  error  is  that  of  the  spring, 
which  may  vary  from  its  normal  rating;  the  error  may  be  determined  by 
proper  testing  apparatus  and  allowed  for.  But  after  making  this  correction, 
even  with  the  best  work,  the  results  are  liable  to  variable  errors  which  may 
amount  to  2  or  3  per  cent.  See  Barrus,  Trans.  A.  S.  M.  E.,  v.  310;  Denton, 
A.  S.  M.  E.,  xi.  329;  David  Smith,  U.  S.  N.,  Proc.  Eng'g  Congress,  1893, 
Marine  Division. 

Indicator  "  Rigs,"  or  Reducing-motions  ;  Interpretation  of  Diagrams  for 
Errors  of  Steam-distribution,  etc.  For  these  see  circulars  of  manufacturers 
of  Indicators;  also  works  on  the  Indicator. 

Table  of  Engine  Constants  for  Use  in  Figuring  Horse- 
power.— "  Horse-power  constant  "  for  cylinders  from  i  inch  to  60  inches  in 
diameter,  advancing  by  8ths,  for  one  foot  of  piston-speed  per  minute  and  one 
pound  of  M.E.P.  Find  the  diameter  of  the  cylinder  in  the  column  at  the 
side.  If  the  diameter  contains  no  fraction  the  constant  will  be  found  in  the 
column  headed  Even  Inches.  If  the  diameter  is  not  in  even  inches,  follow 
the  line  horizontally  to  the  column  corresponding  to  the  required  fraction. 


INDICATED   HORSE-POWER  OF   ENGINES. 


757 


The  constants  multiplied  by  the  piston-speed  and  by  the  M.E.P.  give  the 
horse-power. 


Diameter 
of 
Cylinder. 

Even 
Inches. 

+  Ya 
or 
.125. 

+  H 
or 
.25. 

+  % 
or 
.375. 

+x 

or 
.5. 

+  % 
or 
.625. 

+  K 
or 
.75. 

i-% 
or 
.875. 

1 

.0000238  .0000301 

.0000372 

.0000450 

.0000535 

.0000628 

.0000729 

.0000837 

2 

.0000952  .0001074 

.0001205 

.0001342J  .0001  487 

.0001640 

.0001800 

0001967 

3 

.0002142  .0002324 

.0002514 

.0002711  .0002915 

.0003127 

.0003347 

.0003574 

4 

.00038081.0004050 

.0004299 

.0004554  .0004819 

.0005091 

.0005370 

.0005656 

5 

.0005950|.0006251 

.0006560;  .0006876  .0007199 

.0007530 

.0007869 

.0008215 

6 

.0008568  .0008929 

.00092971.0009672  .0010055 

.0010445 

.0010844 

.0011249 

7 

.0011662  .0012082 

.0012510  .0012944  .0013387 

.0013837 

.0014295 

.0014759 

8 

.00152321.0015711 

.0016198  .0016693'.  0017195 

.0017705 

.0018222 

.0018746 

9 

.0019278 

.0019817 

.0020363  .0020916'  .0021479 

.0022048 

.0022625 

.0023-209 

10 

.0023800 

.0024398 

.00250041  .0025618'  .0026239 

.0026867 

.0027502 

.0028147 

11 

.00287981.0029456 

.0030121 

.0030794J  .0031475 

.003-2163 

.0032859 

.0033561 

12 

.0034272 

.0034990 

.0035714 

.0036447  .0037187 

.0037934 

.0038690 

.0039452 

13 

.0040222 

.0040999 

.0041783 

.0042576 

.0043375 

.0044182 

.0044997 

.0045819 

14 

.0046648 

.0047484 

.0048328 

.0049181 

.0050039 

.0050906 

.0051780 

.0052661 

15 

.0053550 

.0054446 

.0055349 

.0056261  L0057179 

.0058105 

.0059039 

.0059979 

16 

.0060928 

.0061884 

.0062847 

.0063817 

.0064795 

.0065780 

.0066774 

0067774 

17 

.0068782 

.0069797 

.0070819 

.0071850 

.0072887 

.0073932 

.0074985 

.0076044 

18 

.0077112 

.0078187 

.0079268 

.0080360 

.0081452 

.0082560 

.0083672 

.0084791 

19 

.0085918 

.0087052 

.0088193 

.0089343 

.0090499 

.0091663 

.0092835 

.0094013 

20 

.0095200 

.0096393 

.0097594 

.0098803 

.0100019 

.0101243 

.0102474 

.0103712 

21 

.0104958 

.0106211 

.0107472 

.0108739 

.0110015 

.0111299 

.0112589 

.0113886 

22 

.0115192 

.0116505 

.0117825 

.0119152 

.0120487 

.0121830 

.0123179 

.0124537 

23 

.0125902 

.0127274 

.0128654 

.0130040 

.0131435 

.0132837 

.0134247 

.0135664 

24 

.0137088 

.0138519 

.0139959 

.0141405 

.0142859 

.0144321 

.0145789 

.0147266 

25 

.0148750 

.0150241 

.0151739  .01532461.0154759 

.0156280 

.0157809 

.0159345 

26 

.0160888 

.0162439 

.01639971.0165563 

.0167135 

.0168716 

.0170304 

.0171899 

27 

.0173502 

.0175112 

.0176729  .0178355 

.0179988 

.0181627 

.0183275 

.0184929 

28 

.0186592 

.0188262 

.0189939 

.0191624 

.0193316 

.0195015 

.0196722 

.0198436 

29 

.0200158 

.0201887 

.0203C24 

.0205368 

.0207119 

.0-208879 

.0210645 

.0212418 

30 

.0214200 

.0215988 

.0217785 

.0219588 

.0221399 

.0223218 

.0225044 

.02-26877 

31 

.0228718 

.0230566 

.0232422 

.0234285 

.0236155 

.0238033 

.0239919 

.0241812 

32 

.0243712 

.0245619 

.0247535 

.0249457 

.0251387 

.0253325 

.0255269 

.0257222 

33 

.0259182 

.0261149 

.0263124 

.0265106 

.0267095 

.0269092 

.0271097 

.0273109 

34 

.0275128 

.0277155 

.0279189 

.02812311  .0283279 

.0285336 

.0287399 

.0289471 

35 

.0291550 

.0293636 

.0295729 

.0297831 

.0299939 

.0302056 

.0304179 

.0306309 

36 

.0308448 

.0310594 

.0312747 

.0314908 

.0317075 

.0319251 

.03-21434 

.0323624 

37 

.0325822 

.0328027 

.0330239 

.0332460 

.0334687 

.0330922 

.0339165 

.0341415 

38 

.0343672 

.0345937 

.0348209 

.0350489 

.0352775 

.0355070 

.0357372 

.0359681 

39 

.0361998 

.0364322 

.0366654 

.0368993 

.0371339 

.0373694 

.0376055 

.0378424 

40 

.0380800 

.0383184 

.0385575 

.0387973 

.0390379 

.0392793 

.0395214 

.0397642 

41 

.0400078 

.0402521 

.0404972 

.0407430 

.0409895 

.0412368 

.0414849 

.0417337 

42 

.0419832 

.042-2335 

.0424845 

.0427362 

.0429887 

.0432420 

.0434959 

.0437507 

43 

.0440062 

.0442624 

.0445194 

.0447771 

.0450355 

.0452947 

.0455547 

.0458154 

44 

.0460768 

.0463389 

.0466019 

.0468655 

.0471299 

.0473951 

.0476609 

.0479276 

45 

.0481950 

.0484631 

.0487320 

.0490016 

.0492719 

.0495430 

.0498149 

.0500875 

46 

.0503608 

.0506349 

.0509097 

.0511853 

.0514615 

.0517386 

.0520164 

.0522949 

47 

.0525742 

.0528542 

.0531349 

.0534165 

.0536988 

.0539818 

.0542655 

.0545499 

48 

.0548352 

.0551212 

.0554079 

.0556953 

.0559835 

.0562725 

.056562-2 

.0568526 

49 

.0571438 

.0574357 

.0577284  .0580218 

.0583159 

.0586109 

.0589065 

.0592029 

50 

.0595000  .0597979 

.0600965'  .0603959 

.0606959 

.0609969 

.0612984 

.0616007 

51 

.0619038  .0622076 

.0625122!  .0628175 

.0632-235 

.0634304 

.0637379 

.0640462 

52 

.0643552  .0646649 

.0619753  .0652867 

.0655987 

.0659115 

.0662250 

.0665392 

53 

.0668542  .0671699 

.0674864  .0678036 

.0681215 

.0684402 

.0687597 

.0690799 

54 

.0694008  .0697225 

.0700449  .0703681 

.0705293 

.0710166 

.0713419 

,0716681 

55 

.0719950 

.07242-26 

.0726510  .0729801  .0733099 

.0736406 

.0739719 

.0743039 

56 

.0746368 

.0749704 

.  0753047  .  0756398  j  .  0759755 

.0763120 

.0766494  .0769874 

57 

.0773262 

.0776657 

.0780060  .0783476  .0786887 

.0790312 

.0793745 

.0797185 

58 

.0800632  ;.0804087 

.0807549  .0811019  .0814495 

.0817980 

.0821472 

.0824971 

59 

.0828478  .0831992 

.0835514  .0839043  0842579 

.0846123 

.0849675  .0853234 

60 

.0856800  .0860374 

.0863955  .0867543  .0871139 

.0874743 

.08783541.0881973 

758 


THE   STEAM-ENGINE. 


Horse-power  per  Pound  Mean  Effective  Pressure. 

Formula,  Area  in  sq.  in.  X  piston-speed  ^ 


Diam.  of 
Cylinder, 
inches. 

Speed  of  Piston  in  feet  per  minute. 

100 

200 

300 

400      500 

600 

700 

800 

900 

4 

.0381 

.0762 

.1142 

.1523 

.1904 

.2285 

.2666 

.3046 

.3427 

41^3 

.0482 

.0964 

.1446 

.1928 

.2410 

.2892 

.3374 

.3856 

.4338 

5 

.0595 

.1190 

.1785 

.2380 

.2975 

.3570 

.4165 

.4760 

.5355 

5/^ 

.0720 

.1440 

.2160 

.2880 

.3600 

.4320 

.5040 

.5760 

.6480 

6 

.0857 

.1714 

.2570 

.3427 

.4284 

.5141 

.5998 

.6854 

.7711 

Qi£ 

.1006 

.2011 

.3017 

.4022 

.50:28 

.6033 

.7039 

.8044 

.9050 

7 

.1166 

.2332 

.3499 

.4665 

.5831 

.6997 

.8163 

.9330 

1.0496 

33* 

.1339 

.2678 

.4016 

.5355 

.6694 

.8033 

.1)37 

1.0710 

1  2049 

8 

.1523 

.3046 

.4570 

.6093 

.7616 

.9139 

1.066-2 

1.2186 

1  .  3709 

8i^j 

!l720 

.3439 

.5159 

.6878      .8598 

1.0317 

1.2037 

1.3756 

1  .  5476 

9 

.1928 

.3856 

.5783 

.7711      .9639 

1  .  1567 

1.3495 

1.5422 

1.7350 

9Vi3 

.2148 

.4296 

.6444 

.8592 

1.0740 

1.2888 

1  5036 

1.7184 

1.953-2 

10 

.2380 

.4760J     .7140 

.9520    1.1900 

1.4280 

.1.C6GO 

1  .  9040 

2.14:20 

11 

.2880 

.5760 

.8639 

1.1519    1.4399 

1.7279 

2.0159 

2.3038 

2.5818 

12 

.3427 

.68541     .0282 

1.3709    1.7136 

2.05631  2.8990 

2.7418 

3.0845 

13 

.4022 

.8044 

.2067 

1.6089 

2.0111 

2.4133!  2.8155 

3.2178 

3.6200 

14 

.4665 

.9330 

.3994 

1.8659    2.3324 

2.79891  3.2654 

3.7318 

4.19b3 

15 

.5355 

1.0710 

.6065 

2.1420    2.6775 

3.2130    3.7485 

4  2840 

4.8195 

16 

.6093 

.2186 

.8278 

2.4371J  3.0464 

3.6557 

4.2650 

4.874'2 

5.4835 

17 

.6878 

.2756 

.9635 

2.6513;  3.3391 

4.0269 

4.6147 

5.4026 

6.1904 

18 

.7711 

5422 

2.3134 

3.0845,  3.8556 

4.6267 

5.3978 

6.1690 

6.9401 

19 

.8592 

'.7184 

2.5775 

3.4367    4.2959 

5.1551 

6.0143 

6.8734 

7.7326 

20 

.9520 

.9040 

2.8560 

3.8080)  4.7600 

5.7120 

6.6640 

7.6160 

8.5080 

21 

1.0496 

2.'0992 

3.1488 

4.1983    5.2479 

6.2975 

7.3471 

8.3966 

9.4462 

22 

1.1519 

2.3038 

3.4558 

4.6077;  5.7596 

6.9115 

8.0634   9.2154 

10.867 

23 

1.2590 

2.5180 

3.7771 

5.0361    6.2951 

7.5541 

8.8181110  072 

11.331 

24 

1.3709 

2.7418 

4.1126 

5.4635!  6.8544 

8.2253 

9.5963 

10.967 

12.338 

25 

1.4875 

2.9750 

4.4625 

5.9500;  7.4375 

8  9250 

10.413 

11.900 

13.388 

26 

1.6089 

3.2178 

4.8266 

6.4355;  8.0444 

9.  or  34 

11.26-2 

12.871 

14.480 

27 

1.7350 

3.4700 

5.2051 

6.9-101!  8.0751 

10.410 

12.145 

13.880 

15.615 

28 

1.8659 

3.7318 

5.5978 

7.4637    9.329611.196 

13.061 

14.927 

16.793 

29 

2.0016 

4.0032 

6.0047 

8.006310.008 

12.009 

14.011 

16.013 

18.014 

30 

2.1420 

4.2840 

6.4260 

8.568010.710 

12.852 

14.994 

17.136 

19.278 

31 

2.2872 

4.5744 

6.8615 

9.1487  11.436 

13,723 

16.010 

18.297 

20.585 

32 

2.4371 

4.8742 

7.3114 

9.7485|12.186 

14.623 

17.060 

14.497 

21.934 

33 

2.5918 

5.1836 

7.7755 

10.367    12.959 

15.551 

18.143 

20.735 

,23.326 

34 

2.7513 

5.5026 

8.2538 

11.005    13.756 

16.508 

19.259 

22.010 

24.762 

35 

2.9155 

5.8310 

8.7465 

11.662 

14.578 

17.493 

20.409 

23.324 

26.240 

36 

3.0845 

6.1690 

9.2534 

12.338    15.4-22 

18.507 

21.591 

24  .  670 

27.760 

37 

3.2582 

6.5164 

9.7747 

13.033    16.291 

19.549 

22.808 

26.066 

29.324 

38 

3.4367 

6.8734 

10.310 

13.747    17.184 

20.620 

24.057 

27.494 

30.930 

39 

3.6200 

7.2400 

10.860 

14  480 

18.100 

21.720 

25.340 

28.960 

32.580 

40 

3.8080 

7.6160 

11.424 

15.232    19.040 

22.848 

26.656 

30.464 

34.272 

41 

4.0008 

8.0016 

12.002 

16.003    20.004 

24.005 

28.005 

32.006 

36.007 

42 

4.1983 

8.3866,12.585 

16.783    20.982 

25.180 

29.378 

33.577 

37.775 

43 

4.4006 

8.801213.202 

17.602    2-2.003 

26.404 

30.804 

35.205 

39.606 

44 

4.6077 

9.2154 

13.823 

18  431    23.038 

27.646    32.254 

36  861 

41.469 

45 

4.8195 

9.639014.459 

19.278    24.098 

28.917    33.737 

38.556 

43.376 

46 

5.0301 

10.072 

15.108 

20.144    25.180 

30.216 

35.253 

40.289 

45.325 

47 

5.2574 

10.515 

15.772 

21.030 

26.287 

31.545 

36.802 

42.059 

47.317 

48 

5.4835 

10.967 

16.451 

21.934 

27.418 

32.901 

38.385 

43.868 

49.352 

49 

5.7144 

11.429 

17.143 

22.858 

28.572 

34.286 

40.001 

45.715 

51.429 

50 

5.9500 

11.900  117.850 

23.800 

29.750 

35.700 

41.050 

47.600 

53.550 

51 

6.1904 

12.381 

18.571 

24.762 

30.952 

37.142 

43.333 

49.523 

55.713 

52 
53 

6.4355  12.871 
6.6854  13.371 

19.307 
20.056 

25.742 

26.742 

32.178 
3-3.427 

38.613 
40.113 

45.049 
46.798 

51.484    57.920 
53.483    60  169 

54 

6.9401  13.880 

20.8-20 

27.760 

34.700 

41.640    48.581 

55.521 

62.461 

55 

7.1905 

14.399 

21.599 

28.798 

35.998 

43.197 

50.397 

57.596 

64.796 

56 

7.4637 

14.927 

22.391 

29.855 

37.318 

44.782    52.246 

59.709 

67.173 

57 

7.73-26 

15.465 

23.198 

30.930 

38.663    16.396  [54.128 

61.861 

69.594 

58 

8.0063 

16.013 

24.019 

32.025 

40.032    48  038  |56.044 

64.051 

72.057 

59 

8.2849 

16.570 

24.854 

33.139 

41.424 

49.709  157.993 

66.278 

74.563 

60          8.5680 

17.136 

25.704 

34.272 

42.840    51.408  |  59.  976 

68.544    77.112 

INDICATED   HOKSE-POWEK  OF   ENGINES. 


759 


To  draw  the  Clearance-line  on  the  Indicator-diagram, 

the  actual  clearance  not  being  known.— The  clearance-line  may  be  obtained 
approximately  by  drawing  a  straight  line,  cbad,  across  the  compression 
curve,  first  having  drawn  OX  parallel  to  the  atmospheric  line  and  14.7  Ibs. 
below.  Measure  from  a  the  distance  ad,  equal  to  cb,  and  draw  YO  perpen- 
dicular to  OX  through  d;  then  will  TB  divided  by  AT  be  the  percentage  of 


FIG.  139. 


<<xearance.  The  clearance  may  also  be  found  from  the  expansion-line  by 
(instructing  a  rectangle  ejhg,  and  drawing  a  diagonal  gf  to  intersect  the 
line  XO.  This  will  give  the  point  O,  and  by  erecting  a  perpendicular  to  XO 
<4fe  obtain  a  clearance-line  OF. 

Both  these  methods  for  finding  the  clearance  require  that  the  expansion 
und  compression  curves  be  hyperbolas.  Prof.  Carpenter  (Power,  Sept. 
1893)  says  that  with  good  diagrams  the  methods  are  usually  very  accurate, 
a,nd  give  results  which  check  substantially. 

The  Buckeye  Engine  Co.,  however,  say  that,  as  the  results  obtained  are 
/seldom  correct,  being  sometimes  too  little,  but  more  frequently  too  much, 
and  as  the  indications  from  the  two  curves  seldom  agree,  the  operation  has 
little  practical  value,  though  when  a  clearly  defined  and  apparently  undis- 
torted  compression  curve  exists  of  sufficient  extent  to  admit  of  the  applica- 
tion of  the  process,  it  may  be  relied  on  to  give  much  more  correct  results 
than  the  expansion  curve. 

To  draw  the  Hyperbolic  Curve  on  the  Indicator-dia- 
gram.—Select  any  point  I  in  the  actual  curve,  and  from  this  point  draw  a 
line  perpendicular  to  the  line  JB,  meet-  i  q  o  1  M  R 

ing  the  latter  in  the  point  J.    The  line — 

JB  may  be  the  line  of  boiler-pressure, 
but  this  is  not  material ;  it  may  be  drawn 
at  any  convenient  height  near  the  top  of 
diagram  and  parallel  to  the  atmospheric 
line.  From  Jdraw  a  diagonal  to  K.  the 
latter  point  being  the  intersection  of  ( 
the  vacuum  and  clearance  lines;  from  /  - 
draw  1L  parallel  with  the  atmospheric 
line.  From  J/,  the  point  of  intersection 
of  the  diagonal  JK  and  the  horizontal 
line  IL,  draw  the  vertical  line  LM.  The 


FTG.  140. 


point  M  is  the  theoretical  point  of  cut-off,  and  LM  the  cut-off  line.  Fix 
upon  any  number  of  points  1,  2,  3,  etc.,  on  the  line  JB,  and  from  these  points 
draw  diagonals  to  K.  From  the  intersection  of  these  diagonals  with  LM 
draw  horizontal  lines,  and  from  1,  2,  3,  etc.,  vertical  lines.  Where  these  lines 
meet  will  be  points  in  the  hyperbolic  curve. 

Pendulum  Indicator  Rig,'.  —  Power  (Feb.  1893)  gives  a  graphical 
representation  of  the  errors  in  indicator-diagrams,  caused,  by  the  use  of  in- 


760  THE   STEAM-EKGINE. 

correct  form  of  the  pendulum  rigging.  Tt  is  shown  that  the  "  brumbo  " 
pulley  on  the  pendulum,  to  which  the  cord  is  attached,  does  not  gener- 
ally give  as  good  a  reduction  as  a  simple  pin 
attachment.  When  the  end  of  the  pendulum  is 
slotted,  working  in  a  pin  on  the  crosshead,  the 
error  is  apt  to  be  considerable  at  both  ends  of 
the  card.  With  a  vertical  slot  in  a  plate  fixed 
to  the  crosshead,  and  a  pin  on  the  pendulum 
working  in  this  slot,  the  reduction  is  perfect, 
when  the  cord  is  attached  to  a  pin  on  the  pen- 
dulum, a  slight  error  being  introduced  if  the 
brumbo  pulley  is  used.  With  the  connection 
between  the  pendulum  and  the  crosshead  made 
by  means  of  a  horizontal  link,  the  reduction  is 
=7~g>-^L-  nearly  perfect,  if  the  construction  is  such  that 
the  connecting  link  vibrates  equally  above  and 
FIG.  141.  below  the  horizontal,  and  the  cord  is  attached 

by  a  pin.    If  the  link  is  horizontal  at  mid-stroke 

a  seriouj!  error  is  introduced,  which  is  magnified  if  a  brumbo  pulley  also  is 
used.    The  adjoining  figures  show  the  two  forms  recommended. 

Theoretical  Water-consumption  calculated  from  the 
Indicator-card. — The  following  method  is  given  by  Prof.  Carpenter 
(Power,  Sept.  18U3) :  p  =  mean  effective  pressure,  I  =  length  of  stroke  in 
feet,  a  =  area  of  piston  in  square  inches,  a  -*- 144  =  area  in  square  feet,  c  = 
percentage  of  clearance  to  the  stroke,  b  =  percentage  of  stroke  at  point 
where  water  rate  is  to  be  computed,  n  =  number  of  strokes  per  minute, 
60n  =  number  per  hour,  w  —  weight  of  a  cubic  foot  of  steam  having  a  pres- 
sure as  shown  by  the  diagram  corresponding  to  that  at  the  point  where 
water  rate  is  required,  w'  =  that  corresponding  to  pressure  at  end  of  com- 
pression. 

Number  of  cubic  feet  per  stroke  =  z(   100   /14T* 

Corresponding  weight  of  steam  per  stroke  in  Ibs.  =  l(^    "L    /~\IZW* 

lea 
Volume  of  clearance  =  14  400- 

Weight  of  steam  in  clearance  =  . 

Total  weight  of  |   _    (b+c\wa        Icaw'  _      la    r  _        -i 

steam  per  stroke  f  ~  *V1(JO/144       14,400  ~  14,400U  J* 

Total    weight   of  steam  \    _  GOnla  r       ,     ,  /I 

from    diagram    per   hour  f  ~  14^00  L(  J* 

The  indicated  horse-power  is  p  I  a  n  -s-  33,000.  Hence  the  steam-consump. 
tion  per  indicated  horse-power  is 

plan =  ^0  +  C)W  -  CW']' 

33,000 

Changing  the  formula  to  a  rule,  we  have:  To  find  the  water  rate  from  the 
indicator  diagram  at  any  point  in  the  stroke. 

RULE.— To  the  percentage  of  the  entire  stroke  which  has  been  completed 
by  the  piston  at  the  point  under  consideration  add  the  percentage  of  clear- 
ance. Multiply  this  result  by  the  weight  of  a  cubic  foot,  of  steam,  having  a 
pressure  of  that  at  the  required  point.  Subtract  from  this  the  product  of 
percentage  of  clearance  multiplied  by  weight  of  a  cubic  foot  of  steam  hav- 
ing a  pressure  equal  to  that  at  the  end  of  the  compression.  Multiply  this 
result  by  187.50  divided  by  the  mean  effective  pressure.* 

NOTE.— This  method  only  applies  to  points  in  the  expansion  curve  or  be- 
tween cut-off  and  release. 

*  For  compound  or  triple-expansion  engines  read:  divided  by  the  equiva- 
lent mean  effective  pressure,  on  the  supposition  that  all  work  is  done  in  one 
cylinder, 


COMPOUND   EKGIKES. 


761 


The  beneficial  effect  of  compression  in  reducing  the  water- con  sumption  of 
an  engine  is  clearly  shown  by  the  formula.  If  the  compression  is  carried  to 
such  a  point/  that  it  produces  a  pressure  equal  to  that  at  the  point  under 
consideration,  the  weight  of  steam  per  cubic  foot  is  equal,  and  w  —  w'.  In 
this  case  the  effect  of  clearance  entirely  disappears,  and  the  formula 

137  5 
becomes —(bw). 

In  case  of  no  compression,  wf  becomes  zero,  and  the  water-rate  = 

137  5_,_ 

[(6  -\-  c)w}. 

P 

Prof.  Denton  (Trans.  A.  S.  M.  E.,  xiv.  1363)  gives  the  following  table  of 
theoretical  water-consumption  for  a  perfect  Mariotte  expansion  with  steam 
at  150  Ibs.  above  atmosphere,  and  2  Ibs.  absolute  back  pressure  : 


Ratio  of  Expansion,  r. 

M.E.P.,  Ibs.  per  sq.  in. 

Lbs.  of  Water  per  hour 
per  horse-power,  W. 

10 
15 
20 
25 
30 
35 

52.4 

38.7 
30.9 
25.9 
22.2 
19.5 

9.68 
8.74 
8.20 
7.84 
7.63 
7.45 

The  difference  between  the  theoretical  water -consumption  found  by  the 
formula  and  the  actual  consumption  as  found  by  test  represents  "  water  not 
accounted  for  by  the  indicator,1'  due  to  cylinder  condensation,  leakage 
through  ports,  radiation,  etc. 

Leakage  of  Steam.— Leakage  of  steam,  except  in  rare  instances,  has 
so  little  effect  upon  the  lines  of  the  diagram  that  it  can  scarcely  be  detected. 
The  only  satisfactory  way  to  determine  the  tightness  of  an  engine  is  to  take 
it  when  not  in  motion,  apply  a  full  boiler-pressure  to  the  valve,  placed  in  a 
closed  position,  and  to  the  piston  as  well,  which  is  blocked  for  the  purpose  at 
some  point  away  from  the  end  of  the  stroke,  and  see  by  the  eye  whether 
leakage  occurs.  The  indicator-cocks  provide  means  for  bringing  into  view- 
steam  which  leaks  through  the  steam-valves,  and  in  most  cases  that  which 
leaks  by  the  piston,  and  an  opening  made  in  the  exhaust-pipe  or  observa- 
tions at  the  atmospheric  escape-pipe,  are  generally  sufficient  to  determine 
the  fact  with  regard  to  the  exhaust-valves. 

The  steam  accounted  for  by  the  indicator  should  be  computed  for  both 
the  cut-off  and  the  release  points  of  the  diagram.  If  the  expansion-line  de- 
parts much  from  the  hyperbolic  curve  a  very  different  result  is  shown  at 
one  point  from  that  shown  at  the  other.  In  such  cases  the  extent  of  the 
loss  occasioned  by  cj^linder  condensation  and  leakage  is  indicated  in  a  much 
more  truthful  manner  at  the  cut-off  than  at  the  release.  (Tabor  Indicator 
Circular.) 

COMPOUND  ENGINES. 

Compound,  Triple-  and  Quadruple-expansion  Engines. 

— A  compound  engine  is  one  having  two  or  more  cylinders,  and  in  which 
the  steam  after  doing  work  in  the  first  or  high-pressure  cylinder  completes 
its  expansion  in  the  other  cylinder  or  cylinders. 

The  term  "compound"  is  commonly  restricted,  however,  to  engines  in 
which  the  expansion  takes  place  in  two  stages  only — high  and  low  pressure, 
the  terms  triple-expansion  and  quadruple-expansion  engines  being  used  when 
the  expansion  takes  place  respectively  in  three  and  four  stages.  The  number 
of  cylinders  may  be  greater  than  the  number  of  stages  of  expansion,  for 
constructive  reasons;  thus  in  the  compound  or  two-stage  expansion  engine 
the  low-pressure  stage  may  be  effected  in  two  cylinders  so  as  to  obtain  the 
advantages  of  nearly  equal  sizes  of  cylinders  and  of  three  cranks  at  angles  of 
120°.  In  triple  expansion  engines  there  are  frequently  two  low-pressure 
cylinders,  one  of  them  being  placed  tandem  with  the  high-pressure,  and  the 
other  with  the  intermediate  cylinder,  as  in  mill  engines  writh  two  cranks  at 
90°.  In  the  triple-expansion  engines  of  the  steamers  Campania  and  Lucania, 


762 


THE   STEAM-ENGINE. 


with  three  cranks  at  120°,  there  are  five  cylinders,  two  high,  one  intermedi- 
ate, and  two  low,  the  high-pressure  cylinders  being  tandem  with  the  low. 

Advantages  of  Compounding.— The  advantages  secured  by  divid- 
ing the  expansion  into  two  or  more  stages  are  twofold:  1.  Reduction  of  wastes 
of  steam  by  cylinder-condensation,  clearance,  and  leakage;  2.  Dividing  the 
pressures  on  the  cranks,  shafts,  etc.,  in  large  engines  so  as  to  avoid  excessive 
pressures  and  consequent  friction.  The  diminished  loss  by  cylinder-conden- 
sation is  effected  by  decreasing  the  range  of  temperature  'of  the  metal  sur- 
faces of  the  cylinders,  or  the  difference  of  temperature  of  the  steam  at 
admission  and  exhaust.  When  high-pressure  steam  is  admitted  into  a  single- 
cylinder  engine  a  large  portion  is  condensed  by  the  comparatively  ccld 
metal  surfaces;  at  the  end  of  the  stroke  and  during  the  exhaust  the  water 
is  re-evaporated,  but  the  steam  so  formed  escapes  into  the  atmosphere  or 
into  the  condenser,  doing  no  work:  while  if  it  is  taken  into  a  second 
cylinder,  as  in  a  compound  engine,  it  does  work.  The  steam  lost  in  the  first 
cylinder  by  leakage  and  clearance  also  does  work  in  the  second  cylinder. 
Also,  if  there  is  a  second  cylinder,  the  temperature  of  the  steam  exhausted 
from  the  first  cylinder  is  higher  than  if  there  is  only  one  cylinder,  and  the 
metal  surfaces  therefore  are  not  cooled  to  the  same  degree.  The  difference 
In  temperatures  and  in  pressures  corresponding  to  the  work  of  steam  of 
150  Ibs.  gauge-pressure  expanded  20  times,  in  one,  two,  and  three  cylinders, 
is  shown  in  the  following  table,  by  W.  H.  Weightman,  Am.  Mach.,  July  28, 


Single 
Cyl- 
inder. 

Compound 
Cylinders. 

Triple-expansion 
Cylinders. 

Diameter  of  cylinders,  in.  . 

60 

33 
1 
5 

165 

86.11 

53.11 
366° 

259°.  9 
106.1 
399 
290 

112.900 

61 
3.416 
4 

33 
19.68 

15.68 
259°.  9 

184°.  2 
175.7 
403 
290 

84,752 

28 
1 
2.714 

165 
121.44 

60.64 
366° 

293°.  5 
72.5 
269 
238 

64.162 

46 
2.70 
2.714 

60.8 
44.75 

22.35 
293°.  5 

234°.  1 
59.4 
268 
238 

63.817 

61 

4.741 
2.714 

22.4 
16.49 

12.49 
234°.  1 

184°.  2 
49.9 
264 
238 

53.773 

Expansions 

20 

165 
32.96 

28.96 
366° 

184°.  2 
181.8 
800 
322 

455,218 

Initial   steam  -  pressures- 
absolute  —  pounds  .  . 

Mean  pressures,  pounds.  . 
Mean  effective   pressures, 
pounds      .   .  . 

Steam   temperatures  into 
cylinders  

Steam  temperatures  out  of 
the  cylinders  

Difference  in  temperatures 
Horse-power  developed.  .  . 
Speed  of  piston. 

Total  initial  pressures  on 
pistons,  pounds  

46  Woolf  "  and  Receiver  Types  of  Compound  Engines.— 

The  compound  steam-engine,  consisting  of  two  cylinders,  is  reducible  to  two 
forms,  1,  in  which  the  steam  from  the  h.p.  cylinder  is  exhausted  direct  into 
the  1.  p.  cylinder,  as  in  the  Woolf  engine;  and  2,  in  which  the  steam  from  the 
h.  p.  cylinder  is  exhausted  into  an  intermediate  reservoir,  whence  the  steam 
is  supplied  to,  and  expanded  in,  the  1.  p.  cylinder,  as  in  the  "  receiver- 
engine.'1 

If  the  steam  be  cut  off  in  the  first  cylinder  before  the  end  of  the  stroke, 
the  total  ratio  of  expansion  is  the  product  of  the  ratio  of  expansion  in  the 
first  cylinder,  into  the  ratio  of  the  volume  of  the  second  to  that  of  the  first 
cylinder;  that  is,  the  product  of  the  two  ratios  of  expansion. 

Thus,  let  the  areas  of  the  first  and  second  cylinders  be  as  1  to  3^,  the 
strokes  being  equal,  and  let  the  steam  be  cut  off  in  the  first  at^  stroke;  then 

Expansion  in  the  1st  cylinder  ......  ......  1  to  2 

"    "    2d         "        ........................................ 


Total  or  combined  expansion,  the  product  of  the  two  ratios.  .  .  1  to  7 

Woolf   Engine,   without   Clearance—  Ideal    Diagrams.— 

The  diagrams  of  pressure  of  an  ideal  Woolf  engine  are  shown  in  .b'ig.  14ii,  as 
they  would  be  described  by  the  indicator,  according  to  the  arrows.  In  these 
diagrams  pq  is  the  atmospheric  line,  mn  the  vacuum  line,  cd  the  admissior 


COMPOUND  ENGINES. 


763 


line,  dg  the  hyperbolic  curve  of  expansion  in  the  first  cylinder,  and  gh  the  con- 
secutive expansion-line  of  back  pressure 
for  the  return-stroke  of  the  first  piston, 
and  of  positive  pressure  for  the  steam- 
stroke  of  the  second  piston.  At  the  point 
h.  at  the  end  of  the  stroke  of  the  second 
piston,  the  steam  is  exhausted  into  the 
condeuser.  and  the  pressure  falls  to  the 
level  of  perfect  vacuum,  mn. 

The  diagram  of  the  second  cylinder, 
below  gh,  is  characterized  by  the  absence 
of  any  specific  period  of  admission;  the 
whole  of  the  steam-line  gh  being  expan- 
sional,  generated  by  the  expansion  of 
the  initial  body  of  steam  contained  in 
the  first  cylinder  into  the  second.  When 
the  return-stroke  is  completed,  the 
whole  of  the  steam  transferred  from 

the  first    is  Shut    into  the   Second  Cylin-     «         1 

der.    The  final  pressure  and  volume  of   FlGL 

the  steam  in  the  second  cylinder  are  the 

same  as  if  the  whole  of  the  initial  steam  had  been  admitted  at  once  into  the 

second  cylinder,  and  then  expanded  to  the  end  of  the  stroke  in  the  manner 

of  a  single-cylinder  engine. 

The  net  work  of  the  steam  is  also  the  same,  according  to  both  distributions. 

Receiver-engine,  without  Clearance  -Ideal  Diagrams.— 
In  the  ideal  receiver-engine  the  pistons  of  the  two  cylinders  are  con- 
nected to  cranks  at  right  angles  to  each  other  on  the  same  shaft.  The 
receiver  takes  the  steam  exhausted  from  the  first  cylinder  and  supplies  it  to 
the  second,  in  which  the  steam  is  cut  off  and  then  expanded  to  the  end  of 
the  stroke.  On  the  assumption  that  the  initial  pressure  in  the  second  cylin- 
der is  equal  to  the  final  pressure  in  the  first,  and  of  course  equal  to  the  pres- 
sure in  the  receiver,  the  volume  cut  off  in  the  second  cylinder  must  be 
equal  to  the  volume  of  the  first  cylinder,  for  the  second  cylinder  must  admit 
as  much  steam  at  each  stroke  as  is  discharged  from  the  first  cylinder. 

In  Fig.  143  cd  is  the  line  of  admission  and  hg  the  exhaust-line  for  the  first 


FIG.  143.— RECEIVER-ENGINE,  IDEAL 
INDICATOR-DIAGRAMS. 


FIG.  144.— RECEIVER    ENGINE,    IDEAL 
DIAGRAMS  REDUCED  AND  COMBINED. 


cylinder;  and  dg  is  the  expansion-curve  and  pq  the  atmospheric  line.  In 
the  region  below  the  exhaust-line  of  the  first  cylinder,  between  it  and  the 
line  of  perfect  vacuum,  pi,  the  diagram  of  the  second  cylinder  is  formed;  hi, 
the  second  line  of  admission,  coincides  with  the  exhaust-line  hg  of  the  first 
cylinder,  showing  in  the  ideal  diagram  no  intermediate  fall  of  pressure,  and 
ik  is  the  expansion-curve.  The  arrows  indicate  the  order  in  which  the  dia- 
grams are  formed. 

In  the  action  of  the  receiver-engine,  the  expansive  working  of  the  steam, 
though  clearly  divided  into  two  consecutive  stages,  is,  as  in  the  Woolf 
engine,  essentially  continuous  from  the  point  of  cut-off  in  the  first  cylinder 
to  the  end  of  the  stroke  of  the  second  cylinder,  where  it  is  delivered  to  the 
condenser;  and  the  first  and  second  diagrams  may  be  placed  together  and 


764 


THE  STEAM-EXGIKE. 


combined  to  form  a  continuous  diagram.  For  this  purpose  take  the  second 
diagram  as  the  basis  of  the  combined  diagram,  namely,  Jiiklo,  Fig.  144.  The 
period  of  admission,  /u,  is  one  third  of  the  stroke,  and  as  the  ratios  of  the 
cylinders  are  as  1  to  3,  hi  is  also  the  proportional  length  of  the  first  diagram 
as  applied  to  the  second.  Produce  oh  upwards,  and  set  off  oc  equal  to  the 
total  height  of  the  first  diagram  above  the  vacuum-line;  and,  upon  the 
shortened  base  Jii,  and  the  height  /tc,  complete  the  first  diagram  with  the 
steam-line  cd,  and  the  expansion-line  di. 

It  is  shown  by  Clark  (S.  E.,  p.  432,  et  seq.)  in  a  series  of  arithmetical  cal- 
culations, that  the  receiver-engine  is  an  elastic  system  of  compound  engine, 
in  which  considerable  latitude  is  afforded  for  adapting  the  pressure  in  the 
receiver  to  the  demands  of  the  second  cylinder,  without  considerably  dimin- 
ishing the  effective  work  of  the  eugine.  In  the  Woolf  engine,  on  the 
contrary,  it  is  of  much  importance  that  the  intermediate  volume  of  space 
between  the  first  and  second  cylinders,  which  is  the  cause  of  an  interme- 
diate fall  of  pressure,  should  be  reduced  to  the  lowest  practicable  amount. 

Supposing  that  there  is  no  loss  of  steam  in  passing  through  the  engine, 
by  cooling  and  condensation,  it  is  obvious  that  whatever  steam  passes 
through  the  first,  cylinder  must  also  find  its  way  through  the  second  cylin- 
der. By  varying,  therefore,  in  the  receiver-engine,  the  period  of  admission 
in  the  second  cylinder,  and  thus  also  the  volume  of  steam  admitted  for  each 
stroke,  the  steam  will  be  measured  into  it  at  a  higher  pressure  and  of  a  less 
bulk,  or  at  a  lower  pressure  and  of  a  greater  bulk;  the  pressure  and  density 
naturally  adjusting  themselves  to  the  volume  that  the  steam  from  the  re- 
ceiver is  permitted  to  occupy  in  the  second  cylinder.  With  a  sufficiently 
restricted  admission,  the  pressure  in  the  receiver  may  be  maintained  at  the 
pressure  of  the  steam  as  exhausted  from  the  first  cylinder.  On  the  con- 
trary, with  a  wider  admission,  the  pressure  in  the  receiver  may  fall  or 
"drop"  to  three  fourths  or  even  one  half  of  the  pressure  of  the  exhaust- 
steam  from  the  first  cylinder. 

(For  a  more  complete  discussion  of  the  action  of  steam  in  the  Woolf  and 
receiver  engines,  see  Clark  on  the  Steam-engine.) 

Combined  Diagrams  of  Compound  Engines.— The  only  way 
of  making  a  correct  combined  diagram  from  the  indicator-diagrams  of  the 
several  cylinders  in  a  compound  engine  is  to  set  off  all  the  diagrams  on  the 
same  horizontal  scale  of  volumes,  adding  the  clearances  to  the  cylinder  ca- 


FIG.  145. 

pacities  proper.  When  this  is  attended  to,  the  successive  diagrams  fall  ex- 
actly into  their  right  places  relatively  to  one  another,  and  would  compare 
properly  with  any  theoretical  expansion-curve.  (Prof.  A.  B.  W.  Kennedy, 
Proc.  Inst.  M.  E.,  Oct.  1886.) 


COMPOUND   ENGINES. 


765 


This  method  of  combining  diagrams  is  commonly  adopted,  but  there  are 
objections  to  its  accuracy,  since  the  whole  quantity  of  steam  consumed  in 
the  first  cylinder  at  the  end  of  the  stroke  is  not  carried  forward  to  the 
second,  but  a  part  of  it  is  retained  in  the  first  cylinder  for  compression.  For 
a  method  of  combining  diagrams  in  which  compression  is  taken  account  of, 
see  discussions  by  Thomas  Mudd  and  others,  in  Proc.  Inst.  M.  E.,  Feb., 
1887,  p.  48.  The  usual  method  of  combining  diagrams  is  also  criticised  by 
Frank  H.  Ball  as  inaccurate  and  misleading  (Am.  Mach.,  April  12,  1894; 
Trans.  A.  S.  M.  E.,  xiv.  1405,  and  xv.  403). 

Figure  145  shows  a  combined  diagram  of  a  quadruple-expansion  engine, 
drawn  according  to  the  usual  method,  that  is,  the  diagrams  are  first  reduced 
in  length  to  relative  scales  that  correspond  wiih  the  relative  piston-displace- 
ment of  the  three  cylinders.  Then  the  diagrams  are  placed  at  such  distances 
from  the  clearance-line  of  the  proposed  combined  diagram  as  to  correctly 
represent  the  clearance  in  each  cylinder. 

Calculated  Expansions  and  Pressures    in  Two-cylinder 
Compound  Engines*  (James  Tribe,  Am.  Mach.,  Sept.  &  Oct.  1891.) 

TWO-CYLINDER  COMPOUND  NON-CONDENSING. 
Back  pressure  ^  Ib.  above  atmosphere. 


Initial    gauge- 

pressure 

100 

110 

120 

130 

140 

150 

160 

170 

175 

Initial     absolute 

pressure  

115 

125 

135 

145 

155 

165 

175 

185 

190 

Total  expansion  . 

7.39 

7.84 

8.41 

9 

9.61 

10.24 

10.89 

11.56 

11.9 

Exp  a  n  s  i  o  n  s  in 

each  cylinder.. 

2.7 

2.8 

2.9 

3 

3.10 

3.2 

3.3 

3.4 

3.45 

Hyp.  log.  plus  1. 

1.993 

2.029 

2.0G4 

2.028 

2.131 

2.163 

2.193 

2.223 

2.238 

Forward    j  High. 

84.8 

90.5 

96 

101.4 

106.5 

111.5 

116.3 

120.9 

123.2 

pressures  j  Low.. 

31.3 

33  3 

33.1 

33.7 

34.3 

34.8 

35.2 

8).  6 

35.7 

Back          j  High. 

42.5 

44.6 

46.5 

48.3 

50 

51.5 

53 

51.4 

55 

pressures  (  Low.. 

15.5 

15.5 

15.5 

15.5 

15.5 

15.5 

15.5 

15.5 

15.5 

Mean      j  xrio-h 
effective  ^  ™«£ 

42.3 
15.8 

45.9 
16.8 

49.5 
17.6 

53.1 

18.2 

56.5 
18.8 

60 
19.3 

63.3 
19.7 

66.5 
20.1 

68.2 
20.2 

pressures  i 

Ratio-c  y  1  i  n  d  e  r 

areas  

2.67 

2.73 

2.81 

2.91 

3 

3.11 

3.21 

3.31 

3.37 

TWO-CYLINDER  COMPOUND  CONDENSING. 
Back  pressure,  6.5  Ibs.  above  vacuum  . 


Initial  absolute  pressures  
Probable  per  cent  of  loss  
Total  expansions  

105 
2.6 

15.7 
3.96 

115 
2.9 
17 
4.13 

125 
3.3 

18.5 
4.3 

135 
3.6 
20 
4.47 

145 
3.8 
21.5 
4  64 

155 
4.0 
22.7 

4  77 

165 
4.3 
24.2 

4  92 

Hyp.  log.  plus;  1   

2.376 

2.418 

2.458 

2.497 

2  534 

2  562 

2  593 

Mean  forward  j  High 

62  9 

67  3 

71  4 

75  4 

79  3 

83  2 

87 

15  25 

15.55 

15  9 

16  2 

16  5 

16  75 

17  05 

Mean  back     1  High 

26  5 

27  8 

29 

30  2 

31  4 

3-->  4 

33  5 

pressures      "(  Low     

4.3 

4  3 

4  3 

4  3 

4  3 

4  3 

4  3 

f?tea.n       JHigh... 

36.4 

39  5 

42  4 

45  2 

47  9 

50  8 

53  5 

effective    <f^\\ 

10.95 

11.25 

11  6 

11  9 

12  2 

12  45 

12  75 

pressures    ( 
Terminal  j  High 

26  5 

27  8 

29  0 

30  2 

31  4 

32  4 

'33  5 

pressures  |  Low    .   .          .... 

6.4 

6.45 

6  45 

6  5 

6  55 

6  55 

6  6 

Initial  pressure  in  1.  p.  cyl  
Ratio  of  cylinder  areas  

25.3 
3.32 

26.6 
3.51 

27.8 
3.66 

29 
3.8 

30.2 
3  92 

31.4 
4.08 

32.4 
4.19 

The  probable  percentage  of  loss,  line  3,  is  thus  explained:  There  is  always 
a  loss  of  heat  due  to  condensation,  and  which  increases  with  the  pressure  of 
steam.  The  exact  percentage  cannot  be  predetermined,  as  it  depends 
largely  upon  the  quality  of  the  non-conducting  covering  used  on  the  cylin- 
der, receiver,  and  pipes,  etc.,  but  will  probably  be  about  as  shown. 

Proportions  of  Cylinders  in  Compound  Engines.— Authori- 
ties differ  as  to  the  proportions  by  volume  of  the  high -and  low  pressure 
cylinders  v  and  V.  Thus  Grashof  gives  V-r-  v  =  0.85  |/rj  Hrabak,  0.90  VrJ 


766  THE   STEAM-ENGLtfE. 

Werner,  Vr;  and  Rankine,|/j-2,  r  being  the  ratio  of  expansion.    Busley 
makes  the  ratio  dependent  on  the  boiler-pressure  thus: 

Lbs.  per  sq.  in 60  90  105  120 

FH-V =    3  4  4.5  5 

(See  Seaton's  Manual,  p.  95,  etc..  for  analytical  method;  Sennett,  p.  496, 
etc.;  Clark's  Steam-engine, p.  445, etc;  Clark,  Rules,  Tables,  Data, p.  849.  etc.) 

Mr.  J.  McFarlane  Gray  states  that  he  finds  the  mean  effective  pressure  in 
the  compound  engine  reduced  to  the  low-pressure  cylinder  to  be  approxi- 
mately the  square  root  of  6  times  the  boiler-pressure. 

Approximate  Horse-power  of  a  Modern  Compound 
Marine-engine.  (Seaton.)— The  following  rule  will  give  approximately 
the  horse-power  developed  by  a  compound  engine  made  in  accordance  with 

modern  marine  practice.    Estimated  H.P.  =  -^  X  i/P  *  Rx8. 

boUU 

D  =  diameter  of  l.p.  cylinder;  p  =  boiler-pressure  by  gauge; 
R  —  revs,  per  min.;  S  =  stroke  of  piston  in  feet. 

Ratio  of  Cylinder  Capacity  in  Compound  Marine  En- 
gines. (Seaton.) — The  low-pressure  cylinder  is  the  measure  of  the  power 
of  n  compound  engine,  for  so  long  as  the  initial  steam-pressure  and  rate  of 
expansion  are  the  same,  it  signifies  very  little,  so  far  as  total  power  only  is 
concerned,  whether  the  ratio  between  the  low  and  high -pressure  cylinders 
is  3  or  4;  but  as  the  power  developed  should  be  nearly  equally  divided  be- 
tween the  two  cylinders,  in  order  to  get  a  good  and  steady  working  engine, 
there  is  a  necessity  for  exercising  a  considerable  amount  of  discretion  in 
fixing  on  the  ratio. 

In  choosing  a  particular  ratio  the  objects  are  to  divide  the  power  evenly 
and  to  avoid  as  much  as  possible  "drop  "  and  high  initial  strain. 

If  increased  economy  is  to  be  obtained  by  increased  boiler  pressures,  the 
rate  of  expansion  should  vary  with  the  initial  pressure,  so  that  the  pressure 
at  which  the  steam  enters  the  condenser  should  remain  constant.  In  this 
case,  with  the  ratio  of  cylinders  constant,  the  cut-off  in  the  high-pressure 
cylinder  will  vary  inversely  as  the  initial  pressure. 

Let  R  be  the  ratio  of  the  cylinders;  r,  the  rate  of  expansion;  pt  the  initial 
pressure:  then  cut-off  in  high-pressure  cylinder  =  R  -+-  r;  r  varies  with  p^ 
so  that  the  terminal  pressure pn  is  constant  and  consequently  r  =  pi  -±-pn\ 
therefore,  cut-off  in  high-pressure  cylinder  =  R  X  pn  H-  p,. 

Ratios  of  Cylinders  as  Found  in  Marine  Practice.— The 
rate  of  expansion  may  be  taken  at  one  tenth  of  the  boiler-pressure  (or  about 
one  twelfth  the  absolute  pressure),  to  work  economically  at  full  speed. 
Therefore,  when  the  diameter  of  the  low-pressure  cylinder  does  not  exceed 
100  inches,  and  the  boiler-pressure  701hs.,  the  ratio  of  the  low-pressure  to 
the  high-pressure  cylinder  should  be  3.5;  for  a  boiler-pressure  of  80  Ibs.,  3.75; 
for  90  Ibs.,  4.0;  for  100  Ibs.,  4.5.  If  these  proportions  are  adhered  to,  there 
will  be  no  need  of  an  expansion-valve  to  either  cylinder.  If,  however,  to 
avoid  "drop,11  the  ratio  be  reduced,  an  expansion-valve  should  be  fitted  to 
the  high-pressure  cylinder. 

Where  economy 'of  steam  is  not  of  first  importance,  but  rather  a  large 
power,  the  ratio  of  cylinder  capacities  may  with  advantage  be  decreased, 
so  that  with  a  boiler-pressure  of  100  Ibs.  it  may  be  3.75  to  4. 

In  tandem  engines  there  is  no  necessity  to  divide  the  work  equally.  The 
ratio  is  generally  4.  but  v*hen  the  steam-pressure  exceeds  1)0  Ibs.  absolute  4.5 
is  better,  and  for  100  Ibs.  5.0. 

When  the  power  requires  ihat  the  1.  p.  cylinder  shall  be  more  than  100  in. 
diameter,  it  should  be  divided  in  two  cylinders.  In  this  case  the  ratio  of  the 
combined  capacity  of  the  two  1.  p.  cylinders  to  that  of  the  h.  p.  may  be  3.0 
for  85  Ibs.  absolute,  3.4  for  95  Ibs..  3.7  for  105  Ibs..  and  4.0  for  115  Ibs. 

Receiver  Space  in  Compound  Engines  should  be  from  1  to 
1.5  times  the  capacity  of  the  high-pressure  cylinder,  when  the  cranks  are  at 
an  angle  of  from  90°  to  120°.  When  the  cranks  are  at  180°  or  nearly  this, 
the  space  may  be  very  much  reduced.  In  the  case  of  triple-compound  en- 
gines, with  cranks  at  120°,  and  the  intermediate  C3'linder  leading  the  high- 
pressure,  a  very  small  receiver  will  do.  The  pressure  in  the  receiver  should 
never  exceed  half  the  boiler-pressure.  (Seaton.) 


COMPOUND   ENGINES.  767 

Formula  for  Calculating  the  Expansion  and  the  Work 
of  Steam  in  Compound  Engines* 

(Condensed  from  Clark  on  the  "  Steam-engine.") 

a  =  area  of  the  first  cylinder  in  square  inches; 

a'  =  area  of  the  second  cylinder  in  square  inches; 

r  =  ratio  of  the  capacity  of  the  second  cylinder  to  that  of  the  first; 

Z/  =  length  of  stroke  in  feet,  supposed  to  be  the  same  for  both  cylinders; 
I  =  period  of  admission  to  the  first  cylinder  in  feet,  excluding  clearance; 

c  =  clearance  at  each  end  of  the  cylinders,  in  parts  of  the  stroke,  in  feet; 

L'  =  length  of  the  stroke  plus  the  clearance,  in  feet; 

I'  =  period  of  admission  plus  the  clearance,  in  feet; 

s  =  length  of  a  given  part  of  the  stroke  of  the  second  cylinder,  in  feet; 

P  =  total  initial  pressure  in  the  first  cylinder,  in  Ibs.  per  square  inch,  sup- 
posed to  be  uniform  during  admission; 

P'  —  total  pressure  at  the  end  of  the  given  part  of  the  stroke  s; 

p  =.  average  total  pressure  for  the  whole  stroke; 

R  =  nominal  ratio  of  expansion  in  the  first  cylinder,  or  L  -s-  I; 

R'  =  actual  ratio  of  expansion  in  the  first  cylinder,  or  L'  -*- 1'; 
R"  =  actual  combined  ratio  of  expansion,  in  the  first  and  second  cylinders 
together; 

n  =  ratio  of  the  final  pressure  in  the  first  cylinder  to  any  intermediate 
fall  of  pressure  between  the  first  and  second  cylinders; 

N  =  ratio  of  the  volume  of  the  intermediate  space  in  the  Woolf  engine, 
reckoned  up  to,  and  including  the  clearance  of,  the  second  piston, 
to  the  capacity  of  the  first  cylinder  plus  its  clearance.  The  value 
of  N  is  correctly  expressed  by  the  actual  ratio  of  the  volumes  as 
stated,  on  the  assumption  that  the  intermediate  space  is  a  vacuum 
when  it  receives  the  exhaust-steam  from  the  first  cylinder.  In  point 
of  fact,  there  is  a  residuum  of  unexhausted  steam  in  the  interme- 
diate space,  at  low  pressure,  and  the  value  of  N  is  thereby  prac- 
tically reduced  below  the  ratio  here  stated. 

w  —  whole  net  work  in  one  stroke,  in  foot-pounds. 

Ratio  of  expansion  in  the  second  cylinder: 

In  the  Woolf  engine, . 


In  the  receiver-  engine, 


i+nr 

n  -  l)r 


Total  actual  ratio  of  expansion  —  product  of  the  ratios  of  the  thr3e  con- 
secutive expansions,  in  the  first  cylinder,  in  the  intermediate  space,  and 
in  the  second  cylinder, 


In  the  Woolf  engine,  R'  (  r~  -f  N)  . 


U 

In  the  receiver-engine,  r  — ,  or  rR'. 
Combined  ratio  of  expansion  behind  the  pistons  =  —    - — rR'  =  R". 

Work  done  in  the  two  cylinders  for  one  stroke,  with  a  given  cut-off  and  a 
given  combined  actual  ratio  of  expansion: 

Woolf  engine,  iv  =  aP\l'(l  -f  hyp  log  R")  -  <•] ; 
Receiver  engine,  iv  -  ap|_Z'(l  +  hyp  log  R")  -  c(l  +  ^r /_]• 

when  there  is  no  intermediate  fall  of  pressure. 

When  there  is  an  intermediate  fall,  when  the  pressure  falls  to  %,  ^,  ^  of 
the  final  pressure  in  the  1st  cylinder,  the  reduction  of  work  is  0.2$,  1.0$,  4.6# 
of  that  when  thero  is  no  fall. 


768  THE   STEAM-ENGINE. 

Total  work  in  the  two  cylinders  of  a  receiver-engine,  for  one  stroke  for 
any  intermediate  fall  of  pressure, 


EXAMPLE.—  Let  a  =  1  sq.  in.,  P  =  63  Ibs.,  I'  =  2.42  ft.,  n  =  4,  #"  =  5.969, 
c  =  .42  ft.,  r  =  3,  #'  =  2.653; 


w;  =  1  X  63[2.42(5/4  hyp  log  5.969)  -  .42(1  +4  ^g53)]  =  421.55  ft.-lbs. 


€al  culation  of  Diameters  of  Cylinders  of  a  compound  con- 
densing engine  of  2000  H.F.  at  a  speed  of  700  feet  per  minute,  with  100  Ibs. 
boiler-pressure. 

100  Ibs.  gauge-pressure  =  115  absolute,  less  drop  of  5  Ibs.  between  boiler 
and  cylinder  =  110  Ibs.  initial  absolute  pressure.  Assuming  terminal  pres- 
sure in  1.  p.  cylinder  =  6  Ibs.,  and  taking  the  expansion  in  each  cylinder  to 
vary  as  the  square  root  of  the  total  expansion,  we  have: 

Total  expansion  of  steam  in  both  cylinders  =  110  -r-  6  =  18.33. 

Expansion  in  each  cylinder  =  4/18.33  =  4.28. 

Point  of  cut-off  in  each  cylinder,  per  cent  of  stroke,  —  ^  =  23.36. 

1  -f-  hyp  log  of  expansion  in  each  cylinder  =  1  -f  hyp  log  4.28  =  2.454. 

Terminal  and  back  pressure  of  h.  p.  cyl.  and  initial  of  1.  p.  cyl.,  ^-^  = 
25.70  Ibs. 

Average  absolute  pressure  in  h.  p.  cylinder,  25.7    X  2.454  =         63.07  Ibs. 

effective          "         in    "  "        63.07  -  25.70  =         37.37    " 

"         absolute  in  1.  p.          "        6  X  2.454        =         14.72    " 

effective  in    **  cyl.  assum'g31bs.  back  pres.=l  1.72    " 

Assuming  half  the  work,  or  1000  H.P.,  to  be  done  in  the  low-pressure  cylin. 
der, 

Area  of  1.  p.  cyl.  =  -t  -  |3000_x  H.R  _ 

piston-speed  X  av.  effective  pressure 


Area  of  h.  p.  cyl.  =  4023  X  ==      =  7  =  1262  sq.  in.=  40.1  in.  diam. 

Gi.o<  t(j\j  x  uf.of 

11  72 
Ratios  of  cylinder  areas  =  =^«  =  1  to  3.189. 

Of.  Of 

In  this  calculation  no  account  is  taken  of  clearance,  nor  of  drop  between 
cylinders,  nor  of  area  of  piston-rod.  It  also  assumes  that  the  diagrams  in 
both  cylinders  are  the  full  theoretical  diagrams,  with  hyperbolic  expansion 
curves,  with  no  allowance  for  rounding  of  the  corners. 

Calculation  of  Diameters  of  Cylinders  of  a  500  H.P.  Compound  Non-con- 
densing Engine.—  Assuming  initial  pressure  170  Ibs.  above  atmosphere,  back 
pressure  15.5  Ibs.,  absolute  piston-  speed  600  feet  per  minute. 

Total  Expansions  =185_±  15-5  =  J1-9- 

Expansions  in  each  cylinder         =  j/11.9  =  3.45;  hyp  log  =  1.238. 

Terminal  pressure  h.  p.  cyl.         =  185  H-  3.45  =  53.6  Ibs. 

Mean  total  pressure,  tk      "  =  53.6  X  (1  -f-  1.238)  =  120.0. 

Back  pressure  h.  p.  cyl.  =  terminal  pressure  53.6  lbs» 

Mean  effective  pressure  =  120  —  53.6  =  66.4  Ibs. 

Terminal  pressure  1.  pvcyl.  =  53.6  -4-  3.45  =  15.5  Ibs. 

Mean  total  pressure."      '*  =  15.5  X  2.238  =  34.7  Ibs. 

Mean  effective  pressure  1.  p.  cyl.  =  34.7  —  15.5  —  19.2  Ibs. 

Ratio  of  areas  of  cylinders  =  —  ~.  =  1  to  3.46. 

66.4 
Area  of  1.  p.  cyl.  = 

33000  X  H.P.  33000  X  250     , 

=  716  Sq"  in'  =  3°' 


piston-speed  X  M.E.1V          600  X  19.2 
Area  of  h.  p.  cyl.,  716  -f-  3,46  =  207  sq.  in.  =  16.2  in.  diameter, 


TRIPLE-EXPANSION   ENGINES.  769 

TRIPLE-EXPANSION  KN  ft  INKS. 

Proportions  ot"  Cylinders.— H.  H.  Suplee,  Mechanics,  Nov.  1887, 
gives  the  following  method  of  proportioning  cylinders  of  triple-expansion 
engines: 

As  in  the  case  of  compound  engines  the  diameter  of  the  low-pressure 
cylinder  is  first  determined,  being  made  large  enough  to  furnish  the  entire 
power  required  at  the  mean  pressure  due  to  the  initial  pressure  and  expan- 
sion ratio  given;  and  then  this  cylinder  is  only  given  pressure  enough  to  per- 
form one  third  of  the  work,  and  the  other  cylinders  are  proportioned  so  as  to 
divide  the  other  two  thirds  between  them. 

Let  us  suppose  that  an  initial  pressure  of  150  Ibs.  is  used  and  that  900  H.P. 
is  to  be  developed  at  a  piston-speed  of  800  ft.  per  min.,  and  that  an  expan- 
sion ratio  of  16  is  to  be  reached  with  an  absolute  back  pressure  of  2  Ibs. 

The  theoretical  M.E.P.  with  an  absolute  initial  pressure  of  150  -f  14.7  = 
164.7  Ibs.  initial  at  16  expansions  is 

P(\  -f  hyp  log  16)  3.7726 

jg 164.7  X  — jg-  :  =38.83, 

less  2  Ibs.  back  pressure,  =  38.83  -  2  =  36.83. 

In  practice  only  about  0.7  of  this  pressure  is  actually  attained,  so  that 
36.83  X  0.7  =  25.781  Ibs.  is  the  M.E.P.  upon  which  the  engine  is  to  be  pro- 
portioned. 

To  obtain  900  H.P.  we  must  have  33,000  X  900  =  29,700,000  foot-pounds,  and 
this  divided  by  the  mean  pressure  (25.78)  and  by  the  speed  in  feet  (800)  will 
give 


for  the  area  of  the  1.  p.  cylinder,  which  is  about  equivalent  to  43  in.  diam. 

Now  as  one  third  of  the  work  is  to  be  done  in  the  1.  p.  cylinder,  the  M.E.P. 
in  it  will  be  25.78  H-  3  =  8.59  Ibs. 

The  cut-off  in  the  high-pressure  cylinder  is  generally  arranged  to  cut  off 
at  0.6  of  the  stroke,  and  so  the  ratio  of  the  h.  p.  to  the  1.  p.  cylinder  is  equal 
to  16X0.6  =  9.6,  and  the  h.  p.  cylinder  will  be  1440 -$-9.6  =  150  sq.  in.  area,  or 
about  14  in.  diameter,  and  the  M.E.P.  in  the  h.  p.  cylinder  is  equal  to 
9.6  X  8.59  =  82.46  Ibs. 

If  the  intermediate  cylinder  is  made  a  mean  size  between  the  other  two, 
its  size  would  be  determined  by  dividing  the  area  of  the  1.  p.  cylinder  by  the 
square  root  of  the  ratio  between  the  low  and  the  high;  but  in  practice  this  is 
found  to  give  a  result  too  large  to  equalize  the  stresses,  so  that  instead  the 
area  of  the  1.  p.  cylinder  is  found  by  dividing  the  area  of  the  1.  p.  piston  by 
1.1  times  the  square  root  of  the  ratio  of  1.  p.  to  h.  p.  cylinder,  which  in  this 
case  is  1440  H-  (1.1  ^9^6)  =  422.5  sq.  in.,  or  a  little  more  than  23  in.  diam. 

To  put  the  above  into  the  form  of  rules,  we  have 

Area  of  low-pressure  piston ^ 

Area  h.  p.  cyl.  =  Cufc.off  in  h  p  cyl  x  rate  of  expansion. 

Area  of  low-pressure  p'ston 

Area  intermediate  cyl.  = 

1.1  X  V  ratio  of  1.  p.  to  h.  p.  cyl. 

The  choice  of  expansion  ratio  is  governed  by  the  initial  pressure,  and  is 
generally  chosen  so  that  the  terminal  pressure  in  the  1.  p.  cylinder  shall  be 
about  10  Ibs.  absolute. 

Annular  Ring  Method.—  Jay  M.  Whitham,  Trans.  A.  S.  M.  E.,  x. 

577,  gives  the  following  method  of  ascertaining  the  diameter  of  pistons  of 
triple  expansion  engines: 

Lay  down  a  theoretical  indicator-diagram  of  a  simple  engine  for  the  par- 
ticular expansion  desired.  By  trial  find  (with  the  polar  planimeter  or  other- 
wise) the  position  of  horizontal  lines,  parallel  to  the  back-pressure  line,  such 
that  the  three  areas  into  which  they  divide  the  diagram,  representing  low, 
intermediate,  and  high  pressure  diagrams,  marked  respectively  A,  B,  and  C, 
are  equal. 

Find  the  mean  ordinate  of  each  area:  that  of  '*  C  "  will  be  the  mean  un- 
balanced pressure  on  the  small  piston;  that  of  "  B  "  will  be  the  mean  unbal- 
anced pressure  on  the  area  remaining  after  subtracting  the  area  of  the  small 
piston  from  that  of  the  intermediate;  and  that  of  the  area  "A  "  will  denote 


THE   STEAM-ENGINE. 


the  mean  unbalan^^^pr^&saire  on  a  .square InjCh^o-f  *tjh/e?ai^3ular  ring  of  the 
large  piston  otftainedvby  subtracting  tne  intermediate  from  the  large  piston 
,?Wq  tbfisrsee>that ttoe  mean-Ofditiatefe  of-  the4wd  lower  ca**i3»aftt>  onf  annular 

Let  H  =  area  of  small  piston  in  square  inches; 
enuaa<ttct>*tori  tid  f"  Vinter»edfflatei$isw»  to  sqtiare  inches}     saa 
A-IIJHS  Jrf tqr(iif^riu1!'o):arg8< piston  i«  square  inches;  >nim    - 

fera*  m*aa  «« balanced >presaure  per  square  inch  from  card  #G  ''; 

notitmqoiq  ^nu  s 

f  oJ  «i  <)[  to  o-i.tjfti  i 


4-061 

Area  of  small  piston  =  H  =  33,000  X 


Area  of  annular  rin 
bna  .aboooq  to<»1  OOO.OOT^J  =  000 


This  method  is  illustrate^  h^th«?!  following  e^m pie:  Givenl.H.P.  =  3000, 
piston-speed  8  =  900  f  r.  per  min.,  ratio  of  expaHMion  10,  initial  steam-pres- 

'  ity- 


p    .   ^r,". ;.« 


on  i        ''       "''      '"      ''!      !    : 

:  33,000  X  T**-  37-414  X  900  =  980  sq.  in., 


L-  3808-*f '38,000  X 


- 

1 .730  X  i*K) -=i  643^^q;'ln;;  dtain.  90^ 
,f  lo  <>h-  >mti  f.l 

Mr.^liitfe»BJ:  TOooramends  tiner/QjJowJng^yVinder  •rati^siiyhen.tho  piston - 
Bpeedis  from  750  to  1000  fc.  per  njin.,  the,  teifininal; pr^ssiire  4n;  $&)fpge 
cylinder  being  about  10  Ibs.  absolute. 


He  gives  the  following  ratios  from  examination  ota>Ti timber  ;of>  actual 
-0Qgines  f  pt  ^fiJ^ri'i  «»Itj 

,irw)  f 


No.  of , Engines    'S^am-Bdiler  Cylinder  Ratios. 

1     .Avenged.     ^Presjura          h.  p.      '  mt.  | 

3  135  1  2  07  '5- 


11 
2 


140 
145 
150 
160 


,  2.40 
'2.S5 

:;2.54 
2.66 


,00 

5.84;; 

6J90 


TRIPL  K-  E  X  I 'A  N-SIQ  N    ENGINES. 


A  Common  Rule  for  Proportioning?  ttoe.  Cylind^ni^ ^mul- 
tiple expansion  engines  is;  for  two-cylinder  compound  engines,  the  cylinder 
ratio  is  the  square  root  of  the  number  of  expansions,  and  for  triple-expansion 
engines  the  ratios  of  the  high  to  the  intermediate  and  of  .the  intermediate 
to  the' low  are  each  equal  to  the  cube  root  of  the  number;of  expansions,  the 
ratio  of  the  high  to  the  low  being  the  product  of  the  two,  ratios*  that  is,  the 
square  of  the  cube  root  of  the  number  of  expansions.,  ;  Applying, this  rule  to 
the  pressures  above  given,  assuming  a  terminal  pressure  (absolute). of  40 Ibs. 

..jjio  >i-~   — '^..^i.,^y^  vve.have,  for  triple  expansion  e~~: 


,_    .„ 

and  8  IDS.  respectively, 


(Absolute). 
lift  rs*v«j  HI  * 

=  130  — 
140 
150  ! 

160-1  h. 


ilar Pressure,  10  Ibs. 


No.  of  Ex- 


>  1-5  ! 


Cylinder  Ratios, 

'  " 


1  1  to  2:35'toi5.53! 


Termin 


'.$  ibs:  , 


At    />nt      ill-  KJ  i:- 


The  ratio' bf 'the  iJiatiiet^-s1  o  Vi,  LMC  ^ Pft 

the  ratio  of  the  diameterg'Of  the  first  and'mird  cyl'iiiders  is1  the  same  t 
ratio  of  the  areas  of  first  and  second. 

Seaton,  in  _ki|  ^Ijirinf  Engi-ueBeingf,  1*i.ySi3:V\?hift«ttfe»S^f>fe*uMbf  steam  em- 
ployed exceeds  115  ibs.  absolute,  it  is  a'dvisable  to  employ  three  cylinders, 
jthmugh  reach  oti,  whioh,  'the, isteain  expands'in  tufn.  Thfe'i-atio'Of  ttte  16w- 


pressure/  to  , high- pressure,  cylinder  iin  <  this  i  system^  should1  be-'  57  * hftfheh1^ ttofe 
,8t.eaiii-pressure;  is.125  Ibs..  absolute;  when  186  lbs;iahsoliitte,J5l4;'  when  "145 
Ibs.  absolute,  5 . 8 ;  when  155  Ibs.  absolute,  6i3r,;  when  ;  165 '  lb>s. "absolute/  6 . 6. 
The  r&tio,  of  lowipvessure  ito  •imeriiiediate  toy  Harder  Should'1  be^abeiufi  ortte  'naif 
4h<at  between  low-pressure  and  high-pressune,  a*»  ^ivten1  above1.  'That  is; 'If 
tU^  4*a^ip .  <^ili:,R,  to  h..  p,  fe  G,  that  ofi  1.  p.  to  int;  should  be  about *3,' and  cOhy^- 
quehtly  that  of  int.  to  h.  p.  about  2.  In -practice  theu'atio  of  'int. 'to  h;pj'is 
nearly  2.25,  so  that  the  diameter  of  the  int.  cylinder  is  1.5  that  of  the  h.  p. 
The  introduction  of  the  triple-compound  engine  has  admitted  of  ships  being 
propelled  at  higher  rates  of  speed  than  formerly  obtained  without  exceeding 
the  consumption  of  fuel  of  similar  ships  fitted  with  ordinary  .compound 
engines;  in  su"ch  casefe  the  ll'iglier  power  tov obtain  the  speed  has  been  devel- 
oped by  decreasing  the  rate,  of  expansion,  the  low-pressure  cylinder  being 
only  6  times  ffh^j  capacity' of;  the  high-pressure,  with  ^(Working  pressure  of 
17d  Ibs.  absolute.  It  is  novy  ^  very  general  practice  to  inake  tie  diameter  of 

061 


r  of  h.  p.  cyli  ider; 


|sr  of  hf  p.  cyli 


iader.l 


the  low  pressure  clylindei*  equal  to  the  sum 
int.  cylmders;  heiice, 

X:  'if     I"-:  Biarheter!  of  int.f  cylinder  =  1.51tlikmet 
Diameter  |of  1.  p:-cy;linder  =  2.5;dikmet| 

In  this  case  the  ratio  ofi  lyp.  to  h.  p.  is-6  $5;  tlie  ratio  of  int.  |to  h.  p.  is  2.25; 
and  ratio  of  L  p.  tp  int.  is&TS. 
Ratios  of  Cylinders   for  Different    Classes    of  Engines. 

(Proc.  inst.  M.  E.,iFeb.  1^87;  p.  36.)  —  As  lofthe  best  ratios  foit  the  cylinders 
in  a  triple  engine  there  seems  to  be  great  difference  of  opinion.  Considera- 
ble, latitude,  however,  is  due  to  tbe,  requirements  o£;the,;q«se*  ^inasmuch  as 

;  the  same  ratio  would,  h 


it  would  not  be  exp 


be  suitable  for.  an /eco- 


nomical land  ;eng;i ne,  where  the  space  occupied  and  Hie  weight  were,  of 
itiinor  importance,  as  in  a  war  ship,  where  the  conditions  were.re.-verst'd,  ,  Iu 
tlie.land  engine,  for  example,  a  thqoretica}  t,ert;]pinalMpressure  of  about  7 
Ibs.' 'atfeve^  absolute  vacuum  wrould  probably  b,e,ainieqLat»  ;Wihi<Mhi  would  give 
a  ratio  of  capacity  of.  ,Jugh  pressure  tq  low  pressure,  of, ,1,^0;  8l^,;oi:  ,1:  to 
9';' 'Whilst ill  a  war  ship  a  terminal  pressure  would  beirequired  of  12  to  13Jbs. 
which  would  need  a  ratio  of  capacity  of  i  to  5;  yet,  ip^b^ili  these  instances 
the  cylinders  were  correctly  proportioned  ; ami  suitable  to;  the  requirements 
of  the  case.  It  is  obviously  unwise,  there'fpi;e,,  to:  iiitroduce  any  hard-andr 
fast  rule.  /  .  .  ..  |  ,  :,  .,  :  .,,;:,-,  ,.,i  •:.  .  .  ,  •  , 

r.rypes:  of _  Xliree-stage.  Expansio.ii^E.nglnes.rrrl. -iTiiree  cranks 

at  120  deg.  '2.  Two  cranks  \\ilh  1st  and  2d  cylinders  tandem.  3.  Two 
cranks  with '1st  and  3d  cylinders  tandem.  The  most , common  t}rpe  is  the 
first,  with  c.ylinders  arranged  in  the  sequence  high,  intermediate,  low, 


772 


THE   STEAM-ENGINE. 


Sequence  of  Cranks.—  Mr.  Wyllie  (Proc.  lost.  M.  E.,  1887)  favors  the 
sequence  high,  low,  intermediate,  while  Mr.  Mudd  favors  high,  intermediate, 
low.  The  former  sequence,  high,  low,  intermediate,  gave  an  approximately 
horizontal  exhaust-line,  and  thus  minimizes  the  range  of  temperature  and 
the  initial  load;  the  latter  sequence,  high,  intermediate,  low,  increased  the 
range  and  also  the  load. 

Mr.  Morrison,  in  discussing  the  question  of  sequence  of  cranks,  presented 
a  diagram  showing  that  with  the  cranks  arranged  in  the  sequence  high, 
low,  intermediate,  the  mean  compression  into  the  receiver  was  19^  per  cent 
of  the  stroke;  with  the  sequence  high,  intermediate,  low,  it  was  57  percent, 

In  the  former  case  the  compression  was  just  what  was  required  to  keep 
the  receiver-pressure  practically  uniform;  in  the  latter  case  the  compression 
caused  a  variation  in  the  receiver-pressure  to  the  extent  sometimes  of 


. 

Velocity  of  Steam  through  Passages  in  Compound 
.Engines.  (Proc.  Inst.  M.  E.,  Feb.  188?.)—  In  the  SB.  Para,  taking  the  area 
of  the  cylinder  multiplied  by  the  piston-speed  in  feet  per  second  and 
dividing  by  the  area  of  the  port  the  velocity  of  the  initial  steam  through 
the  high-pressure  cylinder  port  would  be  about  100  feet  per  second;  the  ex- 
haust would  be  about  90.  In  the  intermediate  cylinder  the  initial  steam 
had  a  velocity  of  about  180,  and  the  exhaust  of  120.  In  the  low-pressure 
cylinder  the  initial  steam  entered  through  the  port  with  a  velocity  of  250, 
and  in  the  exhaust-port  the  velocity  was  about  140  feet  per  second. 

QUADRUPLE-EXPANSION  ENGINES. 

H.  H.  Suplee  (Trans.  A.  S.  M.  E.,  x.  583)  states  that  a  study  of  14  different 
quadruple-expansion  engines,  nearly  all  intended  to  be  operated  at  a  pres- 
sure of  180  Ibs.  per  sq.  in.,  gave  average  cylinder  ratios  of  1  to  2,  to  3.78,  to 
7.70,  or  nearly  in  the  proportions  1  ,  2,  4,  8. 

If  we  take  the  ratio  of  areas  of  any  two  adjoining  cylinders  as  the  fourth 
root  of  the  number  of  expansions,  the  ratio  of  the  1st  to  the  4th  will  be  the 
cube  of  the  fourth  root.  On  this  basis  the  ratios  of  areas  for  different  pres- 
sures and  rates  of  expansion  will  be  as  follows  : 


Gauge- 
pressures. 

Absolute 
Pressures. 

Terminal 
Pressures. 

Ratio  of 
Expansion. 

Ratios  of  Areas 
of  Cylinders. 

M2 

14.6 

1  :  1.95  :  3.81  :    7.43 

160 

175 

ho 

17.5 

1:2.05:4.18:    8.55 

1   8 

21.9 

1  :  2.16  :  4.68  :  10.12 

(12 

16.2 

1  :2.01  :  4.02:    8.07 

180 

195 

I10 

19.5 

1  :  2.10  :  4.42:    9.28 

1   8 

24.4 

1  :  2.22  :  4.94  :  10.98 

12 

17.9 

1  :2.06:  4.23:    8.70 

200 

215 

-ho 

21.5 

1  :  2.15  :  4.64  :    9.98 

(   8 

26.9 

1  :  2.28:  5.19:  11.81 

12 

19.6 

1  :  2.10:  4.43:    9.31 

220 

235 

{10 

23.5 

1  :  2.20:  4.85:  10.67 

8 

29.4 

1  :  2.33:  5.42:  12.62 

Seaton  says:  When  the  pressure  of  steam  employed  exceeds  190  Ibs.  abso- 
lute, four  cylinders  should  be  employed,  with  the  steam  expanding  through 
each  successively;  and  the  ratio  of  1.  p.  to  h.  p.  should  be  at  least  7.5,  and 
if  economy  of  fuel  is  of  prime  consideration  it  should  be  8;  then  the  ratio 
of  first  intermediate  to  h.  p.  should  be  1.8.  that  of  second  intermediate  to 
first  int.  2,  and  that  of  1.  p.  to  second  int.  2.2. 

In  a  paper  read  before  the  North  East  Coast  Institution  of  Engineers  and 
Shipbuilders,  1890,  William  Russell  Cummins  advocates  the  use  of  a  four- 
cylinder  engine  with  four  cranks  as  being  more  suitable  for  high  speeds 
than  the  three-cylinder  three-crank  engine.  The  cylinder  raiios,  he  claims, 
should  be  designed  so  as  to  obtain  equal  initial  loads  in  each  cylinder.  The 
ratios  determined  for  the  triple  engine  are  1,  2.04.  6.54,  and  for  the  quadru- 
ple 1,  2.08,  4.46,  10.47.  He  advocates  long  stroke,  high  piston- speed,  100  rev- 
olutions per  minute,  and  250  Ibs.  boiler-pressure,  .un  jacketed  cylinders,  and 
separate  steam  and  exhaust,  valves. 


QUAimUPLE-EXPANSIOiST   EHGIHES. 


Diameters  of  Cylinders  of  Recent  Triple-expansion 
Engines,  Chiefly  Marine. 

Compiled  from  several  sources,  1890-1893. 
Diam.  in  inches:  H  =  high  pressure,  /  =  intermediate,  L  —  low  pressure. 


H 

/ 

L 

H 

I 

L 

H 

I 

L 

H 

/ 

L 

* 

5 

8 

16 

25.6 

41 

90 

OC 

j  40 

36 

58 

94 

4% 

7.5 

13 

16J4 

23% 

38.5 

ms 

GO 

"i  40 

38 

61.5 

100 

5 

6.5 

8 
10.5 

12 
16.5 

16.5 

24.5 

J31 
1  81 

23 
23.5 

38 
38 

61 
60 

28  I 

28  r 

56 

86 

7 

9 

12.5 

17 

27 

44 

24 

37 

56 

39 

61 

97 

7.1 

11.8 

18.9 

17 

26.5 

42 

25 

40 

64 

40 

59 

88 

7.5 

12 

19 

17 

28 

45 

26 

42 

69 

40 

67 

106 

8 

11.5 

16 

18 

27 

40 

26 

42.5 

70 

40 

66 

100 

9 

14.5 

22.5 

18 

29 

48 

28 

44 

72 

41 

66 

101 

9.8 

15.7 

25.6 

18 

305. 

51 

29% 

44 

70 

41% 

67 

106% 

10 

16 

25 

18.7 

29.5 

43  .3 

29.5 

48 

78 

42 

59 

92 

11 

K5 

24 

18% 

23.6 

35.4 

30 

48 

77 

43 

66 

92 

11 

18 

25 

19.7 

29.6 

47.3 

32 

46 

70 

43 

68 

110 

11 

18 

30 

20 

30 

45 

32 

51 

82 

43% 

67 

10614 

11.5 

18 

28.5 

j  36 

32 

54 

82 

45 

71 

113 

11.5 

17.5 

30.5 

20 

62.5 

136 

33 

58 

88 

32.5( 

J85.7 

12 

19.2 

30.7 

20 

33 

52 

33.9 

55.1 

84.6 

32.5  | 

08 

1  85.7 

13 

22 

33.5 

21 

32 

48 

34 

54 

85 

J  81.5 

14 

22  4 

36 

21 

36 

51 

34 

50 

90 

4< 

75 

1  81.5 

14.5 

24* 

39 

21.7 

33.5 

49.2 

34.5 

51 

85 

371 

j98 

15 

24 

39 

21.9 

34 

57 

34.5 

57 

92 

37  \ 

<9 

J98 

15 

24.5 

38 

22 

34 

51 

Where  the  figures  are  bracketed  there  are  two  cylinders  of  a  kind.  Two 
28"  =  one  39.6",  two  31"  =  one  43.8",  two  32.5"  =  one  46.0'',  two  36"  =  one 
50.9",  two  37"  =  one  52.3",  two  40"  =  one  56.6",  two  81.5"  =  one  115",  two 
85.7"  =  one  121",  two  98"  =  one  140".  The  average  ratio  of  diameters  of 
cylinders  of  all  the  engines  in  the  above  table  is  nearly  1  to  1.60  to  2.56  and 
the  ratio  of  areas  nearly  1  to  2.56  to  6.55. 

The  Progress  in  Steam-engines  between  1876  and  1893  is  shown 
in  the  following  comparison  of  the  Corliss  engine  at  the  Centennial  Exhibi- 
tion in  1876  and  the  Allis-Coiiiss  quadruple-expansion  engine  at  the  Chicago 
Exhibition. 

1893.  1876. 


Cylinders,  number  ........................  4 

"          diameter  .......................  24,  40,  60,  70  in. 

"          stroke  ..........................  72  in. 

Fly-  wheel,  diameter  ......................  30ft. 

width  of  face  ..................  76  in. 

weight  .........................  136,000  Ibs. 

Revolutions  per  minute  ...................  60 

Capacity,  economical  ....................  2000  H.P. 

maximum  ...................  3000  H.P. 

Total  weight  .............................  650,000  Ibs. 


2 

40  in. 

120  in. 

30ft. 

24  in. 

125,440  Ibs. 

36 

1400  H.P. 

2500  H.P. 

1,360,588  Ibs. 


The  crank-shaft  body  or  wheel-seat  of  the  Allis  engine  has  a  diameter  of 

21  inches,  journals  19  inches,  and  crank  bearings  18  inches,  with  a  total 
length  of  18  feet.    The  crank-disks  are  of  cast  iron  and  are  8  feet  in  diam- 
eter.   The  crank-pins  are  9  inches  in  diameter  by  9  inches  long. 

A  Double-tandem  Triple-expansion  Engine,  built  by  Watts, 
Campbell  &  Co.,  Newark,  N.  J.,  is  described  in  Am.  Mack.,  April  26,  1894. 
It  is  two  three-cylinder  tandem  engines  coupled  to  one  shaft,  cranks  at  90°, 
cylinders  21,  32  and  48  by  60  in.  stroke,  65  revolutions  per  minute,  rated  H.P. 
2000;  fly-wheel  28  feet  diameter,  12  ft.  face,  weight  174,000  Ibs;  main  shaft 

22  in.  diameter  at  the  swell;  main  journals  19  X  38  in.;  crank-pins  9^j  x  10 
in.;    distance  between  centre  lines  of  two  engines  24  ft.   1J4  in-?  Corliss 
valves,  with  separate  eccentrics  for  the  exhaust-valves  '>f  the  l.p.  cylinder. 


gj 

3*1 

6   .: 


s 
= 

i 

5 

Qi 


c 

I: 


„ 


R 


!ut 


•A'UIO 
rUOOg  in  Mm 

•          - 


!>.«i^n 


»J; 


*|M;2J&a3||! 


:gg|g  8-S8S8 

i  C*'f<  <P  <O    O    IN  *J  iO  O 


s 

i     X 
•«»-i  i«;aK    ^ 

3£S5:*  f? 


i^iS'gg'. 

M  WM  «<!•«  «i 


r'^.^^nMivf =  ^ft^rf*1?  t^ffi>ii(i>  *  ^: 

'  ;r»v«KO*.*Vi*  '!'  ^.'"''.HM^ '**!'*. '1B.H 


I 


:  :^'  :  :  :  :d  :  :  :  :-«r: (>:*-:.-  :  :/nCn3-s;v:»o  2up<2ii>>:i  : 


ECONOMIC 


S^AM-ENO!  NrKS. 


ECONOMIC   PERFORMANCE  O,F  . 
Economy  oC  Expansive  >Worfcia|£  un«l«r  Various  Condi 
tions^  Single  CyJindeiti'niY^  owl  «»ri}  »i  :;: 

'<!  "(Abridged  from  Clark  on 
h  «i  orfm&  oroflw  '     •          -••<!     vao   •wnv*jr»rtT    .lon 

1.  SINGLE   C^LII*PE^.S    WITH  SUPERHEA-UED  .bTKAM,    NOXCONDENS 
side  cylinder  locoinotive^  cylinders  An4  stpamr,mp.es  euvelopexi^y 
p,*.    .Net 

'          n.   >o  y.J  «w,J  «»dT 

40<n«*0? 


V8.  her*  .* 


t,  >- 
80 


>mth^srR^<s> 

q.  in. 

"Cutoff,  percent .UiiJJ.ui    $0  i    >%&'>   "30        35 
-Actliatrafcio-'df  expansion  3i91  -3v31  ^.«7    2.53> 
Water  per  I.H. P.  per  hour,  Tii»-)u->  W  »K«ttH.  hu>»  ,T)o  Jjr^oS'  i.»  • 

Ibs.  ,..• IS. 5    19.4      20      21.3    22.2 &L«  n  £ 

-2.  SINGLE  CYLINDERS  WITH  SUPERHEATED  STEAM,  CONDENSING.— The  best 
results  obtafnred)'by  Hirri,  with  a  cylinder  28%  X^67^<m'.' 'and  steam  super- 
heated 150°  F.,  expansicin  ratio  354  to  4^,  total  maximum  pressure  in  cylin- 
der 63  to  69  Ibs.  were  15.€3ana!f5.69l>)^0f  water  perI.H;P;  per  hour. 

3.  SINGLE  CYLINDERS JoV SMALL  SIZE,  8  OR  9  IN.  DIAM., •"•' 
coNpENS^NG.— The  best  results  are  ol 
75, lbs.my,xijtAUW; pressure  in  ftie  cyl 
per  hour. 


iiies. 

'vqfe»' 


Focd-\vatei-  Consumption  of  Diilerent  Ty  pes  t 

-^I'he  following  tables  are  taken  from  the 'circular  of  th,^  Tabor 
(Asheroft  ^Ifg.  Co.,  1889).  In  the  fir$t  of  the  two.cpliinins .unUer 
requfred,  in  the  tables  for  simple '-engiaies,  the  figures ,  are  obtained  by 
Gomputatioh  from  nearly  perfect  indicator-diagrams,  with  allowance  forcyl- 
indeir  condensation  according  to  thte  table  or^  page  753,! but  wdthout1  allow- 
ance for  leakage,  with^back-pressur^  in  the  non-condensing  tabjle  takdn  at  16 
Ibis.  &bove  zero,  and  in  the  condensii^  table  at  3  Ibs.  above  zerb.  Thje  com- 
pression cu¥ve  is  supposed  to  be  hj5)erbolic,  ind  comiriences  iat  0.91]of  the 
return-stroke,  with  a  clearance  bf  3^  of  the  piiiton-displacemenjt. 
Table  No.  2  gives  the-f eed-w«£er  consumption  f-oi--  jacket*  ' 


776 


THE   STEAM-EKGINE. 


densing  engines  of  the  best  class.  The  water  condensed  in  the  jackets  is 
included  in  the  quantities  given.  The  ratio  of  areas  of  the  two  cylinders  are 
as  1  to  4  for  120  Ibs.  pressure;  the  clearance  of  each  cylinder  is  3$:  and  the 
cut  off  in  the  two  cylinders  occurs  at  the  same  point  of  stroke.  The  initial 

Eressure  in  the  1.  p.  cylinder  is  1  Ib.  per  sq.  in.  below  the  back-pressure  of  the 
.  p.  cylinder.  The  average  back  pressure  of  the  whole  stroke  in  the  1.  p. 
cylinder  is  4.5  Ibs.  for  10$  cut-off;  4.75  Ibs.  for  20$  cut-off;  and  5  Ibs.  for  30$ 
cut-off.  The  steam  accounted  for  by  the  indicator  at  cut-off  in  the  h.  p. 
cylinder  (allowing  a  small  amount  for  leakage)  is  .74  at  10$  cut-off,  .78  at 
20$,  and  .82  at  30$  cut-off.  The  loss  by  condensation  between  the  cylinders 
is  such  that  the  steam  accounted  for  at  cut  off  in  the  1.  p.  cylinder,  ex- 
pressed in  proportion  of  that  shown  at  release  in  the  h.  p.  cylinder,  is  .85  at 
10$  cut-off,  .87  at  20$  cut-off,  and  .89-at  30$  cut-off. 

The  data  upon  which  table  No.  3  is  calculated  are  not  given,  but  the  feed- 
water  consumption  is  somewhat  lower  than  has  yet  been  reached  (1894),  the 
lowest  steam  consumption  of  a  triple-exp.  engine  yet  recorded  being  11.7  Ibs. 

TABLE  No.  1. 

FEED-WATER  CONSUMPTION,  SIMPLE  ENGINES. 
NON-CONDENSING  ENGINES.  CONDENSING  ENGINES. 


A 

» 

Feed-water  Re- 

JL 

0^ 

Feed-water  Re- 

o 

1 

quired  per  I.  H.  P. 
per  Hour. 

| 

E 
1 

quired  per  I.H.P. 
per  Hour. 

> 

£ 

*M 

^Bd5 

0 

£ 

I-S 

i'Sio; 

o 
3 

9 

s  * 

"**•-  w  of 

1 

4) 

§3 

^•^  i  a? 

« 

08 

£ 

-So 

•2  if  c8"S 

fc 

rtj 

O  " 
*"'  O 

2^  %•% 

o 

5 

1 

C?S 

tUD^H        *> 

.2  «s  g'J 

S 

£ 

1 

bcc 

B  ao  JJn3 

Per  Cent  Cu 

Initial  Press 
phere,  Ibs. 

h 

Correspondi 
grams  witl 
age,  Ibs. 

il.2.2 

0 

Per  Cent  Cu 

«]§ 

il 

C 

Correspondi 
grams  witl 
age,  Ibs. 

Illf 

pSfiS 

f 

60 

8.70 

37.26 

40.95 

r 

60 

14.42 

18.22 

20.00 

70 

12.39 

30.99 

33.68 

1 

70 

16.96 

17.96 

19.69 

10  J 

80 

16.07 

27.61 

29.88 

80 

19.50 

17.76 

19.47 

90 

19.76 

25.43 

27.43 

1 

90 

22.04 

17.57 

19.27 

i 

100 

23.45 

23.90 

25.73 

I 

100 

24.58 

17.41 

19.07 

j- 

60 

21.12 

27.55 

29.43 

f 

60 

22.34 

17.68 

19.34 

70 

26.57 

25.44 

27.04 

70 

26.03 

17  47 

19.09 

80 

32.02 

21.04 

25.68 

10  \ 

80 

29.72 

17.30 

18.89 

90 

37.47 

23.00 

24.57 

\ 

90 

33.41 

17.15 

18.70 

100 

42.92 

22.25 

23.77 

100 

37.10 

17.02 

18.56 

60 

30.47 

27.24 

29.10 

f 

60 

29.00 

17.93 

19.51 

70 

37.21 

25.76 

27.43 

\ 

70 

33.65 

17.75 

19.27 

30  - 

30 

43.97 

24.71 

26.29 

15  -{ 

80 

38.28 

17.60 

19.09 

90 

50.73 

23.91 

25.38 

90 

42.92 

17.45 

18.91 

100 

57.49 

23.27 

24.68 

i 

100 

47.56 

17.32 

18.74 

60 

37.75 

27.92 

29.63 

f 

60 

34.73 

18.58 

20.09 

70 

45.50 

26.66 

28.18 

70 

40.18 

18.40 

19.85 

40^- 

80 

53.25 

25.76 

27.17 

1 

80 

45.63 

18.27 

19.69 

90 

61.01 

25.03 

26.35 

90 

51.08 

18.14 

19.51 

100 

68.76 

24.47 

25.73 

100 

56.53 

18.02 

19.36 

c 

60 

43.42 

28.94 

30.66 

r 

60 

44.06 

20.19 

21.64 

1 

70 

51.94 

27.79 

29.31 

70 

50.81 

20.04 

21.41 

50  •{ 

80 

60.44 

26.99 

.   28.38 

30  j 

80 

57.57 

19.91 

21.25 

1 

90 

68.96 

26.32 

27.62 

90 

64.32 

19.78 

21.06 

I 

100 

77.48 

25.78 

26.99 

I 

100 

71  .08 

19.67 

20.93 

c 

60 

51.35 

21.63 

22.96 

1 

70 

59.10 

21.49 

22.74 

40*! 

80 

66.85 

21.36 

22.56 

90 

74.60 

21  .24 

22.41 

100 

82.36 

21.13 

22.24 

CALCULATED  PERFORMANCES  OF  STEAM-ENGINES.    777 


TABLE  No.  2. 
FEED-WATER  CONSUMPTION  FOR  COMPOUND  CONDENSING  ENGINE 


Cut-off, 
per  cent. 

Initial  Pressure  above 
Atmosphere. 

Mean  Effective  Press- 
Atmosphere. 

Feed-water 
Required 
per  T.H.P.  per 
Hour,  Lbs. 

H.P.  Cyl., 
Ibs. 

L.P.  Cyl., 
Ibs. 

H.P.  Cyl., 
Ibs. 

L.P.  Cyl., 
Ibs. 

•  i 

80 
100 
120 

4.0 
7.3 
11.0 

11.67 
15.33 
18.54 

2.65 
3.87 
5.23 

16.92 
15.00 
13.86 

20        -j 

80 
100 
120 

4.3 
8.1 
12.1 

26.73 
33.13 
39.29 

5.48 
7.56 
9.74 

14.60 
13.67 
13.09 

-  \ 

80 
100 
120 

4.6 
8.5 

11.7 

37.61 
46.41 
56.00 

7.48 
10.10 
12.26 

14.99 
14.21 
13.87 

TABLE  No.   3. 
FEED-WATER  CONSUMPTION  FOR  TRIPLE -EXPANSION  CONDENSING  ENGINE 


Cut-off, 
per 
cent. 

Initial  Pressure  above 
Atmosphere. 

Mean  Effective  Pressure. 

Feed-water 
Required 
perl.H.P. 
per  Hour, 
Ibs. 

H.P.  Cyl., 

Ibs. 

I.  Cyl., 

Ibs. 

L.P.  Cyl., 
Ibs. 

H.P.  Cyl., 
Ibs. 

I.  Cyl., 
Ibs. 

L.P.  Cyl., 
Ibs. 

y 

120 
140 
160 

37.8 
43.8 
49.3 

1.3 

2.8 
3.8 

38.5 
46.5 
55.0 

17.1 
18.6 
20.0 

6.5 
7.1 
8.0 

12.05 
11.4 
10.75 

40     -I 

120 
140 
160 

38.8 
45.8 
51.3 

2.8 
3.9 
5.3 

51.5 
59.5 
70.0 

22.8 
23.7 
25.5 

8.6 
9.1 
10.0 

11.65 
11.4 
10.85 

g 

120 
140 
160 

39.8 
46.8 
52.8 

3.7 

4.8 
6.3 

60.5 
70.5 

82.5 

26.7 
28.0 
30.0 

10.1 
10.8 
11.8 

12.2 
11.6 
11.15 

Most    Economical    Point   of  Cut-off  in  Steam-engines. 

(See  paper  by  Wolff  and  Denton,  Trans.  A.  S.  M.  E.,  vol.  ii.  p.  147-281 ;  also, 
Ratio  of  Expansion  at  Maximum  Efficiency,  R.  H.  Thurstou,  vol.  ii.  p.  128.) 
— The  problem  of  the  best  ratio  of  expansion  is  not  one  of  economy  of  con- 
sumption of  fuel  and  economy  of  cost  of  boiler  alone.  The  question  of 
interest  on  cost  of  engine,  depreciation  of  value  of  engine,  repairs  of  engine 
etc.,  enters  as  well;  for  as  we  increase  the  rate  of  expansion,  and  thus 
within  certain  limits  fixed  by  the  back-pressure  and  condensation  of  steam 
decrease  the  amount  of  fuel  required  and  cost  of  boiler  per  unit  of  work 
we  have  to  increase  the  dimensions  of  the  cylinder  and  the  size  of  the  en 
gine,  to  attain  the  required  power.  We  thus  increase  the  cost  of  the  engine 
etc.,  as  we  increase  the  rate  of  expansion,  while  at  the  same  time  we  de 
crease  the  fuel  consumption,  the  cost  of  boiler,  etc.  So  that  there  is  in 
every  engine  some  point  of  cut-off,  determinable  by  calculation  and  graphi- 
cal construction,  which  will  secure  the  greatest  efficiency  for  a  given  expen- 
diture of  money,  taking  into  consideration  the  cost  of  fuel,  wages  of  engineer 
and  firemen,  interest  on  cost,  depreciation  of  value,  repairs  to  and  insurance 
of  boiler  and  engine,  and  oil,  waste,  etc.,  used  for  engine.  In  case  of  freight- 
carrying  vessels,  the  value  of  the  room  occupied  by  fuel  should  be  consid- 
ered in  estimating  the  cost  of  fuel. 

Sizes  and  Calculated  Performances  of  Vertical  High- 
speed Engines.— The  following  tables  are  taken  from  a  circular  of  the 
Field  Engineering  Co.,  New  York,  describing  the  engines  made  by  the  Lake 
Erie  Engineering  Works,  Buffalo,  N.  Y.  The  engines  are  fair  representatives 
of  the  type  now  coming  largely  into  use  for  driving  dynamos  directly  with- 
out belts.  The  tables  were  calculated  by  E.  F.  Williams,  designer  of  the 
engines.  They  are  here  somewhat  abridged  to  save  space; 


7.8 


THE    STKAM-KXr.INE. 
Simple  Engfnes-Non-condenslng. 


NOTE.  —  Tie 
WtfikV^pWer 
T;  ratine  of  the  en- 
6  &M 5  Is  at  80  Ibs. 
'•    gauge     pfrlfefcul<e> 
steam  cut-Off <  at 
l^ffeli^ldi. 


<<>  in  pou  iid     Kn«riiie* 


Cylinder 


-^fon-eondensing— 

ad  »ecei^Bf  Jacketed. 


^prcHssiwe 
f 


241'  279 
25M*  323  374 
St3-I6t;433r  502 

..j'  5oS(  617 
572^  7r5t'8S9 


.  press..  .b$ 
Ratiio  of*  ctepft 

Cyl.  condensation,  %. : . 


CALCULATED   PERFORM AJsCKS  O^^fTEAM-ENGINES.  779 


k&Ul  table'  contains 
120  Ibs  i  ratio  4  to  1. 


a*waii-Kii&i«io»5  Bk>BH-c««d«»Mn3.^R 
note   only  J iieketodr,i}«ilaoH  iol 


Mean  effective  press.,  Ibs. !_    85  ^ 

No.  of  expansions/. .....    ,  10 

Per  cent  cyl.  eoodens....  14 

Steam  p;  LH.Bip.hr.,  Ibs.  L 20.70 


Steam p.LHvBip.hr.vlbs.f  20.76    1=19:36       19,25"   ;  17.00     i-17^^0^  p'17.20 
Lbs.coalat81b.evap.  IbH.!'    2.5U    ]•    2.39.      2,40       /.2.1tii  ;i!i  '  2v23  '  ^  .0.13 


780 


THE   STEAM-EKGINB. 


Triple-expansion   Engines— Condensing-  Steam- 
Jacketed. 


Diameter 

14 

Horse-power 
when  Cut- 

Horse-power 
when  Cut- 

Horse-power 
when  Cut- 

Horse-power 
when  Cut- 

Cylinders, 
inches 

i 

9 

A 

ting  off  at  14 
Stroke  in 

ting  off  at  1^ 
Stroke  in 

ting  off  at  y% 
Stroke  in 

ting  off  at  % 
Stroke  in 

o 

a 

First  Cylin- 

First  Cylin- 

First Cylin- 

First Cylin- 

r. 

£& 

der. 

der. 

der. 

der. 

b 

&4 

PH' 

f 

o.9 
>F 

120 

140 

160 

120    140 

160 

120 

140 

160 

120 

140 

160 

W 

hH 

3 

£ 

& 

Ibs. 

Ibs. 

tlbs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

4H 

?V6 

12 

10 

370 

35 

42 

48 

44 

53 

59 

57 

72 

84 

81 

97 

110 

5U 

8V<a 

13U 

12 

318 

45 

68 

62 

56 

67 

76 

73 

92 

107 

104 

123 

140 

6V4 

10V^ 

1614 

14 

277 

67 

79 

92 

83 

100 

112 

108 

137 

159 

154 

183 

208 

7^ 

12 

19 

16 

246 

87 

103 

120 

109 

131 

147;  141 

180 

208 

201 

239 

tt79 

9 

14V6 

22U 

18 

22;> 

125!  148 

172 

156 

187 

211'  203 

257 

299 

289 

348 

390 

10 

16 

25 

20 

185 

154 

183 

212 

192 

231 

260!  250 

317 

368 

356 

423 

481 

HH 

18 

28^£ 

24 

158 

206 

245 

284 

258 

310 

348    335 

426 

494 

477 

568 

645 

13 

22 

33V6 

28 

138 

277 

329 

381 

346 

415 

467    450 

571 

663 

640 

761 

865 

15 

24H 

38 

32 

120 

357 

424 

491 

446 

535 

602    580 

736 

&54 

825 

98! 

1115 

17 

27 

43 

34 

112 

458 

543 

629 

572 

686 

772   744 

944 

1095 

1058 

1258 

1430 

20 

38 

52 

42 

93 

670 

796 

922 

838 

1006 

1131  1089 

1383 

1605 

1551 

1844 

2096 

23^ 

38 

60 

48 

80 

877 

1041 

1206 

1096 

1316 

1480  1424 

1808 

2099 

2028 

2411 

2740 

Mean  effec.  press.,  Ibs. 

16 

19 

22 

20 

24  1    27     26 

33 

38.3 

37 

44 

50 

No.  of  expansions  

26.8 

20.1                   13.4 

8.9 

Percent  cyl.  condens. 

19 

19 

19 

16 

16 

16     12 

12 

12 

8 

8 

8 

St.p.I.H.P.p.hr.Jbs. 

14.7 

13.9 

13.3 

14.3  13.98 

13.214.3 

13.6 

13.0 

15.7 

14.9 

14.2 

Coal  at  8  Ib.  evap.,  Ibs. 

1.8 

1.73 

1.66 

1.78  1.74 

1.651.78 

1.70 

1.62 

1.96 

1.86 

1  .77 

Type  of  Engine  to  be  used  where  Exhaust-steam  is 
needed  for  Heating.— In  many  factories  more  or  less  of  the  steam 
exhausted  from  the  engines  is  utilized  for  boiling,  drying,  heating,  etc. 
Where  all  the  exhaust-steam  is  so  used  the  question  of  economical  use  of 
steam  in  the  engine  itself  is  eliminated,  and  the  high-pressure  simple  engine 
is  entirely  suitable.  Where  only  part  of  the  exhaust-steam  is  used,  and  the 
quantity  so  used  varies  at  different  times,  the  question  of  adopting  a  simple. 
a  condensing,  or  a  compound  engine  becomes  more  complex.  This  problem 
is  treated  by  C.  T.  Main  in  Trans.  A.  S.  M.  E.,  vol.  x.  p.  48.  He  shows  that 
the  ratios  of  the  volumes  of  the  cylinders  in  compound  engines  should  vary 
according  to  the  amount  of  exhaust-steam  that  can  be  used  for  heating.  A 
case  is  given  in  which  three  different  pressures  of  steam  are  required  or 
could  be  used,  as  in  a  worsted  dye-house:  the  high  or  boiler  pressure  for 
the  engine,  an  intermediate  pressure  for  crabbing,  and  low-pressure  for 
boiling,  drying,  etc.  If  it  did  not  make  too  much  complication  of  parts  in 
the  engine,  the  boiler-pressure  might  be  used  in  the  high-pressure  cylinder, 
exhausting  into  a  receiver  from  which  steam  could  be  taken  for  running 
small  engines  and  crabbing,  the  steam  remaining  in  the  receiver  passing 
into  the  intermediate  cylinder  and  expanded  there  to  from  5  to  10  Ibs.  above 
the  atmosphere  and  exhausted  into  a  second  receiver.  From  this  receiver 
is  drawn  the  low-pressure  steam  needed  for  drying,  boiling,  warming  mills, 
etc.,  the  steam  remaining  in  receiver  passing  into  the  condensing  cylinder. 
Comparison  of  the  Economy  of  Compound  and  Single- 
cylinder  Corliss  Condensing  Engines,  each  expanding 
about  Sixteen  Times.  (D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  xii.  943.) 

The  engines  used  in  obtaining  comparative  results  are  located  at  Stations 
I.  and  II.  of  the  Pawtucket  Water  Co. 

The  tests  show  that  the  compound  engine  is  about  30£  more  economical 
than  the  single-cylinder  engine.  The  dimensions  of  the  two  engines  are  as 
follows:  Single  20"  X  48";  compound  15"  and  30^"  X  30".  The  steam 
used  per  horse-power  per  hour  was:  single  20.35  Ibs.,  compound  13.73  Ibs. 

Both  of  the  engines  are  steam-jacketed,  practically  on  the  barrels  only 
with  steam  at  full  boiler-pressure,  viz.  single  106.3  Ibs.,  compound  127.5  Ibs. 


PERFORMANCES  OF  STEAM-ENGINES.  ?8l 

The  steam  -pressure  in  the  case  of  the  compound  engine  is  127  Ibs.,  or  21 
Ibs.  higher  than  for  the  single  engine.  If  the  steam-pressure  be  raised  this 
amount  in  the  case  of  the  single  engine,  and  the  indicator-cards  be  increased 
accordingly,  the  consumption  for  the  single-cylinder  engine  would  be  19.97 
Ibs.  per  hour  per  horse-power. 

Two-cylinder  vs.  Three-cylinder  Compound  Engine.— 
A  VVheelock  triple-expansion  engine,  built  for  the  Merrick  Thread  Co., 
Holyoke,  Mass.,  is  constructed  so  that  the  intermediate  cylinder  may  be  cut 
out  of  the  circuit  and  the  high-pressure  and  low-pressure  cylinders  run  as  a 
two-cylinder  compound,  using  the  same  conditions  of  initial  steam  -pressure 
and  load.  The  diameters  of  the  cylinders  are  12,  16,  and  24£f  inches,  the 
stroke  of  the  first  two  being  36  in.  and  that  of  the  low-pressure  cylinder  48 
in.  The  results  of  a  test  reported  by  S.  M.  Green  and  G.  I.  Rockwood,  Trans. 
A.  S.  M.  E.,  vol.  xiii.  647,  are  as  follows:  In  Ibs.  of  dry  steam  used  per  I.H.P. 
per  hour,  12  and  24Jf  in.  cylinders  only  used,  two  tests  13.06  and  12.76  Ibs., 
average  12.91.  All  three  cylinders  used,  two  tests  12.67  and  12.90  Ibs.,  average 
12.79.  The  difference  is  only  1%,  and  would  indicate  that  more  than  two  cylin- 
ders are  unnecessary  in  a  compound  engine,  but  it  is  pointed  out  by  Prof. 
Jacobus,  that  the  conditions  of  the  test  were  especially  favorable  for  the 
two-cylinder  engine,  and  not  relatively  so  favorable  for  the  three  cylinders. 
The  steam-pressure  was  142  Ibs.  and'the  number  of  expansions  about  25. 
(See  also  discussion  on  the  Rockwood  type  of  engine,  Trans.  A.  S.  M.  E.,  vol. 
xvi.) 

Effect  of  Water  contained  in  Steam  on  the  Efficiency  of 
the  Steam-engine.  (From  a  lecture  by  Walter  C.  Kerr,  before  the 
Franklin  Institute,  1891.)  -Standard  writers  make  little  mention  of  the  effect 
of  entrained  moisture  on  the  expansive  properties  of  steam,  but  by  common 
consent  rather  than  any  demonstration  they  seem  to  agree  that  moisture 
produces  an  ill  effect  simply  to  the  percentage  amount  of  its  presence. 
That  is,  5%  moisture  will  increase  the  water  rate  of  an  engine  5#. 

Experiments  reported  in  1893  by  R.  C.  Carpenter  and  L.  S.  Marks,  Trans. 
A.  S.  M.  E.,  xv.,  in  which  water  in  varying  quantity  was  introduced  into  the 
steam-pipe,  causing  the  quality  of  the  steam  to  range  from  99$  to  58%  dry, 
showed  that  throughout  the  range  of  qualities  used  the  consumption  of  dry 
steam  per  indicated  horse-power  per  hour  remains  practically  constant,  and 
indicated  that  the  water  was  an  inert  quantity,  doing  neither  good  nor  harm. 

It  appears  that  the  extra  work  done  by  the  heat  of  the  entrained  water 
during  expansion  is  sensibly  equal  to  the  extra  negative  work  which  it  does 
during  exhaust  and  compression,  that  the  heat  carried  in  by  the  entrained 
water  performs  no  useful  function,  and  that  a  fair  measure  of  the  economy 
of  an  engine  is  the  consumption  of  dry  and  saturated  steam. 

Relative  Commercial  Economy  of  Best  Modern  Types  of 
Compound  and  Triple-expansion  Engines.  (J.  E.  Denton, 
American  Machinist,  Dec.  17,  1891.)  —  The  following  table  and  deductions 
si  low  the  relative  commercial  economy  of  the  compound  and  triple  type  for 
the  best  stationary  practice  in  steam  plants  of  500  indicated  horse-power. 
The  table  is  based  on  the  tests  of  Prof.  Schroter,  of  Munich,  of  engines  built 
at  Augsburg,  and  those  of  Geo.  H.  Barrus  on  the  best  plants  of  America,  and 
of  detailed  estimates  of  cost  obtained  from  several  first-class  builders. 


13'6 


Trip  motion,  or  Corliss  engines  of    fLbs.  water  per  hour  per  I  12  K.R    10  on 
the    triple-expansion    four-cylin-    |    H.  P.,  by  measurement.  ( 
der-receiver  condensing  type,  ex-  -{  Lbs.  coal  per  hour  per  | 
panding  22  times.  Boiler  pressure,    j    H.  P.,  assuming  8.5  Ibs.  V  1.48      1.50 
150  Ibs.  (.   actual  evaporation.        ) 

The  figures  in  the  first  column  represent  the  best  recorded  performance 
(1891),  and  those  in  the  second  column  the  probable  reliable  performance. 

Increased  cost  of  triple  -expansion  plant  per  horse-power,  including 
boilers,  chimney,  heaters,  foundations,  piping  and  erection  ..........  $4.50 

The  following  table  shows  the  total  annual  cost  of  operation,  with  coal  at 
$4.00  per  ton,  the  plant  running  300  days  in  the  year,  for  10  hours  and  for 
24  hours  per  day: 


ii'  10  ..ftdi  71.* r  gi  * 


hmTomnoo  9fft  to  < 


erf.t  ni 


r^ri 


;  ........ 


10  - .,  »*,»•>  «dt  cfffajjom 


r-     -.•j.:-'^ 


Expense  fefc^afr 


'i... ...: 

riJ>feplahtl'K!'Lf;  ....... 

""'~  '"'•;.•: . . . .  . . 


-.  ...  ..... 

AriftiM  tieprfebSatiofc-  at?  t£%*§flia9&Qn)!YP.  ?«•• 


day,  at  $0.50,  or  15$  ot  <>xtra  fuel  < 
Animal  exti?a><?Qst  0f impairs  at  3$  ori  $4.50  per 

24  UOdttUt>(vi  .  W.*U  *#ftf.07f  J  ,tr""" 


Per  H.P. 

'' 


«i!58O    OY/J 

ioq  v 


'J^^lBRjfj; 
W    i 

zr" 


-      ; 
nft  eri^ 


per 


0.06 

$0 . 67 
r.23 


;-0'Wj 

,>wjl  bnji 
6  edoua 
.ni 

•A 
ta«  81  ,9014 

.v.-   •-••. 


Thf*  saving  betwefeu  tlie  .conii>oimd  anxl  triply,  ,typ,es  is;much  less  than  that 
involved  in  the  '"'step  from'  tliie  single-expansion  condensing  to  the  compound 


:o  ilie  rxti-a  cost  of  ijte  i.riyie  engine  and 
1,1  je  same  or  slighfly  more,  owing  to  their 
e  sfugle "versus  the  compound,  however, 
it|pf.  the  coiupouncj  ..engine  is.  off  set  by  the 

of  .the  plants  at  S33.50,   $36.50'and  '$41  p*?r  horse- 
figures  in  the  ta-^le  imply  that  tht^  total  annual  ^av- 

Iflowir^'R^'iiBv  ni  'iiikv?  iloidw  ni     vz 

: power  pjant  costs  $18,250,.  and  saves  about  $1630 
.4SK5  for  24  hours1  Service,  per  year  oveY  a  single 
'liat  is,  the  corupound  saves  its  extra  cp,s^ in,.^0-hour 
ne  yt-ur.  or  in  2-l-ln.»ur  service  in  four  months. 
•oi-se-power  plaint  costs  $20,500,' .ant]  Sftyes  about.  $114  per 
•vice,  or  S^26  in  24-hour  ser\ 'ice,  ovei-  a  compound  plant, 
extra  cost  in  10-hour  service  in.uboMt  10^4  years,  or  iu  24* 
^iit  ^  years. 

inii-eiiiiiiie     at      ^Iil\\i 
"     (S  ' 


.       • 7  .       .     .  ,7    ,  - '      »-VT         -i-  •      Wl 

iy  oi  the  bte;ini  engme,-  by  K.  |f,,Thurst^,  TJ-««S.. 
"ylinders  2S,  4S  and  7 1  in.  by  60  in? stroke;'  ratios  of 
Volurnes'l  to  3  to  7:  total  nmnber  of  expansions J9.(5o;  clearances,  h.p. 
1.1;';  int.  l.f>£:  1.  p.  0,77^;'  volume  of  receivers:  1st,  101.3  cu.  ft.;  2d,  181  cu.. 
ft:;  sream-pressure  gauge  during  test,  average  121.5  Ibs.:  vacuum  13.84  Ibs. 
per  minute;  indicated  horse-powe.r,,h.p.  175,4,  int. 
,  ^73.9; 'total  friction,  horse-power  5.-J. 91,  =  9.22^5  dry 
our  '11.078:  n.T.U.  per  I.H.P.  per  min.  517.6;  duty  in 
"~:  per  million  B.T.U.,  137,656,000. 


steam  . 

foot-pounds 

Steam  per  I.  II.  i1.  'per  "hour,'  f  roiu;dia.gram,  at  cut-off  .  .  .  .     0.35 
'  4  - 


r  bj*  indicator  at  cuih-off,  per  cent,  ..  87.1 


10.0  • 


Economy    of    tlie    T\va-  cylinder    Compound 

engin^»»—  Repeated  jtests  of  the  Pawtucket-Corliss  eiij-ine, 
15  and  30^  by  30  in.  stroke,  gave  a  water  consumption  of  13.69  to  14  J  6  ll>s. 
per  I.H.P,  per  hour,  Steam-pressure  13$  ;lbs,  ;  revoiutioos  -per  injn.  48  ; 
expansions  about  16.  Cylinders  jacketed.  The  lowest  water  rate  \vas  with 
jackets  in  use;  both  jackets  supplied  with  steam  of  boiler  pressure.  The 
average  '^avin^  due  to  jackets  was  only  about  2££  per1  'cent.  (TrahsV  A.  S. 
MICE4  xi.  328  an<*^1038;  xiii^l763;  ^ 

,  This  record  was  beaten  in  1894  by  a  Leavitt  pumping.-engine  at  Louisville. 
Ky.  (Trans.  A.  S.  M.  E.  xvi.)  Cylinders  27.^1  and  54.13  m.  diam.  by  10  ft 
stroke^1  f  eVdliitfous"  per  ^  ihih.  '18157:  piston  speed  371.5ft,;  expansions  20.^,- 
steam-  pressure,  gauge,  140  Ibs,  Cylinders  and  receiver  jacketed.  Steam 


1HT 
PERFORMANCES  OF  STEAM-EKGINES. 


ffl 


to  {..HO!  o)  P.K  .>.iH>i.»;brrr>  1o  ^itjtn  «* 

used  p<M-  I.IT. P.  per  hour,  12.223  Ibsi  <  Duty  per  million >B.T.€r.  ^'138,126,00® 
ft.;li»s.  i^q  lA9)rnono09  H80dW  enh)i 

Test  of  a  Triple-expansion  IMimping-engine  with  and 
without  Jacfcets^  at  L0JeHi*np I»tt,ctty  Prof .  J,  Ev  Dentan?<,/Rratis>.<>AJ 
S.  M.  E.,  xiv.  1340).— Oylindens  24,  84  and  54  in;  by#6  M^stJroHei'^irev 
min. ;  H.P.  developed  'about  820 ;  boiter-presstine  IfiO  Itee;  f5esr.6j  mdde'on 
different  days  with  different  sets- of  conditions  in  ja€keOsu:iAt  150'lbs.  1 
preissure,  and  about  20  expansions;  with  any  pifess«re- >ab(¥vfe ;4& lbs<  m  i 
the  ja.cke'ts .and  reheaters, '^r  with  no  prgssro-e  m  thQ  -big* 
forihance  was  as  follows:  With  2-5#  of  moisture  iiLtWest* 
engiee^the  5^6keis  'tisfed  'IC^of ^cbe«totali  f  efed^wat&p.^  A^o\it  ^0^«f  itJieiiatfetei5? 
was  condensed  during  admission  to  the  high  cylinders  and  ia&oiu&lfliSSjlbs? 
of  feed-water  was  consumed  per  hour  per  indicated  horse-power.  With  no 
jacket*  0r^reheatei-^iii-<aGtion  the  feed- water  eon sii5®p6io«WAfe  14i99Llfts.,  or 
SM  more  than  with  jackets  and  reheaters.  The  .consumption  of  lubricating: 
Qii^was  tA^thirdtl'tf  a  gallon  of  itiachiHepil  adi&ne  and  three .«rfer  gaf-1 
Ions  of  cylinder  pifper  21  h'ours.  The  friction  Q'fjjjie  engine  iSW 
different  daVs  va'rled  from :5.1#to  8.7^.; 

liable  to  an  efrur  of  one  per  cent,  wliich  is  prob 

for  fthe  most  careful  dettii-minatious,  the^teani^ , ... 

foJlowing^on-ditioiis: 
(jt>  Any  pressure,  from  43  to  131  in  the  interme.d^te  ap^M^^^ 

-(/>)  Any; pressure  from  0  to  151  in  the  jacket  of  1  

{O  Anj  cut-off  from  21;f  to  23jJ  in  high  cylinder,  fro 
nWiate  cylinder,  from  40^  to  53,1  in  low  cylinder,; -.,  b«ol  Jo  ^ 

Water  Consumption  of  Three  Types 

(B.  Donkin,  Jr.,  Eiiy'y^  Jan. .15,  1 

Sl-MMAUY   AND    AVERAGES    OF  TM'ESTY-tfN'K   JVHMSHKD    KxPFCItbrRNTS   b^   tHfC 

--      O. „.,...,  ,VE  \LI,      HOP""^"'»'        /VvVH^-OTV,, 

Jg:  SSRB^ 


itiou,  pounds  per 
.  I;H,P.  per  houi\ 


pipe   water  and 
Jacket  -.Wafted:* 


Triple-expansion  Oorliss  engine  at  Narragansett  E,  L.-  Go*,  ^PpoVldeiKje;  R; 
I.,  builtJ  by  E.  P:  Allis  Co.  Cylinder  14,  25  and  33  in.  by:48iBi  ft&oltetasted  at; 
99  revs. -per  min.;  -125 lha.  steam-pressures',  steam  per  I. H:P;  per  hour  12  $4 
Ibs.;  H.P.  5161  ^A  full  account  of  this  engine,  with :  records -of  testfe>is  given  by 
J.  T,  H^nthtorn,  m  Trails.  A/&  M.  E.,  xii.  643.  Ijjii  ol  roale  or 

Backeye cross  compound  engine,  tested  at  Chicago  Exposition,  'by Geo. 
H.;  Betrrus  (TSvL^-g  Record,  Feb;  17,  1894).  Cylinder  14  and  28% 24  in.  stroke;  - 
tested  at  165  r.  p.  m.;  120  Ibs.  steam-pressure.  I. H.P.  in  four  tests  condens- 
ing arid  one  non-condensing. .. 295  224  128  277  .  267 

Steam  per  horse-power  per  hour 16.07    15>71  •<  17. 22    16.07    23.24 

Relative  Economy  of  Compound  Non-condensf ng  En- 
gines under  Variable  I^oads.— F,  M,  Ripes,.in  a  paper  on  the  Steam 
Distribution  in  a  Form  of  Single-acting  Engine  (Trans.  A.  S.  M.  E.  xh'i.  5.37.K- 
discusses  an  engii;e  designed  to  meet  the  following  problem  ;  Given  an 


784  THE   STEAM-ENGIKE. 

extreme  range  of  conditions  as  to  load  or  steam -pressure,  either  or  both,  to 
fluctuate  together  or  apart,  violently  or  with  easy  gradations,  to  construct 
an  engine  whose  economical  performance  should  be  as  good  as  though  the 
engine  were  specially  designed  for  a  momentary  condition— the  adjustment 
to  be  complete  and  automatic.  In  the  ordinary  non-condensing  compound 
engine  with  light  loads  the  high-pressure  cylinder  is  frequently  forced  to 
supply  all  the  power  and  in  addition  drag  along  with  it  the  low-pressure 
piston,  whose  cylinder  indicates  negative  work.  Mr.  Rites  shows  the 
peculiar  value  of  a  receiver  of  predetermined  volume  which  acts  as  a  clear- 
ance chamber  for  compression  in  the  high-pressure  cylinder.  The  Westing- 
house  compound  single-acting  engine  is  designed  upon  this  principle.  The 
following  results  of  tests  of  one  of  these  engines  rated  at  175  H.P.  for  most 
economical  load  are  given  : 

WATER  RATES  UNDER  VARYING  LOADS,  LBS.  PER  H.P.  PER  HOUR. 

Horse-power...  ,.   210         170         140         115         100          80          50 

Non-condensing 22.6       21.9       22.2       22.2       22.4       24.6       28.8 

Condensing 18.4        18.1        18.2        18.2        18.3        18.3       20.4 

Efficiency  of  Non-condensing  Compound  Engines,    (W. 

Lee  Church,  Am.  Macti.,  Nov.  19,  1891.) — The  compound  engine,  non-con- 
densing, at  its  best  performance  will  exhaust  from  the  low-pressure  cylin- 
der at  a  pressure  2  to  6  pounds  above  atmosphere.  Such  an  engine  will  be 
limited  in  its  economy  to  a  very  short  range  of  power,  for  the  reason  that 
its  valve-motion  will  not  permit  of  any  great  increase  beyond  its  rated 
power,  and  any  material  decrease  below  its  rated  power  at  once  brings  the 
expansion  curve  in  the  low-pressure  cylinder  below  atmosphere.  In  other 
words,  decrease  of  load  tells  upon  the  compound  engine  somewhat  sooner, 
and  much  more  severely,  than  upon  the  non-compound  engine.  The  loss 
commences  the  moment  the  expansion  line  crosses  a  line  parallel  to  the 
atmospheric  line,  and  at  a  distance  above  it  representing  the  mean  effective 
pressure  necessary  to  carry  the  frictional  load  of  the  engine.  When  expan- 
sion falls  to  this  point  the  low-pressure  cylinder  becomes  an  air-pump  over 
more  or  less  of  its  stroke,  the  power  to  drive  which  must  come  from  the 
high-pressure  cylinder  alone.  Under  the  light  loads  common  in  many 
industries  the  low-pressure  cylinder  is  thus  a  positive  resistance  for  the 
greater  portion  of  its  stroke.  A  careful  study  of  this  problem  revealed  the 
functions  of  a  fixed  intermediate  clearance,  always  in  communication  with 
the  high-pressure  cylinder,  and  having  a  volume 'bearing  the  same  ratio  to 
that  of  the  high-pressure  cylinder  that  the  high-pressure  cylinder  bears  to 
the  low-pressure.  Diagrams  were  laid  out  on  this  principle  and  justified 
until  the  best  theoretical  results  were  obtained.  The  designs  were  then  laid 
down  on  these  lines,  and  the  subsequent  performance  of  the  engines,  of 
which  some  600  have  been  built,  have  fully  confirmed  the  judgment  of  the 
designers. 

The  effect  of  this  constant  clearance  is  to  supply  sufficient  steam  to  the 
low-pressure  cylinder  under  light  loads  to  hold  it's  expansion  curve  up  to 
atmosphere,  and  at  the  same  time  leave  a  sufficient  clearance  volume  in  the 
high-pressure  cylinder  to  permit  of  governing  the  engine  on  its  compression 
under  ligh*  loads. 

Econc-my  of  Engines  under  Varying  Loads.  (From  Prof. 
W.  C.  Unwin's  lecture  before  the  Society  of  Arts,  London,  1892.)— The  gen- 
eral result  of  numerous  trials  with  large  engines  was  that  with  a  constant 
load  an  indicated  horse-power  should  be  obtained  with  a  consumption  of 
\Y»,  pounds  of  coal  per  indicated  horse-power  for  a  condensing  engine,  and 
\%  pounds  for  a  non-condensing  engine,  figures  which  correspond  to  about 
!%  pounds  to  2*4  pounds  of  coal  per  effective  horse-power.  It  was  much  more 
iifficult  to  ascertain  the  consumption  of  coal  in  ordinary  every-day  work, 
but  such  facts  as  were  known  showed  it  was  more  than  on  trial. 

In  electric-lighting  stations  the  engines  work  under  a  very  fluctuating 
load,  and  the  results  are  far  more  unfavorable.  An  excellent  Willans  non- 
condensing  engine,  which  on  full-load  trials  worked  with  under  2  pounds 
per  effective  horse-power  hour,  in  the  ordinary  daily  working  of  the  station 
used  7}4  pounds  per  effective  horse-power  hour  in  1886,  which  was  reduced 
to  4.3  pounds  in  1890  and  3.8  pounds  in  1891.  Probably  in  very  few  cases 
were  the  engines  at  electric-light  stations  working  under  a  consumption  of 
41-i}  pounds  per  effective  horse-po.wer  hour.  In  the  case  of  small  isolated 
motors  working  with  a  fluctuating  load,  still  more  extravagant  results  were 
obtained, 


PERFORMANCES   OF   STEAM-ENGINES.  785 

ENGINES  IN  ELECTRIC  CENTRAL  STATIONS. 

Year 1886.   1890.  1892. 

Coal  used  per  hour  per  effective  H.P 8.4      5.6      4.9 

"        "    «•*•        "       "    indicated  "   6.5      4.35    3.8 

At  electric-lighting:  stations  the  load  factor,  viz.,  the  ratio  of  the  average 
load  to  the  maximum,  is  extremely  small,  and  the  engines  worked  under 
very  unfavorable  conditions,  which  largely  accounted  for  the  excessive  fuel 
consumption  at  these  stations. 

In  steam-engines  the  fuel  consumption  has  generally  been  reckoned  on 
the  indicated  horse-power.  At  full-power  trials  this  was  satisfactory 
enough,  as  the  internal  friction  is  then  usually  a  small  fraction  of  the  total. 

Experiment  has,  however,  shown  that  the  internal  friction  is  nearly  con- 
stant,  and  hence,  when  the  engine  is  lightly  loaded,  its  mechanical  efficiency 
is  greatly  reduced.  At  full  load  small  engines  have  a  mechanical  efficiency 
of  0.8  to  0.85,  and  large  engines  might  reach  at  least  0.9,  but  if  the  internal 
friction  remained  constant  this  efficiency  would  be  much  reduced  at  low 
powers.  Thus,  if  an  engine  working  at  100  indicated  horse  power  had  an  effi- 
ciency of  0.85,  then  when  the  indicated  horse-power  fell  to  50  the  effective 
horse-power  would  be  35  horse-power  and  the  efficiency  only  0.7.  Similarly, 
at  25  horse-power  the  effective  horse-power  would  be  10  and  the  efficiency 
0.4. 

Experiments  on  a  Corliss  engine  at  Creusot  gave  the  following  results  : 

Effective  power  at  full  load 1 .0         0.75       0.50       0.25       0.125 

Condensing,  mechanical  efficiency 0.82       0.79       0.74        0.63       0.48 

Non-condensing,  "  "          0.86       0.83       0.78       0.67       0.52 

At  light  loads  the  economy  of  gas  and  liquid  fuel  engines  fell  off  even 
more  rapidly  than  in  steam-engines.  The  engine  friction  was  large  and 
nearly  constant,  and  in  some  cases  the  combustion  was  also  less  perfect  at 
light  loads.  At  the  Dresden  Central  Station  the  gas-engines  were  kept 
working  at  nearly  their  full  power  by  the  use  of  storage-batteries.  The 
results  of  some  experiments  are  given  below  : 


rake-load,  per 
cent  of  full 

Gas-engine,  cu.  ft. 
of  Gas  per  Brake 

Petroleum  Eng., 
Lbs.of  Oil  per 

Petroleum  Eng., 
Lbs.  of  Oil  per 

Power. 
100 

H.P.  per  hour. 
22.2 

B.H.P.  per  hr. 
0.96 

B.H.P.  per  hr. 

0.88 

75 

23.8 

1.11 

0.99 

59 

28.0 

1.44 

1.20 

20 

40.8 

2.38 

1.82 

66.3 

4.25 

3.07 

Steam  Consumption  of  Engines  of  Various  Sizes.— W.  C. 

Unwin  (Cassier's  Magazine,  1894)  gives  a  table  showing  results  of  49  tests  of 
engines  of  different  types.  In  non-condensing  simple  engines,  the  steam 
consumption  ranged  from  65  Ibs.  per  hour  in  a  5-horse-power  engine  to  22 
Ibs,  in  a  134-H.P.  Harris-Corliss  engine.  In  non-condensing  compound  en- 
gines, the  only  type  tested  was  the  Willans,  which  ranged  from  27  Ibs.  in  a 
10  H.P.  slow-speed  engine,  122  ft.  per  minute,  with  steam-pressure  of  84  Ibs. 
10  19.2  Ibs.  in  a  40-H.P.  engine,  401  ft.  per  minute,  with  steam-pressure  165 
Ibs.  A  Willans  triple-expansion  non-condensing  engine,  39  H.P.,  172  Ibs. 
pressure,  and  400  ft.  piston  speed  per  minute,  gave  a  consumption  of  18.5  Ibs. 
In  condensing  engines,  nine  tests  of  simple  engines  gave  results  ranging  only 
from  18.4  to  22  Ibs.,  and,  leaving  out  a  beam  pumping-engine  running  at  slow 
speed  (240  ft.  per  minute)  and  low  steam -pressure  (45  Ibs.),  the  range  is  only 
from  18.4  to  19.8  Ibs.  In  compound-condensing  engines  over  100  H.P.,  in  13 
tests  the  range  is  from  13.9  to  20  Ibs.  In  three  triple-expansion  engines  the 
figures  are  11.7,  12.2,  and  12.45  Ibs.,  the  lowest  being  a  Sulzer  engine  of  360 
H.P.  In  marine  compound  engines,  the  Fusiyama  and  Colchester,  tested 
by  Prof.  Kennedy,  gave  steam  consumption  of  21.2  and  21.7  Ibs.;  and  the 
Meteor  and  Tartar  triple-expansion  engines  gave  15.0  and  19.8  Ibs. 

Taking  the  most  favorable  results  which  can  be  regarded  as  not  excep- 
tional, it  appears  that  in  test  trials,  with  constant  and  full  load,  the  expen- 
diture of  steam  and  coal  is  about  as  follows: 

Per  Indicated  Horse-      Per  Effective  Horse- 
power Hour.  power  Hour. 

Kind  of  Engine.  / * »  / ' * 

Coal,          Steam,  Coal,          Steam, 

Ibs.  Ibs.  Ibs.  Ibs. 

Non-condensing 1.80  16.5  2.00  18.0 

Condensing 1.50  13.5  1.75  15.8 


THE   STEAM-EKGIXE. 

Tf  ' 

Theseqfftajftte^  rgggrded  as?  minimum  valuer  .rarely .surpassed  by  th^most 
efficient-  pia^nery,  and    only  reached  with    ve^y  goo.4  auaehiuery  in  the 

JUpads  are 


£  IT    -  iv  •  c   '  A."  '• '  i 

favorable  (Nmxiitmijs  of  a  test  trial. 
Small  Uiigines  and  I^iiji'ines  \vitli  Jl 


KMft.W' 

COAL  CONSUMPTION  PER  INDICATED  HORSK-PO-WF/R  IN  SMALL  ENGINES*. 

PirobajlrieslI.H'.B;  -at  fulMoad.  v.     •I*?*-'  iJ^J  ^  «0^>  45         75         60    '•    CO 
Averag^I.H.P.'dumig  obser- 

Coal t^t?1i.if:pj  per  "hoer  dur-    "'— <-^ ^UBnv.  bjiol  Ihri'JA     Ssoufx 

ing  observuMonvlbs '..••?,«».(•)•      21 .25    22-;01"- --18:13  '  11;.«H      9; 53      8.50 

It  is  largely  to  repine -s-ucU^ng-iiies  as  i,ho  above  .that  po\ver   will  bt^  dis- 
tri,but.ed  1'i'oui  cenlral  stations.  lB»ibni  srfJ  fl 

fRa    Sleaui  <:<i 
Tests  at  Roy^d  Agricultural  Soci^ty^ 

bBOi  liii't  J^  Tfi'WiM:; 

-1-^4 ^  ,,...,-        .... 


. 
A 

en  sing,  fixed  cut-Mf^  Meyer  valve. 
70.  e         STEAM-CONSUMPTION,  LBS.  PER  I.B&#?PKR  HOUR. 


Stoain-<'oiiMins  plion  f  of     I  :n-  i  IM  x  ;  at    Various    Speeds. 

entpn  and  JacobiJ^'Trans.  A.  S.  M.  E,/^.  722)—  17  x  30 

' 


30  in 


Fi^ur^r^n  f rcfm  plotted  ^iagVam  -of 'ivsultn. 

^evs.  per  Via.....      8     12    1(J      20;,.24        32        40   -  .  '48-  '•.•'••  5$  72     -8& 

^cut.off,l^;;...  .  39!.35    32     :^0      29.3      29      28,7:;  28.5  -.88  3  ..28    :  27.7 

•SO      Ml.    A1       oQ-r,        t>Q        .9«   4        ->«        O^  ;«      O7- 1  O«  ,  Q      or,   « 


4 :     I  •  • ' joqaopo-  *^M i*: 

.:      lOCKj'*    ' 


2fl:5      29      -2^.4      2»>r^7J5  /27ia-QG;3;  25.6 
4, , i  33. 1 1    •;  32     . 30 ,8   ,29  -.8  •  •&.  t)  ;  28  ;8-    28 . 7     .... 

STEAM- CONWU JIPTION ;.' OS1  ^AME  EN.GINE  ;  FIXED  SP^IX,  CQ,  t^p vs. ,  P'E LI  ^1 1 N, 
Varying  cu^of^:  compartni  with  throttling.- engine  -foh:sanHf)jlioirSe-po\ver 
9V>;  •-   •     .  . 

0,1     0.15    0  2    0  25-  &8la&kafy&?&$a<lt&0WA 
•29-  '27.5    "27      27   •   27V2  27.8   28V5-;;:1  l^'.,l!:.;; 
•m     34:2   32.2'3i:5  ^Stf:4*31V(5  ;^2:2  3^.1  :50.5    ,'iO 
-i     .edl  B.8]  cw  -s-  ^  a 

UT-OFF^  FOR  C^JKRESPOND'lNO'ilottSK^-'PCrWEHS. 

!:  42       37    -!33:8I  31V5  ;  -2d.:«j!  r-'.1.-.'   :. . . ;     ...    ..   .    .:. 

—  wiusv..-'  ...v    50:1';;49    4<3r8lM4'.0:    '41;    ......:.'   .:.... 

•    ;-.  i  ."••'•-:  :    b»nf3 

Some  of  t-jtus  principal- eonclusionsifrontthis  serie^ftf!  tests  ar&  as  follows  : 
1.  There Js  a  d,i6ti»et  gain  ia economy  of  steam  as<the!spe©di  increaees  for 


'-•i-*i 
I.H  001 


.  . 

y>,  y&  and  J4  cut  -oil'  at  90.Jbsv  pressure!    Tiiei  loss  ftineconomy  foi'  abdot  » 
cut-off  is  at  the  rate  of  1/12  Ibr  of  -water  per  H,P.;£or>4ach  t  decrease  of  a 
revo^ujyoijivp^r/ttiimi^e  froati  8(>:ta  ^:  revolutions,  and  at  the  rate  of  %  Ib.  of 
water  bj^Lq^r^§  revolutions.    Alsooatall*  stpeeds  the  ^4  cut-off  is  more  eco- 


2.  i^gi^lbs.  bp4ieE-pressuiie.>art8  above4^  cut-off,  to  produce  a  given  H.P. 
require^  about  2Q&;less  steam i-than  to  cut  off  at  %  stroke  and  regulate  by  the 
throttg|i 

3.  ^Foir  the  sajijei  conditions  iwith  GOvlbs.   boiler-pressure,    to  obtain,  by 
throttling,  the  same  mean  effective  pressure  at  %  cut -off  that  is  obtained  by 


78? 


aoiJoinq  aid  ni  J&fti  liouuqo  sd1  he«K9'fqx9 

off  about  i/{,  require*  about,  8G&{ 


nd  ilivAdJ  -G  -3  /iM 
{ftiofte  steam  than  for  th*e  latter 

.  .    fraiie-^niq«nij'j  iaatouJwn11!  BJ|? 

Pi8tpii*s*i*ee«i,ili  ..ilflnjcintes.  (ProevInst.'M.  E*.,  July,  1883,  p. 
3-21).—  The  torpedo  ,  boat  i$  aii  excellent  example  of  tbe  advancfe  -towards 
high;  speeds,  and  shows  what.  can  be  accomplished  by  studying  tightness 
and  strength  in  combination.  In  runmng-at-siS^iknotd  -an  liour,  a.ri  engine 
with  cylinders  of  16  in.  stroke,  will  mak*?  48Q  re  tplatit3.es  .'tper  minhte;  which 
gives  1280  ft.  per  minute  for  piston-speed;  aini'itms  Remarked  that  engines 
running  at  that  high  rate  work  muell  more  smoothly  than  at  lower  speeds, 
and  that  the"  difficulty  of  fabrication  diminishes  as  the  speed  inoreaKe^i 

A  Highspeed!  'Corliss  Engine.  .^A  -Ooriiss.  engine,  ^0  x  42  in.,  has 
been  running  a  wire-  rod  mill  at  .the  T  rent  en:;  Ifort  Go.  's-  works  since  1^77,  at 
160  revolutions  or  -1V<JO  ft.  piston-speed,  per  minute  (Trans,  A.  S.  M.  E.,  ii. 
72).  A  .piston-speejd.  of  T-200  ft.  pur.,  mhh  .has  been  realized  In  locomotive 
practice,  .  .^H  -/<j  uiiig  aril  •i^lJJSi^g  erii  ^o-Joo  od3  islioila  y.> 

The.  I-,iiui(;»lioii  'of  ^^  JEugiiiei^spee^.  ;v  (C^si  T-.  -Porte*,  in  a  paper 
on  the"  Limitation.  of  Engine  -wpeed,  Trmis.  A.  S.  M.  E.,  xiv.  -806.  •)—  The 
practical  linwta,ti««i  to.  high  rc>tativfe8p^clhii>statiQBai-y  FeeiprocatMTg  stfearn  - 
engines  is  not  found  in  the  clanger  of  heating-oh*  of  -excessive  wear,  nor,  as 
is,  ^generally  belie-yed,  m  the  ct-nt-rifugak  forqe--of  the  flyl-whee5!,  uor  in  the 
tendency  to  knock  iu  the  centres,  iioruurvibEa-tiomL  -?He  gJv®»utwdiob-jections 
to  very  high  speeds:  First,  that  ;>  engines'  ought  •tidittaiiti8  itni  as  fast  as 
they  can  "be;"  second,  the  large  amount  J3§f-?steiste  T6om'i«"W>B  port,  which 
is  ,  Tf&WlfoSpnO9£Wtiitoai  jj&n^toa.uJ[&*hm  qtqpa&tinlG  rt^peet'-of 
economy  of  steain,  the  ,ihjgh>s.pBed,gei>^oellifi«d^aa^^rJpi>(n^!d>5a-  iailui'e. 
Large  gain  was  looked  for.  from  high  speed,  because  the  doss  by  condensa* 
tion  ou  a  given  surfaces  o.uld  be  divided  into  a  greater  ivfeJig%t  of  ste^im,  'but 
this  expectation  lias  >H>t]b^6aiJiAfe*lKzed.  For  tMsmnsatfefat't^^y-il•tej1lt•  we 
have  to  lay  the  blame  chiefly  on  the  excessive  amount  of  waste  roottivi  The 
ordinary  method  of  expressing  the  amount  of  waste  room  in  the  percentage 
added  ,by  it  to  the  .total  pi  stem  displacement,  is  a  misleading  ofcte)ilt>«hould 
be  expressed  as  the  percentage  which  it  adds  to  the  length  'd>f!k1te&ni  admis- 
sion;  -For  exmnple^  i£the  st^iam^s  euttoff  at  J/S  of  the  stroke,*  8^!a£eted  b}'- 
the  waste  room  to  the  total  ..piston  displacement  means  40^  'added  to  the 
volume  of  steam  ad  m  J.T  te(  1  .  I'Jigiiias  M  four,  five  and  si  x<  i  f  6e«  -^tij-ahte  may 
properly  be  run  at  from  700  to  800  ft.  of  piston  travel  per  minute,  but  for 
ordmary.^iaes,  say^:>lr,;ljoriej,'.  t'>00  fh  p^mirnite  should  -be  the  limit. 

Influence  of  tlie  SfceaJUt-jsLelteti---  Tests  of  mmierottseTigmies  with 
aud  Without  s.tea^^ja^iete-^hbw^ti^-^^^eedi^g  divei'sity  oS  results,  ranging 
all  the  way  i  ropj  SQ^snviug  -dowji  :to  zero,  or  even  ii)  sortie  cases  •showing  an 
actual  loss  .  TJ  u  >  <  .  p  i  u  ioi  us  ot  ettgSHjmjva'a^rfeiS)  ^datfe  ,•  (4894)  is  also  as  di  verse  as 
the  results,  but  there  is  a.  tendency  towards  a  general  belief  that  the  jacket  is 
not  as  valuable  au^gp^tj^^g^-.toai^engiefi  aa  wias  formerly  supposed,  A-n  ex- 
tensive resuin  e  of  facts  uu«.i,  «,>|ai  lions  on  .the  steam-aacketas  given  by  Prof  . 
Thurston.  in  Trans,  A.  S.  M.  K,,.xiv,  4G2.  8.ee;-also  'Trans:  ^  A*  Si  M.  E.,  xiv. 
873  aud  1340;  xiii.  170;  xii.  J20  aud  UWO:  aiid  Jour.  F:  I.,  April,  1891,  p.  276. 
The  foil  owing"  are  a  few  state  men  t*;  selected  ifrehi  ^' 


T,he  result  of  tests  reported,  by.  the  re«mi<l^iJOiriij|itfeefC«ist^ni.ja 
appointed  by  the  British  Institution  of  Mettoiical  iEagineerrS'in  188(5,  indi- 
cate an  increased  efficiency  due  to  the  use  of  the  steam-jacket  of  from  \%  to 
over  30#,  according  to  varying  circtniistaiices. 

Bennett  asserts  .that,  ".it  .  has  ~beenFacmndantly  proved  that  steam- 
jackets  are  not  only  advisable  bureibsolutely  necessary,  in  order  that  high 
rates  of  expansion  may  be  efticieml.y  carried  o^t.^ncLthe.  greatest  possible 
economy  of  heat  attairied.'" 

IsherWbod  finds  the  ga'in  by  'its  use,  .'under,  the  conditions  of  ordinary 
practice,'  as  a  general  average;  to  be  about  ^0'.  on  small  and  8^"  or'  ()%  on 
large  engines,  varying  through  intermediate  values  with  intermediate  sizes, 
it  being  understood  that  theTJacket  has  an-effeetiyie,  <$ircuh$$iou,  and  that 
botn  heads  and  sWe^*lTjatil*e\W>' 

Professor  Unwin  considers  that  "  in  all  cases  and  on  all  cylinders  the 
jacket  is  useful:  provided,  of  Bourse,  ordinary,  not  superheated,  steam  is 
used^b«*Tfi-6^aVaM^M  may  diminish  to  an  amount  not  worth  the  interest, 
on  extra  cost." 

Professor  Cotter-ill  says":  l.-'xi-oi-ience  shows  that  a  steam-jacket  is  advan- 
tageous, but  the  amount  to  tv  gains  -d  will  vary  according  to  circumstances. 
In  many  eas'es  it  may  We  That  (lu>  advantage  is  small.  Great  caution  is 
neces^alt'y  ''iff  _Ylr;Vwing  foiicltisipri's  from  any  special  set  of  expei'inients  on, 
the  influvl^^^br  ^JicKre'tlng.^  " 


788  THE   STEAM-EXGIHE. 

Mr.  E.  D.  Leavitt  has  expressed  the  opinion  that,  in  his  practice,  steam 
jackets  produce  an  increase  of  efficiency  of  from  15$  to  20$. 

In  the  Pawtucket  pumping  engine,  15  and  30^  X  30  in.,  50  revs,  per  mhi., 
steam-pressure  125  Ibs.  gauge,  cut-off  14  m  h.p.  and  Vs  m  1-P-  cylinder,  the 
barrels  only  jacketed,  the  saving  by  the  jackets  was  from  \%  to  4$. 

The  superintendent  of  the  Holly  Mfg.  Co.  (compound  purnping-engines) 
says:  "In  regard  to  the  benefits  derived  from  steam-jackets  on  our  steam- 
cylinders,  I  am  somewhat  of  a  skeptic.  From  data  taken  on  our  own  en- 
gines and  tests  made  I  am  yet  to  be  convinced  that  there  is  any  practical 
value  in  the  steam-jacket."  .  .  .  "  You  might  practically  say  that  there 
is  no  difference." 

Professor  "Schroter  from  his  work  on  the  triple-expansion  engines  at  Augs- 
burg, and  from  the  results  of  his  tests  of  the  jacket  efficiency  on  a  small 
engine  of  the  Sulzer  type  in  his  own  laboratory,  concludes:  (1)  The  value 
of  the  jacket  may  vary  within  very  wide  limits,  or  even  become  nega- 
tive. (2)  The  shorter  the  cut-off  the  greater  the  gain  by  the  use  of  a 
jacket.  (3)  The  use  of  higher  pressure  in  the  jacket  than  in  the  cylinder 
produces  an  advantage.  The  greater  this  difference  the  better.  (4)  The 
high  -pressure  cylinder  may  be  left  un  jacketed  without  great  loss,  but  the 
others  should  always  be  jacketed. 

The  test  of  the  Laketon  triple-expansion  pumping-engine  showed  a  gain 
of  8.3$  by  the  use  of  the  jackets,  but  Prof.  Denton  points  out  (Trans.  A.  .S 
M.  EM  xiv.  1412)  that  all  but  1.9$  of  the  gain  was  ascribable  to  the  greater 
range  of  expansion  used  with  the  jackets. 

Test  of*  a  Compound  Condensing  Engine  with  and  with- 
out Jackets  at  different  Loads.  (R.  C.  Carpenter,  Trans.  A.  S. 
M.  E.,  xiv.  428.)  —  Cylinders  9  and  10  in.x!4  in.  stroke;  112  Ibs.  boiler-pressure; 
rated  capacity  100  H.P.  ;  265  revs,  per  min.  Vacuum,  23  in.  From  the  results 
of  several  tests  curves  are  plotted,  from  which  the  following  principal  figures 
are  taken. 

Indicated  H.P  .........     30      40     50      60      70      80      90  100    110     120  125 

Steam  per  I.H.P.  per  hour: 

With  jackets,  Ibs  .....  22.6  21,4  20.3  19.6    19    18.7  18.6  18.9    19.5    20.4  21.0 

Without  jackets,  Ibs  ..............   22.    20.519.6  19.2  19.1     19.3    20.1  .... 

Saving  by  jacket,  p.  c  .............   10.9    7.3    4.6     3.1  1.0-1.0-1.5  .... 

This  table  gives  a  clue  to  the  great  variation  in  the  apparent  saving  due  to 
the  steam-jacket  as  reported  by  different  experimenters.  With  this  par- 
ticular engine  it  appears  that  when  running  at  its  most  economical  rate  of 
100  H.P.,  without  jackets,  very  little  saving  is  made  by  use  of  the  jackets. 
When  running  light  the  jacket  makes  a  considerable  saving,  but  when  over- 
loaded it  is  a  detriment. 

At  the  load  which  corresponds  to  the  most  economical  rate,  with  no  steam 
in  jackets,  or  100  H.P.,  the  use  of  the  jacket  makes  a  saving  of  only  \%\  but 
at  a  load  of  60  H.P.  the  saving  by  use  of  the  jacket  is  about  11$,  and  the 
shape  of  the  curve  indicates  that  the  relative  advantage  of  the  jacket  would 
be  still  greater  at  lighter  loads  than  60  H.P. 

Counterbalancing  Engines.—  Prof.  Unwin  gives  the  formula  for 
counterbalancing  vertical  engines: 


(1) 


in  which  W^  denotes  the  weight  of  the  balance  weight  and  p  the  radius  to 
its  centre  of  gravity,  W^  the  weight  of  the  crank-pin  and  half  the  weight  of 
the  connecting-rod,  and  r  the  length  of  the  crank.  For  horizontal  engines: 


to 


in  which  W3  denotes  the  weight  of  the  piston,  piston-rod,  cross-head,  and 
the  other  half  of  the  weight  of  the  connecting-rod. 

The  American  Machinist,  commenting  on  these  formulae,  says:  For  hori- 
zontal engines  formula  (2)  is  often  used;  formula  (1)  will  give  a  counter- 
balance too  light  for  vertical  engines.  We  should  use  formula  (2)  for 
computing  the  counterbalance  for  both  horizontal  and  vertical  engines, 
excepting  locomotives,  in  which  the  counterbalance  should  be  heavier. 


PERFORMANCES   OF   STEAM-ENGINES. 


789 


Preventing  Vibrations  of  Kngines.— Many  suggestions  have 
been  made  for  remedying  the  vibration  and  noise  attendant  on  the  working 
of  the  big  engines  which  are  employed  to  run  dynamos.  A  plan  which  has 
given  great  satisfaction  is  to  build  hair-felt  into  the  foundations  of  the 
engine.  An  electric  company  has  had  a  90-horse-power  engine  removed 
from  its  foundations,  which  were  then  taken  up  to  the  depth  of  4  feet.  A 
layer  of  felt  5  inches  thick  was  then  placed  on  the  foundations  and  run  up  2  feet 
on  all  sides,  and  on  the  top  of  this  thn  brickwork  was  built  up. — Safety  Valve. 

Steam-engine  Foundations  Embedded  in  Air.— In  the  sugar- 
refinery  of  Ulaus  Spreckels,  at  Philadelphia,  Pa.,  the  engines  are  distributed 
Cctic'ally  all  over  the  buildings,  a  large  proportion  of  them  being  on  upper 
rs.    Some  are  bolted  to  iron  beams  or  girders,  and  are  consequently 
innocent  of  all  foundation.    Some  of  these  engines  ran  noiselessly  and  satis- 
factorily, while  others  produced  more  or  less  vibration  and  rattle.    To  cor- 
rect the  latter  the  engineers  suspended  foundations  from  the  bottoms  of  ihe 
engines,  so  that,  in  looking  at  them  from  the  lower  floors,  they  were  literally 
hanging  in  the  air.—  Iron  Aqe,  Mar.  J3,  1890. 

Cost  of  Coal  for  Steam-power.— The  following  table  shows  the 
amount  and  the  cost  of  coal  per  day  and  per  year  for  various  horse-powers, 
from  1  to  1000,  based  on  the  assumption  of  4  Ibs.  of  coal  being  used  per  hour  . 
per  horse-power.  It  is  useful,  among  other  things,  in  estimating  the  saving 
that  may  be  made  in  fuel  by  substituting  more  economical  boilers  and 
engines  for  those  already  in  use.  Thus  with  coal  at  $3.00  per  ton,  a  saving 
of  $9000  per  year  in  fuel  may  be  made  by  replacing  a  steam  plant  of  1000 
H.P.,  requiring  4  Ibs.  of  coal  per  hour  per  horse-power,  with  one  requiring 
only  2  Ibs. 


Coal  Consumption,  at  4  Ibs. 

per  H.P.  per  hour  ;  10  hours  a 
day  ;  300  days  in  a  Year. 

$1.50. 

$2.00. 

$3.00. 

$4.00. 

'<L> 

1 

Lbs. 

Long  Tons. 

Short 
Tons. 

Per 
Short  Ton. 

Per 
Short  Ton. 

Pei- 
Short  Ton. 

Per 
Short  Ton. 

e 

o 

Cost  in 

Cost  in 

Cost  in 

Cost  in 

Dollars. 

Dollars. 

Dollars. 

Dollars. 

Per 

Per 

Per 

Per 

Pei- 

Day. 

Day. 

Year. 

Day. 

Year 

Per 

Pei- 

Per 

Per 

Per 

Per 

Per 

Per 

Day. 

Year 

Day. 

Year. 

Day. 

Year. 

Day. 

Year 

1 

40 

.0179 

5.357 

.02 

6 

.03 

9 

.04 

12 

.06 

18 

08 

24 

10 

400 

.1786 

53.57 

.20 

60 

.30 

90 

.40 

120 

.60 

180 

.80 

240 

35 

1,000 

.4464 

133.92 

.50 

150 

.75 

225 

1,00 

300 

1.50 

450 

2.00 

600 

50 

2,000 

.8928 

267.85 

1.00 

300 

1.50 

450 

2.00 

600 

3.00 

900 

4.00 

1,200 

75 

3,000 

1.3393 

401.78 

1  50 

450 

2.25 

675 

3.00 

900 

4.50 

1,350 

G.OO 

1,800 

100 

4,000 

1.7857 

535.71 

2.00 

600 

3.00 

900 

4.00 

1,200 

6.00 

1,800 

800 

2,400 

150 

6,000 

2.6785 

8<U  56 

3.00 

900 

4.50 

1,350 

6.00 

1,800 

9.00 

2,700 

12.00 

3,600 

200 

8,ooe 

3.5714  1,071.42 

4.00 

1,200 

6.00 

1,800 

8.00 

2,400 

12.00 

3,600 

16.00 

4,  8(10 

250 

10,000 

4.4642  1,339.27 

5.00 

1,506 

7.50 

2,250 

10.00  j     3,000 

15.00 

4,500 

20.00 

ii.  000 

300 

12,000 

53571  1.607.K! 

6.00 

1.XOO 

9.00 

2,700 

12.00 

3,600 

18.00 

5,400 

24.00 

7,200 

.350 

11,000 

6.2500 

1,874.98 

7.00 

2.100 

10.50 

3,150 

14.00 

4,200 

21.00 

6,200 

28.00 

8,400 

400 
450 

16,000 
18,000 

7.U2S 
8.0356 

2,142.84 
2,410.0'J 

8.00 
9.00 

'.MOO 
2,700 

12.00 

13.50 

3,600 
4,050 

16.00 
1800 

4,800 
5,400 

24.00 
27.00 

7,200 
8,100 

*•>.<«) 
3600 

9,600 
10,800 

500 
600 
700 

20,000 
24,000 
28,000 

8.9285 
10.7142 
12.4999 

2  .,678.55 
:'..->  If.-.T, 

:;,74'.i.'.i7 

10.00!  3,000 
12.00:  3,600 
14.00!  4,200 

15.00 

IS.  00 
21.00 

4,500 
5,400 
6,300 

20.00 
24.00 
28.00 

6,000 

7,200 
8,400 

30.00 
36.00 
42.00 

9,000 
10,800 
11,600 

40.00 
48.00 
56.00 

12,000 
14,400 
16,800 

800 

32,000 

14.2856 

4,285.68 

16.00!  4.800    24.00 

7,200 

32.00 

9,600 

48.00 

12,400 

64.00 

\\},->M 

900 

M.OOO 

16.0713 

4,821.39 

18.00    5,400 

27.00 

8,100 

36.00 

10,80t 

54.00 

14,200 

7-:\00 

•.'1.1,111! 

1,000 

40,000 

17.8570 

5,357.10 

20.00|  6,000 

30.00 

9,000 

40.00 

12,001 

60.00 

18,000 

80.00 

24.000 

Storing  Steam  Heat.— There  is  no  satisfactory  method  for  equalizing 
t  FiV  load  on  the  engines  and  boilers  in  electric-light  stations.  Storage-batteries 
have  been  used,  but  they  are  expensive  in  first  cost,  repairs,  and  attention. 
Mr.  Halpin,  of  London,'  proposes  to  store  heat  during  the  day  in  specially 
constructed  reservoirs.  As  the  water  in  the  boilers  is  raised  to  250  Ibs.  pres- 
sure, it  is  conducted  to  cylindrical  reservoirs  resembling  English  horizontal 
boilers,  and  stored  there  for  use  when  wanted.  In  this  way  a  comparativelv 
small  boiler-plant  can  be  used  for  heating  the  water  to  250  Ibs.  pressure  all 
through  the  twenty-four  hours  of  the  day,  and  the  stored  water  may  be 
drawn  on  at  any  time,  according  to  the  magnitude  of  the  demand.  The 


TUB    STKAAI.-B.X.MMS. 


steam-engines  are  to  be  worked  by  the  steam 
pressure  from:  this  water,  atr* tfog ^alv 


}  itlOl'1  3 
I  .P/IOOft  ' 


tioB  of  a  condensing  electric  light  engine  is  about  IS  Ibs. 
hour,  ^ueh-:a -reservoir  would  supply  286  effective  hot 
4878;  <JB  SZrahce,  this  method  of  storing  steam  was  i 
M.  Francq,  the  engineer,  designed  a  smokeless  locomotive t 
power  suppliedii)y  «  reBerv^l»<^^fahmigi  400 -gall 6n'S  '6f  \ra^ei "  at  220  Ihs. 
pressure:.  The  reservoir  Was  charged  with  steam  from  a  'stationary  boiler 
'ft*roae.end  of  the  tramway,     -jo-iq  WKI  &  ,» 

€ost<of  Steam-powfelV  (Chas?  T.  Main,  A.  ftVfy.  '$.,' x;  48.)--  Estimated 
costs  in  New  England  in  1888, per  horne-power,  based  tni  engines  of  10Q(JH..P. 

I  nioil  HI*> 

i-  ^MlW*^^^™1 

8..  f  |f  $f  S 

'     29.50 


4.  Total  engine  plant^S1^ 

5.  Depreciatioi)i^iM>y£e|tai-oofifttii<|  -m/ui.-ji 

6.  Repairs,  2^            "       "'       "     0.80  0.66 

7.  Interest,  5^           "       "       "     2.00  1.65 

8.  Taxation,  1.5$  on  %  cost 0.45  0.371 

9.  Insurance  on  engine  and  house 0.165  O.138 

10.  Total  of  lines  5.  6,  7,  8,  9 5.015  4.139  " 

11.  Cost  boilers,  feed-pump?,  etc..   .,/ 9.33     . ,  .     l$,m 

12.  Boiler-house... :.....................  2.92  4.17 

13.  Chimney  and  flues .• 6.11  7.30 

14.  Total  boiler-plant ; 18.36  24.80 

•  :   •                  •      ••  ;    _t  •     _ .   . 

15.  Depreciation,  5^  on  total  cost 0.018  l.«40 

16.  Repairs,  ••#•,      ..."       4>       #\    .  t . . . . .-.  -.-. 367,  .496 

17.  Interest,  S#           \\     *#        "    ... ; 918  1.240 

18.  Taxation,  1.5^  on  %  cost 207  .279 

19.  Insurance,  0.5$- on  total  cost. ...........  i-. .  >092  .121 

20.  Total  of  lines  15  to  19  ............  2.502:  3^379 

21.  Coal  used  per  I.H.P.  per  hour,  Ibs 1,75  2.50    n 

22.  Cost  of, , 'coal  'per  I.H.P.   per, day  of  10J4  cts.      •          cts. 

hours  at  $5,00  per  ton  of  2240  Ibs.... ...;  4.00  5.72 

23.  Attendance  of  engine  per  day. 0.60  0.40 

24.  "    ..,•;";. boilers   u       "' ,....  0.53  0.75 

25.  Oil,  wasteland*  supplies,  per  day 0;20  0.22 

26.  Total^aily  expense.;  l.J..... ....  5.38  7.09 


16JOO 
5.00 

8.-00 

29.  flO 


cts. 
6.86 
0.35 
0.90 

0.20 

8.31 


27.  Yearly  ruimitie   expense,  308  days,    per 

I.H.P $16.570 

28 ;  Totalyearly  expense,  lines  10.  20,;  and  27. ;     34.08T1 

21).  Total  yearly  expense  per  1,14  P.  for  power  >'•'"<>  l)ll-i' 
if  50^  of  exhaw.8t*s.featn  'is;  used  for  'heat-     ' r 
ing  .... .;;.  i    ... ...;......    ......     12:507' 

30.  Total  if  all  ex.-steam  fe  used  for  heating: . .  .    8,624 


When  ei'h'aust-steaiu  01;  a  part  of  the:rec, 
if  parr  of  the  steam  in  a  t'-on.'lensing  engine 
aijd  used  for*  other  purposes  than  power,  I 


$21.837 
'«&5- 


14:907 
7.916 


used  for  heating,  or 
the  condenser. 


K  GT  A  K  Y    ST  K  A  M  -  K  N  (4  1  NES. 
i     •  •  -'  .  •  -;  -irt-.XTz 


be  deducted  from  the  cost  of  the  total  amount  of  steam  generated,  in  order 
to  arrive  Mt  the  cost,  properly  chargeable  to  vpowbvja  (Fkw^fig»fes*ii4JrreSF29 
and  30  are  -based  •  on  ah  'assumption  "made  by  Mi4.  Main  of  losses  of  heat 
amounting:  to  ^%  between  the  boiler  and  the  exhAusfe-pipe,  an  allowance 
which  is  probably  too  large/'  :  'y  •"•'  "  • 
wannoTtag  '  .  val^rta  [Jt9if»ft<r£ 


Steam  Turbines.  -The  steam  turbine  is  a  small  t 
runs  with  steam  as  the  ordinary  turbine  does  with  water.     (For  description 


. 

of  the  Parson^MeiSJIovf  ^eaffiSfuAl^e^<ie«rfMfet^M3CJHaiaaism,  p.  298, 
etc.)  The  Parsons  turbine  is  a  series  of  parallel-flow  turbines  mounted  side 
by  side  OM  a  shaft;  the  Dow  iurbm»!i*d<serte9<<{»ffsar^iM  luteanb&liferiRBr- 
bines,  placed  like  a  series  tDf  'cbnesmtrie  rings  id  avshigM^iiaHairaTSfeationar^ 
guide-ring  being-  between  ea«lr  pair  ofnn^otvabflefirfnjgsx^^The^enids:  pf  the 
steam  turbines  '«normoti8ly  exceed  throve  of.  •aiaw-fo'Mm  of  ^g^ae^vith  reeip- 
rocating'pistonv  ov  evfeii  of.  foh&^w-esdled  ••notdry.et^nesy.'Vbeftteref^-  and  four- 
cylinder  engines  of  the  >Brothe#liaekF%:f»,r  **f  wT&iali  'fehe<  SEveral  cylinders 
are  usually  grouped  radiaHy  aboait  a^beoiJi^ir^ra^t'aTidisiiafe^s©ffeen  exce-edt 
1000  revolutions  per  -minute,'  and  haven  toe«sai  «MrveiiiMiexperini6tttaVly>^bovie> 
2000;  but  the  ste^nKti^bifief  oft  Parsori«>i¥[ak0s  l^^OOftiaiidjGPeji  20;QOO  ,revolu*  , 
tiotis;  and1  -the  t)0w  -tt*f  bine  ^i^fepute*  tx»  bjame  ajkafa  wb£&,00&)  K'Seei  Tran  Si. 
A.  S.  M.  E.t  vol.  x;  p.-g80,  and  xii.  f>.  88S;  Toransi  f  Atfsbot  ^ftiEng^g  Societies, 
-  '  ' 


' A;  I>ow  turbine; __._.._-„__.     ._„„,____ 

H.P.-;with  a  consumption  of  47  Ibs. •  of  •  geeaifopeirffivPypeavhonr^-the  teteam- 
pressure  being  70  Ibs".  ;The~ •••Dmr^iirbtft'ftftB  ofeedMsaisqoiiKfc&e,  tiy£iwheek*!f  the 
He-well  torpedo.  Tlie  dimensions  of  the  wheel  are  13.8  in.  diam..  GJ»ia:^ 
width,,  radius  of  gyration  5.57  in.  The  energy  stored  in  it  at  10,000  revs. 

per  mini  is  500,000  ftUlbs.        -Oi  £{  oi  $*     TOWOffol  1O  e^onft  !<>•  Jw^jnfolrfT 

The  De  'Laval  tite<a>i  Tttfbf'ni*,'  'shown  at  the-'  Clhicago  eihibition, 
1893,  is  a  reaction  wheel  somewhat  similar  to  the  Pelton  water-wheel.  The 
steam  jet  is  directed  by  a ,  nozzie  against,  r,Re^i];uiiHif^iJ* TwrtflMWtlplilOa 
small  angle  and  tafi^eiiiiallv  against  ttht^ciremnfeTBBee^oiJ  the]  niediuiri: 


The  steam  is  expati^defd  td'tlie  pf essttJ-e  of;  th^- swrrorindlngs  ^before? 
ing  at  the  b Fades.  This  expansion  takes  place; ii&  fche  iio^gle<.andt  is  <^u^ed 
sirtt^ly  by  making-its  sides  diverging.  As  the  steam  passes  through  this 
jhanriel  its  specific  volumes  increased  in  a  greater  proportion ; -than .  .the.- 
cross  section  of  the  channel,  and  for;  this  reason  its  velocity  is  increased,' 
ah'd  also  its  momentum,  till- the  end  of  theF  expansion  at  the  last  sectional 
az--ecK>f,the.^.^le..  The  greater  the^expansion  iu  the(,n«?^.the?g;;eater  jts 
velocity  at, tins  point.  A  pressure  of  *u  lbs.:  and  expansion  to  an  absolute 
pressure  of  one.  atmosphere  give  a  final  velocity  of  a.b«>ut  ^1\!5  ft.  per  second. 

Expansion  is  carried  further  in  this  steaui. turbine,  than  in  ordinary  steairi- 
ftU'gines.    This  is, ©n, account , of  the  steam  expanding  completely  during  it? 


j,, -^ 

periphery— as  h;igh  a/s>1300  to  1050  ft.  per,  second.  "The  centrifugal  force, 
'VAV^rtJBLel^sa,  ^Ujts^iimjfr  tt»,the  use  of  .ve.-y  lii.u'h  vtJoci&ie^.  In  the  5  horse- 
power turbine  the  velocity  of  periphery  'is  574  ft.  per  second, .ai>d  the^uum- 
i»er\of .TqwAtfltois  mm  mr  «^fif|tft,  ^^d  TObqHvp  io  Jai^OT.to  M  , 
(.  Hqwever  qarefully  the  turbine, may  be.  manufactured,  it  i,s  iun>ossiblev  on 
nccount  of  unevenness  of  the  material,  to  get  its  "centre  or  gravity  to  corre- 
spond exactly  to  its  geometrical  axle\o£  vf volution;  and  however  small  this 
difference  nray-be,  it  becomas<^ery  ^ojiceatofe-ati^ieb^liigh  falQeitiesk  l>e 
Laval  has  succeeded  in  solving  the  pmbfem  by  providing  the  turbine  with  a 
(tle-xible  shaft.  This  yielding  shaft  allows  the  turbine  at  the,. high  rate  of 
speed  to' adjust 'itself  and  revolve  around  its -Hrafe  ^eH^F^o'f  gravity,  the 
centre  line  of  the  shaft  meanwhile  describing  a  suvface  pf  revolution. 

In  the  gearing-box  the  s,peed  is  ivdiuj.'d  fr'om  '30.000  revolutions  >t&mti' 
by  means  of  a  driver  on  the  turbine  shafts,  which  sets  in  Hiotion "a  cog- 
wheel of  10  times  its  own  dlarmeter.  -'Therfe'  gearings  af'e  provided  with  spiral 
i»ogs  placed  at  an  angle  of  about  45°.  The  shaft  of  the  larger  cog-wheel,, 
running  at  a  speed  of  3000  revolutions,  is  provided  at  its  outer  end  with  a 
'  ransmission  of  the  power 


792  THE   STEAM-ENGINE, 

Rotary  Steam-engines,  other  than  steam  turbines,  have  been 
invented  by  the  thousands,  bm  not  one  has  attained  a  commercial  success. 
The  possible  advantages,  such  as  saving  of  space,  to  be  gained  by  a  rotary 
erg-ine  are  overbalanced  by  its  waste  of  steam. 

The  Tower  Spherical  Engine,  one  of  the  most  recent  forms  of 
rotary-engine,  is  described  in  Froc.  Inst.  M.  E.,  1885,  also  in  Modern 
Mechanism,  p.  296. 

DIMENSIONS  OF  PARTS  OF  ENGINES. 

The  treatment  of  this  subject  by  the  leading  authorities  on  the  steam-en- 
gine is  very  unsatisfactory,  being  a  confused  mass  of  rules  and  formulae 
based  partly  upon  theory  and  partly  upon  practice.  The  practice  of  builders 
shows  an  exceeding  diversity  of  opinion  as  to  correct  dimensions.  The 
treatment  given  below  is  chiefly  the  result  of  a  study  of  the  works  of  Rankine, 
Seaton,  Unwin,  Thurston,  Marks,  and  Whitham,  and  is  largely  a  condensa- 
tion of  a  series  of  articles  by  the  author  published  in  the  American  Ma- 
chinist, in  1894,  with  many  alterations  and  much  additional  matter.  In  or- 
der to  make  a  comparison  of  many  of  the  formulas  they  have  been  applied 
to  the  assumed  cases  of  six  engines  of  different  sizes,  and  in  some  cases 
this  comparison  has  led  to  the  construction  of  new  formulae. 

Cylinder.  ( Whitham. )— Length  of  bore  =  stroke  +  breadth  of  piston- 
ring  —  y&  to  %  in;  length  between  heads  =  stroke  -f  thickness  of  piston  4- 
sum  of  clearances  at  both  ends;  thickness  of  piston  =  breadth  of  ring  -f- 
thickness  of  flange  on  one  side  to  carry  the  ring  +  thickness  of  follower- 
plate. 

Thickness  of  flange  or  follower —    %  to  ^  in.          %  in.  1  in. 

For  cylinder  of  diameter 8  to  10  in.  36  in.  60  to  100  in. 

Clearance  of  Piston*  (Seaton.)— The  clearance  allowed  varies  with 
the  size  of  the  engine  from  %to%  in.  for  roughness  of  castings  and  1/16  to 
J/6  in.  for  each  working  joint.  Naval  and  other  very  fast-running  engines 
have  a  larger  allowance.  In  a  vertical  direct-acting  engine  the  parts  which 
wear  so  as  to  bring  the  piston  nearer  the  bottom  are  three,  viz.,  the  shaft 
journals,  the  crank-pin  brasses,  and  piston-rod  gndgeon-brasses. 

Thickness  of  Cylinder.  (Thurston.) — For  engines  of  the  older 
types  and  under  moderate  steam-pressures,  some  builders  have  for  many 
years  restricted  the  stress  to  about  2550  Ibs.  per  sq.  in. 

t  =  aPlD  +  b (1) 

is  a  common  proportion;  £,  D,  and  b  being  thickness,  diam.,  and  a  constant 
added  quantity  varying  from  0  to  ^  in.,  all  in  inches;  px  is  the  initial  unbal- 
anced steam-pressure  per  sq.  in.  In  this  expression  b  is  made  larger  for 
horizontal  than  for  vertical  cylinders,  as,  for  example,  in  large  engines  0.5 
in  the  one  case  and  0.2  in  the  other,  the  one  requiring  re-boring  more  than 
the  other.  The  constant  a  is  from  0.0004  to  0.0005:  the  first  value  for  verti- 
cal cylinders,  or  short  strokes;  the  secor»d  for  horizontal  engines,  or  for 
long  strokes. 
Thickness  of  Cylinder  and  its  Connections  for  marine 

Engines.     (Seaton). — D  =  the  diam.  of  thec3'linder  in  inches;  p  —  load  on 

the  safety-valves  in  Ibs.  per  sq.  in.;  /,  a  constant  multiplier  =  thickness  of 

barrel  4-  .25  in. 
Thickness  of  metal  of  cylinder  barrel  or  liner,  not  to  be  less  than  p  x  D  -*- 

3000  when  of  cast  iron.* (2) 

Thickness  of  cylinder-barrel  =  -         •  4.-  0.6  in (3) 

"  liner  =  1.1  X/. (4) 

Thickness  of  liner  when  of  steel  p  X  D  •*•  6000  4-  0.5 
metal  of  steam-ports          =0.6    X  /. 
"        valve-box  sides    =0.65X./. 

*  When  made  of  exceedingly  good  material,  at  least  twice  melted,  the 
thickness  may  be  0.8  of  that  given  by  the  above  rules. 


DIMENSIONS   OF   PARTS   OF   ENGINES. 


793 


Thickness  of  metal  of  valve-box  covers  =  0.7    X  /. 

"  "       cylinder  bottom  =  1.1    X /,  if  single  thickness. 

"     =  0.65  X  /,  if  double 

'*  "  "        covers  =  1.0    X/,  if  single         " 

=  0.6    x/,  if  double       " 


cylinder  flange 

cover-flange  = 
"  valve-box  "  = 
"  door- flange  = 
"  face  over  ports  = 

"       false-face 


. 

X/. 
X/ 

x/. 
x/. 


X  /,  when  there  is  a  false-face. 
=  0.8    X  /.  when  cast  iron. 
=  0.6    X  /,  when  steel  or  bronze. 


Whitham  gives  the  following  from  different  authorities: 


VanBuren-^0-00012^0-15^ & 

'  I  t  =  0.03  VDp (6) 


Tredgold  :     t  =  l- 


1900 


Weisbach:     t  =  0.8  4-  0.00033pl>. 
Seaton  :          £  =  0.5  4-  0.0004pZ). 


(7) 

(8) 

(9) 

TTaswoll  •     j*  =  0.0004pD+^(vertical); (10) 

'     {£  =  0.0005pZ>4-  ^(horizontal) (11) 

Whitham  recommends  (6).  where  provision  is  made  for  the  reboring,  and 
where  ample  strength  and  rigidity  are  secured,  for  horizontal  or  vertical 
cylinders  of  large  or  small  diameter;  (9)  for  large  cylinders  using  steam 
under  100  Ibs.  gauge- pressure,  and 

t  =  0.003D  l/p  for  small  cylinders (12) 

Marks  gives  t  =  0.00028pD (13) 

This  is  a  smaller  value  than  is  given  by  the  other  formulae  quoted;  but 
Marks  says  that  it  is  not  advisable  to  make  a  steam -cylinder  less  than  0.75 
in.  thick  under  any  circumstances. 

The  following  table  gives  the  calculated  thickness  of  cylinders  of  engines 
of  10,  30,  and  50  in.  diam.,  assuming  p  the  maximum  unbalanced  pressure  on 
the  piston  =  100  Ibs.  per  sq.  in.  As  the  same  engines  will  be  used  for  calcu- 
lation of  other  dimensions,  other  particulars  concerning  them  are  here 
given  for  reference. 


DIMENSIONS,  ETC.,  OP  ENGINES. 


Engine  No  

1  and  2. 

3  and  4. 

5  and  6. 

Indicated  horse  -power  I.H 

p 

50 
10 
1     ....        2 

450 
30 
2^6     ....       5 
130      ...     65 
650 
706.86 
32.3 
70,686 
100 

1250 
50 
4     ....       8 
90     ....     45 
700 
1963.5 
30 
196,350 
100 

Diam.  of  cyl.,  in    

D 

T 

Stroke,  feet.  

Revs,  per  min  

T 

A 

250     ...       125 
500 
78.54 
42 
7854 
100 

Piston  speed,  ft.  per  min  

Area  of  piston,  sq.  in  a 
Mean  effective  pressure  M.E.P. 
Max.  total  unbalanced  press  P 
Max.  total  per  so.  in.  .              .  .  .» 

ftfK^K&S.<$f  b^  'OvfciKmcR      t 


THE    STO A  M-K'N  ( 1 1  N"  M. 
\'<    -7.fi- 


5  arid  0. 


(1)  .0004pDsrf-  0.5;  short,  stroke  Jl  ' 
(1)  .OOOSpD  +  0.5V  'loiiW  ^trdke  .  .?.  . 
(2)  .00033pZ>  . 

1?00 

1.70  1, 

2.QO 

agoo 

1  67 

(3)  .0002p7)-h0.6  ;....... 

'^80''  ''   ! 

/•>">     J     JQ 

1.460 

(5)  .0001p7)-}-.15  I/D  

.57 

/IjRW 

1^56 

(6)  .03  y'Dp  ;...        i 

•->«t  ]  6f 

GO 

•i  1  71' 

2-'/7G 

{  '      i9oo;;;^      •';•••*••'  ; 

1.13 

1.79 

2  45 

(9)  .0004pD  -f-  0  5 

90 

•  ,    •  I-  70 

I*]     TS-iSO^ 

(10)  .0004pD  +  ^  (vertical)     

.53 

1.33 

2.13 

(^  .OOOopD  -}-  y%  (hor^qntat)  .  ,  .  .  , 

1.63 

2.63 

(i-a  .003D  |7p  (small  engines)  A 

(  1  M  \      nOffOftri  Tf               

•^kj 

•  ''•'•'.'.•:.•  ^ 

n  '^'^'' 

.84(?) 

1.40(?) 

Averaige"  of  fir  st'eleven  ,   

.76 

-__j  Ji  

2.26 

•  •  O^ie  ^ae*  -tf  or  mit)£U  <^3»r«8powLlaof  es  «>*gn»ileJ^nehg:^h  'of  'e'ast  ir 

vff  »%r 
w»<ty! 


thickness,  at  the  edges  and  in  the 
cylinder.  Ati  excess  of  not  less  than  25#  is  usual  It  may  be  thinner  in  the 
middle^  Where  ma(^^JW^WtW»  ^Sf  <en«WOB,^fUwo  disks  with  inter- 
i^diate  radjainig,  connecting  ribs  or  ftofa*  ^slmt  se^rjwi  ,  WhMi  is  safe 
against  shearing  is  probably  ample.  An  examination  of  the  designs  of 
experienced  builders,  by  Professor  Thurston,  gave, 

;nwojup  aNtiftfRn  I»MJO  WMjm  n«-»vr^  pflTwnJ  BUI  i 

^  £.  4^fefu  ai  fk^wl^ixa  ?<>n  KI  Ji  i«iJsi  f  fi?x  «^-ijBf< 
~  3000  ^^'-  .!-7n,':i  .-,MM-;M:    ,-       '-'     i'      '      ' 

D  being  fcl>e  diaineterloMhatitrfifdl^nis^iMtthuttile  Uiwl^ndssJs  takwi. 

Thurstonnlsoi;ives  r     •  .•«OSt)*JlliuO!Wl.E    "."*'.'  J  -     -     - 

\,     .       .'•  i  ,       v'u-*^1^7'     -ni  .pa  ibq  .«dl  (Iftl       iioteiq«d1 

Mark^giMt^jij  feAdWM|^iJo  .vi<f>i  -ir.-ti.i'     •    .-  .-     -    uoiJw 

He  also  says  a  good  practical  rule  for  pressures  under  lOfrfrisYper  Hf}!.  fnVfs 
to  make  tlie  thickness  of  the  cylinder-heads  1J4  times  that  of  the  walls;  and 
applying  this  factor  toa^tlf,pi;p^ila  ,fpy  tj^^kjiesf?  ,<j>f  walls,  or  .000£8p/>,  we 
have 

.     (4) 

,,,; 
;    (5) 


is  equal  to  .-OGOSpD  +  .  25  inch-.- 


Whitb^m  quote* 

t-U 

*Xjg|  ,  ,  .    . 

Season's  forjmula  0ST  cylinder  bottoms,  qpoted  above,  is     a\    i ,  -;  jo   !XiBiu 
/  =  l.lAifi(Vhich/^V0002p7)4-  .85Jwbh,  or  /  =  .00(»22;)Z)  -|-'vr»3.     .     («) 
'  Apnlwing^he1  aboy^ .forniiila^  to.tUe  ehgiibes  of  10.  30,  and  5p  iiv^lie's  diame- 
ter, with. maximum  Jun balanced  steam-i^ssure  of'tOO'lbs.  t>er  s<j.  in..  \ve 


have  ijl 


ind,er  diarneter,  |n,ches  =?, 5    iff 

(1)  f  ^JoOOSsU^-f-  '^          ^'      -53  1.25':n  M.Hf-r 

(2)  <  =  .0057)  V'p  +  .25       'a       .75  1.75  2.75 

(3)  <  =  .003D  Vp  =      -30          .90  1.50 

(4)  *  =  .000357)p  =       .35  1.05  1.75 

(5)  f  =  .OOOSDw  4-  .25          =       .75  1.75  2.75 

(6)  t  =  .0002-Wp  +  .93         =1.15  1.59  2.03 

Averageof6 65  1.38  2.10 


DIM 


^  ot]  ENGINES. 


The  average  is  exp 
Meyer's  "Modern 
cylinder-heads  for 


For  diameters,  In  .  . 
Thickness,  in...  ...:•. 


ed  by  ;t  h  (?  formula  ^'.O 
ocomouve  Construction,11  p.  2 


:.-ai  ^iijt 

16  to  l&j  *»»  $4*tp  15 
1       anh-anfjfo& 

t  Atm 


.   '.31  inch.' 

.ves  for  locomotive 


11  to  13*      9  to  10 


..  .      . 

Taking  the  pressure  -.at  120  Ibs.  per-,$cjiiirc.^tbfe  thicknesses  1*4  inland  %  in. 
for  cylinders  28  ancfc/iO  in.  diatu.^  -?r^paqt  lively  v'^oferespond  to  the  formula 
t  -  .00035  Dp  -KaSaiiMjhw  ^m  ^uJ->.««|  )<>  ilUmwf  odT 

Web-stiffened*  eylinder-covers.^Seaton,;  objec^i->tei)^et)s  for 
stiffening  cast-iron  ,uyMnder-  covers  asja>souiMS«K)s§<diaagfec,  .(The  Qtiiain'  on 
the  web  is  one  of  tension,  >a*8d  ;ifi]tb)WeijS^Uld-dbe^  niek  or  defiio^in  the 
outer  edge  <  of  the  web/  the  sudden  appliGatiefli^of^sti'aiin  jig  japt  (to*  start  a 
crack.  He-Be®oJEB«tteiwis  that  high-pressure  cylinders  over  24  iw,  -awd  low- 
pressui'e  c5rlindBEs^>\'^p  4£)  in.  diam.  should^jjaveitheiKJ^overs  east  hollow, 
with  two  thicknes«e83o6  metal.  The  depth  of  the  cover  at  the^aidldle  should 
be  about  J4  the  diam.  of  the  piston  for  pressures  of  80  Ibs.  and  upwards, 
and  that  o£J,he  Jpw^pr^^s^^^j^d^iv^p^^p^  a  ^ftm^und,engine  equal-to 
that  of  l^^teh,pr^^m-PYiinc}evKr>?4potHt3r;  rule  js  t.o  make,  the  deptl;;  at 
the  middle  not  les^.th^a  ^,4;iimes-,th^  dimeter  of  tke  .  pisOon-rod.  In  the 
British  Nav^sWq^lind^rKCO^i^iare  nuul^  of,.  steejl  castings,  %  tip  -.1J4  in. 
tlii^k,  geper^y  cast  ^it^ujti.w^s,  ^iff;n^s§;b«i;]g,^Uta,me4  by,  their  foru»? 
which  is  of.t,$n  a,  s^ritts-jof,  GpRr^gaftipp^,  ,,,,,,,  bhjori  . 

Cyliii^er-lie^A  WoUsi^rt^iaW^^^,  feoit^ir^le,  fqv  cyjjnder-head  = 
diameter  of  cylinder  +  2  X  thickness  of  cylinder  -f  2  X  diajmQta?  ,-Qf  >  bolts. 
The  bolts  should  not  be  more  than  6  iuclios  apart  (Whitham). 

Marks  gives  for  nurnber'of  bolts  b  =  "—  =  .Oodis?!—  —  ,  in  which  c  "— 


area  bf  -ftj»iqgie  feol<J,}lpjrf:I\)oiler-pressure  in  Ibs.  persq.  in.;  5000  Ibs.  is  taken 
as  the  safe  strain  per  sq.  in.  on  the  nominal  area  of  the  bolt. 

Seaton  ;^ays:  Cylinder-cover  studs  and  -bolts,  4Wfeft*:nia$ei  of^  ^tfeel,  should 
bu  of  sudlt  aA  size  "tba£  the  ^rain-  in  them-does  noftfecteed'SOOO  Ibs,  pel'  s<j.  in. 
When  offers  thari%*inch  diameter  ir,«h0uL*^bt  exceed  4500  Ibsr*  >pe¥'&i?to. 
When  of  won  the  strain  should-  be  «  U-  >  rf-ibjsvid 

Tliurstmi  says  :  'Cylinder  flanges-  are  ma$e  a  mtte  thicker  than  the  'cylin- 
der, and  usually  of  equal  thickness  with  the  flanges  of  the  heads.  Cylinder- 
bolts  should  be  'so-  closely  Spal'-*daiS*ribt*t^  alto\v-st>rfcigi  ' 

and  leakage,  say, 


*f»<$0*^&^0ft,»^£^»lfcfl 
snzbtif)  ^  atbiyr  mil  ba«  ;d'Mfi^»  -4 


. 

80.  4-  JH»    H 

in.  by  tbe  formula, 

of  poirsible.overstrain 


•druetlou  of  Ordinary  Pis- 

r  of  iu'e  pinion  in  inches.  /.>  the  eftVc- 
>i!8tant  multiplier,  found  as  follows: 


ut'tiou  ol  Ordinary  Pis- 

1)1  '  '  '  ""  •*  ~ •  *  •-'       ** 

c,,n 

•\'p  4-  t. 


796  THE   STEAM-ENGINE. 

The  thickness  of  front  of  piston  near  the  boss  =0.2    X  X 

**       rim    =  0.17  X  x. 
back  =0.18  xx. 

boss  around  the  rod  =0.3    XX. 

flange  inside  packing-ring         =  0.23  X  x. 
"       at  edge  =  0.25  X  x. 

packing-ring  =  0.15  X  x. 

junk-ring  at  edge  —  0.23  X  x. 

"         inside  packing-ring  .—  0.21  X  x. 
"         at  bolt-holes  =  0.35  X  x. 

metal  around  piston  edge          =  0.25  x  x. 
The  breadth  of  packing-  ring  =  0.63  X  x. 

depth  of  piston  at  centre  =1.4    X  «. 

lap  of  junk-ring  on  the  piston  =  0.45  X  x. 

space  between  piston  body  and  packing-ring  =0.3    X  x. 
diameter  of  junk-ring  bolts  =0.1    X  x  -f  0.25  in. 

pitch  =  10  diameters. 

number  of  webs  in  the  piston  =  (D  -f-  20)  H-  12. 

thickness  =  0.18x#. 


4. 

Marks  gives  the  approximate  rule:   Thickness  of  piston  -head=  \^ld,  in 
hich  I  =  length  of  stroke,  and  d  =  diameter  of  cylinder  in  inches.    Whit- 


rea        o    rng-ace  sou      never  excee  s.  per  sq.   n.        e  aso  gves 

a  formula  much  used  in  this  country:  Breadth  of  ring-face  =  0.15  X  diam- 


For our  engines  we  have  diameter  .=  ..............         10  30  50 

Thickness  of  piston  -head. 

Marks,    |/TD;  long  stroke....-  ....................  3.31  5.48  7.00 

Marks,      "    ;  short  stroke  .......................  3.94  6.51  8.32 

Seaton,  depth  at  centre  =  I  Ax  .................  4.30  9.80  15.40 

Seaton,  breadth  of  ring  =  .68?  ..................  1.89  4.41  6.93 

Whitham,  breadth  of  ring  =  .15D  ........   .......  1.50  4.50  7.50 

Diameter  of  Piston  Packing-  rings.  —  These  are  generally 
turned,  before  they  are  cut,  about  J4  inch  diameter  larger  than  the  cylinder, 
for  cylinders  up  to  20  inches  diameter,  and  then  enough  is  cut  out  of  the  ring 
to  spring  them  to  the  diameter  of  the  cylinder.  For  larger  cylinders  the 
rings  are  turned  proportionately  larger.  Seaton  recommends  an  excess 
of  \%  of  the  diameter  of  the  cylinder. 

Cross-section  of  the  Rings.—  The  thickness  is  commonly  made 
l/30th  of  the  diam.  of  cyl.  -f-  V&  inch,  and  the  width  =  thickness  -f-  V&  inch. 
For  an  eccentric  ring  the  mean  thickness  may  be  the  same  as  for  a  ring  of 
uniform  thickness,  and  the  minimum  thickness  =  %  the  maximum. 

A  circular  issued  by  J.  H.  Dunbar,  manufacturer  of  packing  -rings, 
Youngstown,  O.,  says:  Unless  otherwise  ordered,  the  thickness  of  rings  will 
be  made  equal  to  ."03  X  their  diameter.  This  thickness  has  been  found 
to  be  satisfactory  in  practice.  It  admits  of  the  ring  being  made  about  3/16" 
to  the  foot  larger  than  the  cylinder,  and  has,  when  new,  a  tension  of  about 
two  pounds  per  inch  of  circumference,  which  is  ample  to  prevent  leakage 
il  the  surface  of  the  ring  and  cylinder  are  smooth. 

As  regards  the  width  of  rings,  authorities  "  scatter  "  from  very  narrow  to 
very  wide,  the  latter  being  fully  ten  times  the  former.  For  instance,  Unwin 
gives  W  =  d  .014  -f  .08.  Whitham's  formula  is  W  =  d  .15.  In  both  for- 
mulae W  is  the  width  of  the  ring  in  inches,  and  d  the  diameter  of  the  cylinder 
in  inches.  Unwinds  formula  makes  the  width  of  a  20"  ring  W  =  20  X  .014 
-f-  .08  =  .36",  while  Whitham's  is  20  X  .15  =  3"  for  the  same  diameter  of 
ring.  There  is  much  less  difference  in  the  practice  of  engine-builders  in  this 
respect,  but  there  is  still  room  for  a  standard  width  ot  ring.  It  is  believed 
that  for  cylinders  over  16"  diameter  %"  is  a  popular  and  practical  width, 
and  y^'  for  o  vlinders  of  that  size  and  under. 

Fit  of  Piston-rod  into  Piston.  (Seaton.)—  The  most  convenient 
and  reliable  practice  is  to  turn  the  piston-rod  end  with  a  shoulder  of  1/1C 
inch  for  small  engines,  and  V£  inch  for  large  ones,  make  the  taper  3  in.  to 


DIMENSIONS   OF    PARTS   OF   ENGINES.  7U7 


the  foot  until  the  section  of  the  rod  is  three  fourths  of  that  of  the  body,  then 
turn  the  remaining  part  parallel;  the  rod  should  then  fit  into  the  pi.ston  sc 
as  to  leave  y%  inch  between  it  and  the  shoulder  for  large  pistons,  and  1/16  in. 
for  small.  The  shoulder  prevents  the  rod  from  splitting  the  piston,  and 
allows  of  the  rod  being  turned  true  after  long  wear  without  encroaching  on 
the  taper. 

The  piston  is  secured  to  the  rod  by  a  nut,  and  the  size  of  the  rod  should 
be  such  that  the  strain  on  the  section  at  the  bottom  of  the  thread  does  not 
exceed  5500  Ibs.  per  sq.  in.  for  iron,  7000  Ibs.  for  steel.  The  depth  of  this  nut 
need  not  exceed  the  diameter  which  would  be  found  by  allowing  these 
strains.  The  nut  should  be  locked  to  prevent  its  working  loose. 

Diameter  of  .Piston-rods.—  Unwin  gives 


d"  =  bD  \^>, 


in  which  D  is  the  cylinder  diameter  in  inches,  p  is  the  maximum  unbalanced 
pressure  in  Ibs.  per  sq.  in.,  and  the  constant  b  =  0.0167  for  iron,  and  b  = 
0.0144  for  steel.  Thurston,  from  an  examination  of  a  considerable  number 
of  rods  in  use,  gives 


(L  in  feet,  D  and  d  in  inches),  in  which  a  =  10,000  and  upward  in  the  various 
types  of  engines,  the  marine  screw  engines  or  ordinary  fast  engines  on 
iihore  giving  the  lowest  values,  while  li  low-speed  engines"  being  less 
liable  to  accident  from  shock  give  a  —  15,000,  often. 

Connections  of  the  piston-rod  to  the  piston  and  to  thecrosshead  should 
have  a  factor  of  safety  of  at  least  8  or  10.  Marks  gives 

d"  =  0.0179D  Vp,  for  iron;    for  steel  d"        -  0.0105D  Vp;  .    .    (3) 

4   , 4 

and  d"  •-  0.03901  y DH^p,  for  iron;    for  steel  d"  =  0.03525  |/D2Z2p,      (4) 

in  which  I  is  the  length  of  stroke,  all  dimensions  in  inches.  Deduce  the 
diameter  of  piston-rod  by  (3),  and  if  this  diameter  is  less  than  1/121,  then  use 
(4). 

Diameter  of  cylinder     ,_ 
Seaton  gives:  Diameter  of  piston-rod  =  —         — ^ —          -  yp. 

The  following  are  the  values  of  F: 

Naval  engines,  direct-acting F  —  60 

"  return  connnecting-rod,  2  rods F  =  80 

Mercantile  ordinary  stroke,  direct-acting F  =  50 

long  F  -  48 

very  long  "  F  =  45 

medium  stroke,  oscillating F  =  45 

NOTE. — Long  and  very  long,  as  compared  with  the  stroke  usual  for  the 
power  of  engine  or  size  of  cylinder. 

In  considering  an  expansive  engine  p,  the  effective  pressure  should  be 
taken  as  the  absolute  working  pressure,  or  15  Ibs.  above  that  to  which  the 
boiler  safety-valve  is  loaded ;  for  a  compound  engine  the  value  of  p  for  the 
high-pressure  piston  should  be  taken  as  the  absolute  pressure,  less  15  Ibs., 
or  the  same  as  the  load  on  the  safety-valve;  for  the  medium-pressure  the 
load  may  be  taken  as  that  due  to  half  the  absolute  boiler-pressure-  and  for 
tho  low-pressure  cylinder  the  pressure  to  which  the  escape-valve  is  loaded 
-\-  15  Ibs.,  or  the  maximum  absolute  pressure,  which  can  be  got  in  the  re- 
ceiver, or  about  25  Ibs.  It  is  an  advantage  to  make  all  the  rods  of  a  com- 
pound engine  alike,  and  this  is  now  the  rule. 

Applying  the  above  formulae  to  the  engines  of  10,  30,  and  50  in.  diameter, 
both  short  and  long  stroke,  we  have: 


THE   STEAM-ENGINE* 


Diameter  of  Piston-rods. 


Diameter  of  Cylinder,  inches  ... 

U 

.-    3C 

5< 

> 

Stroke,  inches  ...  ........./ 

12 

*\  '•'• 

'SO' 

60' 

48'  '' 

03 

Unwin,  iron,  .0167Z)  \('p<  .      ..„. 

1.67 

1  07 

'  5  01 

5  01  ' 

8  35 

8  35 

Uuwin,  steel,  MUD  I  p....  .......,- 

1.44 

1.44  : 

,4.32: 

7.20 

7.20 

Thurston  ^™^-Hi4t^-.  (£  in  feet). 

Thurston,  same  with  a  =  15,000  
•Marks  iron    j0179D|i>           ••     .**••• 

1.13 

»    i  -  !  8  « 

1.40 

f'».'12' 

3.88 

5.10 

6.35 

Marks,  iron,  .03901  ^D^Fp  ,  ,  .  ..  ..  . 

1.79 

1.35 

yftl 

5.37 

5.37 

8.95 

8.95 

:I8.54 

Marks,  steel,  .0105  //  \'p  V.^.f1.1:^ 
Marks,'  steel,  5)35'25  VlWp  '......  

Seaton,  naval  engines,  —  V«  .  .  .  ft  .  ... 

1.22 



1.73 

1 

3.34^- 



*iw 

lit  iii  & 
8  35 

...... 

•7:72 

,    .    .    .    .      6Qi  r  ^  • 
Seaton,  land  engine,  •—  A/n 

? 

,    fmi 

•.m',;.' 

V    :':..' 

r\'.'r  -.'-' 

'  Average  of  cf  bur  ^f'oi*  iron            .     ... 

'  I  '  j" 

•i  '  «•) 

i       '  .  !  • 

.  -    '  u  >   -. 

(J3 

; 

1  •  .82  , 

f' 

5,26 

,7.11 

8.74 

?iston-rod  Guides.— The  thrust  on,  the  euide^when  the,conneptu)eT 

I  is  at  its  maximum  a.iffle  with  tile;  line  of  the  pistn.i-HHl,.  iy  found^rom 
:  formula:  Thrust •=  total  It^d'bti^il^iV'x 'taifgent  of  m^^^  angle 


The  figures  in  brackets  opposite  ''Marks'  third  formula  would  pe'  rejected 
since  they  are  less  than  >£  of  the  stroke.  '  aiicl  the  figures  denVed  by  his 
fourth  formula  \vould  be  taken  instead.  The  figure  1.79  opposite  his  first 
formula  would  h^rejected.fpr,  thp  engine  of  ^iucj)  ^trttlw/.  .u  -i; 

An  empirical'  f  orrimla  which  gives  results  approximating  the  above  aver- 
ages is  d"  =  .013  VDlp. 

The  Calculated  vesults  frbimUhisifo 
tively,  1.42,  1.88,  3.90,  5.01,  0.37,  9.01. 

pi 

the  formula:  Thrust  =  total  It^cl'bti^i^ 

of  connecting-rod  =  p  tan  0.     This  angle,  0,  is  the  angle  whose  sine  =  half 

stroke  of  piston  •**  lengtlt  !0ifiicon  necting-rod. 

Ratio  of  'length  of  cofmecting-rod  to  stroke.'  ---- 

Maximum  angle  of  connecting-rod  with  line  of 
piston-rod  .............................   :.,v.i.  >! 

Tangent  of  the  angle  ............................  258 

Secant  of  tl^angle  .....................  .  ;  .  .  .  .  .)    1^082?  ' 

SeatoiTsays:  The  area  of  the  y,-uide-\)Jock  or  si  jppep,  surface,.  on  which  the 
thrust  i§,  taken  should  in  no  case  be  less  than  will  adnjiifyof  a  pressure  of  400 
Ibs.  on  the  square  inch;  and  for  good  working  thp,&e  surfaces  which  take  the 
thrust  when  going  ahead  should  b^.sqfficjen^y  larg^.^u  prevent  the  maxi- 
mum pressure  exceeding  lOOlbs.  per  sq.  in.  When  the  surfaces  are  kept 
well  lubricated  this  allowance  may  b;e  exceeded.  ; 

Thurston  say's:  The  rubbing  surfaces  of  guides  ai-e^so  proportioned.  that 
if  Fbe  their  relative  velocity  in  .feet  per  minute,,,  an/lp  be  the'  intensity  of 
pressure  on  the  guide  in  Ibs.  per  sq.  in.,  p.  V  <  .)50i,QQO  ^and  p  V  >  4Q.OOO. 

The  lower  is  the  safer  limit;  bin  for  marine  and  statiqnary  engines.it  is 
owable  to  'take  p  '=  60,000-^  F.  According  to  Eankine,  for  locomotives, 


2^ 


.204 
1.0206  ' 


.169 
1.014 


allow 


44800 
p  —  __,  —  -—y  where  p  is  Ihe  :press(m'6  in1  Ibs.  per  sq\  in.  and  V  the  velocity  of 

rubbing  in  feet  pe,r  minute.  ,:  This  includes.  tl*e  sum  of  all  -pressures  forcing 
the  two  rubbing  surfaces  together.  »; 

Some  British  builders  of  portable  engines  restrict  the  pressure  between 
the  guides  and  cross-heads  to  less  than  40,  sometime^  >35  Ibs",  per  square  inch. 

For  a  mean  velocity  of  0<)0  feet  per  ininute.  Prof.  Thurston's  formulas 
give,  p  <  100,  p  >  60.7;  Rankine's  gives-jy  •==  72,2  ibs.  per  sq.  in. 


I)  I  M  K  N  ft  1  0  N  »S   U  F    L!  A  J  ITS   O  F    If  N  G  IN  ES.  7  D  9 

Whitham  gives,  &l^  ^t(\-\t.  r'^,  (\  •  ^rr 

''A=  area  of  slides  in  square  inches  =  _— 

,a 

in  :  which  P 
our  piston,  i 


says:  The  normal  pressure  on  the  slide  may  be  as  high  as  500  Ibs.  per  sq.  in., 
but  this  is  when  tlia^'te*g»0$fcl*»4fceHfc)*i  tadfMa&Mlllfcai  dust.  Station- 
ary and  marine  engines  are  usually  designed  to  carry  100  Ibs.  per  sq.  in., 


and  tjie  area  in  th,i,s  caselis  reduced  fitorn  50#  to  M%  by. 

tive  engines  ithe  pressure!  range's  frorri  40  10  50  Itfs.  persq.  TO.  '-of  'slide,  on  ac- 
count of  the!  inaccessibility  of  the  slide,  dirt,  cinder,  etc. 
There  is  perfect  agreeineftt  am^hgithe  authorities  -as  to  the  "formula  for 
of  the  slidek,  A''*=  P  fil'h  Q  •*"•?;<)  I  but  -tlie  va^l^  igSVeto>tO'^,!  *he  allo^- 


,  ,  , 

able  pressure  per  square  linch,  ranges  all  the  way  from  35  Ibs.  to\500  Ibs. 
The  €dnit«Ctittgiif<idJ   \Bfrtlo\  of-  length  */  ^^kecti^-rod  to  tenyth 


of  stroke.—  Experience  has  led  generally  to  the  ratio  of  2  or  2%  to  1,  the 
latter  giving  a  longhand  easy-w^rkpib  rpd,.thefprmer(ajfra\tib[qr)  short,  but 
yet  a  manageable  one  (Tliurstow).  Wtitham  gives  the  ratio  of  from  2  to  414, 
and  'Marks  from  2  io  4.  II.  8  "r  -*\  i  \^\  ^^r,\ 

Dimensions  of  tfie  Connect  iny-rofy  —  The  calculation  of  the  diameter  of 
a  connecting-rod  on  a  fh-eoretic^bfisiSj  considewng  .\t{as<a  ^tf  utj  subj^ctito 
both  compressive  and  bending  jsiresses,  and  also  to  stress  due  to  its  inertia, 
in  ,  high-spe0d  ;  /engines,  is  fturte  complicated.  See  Whitham^  8team-epgiitie 
Design,  p.  211  :  Thurston,  Manual  of  S.  E.,  p.  100.  Empirical  formulas  are  as 
follows?  For,  cfi-ouiari-ods.  lai-ges-c'at  the  middle,  D  .=  diam^df  Cylinder,  /  .'*= 
length  of  cohnectiiig-rod  in  ,incl)e^,  p  ±=  inaxijnum^teani-pres(sur,e  per  sq.  in. 


(1)  Whitham,  diamf  at  middle,  d"^  0.0272  V  Dl  Vp. 

(2)  Whitham,  diam.  at  necks,  d"  -  1.0  to  1.1  x  diam.  of  piston-rod. 

-  * 


'  '•••••'  :';  Ifp&Myt         -    ••  ' 

/4ian%^at;ii«cl^i.d^^rar,r  #P*    I  a  .vt-xl  ittfttuiiib  (n 

•  •  '  '     •  _       •>••     Mill*  ItfW    "ic>>'      b^i"rxjtM 

;  (5)  Marks,:  diam.,  di';-.=»  .-O^OlTaB^pHf^diana.  sis  greater  .than  ,1/34  length.  ; 

:0)  toks,  diam./^,  =,5,02^ 
1/24  length., 

-f'  C7,  '/)  ih^imJlies;'  L  in 

nd  C''=  ^-inch-foy  faSt^ngtoe^,1^  i:0.08'a'rtdiO  ±h  %  inch  for 
moderate  speeid/!  : 

(T(^S.®esbMn,Q§^^(  Th«mod)  may.  be  considered  as  a  strut  free  at  both  ends, 
atid  i,  '  paletilaJbiB^i  i  tfe  dilaip  0e  r  accord  in  gly  , 

A  'f>(]  "-L  4  a?'"*)  ^ 
l<  »  J  ;  -,  diameter;  at.  middle  »=  !     ^'W8"'3'  bwi~a*»  **'>•">  ?*»»<>'> 

4y"-?..  ;      L  ;          t\ 

'tHito'lP  l±irtti6*tdValfi6ift!l'  bti  rp1^drt'^fttlilt?ip(FiM  ttftH^  ^ae^arit'O*  theimaxi^ 
mum  angle  of  obliquity  of  the  connecting-rod.  f>«  v^uwoe»aoo'j 

fitFby^i%fg-Ti!t  iron  ahti  iniy'it^F^i^takeb'afrl-'/SOOO'/'i  Ttte^followiug^re 

tfef  v^oe«  of  r  in  practice:        ^fiod  J«  l>-,i  , 

;f'K^val  'engines-ftifoct-actlMg  ;'  ^y^-«t^ll; 

^   i     ;B^tm-n  bOn'nb^itjg^rdd  '  y^  -^  i!»to  '13rold: 
1    "    '•••  ii.f^^iii    to  .."  r  -  8   to^9i    moidern; 

"  «*  "'  iHT>lifaki;  r  =  l'1.5-to'I3: 


. 

Mercantile"  '    '^D^ect^ctm^,  'dMinary1  -'f  =!12: 
»IL  - 


loiig  slirdk«  r  =  18  to  16. 

.;••-.     i  •   .  :      ......:-.;.;:      i    -.  .   : 

(9)  The  following  empirical  formula  is  igiven:  by  Se-aton  as  agreeing  closely 

WfithigoxDd  modieif  a/  practice  t  i 
Diameter  of   cortriectlrig-rM^ate  mirldle  -  \'J'K-^  4,  /  -  -i  length  of  rod  in 

inches,  and  ^=  O.OJJ  ^ejective  l^ad  on  piston  in  pounds^ 


800 


THE    STEAM-ENGINE. 


The  diam.  at  the  ends  may  be  0.875  of  the  diam.  at  the  middle. 

Beaton's  empirical  formula  when  translated  into  terms  of  D  andp  is  the 

same  as  the  second  one  by  Marks,  viz.,  d"  -  0.02758  V  Dl  \f^>.  Whitham's 
(1)  is  also  practically  the  same. 

(10)  Taking  Beaton's  more  complex  formula,  with  length  of  connecting 
rod  =  2.5  X  length  of  stroke^and  r  =  12  and  16,  respectively,  it  reduces  to: 
Diam.  at  middle  =  .02294  yp  and  .02411  yp  for  short  and  long  stroke  en- 
gines, respectively. 

Applying  the  above  formulas  to  the  engines  of  our  list,  we  have 

Diameter  of  Connecting-rods. 


Diameter  of  Cylinder,  inches  

1 

o 

g 

o 

5 

o 

St  roke,  inches  

12 

24 

30 

60 

48 

96 

Length  of  connecting-rod  1  

30 

60 

75 

150 

120 

240 

(3)  d"  -  —  Vp  ~  .0182Z)  Vp  

1  82 

1  82 

5  46 

5  46 

9  09 

9  09 

(5)  d"  —  .0179D  yp       

1  79 

5.37 

8.95 

(6)  d"  =  .027584/Dl  \'p  

2.14 

5.85 

9.51 

(7)  d"  =  0.154/DZ,  Vp  -f  y%  

2.87 

7.00 

11.11 

(7)  d"  =  0.081/D.L  j/p  +  94  
(9)  d"  -  .03  yiP.  

2.67 

2.54 
2.67 

7  97 

5.65 
7  97 

13  29 

8.75 
13  29 

HO)  d"  =  .02294  1/P;  .02411  VP.  

2.03 

2.14 

6.09 

6.41 

10.16 

10.68 

Average  

2.24 

2.26 

6.38 

6.27 

10.52 

10.26 

Formulae  5  and  6  (Marks),  and  also  formula  10  (Seaton),  give  the  larger 
diameters  for  the  long-stroke  engine;  formulae  7  give  the  larger  diameters 
for  the  short-stroke  engines.  The  average  figures  show  but  little  difference 
in  diameter  between  long- and  short-stroke  engines;  this  is  what  might  be 
expected,  for  while  the  connecting-rod,  considered  simply  as  a  column, 
would  require  an  increase  of  diameter  for  an  increase  of  length,  the  load 
remaining  the  same,  yet  in  an  engine  generally  the  shorter  the  connecting- 
rod  the  greater  the  number  of  revolutions,  and  consequently  the  greater  the 
strains  due  to  inertia.  The  influences  tending  to  increase  the  diameter 
therefore  tend  to  balance  each  other,  and  to  render  the  diameter  to  some 
extent  independent  of  the  length.  The  average  figures  correspond  nearly 
to  the  simple  formula  d"  =  .021Z>  1/p.  The  diameters  of  rod  for  the  three 
diameters  of  engine  by  this  formula  are,  respectively,  2.10,  6.30,  and  10.50  in. 
Since  the  total  pressure  on  the  piston  P  —  ,7854D2jp,  the  formula  is  equiva- 
lent to  d'  =  .0237  yp. 

Connecting-rod  Ends.— For  a  connecting-rod  end  of  the  marine 
type,  where  the  end  is  secured  with  two  bolts,  each  bolt  should  be  propor- 
tioned for  a  safe  tensile  strength  equal  to  two  thirds  the  maximum  pnll  or 
thrust  in  the  connecting-rod. 

The  cap  is  to  be  proportioned  as  a  beam  loaded  with  the  maximum  pull 
of  the  connecting-rod,  and  supported  at  both  ends.  The  calculation  should 
be  made  for  rigidity  as  well  as  strength,  allowing  a  maximum  deflection  of 
1/100  inch.  For  a  strap-and-key  connecting-rod  end  the  strap  is  designed  for 
tensile  strength,  considering  that  two  thirds  of  the  pull  on  the  connecting- 
rod  may  come  on  one  arm.  At  the  point  where  the  metal  is  slotted  for  the 
key  and  gib,  the  straps  must  be  thickened  to  make  the  cross-section  equal 
to  that  of  the  remainder  of  the  strap.  Between  the  end  of  the  strap  and  the 
slot  the  strap  is  liable  to  fail  in  double  shear,  and  sufficient  metal  must  be 
provided  at  the  end  to  prevent  such  failure. 

The  breadth  of  the  key  is  generally  one  fourth  of  the  width  of  the  strap, 
and  the  length,  parallel  to  the  strapj  should  be  such  that  the  cross-section 
will  have  a  shearing  strength  equal  to  the  tensile  strength  of  the  section  of 
the  strap.  The  taper  of  the  key  is  generally  about  %  inch  to  the  foot. 


DIMENSIONS   OF   PARTS   OF   ENGINES. 


801 


Tapered  Connecting-rods.— In  modern  high-speed  engines  it  is 
customary  to  make  the  connecting-rods  of  rectangular  instead  of  circular 
section,  the  sides  being  parallel,  and  the  depth  increasing  regularly  from 
the  crosshead  end  to  the  crank-pin  end.  According  to  Grashof,  the  bending 
action  on  the  rod  due  to  its  inertia  is  greatest  at  6/10  the  length  from  the 
crosshead  end,  and,  according  to  this  theory,  that  is  the  point  at  which  the 
section  should  be  greatest,  although  in  practice  the  section  is  made  greatest 
at  the  crank-pin  end. 

'Professor  Thurston  f urnishes  the  author  with  the  following  rule  for  tapered 
connecting-rod  of  rectangular  section:  Take  the  section  as  computed  by  the 

formula  d"  —  O.lVDL  Vp  +  3/4  for  a  circular  section,  and  for  a  rod  4/3  the 
actual  length,  placing  the  computed  section  at  2/3  the  length  from  the  small 
end,  and  carrying  the  taper  straight  through  this  fixed  section  to  the  large 
end.  This  brings  the  computed  section  at  the  surge  point  and  makes  it 
heavier  than  the  rod  for  which  a  tapered  form  is  not  required. 
Taking  the  above  formula,  multiplying  L  by  4/3,  and  changing  it  to  I  in 

inches,  it  becomes  d  =  1/30  V Dl  Vp  -f-  3/4".  Taking  a  rectangular  section 
of  the  same  area  as  the  round  section  whose  diameter  is  d,  and  making  the 
depth  of  the  section  h  =  twice  the  thickness  t,  we  have  .7854d2  =  ht  =  2£2, 

whence  t  -  .627<2  =  .0209  V Dl  \/p  -f-  .47",  which  is  the  formula  for  the  thick- 
ness or  distance  between  the  parallel  sides  of  the  rod.  Making  the  depth  at 
the  crosshead  end  =  1.5£,  and  at  2/3  the  length  =  2£,  the  equivalent  depth  at 
the  crank  end  is  2.25J.  Applying  the  formula  to  the  short-stroke  engines  of 
our  examples,  we  have 


Diameter  of  cylinder,  inches  

10 

30 

59 

12 

30 

48 

30 

75 

120 

Thickness,  t  —  .0209  ty'  Dl  \/p  -f-  .47  -  

1  61 

8.60 

5  59 

Depth  at  crosshead  end,  1  5t  —  

2  42 

5  41 

8  39 

Depth  at  crank  end,  2%t  

3.62 

8.11 

12  58 

The  thicknesses  t,  found  by  the  formula  t  =  .0209  \  Dl  \/p  -f-  .47,  agree 
closely  with  the  more  simple  formula  t  =  .01D  \/p  -f-  .60",  the  thicknesses 
calculated  by  this  formula  being  respectively  1.6,  3.6,  and  5.6  inches. 

The  Crank-pin.— A  crank-pin  should  be  designed  (1)  to  avoid  heating, 
(2)  for  strength,  (3)  for  rigidity.  The  heating  of  a  crank-pin  depends  on  the 
pressure  on  its  rubbing-surface,  and  on  the  coefficient  of  friction,  which 
latter  varies  greatly  according  to  the  effectiveness  of  the  lubrication.  It  also 
depends  upon  the  facility  with  which  the  heat  produced  may  be  carried 
away:  thus  it  appears  that  locomotive  crank-pins  may  be  prevented  to  some 
degree  from  overheating  by  the  cooling  action  of  the  air  through  which  they 
pass  at  a  high  speed. 


Marks  gives  I  =  .0000247  fpND*  =  1.038/ 


(I.H.P.) 


Whitham  gives  I  =  0.9075/ 


(LH.P.) 


0) 
(2) 


In  which  I  =  length  of  crank-pin  journal  in  inches,  f  —  coefficient  of  friction, 
which  may  be  taken  at  .03  to  .05  for  perfect  lubrication,  and  .08  to  .10  for  im- 
perfect; p  =  mean  pressure  in  the  cylinder  in  pounds  per  square  inch;  D 
—  diameter  of  cylinder  in  inches;  N  =  number  of  single  strokes  per  minute; 
I.H.P.  =  indicated  horse-power;  L  —  length  of  stroke  in  feet.  These 
formulae  are  independent  of  the  diameter  of  the  pin,  and  Marks  states  as  a 
general  law,  within  reasonable  limits  as  to  pressure  and  speed  of  rubbing, 
the  longer  a  bearing  is  made,  for  a  given  pressuve  and  number  of  revolutions, 
the  cooler  it  will  work ;  and  its  diameter  Las  no  effect  upon  its  heating. 
Both  of  the  above  formulae  are  deduced  empirically  from  dimensions  of 
crank-pins  of  existing  marine  engines.  Marks  says  that  about  one-fourth 
the  length  required  for  crank-pins  of  propeller  engines  will  serve  for  the  pins 
of  side-wheel  engines,  and  one  tenth  for  locomotive  engines,  making  the 


802  THE   STEAM-ENGINE. 

formula  for  locomotive  crank-pins  I  =  .00000247  fpND*.  or  if  p  =  i50,  / 
=  .OS,  and  N  =  600.  I  =  .013D2. 

Whitham  recommends  for  pressure  per  square  inch  of  projected  area,  for 
naval  engines  500  pounds,  for  merchant  engines  400  pounds,  for  paddle-wheel 
engines  800  to  900  pounds. 

Thurston  says  the  pressure  should,  in  the  strain-engine,  never  exceed  500 
or  600  pounds  per  square  inch  for  wrought-iron  pins,  or  about  twice  that 
figure  for  steel.    He  gives  the  formula  for  length  of  a  steel  pin,  in  inches, 

I  =  PR  -H  600,000,       .......    ,.    .     (3) 

in  which  P  and  R  are  the  mean  total  load  on  the  pin  in  pounds,  and  the 
number  of  revolutions  per  minute.  For  locomotives,  the  divisor  may  be 
taken  as  500,000.  Where  iron  is  used  this  figure  should  be  reduced  to  300,000 
and  250,000  for  the  two  cases  taken.  Pins  so  proportioned,  if  well  made  and 
well  lubricated,  may  always  be  depended  upon  to  run  cool;  if  not  well 
formed,  perfectly  cylindrical,  well  finished,  and  kept  well  oiled,  no  crank-pin 
can  be  relied  upon.  .It  is  assumed  above  that  good  bronze  or  white-metal 
bearings  are  used. 

Thurston  also  says  :  The  size  of  crank  -pins  required  to  prevent  heating  of 
the  journals  may  be  determined  with  a  fair  degree  of  precision  by  either  of 
the  formulae  given  below  : 


PV 


PAT 
I  =     =-       (Van  Buren,  1866)  ........    (6) 


The  first  two  formulae  give  what  are  considered  by  their  authors  fair  work- 
ing proportions,  and  the  last  gives  minimum  length  for  iron  pins.  (V  ~ 
velocity  of  rubbing-surface  in  feet  per  minute.) 

Formula  (1)  was  obtained  by  observing  locomotive  practice  in  which  great 
liability  exists  of  annoyance  by  dust,  and  great  risk  occurs  from  inaccessi- 
bility while  running,  and  (2)  by  observation  of  crank-pins  of  naval  screw- 
engines.  The  first  formula  is  therefore  not  well  suited  for  marine  practice. 

Steel  can  usually  be  worked  at  nearly  double  the  pressure  admissible  with 
iron  running  at  similar  speed. 

Since  the  length  of  the  crank-pin  will  be  directly  as  the  power  expended 
upon  it  and  inversely  as  the  pressure,  we  may  take  it  as 

I.H.P. 
I  =  «—  7—  ,  ...........    (7) 

j_/ 

in  which  a  is  a  constant,  and  L  the  stroke  of  piston,  in  feet.  The  values  of 
the  constant,  as  obtained  by  Mr.  Skeel,  are  about  as  follows:  a  =  0.04  where 
water  can  be  constantly  used;  a  =  0.045  where  water  is  not  generally  used; 
a  =  0.05  where  water  is  seldom  used;  a  =  0.06  where  water  is  never  needed. 
Unwin  gives 

(8 


in  which  r  =  crank  radius  in  inches,  a  =  0.3  to  a  =  0.4  for  iron  and  for  marine 
engines,  and  a  =  0.066  to  a  =  0.1  for  the  case  of  the  best  steel  and  for  loco- 
motive work,  where  it  is  often  necessary  to  shorten  up  outside  pins  as  much 
as  possible. 

J.  B.  Stanwood  (Eng^g,  June  12,  1891),  in  a  table  of  dimensions  of  parts  of 
American  Corliss  engines  from  10  to  30  inches  diameter  of  cylinder,  gives 
sizes  of  crank-pins  which  approximate  closely  to  the  formula 

I  =  .2757)"  +  .Bin.;    d  =  ,25Z>"  ........     (9) 

By  calculating  lengths  of  iron  crank-pins  for  the  engines  10.  30,  and  50  inches 
diameter,  long  and  short  stroke,  by  the  several  formulee  above  given,  it  is 
found  that  there  is  a  great  difference  in  the  results,  so  that  one  formula  in 
certain  cases  gives  a  length  three  times  as  great  as  another.  Nos.  (4),  (5),  and 
(6)  give  lengths  much  greater  than  the  others.  Marks  (1),  Whitham  (2), 
Thurston  (7),  I  =  .06  I.H.P.  -s-  L,  and  Unwin  (8),  I  =  0,4  I.H.P.  -*-  r,  give  re- 
sults which  agree  more  closely. 


DIMENSIONS   OF    PARTS   OF    ENGINES. 


803 


The  calculated  lengths  of  iron  crank-pins  for  the  severaf  cases  by  formulae 
CO,  (2),  (7),  and  (8)  are  as  follows: 

Length  of  Crank-pins. 


Diameter  of  cylinder  D 

10 
1 
250 
50 

7,854 
42 
3,299 

2.18 
2  59 

s'.oo 

3.33 
2.50 

10 
2 
125 

50 

7.854 
42 
3,299 

1.09 
1.30 
1.50 
1.67 
•i.25 

30 

450 
70,686 
32.3 
22,832 

8.17 
9.34 
10.80 
12.0 
9.0 

30 
5 

65 
450 
70,686 
32.3 
22,832 

4.08 
4.67 
5.40 
6.0 
4.5 

50 
4 
90 
1,250 
196,350 
30 
58,905 

14.18 
16.22 
18.75 
20.83 
15.62 

50 

8 
45 
1,250 
196,350 
30 
58,905 

7.09 
8.11 
9.38 
10.42 
7.81 

Stroke                             L  (ft.) 

Revolutions  per  minute                        R 

Horse-power                    I.H.P 

Maximum  pressure                            Ibs 

Mean  pressure  per  cent  of  max  
Mean  pressure      P. 

Length  of  crank-pin 

(1)  Whitham,  1  =  .9075  X  .05  I.H.P.  -*-  L. 
(2)  Marks,       1  =  1.038  X  .05  I.H.P.  -5-  L. 
(7)Thurston,  1=  .06  I.H.P.  -i-L  
(8)  Unwin        Z  =  4IHP  —  r 

(8)        "            1—  3IH.P  -*-  r  

Average  

2.72 

1.36 

9.86 

4.93 

17.12 

8.56 

(8)  Unwin  best  steel  1       ji—  —l£j 

.83 
1.37 

.42 

.69 

3.0 
4.95 

1.5 
2.47 

5.21 

8.84 

2.61 
4.42 

(^  Thiir<;ton    ^trol        I 

The  calculated  lengths  for  the  long-stroke  engines  are  too  low  to  prevent 
excessive  pressures.  See  "  Pressures  on  the  Crank-pins,"  below. 

The  Strength  of  the  Crank-pin  is  determined  substantially  as  is 
that  of  the  crank.  In  overhung  cranks  the  load  is  usually  assumed  as 
c.-irried  at  its  extremity,  and,  equating  its  moment  with  that  of  the  resist- 
ance of  the  pin, 

%Pl  =  1/32M3,    and    d  =  //5^, 

in  which  d  =  diameter  of  pin  in  inches,  P  =  maximum  load  on  the  piston, 
t  =  the  maximum  allowable  stress  on  a  square  inch  of  the  metal.     For  iron 
it  may  be  taken  at  9000  Ibs.    For  steel  the  diameters  found  by  this  formula 
may  be  reduced  10%.    (Thurston.) 
Unwin  gives  the  same  formula  in  another  form,  viz.: 


the  last  form  to  be  used  when  the  ratio  of  length  to  diameter  is  assumed. 
For  wrought  iron,  t  —  6000  to  9000  Ibs.  per  sq.  in., 


¥  =  .004! 


to  ;0827 


4-  =  .0291  to  .0238. 


For  steel,  t  -  9000  to  13,000  Ibs.  per  sq.  in., 


=  .0827  to  .0723;       A =  .0238  to  .0194. 

t  y      t 


Whitham  gives  d  =  0.0827  |/PZ  =  2.1058. 


X  I.H.P. 
LR 


for  strength,   and 


d  =  0.405  V  P/3  for  rigidity,  and  recommends  that  the  diameter  be  calculated 
by  both  formulae,  and  the  largest  result  taken.  The  first  is  the  same  as 
Un win's  formula,  with  t  taken  at  9000  Ibs.  per  sq.  in.  The  second  is  based 
upon  an  erroneous  assumption. 


804 


THE    STEAM-ENGIXE. 


Marks,  calculating  the  diameter  for  rigidity,  gives 
d  =  0.066  \/pl*D*  =  0.945 


p  =  maximum  steam-pressure  in  pounds  per  square  inch,  D  —  diameter  of 
cylinder  in  inches,  L  =  length  of  stroke  in  feet,  N=  number  of  single  strokes 
per  minute.  He  says  there  is  no  need  of  an  investigation  of  the  strength  of 
a  crank-pin,  as  the  condition  of  rigidity  gives  a  great  excess  of  strength. 

Marks's  formula  is  based  upon  the  assumption  that  the  whole  load  may  be 
concentrated  at  the  outer  end,  and  cause  a  deflection  of  .01  inch  at  that 
point. 

It  is  serviceable,  he  says,  for  steel  and  for  wrought  iron  alike. 

Using  the  average  lengths  of  the  crank-pins  already  found,  we  have  the 
following  for  our  six  engines  : 

Diameter  of  Crank-pins. 


Diameter  of  cylinder  

10 

10 

30 

30 

50 

50 

Stroke  ft        

1 

2 

2^ 

5 

4 

8 

Length  of  crank-pin  

o  72 

1  36 

9  86 

4  93 

17  1° 

8  56 

3  /  5.1PZ 
TJnwin   (j  —  A  /  • 

2  29 

1  82 

7  34 

5  82 

12  40 

9  84 

Marks    d-  066  typl*D*  

1  39 

.85 

6.44 

3.78 

12  41 

7.39 

ing  angle  of  the  connecting-rod,  we  have  the  following,  using  the  averag 
lengths  already  found,  and  the  diameters  according  to  Unwin  and  Marks: 


Engine  No  

1 

0 

3 

4 

5 

6 

Diameter  of  cylinder,  inches  

10 

10 

30 

30 

50 

50 

Stroke  feet 

1 

2 

iy> 

5 

4 

8 

Mean  pressure  on  pin  pounds  

3.299 
6.23 

3,299 
236 

22,832 
72.4 

22,832 
28.7 

58,905 
212.3 

58,905 
84.2 

Projected  area  of  pin,  Unwin  

"      "     "     Marks  

3.78 

1.16 

63.5 

18.6 

212.5 

63.3 

Pressure  per  square  inch,  Unwin  
Marks  

530 

873 

1.308 
2i845 

315 
360 

796 
1,228 

277 

277 

700 
930 

The  results  show  that  the  application  of  the  formulae  for  length  and  diam- 
eter of  crank-pins  give  quite  low  pressures  per  square  inch  of  projected 
area  for  the  short-stroke  high-speed  engines  of  the  larger  sizes,  but  too  high 
pressures  for  all  the  other  engines.  It  is  therefore  evident  that  after  calcu- 
lating the  dimensions  of  a  crank-pin  according  to  the  formulae  given  that  the 
results  should  be  modified,  if  necessary,  to  bring  the  pressure  per  square 
inch  down  to  a  reasonable  figure. 

In  order  to  bring  the  pressures  down  to  .500  pounds  per  square  inch,  we 
divide  the  mean  pressures  by  500  to  obtain  the  projected  area,  or  product 
of  length  by  diameter.  Making  I  =  1.5d  for  engines  Nos.  1,  2,  4  and  6,  the 
revised  table  for  the  six  engines  is  as  follows  : 


Engine,  No 

Length  of  crank- pin,  inches. . . . 
Diameter  of  crank-pin 


12345  6 

...  3.15    3.15    9.86    8.37    17.12    13.30 
2.10    2.10    7.34    5.58    12.40      8.87 


Crossheacl-pin  or  Wrist-pin, — Whitham  says  the  bearing  surface 
for  the  wrist-pin  is  found  by  the  formula  for  crank-pin  design.  8eaton  says 
the  diameter  at  the  middle  must,  of  course,  be  sufficient  to  withstand  the 
bending  action,  and  generally  from  this  cause  ample  surface  is  provided  for 
good  working;  but  in  any  case  the  area,  calculated  by  multiplying  the  diam- 
eter of  the  journal  by  it's  length,  should  be  such  that  the  pressure  does  not 
exceed  1200  Ibs.  per  sq.  in.,  taking  the  maximum  load  on  the  piston  as  the 
total  pressure  on  it. 

For  small  engines  with  the  gudgeon  shrunk  into  the  jaws  of  the  connect- 


DIMENSIONS  OF   PARTS  OP  ENGINES.  805 

ing-rod,  and  working  in  brasses  fitted  into  a  recess  in  the  piston-rod  end  and 
secured  by  a  wrought- iron  cap  and  two  bolts,  Seaton  gives: 

Diameter  of  gudgeon  =  1.25  X  diam.  of  piston-rod. 
Length  of  gudgeon  =  1.4  X  diam.  of  piston-rod. 

If  the  pressure  on  the  section,  as  calculated  by  multiplying  length  by 
diameter,  exceeds  1200  Ibs.  per  sq.  in.,  this  length  should  be  increased. 

J.  B.  Stanwood,  in  his  "Ready  Reference1'  book,  gives  for  length  of 
crosshead-pin  0.25  to  0.3  diarn.  of  piston,  and  diam.  =  0.18  to  0.2  diam.  of 
piston.  Since  he  gives  for  diam.  of  piston-rod  0.14  to  0.17  diam.  of  piston, 
his  dimensions  for  diameter  and  length  of  crosshead-piu  are  about  1.25  and 
1 .8  diam.  of  piston-rod  respectively.  Taking  the  maximum  allowable  press- 
ure at  1200  Ibs.  per  sq.  in.  and  making  the  length  of  the  crosshead-pin  = 
4/3  of  its  diameter,  we  have  d  =  |/ P-s-40,  I  =  \f~P  •*•  30,  in  which  P  =  max- 
imum total  load  on  piston  in  Ibs.,  d  =  diam.  and  I  =  length  of  pin  in  inches. 
For  the  engines  of  our  example  we  have: 

Diameter  of  piston,  inches 10  30  50 

Maximum  load  on  piston,  Ibs 7854  70,686  196,350 

Diameter  of  crosshead-pin,  inches 2.22  6.65  11.08 

Length  of  crosshead-pin,  inches 2.96  8.86  14.77 

Stanwood^  rule  gives  diameter,  inches 1.8to2  5.4  to  6  9.0    to  10 

Stanwood's  rule  gives  length,  inches 2. 5  to  3  7. 5  to  9  12.5  to  15 

atanwood's  largest  dimensions  give  pressure 

per  sq.  in.,  Ibs  1309  1329  1309 

Which  pressures  arc  greater  than  the  maximum  allowed  by  Seaton. 

Tlie  Crank  -arm . — The  crank-arm  is  to  be  treated  as  a  lever,  so  that 
if  a  is  the  thickness  in  direction  paraLel  to  the  shaft-axis  and  b  its  breadth 
at  a  section  x  inches  from  the  crank-pin  centre,  then,  bending  moment  M 
at  that  section  =  Px,  P  being  the  thrust  of  the  connecting-rod,  and  /  the 
safe  strain  per  square  inch, 

fab*         ,     a  X  62        T  6!F 

Px  =  ^— - —    arid    — 2 —   -  -7,     or    a  =       ^  -;    6  = 


If  a  crank-arm  were  constructed  so  that  6  varied  as  Vx  (as  given  by  the 
above  rule)  it  would  be  of  such  a  curved  form  as  to  be  inconvenient  to  man- 
ufacture, and  consequently  it  is  customary  in  practice  to  find  the  maxi- 
mum value  of  b  and  draw  tangent  lines  to  the  curve  at  the  points  ;  these 
lines  are  generally,  for  the  same  reason,  tangential  to  the  boss  of  the  crank- 
arm  at  the  shaft. 

The  shearing  strain  is  the  same  throughout  the  crank-arm;  and,  conse- 
quently, is  large  compared  with  the  bending  strain  close  to  the  crank -pin  ; 
and  so  it  is  not  sufficient  to  provide  there  only  for  bending  strains.  The 
section  at  this  point  should  be  such  that,  in  addition  to  what  is  given  by  the 
calculation  from  the  bending  moment,  there  is  an  extra  square  inch  for 
every  8000  Ibs.  of  thrust  on  the  connecting-rod  (Seaton). 

The  length  of  the  boss  h  into  which  the  shaft  is  fitted  is  from  0.75  to  1 .0 
of  the  diameter  of  the  shaft  D,  and  its  thickness  e  must  be  calculated  from 
the  twisting  strain  PL.  (L  =  length  of  crank.) 

For  different  values  of  length  of  boss  h,  the  following  values  oi'  thickness 
of  boss  e  are  given  by  Seaton: 

When  h  =  Z>,  then  e  =  0.35  D;  if  steel,  0.3. 
h  =  0.9  D,  then  e  =  0.38  7),  if  steel,  0.32. 
h  -  0.8  D,  then  e  -  0.40  Z),  if  steel,  0.33. 
h  =  0.7  D.  then  e  =  0.41  D,  if  steel,  0.34. 

The  crank-eye  or  boss  into  which  the  pin  is  fitted  should  bear  the  same 
relation  to  the  pin  that  the  boss  does  to  the  shaft. 

The  diameter  of  the  shaft-end  onto  which  the  crank  is  fitted  should  be 
1.1  X  diameter  of  shaft. 

Thurston  says:  The  empirical  proportions  adopted  by  builders  will  com- 
monly be  found  to  fall  well  within  the  calculated  safe  margin.  These  pro- 
portions are,  from  the  practice  of  successful  designers,  about  as  follows  : 

For  the  wrought-iron  crank,  the  hub  is  1.75  to  1.8  times  the  least  diameter 
of  that  part  of  the  shaft  carrying  full  load;  the  eye  is  2.0  to  2.25  the  diame- 
ter of  the  inserted  portion  of' the  pin,  and  their  depths  are,  for  the  hub,  1.0 
to  1.2  the  diameter  of  shaft,  and  for  the  eye,  1.25  to  1.5  the  diameter  of  pin. 


806 


THE   STEAM-ENGINE. 


The  web  is  made  0.7  to  0.75  the  width  of  adjacent  hub  or  eye,  and  is  given  a 
depth  of  O.b  to  0.6  that  of  adjacent  hub  or  eye. 

For  the  cast-iron  crank  the  hub  and  eye  are  a  little  larger,  ranging  in 
diameter  respectively  from  1.8  to  2  and  from  2  to  2.2  times  the  diameters  of 
shaft  and  pin.  The  flanges  are  made  at  either  end  of  nearly  the  full  depth 
of  hub  or  eye.  Cast-iron  has,  however,  fallen  very  generally  into  disuse. 

The  crank-shaft  is  usually  enlarged  at  the  seat  of  the  crank  to  about  1.1 
its  diameter  at  the  journal.'  The  size  should  be  nicely  adjusted  to  allow  for 
the  shrinkage  or  forcing  on  of  the  crank.  A  difference  of  diameter  of  one 
fifth  of  \%,  will  usually  suffice  ;  and  a  common  rule  of  practice  gives  an 
allowance  of  but  one  half  of  this,  or  .001. 

The  formulae  given  by  different  writers  for  crank-arms  practically  agree, 
since  they  all  consider  the  crank  as  a  beam  loaded  at  one  end  and  fixed  at 
the  other.  The  relation  of  breadth  to  thickness  may  vary  according  to  the 
taste  of  the  designer.  Calculated  dimensions  for  our  six  engines  are  as  f  ol 
lows  : 

Dimensions  of  Crank-arms. 


Diam.  of  cylinder,  ins.  .  . 

10 

10 

30 

30 

50 

50 

Stroke  $,  ins  

12 

24 

30 

60 

48 

96 

Max.  pressure  on  pin  P, 
(approx.)  Ibs         

7854 

7854 

70,686 

70,686 

19(5  350 

196,350 

Diam.  crank-pin  d  

2.10 

2.10 

7.34 

5.58 

12.40 

8.87 

VI.H.P. 

) 

Diam.shaft,a4/       R    D 

^8.74 

3.46 

7.70 

9.70 

12.55 

15.82 

(a  =  4.69,  5.09  and  5.22).. 

J 

Length  of  boss,  .8D  

2.19 

2  77 

6.16 

7.76 

10.04 

12.65 

Thickness  of  boss,  AD.  . 

1.10 

l!39 

3.08 

3.88 

5.02 

6.32 

Diarn.  of  boss,  1?8Z>  

4  93 

6.23 

13  86 

17.46 

22.59 

28.47 

Length  crank-pin  eye,  .8d 

1.76 

1.76 

5.87 

4.48 

9.92 

7.10 

Thickness   of    crank-pin 

eye,  Ad  

.88 

.88 

2.94 

2.23 

4.46 

3.55 

Max.  mom.  Tat  distance 

%S  —  %D  from  centre 

of  pin,  inch-lbs  

37,  149 

80,661 

788,149 

1,848,439 

3,479,322 

7,871,671 

Thickness  of  crank-arm 

a  =  .75D  

2.05 

2.60 

5.78 

7.28 

9.41 

11.87 

Greatest  breadth, 

bmj/SJJS- 

3.48 

4.55 

9.54 

13.0 

15.7 

21.0 

Min.mom.  T0  at  distance 

d  from  centre  of  pin=rPrf 

16,493 

16,493 

528,835 

394,428 

2,434,740 

1,741,625 

Least  breadth, 

b*  =  Y  9000a 

2.32 

2.06 

7.81 

6.01 

13.13 

9.89 

The  Shaft.—  Twisting  Resistance.— From  the  general  formula 
for  torsion,  we  have:  T=  ^  d*S  =  .19635d3S,  whence  d  =  I/  -~^-,  in  which 

T  =  torsional  moment  in  inch-pounds,  d  =  diameter  in  inches,  and  S  —  the 
shearing  resistance  of  the  material  in  pounds  per  square  inch. 

If  a  constant  force  P  were  applied  to  the  crank-pin  tangentially  to  its  path, 
the  work  done  per  minute  would  be 

PX£X^X#  =  33,000  X  I.H.P., 

in  which  L  =  length  of  c~ank  in  inches,  and  R  —  revs,  per  min.,  and  the 

I  H  P 
mean  twisting  moment  T  =         '       X  63,025.    Therefore 


3/5.17' 

=V -s= 


S/331,42?LH.P. 


DIMENSIONS   OF   PARTS   OF   ENGINES. 


807 


This  may  take  the  form 


j^X*or<l  =  «yi-H-P- 


R 

in  which  Fand  a  are  factors  that  depend  on  the  strength  of  the  material 
and  on  the  factor  of  safety.  Taking  S  at  45,000  pounds  per  square  inch  for 
wrought  iron,  and  at  60,000  for  steel,  we  have,  for  simple  twisting  by  a  uni- 
form tangential  force, 


Factor  of  safety    =    5 

Iron F=  35.7 

Steel jP=  26.8 


6         8        10 
42.8    57.1    71.4 
32.1    42.8    53.5 


5       6        8        10 
a  =3. 3    3.5    3.85    4.15 
a  =  3.0    3. 18  3. 5      3.77 


Unwin,  taking  for  safe  working  strength  of  wrought  iron  9000  Ibs.,  steel 
13,500  Ibs.,  and  cast  iron  4500  Ibs.,  gives  a  =  3.294  for  wrought  iron,  2.877  for 
steel,  and  4.15  for  cast  iron.  Thurston,  for  crank-axles  of  wrought  iron, 
gives  a  =  4.15  or  more. 

Seaton  says:  For  wrought  iron,/,  the  safe  strain  per  square  inch,  should 
not  exceed  9000  Ibs.,  and  when  the  shafts  are  more  than  10  inches  diameter, 
8000  Ibs.  Steel,  when  made  from  the  ingot  and  of  good  materials,  will  ad- 
mit of  a  stress  of  12,000  Ibs.  for  small  shafts,  and  10,000  Ibs.  for  those  above 
10  inches  diameter. 

The  difference  in  the  allowance  between   large  and  small  shafts  is  to  com- 
pensate for  the  defective  material  observable  in  the  heart  of  large  shafting, 
owing  to  the  hammering  failing  to  affect  it. 
a  /"i  jj  p 

The  formula  d  —  a  {/     '    '     assumes  the  tangential  force  to  be  uniform 


and  that  it  is  the  only  acting  force.  For  engines,  in  which  the  tangential 
force  varies  with  the  angle  between  the  crank  and  the  connecting-rod,  and 
with  the  variation  in  steam-pressure  in  the  cylinder,  and  also  is  influenced 
by  the  inertia  of  the  reciprocating  parts,  and  in  which  also  the  shaft  may  be 
subjected  to  bending  as  well  as  torsion,  the  factor  a  must  be  increased,  to 
provide  for  the  maximum  tangential  force  and  for  bending. 

Seaton  gives  the  following  table  showing  the  relation  between  the  maxi- 
mum and  mean  twisting  moments  of  engines  working  under  various  condi- 
tions, the  momentum  of  the  moving  parts  being  neglected,  which  is  allow- 
able: 


Max. 

Description  of  Engine. 

Steam  Cut-off 
at 

Twist 
Divided 
by 
Mean 
Twist. 

Cube 
Root 
of  the 
Ratio. 

Mome't 

0  2 

2.625 

.38 

0.4 

2.125 

.29 

ti                                   tt 

0.6 

1.835 

.22 

tt                                   I. 

0.8 

1.698 

.20 

Two-cylindev  expansive,  cranks  at  90°  

0.2 

1.616 

.17 

»t                  **                    it 

0.3 

1.415 

.12 

tt                  ti                    tt 

0.4 

1.298 

.09 

*t                  tt                    tt 

0.5 

1.256 

.08 

•                                           ii                                               it 

0.6 

1.270 

.08 

it                                            it                                                if 

0.7 

1.329 

.10 

**                                           »*                                               »4 

0.8 

1.357 

.11 

Three-cylinder  compound,  cranks  120°  — 

h.p.  0.5,  l.p.  0.66 

1.40 

1.12 

1.  p.  cranks    ) 

tt           tt 

1    9fi 

1    O8 

opposite  one  a-other,  and  h.p.  midway  f 

1  .  *O 

1  .  UO 

Seaton  also  gives  the  following  rules  for  ordinary  practice  for  ordinary 
two-cylinder  marine  engines: 


3/IHP 
Diameter  of  the  tunnel-shafts  =i/  -—--XF,  or 


IHP 


808  THE   STEAM-ENGINE. 

Compound  engines,  cranks  at  right  angles: 

Boiler  pressure  70  Ibs.,  rate  of  expansion  6  to  7,  F  —  70,  a  =  4  12. 
Boiler  pressure  80  Ibs.,  rate  of  expansion  ?  to  8,  F  =  72,  a  =  4.16. 
Boiler  pressure  90  Ibs.,  rate  of  expansion  8  to  9,  F  —  75,  a  =  4.22. 

Triple  compound,  three  cranks  at  120  degrees: 

Boiler  pressure  150  Ibs.,  rate  of  expansion  10  to  12,  F=  62,  a  =  3  96 
Boiler  pressure  160  Ibs.,  rate  of  expansion  11  to  13,  F  =  64,  a  =  4. 
Boiler  pressure  170  Ibs.,  rate  of  expansion  12  to  15,  F  =  67,  a  —  4.06. 

Expansive  engines,  cranks  at  right  angles,  and  the  rate  of  expansion  5. 
boiler-pressure  60  Ibs.,  F  =  90,  a  =  4.48. 


nee  for 

..  -.iig  moment  if  we  take  it  as  equal  to  the 
ratio  of  the  maximum  to  the  mean  pressure  on  the  piston.  The  factor  a, 
then,  in  the  formula  for  diameter  of  the  shaft  will  be  multiplied  by  the  cube 

root  of  this  ratio,  ™l/~  =1.34,  A/  ~  =  1-45,  and  l/~  =  1.49   for  the 

10,  30,  and  50-in.  engines,  respectively.  Taking  a  =  3.5,  which  corresponds 
to  a  shearing  strength  of  60,000  and  a  factor  of  safety  of  8  for  steel,  or  to 
45,000  and  a  factor  of  6  for  iron,  we  have  for  the  new  coefficient  a}  in  the 

formula  dl  =  Ol  //-—£*,  the  values  4.69,  5.08,  and  5.22,  from  which  we 

obtain  the  diameters  of  shafts  of  the  six  engines  as  follows: 

Engine  No  .........................      1  2  3  4  5  6 

Diam.ofcyl  ........  ................      10         10         30         30  50  50 

Horse-power,  I.H.P  ................      50         50        450       450  1250  1250 

Revs,  per  min.,  R  .......  ____  .......     250        125        130        65  90  45 

Diam.  of  shaft  d  =a1l^L¥l....    2.74      3.46      7.67      9.70      12.55      15.82 


These  diameters  are  calculated  for  twisting  only.  When  the  shaft  is  also 
subjected  to  bending  strain  the  calculation  must  be  modified  as  below  : 

Resistance  to  Bending.—  The  strength  of  a  circular-section  shaft 
to  resist  bending  is  one  half  of  that  to  resist  twisting.  If  B  is  the  bending 
moment  in  inch-lbs.,  and  d  the  diameter  of  the  shaft  in  inches, 


"W  X/?  and  d  =  i/J  X 


X10.2; 

/  is  the  safe  strain  per  square  inch  of  the  material  of  which  the  shaft  is 
composed,  and  its  value  may  be  taken  as  given  above  for  twisting  (Seaton). 

Equivalent  Twisting  Moment.— When  a  shaft  is  subject  to 
both  twisting  and  bending  simultaneously,  the  combined  strain  on  any  sec- 
tion of  it  may  be  measured  by  calculating  what  is  called  the  equivalent 
twisting  moment;  that  is,  the  two  strains  are  so  combined  as  to  be  treated 
as  a  twisting  strain  only  of  the  same  magnitude  and  the  size  of  shaft  cal- 
culated accordingly.  Rankinegave  the  following  solution  of  the  combined 
action  of  the  two  strains. 

If  T  =  the  twisting  moment,  and  B  =  the  bending  moment  on  a  section  of 
a  shaft,  then  the  equivalent  twisting  moment  Tt  =  B  +  VjB2  -j-  T2. 

Seaton  says:  Crank-shafts  are  subject  always  to  twisting,  bending,  and 
shearing  strains;  the  latter  are  so  small  compared  with  the  former  that 
they  are  usually  neglected  directly,  but  allowed  for  indirectly  by  means  of 
the  factor  /. 

The  two  principal  strains  vary  throughout  the  revolution,  and  the  maxi- 
mum equivalent  twisting  moment  can  only  be  obtained  accurately  by  a 
series  of  calculations  of  bending  and  twisting  moments  taken  at  fixed  inter- 
vals, and  from  them  constructing  a  curve  of  strains. 

Considering  the  engines  of  our  examples  to  have  overhung  cranks,  the 
maximum  bending  moment  resulting  from  the  thrust  of  the  connecting- rod 
on  the  crank-pin  will  take  place  when  the  engine  is  passing  its  centres 
(neglecting  the  effect  of  the  inertia  of  the  reciprocating  parts),  and  it  will 
be  the  product  of  the  total  nressure  on  the  piston  by  the  distance  between 


DIMENSIONS   OF   PAKTS   OF    ENGINES. 


809 


two  parallel  lines  passing  through  the  centres  of  the  crank-pin  and  of  the 
shaft  bearing,  at  right  angles  to  their  axes;  which  distance  is  equal  to 
Y%  length  of  crank-pin  bearing  -f  length  of  hub-}-^  length  of  shaft-bearing  -f 
any  clearance  that  may  be  allowed  between  the  crank  and  the  two  bearings. 
For  our  six  engines  we  may  take  this  distance  as  equal  to  ^  length  of 
crank-pin  -f-  thickness  of  crank-arm  -f  1.5  X  the  diameter  of  the  shaft  as 
already  found  by  the  calculation  for  twisting.  The  calculation  of  diameter 
is  then  as  below: 


Engine  No. 

1 

2 

3 

4 

5 

6 

Diam.  of  cyl.,  in.   . 
Horse-power  

10 
50 

10 
50 

30 

450 

30 
450 

50 
1250 

50 

1250 

Revs,  per  min..   .. 
Max.  press,  on  pis,P 
Leverage,*  Lin  — 
Bd.mo.P-Lrr.Bin.-lb 
Twist  mom  T. 

250 
7,854 
6.32 
49,637 
47  124 

125 
7,854 
7.94 
62,361 
94  248 

130 
70,686 
22.20 
1,569,222 
1  060  290 

65 
70,686 
26.00 
1,837,836 
2  120  580 

90 
196,350 
36.80 
7,225,680 
4  712  400 

45 

196,350 
42.25 
8,295,788 
9  424  800 

Equiv.  Twist,  mom. 

r1=Jg+  yBt+T* 

(approx.)  

118,000 

175,000 

3,463,000 

4,647,000 

15,840,000 

20,850,000 

*  Leverage  =  distance  between  centres  of  crank-pin  and  shaft  bearing  = 


Having  already  found  the  diameters,  on  the  assumption  that  the  shafts 
were  subjected  to  a  twisting  moment  Tonly,  we  may  find  the  diameter  for 
resisting  combined  bending  and  twisting  by  multiplying  the  diameters 
already  found  by  the  cube  roots  of  the  ratio  2\  -H  r,  or 


Giving  corrected  diameters  d:  =. 


1.40 
3.84 


1.27 
4.39 


1.46 
11.35 


1.34        1.64        1.36 
12.99      20.58      21.52 


By  plotting  these  results,  using  the  diameters  of  the  cylinders  for  abscissas 
and  diameters  of  the  shafts  for  ordinates,  we  find  that  for  the  long-stroke 
engines  the  results  lie  almost  in  a  straight  line  expressed  by  the  formula, 
diameter  of  shaft  =  .43  X  diameter  of  cylinder;  for  the  short -stroke  engines 
the  line  is  slightly  curved,  but  does  not  diverge  far  from  a  straight  line 
whose  equation  is^  diameter  of  shaft  =  .4  diameter  of  cylinder.  Using  these 
two  formulas,  the  diameters  of  the  shafts  will  be  4.0,  4.3,  12.0,  12.9,  20.0,  21.5. 

J.  B.  Stanwood,  in  Engineering,  June  12,  1891,  gives  dimensions  of  shafts 
of  Corliss  engines  in  American  practice  for  cylinders  10  to  30  in.  diameter. 
The  diameters  range  from  4  15/16  to  14  15/ 16,  following  precisely  the  equation, 
diameter  of  shaft  =  ^  diameter  of  cylinder  -  1/16  inch. 

Fly-wlieel  Shafts.— Thus  far 'we  have  considered  the  shaft  as  resist- 
ing the  force  of  torsion  and  the  bending  moment  produced  by  the  pressure 
on  the  crank-pin.  In  the  case  of  fly-wheel  engines  the  shaft  on  the  opposite 
side  of  the  bearing  from  the  crank  pin  has  to  be  designed  with  reference  to 
the  bending  moment  caused  by  the  weight  of  the  fly  wheel,  the  weight  of 
the  shaft  itself,  and  the  strain  of  the  belt.  For  engines  in  which  there  is  an 
outboard  bearing,  the  weight  of  fly-wheel  and  shaft  being  supported  by 
two  bearings,  the  point  of  the  shaft  at  which  the  bending  moment  is  a 
maximum  may  be  taken  as  the  point  midway  between  the  two  bearings  or 
at  the  middle  of  the  fly-wheel  hub,  and  the  amount  of  the  moment  is  the 
product  of  the  weight  supported  by  one  of  the  bearings  into  the  distance 
from  the  centre  of  that  bearing  to  the  middle  point  of  the  shaft.  The  shaft 
is  thus  to  be  treated  as  a  beam  supported  at  the  ends  and  loaded  in  the 
middle.  In  the  case  of  an  overhung  fly-wheel,  the  shaft  having  only  one 
bearing,  the  point  of  maximum- moment  should  be  taken  as  the  middle  of 
the  bearing,  and  its  amount  is  very  nearly  the  product  of  half  the  weight 
of  the  fly-wheel  and  the  shaft  into  the  distance  from  the  middle  of  its  hub 
from  the  middle  of  the  bearing.  The  bending  moment  should  be  calculated 
and  combined  with  the  twisting  moment  as  above  shown,  to  obtain  the 
equivalent  twisting  moment,  and  the  diameter  necessary  at  the  point  of 
maximum  moment  calculated  therefrom. 

In  the  case  of  our  six  engines  we  assume  that  the  weights  of  the  fly- 
wheels, together  with  the  shaft,  are  double  the  weight  of  fly-wheel  rim 

I  H  P 
obtained  from  the  formula,. W=  785,400  -537™'  (given    under    Fly-wheels); 


810 


THE   STEAM-ENGINE. 


that  the  shaft  is  supported  by  an  outboard  bearing,  the  distance  between 
the  two  bearings  being  2^,  5,  and  10  feet  for  the  10-in.,  30-in.,  and  50-in. 
engines,  respectively.  The  diameters  of  the  fly-wheels  are  taken  such 
that  their  rim  velocity  will  be  a  little  less  than  6000  feet  per  minute. 

Engine  No 1  3  3  4  5  6 

Diam.  of  cyl.,  inches 10  10  30  30  50  50 

Diam.  of  fly-wheel,  ft 7.5  15  14.5  29  21  42 

Revs,  per  min 250  125  130  65  90  45 

Half  wt.fly-wh'l  and  shaft,lb.  268  536  5,963  11,936  26.470  52,940 

Lever  arm  for  max.mom.,in.  15  15  30  30  60  60 

Max.  bending  moment,  in.-lb.  4020  8040  179,040  358,080  1,588,200  3,176,403 

As  these  are  very  much  less  than  the  bending  moments  calculated  from 
the  pressures  on  the  crank -pin,  the  diameters  already  found  are  sufficient 
for  the  diameter  of  the  shaft  at  the  fly-wrheel  hub. 

In  the  case  of  engines  with  heavy  band  fly-wheels  and  with  long  fly-wheel 
shafts  it  is  of  the  utmost  importance  to  calculate  the  diameter  of  the  shaft 
with  reference  to  the  bending  moment  due  to  the  weight  of  the  fly-wheel 
and  the  shaft. 

B.  H.  Coffey  (Power,  October,  1892)  gives  the  formula  for  combined  bend- 
ing and  twisting  resistance,  T,  =  .196d3S,  in  which  7\  =  B  +  |/52-f  T2;  T 
being  the  maximum,  not  the  mean  twisting  moment;  and  finds  empirical 
working  values  for  .1968  as  below.  He  says:  Four  points  should  be  consid- 
ered in  determining  this  value:  First,  the  nature  of  the  material;  second, 
the  manner  of  applying  the  loads,  with  shock  or  otherwise;  third,  the  ratio 
of  the  bending  moment  to  the  torsional  moment— the  bending  moment  in  a 
revolving  shaft  produces  reversed  strains  in  the  material,  which  tend  to  rup- 
ture it:  fourth,  the  size  of  the  section.  Inch  for  inch,  large  sections  are 
weaker  than  small  ones.  He  puts  the  dividing  line  between  large  and  small 
sections  at  10  in.  diameter,  and  gives  the  following  safe  values  of  S  X  .196  for 
steel,  wrought  iron,  and  cast  iron,  for  these  conditions. 

VALUE  OF  S  X  .196. 


Ratio. 

Heavy  Shafts 
with  Shock. 

Light  shafts  with 
Shock.    Heavy 
Shafts  No  Shock. 

Light  Shafts 
No  Shock. 

BtoT. 

Steel. 

Wro't 
Iron. 

880 
785 
715 
655 

Cast 
Iron. 

440 
393 
358 
328 

Steel. 

1566 
1410 
1281 
1176 

Wro't 
Iron. 

Cast 
Iron. 

Steel. 

Wro't 
Iron. 

Cast 
Iron. 

3  to  10  or  less  
3  to  5  or  less    
1  to  1  or  less  .  .   . 

1045 
941 

855 
784 

1320 
1179 
1074 
984 

660 
589 
537 
492 

2090 

1882 
1710 
1568 

1760 
1570 
1430 
1310 

880 
785 
715 
655 

B  greater  than  T.  . 

Mr.  Coffey  gives  as  an  example  of  improper  dimensions  the  fly-wheel 
shaft  of  a  1500  H.P.  engine  at  Willimantic,  Conn.,  which  broke  while  the  en- 
gine was  running  at  425  H.P.  The  shaft  was  17  ft.  5  in.  long  between  centres 
of  bearings,  18  in.  diam.  for  8  ft.  in  the  middle,  and  15  in.  diam.  for  the  re- 
mainder, including  the  bearings.  It  broke  at  the  base  of  the  fillet  connect- 
ing the  two  large  diameters,  or  56^  in.  from  the  centre  of  the  bearing.  He 
calculates  the  mean  torsional  moment  to  be  446,654  inch -pounds,  and  the 
maximum  at  twice  the  mean;  and  the  total  weight  on  one  bearing  at  87,530 
Ibs.,  which,  multiplied  by  56^  in.,  gives  4,945,445  in.-lbs.  bending  moment  at 
the  fillet.  Applying  the  formula  7\  =  B  +  VB*  +  3T2,  gives  for  equivalent 
twisting  moment  9,971,045  in.-lbs.  Substituting  this  value  in  the  formula 
T!  -  .196,  vSd3  gives  for  S  the  shearing  strain  15,070  Ibs.  per  sq.  in.,  or  if  the 
metal  had  a  shearing  strength  of  45,000  Ibs.,  a  factor  of  safety  of  only  3. 
Mr.  Coffey  considers  that  6000  Ibs.  is  all  that  should  be  allowed  for  S  under 
these  circumstances.  This  \vould  give  d  =  20.35  in.  If  we  take  from  Mr. 
Coffey's  table  a  value  of  .1965  =  1100,  we  obtain  d3  =  9000  nearly,  or  d  =  20.8 
in.,  instead  of  15  in.,  the  actual  diameter. 

Length  of  Shaft-bearings.— There  is  as  great  a  difference  of 
opinion  among  writers,  and  as  great  a  variation  in  practice  concerning  length 
of  journal-bearings,  as  there  is  concerning  crank-pins.  The  length  of  a 


DIMENSIONS   OF   PARTS   OF   ENGINES.  811 

journal  being  determined  from  considerations  of  its  heating,  the  observa- 
tions concerning  heating  of  crank-pins  apply  also  to  shaft-bearings,  and  the 
formulas  for  length  of  crank-pins  to  avoid  heating  may  also  be  used,  using 
for  the  total  load  upon  the  bearing  the  resultant  of  all  the  pressures  brought 
upon  it,  by  the  pressure  on  the  crank,  by  the  weight  of  the  fly-wheel,  and  by 
the  pull  of  the  belt.  After  determining  this  pressure,  however,  we  must 
resort  to  empirical  values  for  the  so-called  constants  of  the  formulae,  really 
variables,  which  depend  on  the  power  of  the  bearing  to  carry  away  heat, 
and  upon  the  quantity  of  heat  generated,  which  latter  depends  on  the  pres- 
sure, on  the  number  of  square  feet  of  rubbing  surface  passed  over  in  a 
minute,  and  upon  the  coefficient  of  friction.  This  coefficient  is  an  exceed- 
ingly variable  quantity,  ranging  from  .01  or  less  with  perfectly  polished 
journals,  having  end-play,  and  lubricated  by  a  pad  or  oil-bath,  to  .10  or  more 
with  ordinary  oil-cup  lubrication. 

For  shafts  resisting  torsion  only,  Marks  gives  for  length  of  bearing  I  = 
.0000247/pJVD2,  in  which /is  the  coefficient  of  friction,  p  the  mean  pressure 
in  pounds  per  square  inch  on  the  piston,  i^the  number  of  single  strokes  per 
minute,  and  D  the  diameter  of  the  piston.  For  shafts  under  the  combined 
stress  due  to  pressure  on  the  crank-pin,  weight  of  fly-wheel,  etc.,  he  gives 
the  following:  Let  Q  =  reaction  at  bearing  due  to  weight,  8  —  stress  due 
steam  pressure  on  piston,  and  R-^—  the  resultant  force;  for  horizontal  engines, 
Jf?x  =  VQ2  -f-  Sa,  for  vertical  engines  R^  =  Q  -\-  S,  when  the  pressure  on  the 
crank  is  in  the  same  direction  as  the  pressure  of  the  shaft  on  its  bearings, 
and  R!  =  Q  —  S  when  the  steam  pressure  tends  to  lift  the  shaft  from  its 
bearings.  Using  empirical  values  for  the  work  of  friction  per  square  inch 
of  projected  area,  taken  from  dimensions  of  crank-pins  in  marine  vessels, 
he  finds  the  formula  for  length  of  shaft-journals  I  —  .(WOQ825/KJVi  and 
recommends  that  to  cover  the  defects  of  workmanship,  neglect  of  oiling, 
and  the  introduction  of  dust,  /  be  taken  at  .16  or  even  greater.  He  says 
that  500  Ibs.  per  sq.  in.  of  projected  area  may  be  allowed  for  steel  or  wrought- 
iron  shafts  in  brass  bearings  with  good  results  if  a  less  pressure  is  not  attain- 
able without  inconvenience.  Marks  says  that  the  use  of  empirical  rules  that 
do  not  take  account  of  the  number  of  turns  per  minute  has  resulted  in  bear- 
ings much  too  long  for  slow- speed  engines  and  too  short  for  high-speed 
engines. 

Whitham  gives  the  same  formula,  with  the  coefficient  .00002575. 

Thurston  says  that  the  maximum  allowable  mean  intensity  of  pressure 

PV 
may  be,  for  all  cases,  computed  by  his  formula  for  journals,  I  =       nnn,j»  or 

P(  V  \-  20) 
by  Rankine's,  I  =     A  t  0T!  ,  -,  in  which  P  is  the  mean  total  pressure  in  pounds, 

44,800a 

Fthe  velocity  of  rubbing  surface  in  feet  per  minute,  and  d  the  diameter  of 
the  shaft  in  inches.  It  must  be  borne  in  mind,  he  says,  that  the  friction  work 
on  the  main  bearing  next  the  crank  is  the  sum  of  that  due  the  action  of  the 
piston  on  the  pin.  and  that  due  that  portion  of  the  weight  of  wheel  and 
shaft  and  of  pull  of  the  belt  which  is  carried  there.  The  outboard  bearing 
carries  practically  only  the  latter  two  parts  of  the  total.  The  crank-shaft 
journals  will  be  made  longer  on  one  side,  and  perhaps  shorter  on  the  other, 
than  that  of  the  crank-pin,  in  proportion  to  the  work  falling  upon  each,  i.e., 
to  their  respective  products  of  mean  total  pressure,  speed  of  rubbing  sur- 
faces, and  coefficients  of  friction. 

Unwin  says:  Journals  running  at  150  revolutions  per  minute  are  often 
only  one  diameter  long.  Fan  shafts  running  150  revolutions  per  minute  have 
journals  six  or  eight  diameters  Ions:.  The  ordinary  empirical  mode  of  pro- 
portioning the  length  of  journals  is  to  make  the  length  proportional  to  the 
diameter,  and  to  make  the  ratio  of  length  to  diameter  increase  with  the 
speed.  For  wrought-iron  journals: 

Revs,  per  min.  =     50     100    150  200    250    500    1000        ^  =  .004#  -f 1. 
Length -*- diam.  =  1.2     1.4    1.61.8    2.0    3.0     5.0. 

Cast-iron  journals  may  have  I  -f-  d  —  9/10,  and  steel  journals  I  -5-  d  =  1£4, 
of  the  above  values. 

0  4  TT  P 
Unwin  gives  the  following,  calculated  from  the  formula  I  =    '- — *,  in 

which  r  is  the  crank  radius  in  inches,  and  H.P.  the  horse-power  transmitted 
to  the  crank- pin, 


812 


THE   STEAM-ENGINE. 
THEORETICAL  JOURNAL  LENGTH  IN  INCHES. 


Load  on 
Journal 
in 
pounds. 

Revolutions  of  Journal  per  minute. 

50 

100 

200 

300 

500 

1000 

1,000 
2,000 
4,000 
5,000 
10,000 
15,000 
20,000 
30,000 
40,000 
50,000 

.2 
.4 
.8 
1.0 
2. 
3. 
4. 
6. 
8. 
10. 

.4 
.8 
1.6 
2. 
4. 
6. 
8. 
12. 
16. 
20. 

.8 
1.6 
3.2 
4. 
8. 
12. 
16. 
24. 
32. 
40. 

1.2 
2.4 
4.8 
6. 
12. 
18. 
24. 
36. 

4! 
8. 
10. 
20. 
30. 
40. 

4. 

8. 
16. 
20. 
40. 

Applying  these  different  formluse  to  our  six  engines,  we  have: 


Engine  No 

1 

2 

3 

4 

5 

6 

10 

10 

30 

30 

50 

50 

50 

50 

450 

450 

1.250 

1.250 

Revs  per  min           

250 

125 

130 

65 

90 

45 

Mean  pressure  on  crank-pin  =  S  
Half  wt.  of  fly-wheel  and  shaft  =  Q.. 
Resultant  press,  on  bearing 

3,299 
268 

3,299 
536 

23,185 
5,968 

23,185 
11,936 

58,905 
26,470 

58,905 
52,940 

VQ*  +  S*  =  R1. 
Diam.  of  shaft  journal  

3,310 
3  84 

3.335 
4.39 

23,924 
11  35 

26,194 
12.99 

64,580 
20.58 

79,200 
21.52 

Length  of  shaft  journal: 
Marks,       1  =  .0000325/fl,  N(  f=  .  1  0) 
Whitham,  I  =  .0000515/#,#(/=  10). 

PV 
Thurston,  1  — 

5.38 
4.27 

3  61 

2.71 
2.15 

1  82 

20.87 
16.53 

14  00 

11.07 

8.77 

7  43 

37.78 
29.95 

25  36 

23.17 
18.35 

15  55 

60,000d 

P(F+20) 
Rankine,  1  —  —  —  ^  ...  

5  22 

2  78 

21  70 

10  85 

35  16 

22  47 

44,800d 
Unwin,       1  -  (.004R  f  l)d     

7  68 

6  59 

17  25 

ifi  3fi 

°7  99 

25  39 

0.4  H.P. 
Unwin        Z  —           — 

3  33 

1  60 

12  00 

6  00 

20  83 

10  42 

r 

Average  

4.92 

2.99 

17.05 

10.00 

29.54 

19.22 

If  we  divide  the  mean  resultant  pressure  on  the  bearing  by  the  projected 
area,  that  is,  by  the  product  of  the  diameter  and  length  of  the  journal,  using 
the  greatest  and  smallest  length  out  of  the  seven  lengths  for  each  journal 
given  above,  we  obtain  the  pressure  per  square  inch  upon  the  bearing,  as 
follows: 


Engine  No  

1 

2 

3 

4 

5 

G 

Pressure  per  sq.  in.,  shortest  journal. 
Longest  journal  ,  

259 
112 

455 
115 

176 
97 

336 
123 

151 

83 

353 
145 

Average  journal 

175 

254 

124 

202 

106 

191 

Journal  of  length  =  diam  

173 

155 

175 

Many  of  the  formulae  give  for  the  long-stroke  engines  a  length  of  journal 
less  than  the  diameter,  but  such  short  journals  are  rarely  used  in  practice. 
The  last  line  in  the  above  table  has  been  calculated  on  the  supposition  that 


DIMENSIONS   OF   PARTS  OF   ENGINES.  813 

the  journals  of  the  long-stroke  engines  are  made  of  a  length  equal  to  the 
diameter. 

In  the  dimensions  of  Corliss  engines  given  by  J.  B.  Stan  wood  (Eng.,  June 
12,  1891),  the  lengths  of  the  journals  for  engines  of  diam.  of  cyl.  10  to  20  in. 
are  the  same  as  the  diam.  of  the  C37linder,  and  a  little  more  than  twice  the 
diam.  of  the  journal.  For  engines  above  20  in.  diam.  of  cyl.  the  ratio  of 
length  to  diam.  is  decreased  so  that  an  engine  of  30  in.  diam.  has  a  journal 
20  iu.  long,  its  diameter  being  14£f  in.  These  lengths  of  journal  are  greater 
than  those  given  by  any  of  the  formulae  above  quoted. 

There  thus  appears  to  be  a  hopeless  confusion  in  the  various  formulae  for 
length  of  shaft  journals,  but  this  is  no  more  than  is  to  be  expected  from  the 
variation  in  the  coefficient  of  friction,  and  in  the  heat-conducting  power  of 
journals  in  actual  use,  the  coefficient  varying  from  .10  (or  even  .16  as  given 
by  Marks)  down  to  .01,  according  to  the  condition  of  the  bearing  surfaces 

PV 
and  the  efficiency  of  lubrication.   Thurston's  formula,  I  =  -,  reduces  to 


the  coefficients  of  PR  are,  respectively,  .0000065  and  .00000515.  Taking  the 
mean  of  these  three  formulae,  we  have  I  =  .0000053P^,  if  /  =  .10  or  I  = 
.000053/P^  for  any  other  value  off.  The  author  believes  this  to  be  as  safe 
a  formula  as  any  for  length  of  journals,  with  the  limitation  that  if  it  brings 
a  result  of  length  of  journal  less  than  the  diameter,  then  the  length  should 
Le  made  equal  to  the  diameter.  Whenever  with  /=  .10  it  gives  a  length 
which  is  inconvenient  or  impossible  of  construction  on  account  of  limited 
space,  then  provision  should  be  made  to  reduce  the  value  of  the  coefficient 
of  friction  below  .10  by  means  of  forced  lubrication,  end  play,  etc.,  and  to 
carry  away  the  heat,  as  by  water-cooled  journal-boxes.  The  value  of  P 
should  be  taken  as  the  resultant  of  the  mean  pressure  on  the  crank,  and  the 
load  brought  on  the  bearing  by  the  weight  of  the  shaft,  fly-wheel,  etc.,  as 
calculated  by  the  formula  already  given,  viz.,  Rl  =  ^Q'*  -f-  S2  for  horizontal 
engines,  and  R^  =  Q  -(-  8  for  vertical  engines. 

For  our  six  engines  the  formula  I  =  .0000053P.R  gives,  with  the  limitation 
for  the  long-stroke  engines  that  the  length  shall  not  be  less  than  the  diam- 
eter, the  following: 

EngineNo...  .......  .  ..................        123456 

Length  of  journal  ....................    4.39    4.39    16.48    12.99    30.80    21.52 

Pressure  per  square  inch  on  journal.  .      196      173      128        155        102       171 

Crank  -  shafts    with    Centre-crank    and    Double-crank 

Arms.—  In  centre-crank  engines,  one  of  the  crank-arms,  and  its  adjoining 
journal,  called  the  after  journal,  usually  transmit  the  power  of  the  engine 
to  the  work  to  be  done,  and  the  journal  resists  both  twisting  and  bending 
moments,  while  the  other  journal  is  subjected  to  bending  moment  only. 
For  the  after  crank-journal  the  diameter  should  be  calculated  the  same  as 
for  an  overhung  crank,  using  the  formula  for  combined  bending  and  twist- 
ing moment,  Tl  =  B  -\-  tyE*  -f  2'2,  in  which  Tl  is  the  equivalent  twisting 
moment,  B  the  bending  moment,  and  T  the  twisting  moment.  This  value 

3  /R     1  rp 

of  TI  is  to  be  used  in  the  formula  diameter  =  //  ,..'    .  .    The  bending  mo- 


3 /R     1  rp 

=  //  ,..'    .  . 


ment  is  taken  as  the  maximum  load  on  piston  multiplied  by  one  fourth  of 
the  length  of  the  crank-shaft  between  middle  points  of  the  two  journal 
bearings,  if  the  centre  crank  is  midway  between  the  bearings,  or  by  one 
half  the  distance  measured  parallel  to  the  shaft  from  the  middle  of  the 
crank-pin  to  the  middle  of  the  after  bearing.  This  supposes  the  crank- 
shaft to  be  a  beam  loaded  at  -its  middle  and  supported  at  the  ends,  but 
Whitham  would  make  the  bending  moment  only  one  half  of  this,  consider- 
ing the  shaft  to  be  a  beam  secured  or  fixed  at  the  ends,  with  a  point  of  con- 
trafiexure  one  fourth  of  the  length  from  the  end.  The  first  supposition  is 
the  safer,  but  since  the  bending  moment  will  in  any  case  be  much  less  than 
the  twisting  moment,  the  resulting  diameter  will  be  but  little  greater  than 
if  WhithanVs  supposition  is  used.  For  the  forward  journal,  which  is  sub- 

3/iY)  97? 

jected  to  bending  moment  only,  diameter  of  shaft  =  A  /  -  '      ,  in  which  B 


814 


THE   STEAM-ENGIKE. 


is  the  maximum  bending  moment  and  S  the  safe  shearing  strength  of  the 
metal  per  square  inch. 

For  our  six  engines,  assuming  them  to  be  centre-crank  engines,  and  con- 
sidering the  crank-shaft  to  be  a  beam  supported  at  the  ends  and  loaded  in 
the  middle,  and  assuming  lengths  between  centres  of  shaft  bearings  as 
given  below,  we  have: 


Engine  No  

1 

2 

3 

4 

5 

6 

Length  of  shaft,  assumed, 
inches   L            

20 

7,854 

39,270 
47,124 

101,000 
3.98 

3.68 

24 

7,854 

49,637 
94,248 

156,000 
4.60 

3.99 

48 
70,686 

848,232 
1,060,290 

2,208,000 
11.15 

10.28 

60 
70,686 

1.060,290 
2,120,580 

3,430,000 
13.00 

11.16 

76 
196,350 

3,729,750 
4,712,400 

9,740,000 
18.25 

16.82 

96 
196,350 

4,712,400 
9,424,800 

15,240,000 
21.20 

18.18 

Max.  press,  on  crank-pin,  P 
Max.     bending     moment, 
B  —  Y±PL  inch-lbs  

Twisting  moment    T 

Equiv.    twisting  moment, 

B  \  VB*  \  r2 

Diameter  of  after  journal, 

V    8000 
Diam.  of  forward  journal, 
,         3/10.25 

Q,.    —      t  /                    ,       

y     8000   ' 

The  lengths  of  the  journals  would  be  calculated  in  the  same  manner  as  in 
the  case  of  overhung  cranks,  by  the  formula  I  =  .000053/P#,  in  which  P  is 
the  resultant  of  the  mean  pressure  due  to  pressure  of  steam  on  the  piston, 
and  the  load  of  the  fly-wheel,  shaft,  etc.,  on  each  of  the  two  bearings. 
Unless  the  pressures  are  equally  divided  between  the  two  bearings,  the 
calculated  lengths  of  the  two  will  be  different;  but  it  is  usually  customary 
to  make  them  both  of  the  same  length,  and  in  no  case  to  make  the  length 
less  than  the  diameter.  The  diameters  also  are  usually  made  alike  for  the 
two  journals,  using  the  largest  diameter  found  by  calculation. 

The  crank-pin  for  a  centre  crank  should  be  of  the  same  length  as  for  an 
overhung  crank,  since  the  length  is  determined  from  considerations  of 
heating,  and  not  of  strength.  The  diameter  also  will  usually  be  the  same, 
since  it  is  made  great  enough  to  make  the  pressure  per  square  inch  on  the 
projected  area  (product  of  length  by  diameter)  small  enough  to  allow  of 
free  lubrication,  and  the  diameter  so  calculated  will  be  greater  than  is  re- 
quired for  strength. 

Crank-shaft  with  Tiro  Cranks  coupled  at  90°.  —  If  the 
whole  power  of  the  engine  is  transmitted  through  the  after  journal  of  the 
after  crank-shaft,  the  greatest  twisting  moment  is  equal  to  1.414  times  the 
maximum  twisting  moment  due  to  the  pressure  on  one  of  the  crank-pins. 
If  T  =  the  maximum  twisting  moment  produced  by  the  steam-pressure  on 
one  of  the  pistons,  then  Tl  the  maximum  twisting  moment  on  the  after  part 
of  the  crank-shaft,  and  on  the  line-shaft,  produced  when  each  crank  makes 
an  angle  of  45°  with  the  centre  line  of  the  engine,  is  1.4147'.  Substituting 
this  value  in  the  formula  for  diameter  to  resist  simple  torsion,  viz.,  d  = 

or    d  =  1 .932  A*/ — ,  in  which  T  is 


the  maximum  twisting  moment  produced  by  one  of  the  pistons,  d  =  diam- 
eter in  inches,  and  -S  =  safe  working  shearing  strength  of  the  material. 
For  the  forward  journal  of  the  after  crank,  and  the  after  journal  of  the 
forward  crank,  the  torsional  moment  is  that  due  to  the  pressure  of  steam 
on  the  forward  piston  only,  and  for  the  forward  journal  of  the  forward 
crank,  if  none  of  the  power  of  the  engine  is  transmitted  through  it,  the 
torsional  moment  is  zero,  and  its  diameter  is  to  be  calculated  for  bending 
moment  only. 

For  Combined  Torsion  and  Flexure.— Let  Bt  =  bending  mo- 
ment on  either  journal  of  the  forward  crank  due  to  maximum  pressure  011 


DIMENSIONS   OF   PARTS  OF   ENGINES.  815 

forward  piston,  P2  =  bending  moment  on  either  journal  of  the  after  crank 
due  to  maximum  pressure  on  after  piston,  2\  —  maximum  twisting  moment 
on  after  journal  of  forward  crank,  and  T2  =  maximum  twistiug  moment  on 
after  journal  of  after  crank  due  to  pressure  on  the  after  piston. 
Then  equivalent  twisting  moment  on  after  journal  of  forward  crank  =  Bl 

4-  VBJ  +  2\a.  _ 

On  forward  journal  of  after  crank  =  B.2  -f-  \fBJ  +  2\8. 

On  after  journal  of  after  crank  =  #2  -f-  \/Bf  -f  (2\  -f  T,)a. 

These  values  of  equivalent  twisting  moment  are  to  be  used  in  the  formula 

3/5~7r 

for  diameter  of  journals  d  =  A/  —  —    For  the  forward  journal  of  the 
*       8 


forward  crank-shaft  d  = 


It  is  customary  to  make  the  two  journals  of  the  forward  crank  of  one 
diameter,  viz.,  that  calculated  for  the  after  journal. 

For  a  Three-cylinder  I£ngine  with  cranks  at  120°,  the  greatest 
twisting  moment  on  the  after  part  of  the  shaft,  if  the  maximum  pressures 
on  the  three  pistons  are  equal,  is  equal  to  twice  the  maximum  pressure  on 
any  one  piston,  and  it  takes  place  when  two  of  the  cranks  make  angles  of 
30°  with  the  centre  line,  the  third  crank  being  at  right  angles  to  it.  (For  de- 
monstration. see  Whitham's  "  Steam-engine  Design,'1  p.  252.)  For  combined 
torsion  and  flexure  the  same  method  as  above  given  for  two  crank  engines 
is  adopted  for  the  first  two  cranks;  and  for  the  third,  or  after  crank,  if  all 
the  power  of  the  three  cylinders  is  transmitted  through  it,  we  have  the 
equivalent  twisting  moment  on  the  forward  journal  =  /?3-f-  t^s'-H^+Tj)*, 
and  on  the  after  journal  =  J53  -f  \'B^  +  (l\  -h  Ta  -f-  I^)2,  B3  and  T3  being 
respectively  the  bending  and  twisting  moments  due  to  the  pressure  on  the 
third  piston. 

Crank  -  .shafts  for  Triple-expansion  Marine  Engines, 
according  to  an  article  in  The  Engineer,  April  25,  1890,  should  be  made 
larger  than  the  formula?  would  call  for,  in  order  to  provide  for  the  stresses 
due  to  the  racing  of  the  propeller  in  a  sea-way,  which  can  scarcely  be  cal- 
culated. A  kind  of  unwritten  law  has  sprung  up  for  fixing  the  size  of  a 
crank-shaft,  according  to  which  the  diameter  of  the  shaft  is  made  about 
0.45Z>,  where  D  is  the  diameter  of  the  high-pressure  cylinder.  This  is  for 
solid  shafts.  When  the  speeds  are  high,  as  in  war-ships,  and  the  stroke 
short,  the  formula  becomes  0.4D,  even  for  hollow  shafts. 

The  Valve-stem  or  Valve-rod.—  The  valve-rod  should  be  designed 
to  move  the  valve  under  the  most  unfavorable  conditions,  which  are  when 
the  stem  acts  by  thrusting,  as  a  long  column,  when  the  valve  is  unbalanced 
(a  balanced  valve  may  become  unbalanced  by  the  joint  leaking)  and  when  it 
is  imperfectly  lubricated.  The  load  on  the  valve  is  the  product  of  the  ar^a 
into  the  greatest  unbalanced  pressure  upon  it  per  square  inch,  and  the  co- 
efficient of  friction  may  be  as  high  as  20^.  The  product  of  this  coefficient 
and  the  load  is  the  force  necessary  to  move  the  valve,  which  equals  the 
maximum  thrust  on  the  valve-rod.  From  this  force  the  diameter  of  the 
valve  -rod  may  be  calculated  by  Hodgkinson's  formula  for  columns.  An 

empirical  formula  given  by  Sea  ton  is:    Diam.  of  rod  =  d  =  A/-^-  ,  in  which 

I  =  length  and  b  —  breadth  of  valve,  in  inches;  p  =  maximum  absolute 
pressure  on  the  valve  in  Ibs.  per  sq  in.,  and  Fa.  coefficient  whose  values  are, 
for  iron:  long  rod  10,000,  short  12,000;  for  steel:  long  rod  12.000,  short  14,500. 

Whitham  gives  the  short  empirical  rule:  Diam.  of  valve-rod  =  1/30  diam. 
of  cyl.  =  %  diam  of  piston-rod. 

Size  of  Slot-link.    (Seaton.)—  Let  D  be  the  diam.  of  the  valve  rod 


then  Diameter  of  block-pin  when  overhung  =  D. 

"    secured  at  both  ends  =  0.75  x  D. 

eccentric-  rod  pins  =0.7    x  D. 

suspension  rod  pins  =  0.55  X  D. 

pin  when  overhung  =  0.75  X  D. 


816  THE  STEAM-EHGIHE. 

Breadth  of  link  =  0.8  to  0.9  X  D. 

Length  of  block  =  1.8  to  1.6  X  D. 

Thickness  of  bars  of  link  at  middle  =  0.7  X  D. 

If  a  single  suspension  rod  of  round  section,  its  diameter  =  0.7    X  D. 
If  two  suspension  rods  of  round  section,  their  diameter  =  0.55  x  D. 
Size  of  Double-bar  Links.—  When  the  distance  between  centres  of 
eccentric  pins  —  6  to  8  times  throw  of  eccentrics  (throw  —  eccentricity  = 
half  -travel  of  valve  at  full  gear)  D  as  before  : 

Depth  of  bars  =  1.25  X  D  -f  %  in. 

Thickness  of  bars  =0.5    x  D  -j-  ^  in. 

Length  of  sliding-blqck  =  2.5  to  3  x  D, 

Diameter  of  eccentric-rod  pins  =  0.8  x  D  -j-  14  in. 
41       centre  of  sliding-block  =  1.3  X  D. 

When  the  distance  between  eccentric  -rod  pins  =  5  to  5J4  times  throw  of 
eccentrics: 

Depth  of  bars  =  1.25  x  D  4-  \%  in. 

Thickness  of  bars  =0.5    x  D  -f  J4  in. 

Length  of  sliding-block  =  2.5  to  3  X  D. 

Diameter  of  eccentric-  rod  pins  =  0.75  X  D. 

Diameter  of  eccentric  bolts  (top  end)  at  bottom  of  thread  =  0.42  x  D  when 
of  iron,  and  0.38  x  D  when  of  steel. 

Tlie  Eccentric.—  Diam.  of  eccentric-sheave  =  2.4  x  throw  of  eccentric 
-j-  1.2  X  diam.  of  shaft.  D  as  before 

Breadth  of  the  sheave  at  the  shaft  ..................  =  1.15  X  D  -f-  0.65  inch 

Breadth  of  the  sheave  at  the  strap  ..................  =  D  +  0.6  inch. 

Thickness  of  metal  around  the  shaft  ..............  =  0.7  X  D  -f  0.5  inch, 

Thickness  of  metal  at  circumference  ...............  =  0.6  x  D  -J-  0.4  inch. 

Breadth  of  key  ......................................  =  0.7  X  D  -f-  0.5  inch. 

Thickness  of  key  .................................  =  0.25  X  -D  +  0.5  inch. 

Diameter  of  bolts  connecting  parts  of  strap  ........  =  0.6  x  D  +  0.1  inch. 

THICKNESS  OP  ECCENTRIC-STRAP. 

When  of  bronze  or  malleable  cast  iron: 
Thickness  of  eccentric-strap  at  the  middle  .........  =  0.4  x  D  4  0.6  inch. 

1    sides  ...........  =  0.3  X  D  +  0.5  inch. 

When  of  wrought  iron  or  cast  steel: 
Thickness  of  eccentric-strap  at  the  middle  ..........  =  0.4    X  D  -f-  0.5  inch, 

"      "    "    sides  ............   =  0.27  X  D  -f  0.4  inch 

Xlie  Eccentric-rod,  —  The  diameter  of  the  eccentric-rod  in  the  body 
and  at  the  eccentric  end  may  be  calculated  in  the  same  way  as  that  of  the 
connecting-rod,  the  length  being  taken  from  centre  of  strap  to  centre  of 
pin.  Diameter  at  the  link  end  =  0.8Z>  -f  0.2  inch. 

This  is  for  wrought-iron;  no  reduction  in  size  should  be  made  for  steel. 

Eccentric-rods  are  often  made  of  rectangular  section. 

R-eversing-gear  should  be  so  designed  as  to  have  more  than  sufficient 
strength  to  withstand  the  strain  of  both  the  valves  and  their  gear  at  the 
same  time  under  the  most  unfavorable  circumstances;  it  will  then  have  the 
stiffness  requisite  for  good  working. 

Assuming  the  work  done  in  reversing  the  link-motion,  W,  to  be  only  that 
due  to  overcoming  the  friction  of  the  valves  themselves  through  their  whole 
travel,  then,  if  T  be  the  travel  of  valves  in  inches;  for  a  compound  engine 

T  (I  X  bXff^    ,    T  (V  XV  xp*\ 
~  12V         5         /  +  12V  5  /' 

I1.  bl  andp1  being  length,  breadth  and  maximum  steam-pressure  on  valve 
of  the  second  cylinder;  and  for  an  expansive  engine 


To  provide  for  the  friction  of  link-motion,  eccentrics  and  other  gear,  and 
for  abnormal  conditions  of  the  same,  take  the  work  at  one  and  a  half  times 
the  above  amount. 


FLY-WHEELS.  817 

To  find  the  strain  at  any  part  of  the  gear  having  motion  when  reversing, 
divide  the  work  so  found  by  the  space  moved  through  by  that  part  in  feet; 
the  quotient  is  the  strain  in  pounds;  and  the  size  may  be  found  from  the 
ordinary  rules  of  construction  for  any  of  the  parts  of  the  gear.  (Seaton.) 

Engine-frames  or  Bed-plates.— No  definite  rules  for  the  design 
of  engine-frames  have  been  given  by  authors  of  works  on  the  steam-engine. 
The  proportions  are  left  to  the  designer  who  uses  "  rule  of  thumb,"  or 
copies  from  existing  engines.  F.  A.  Halsey  (Am.  Much.,  Feb.  14,  1895)  has 
made  a  comparison  of  proportions  of  the  frames  of  horizontal  Corliss 
engines  of  several  builders.  The  method  of  comparison  is  to  compute  from 
the  measurements  the  number  of  square  inches  in  the  smallest  cross-sec- 
tion of  the  frame,  that  is,  immediately  behind  the  pillow-block,  also  to 
compute  the  total  maximum  pressure  upon  the  piston,  and  to  divide  the 
latter  quantity  by  the  former.  The  result  gives  the  number  of  pounds 

Eressure  upon  the  piston  allowed  for  each  square  inch  of  metal  in  the 
'ame.  He  finds  that  the  number  of  pounds  per  square  inch  of  smallest 
section  of  frame  ranges  from  217  for  a  10  X  30-in.  engine  up  to  575  for  a 
28  X  48-inch.  A  30  X  60-inch  engine  shows  350  Ibs.,  and  a  32-inch  engine 
which  has  been  running  for  many  years  shows  667  Ibs.  Generally  the 
strains  increase  with  the  size  of  the  engine,  and  more  cross- section  of  metal 
is  allowed  with  relatively  long  strokes  than  with  short  ones. 

From  the  above  Mr.  Halsey  formulates  the  general  rule  that  in  engines 
of  moderate  speed,  and  having  strokes  up  to  one  and  one-half  times  the 
diameter  of  the  cylinder,  the  load  per  square  inch  of  smallest  section 
should  be  for  a  10-inch  engine  300  pounds,  which  figure  should  be  increased 
for  larger  bores  up  to  500  pounds  for  a  30-  inch  cylinder  of  same  relative 
stroke.  For  high  speeds  or  for  longer  strokes  the  load  per  square  inch 
should  be  reduced. 

FLY-WHEELS. 

The  function  of  a  fly- wheel  is  to  store  up  and  to  restore  the  periodical  fluc- 
tuations of  energy  given  to  or  taken  from  an  engine  or  machine,  and  thus 
to  keep  approximately  constant  the  velocity  of  rotation.  Rankine  calls  the 

A  7? 

quantity  —  —  the  coefficient  of  fluctuation  of  speed  or  of  unsteadiness,  in 

*-^o 

which  E0  is  the  mean  actual  energy,  and  &E  the  excess  of  energy  received  or 
of  work  performed,  above  the  mean,  during  a  given  interval.  The  ratio  of 
the  periodical  excess  or  deficiency  of  energy  A#to  the  whole  energy  exerted 
in  one  period  or  revolution  General  Morin  found  to  be  from  1/6  to  J4  f°r 
single-cylinder  engines  using  expansion;  the  shorter  the  cut  off  the  higher 
the  value.  For  a  pair  of  engines  with  cranks  coupled  at  90°  the  value  of  the 
ratio  is  about  J4,  and  for  three  engines  with  cranks  at  120°,  1/12  of  its  value 
for  single-cylinder  engines.  For  tools  working  at  intervals,  such  as  punch- 
ing, slotting  and  plate-cutting  machines,  coining-presses,  etc.,  &E\s  nearly 
equal  to  the  whole  work  performed  at  each  operation. 

A_£J 
A  fly-wheel  reduces  the  coefficient  tT^r  to  a  certain  fixed  amount,  being 

4MiQ 

about  1/32  for  ordinary  machinery,  and  1/50  or  1/60  for  machinery  for  fine 
purposes. 

If  m  be  the  reciprocal  of  the  intended  value  of  the  coefficient  of  fluctua- 
tion of  speed,  A.Ethe  fluctuation  or  energy,  /the  moment  of  inertia  of  the 

fly-wheel  alone,  and  «0  its  mean  angular  velocity,  J  =  — — ".    As  the'rim  of 

°o 

a  fly-wheel  is  usually  heavy  in  comparison  with  the  arms,  /may  be  taken 
to  equal  Wr2,  in  which  W  =  weight  of  rim  in  pounds,  and  r  the  radius  of  the 

wheel;  then  W  =  m^  2    =  — '—t — ,  if  v  be  the  velocity  of  the  rim  in  feet  per 

second.    The  usual  mean  radius  of  the  fly-wheel  in  steam-engines  is  from 
three  to  five  times  the  length  of  the  crank.    The  ordinary  values  of  the  prod- 
uct mg,  the  unit  of  time  being  the  second,  lie  between  1000  and  2000  feet. 
(Abridged  from  Rankine,  S  E.,  p.  62.) 
Thurston    gives    for  engines  with    automatic  valve-gear  W  =  250,000 

,  in  which  A  —  area  of  piston  in  square  inches,  S  =  stroke  in  feet,  p  = 

mean  steam  pressure  in  Ibs.  per  sq.  in.,  R  =  revolutions  per  minute,  D  =  out- 
side diameter  of  wheel  in  feet.  Thurston  also  gives  for  ordinary  forms  of 


818  THE    STEAM-ENGINE. 

non-  condensing  engine  with  a  ratio  of  expansion  between  8  and  5,  W  ^. 

p-,  in  which  a  ranges  from  10,000,000  to  15,000,000,  averaging  12,000,000. 
2 


For  gas-engines,  in  which  the  charge  is  fired  with  every  revolution,  the  Amer- 
ican Machinist  gives  this  latter  formula,  with  a  doubled,  or  24,000,000. 
Presumably,  if  the  charge  is  fired  every  other  revolution,  a  should  be  again 
doubled. 

Rankine  ("  Useful  Rules  and  Tables,"  p.  247)  gives  W  =  475,000  T^L  ,  in 

which  Fis  the  variation  of  speed  per  cent,  of  the  mean  speed.  Thurston  s 
first  rule  above  given  corresponds  with  this  if  we  take  Fat  1.9  per  cent. 

Hartnell  (Proc.  Inst.,  M.  E.  1882,  427)  says:  The  value  of  F,  or  the 
variation  permissible  in  portable  engines,  should  not  exceed  3  per  cent,  with 
an  ordinary  load,  and  4  per  cent  when  heavily  loaded.  In  fixed  engines,  for 
ordinary  purposes.  F  =  2^  to  3  per  cent.  For  good  governing  or  special 
purposes,  such  as  cotton  -spinning,  the  variation  should  not  exceed  1J^  to  2 
per  cent. 

F.  M.  Rites  (Trans.  A.  S.  M.  E.,  xiv.  100)  develops  anew  formula  for  weight 

C  X  I  H  P  0 

of  rim,  viz.,  W  =  —  J&fyiT""'  •>  an(*  wefent  of  rim  per  horse-power  =  ™f™i  in 

which  C  varies  from  10,000,000,000  to  20,  000,000,000;  also  using  the  latter  value 

71/7,2  iy    Q  142/)27?a 

of  C,  he  obtains  for  the  energy  of  the  fly-wheel  ^-  =  ^-  ^^0  = 
CXH.P.(3.14)2Z>2£2  850,000  H.P.  850,000 

--  wheel  energy  per  HP-  =  ™ 


The  limit  of  variation  of  speed  with  such  a  weight  of  wheel  from  excess  of 
power  per  fraction  of  revolution  is  less  than  .0028. 

The  value  of  the  constant  C  given  by  Mr.  Rites  was  derived  from  practice 
of  the  Westinghouse  single-acting  engines  used  for  electric-lighting.  For 
double-acting  engines  in  ordinary  service  a  value  of  C  =  5,000,000,000  would 
probably  be  ample. 

From  these  formulae  it  appears  that  the  weight  of  the  fly-wheel  for  a  given 
horse-power  should  vary  inversely  with  the  cube  of  the  revolutions  and  the 
square  of  the  diameter. 

J.  B.  Stan  wood  (Eng'g,  June  12,  1891)  says:  Whenever  480  feet  is  the 
lowest  piston-speed  probable  for  an  engine  of  a  certain  size,  the  fly-wheel 
weight  for  that  speed  approximates  closely  to  the  formula 

tr=  700,000^. 

W  =  weight  in  pounds,  d  =  diameter  of  cylinder  in  inches,  s  =  stroke  in 
inches.  D  =  diameter  of  wheel  in  feet,  R  =  revolutions  per  minute,  corre 
spending  to  480  feet  piston  -speed. 

In  a  Ready  Reference  Book  published!  by  Mr.  Stanwood,  Cincinnati,  1892, 
he  erives  the  same  formula,  with  coefficients  as  follows:  For  slide-valve  en- 
gines, ordinary  duty,  350,000;  same,  electric-lighting,  700,000;  for  automatic 
high-speed  engines,  1,000,000;  for  Corliss  engines,  ordinary  duty  700,000, 
electric-lighting  1,000,000. 

u  AS 

Thurston's  formula  above  given,  W  —    •       ,  with  a  =  12,000,000,  when  re- 

d2s 
duced  to  terms  of  d  and  s  in  inches,  becomes  W  =  785,400      ' 

2  AS  PR 
If   we   reduce  it  to  terms  of  horse-power,  we   have  I.H.P.  =    00        » 

0»3,000 

iti  which  P  =  mean  effective  pressure.  Taking  this  at  40  Ibs.,  we  obtain 
W  =  5,000,000,000^^.  If  mean  effective  pressure  =  30  Ibs.,  then  JF  = 

T  "FT  P 

6,666,000,000-^^. 

Emil  Theiss  (Am.  Mach.,  Sept.  7  and  14,  1893)  gives  the  following  values 
or  d,  the  coefficient  of  steadiness,  which  is  the  reciprocal  of  what  Rankine 
calls  the  coefficient  of  fluctuation  : 


ELY-WHEELS. 


819 


For  engines  operating- 
Hammering  and  crushing  machinery d=   5 

Pumping  and  shearing  machinery d  =  20  to   30 

Weaving  and  paper-making  machinery d  =  40 

Milling  machinery d  =  50 

Spinning  machinery . .  d  —  50  to  100 

Ordinary  driving-engines  (mounted  on  bed-plate), 

belt  transmission ...   d  =  35 

Gear-wheel  transmission d  =  50 

/7\xT  TT  p 

Mr.  Theiss's  formula  for  weight  of  fly-wheel  in  pounds  is  W=  i  X       2* — — '» 

where  d  is  the  coefficient  of  steadiness,  V  the  mean  velocity  of  the  fly- 
wheel rim  in  feet  per  second,  n  the  number  of  revolutions  per  minute,  i  — 
a  coefficient  obtained  by  graphical  solution,  the  values  of  which  for  dif- 
ferent conditions  are  given  in  the  following  table.  In  the  lines  under  "cut- 
off,1' p  means  "  compression  to  initial  pressure,"  and  O  "  no  compression  ": 

VALUES  OF  i.    SINGLE-CYLINDER  NON-CONDKNSING  ENGINES. 


Piston- 
speed,  ft. 
per  min. 

Cut-off,  1/6. 

Cut-off,  J4. 

Cut-off,  ^. 

Cut-off,  & 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

200 
400 
600 
800 

272,690 
240,810 
194,670 

158,200 

218,580 
187,430 
145,400 
108,690 

242.010 
208,200 
168.590 
162,070 

209,170 
179,460 
136,460 
135,260 

220,760 
188,510 
165,210 

201,920 
170.040 
146,610 

193,340 
174,630 

182,840 
167,860 

SINGLE-CYLINDER  CONDENSING  ENGINES. 


*£a 

2vS 

O?   <D   . 

£81 
03   P- 

200 
400 
600 

Cut-off,  J4 

Cut-off,  1/6. 

Cut-off,  14. 

Cut-off,  i£ 

Cut-off,  y%. 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

O 

Corn  p. 
P 

0 

265,560 
194,550 
148,780 

176,560 
117,870 
140,090 

234,160 
174,380 

173,660 
118,350 

204,210 
164,720 

167,140 
133,080 

189,600 
174,630 

161,830 
151,680 

172,690 

156,990 

TWO-CYLINDER  ENGINES,  CRANKS  AT  90°. 


a^.5 
3-eS 
•22  g  u 

s&g 

5s  & 

Cut-off,  1/6. 

Cut-off,  y± 

Cut-off,  M. 

Cut-off,  l^. 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

0 

Comp. 
P 

O 

200 
400 
600 

800 

71,980 
70,160 
70,040 
70,040 

[  Mean 
[60,140 
J 

59,420 
57,000. 
57,480 
60,140 

!  Mean 
f  54,340 
J 

49,272 
49,150 
49,220 

(_  Mean 

r  50,000 

37,9-.>0 
35,500 

\  Mean 
f  36,950 

THREE-CYLINDER  ENGINES,  CRANKS  AT  120°. 


c^.5 
S-oS 
.2  %  ^ 

P^aR 

OD  ft 

Cut-off,  1/6. 

Cut  -off,  M- 

Cut-off,  J4 

Cut-off,  ^. 

Comp. 
P 

0 

Comp. 
P 

O 

Comp. 
P 

O 

Comp. 
P 

0 

200 
800 

33,810 
30,190 

32,240 
31,570 

33,810 
35,140 

35,500 
33,810 

34,540 
36,470 

33,450 
32,850 

35,260 
33,810 

32,370 
32,370 

As  a  mean  value  of  ?'  for  these  engines  we  may  use  33,810. 


820  THE   STEAM-ENGINE. 

Centrifugal  Force  in  Fly-wheels.—  Let  W  =  weight  of  riin  in 
pounds;  R  —  mean  radius  of  rim  in  feel;  r  =  revolutions  per  minute,  g  — 
'62.1(5;  v  =  velocity  of  rim  in  feet  per  second  =  2nRr-+-  CO. 

Wr2          4PF7T2/??-2 

Centrifugal  force  of  whole  rim  =  F  =  -  -  -  =  .000341  WRr*. 

gR 


The  resultant,  acting  at  right  angles  to  a  diameter  of  half  of  this  force, 
tends  to  disrupt  one  half  of  the  wheel  from  the  other  half,  and  is  resisted  by 
the  section  of  the  rim  at  each  end  of  the  diameter.  The  resultant  of  half  the 

radial  forces  taken  at  right  angles  to  the  diameter  is  1  -*-  y$n  =  -  of  the  sum 

of  these  forces;  hence  the  total  force  F  is  to  be  divided  by  2  x  2  X  1.5708 
=  6.2832  to  obtain  the  tensile  strain  on  the  cross-section  of  the  rim,  or,  total 
strain  on  the  cross-section  =  S  =  .00005427  WRr*.  The  weight  W^  of  a 
rim  of  cast  iron  1  inch  square  in  section  is  ZirR  X  3.125  =  19.635.R  pounds, 
M-hence  strain  per  square  inch  of  sectional  area  of  rim  =  Sl  =  .0010656.S2>2 
=  .0002664Z)2?-2  =  .0000270  F2,  in  which  D  =  diameter  of  wheel  in  feet,  and  F 
is  velocity  of  rim  in  feet  per  minute.  £j  =  .0972v2,  if  v  is  taken  in  feet  per 
second. 

For  wrought  iron  ..........  Sl  =  .0011366.RV2  =  .0002842DV2  =  .0000288F2. 

For  steel  .................  Sx  =  .001  1593.RV2  =  .  0002901  DVa  =  .0000294  F2 

For  wood  ..................  Si  =  .0000888JS2r2  =  .0000222L*2?-2  =  .00000225  F  2. 

The  specific  gravity  of  the  wood  being  taken  at  0.6  =  37.5  Ibs.  per  cu.  ft., 
or  1/12  the  weight  of  cast  iron. 

Example.—  Required  the  strain  per  square  inch  in  the  rim  of  a  cast-iron 
wheel  30  ft.  diameter,  60  revolutions  per  minute. 

Answer.  152  X  602  X  .0010656  =  863.1  Ibs. 

Required  the  strain  per  square  inch  in  a  cast-iron  wheel-rim  running  a 
mile  a  minute.  Answer.  .000027  X  52802  =  752.7  Ibs. 

In  cast-iron  fly-wheel  rims,  on  account  of  their  thickness,  there  is  difficulty 
in  securing  soundness,  and  a  tensile  strength  of  10,000  Ibs.  per  sq.  in.  is  as 
much  as  can  be  assumed  with  safety.  Using  a  factor  of  safety  of  10  gives  a 
maximum  allowable  strain  in  the  rim  of  1000  Ibs.  per  sq.  in.,  which  corre- 
sponds to  a  rim  velocity  of  6085  ft.  per  minute. 

For  any  given  material,  as  cast  iron,  the  strength  to  resist  centrifugal  force 
depends  only  on  the  velocity  of  the  rim,  and  not  upon  its  bulk  or  weight. 

Chas.  E.  Emery  (Cass.  Mag.,  1892)  says:  By  calculation  half  the  strength 
of  the  arms  is  available  to  strengthen  the  rim,  or  a  trifle  more  if  the  fly- 
wheel centres  are  relatively  large.  The  arms,  however,  are  subject  to  trans- 
verse strains,  from  belts  and  from  changes  of  speed,  and  there  is,  moreover, 
no  certainty  that  the  arms  and  rim  will  be  adjusted  so  as  to  pull  exactly 
together  in  resisting  disruption,  so  the  plan  of  considering  the  rim  by  itself 
and  making  it  strong  enough  to  resist  disruption  by  centrifugal  force  within 
safe  limits,  as  is  assumed  in  the  calculations  above,  is  the  safer  way. 

It  does  not  appear  that  fly-wheels  of  customary  construction  should  be 
unsafe  at  the  comparatively  low  speeds  now  in  common  use  if  proper 
materials  are  used  in  construction.  The  cause  of  rupture  of  fly-wheels  that 
have  failed  is  usually  either  the,  "  running  away  "  of  the  engine,  such  as  may 
be  caused  by  the  breaking  or  slackness  of  a  governor-belt,  or  incorrect 
design  or  defective  materials  of  the  fly-wheel. 

Chas.  T.  Porter  (Trans.  A.  S.  M.  E.,  xiv.  808)  states  that  no  case  of  the 
bursting  of  a  fly-wheel  with  a  solid  rim  in  a-high-speed  engine  is  known.  He 
attributes  the  bursting  of  wheels  built  in  segments  to  insufficient  strength 
<«f  the  flanges  and  bolts  by  which  the  segments  are  held  together.  (See  also 
Thnrston,  "  Manual  of  the  Steam-engine.'1  Part  II,  page  413,  etc.) 

A  mi*  of  Fly-wheels  and  Pulleys.  —  Professor  Torrey  (Am. 
Mack.,  July  30,  1891)  gives  the  following  formulafor  arms  of  elliptical  cross- 
section  of  cast-iron  wheels  : 

W  =  load  in  pounds  acting  on  one  arm;  S  =  strain  on  belt  in  pounds  per 
inch  of  width,  taken  at  56  for  single  and  112  for  double  belts;  v  =  width  of 
belt  in  inches;  n  =  number  of  arms;  L  =  length  of  arm  in  feet;  b  =  breadth 

of  arm  at  hub;    d  =  depth  of  arm  at  hub,  both  in  inches  :     W  =  ~-> 

WL  U  ' 

b  —  rr-^  .    The  breadth  of  the  arm  is  its  least  dimension  =  minor  axis  of 

c/Oa-* 

the  ellipse,  and  the  depth  the  major  axis.  This  formula  is  based  on  a  factor 
of  safety  of  10, 


FLY-WHEELS.  821 

In  using  the  formula,  first  assume  some  depth  for  the  arm,  and  calculate 
the  required  breadth  to  go  with  it.  If  it  gives  too  round  an  arm,  assume 
the  breadth  a  little  greater,  and  repeat  the  calculation.  A  second  trial  will 
almost  always  give  a  good  section. 

The  size  of  the  arms  at  the  hub  having  been  calculated,  they  may  be 
somewhat  reduced  at  the  rim  end.  The  actual  amount  cannot  be  calculated, 
as  there  are  too  many  unknown  quantities.  However,  the  depth  and 
breadth  can  be  reduced  about  one  third  at  the  rim  without  danger,  and  this 
will  give  a  well-shaped  arm. 

Pulleys  are  often  cast  in  halves,  and  bolted  together.  When  this  is  done 
the  greatest  care  should  be  taken  to  provide  sufficient  metal  in  the  bolts. 
This  is  apt  to  be  the  very  weakest  point  in  such  pulleys.  The  combined  area 
of  the  bolts  at  each  joint  should  be  about  28/100  the  cross-section  of  the  pul 
ley  at  that  point.  (Torrey.) 


Unwin  gives  d  =  0.6337 4/  ~^~  for  single  belts  ; 

'~BL) 
d  =  0.798  y  -Jp  for  double  belts; 

D  being  the  diameter  of  the  pulley,  and  B  the  breadth  of  the  rim,  both  in 
inches.  These  formulae  are  based  on  an  elliptical  section  of  arm  in  wrhich 
/>  =  OAd  or  d  =  2.56  on  a  width  of  belt  =  4/5  the  width  of  the  pulley  rim, 
a  maximum  driving  force  transmitted  by  the  belt  of  56  Ibs.  per  inch  of  width 
for  a  single  belt  and  112  Ibs.  for  a  double  belt,  and  a  safe  working  stress  of 
cast  iron  of  2250  Ibs.  per  square  inch. 
If  in  Torrey 's  formula  we  make  b  =  0.4d,  it  reduces  to 


*/WL 
=  Y    187^5 


Example.—  Given  a  pulley  10  feet  diameter;  8  arms,  each 4  feet  long;  face, 
36  inches  wide;  belt,  30  inches:  required  the  breath  and  depth  of  the  arm  at 
the  hub.  According  to  Unwin, 


s  /BD                  3  /36  X  120 
d  =  0.6337 1/  —  =  0.633  j/  § —  =  5.16  for  single  belt,  b  =  2.06; 

3  /RD                 3  /36  X  120 
d  =  0.798  A/  —  =  0.798 //  — g =  6.50  for  double  belt,  b  =  2.60. 

According  to  Torrey,  if  we  take  the  formula  b  =  — —  and  assume   d  •—  5 

and  6.5  inches,  respectively,  for  single  and  double  belts,  we  obtain  6  =  1.08 
arid  1.33,  respectively,  or  practically  only  one  half  of  the  breadth  according 
to  Unwin.  and.  since  transverse  strength  is  proportional  to  breadth,  an  arm 
only  one  half  as  strong. 

Torrey's  formula  is  said  to  be  based  on  a.  factor  of  safety  of  10,  but  this 
factor  can  be  only  apparent  and  not  real,  since  the  assumption  that  the 
strain  on  each  arm  is  equal  to  the  strain  on  the  belt  divided  by  the  number 
of  arms,  is,  to  say  the  least,  inaccurate.  It  would  be  more  nearly  correct  to 
say  that  the  strain  of  the  belt  is  divided  among  half  the  number  of  arms. 
Unwin  makes  the  same  assumption  in  developing  his  formula,  but  says  it  is 
only  in  a  rough  sense  true,  and  that  a  large  factor  of  safety  must  be  allowed. 
He  therefore  takes  the  low  figure  of  2250  Ibs.  per  square 'inch  for  the  safe 
working  strength  of  cast  iron.  Unwin  says  that  his  equations  agree  well 
with  practice. 

Diameters  of  Fly-wheels  for  Various  Speeds.— If  6000  feet 
per  minute  be  the  maximum  velocity  of  rim  allowable,  then  6000  =  nRD,  in 
which  R  =  revolutions  per  minute,  and  D  =  diameter  of  wheel  in  feet, 

6000       1910 
whence  D  =  — —  =  — — . 


822 


THE   STEAM-ENGINE. 


MAXIMUM  DJAMETKR  OF  FLY-WHEEL  ALLOWABLE  FOR  DIFFERENT  NUMBERS 
OF  REVOLUTIONS. 


Revolutions 
per  minute. 

Assuming:  Maximum  Speed  of 
5000  feet  per  minute. 

Assuming  Maximum  Speed 
of  6000  feet  per  minute. 

Circum.  ft. 

Diam.  ft. 

Circum.  ft. 

Diam.  ft. 

40 

125 

39.8 

150. 

47.7 

50 

100 

31.8 

120. 

38.2 

60 

83.3 

26.5 

100. 

31.8 

70 

71.4 

22.7 

85.72 

27.3 

80 

62.5 

19.9 

75.00 

23.9 

90 

55.5 

17.7 

66.66 

21.2 

100 

50. 

15.9 

60.00 

19.1 

120 

41.67 

13.3 

50.00 

15.9 

140 

35.71 

11.4 

42.86 

13.6 

160 

31.25 

9.9 

37.5 

11.9 

180 

27.77 

8.8 

33.33 

10.6 

200 

25.00 

8.0 

30.00 

9.6 

220 

22.73 

7.2 

27.27 

8.7 

240 

20.83 

6.6 

25.00 

8.0 

260 

19.23 

6.1 

23.08 

7.3 

280 

17.86 

5.7 

21.43 

6.8 

300 

16.66 

5.3 

20.00 

6.4 

350 

14.29 

4.5 

17.14 

5.5 

400 

12.5 

4.0 

15.00 

4.8 

450 

11.11 

3.5 

13.33 

4  2 

500 

10.00 

3.2 

12.00 

3^8 

Strains  in  the  Rims  of  Fly-band  Wheels  Produced  by 
Centrifugal  Force.  (James  B.  Stanwood,  Trans.  A.  S.  M.  E.,  xiv.  251.) 
—Mr.  Stan  wood  mentions  one  case  of  a  fly-band  wheel  where  the  periphery 
velocity  on  a  17'  9"  wheel  is  over  7500  ft.  per  minute. 

In  band  saw -mil  Is  the  blade  of  the  saw  is  operated  successfully  over 
wheels  8  and  9  ft.  in  diameter,  at  a  periphery  velocity  of  9000  to  10,000  ft.  per 
minute.  These  wheels  are  of  cast  iron  throughout,  of  heavy  thickness,  with 
a  large  number  of  arms. 

In  shingle-machines  and  chipping-machines  where  cast-iron  disks  from  2  to 
5  ft.  in  diameter  are  employed,  with  knives  inserted  radially,  the  speed  is 
frequently  10,000  to  11,000  ft.  per  minute  at  the  periphery. 

If  the  rim  of  a  fly-wheel  alone  be  considered,  the  tens'ile  strain  in  pounds 

F2 
per  square  inch  of  the  rim  section  is  T  —  — -  nearly,  in  which  V  =  velocity 

in  feet  per  second;  but  this  strain  is  modified  by  the  resistance  of  the  arms, 
which  prevent  the  uniform  circumferential  expansion  of  the  rim,  and  induce 
a  bending  as  well  as  a  tensile  strain.  Mr.  Stanwood  discusses  the  strains  in 
band-wheels  due  to  transverse  bending  of  a  section  of  the  rim  between  a 
pair  of  arms. 

When  the  arms  are  few  in  number,  and  of  large  cross-section,  the  ring 
will  be  strained  transversely  to  a  greater  degree  than  Avith  a  greater  number 
of  lighter  arms.  To  illustrate  the  necessary  rim  thicknesses  for  various 
rim  velocities,  pulley  diameters,  number  of  arms,  etc.,  the  following  table 
is  given,  based  upon  the  formula 


in  which  t  —  thickness  of  rim  in  inches,  d  —  diameter  of  pulley  in  inches, 
JV  =  number  of  arms,  V  =  velocity  of  rim  in  feet  per  second,  and  F  =  the 
greatest  strain  in  pounds  per  square  inch  to  which  any  fibre  is  subjected. 
The  value  of  F  is  taken  at  6000  Ibs.  per  sq.  in. 


FLY-WHEELS. 


823 


Thickness  of  Rims  in  Solid  Wheels, 


Diameter  of 
Pulley  in 
inches. 

Velocity  of 
Rim  in  feet  per 
second. 

Velocity  of 
Rim  in  feet  per 
minute. 

No.  of 
Arms. 

Thickness  in 
inches. 

24 

50 

3,000 
5  °80 

6 
6 

2/10 
15/32 

24 

AQ 

88 

5,280 

6 

15/16 

108 
108 

184 
184 

11,040 
11,040 

16 
36 

!__ 

rim  velocity 


_ 

r  all  wheels  be  assumed  to  be  88  ft.  per  sec- 
"  theformulabecomes 


the  formula  becomes  ^ 

t=    N*(  F         ^j 

or  for  a  fixed  maximum  rim  velocity  of  88  ft.  per  second  and  F  =  6000  Ibs., 
t  =  l^df  In  segmental  wheels  it  is  preferable  to  have  the  joints  opposite 
the  arm's  Wheels  in  halves,  if  very  thin  rims  are  to  be  employed,  should 

S^'S?sSSs^*%?iS 

Weight  (calculated)  of  ash  rim 31<855    lbs- 

41          ~f  IDA  o».-mc  (fntirin rv  4o.()^U) 


Ihe  wheel  was  tested  at  76  revs,  per  min.,  being  a  surface  speed  of  nearly 
7SJOO  feet  per  minute. 


854  THE   STEAM-ENGINE. 

Mr.  Manning  discusses  the  relative  safety  of  cast  iron  and  of  wooden 
wheels  as  follows:  As  for  safety,  the  speeds  being  the  same  in  both 
cases,  the  hoop  tension  in  the  rim  per  unit  of  cross-section  would  be  directly 
as  the  weight  per  cubic  unit;  and  its  capacity  to  stand  the  strain  directly  as 
the  tensile  strength  per  square  unit;  therefore  the  tensile  strengths  divided 
by  the  weights  will  give  relative  values  of  different  materials.  Cast  iron 
weighing  450  Ibs.  per  cubic  foot  and  with  a  tensile  strength  of  1,440,000 Ibs. 
per  square  foot  would  give  a  value  of  1,440,000-^-450:=  3200,  whilst  ash,  of 
which  the  rim  was  made,  weghing  34  Ibs.  per  cubic  foot,  and  with  1,152,000 
Ibs.  tensile  strength  per  square  foot,  gives  a  result  1,152,000 -r- 34  =  33,882, 
and  33,882  -f-  3200  =  10.58,  or  the  wood-rimmed  pulley  is  ten  times  safer 
than  the  cast-iron  when  the  castings  are  good.  This  would  allow  the  wood- 
rimmed  pulley  to  increase  its  speed  to  1/10.58  =3.25  times  that  of  a  sound 
cast-iron  one  with  equal  safety. 

Wooden  Fly-wlieel  of  the  Willimantic  Linen  Co.  (Illus- 
trated in  Power,  March,  1893.)— Rim  28  ft.  diam.,  110  in.  face.  The  rim  is 
carried  upon  three  sets  of  arms,  one  under  the  centre  of  each  belt,  with  12 
arms  in  each  set. 

The  material  of  the  rim  is  ordinary  whitewood,  %  in.  iu  thickness,  cut  into 
segments  not  exceeding  4  feet  in  length,  and  either  5  or  8  inches  in  width. 
These  were  assembled  by  building  a  complete  circle  13  inches  in  width,  first 
with  the  8  inch  inside  and  the  5-inch  outside,  and  then  beside  it  another  cir- 
cle with  the  widths  reversed,  so  as  to  break  joints.  Each  piece  as  it  was 
added  was  brushed  over  with  glue  and  nailed  with  three-inch  wire  nails  to 
the  pieces  already  in  position.  The  nails  pass  through  three  and  into  the 
fourth  thickness.  At  the  end  of  each  arm  four  14-inch  bolts  secure  the 
rim,  the  ends  being  covered  by  wooden  plugs  glued  and  driven  into  the  face 
of  the  \vheel. 

Wire-wound  Fly-wlieels  for  Extreme  Speeds.  (Eng'gNews, 
August  2,  1890.)— The  power  required  to  produce  the  Mannesmann  tubes  is 
very  large,  varying  from  2000  to  10,000  H.P.,  according  to  the  dimensions  of 
the  tube.  Since  this  power  is  only  needed  for  a  short  time  (it  takes  only  30 
to  45  seconds  to  convert  a  bar  10  to  12  ft.  long  and  4  in.  in  diameter  into  a 
tube),  and  then  some  time  elapses  before  the  next  bar  is  ready,  an  engine  of 
1200  H.P.  provided  with  a  large  fly-wheel  for  storing  the  energy  will  supply 
power  enough  for  one  set  of  rolls.  These  fly-wheels  are  so  large  and  run  at 
such  great  speeds  that  the  ordinary  method  of  constructing  them  cannot  be 
followed.  A  wheel  at  the  Mannesmann  Works,  made  in  Komotau,  Hungary, 
in  the  usual  manner,  broke  at  a  tangential  velocity  of  125  ft.  per  second. 
The  fly-wheels  designed  to  hold  at  more  than  double  this  speed  consist  of  a 
cast-iron  hub  to  which  two  steel  disks,  20  ft.  in  diameter,  are  bolted;  around 
the  circumference  of  the  wheel  thus  formed  70  tons  of  No.  5  wire  are  wound 
under  a  tension  of  50  Ibs.  In  the  Mannesmann  Works  at  Land  ore,  Wales, 
such  a  wheel  makes  240  revolutions  a  minute,  corresponding  to  a  tangential 
velocity  of  15,080  ft.  or  2.85  miles  per  minute. 

THE    SLIDE-VALVE. 

Definitions.— Travel  —  total  distance  moved  by  the  valve. 

Throw  of  the  Eccentric  —  eccentricity  of  the  eccentric  =  distance  from  the 
centre  of  the  shaft  to  the  centre  of  the  eccentric  disk  =  ^  the  travel  of  the 
valve.  (Some  writers  use  the  term  "  throw  "  to  mean  the  whole  travel  of 
the  valve.) 

Lap  of  the  valve,  also  called  outside  lap  or  steam-lap  =  distance  the  outer 
or  steam  edge  of  the  valve  extends  beyond  or  laps  over  the  steam  edge  of 
the  port  when  the  valve  is  in  its  central  position. 

Inside  lap,  or  exhaust-lap  -  distance  the  inner  or  exhaust  er?ge  of  the 
valve  extends  beyond  or  laps  over  the  exhaust  edge  of  the  port  when  the 
valve  is  in  its  central  position.  The  inside  lap  is  sometimes  made  zero,  or 
even  negative,  in  which  latter  case  the  distance  between  the  edge  of  the 
valve  and  the  edge  of  the  port  is  sometimes  called  exhaust  clearance,  or 
inside  clearance. 

Lead  of  the  valve  —  the  distance  the  steam-port  is  opened  when  the  engine 
is  on  its  centre  and  the  piston  is  at  the  beginning  of  the  stroke. 

Lead-angle  =  the  angle  between  the  position  of  the  crank  when  the  valve 
begins  to  be  opened  and  its  position  when  the  piston  is  at  the  beginning  of 
the  stroke. 

The  valve  is  said  to  have  lead  when  the  steam-port  opens  before  the  piston 


THE   SLIDE- VA 


begins  its  stroke.  If  the  piston  begins  its  stroke  before  the  admission  of 
steam  begins  the  valve  is  said  to  have  negative  lead,  and  its  amount  is  the 
lap  of  the  edge  of  the  valve  over  the  edge  of  the  port  at  the  instant  when 
the  piston  stroke  begins. 

Lap-angle  =  the  angle  through  which  the  eccentric  must  be  rotated  to 
cause  the  steam  edge  to  travel  from  its  central  position  the  distance  of  the 
lap. 

Angular  advance  of  the  eccentric  =  lap-angle  -\-  lead  angle. 

Linear  advance  =  lap  4-  lea1 1. 

Elieet  of  L&p,  iLead.  etc.9  upon  the  Steam  Distribution.— 
Given  valve-travel  2%  in.,  lap  %  in.,  lead  l/i«3  in.,  exhaust-lap  ^  in.,  re- 
quired crank  position  for  admission,  cut-off,  release  and  compression,  arid 
greatest  port-opening.  (Halsey  on  Slide-valve  Gears.)  Draw  a  circle  of 
diameter  fh  =•  travel  of  valve.  From  O  the  centre  set  off  Oa  =  lap  and  ab 
—  lead,  erect  perpendiculars  Oe,  ac,  bd;  then  ec  is  the  lap-angle  and  cd  the 
lead-angle,  measured  as  arcs.  Set  off  fg ;  =  cd,  the  lead-angle,  then  Og  is 
the  position  of  the  crank  for  steam  admission.  Set  off  2ec-f  cd  from  h  to  z; 
then  Oi  is  the  crank-angle  for  cut-off,  and/fc-s-//i  is  the  fraction  of  stroke 
completed  at  cut-off.  Set  off  Ol  =  exhaust-lap  and  draw  Ini:  em  is  the 
exhaust-lap  angle.  Set  off  hn  =  ec  —  cd  -\-ern,  and  On  is  the  position  of 
crank  at  release.  Set  off  fp  —  ec  -j-  cd  -f  em,  and  Op  is  the  position  of  crank 
tor  compression,  fo  -f-  fh  is  the  fraction  of  stroke  completed  at  release,  and 
hq  -*-  hf  is  the  fraction  of  the  return  stroke  completed  when  compression 
begins;  Oh,  the  throw  of  the  eccentric,  minus  Oa  the  lap,  equals  ah  the 
maximum  port-opening. 

If  a  valve  has  neither  lap  nor  lead,  the  line  joining  the  centre  of  the  eccen- 


^^-~~- 

^9    Cut-Off 

^^^ 

,' 

.^TS-sj  <r* 

^r 

/  '      > 

/ 

i 

/  i        / 

N 

? 

/ 

j 

/ 

/ 

N^ 

/ 

j 

/       /  / 

N, 

/ 

i 

*       /'  x/ 
/    // 

V-tt 

^-VRele 

/ 

i 

A    1 

l 

'    /  ft 

xx-xX               \ 

f 

j 

•    t  /  i 

x. 

\ 

/ 

l 
i 
l 

/   x  ff        s' 

/  *      \  '' 

\ 

'// 

,' 

9. 

^ 

*          \ 

0^            k      a 

6          o 

\  Admission                                  /                                            M  —  -&-*>**•  —  •--: 
\                                                  /         fc  -Lap  >|    j     Opening 

\                  /                                      / 

'ompressida 


FIG.  146. 

trie  disk  and  the  centre  of  the  shaft  being  at  right  angles  to  the  line  of  the 
crank,  the  engine  would  follow  full  stroke,  admission  of  steam  beginning  at 
the  beginning  of  the  stroke  and  ending  at  the  end  of  the  stroke. 

Adding  lap  to  the  valve  enables  us  to  cut  off  steam  before  the  end  of  the 
stroke;  the  eccentric  being  advanced  on  the  shaft  an  amount  equal  to  the 
lap-angle  enables  steam  to  be  admitted  at  the  beginning  of  the  stroke,  as 


THE    STEAM-ENGINE. 


before  lap  was  added,  and  advancing  it  a  further  amount  equal  to  the  lead 
angle  causes  steam  to  be  admitted  before  the  beginning  of  the  stroke. 

Having  given  lap  to  the  valve,  and  having  advanced  the  eccentric  on  the 
shaft  from  its  central  position  at  right  angles  to  the  crank,  through  the 
angular  advance  =  lap-angle  and  lead-angle,  the  four  events,  admission, 
cut-off,  release  or  exhaust-opening,  and  compression  or  exhaust -closure, 
take  place  as  follows:  Admission,  when  the  crank  lacks  the  lead-angle  of 
having  reached  the  centre;  cut-off,  when  the  crank  lacks  two  lap-angles  and 
one  lead-angle  of  having  reached  the  centre.  During  the  admission  of 
steam  the  crank  turns  through  a  semicircle  less  twice  the  lap-angle.  The 
greatest  port-opening  is  equal  to  half  the  travel  of  the  valve  less  the  lap. 
Therefore  for  a  given  port-opening  the  travel  of  the  valve  must  be  in- 
creased if  the  lap  is  increased.  When  exhaust-lap  is  added  to  the  valve  it 
delays  the  opening  of  the  exhaust  and  hastens  its  closing  by  an  angle  of 
rotation  equal  to  the  exhaust- lap  angle,  which  is  the  angle  through  which 
the  eccentric  rotates  from  its  middle  position  wrhile  the  exhaust  edge  of  the 
valve  uncovers  its  lap.  Release  then  takes  place  when  the  crank  lacks  one 
lap-angle  and  one  lead-angle  minus  one  exhaust-lap  angle  of  having  reached 
the  centre,  and  compression  when  the  crank  lacks  lap-angle  +  lead-angle -)- 
exhaust-lap  angle  of  having  reached  the  centre. 

The  above  discussion  of  the  relative  position  of  the  crank,  piston,  and 
valve  for  the  different  points  of  the  stroke  is  accurate  only  with  a  connect- 
ing-rod of  infinite  length. 

For  actual  connecting-rods  the  angular  position  of  the  rod  causes  a 
distortion  of  the  position  of  the  valve,  causing  the  events  to  take  place  too 
late  in  the  forward  stroke  and  too  enrly  in  the  return.  The  correction  of  • 
this  distortion  may  be  accomplished  t  >  some  extent  by  setting  the  valve  so 
as  to  give  equal  lead  on  both  forward  and  return  stroke,  and  by  altering 
the  exhaust-lap  on  one  end  so  as  to  equalize  the  release  and  compression. 
F.  A.  Halsey,  in  his  Slide-valve  Gears,  describes  a  method  of  equali/ing  the 
cut-off  without  at  the  same  time  affecting  the  equality  of  the  lead.  In 
designing  slide-valves  the  effect  of  angularity  of  the  connecting-rod  should 
be  studied  on  the  drawing-board,  and  preferably  by  the  use  of  a  model. 

Sweet's  Valve-diagram.-  To  find  outside  and  inside  lap  of  valve 
for  different  cut-offs  and  compressions  (see  Fig.  147):  Draw  a  circle  whose 


A1    M1 


FIG.  147.— Sweet's  Valve-diagram. 


diameter  equals  travel  of  valve.  Draw  diameter  BA  and  continue  to  A1, 
so  that  the  length  AA1  b*ars  the  same  ratio  to  XA  as  the  length  of  connect- 
ing-rod does  to  length  of  engine-crank.  Draw  small  circle  E  with  a  diam- 
eter equal  to  lead.  Lay  off  AC  so  that  ratio  of  AC  to  AB=  cut-off  in 
parts  of  the  stroke.  Erect  perpendicular  CD.  Draw  DL  tangent  to  E\ 
draw  XS  perpendicular  to  DL\  XS  is  then  outside  lap  of  valve. 

To  find  release  and  compression:  If  there  is  no  inside  lap,  draw  FE 
through  X  parallel  to  DL.  F  and  7?  will  be  position  of  crank  for  release 
and  compression.  If  there  is  an  inside  lap,  draw  a  circle  about  X,  in  which 
radius  XY  equals  inside  lap.  Draw  HG  tangent  to  this  circle  and  parallel 
to  DL',  then  H  and  G  are  crank  position  for  release  and  compression. 
Draw  HN  and  MG,  then  AN  is  piston  position  at  release  and  A M  piston 
position  at  compression,  AB  being  considered  stroke  of  engine. 

To  make  compression  alike  on  each  stroke  it  is  necessary  to  increase  the 
inside  lap  on  crank  end  of  valve,  and  to  decrease  by  the  same  amount  the 


THE   SLIDE-VALVE. 


827 


inside  lap  on  back  end  of  valve.  To  determine  this  amount,  through  M  with 
a  radiusltfSP  -  AA\  draw  arc  If  P,  from  P  draw  PT  perpendicular  tc ,AB. 
then  TM  is  the  amount  to  be  added  to  inside  lap  on  crank  end  and  to  be 
deducted  from  inside  lap  on  back  end  of  valve,  inside  lap  being  XT. 

For  the  Rilqram.  Valve  Diagram,  see  Halsey  on  Slide-valve  Gears. 

The  Zeuiier  Valve-diagram  is  given  in  most  of  the  works  on  the 
steam-engine,  and  in  treatises  on  valve -gears,  as  Zeuner  s,  Peabody  s,  and 


A' 


K 


FIG.  148.— Zeuner's  Valve-diagram. 


Spangler's  The  following  is  condensed  from  Holmes  on  the  Steam-engine: 
Describe  a  circle,  with  radius  OA  equal  to  the  half  travel  of  the  valve. 
From  O  measure  off  OB  equal  to  the  outside  lap,  and  BC  equal  to  the  lead. 
When  the  crank-pin  occupies  the  dead  centre  A,  the  valve  has  already 
moved  to  the  right  of  its  central  position  by  the  space  OB  4-  BC.  From  C 
erect  the  perpendicular  CE  and  join  OE.  Then  will  OE  be  the  position 
occupied  by  the  line  joining  the  centre  of  the  eccentric  with  the  centre  of 
i  he  crank-shaft  at  the  commencement  of  the  stroke.  On  the  line  OE  as 
diameter  describe  the  circle  OCE  ;  then  any  chords,  as  Oe,  OE,  Oe',  will 
represent  the  spaces  travelled  by  the  valve  from  its  central  position  when 
the  crank-pin  occupies  respectively  the  positions  opposite  to  D,  E,  and  F. 
Before  the  port  is  opened  at  all  the  valve  must  have  moved  from  its  central 
position  by  an  amount  equal  to  the  lap  OB.  Hence,  to  obtain  the  space  by 
which  the  port  is  opened,  subtract  from  each  of  the  arcs  Oe,  OE,  etc.,  a 
length  equal  to  OB.  This  is  represented  graphically  by  describing  from 
centre  O  a  circle  with  radius  equal  to  the  lap  OB  ;  then  the  spaces  fe  gE, 
etc  intercepted  between  the  circumferences  of  the  lap-circle  Bfe'  and  the 
valve-circle  OCE,  will  give  the  extent  to  which  the  steam-port  is  opened 

At  the  point  fc,  at  which  the  choi  1  Ok  is  common  to  both  valve  and  lap 
circles  it  is  evident  that  the  valve  1  as  moved  to  the  right  by  the  amount  of 
the'lap  and  is  consequently  just  on  the  point  of  opening  the  steam-port. 
Hence  the  steam  is  admitted  before  the  commencement  of  the  stroke,  when 
the  crank  occupies  the  position  OH,  and  while  the  portion  HA  of  the  revo- 


328  THE   STEAM-EKGINE. 

lution  still  remains  to  be  accomplished.  When  the  crank-pin  reaches  the 
position  A,  that  is  to  say,  at  the  commencement  of  the  stroke,  the  port  is 
already  opened  by  the  space  OG  —  OB  =  BC,  called  the  lead.  From  this 
point  forward  till  the  crank  occupies  the  position  O^the  port  continues  to 
open,  but  when  the  crank  is  at  OE  the  valve  has  reached  the  furthest  limit 
of  its  travel  to  the  right,  and  then  commences  to  return,  till  when  in  the 
position  OF  the  edge  of  the  valve  just  covers  the  steam-port,  as  is  shown 
by  the  chord  Oe',  being  again  common  to  both  lap  and  valve  circles.  Hence 
when  the  crank  occupies  the  position  OF  the  cut-off  takes  place  and  the 
steam  commences  to  expand,  and  continues  to  do  so  till  the  exhaust  opens. 
For  the  return  stroke  the  steam-port  opens  again  at  H'  and  closes  at  F' ' . 

There  remains  the  exhaust  to  be  considered.  When  the  line  joining  the 
centres  of  the  eccentric  and  crank-shaft  occupies  the  position  opposite  to 
OG  at  right  angles  to  the  line  of  dead  centres,  the  crank  is  in  the  line  OP  at 
right  angles  to  OE  ;  and  as  OP  does  not  intersect  either  valve-circle  the 
valve  occupies  its  central  position,  and  consequently  closes  the  port  by  the 
amount  of  the  inside  lap.  The  crank  must  therefore  move  through  such 
an  angular  distance  that  its  line  of  direction  OQ  must  intercept  a  chord  on 
the  valve-circle  OK  equal  in  length  to  the  inside  lap  before  the  port  can  be 
opened  to  the  exhaust.  This  point  is  ascertained  precisely  in  the  same 
manner  as  for  the  outside  lap,  namely,  by  drawing  a  circle  from  centre  O, 
with  a  radius  equal  to  the  inside  lap;  this  is  the  small  inner  circle  in  the 
figure.  Where  this  circle  intersects  the  two  valve-circles  we  get  four  points 
which  show  the  positions  of  the  crank  when  the  exhaust  opens  and  closes 
during  each  revolution.  Thus  at  Q  the  valve  opens  the  exhaust  on  the  side 
of  the  piston  which  we  have  been  considering,  while  at  R  the  exhaust  closes 
and  compression  commences  and  continues  till  the  fresh  steam  is  read- 
mitted at  H. 

Thus  the  diagram  enables  us  to  ascertain  the  exact  position  of  the  crank 
when  each  critical  operation  of  the  valve  takes  place.  Making  a  resume  of 
these  operations  of  one  side  of  the  piston,  we  have:  Steam  admitted  before 
the  commencement  of  the  stroke  at  H.  At  the  dead  centre  A  the  valve  is 
already  opened  by  the  amount  BC.  At  E  the  port  is  fully  opened,  and 
valve  has  reached  one  end  of  its  travel.  At  .F steam  is  cut  off,  consequently 
admission  lasted  f rom  H  to  F.  At  P  valve  occupies  central  position,  and 
ports  are  closed  both  to  steam  and  exhaust.  At  Q  exhaust  opened,  conse- 
quently expansion  lasted  from  .Fto  Q.  At  K  exhaust  opened  to  maximum 
extent,  and  valve  reached  the  end  of  its  travel  to  the  left.  At  R  exhaust 
closed,  and  compression  begins  and  continues  till  the  fresh  steam  is  admitted 
atH. 

PROBLEM. — The  simplest  problem  which  occurs  is  the  following  :  Given 
the  length  of  throw,  the  angle  of  advance  of  the  eccentric,  and  the  laps  of 
the  valve,  find  the  angles  of  the  crank  at  which  the  steam  is  admitted  and 
cut  off  and  the  exhaust  opened  and  closed.  Draw  the  line  OE,  representing 
the  half-travel  of  the  valve  or  the  throw  of  the  eccentric  at  the  given  angle 
of  advance  with  the  perpendicular  OG.  Produce  OEto  K.  On  OjBand  OK 
as  diameters  describe  the  two  valve-circles.  With  centre  and  radii  equal  to 
the  given  laps  describe  the  outside  and  inside  lap-circles.  Then  the  inter- 
section of  these  circles  with  the  two  valve-circles  give  points  through  which 
the  lines  OH,  OF,  OQ,  and  OR  can  be  drawn.  These  lines  give  the  required 
positions  of  the  crank. 

Numerous  other  problems  will  be  found  in  Holmes  on  the  Steam-engine, 
inch  id  ing  problems  in  valve-setting  and  the  application  of  the  Zeuner  dia- 
gram to  link  motion  and  to  the  Meyer  valve-gear. 

Port  Opening.— The  area  of  port  opening  should  be  such  that  the  ve- 
locity of  the  steam  in  passing  through  it  should  not  exceed  6000  ft.  per  in  in. 
The  ratio  of  port  area  to  piston  area  will  then  vary  with  the  piston-speed  as 
follows: 
For  speed^of^iston,  j_     1(X)    m    ^    40Q    5(/0    600    ?00    g()0    900    10QO    ]200 

Port  area .  =  piston  |_     01?    Q33     Q5   >Q67  >Q83     ^     >1Q7   >133     15      16?       ^ 

di  ea  x 
For  a  velocity  of  6000  ft.  per  min., 

sq.  of  diam.  of  cyl.  X  piston  speed 
Jrort  area  =  — •  — '••AQQ - . 

The  length  of  the  port  opening  may  be  equal  to  or  something  less  than  the 
diameter  of  the  cylinder,  and  the  width  =  area  of  port  opening  -4-  its  length. 

The  bridge  between  steam  and  exhaust  ports  should  be  wide  enough  to 
prevent  a  leak  of  steam  into  the  exhaust  due  to  overtravel  of  the  valve. 


THE    SLIDE-VALVE. 


829 


Auchincloss  gives:  Width  of  exhaust  port  =  width  of  steam  port  + 
U  travel  of  valve  —  width  of  bridge. 

Lead.  (From  Peabody's  Valve-gears.)— The  lead,  or  the  amount  that 
the  valve  is  open  when  the  engine  is  on  a  dead  point,  varies,  with  the  type 
and  size  of  the  engine,  from  a  very  small  amount,  or  even  nothing,  up  to  % 
of  an  inch  or  more.  Stationary -engines  running  at  slow  speed  may  have 
from  1/64  to  1/16  inch  lead.  The  effect  of  compression  is  to  fill  the  waste 
space  at  the  end  of  the  cylinder  with  steam;  consequently,  engines  having 
much  compression  need  less  lead  Locomotive-engines  having  the  valves 
controlled  by  the  ordinary  form  of  Stephenson  link-motion  may  have 
a  small  lead  when  running  slowly  and  with  along  cut-off,  but  when  at  speed 
with  a  short  cut-off  the  lead  is  at  least  y±  inch;  and  locomotives  that  have 
valve-gear  which  gives  constant  lead  commonly  have  J4  inch  lead.  The 
lead  angle  is  the  angle  the  crank  makes  with  the  line  of  dead  points  at 
admission.  It  may  vary  from  0°  to  8°. 

Inside  Lead.— Weisbach  (vol.  ii.  p.  296)  says:  Experiment  shows  that 
the  earlier  opening  of  the  exhaust  ports  is  especially  of  advantage,  and  in 
the  best  engines  the  lead  of  the  valve  upon  the  side  of  the  exhaust,  or  the 
inside  lead;  is  1/25  to  1/15;  i.e.,  the  slide-valve  at  the  lowest  or  highest  posi- 
tion of  the  piston  has  made  an  opening  whose  height  is  1/25  to  1/15  of  the 
whole  throw  of  the  slide-valve.  The  outside  lead  of  the  slide-valve  or  the 
lead  on  the  steam  side,  on  the  other  hand,  is  much  smaller,  and  is  often 
only  1/100  of  the  whole  throw  of  the  valve. 

Effect  of  Changing  Outside  Lap,  Inside  Lap,  Travel 
and  Angular  Advance.    (Thurston.) 


Admission 

Expansion 

Exhaust 

Compression 

Incr. 
O.L. 

is  later, 
ceases  sooner 

occurs  earlier, 
continues  longer 

is  unchanged 

begins  at 
same  point 

Incr. 
I.L. 

unchanged 

begins  as  before, 
continues  longer 

occurs  later, 
ceases  earlier 

begins  sooner, 
continues  longer 

Incr. 
T. 

begins  sooner, 
continues  longer 

begins  later, 
ceases  sooner 

begins  later, 
ceases  later 

begins  later, 
ends  sooner 

Incr. 
A.  A. 

begins  earlier, 
period  unaltered 

begins  soonen, 
per.  the  same 

begins  earlier, 
per.  unchanged 

begins  earlier, 
P3r.  the  same 

Zeuner  gives  the  following  relations  (Weisbach-Dubois,  vol.  ii.  p.  307): 
If  -S  =  travel  of  valve,  p  =  maximum  port  opening; 
L  =  steam-lap,  I  =  exhaust-lap; 

R  =  ratio  of  steam -lap  to  half  travel  =  — ,    L  =  —  X  S; 

.00  «6 

r  =  ratio  of  exhaust  lap  to  half  travel  =  -— ,    I  =  |  x  S', 

S  =  2p  +  2L  =  2p  +  2R  +  S-,    8=  r^=. 

i  —  K 

If  a  =  angle  HOP  between  positions  of  crank  at  admission  and  at  cut-off, 
and  /3  =  angle  QOR  between  positions  of  crank  at  release  and  at 

compression,  then  R  =  M8'"?.*?,— };    ''  =  !'"ta<18°°  ~  * 


sin  J 


sin 


Ratio  of  Lap  and  of  Port-opening  to  Valve-travel.— The 

table  on  page  831,  giving  the  ratio  of  lap  to  travel  of  valve  and  ratio  of  travel 
to  port  opening,  is  abridged  from  one  given  by  Buel  in  Weisbach-Dubois, 
vol.  ii.  It  is  calculated  from  the  above  formulae.  Intermediate  values  may 
be  found  by  the  formulae,  or  with  sufficient  accuracy  by  interpolation  from 
the  figures  in  the  table.  By  the  table  on  page  830  the  crank-angle  may  be 
found,  that  is,  the  angle  between  its  position  when  the  engine  is  on  the 
centre  and  its  position  at  cut-off,  release,  or  compression,  when  these  are 
known  in  fractions  of  the  stroke.  To  illustrate  the  use  of  the  tables  the 
following  example  is  given  by  Buel:  width  of  port  =  2. 2  in.;  width  of  port 
opening=  width  of  port  -j-  0.3  in.;  over  overtravel  =  2.5  in.:  length  of 
connecting-rod  =  2^  times  stroke;  cut-off.  .75  of  stroke;  release,  .95  of 
stroke;  lead-angle,  10°.  From  the  first  table  we  find  crank-angle  =  114.6; 


830 


THE   STEAM-ENGINE. 


add  lead-angle,  making  124.6.°  From  the  second  table,  for  angle  between 
admission  arid  cut-off,  125°,  we  have  ratio  of  travel  to  port-opening  =  3.72, 
or  for  124.6°  =  3.74,  which,  multiplied  by  port-opening  2.5,  gives  9.45  in 
travel.  The  ratio  of  lap  to  travel,  by  the  table,  is  .2324,  or  9.45  X  .2324  =  2.2 
in.  lap.  For  exhaust-lap  we  have,'  for  release  at  .95,  crank-angle  =  151.3: 
add  lead-angle  10°  =  161.3°.  From  the  second  table,  by  interpolation,  ratio 
of  lap  to  travel  =  .0811,  and  .0811  X  9.45  =  0.77  in.,  the  exhaust-lap. 

Lap-angle  =  %  (180°  —  lead-angle  —  crank-angle  at  cut-off); 

=  y%  (180°  -  10  -  114.6;  =  27.7°. 

Angular  advance    =  lap-angle  X  lead-angle  =  27.7  -f-  10  =  37.7°. 
Exhaust  lap-angle  =  crank-angle  at  release  -j-  lap-angle  -f-  lead-angle  —  180°; 

-  151.3  -f  27.7  -j-  10  -  180°  =  9°. 
Crank-angle  at  com-  J 

pression  measured  >  =  180°  —  lap-angls  —  lead-angle  —  exhaust  lap-angle; 
on  return  stroke     ) 

=  180  -  27.7  -  10  -  9  =  133.3°  ;  corresponding,    by 
table,  to  a  piston  position  of  .81  of  the  return  stroke;  or 
CranK-angle  at  compression  =  180°  —  (angle  at  release  -  angle  at  cut-off) 

-j-  lead-angle; 

=  180    -  (151.3-  114.6)4-10  =  133.3°. 

The  positions  determined  above  for  cut-off  and  release  are  for  the  forward 
stroke  of  the  piston.    On  the  return  stroke  the  cut-off  will  take  place  at 


the  same  angle,  114.6°,  corresponding  by  table  to  66.6$  of  the  return 
stroke,  instead  of  75$.  By  a  slight  adjustment  of  the  angular  advance 
and  the  length  of  the  eccentric  rod  the  cut-off  can  be  equalized.  The 


,        ., 

stroke,  instead  of   75$.    By  a  slight  adjustment  of   the   angular   advance 
and  the  length  of  the  eccentric    rod  the  cut-off   can    be  equ 
width  of  the  bridge  should  be  at  least  2.5  -f-  0.;25  —  2.2  =  0.55  in. 

Crank  Angles  for  Connecting-rods  of  Different  Length. 

FORWARD  AND  RETURN  STROKES. 


'raction  of 
troke  from 
imencement. 

Ratio  of  Length  of  Connecting-rod  to  Length  of  Stroke. 

2 

2« 

3 

3H 

4 

5 

Infi 
nite. 

For. 

"CO  C 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

For. 

Ret. 

or 

5 

Ret. 

.01 

10.3 

13  2 

10.5 

12.8 

10.6 

12.6 

10.7 

12.4 

10.8 

12.3 

10.9 

12.1 

11.5 

.02 

14.6 

18.7 

14.9 

18.1 

15.1 

17.8 

15.2 

17.5 

15.3 

17.4 

15.5 

17.1 

16.3 

.03 

17.9 

22.9 

18.2 

22.2 

18.5 

21.8 

18.7 

21.5 

18.8 

21.3 

19  0 

21.0 

19.9 

.04 

20.7 

26.5 

21.1 

25.7 

21.4 

25.2 

21.6 

24.9 

21.8 

24.6 

22.0 

24.3 

23.1 

.05 

23.2 

29.6 

23.6 

28.7 

24.0 

28.2 

24.2 

27.8 

24.4 

27.5 

24.7 

27.2 

25.8 

.10 

33.1 

41.9 

33.8 

40.8 

34.3 

40.1 

34.6 

39.6 

34.9 

39.2 

35.2 

38.7 

36  9 

.15 

41 

51.5 

41.9 

50.2 

42.4 

49.3 

42.9 

48.7 

43.2 

48.3 

43.6 

47.7 

45.6 

.20 

48 

59.6 

48.9 

58.2 

49.6 

57.3 

50.1 

56.6 

50.4 

56.2 

50.9 

55.5 

53.1 

.25 

54.3 

66.9 

55.4 

65.4 

56.1 

64.4 

56.6 

63.7 

57.0 

63.3 

57.6 

62.6 

60.0 

.30 

60.3 

73.5 

61.5 

72.0 

62.2 

71.0 

62.8 

70.3 

63.3 

69.8 

63.9 

69.1 

66.4 

.35 

66.1 

79  8 

67.3 

78.3 

68.1 

77.3 

68.8 

76.6 

69  2 

76.1 

69.9 

75.3 

72.5 

.40 

71.7 

85.8 

73.0 

84.3 

73.9 

83.3 

74.5 

82.6 

75.0 

82.0 

75.7 

81.3 

78.5 

.45 

77.2 

91.5 

78.6 

90.1 

79.6 

89.1 

80.2 

88.4 

80.7 

87.9 

81.4 

87.1 

84.3 

.50 

82.8 

97.2 

84.3 

95.7 

85.2 

94.8 

85.9 

94.1 

86.4 

93.6 

87.1 

92  9 

90.0 

.55 

88.5 

102.8 

89.9 

101.4 

90.9 

100.4 

91.6 

99.8 

92.1 

99  3 

92.9 

98  G 

95.7 

.60 

94.2 

108.3 

95.7 

107.0 

96.7 

106.1 

97.4 

105.5 

98.0 

105.0 

98.7 

104.3 

101.5 

.65 

100.2 

113.9 

101.7 

112.7 

102.7 

111.9 

103.4 

111.2 

103.9 

110.8 

104.7 

110.1 

107.5 

.70 

106.5 

119.7 

108.0 

118.5 

109.0 

117.8 

109.7 

117.2 

110.2 

116.7 

110.9 

116.1 

113.6 

.75 

113.1 

125.7 

114.6 

124.6 

115.6 

123.9 

116.3 

123.4 

116.7 

123.0 

117.4 

122.4 

120.0 

.80 

120.4 

132 

121.8 

131.1 

122.7 

130.4 

123.4 

129.9 

123.8 

129.6 

124.5 

129.1 

126.9 

.85 

128.5 

139 

129.8 

138.1 

130.7 

137.6 

131.3 

137.1 

131.7 

136.8 

132.3 

136.4 

134.4 

.90 

138.1 

146.9 

139.2 

146.2 

139.9 

145.7 

140.4 

145.4 

140.8 

145.1 

141.3 

144.8 

143.1 

.95 

150.4 

156.8 

151.3 

156.4 

151.8 

156.0 

152.2 

155.8 

152.5 

155.6 

152.8 

155.3 

154.2 

.96 

153.5 

159.3 

154.3 

158.9 

154.8 

158.6 

155.1 

158.4 

155.4 

158.2 

155.7 

158.0 

156  9 

.97 

157.1 

162.1 

157.8 

161.8 

158.2 

161.5 

158.5 

161.3 

158.7 

161.2 

159.0 

161.0 

160.1 

.98 

161.3 

165.4 

161.9 

165.1 

162.2 

164.9162.5 

164.8 

162.6 

164.7 

162.9 

164.5 

163.7 

.99 

166.8 

169.7 

167.2 

169.5 

167.4 

169.4 

167.6 

169.3 

167.7 

169.2 

167.9 

169.1 

168.5 

1.00 

180 

180 

180    1  180 

180 

180 

180 

180 

180 

180 

180 

180 

180 

THE   SLIDE-VALVE. 


831 


Relative  Motions  of  Cross-head  and  Crank.  -If  L  =  length 
of  connecting-rod,  R  =  length  of  crank,  0  —  angle  of  crank  with  centre  line 
of  engine,  D  —  displacement  of  cross-head  from  the  beginning  of  its  stroke, 

D  =  R(l  -  cos  0)  =  L  -  VL?  -  R*  sin2  0. 
Lap  and  Travel  of  Val  ve. 


c'Sseg 

o 

0  L 

2ofc"  A 

0 

|| 

c  ofcS 

o 

Se 

li|a 

"3 

If 

fs28 

1 

c  ~  9  o 

H«^o 

1 

3^. 

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6'5O^3 

o3 

1-1  If 

§-io_ 

«w~£ 

o'5o 

S 

«*--  i- 

fepi"s§ 

O 

s 

^fc-cjl 

o 

iE 

a^a§ 

c 

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a> 

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1 

If 

|^c|^ 

o. 

2 

ju 

§|«|. 

1*8 

•sl 

l!* 

ypf  II 

s 

!IP| 

1"' 

.2-3 

y* 

!?<pft 

ife- 
w 

K 

co<Joa 

^ 

^  P  c 
M 

=  o<5oa 

1 

&~'~ 

30° 

.4830 

58.70 

85° 

.3686 

7.61 

135° 

.1913 

3.24 

35 

.4769 

43.22 

90 

.8536 

6.83 

140 

.1710 

3.04 

40 

.4699 

33.17 

95 

.3378 

6.17 

145 

.1504 

2.86 

45 

.4619 

26.27 

100 

.3214 

5.60 

150 

.1294 

2.70 

50 

.4532 

21.34 

105 

.3044 

5.11 

155 

.1082 

2.55 

55 

.4435 

17.70 

110 

.2868 

4.69 

160 

.0868 

2  42 

60 

.4330 

14.93 

115 

.2687 

4.32 

165 

.0653 

2.30 

65 

.4217 

12.77 

120 

.2500 

4.00 

170 

.0436 

2.19 

70 

.4096 

11.06 

125 

.2309 

3.72 

17'5 

.0218 

2.09 

75 

.3967 

9.68 

130 

2113 

3.46 

180 

0000 

2.00 

80 

.3830 

8.55 

PERIODS  OF  ADMISSION,  OR  CtTT-OFF,  FOR  VARIOUS 
L.APS  AND  TRAVELS  OF  SLIDE-VALVES. 

The  two  following  tables  are  from  Clark  on  the  Steam-engine.  In  the  first 
table  are  given  the  periods  of  admission  corresponding  to  travels  of  valve 
of  from  12  in.  to  2  in.,  and  laps  of  from  2  in.  to  %  in.,  wir,h  y±  in.  and  %  in.  of 
lead.  With  greater  leads  than  those  tabulated,  the  steam  would  be  cut  off 
earlier  than  as  shown  in  the  table. 

The  influence  of  a  lead  of  5/16  in.  for  travels  of  from  \%  in.  to  6  in.,  and 
laps  of  from  y2  in.  to  1^  in.,  as  calculated  for  in  fche  second  table,  is  exhibited 
by  comparison  of  the  periods  of  admission  in  thft  table,  for  the  same  lap  and 
travel.  The  greater  lead  shortens  the  period  of  admission,  and  increases  the 
range  for  expansive  working. 

Periods   of  Admission*  or   Points   of  Cut-off,  for  Given 
Travels  and  Laps  of  Slide-valves. 


><w  (£ 

1 

Periods  of  Admission,  or  Points  of  Cut  off,  for  the  following 
Laps  of  Valves  in  inches. 

H°> 

3 

2 

1% 

m 

m 

1 

% 

H 

% 

K 

% 

in. 

in. 

£ 

% 

% 

% 

% 

% 

% 

% 

% 

% 

12 

M 

88 

90 

93 

95 

96 

97 

98 

98 

99 

99 

10 

82 

87 

89 

92 

95 

96 

97 

98 

98 

99 

8 

/4 

72 

78 

84 

88 

92 

94 

95 

96 

98 

98 

6 

J4 

50 

62 

71 

79 

86 

89 

91 

94 

96 

97 

5^ 

i^ 

43 

56 

68 

77 

85 

88 

91 

94 

96 

97 

5 

x^ 

32 

47 

61 

72 

82 

86 

89 

92 

95 

97 

4Vi> 

1^ 

14 

35 

51 

66 

78 

83 

87 

90     I    94 

96 

4  " 

\A 

17 

39 

57 

72 

78 

83 

88         92 

95 

\£ 

20 

44 

63 

71 

79 

84 

90 

94 

3  3 

\£ 

23 

50 

61 

71 

79 

86 

91 

I/ 

27 

43 

57 

70 

80 

86 

2 

^ 

33 

52 

70 

81 

832 


THE   STEAM-ENGINE. 


Periods  of  Admission,   or    Points   of  rut-off,   for   given 
Travels  and  Laps  of  Slide-valves. 

Constant  lead,  5/1 G. 


Travel  . 

I 

^ap. 

Inches. 

*i 

% 

% 

% 

1 

Ifc 

m 

1% 

I& 

is/ 

19 

1% 

39 

W* 

47 

17 

2 

55 

34 

W* 

61 

42 

14 

%y 

65 

f)0 

30 

2§/ 

68 

55 

38 

13 

at? 

71 

59 

45 

27 

ORZ 

74 

63 

49 

36 

12 

oa/ 

76 

67 

56 

43 

26 

38 

78 

70 

59 

47 

82 

11 

8 

80 

73 

62 

50 

38 

23 

3l£ 

81 

74 

65 

55 

44 

30 

10 

3K 

83 

76 

68 

59 

48 

34 

22 

3% 

84 
85 

78 
80 

71 
73 

62 

64 

51 
53 

40 
45 

29 
34 

9 

20 

4 

4^4 

4V£ 
4% 
5 
£ 

86 
87 
87 
88 
89 
90 
92 
93 
94 
95 

81 
82 
83 
84 
86 
87 
89 
90 
92 
93 

75 

76 
78 
79 
81 
83 
85 
87 
89 
91 

66 

68 
70 
72 
76 
79 
81 
83 
86 
88 

57 
60 
63 
66 
70 
73 
76 
78 
82 
85 

49 
52 
55 
58 
63 
67 
70 
73 
78 
82 

38 
42 
46 
49 
56 
61 
65 
67 
73 
78 

26 
32 
36 
40 
47 
54 
58 
62 
68 
74 

9 
19 
25 
20 
37 
45 
51 
56 
63 
69 

Diagram  for  Port-opening,  Cut-off,  and  Lap.— The  diagram 
on  the  opposite  page  was  published  in  Power,  Aug.,  1893.  It  shows  at  a 
glance  the  relations  existing  between  the  outside  lap,  steam  port-opening, 
and  cut-off  in  slide  valve  engines. 

In  order  to  use  the  diagram  to  find  the  lap,  having  given  the  cut-off  and 
maximum  port-opening,  follow  the  ordinate  representing  the  latter,  taken 
on  the  horizontal  scale,  until  it  meets  the  oblique  line  representing  the  given 
cut-off.  Then  read  off  this  height  on  tlie  vertical  lap  scale.  Thus,  with  a 
port-opening  of  1*4  inch  and  a  cut-off  of  .50,  the  intersection  of  the  two  lines 
occurs  on  the  horizontal  3.  The  required  lap  is  therefore  3  in. 

If  the  cut  off  and  lap  are  given,  follow  the  horizontal  representing  the 
latter  until  it  meets  the  oblique  line  representing  the  cut-off.  Then  vertically 
below  this  read  the  corresponding  port-opening  on  the  horizontal  scale. 

If  the  lap  and  port-opening  are  given,  the  resulting  cut-off  may  be  ascer- 
tained by  finding  the  point  of  intersection  of  the  ordinate  representing  the 
port-opening  with  the  horizontal  representing  the  lap.  The  oblique  line 
passing  through  the  point  of  intersection  will  give  the  cut-off. 

If  it  is  desired  to  take  lead  into  account,  multiply  the  lead  in  inches  by  the 
numbers  in  the  following  table  corresponding  to  the  cut-off,  and  deduct  the 
result  from  the  lap  as  obtained  from  the  diagram: 


Cut-off. 

Multiplier. 

Cut-off. 

Multiplier. 

.20 

4.717 

.60 

.358 

.25 

3.731 

.625 

.288 

.30 

3.048 

.65 

222 

.33 

2.717 

.70 

'.103 

.375 

2.381 

.75 

.000 

.40 

2.171 

.80 

0.904 

.45 

1.930 

.85 

0.815 

.50 

1.706 

.875 

0.772 

.55 

1.515 

.90 

0.731 

THE   SLIDE-VALYE. 


833 


.685 


1234 

Maximum  Steam  Port  opening  in  Inches. 

DIAGRAM   FOR  SLIDE  VALVES. 

FIG.  149, 


834  THE   STEAM-EKGIXE. 

I*iston« valve, — The  piston-valve  is  a  modified  form  of  the  slide-valve^ 
The  lap,  lead,  etc.,  are  calculated  in  the  same  manner  as  for  the  common 
slide-valve.  The  diameter  of  valve  and  amount  of  port-opening  are  calcu- 
lated on  the  basis  that  the  most  contracted  portion  of  the  steam-passagu 
between  the  valve  and  the  cylinder  should  have  an  area  such  that  the 
velocity  of  steam  through  it  will  not  exceed  6000  ft.  per  minute.  The  area 
of  the  opening  around  the  circumference  of  the  valve  should  be  about  double 
the  area  of  the  steam-passage,  since  that  portion  of  the  opening  that  is 
opposite  from  the  steam-passage  is  of  little  effect. 

Setting  the  Valves  of  an  Engine.— The  principles  discussed 
above  are  applicable  not  only  to  the  designing  of  valves,  but  also  to  adjust- 
ment of  valves  that  have  been  improperly  set ;  but  the  final  adjustment  of 
the  eccentric  and  of  the  length  of  the  rod  depend  upon  the  amount  of  lost 
motion,  temperature,  etc.,  and  can  be  effected  only  after  trial.  After  the 
valve  has  been  set  as  accurately  as  possible  when  cold,  the  lead  and  lap  for 
the  forward  and  return  strokes  being  equalized,  indicator  diagrams  should 
betaken  and  the  length  of  the  eccentric-rod  adjusted,  if  necessary,  to  cor^ 
reot  slight  irregularities. 

To  Put  an  Engine  on  its  Centre.— Place  the  engine  in  a  posi- 
tion where  the  piston  will  have  nearly  completed  its  outward  stroke,  and 
opposite  some  point  on  the  cross-head,  such  as  a  corner,  make  a  mark  upon 
the  guide.  Against  the  rim  of  the  pulley  or  crank-disk  place  a  pointer  and 
mark  a  line  with  it  on  the  pulley.  Then  turn  the  engine  over  the  centre  until 
the  cross-head  is  again  in  the  same  position  on  its  inward  stroke.  This  will 
bring  the  crank  as  much  below  the  centre  as  it  was  above  it  before.  With  the 
pointer  in  the  same  position  as  before  make  a  second  mark  on  the  pulley- 
rim.  Divide  the  distance  between  the  marks  in  two  and  mark  the  middle 
point.  Turn  the  engine  until  the  pointer  is  opposite  this  middle  point,  and 
it  will  then  be  on  its  centre.  To  a-void  the  error  that  may  arise  from  the 
looseness  of  crank-pin  and  wrist-pin  bearings,  the  engine  should  be  turned 
a  little  above  the  centre  and  then  be  brought  up  to  it,  so  that  the  crank  pin 
will  press  against  the  same  brass  that  it  does  when  the  first  two  marks  are 
made. 

Link-motion. — Link-motions,  of  which  the  Stephenson  link  is  the 
most  commonly  used,  aredesigned  for  two  purposes:  first,  for  reversing  the 
motion  of  the  engine,  and  second,  for  varying  the  point  of  cut-off  by  varying 
the  travel  of  the  valve.  The  Stephenson  link  motion  is  a  combination  of 
two  eccentrics,  called  the  forward  and  back  eccentric,  with  a  link  connect- 
ing the  extremeties  of  the  eccentic-rods;  so  that  by  varying  the  position  of 
the  link  the  valve  rod  may  be  put  in  direct  connection  with  either  eccentric, 
or  may  be  given  a  movement  controlled  in  part  by  one  and  in  part  by  the 
other  eccentric.  When  the  link  is  moved  by  the  reversing  lever  into  a  posi- 
tion such  that  the  block  to  which  the  valve-rod  is  attached  is  at  either  end 
of  the  link,  the  valve  receives  its  maximum  travel,  and  when  the  link  is  in 
mid-gear  the  travel  is  the  least  and  cut-off  takes  place  early  in  the  stroke. 

In  the  ordinary  shifting-link  with  open  rods,  that  is,  not  crossed,  the  lead 
of  the  valve  increases  as  the  link  is  moved  from  full  to  mid-gear,  that  is,  as 
the  period  of  steam  admission  is  shortened.  The  variation  of  lead  is  equa- 
lized for  the  front  and  back  strokes  by  curving  the  link  to  the  radius  of  the 
eccentric-rods  concavely  to  the  axles.  With  crossed  eccentric-rods  the  lead 
decreases  as  the  link  is  moved  from  full  to  mid-gear.  In  a  valve-motion 
with  stationary  link  the  lead  is  constant.  (For  illustration  see  Clark's  Steam- 
engine,  vol.  ii.  p.  22.) 

The  linear  advance  of  each  eccentric  is  equal  to  that  of  the  valve  in  full 
gear,  that  is,  to  lap-}-  lead  of  the  valve,  when  the  eccentric-rods  are  attached 
to  the  link  in  such  position  as  to  cause  the  half- travel  of  the  valve  to  equal 
the  eccentricity  of  the  eccentric. 

The  angle  between  the  two  eccentric  radii,  that  is,  between  lines  drawn 
from  the  centre  of  the  eccentric  disks  to  the  centre  of  the  shaft  equals  180° 
less  twice  the  angular  advance. 

Buel,  in  Appleton's  Cyclopedia  of  Mechanics,  vol.  ii.  p.  316,  discusses  the 
Stephenson  link  as  follows:  "  The  Stephenson  link  does  not  give  a  perfectly 
correct  distribution  of  steam;  the  lead  varies  for  different  points  of  cut-off. 
The  period  of  admission  and  the  beginning  of  exhaust  are  not  alike  for  both 
ends  of  the  cylinder,  and  the  forward  motion  varies  from  the  backward. 

"  The  correctness  of  the  distribution  of  steam  by  Stephenson ''s  link-motion 
depends  upon  conditions  which,  as  much  as  the  circumstances  will  permit, 
ought  to  be  fulfilled,  namely:  1.  The  link  should  be  curved  in  the  arc  of  a 
Circle  whose  radius  is  equal  to  the  length  of  the  eccentric- rod.  2,  The/ 


THE   SLIDE-VALVE. 


835 


eccentric-rods  ought  to  be  long ;  the  longer  they  are  in  proportion  to  the 
eccentricity  the  more  symmetrical  will  the  travel  of  the  valve  be  on  both 
sides  of  the  centre  of  motion.  3.  The  link  ought  to  be  short.  Each  of  its 
points  describes  a  curve  in  a  vertical  plane,  whose  ordinatesgrow  larger  the 
farther  the  considered  point  is  from  the  centre  of  the  link;  and  as  the  hori- 
zontal motion  only  is  transmitted  to  the  valve,  vertical  oscillation  will  cause 
irregularities.  4.  The  link-hanger  ought  to  be  long.  The  longer  it  is  the 
nearer  will  be  the  arc  in  which  the  link  swings  to  a  straight  line,  and  thus 
the  less  its  vertical  oscillation.  If  the  link  is  suspended  in  its  centre,  the 
curves  that  are  described  by  points  equidistant  on  both  sides  from  the  centre 
are  not  alike,  and  hence  results  the  variation  between  the  forward  and  back- 
ward gear.  If  the  link  is  suspended  at  its  lower  end,  its  lower  half  will  have 
less  vertical  oscillation  and  the  upper  half  more.  5.  The  centre  from  which 
the  link-hanger  swings  changes  its  position  as  the  link  is  lowered  or  raised, 
and  also  causes  irregularities.  To  reduce  them  to  the  smallest  amount  the 
arm  of  the  lifting-shaft  should  be  made  as  long  as  the  eccentric-rod,  and  the 
centre  of  the  lifting-shaft  should  be  placed  at  the  height  corresponding  to 
the  central  position  of  the  centre  on  which  the  link-hanger  swings." 

All  these  conditions  can  never  be  fulfilled  in  practice,  and  the  variations 
in  the  lead  and  the  period  of  admission  can  be  somewhat  regulated  in  an 
artificial  way,  but  for  one  gear  only.  This  is  accomplished  by  giving  differ- 
ent lead  to  the  two  eccentrics,  which  difference  will  be  smaller  tbe  longer  the 
eccentric-rods  are  and  the  shorter  the  link,  and  by  suspending  *he  link  not 
exactly  on  its  centre  line  but  at  a  certain  distance  from  it,  giving  what  is 
called  "  the  offset." 

For  application  of  the  Zeuner  diagram  to  link-motion,  see  Holmes  on  the 
Steam-engine,  p.  290.  See  also  Clark's  Railway  Machinery  (1855),  Clark's 
Steam-engine  and  Zeuner's  and  Auchincloss's  Treatises  on  Slide-valve 
Gears. 

The  following  rules  are  given  by  the  American  Machinist  for  laying  out  a 
link  for  an  upright  slide-valve  engine.  By  the  term  radius  of  link  is  meant 
the  radius  of  the  link- arc  ab,  Fig.  150,  drawn  through  the  centre  of  the  slot; 


FIG.  150. 

this  radius  is  generally  made  equal  to  the  distance  from  the  centre  of  shaft 
to  centre  of  the  link-block  pin  P  when  the  latter  stands  midway  of  its  travel. 
The  distance  between  the  centres  of  the  eccentric-rod  pins  e^  e%  should  not 
be  less  than  2^  times,  and,  when  space  will  permit,  three  times  the  throw  of 
the  eccentric.  By  the  throw  we  mean  twice  the  eccentricity  of  the  eccentric. 
Che  slot  link  is  generally  suspended  from  the  end  next  to  the  forward  eccen- 
tric at  a  point  in  the  link-arc  prolonged.  This  will  give  comparatively  a 
^mall  amount  of  slip  to  the  link-block  when  the  link  is  in  forward  gear;  but; 
this  slip  will  be  increased  \\heu  tlw  link  is  iu  backward  gear,  This  increase 


836  THE   STEAM-ENGIKE. 

of  slip  is,  however,  considered  of  little  importance,  because  marine  engines, 
as  a  rule,  work  but  very  little  in  the  backward  gear.  When  it  is  necessary 
that  the  motion  shall  he  as  efficient  in  backward  gear  as  in  forward  gear, 
then  the  link  should  be  suspended  from  a  point  midway  bet  ween  the  two 
eccentric-rod  pins;  in  marine  engine  practice  this  point  is  generally  located 
on  the  link-arc;  for  equal  cut  off  s  it  is  better  to  move  the  point  of  suspen- 
sion a  small  amount  towards  the  eccentrics. 

For  obtaining  the  dimensions  of  the  link  in  inches  :  Let  L  denote  the 
length  of  the  valve,  B  the  breadth,  p  the  absolute  steam-pressure  per  sq. 
in.,  and  E  a  factor  of  computation  used  as  below;  then  R  =  .01  \  LxB  X  p. 

Breadth  of  the  link  .............  .  ..................  =   R  X  1.8 

Thickness  T  of  the  bar  .....................  ........  =   Rx    .8 

Length  of  sliding-block  ............................  =   R  x  2.5 

Diameter  of  eccentric-rod  pins  .................   =  (R  X    .7)  -f-  ^4 

Diameter  of  suspension  -rod  pin  ....................  =  (R  x    .6)4-^4 

Diameter  of  suspension-  rod  pin  when  overhung..  =  (R  X    .8)  -j-  /4 
Diameter  of  block-pin  when  overhung  ............  =   R  -f-  14 

Diameter  of  block-pin  when  secured  at  both  ends  =  (R  X    .8)  -j-  M 

The  length  of  the  link,  that  is,  the  distance  from  a  to  6,  measured  on  a 
straight  line  joining  the  ends  of  the  link-arc  in  the  slot,  should  be  such  as  to 
allow  the  centre  of  the  link-block  pin  Pto  be  placed  in  a  line  with  the  eccen- 
tric-rod pins,  leaving  sufficient  room  for  the  slip  of  the  block.  Another  type 
of  link  frequently  used  in  marine  engines  is  the  double  bar  link,  and  this 
type  is  again  divided  into  two  classes:  one  class  embraces  those  links  which 
have  the  eccentric-rod  ends  as  well  as  the  valve-spindle  end  between  the 
bars,  as  shown  at  B  (with  these  links  the  travel  of  the  valve  is  less  than 
the  throw  of  the  eccentric);  the  other  class  embraces  those  links,  shown  at 
C,  for  which  the  eccentric  -rods  are  made  with  fork-ends,  so  as  to  connect  to 
studs  on  the  outside  of  the  bars,  allowing  the  block  to  slide  to  the  end  of  the 
link,  so  that  the  centres  of  the  eccentric-rod  ends  and  the  block-pin  are  in 
line  when  in  full  gear,  making  the  travel  of  the  valve  equal  to  the  throw  of 
the  eccentric.  The  dimensions  of  these  links  when  the  distance  between 
the  eccentric-rod  pins  is  2^  to  2%  times  the  throw  of  eccentrics  can  be 
found  as  follows: 


Depth  of  bars  ........   ..................  .  .........  =  (E  X 

Thickness  of  bars  ..............   ...............  =  (R  X      .5)  -f  J4" 

Diameter  of  centre  of  sliding-block  ...........     =  R  X  1.8 

When  the  distance  between  the  eccentric-rod  pins  is  equal  to  3  or  4  times 
the  throw  of  the  eccentrics,  then 

Depth  of  bars  .....................................   =  (R  X  1.25)+%" 

Thickness  of  bars  ................................  =  (R  X     .5)-f-J4" 

All  the  other  dimensions  may  be  found  by  the  first  table.  These  are  em- 
pirical rules,  and  the  results  may  have  to  be  slightly  changed  to  suit  given 
conditions.  In  marine  engines  the  eccentric-rod  ends  for  all  classes  of  links 
have  adjustable  brasses.  In  locomotives  the  slot-link  is  usually  employed, 
and  in  these  the  pin-holes  have  case-hardened  bushes  driven  into  the  pin- 
holes,  and  have  no  adjustable  brasses  in.  the  ends  of  the  eccentric-  rods.  The 
link  in  B  is  generally  suspended  by  one  of  the  eccentric-rod  pins;  and  the 
link  in  C  is  suspended  by  one  of  the  pins  in  the  end  of  the  link,  or  by  one  of 
the  eccentric-  rod  pins. 

Other  Forms  of  Valve-Gear,  as  the  Joy,  Marshall,  Hackworth, 
Bremme,  Walschaert,  Corliss,  e;c.,  are  described  in  Clark's  Steam-engine, 
vol.  ii.  The  design  of  the  Reynolds-  Corliss  valve-gear  is  discussed  by  A.  H. 
Eldridge  in  Power,  Sep.  1893.  See  also  Henthorn  on  the  Corliss  engine. 
Rules  for  laying  down  the  centre  lines  of  the  Joy  valve-gear  are  given  in 
American  Machinist,  Nov.  13,  1890.  For  Joy's  "  Fluid-  pressure  Reversing- 
valve,"  see  Eng'g^  May  25,  1894. 

GOVERNORS. 


GOVERNORS.  837 

compared  with  the  weight  of  the  balls)  bears  to  the  radius  r  of  the  circle 
described  by  the  centres  of  the  balls  the  ratio 

h  _  weight  w     _  gr 

r  ~~  centrifugal  force  ~~    wv*  ~  i;2' 
~gr 

which  ratio  is  independent  of  the  weight  of  the  balls,  v  being  the  velocity 
of  the  centres  of  the  balls  in  feet  per  second. 

If  T  =  number  of  revolutions  of  the  balls  in  1  second,  v  =  2irrT  =  ar,  in 
which  a  =  the  angular  velocity,  or  2irT,  and 

0r«  g  0.8146  ,  9.775  . 

h  =    tfT  =  4^T*    °r    h  =  ~^~  feet  =  ~W  mCheS' 

35190 
g  being  taken  at  32.16.    If  ^V  =  number  of  revs,  per  minute,  &  = -TRJ- 

inclies 

For  revolutions  per  minute 40         45         50         60         75 

The  height  in  inches  will  be 21.99    17.38    14.08    9.775    6.256 

Number  of  turns  per  minute  required  to  cause  the  arms  to  take  a  given 
angle  with  the  vertical  axis:  Let  Z  =  length  of  the  arm  in  inches  from  the 
centre  of  suspension  to  the  centre  of  gyration,  and  a  the  required  angle; 
then 


TTT-  /       <joic/v>  mn  a    .    /  J  io*r  f>   .    /     1 


=  187.C|/J 


I  COS    a  y     2  COS  a  '    \      h 

The  simple  governor  is  not  isochronous;  that  is,  it  does  not  revolve  at  a 
uniform  speed  in  all  positions,  the  speed  changing  as  the  angle  of  the  arms 
changes.  To  remedy  this  defect  loaded  governors,  such  as  Porter's,  are 
used.  From  the  balls  of  a  common  governor  whose  collective  weight  is  A 
let  there  be  hung  by  a  pair  of  links  of  lengths  equal  to  the  pendulum  arms 
a  load  B  capable  of  sliding  on  the  spindle,  having  its  centre  of  gravity  in 
the  axis  of  rotation.  Then  the  centrifugal  force  is  that  due  to  A  alone,  and 
the  effect  of  gravity  is  that  due  to  A  -f  2B;  consequently  the  altitude  for  a 
given  speed  is  increased  in  the  ratio  (A  +  %B)  :  A,  as  compared  with  that  of 
a  simple  revolving  pendulum,  and  a  given  absolute  variation  in  altitude  pro- 
duces a  smaller  proportionate  variation  in  speed  than  in  the  common  gover- 
nor. (Rankine,  S.  E.,  p.  551.) 

For  the  weighted  governor  let  I  =  the  length  of  the  arm  from  the  point  of 
suspension  to  the  centre  of  gravity  of  the  ball,  and  let  the  length  of  the  sus- 
pending-link,  Zx  —  the  length  of  the  portion  of  the  arm  from  the  point  of 
suspension  of  the  arm  to  the  point  of  attachment  of  the  link;  G  =  the  weight 
of  one  ball,  Q  —  half  the  weight  of  the  sliding  weight,  h  =  the  height  of  the 
governor  from  the  point  of  snsperision  to  the  plane  of  revolution  of  the 
balls,  a  —  the  angular  velocity  =  2irT,  Tbeing  the  number  of  revolutions  per 

second;  then  „  =  A/3-±i°(, +'f |);    ft  =?|1?(,+81'|)    in  feet,  or 

h  =  -^-  (l  +  -y  YT)  in  inches,  N  being  the  number  of  revolutions  per 

minute. 

For  various  forms  of  governor  see  App.  Cycl.  Mech.,  vol.  ii.  61.  and  Clark's 
Steam-engine,  vol.  ii.  p.  65. 

To  Change  the  Speed  of  an  Engine  Having  a  Fly-ball 
Governor.—  A  slight  difference  in  the  speed  of  a  governor  changes  the 
position  of  its  weights  from  that  required  for  full  load  to  that  required  for 
no  load.  It  is  evident  therefore  that,  whatever  the  speed  of  the  engine,  the 
normal  speed  of  the  governor  must  be  that  for  which  the  governor  was  de- 
signed ;  i.e.,  the  speed  of  the  governor  must  be  kept  the  same.  To  change  the 
speed  of  the  engine  the  problem  is  to  so  adjust  the  pulleys  which  drive  the 
governor  that  the  engine  at  its  new  speed  shall  drive  it  just  as  fast  as  it  was 
driven  at  its  original  speed.  In  order  to  increase  the  engine-speed  we  must 
decrease  the  pulley  upon  the  shaft  of  the  engine,  i.e.,  the  driver,  or  increase 
that  on  the  governor,  i.e.,  the  driven,  in  the  proportion  that  the  speed  of  the 
engine  is  to  be  increased. 


838  THE   STEAM-EHGIHE. 

Fly-wtieel  or  Shaft  Governors.— At  the  Centennial  Exhibition 
in  1876  there  were  shown  a  few  steam-engines  in  which  the  governors  were 
contained  in  the  fly-wheel  or  band-wheel,  the  fly-balls  or  weights  revolving 
around  the  shaft  in  a  vertical  plane  with  the  wheel  and  shifting  the  eccen- 
tric so  as  automatically  to  vary  the  travel  of  the  valve  and  the  point  of  cut- 
off. This  form  of  governor  has  since  come  into  extensive  use,  especially  for 
high-speed  engines.  In  its  usual  form  two  weights  are  carried  on  arms  the 
ends  of  which  are  pivoted  to  two  points  on  the  pulley  near  its  circum- 
ference, 180°  apart.  Links  connect  these  arms  to  the  eccentric.  The 
eccentric  is  not  rigidly  keyed  to  the  shaft  but  is  free  to  move  trans- 
versely across  it  for  a  certain  distance,  having  an  oblong  hole  which  allows 
of  this  movement.  Centrifugal  force  causes  the  weights  to  fly  towards  the 
circumference  of  the  wheel  and  to  pull  the  eccentric  into  a  position  of  min- 
imum eccentricity.  This  force  is  resisted  by  a  spring  attached  to  each  arm 
which  tends  to  pull  the  weights  towards  the  shaft  and  shift  the  eccentric  to 
the  position  of  maximum  eccentricity.  The  travel  of  the  valve  is  thus 
varied,  so  that  it  tends  to  cut  off  earlier  in  the  stroke  as  the  engine  increases 
its  speed.  Many  modifications  of  this  general  form  are  in  use.  For  discus- 
sions of  this  form  of  governor  see  Hartnell,  Proc.  Inst.  M.  E.,  1882,  p.  408; 
Trans.  A.  S.  M.  E.,  ix.  300;  xi.  1081  ;  xiv.  9^;  xv.  929  ;  Modern  Mechanism, 
p.  399;  Whitham's  Constructive  Steam  Engineering;  J.  Begtrup,  Am.  Much.. 
Oct.  19  and  Dec.  14,  1893.  Jan.  18  and  March  1,  1894. 

Calculation  of  Springs  for  Shaft-governors.  (Wilson  Hart- 
nell, Proc.  Inst.  M.  E.,  Aug.  1882.)— The  springs  for  shaft-governors  may  be 
conveniently  calculated  as  follows,  dimensions  being  in  inches: 

Let  W  =  weight  of  the  balls  or  weights,  in  pounds; 

»*!  and  r2  =  the  maximum  and  minimum  radial  distances  of  the  centre 
of  the  balls  or  of  the  centre  of  gravity  of  the  weights; 

It  and  Z3  =  the  leverages,  i.e.,  the  perpendicular  distances  from  the  cen 
tre  of  the  weight-pin  to  a  line  in  the  direction  of  the  centrifugal  force, 
drawn  through  the  centre  of  gravity  of  the  weights  or  balls  at  radi1 
71!  and  r2 ; 

7W.,.  and  wia  =  the  corresponding  leverages  of  the  springs; 

Ci  and  C2  =  the  centrifugal  forces,  for  100  revolutions  per  minute,  a» 
radii  i\  and  ra; 

Pl  and  P<i  —  the  corresponding  pressures  on  the  spring; 

(It  is  convenient  to  calculate  these  and  note  them  down  for  reference.  I 

C3  and  C4  =  maximum  and  minimum  centrifugal  forces; 

S  =  mean  speed  (revolutions  per  minute); 

Si  and  £2  =  the  maximum  and  minimum  number  of  revolutions  pet 
minute: 

P3  and  P4  —  the  pressures  on  the  spring  at  the  limiting  number  of  revo- 
lutions (i'j  and  /Sjj); 

P4  -  P3  =  D  =  the  difference  of  the  maximum  and  minimum  pressures 
on  the  springs; 

V  =  the  percentage  of  variation  from  the  mean  speed,  or  the  sensitive 
ness; 

t  =  the  travel  of  the  spring; 

u  =  the  initial  pressure  on  the  spring; 

v  —  the  stiffness  in  pounds  per  inch; 

w  =  the  maximum  pressure  =  u  -{- 1. 

The  mean  speed  and  sensitiveness  desired  are  supposed  to  be  given.   Then 
<?         Q       8V.  e         Q_L6>F. 

*l  =  8~m\  s*  =  s+m> 

d  =  0.28  X  rx  X  W\  Ca  =  0.28  X  ra  X  W\ 


D  P,  P4 

V  =  —  ,    U  —    ~ -       MJ    —    — 
t   '  V*  V 

It  is  usual  to  give  the  spring-maker  the  values  of  P4  and  of  v  or  w.    To 
ensure  proper  space  being  provided,  the  dimensions  of  the  spring  should  be 


COHDENSERS,  AIR-PUMPS,  ETC. 


839 


calculated  by  the  formulae  for  strength  and  extension  of  springs,  and  the 
least  length  of  the  spring  as  compressed  be  determined. 


The  governor-power  =  : 


xf. 


With  a  straight  centripetal  line,  the  governor-power 

_  C3  -f  C4  v  /*i  -  rA 
2          X  V      12      /' 

For  a  preliminary  determination  of  the  governor-power  it  may  be  taken 
as  equal  to  this  in  all  cases,  although  it  is  evident  that  with  a  curved  cen- 
tripetal line  it  will  be  slightly  less.  The  difference  D  must  be  constant  for 
the  same  spring,  however  great  or  little  its  initial  compression.  Let  the 
spring  be  screwed  up  until  its  minimum  pressure  is  jP5.  Then  to  find  the 
speed  P6  =  Pfc  +  D, 


The  speed  at  which  the  governor  would  be  isochronous  would  be 
lOOj 


Suppose  the  pressure  on  the  spring  with  a  speed  of  100  revolutions,  at  the 
maximum  and  minimum  radii,  was  200  Ibs.  and  100  Ibs.,  respectively,  then 
the  pressure  of  the  spring  to  suit  a  variation  from  95  to  105  revolutions  will 

/  OR  \  2  /105\2 

be  100  X  \£fi)    =  90-2  and  200  X  \^QQ)  =  220-5-     That   is,  the    increase 

of  resistance  from  the  minimum  to  the  maximum  radius  must  be  220  -  90  = 
130  Ibs. 

The  extreme  speeds  due  to  such  a  spring,  screwed  up  to  different  press- 
ures, are  shown  in  the  following  table: 


Revolutions  per  minute,  balls  shut    

80 

90 

9*> 

100 

110 

T>0 

Pressure  on  springs  balls  shut  . 

64 

81 

90 

100 

1°1 

144 

Increase  of  pressure  when  balls  open  fully  •  .... 

130 

130 

ISO 

130 

1SO 

130 

Pressure  on  springs,  balls  open  fully  

194 

?11 

990 

980 

951 

974 

Revolutions  per  minute,  balls  open  fully 

98 

10? 

105 

10? 

ua 

11? 

Variation,  per  cent  of  mean  speed  

10 

fi 

5 

3 

i 

-1 

The  speed  at  which  the  governor  would  become  isochronous  is  114. 

Any  spring  will  give  the  right  variation  at  some  speed  :  hence  in  experi- 
menting with  a  governor  the  correct  spring  may  be  found  from  any  wrong 
one  by  a  very  simple  calculation.  Thus,  if  a  governor  with  a  spring  whose 
stiffness  is  50  Ibs.  per  inch  acts  best  when  the  engine  runs  at  95,  90  being  its 


proper  speed,  then  50  X 


=  45  l^>s.  is  the  stiffness  of  spring  required. 


To  determine  the  speed  at  which  the  governor  acts  best,  the  springs  may 
be  screwed  up  until  it  begins  to  "  hunt  ''  and  then  slackened  until  the  gov- 
ernor is  as  sensitive  as  is  compatible  with  steadiness. 


CONDENSERS,  AIR-PUMPS    CIRCUJLATING- 
PUMPS,  ETC. 

Tlie  Jet  Condenser.  (Chiefly  abridged  from  Seaton's  Marine  Engi- 
neering.)— The  jet  condenser  is  now  uncommon,  being  generally  supplanted 
by  the  surface  condenser.  With  the  jet  condenser  a  vacuum  of  24  in.  was 
considered  fairly  good,  and  25  in.  as  much  as  was  possible  with  most  conden- 
sers; the  temperature  corresponding  to  24  in.  vacuum,  or  3  Ibs.  pressure  ab- 
solute, is  140°.  In  practice  the  temperature  in  the  hot-well  varies  from  110° 
to  120°,  and  occasionally  as  much  as  130°  is  maintained.  To  find  the  quantity 
of  injection- water  per  pound  of  steam  to  be  condensed:  Let  Tl  —  tempera- 
ture of  steam  at  the, exhaust  pressure;  T0  =  temperature  of  the  cooling- 


840  THE   STEAM-EHGIKE. 

water;  T3  =  temperature  of  the  water  after  condensation,  or  of  the  hot-  well; 
Q  =  pounds  of  the  cooling-  water  per  Ib.  of  steam  condensed;  then 

1114° 


TT7TT 

Another  formula  is:    Q  =  —  —  ,  in  which  W  is  the  weight  of  steam  con- 

densed, H  the  units  of  heat  given  up  by  1  Ib.  of  steam  in  condensing,  and 
R  the  rise  in  temperature  of  the  cooling-  water. 

This  is  applicable  both  to  jet  and  to  surface  condensers.  The  allowance  made 
for  the  injection  -water  of  engines  working  in  the  temperate  zone  is  usually 
27  to  30  times  the  weight  of  steam,  and  for  the  tropics  SO  to  35  times;  30 
times  is  sufficient  for  ships  which  are  occasionally  in  the  tropics,  and  this  is 
what  was  usual  to  allow  for  general  traders. 

Area  of  injection  orifice  =  weight  of  injection-  water  in  Ibs.  per  min.  H-  650 
to780. 

A  rough  rule  sometimes  used  is:  Allow  one  fifteenth  of  a  square  inch  for 
every  cubic  foot  of  water  condensed  per  hour. 

Another  rule:  Area  of  injection  orifice  =  area  of  piston  -4-  250. 

The  volume  of  the  jet  condenser  is  from  one  fourth  to  one  half  of  that  of 
the  cylinder.  It  need  not  be  more  than  one  third,  except  for  very  quick- 
running  engines. 

Ejector  Condensers.—  For  ejector  or  injector  condensers  (Bulkley's, 
Schutte's,  etc.)  the  calculations  for  quantity  of  condensing-  water  is  the  same 
as  for  jet  condensers. 

The  Surface  Condenser-  Cooling  Surface.—  Peclet  found  that 
with  cooling  water  of  an  initial  temperature  of  (38°  to  77°.  one  sq.  ft.  of  copper 
plate  condensed  21.5  Ibs.  of  steam  per  hour,  while  Joule  states  that  100*  Ibs. 
per  hour  can  be  condensed.  In  practice,  with  the  compound  engine,  brass 
condenser-tubes,  18  B.W.G  thick,  13  Ibs.  of  steam  per  sq.  ft.  per  hour,  with 
the  cooling-  water  at  an  initial  temperature  of  CO0,  is  considered  very  fair 
work  when  the  temperature  of  the  feed-  water  is  to  be  maintained  at  1^0°. 
It  has  been  found  that  the  surface  in  the  condenser  may  be  half  the  heating 
surface  of  the  boiler,  and  under  some  circumstances  considerably  less  than 
this.  In  general  practice  the  following  holds  good  when  the  temperature  of 
sea-water  is  about  60°  : 

Terminal  pres.,  Ibs.,  abs...         30       20          15         12^         10          8  6 

Sq.  ft.  per  I.H.P  ............        3       2.50       2.25       2.00       1.80        l.GO        1.50 

For  ships  whose  station  is  in  the  tropics  the  allowance  should  be  increased 
by  20$.  and  for  ships  which  occasionally  visit  the  tropics  10$  increase  will 
give  satisfactory  results.  If  a  ship  is  constantly  employed  in  cold  climates 
W  less  suffices 

Wbitbam  (Steam-engine  Design,   p.  283,  also  Trans.  A.  S.  M.  E.,  ix.  431) 

gives  the  following:  S  =  -r-=  -  -  ,  in  which  S  =  condensing-surface  in  sq. 

CK(  ±  i  —  t  ) 

ft.;  T!  =  temperature  Fahr.  of  steam  of  the  pressure  indicated  by  the 
vacuum-gauge;  t  =  mean  temperature  of  the  circulating  water,  or  the 
arithmetical  mean  of  the  initial  and  final  temperatures;  L  =  latent  heat  of 
saturated  steam  at  temperature  7\  ;  k  =  perfect  conductivity  of  1  sq.  ft.  of 
the  metal  used  for  the  condensing-surface  for  a  range  •  f  1°  F.  (or  557  B.T.U. 
per  hour  for  brass,  according  to  Ishervvood's  experiments):  c  =  fraction  de- 
noting the  efficiency  of  the  condensing  surface;  W  =  pounds  of  steam  con- 
densed per  hour.  From  experiments  by  Loring  and  Emery,  on  U.S.S.  Dallas, 
c  is  found  to  be  0.323,  and  ck  —  180;  and  the  equation  becomes 

s=       WL 


180(2'!  -  0  * 

Whitham  recommends  this  formula  for  designing  engines  having  indepen- 
dent circulating  pumps.  When  the  pump  is  worked  by  the  main  engine  the 
value  of  S  should  be  increased  about  10$. 

Taking  Tl  at  135°  F.,  and  L  =  1020,  corresponding  to  25  in.  vacuum,  and  t 

for  summer  temperatures  at  75°,  we  have:    S  =  —   =  -— -. 

Condenser  Tubes  are  generally  made  of  solid-drawn  brass  tubes,  and 
tested  both  by  hydraulic  pressure  and  steam.  They  are  usually  made  of  a 
composition  of  68$  of  best  selected  copper  and  32$  of  best  Silesian  spelter. 


COKDE^SERS,  AIR-PUMPS,  ETC. 


841 


The  Admiralty,  however,  always  specify  the  tubes  to  be  made  of  70#  of  best 
selected  copper  and  to  have  \%  of  tin  in  the  composition,  and  test  the  tubes 
to  a  pressure  of  300  Ibs.  per  sq.  in.  (Seaton.) 

The  diameter  of  the  condenser  tubes  varies  from  ^  inch  in  small  conden- 
sers, when  they  are  very  short,  to  1  inch  in  very  large  condensers  and  long 
tubes.  In  the  mercantile  marine  the  tubes  are,  as  a  rule,  %  inch  diameter 
externally,  and  18  B.W.G.  thick  (0.049  inch);  and  16  B.W.G.  (0.065),  under 
some  exceptional  circumstances.  In  the  British  Navy  the  tubes  are  also, 
as  a  rule,  %  inch  diameter,  and  18  to  19  B  W.G.  thick,  tinned  on  both  sides; 
when  the  condenser  is  made  of  brass  the.Admiralty  do  not  require  the  tubes 
to  be  tinned.  Some  of  the  smaller  engines  have  tubes  %  inch  diameter,  and 
19  B.W.G.  thick.  The  smaller  the  tubes,  the  larger  is  the  surface  which 
can  be  got  in  a  certain  space. 

In  the  merchant  service  the  almost  universal  practice  is  to  circulate  the 
water  through  the  tubes. 

Whitham  says  the  velocity  of  flow  through  the  tubes  should  not  be  less 
than  400  nor  more  than  TOO  ft.  per  rnin. 

Tube-plates  are  usually  made  of  brass.  Rolled-brass  tube-plates 
should  be  from  1.1  to  1.5  times  the  diameter  of  tubes  in  thickness,  depending 
on  the  method  of  packing.  When  the  packings  go  completely  through  the 
plates  the  latter,  but  when  only  partly  through  the  former,  is  sufficient. 
Hence,  for  ^-inch  tubes  the  plates  are  usually  %  to  1  inch  thick  with  glands 
and  tape-packings,  and  1  to  1*4  inch  thick  with  wooden  ferrules. 

The  tube-plates  should  be  secured  to  their  seatings  by  brass  studs  and 
nuts,  or  brass  screw-bolts;  in  fact  there  must  be  no  wrought  iron  of  any 
kind  inside  a  condenser.  When  the  tube-plates  are  of  large  area  it  is  advis- 
able to  stay  them  by  brass-rods,  to  prevent  them  from  collapsing. 

Spacing  of  Tubes,  etc.— The  holes  for  ferrules,  glands,  or  india- 
rubber  are  usually  J4  inch  larger  in  diameter  than  the  tubes;  but  when  ab- 
solutely necessary  the  wood  ferrules  may  be  only  3/3'2  inch  thick. 

The  pitch  of  tubes  when  packed  with  wood  ferrules  is  usually  *4  inch 
more  than  the  diameter  of  the  ferrule-hole.  For  example,  the  tubes  are 
generally  arranged  zigzag,  and  the  number  which  may  be  fitted  into  a 
square  foot  of  plate  is  as  follows: 


Pitch  of 
Tubes. 

No,  in  a 
sq.  ft. 

Pitch  of 
Tubes. 

No.  in  a 
sq.  ft. 

Pitch  of 
Tubes. 

No.  in  a 
sq.  ft. 

1" 

1  1/16" 
W 

172 
150 
137 

1  5/32" 
1  3/16" 
1  7/32" 

128 
121 
116 

W 
1  9/32'' 
1  5/16" 

110 
106 
99 

Quantity  of  Cooling  Water.—  The  quantity  depends  chiefly  upon 
its  init.ial  temperature,  which  in  Atlantic  practice  may  vary  from  40°  in  the 
winter  of  temperate  zone  to  80°  in  subtropical  s^as.    To  raise  the  tempera- 

line  tu  avu     111  uic  UUUUOINSTTI    win  ici-juiic  mice  nines  its  many   mermen  units 

in  the  former  case  as  in  the  latter,  and  therefore  only  one  third  as  much 
cooling-  water  will  be  required  in  the  former  case  as  in  the  latter. 

TI  =  temperature  of  steam  entering  the  condenser; 
TO  =  "  circulating-  water  entering  the  condenser; 

T2  =  "       leaving  the  condenser; 

T3  =  "  water  condensed  from  the  steam; 

Q  =  quantity  of  circulating  water  in  Ibs.  = 


It  is  usual  to  provide  pumping  power  sufficient  to  supply  40  times  the 
weight  of  steam  for  general  traders,  and  as  much  as  50  times  for  ships  sta- 
tioned in  subtropical  seas,  when  the  engines  are  compound.  If  the  circulat- 
ing-pump is  double-acting,  its  capacity  may  be  1/53  in  the  former  and  1/42 
in  the  latter  case  of  the  capacity  of  the  low-pressure  cylinder. 

Air-pump.—  The  air-pump'  in  all  condensers  abstracts  the  water  con- 
densed and  the  air  originally  contained  in  the  water  when  it  entered  the 
boiler.  In  the  case  of  jet-condensers  it  also  pumps  out  the  water  of  con- 
densation and  the  air  which  it  contained.  The  size  of  the  puinp  is  calculated 
from  these  conditions,  making  allowance  for  efficiency  of  the  pump. 


842 


THE   STEAM-ENGINE. 


Ordinary  sea-water  contains,  mechanically  mixed  with  it,  1/20  of  its  vol- 
ume of  air  when  under  the  atmospheric  pressure.  Suppose  the  pressure  in 
the  condenser  to  be  2  Ibs.  and  the  atmospheric  pressure  15  Ibs.,  neglecting 
the  effect  of  temperature,  the  air  on  entering  the  condenser  will  be  expanded 
to  15/2  times  its  original  volume;  so  that  a  cubic  foot  of  sea-  water,  when  it 
has  entered  the  condenser,  is  represented  by  19/20  of  a  cubic  foot  of  water 
and  15/40  of  a  cubic  foot  of  air. 

Let  3  be  the  volume  of  water  condensed  per  minute,  and  Q  the  volume  of 
sea-  water  required  to  condense  it;  and  let  T.z  be  the  temperature  of  the 
condenser,  and  2\  that  of  the  sea-water. 

Then  19/20  (q  -J-  Q)  will  be  the  volume  of  water  to  be  pumped  from  the 
condenser  per  minute, 


and       (3  +Q)X 


p 


the  quantity  of  air. 


If  the  temperature  of  the  condenser  be  taken  at  120°,  and  that  of  sea- 
water  at  60°,  the  quantity  of  air  will  then  be  .418(2  -f  Q),  so  that  the  total 
volume  to  be  abstracted  will  be 

.95(g  -f  Q)  +  .418(g  +  Q)  =  1.868(3  -f  Q). 

If  the  average  quantity  of  injection-water  be  taken  at  26  times  that  con- 
densed, q  -f  Q  will  equal  27q.  Therefore,  volume  to  be  pumped  from  the 
condenser  per  minute  =  373,  nearly. 

In  surface  condensation  allowance  must  be  made  for  the  water  occasion- 
ally admitted  to  the  boilers  to  make  up  for  waste,  and  the  air  contained  in 
it,  also  for  slight  leak  in  the  joints  and  glands,  so  that  the  air-pump  is  made 
about  half  as  large  as  for  jet-condensation. 

The  efficiency  of  a  single-acting  air-pump  is  generally  taken  at  0.5,  nnd 
that  of  a  double-acting  pump  at  0.35.  When  the  temperatur  of  the  sea  is 
60°,  and  that  of  the  (jet)  condenser  is  120°,  Q  being  the  volume  of  the  cooling 
water  and  q  the  volume  of  the  condensed  water  in  cubic  feet,  and  n  the 
number  of  strokes  per  minute, 

The  volume  of  the  single-acting  pump  =  2.74 


The  volume  of  the  double-acting  pump  =  4(  "     q  J  • 


The  following  table  gives  the  ratio  of  capacity  of  cylinder  or  cylinders  to 
that  of  the  air-pump;  in  the  case  of  the  compound  engine,  the  low-pressure 
cylinder  capacity  only  is  taken. 


Description  of  Pump. 

Description  of  Engine. 

Ratio. 

Single- 
Double 

acting  vertical  

acting  horizontal.. 
in 

Jet-cond< 
Surface 
Jet 
Surface 
Surface 
Jet 
Surface 
Jet 
Surface 
Surface 

insing,  expansion  1^  to  2  — 
"           I^to2.... 
"          3     to5.... 
"          3     to  5... 
compound                . 

6  to   8 
8  to  10 
10  to  12 
12  to  15 
15  to  18 
10  to  13 
13  to  16 
16  to  19 
19  to  24 
24  to  28 

expansion  1^  to  2  — 

iy2  to  2.... 

"           3     to  5  ... 
"           3     to  5  ... 
compound     

The  Area  through  Valve-seats  and  past  the  valves  should  not  be 
less  than  will  admit  the  full  quantity  of  water  for  condensation  at  a  velocity 
not  exceeding  400  ft.  per  minute.  In  practice  the  area  is  generally  in 
excess  of  this. 


Area  through  foot-  valves     =  D2  X  S- 
Area  through  head-valves     =  D2  X  S- 


-  1000  square  inches. 

-  800  square  inches. 
Diameter  of  discharge  -pipe  =  D  X  VS  •*•  35  inches. 

D  =  diam.  of  air-pump  in  inches,  S  =  its  speed  in  ft.  per  min. 


James  Tribe  (Am.  Mach.,  Oct.  8,  1891)  gives  the  following  rule  for  air- 


CONDENSERS,  AIR-PUMPS,  ETC.  843 

pumps  used  with  jet-condensers:  Volume  of  single-acting  air-pump  driven 
by  main  engine  =  volume  of  low-pressure  cylinder  in  cubic  feet,  multiplied 
by  3.5  and  divided  by  the  number  of  cubic  feet  contained  in  one  pound  of 
exhaust-steam  of  the  given  density.  For  a  double-acting  air-pump  the 
same  rule  will  apply,  but  the  volume  of  steam  for  each  stroke  of  the  pump 
will  be  but  one  half.  Should  the  pump  be  driven  independently  of  tile 
engine,  then  the  relative  speed  must  be  considered.  Volume  of  jet-con- 
denser =  volume  of  air-pump  X  4.  Area  of  injection  valve  =  vol.  of  air- 
pump  in  cubic  inches  H-  520. 

Circulating-pump. — Let  Q  be  the  quantity  of  cooling  water  in  cubic 
fe^t,  n  the  number  of  strokes  per  minute,  and  8  the  length  of  stroke  in  feet. 

Capacity  of  circulating-pump  =  Q  -*-  n  cubic  feet. 

Diameter  "         "  *'        =  13.55 A/ — Scinches. 

Y    11  X  o 

The  following  table  gives  the  ratio  of  capacity  of  steam- cylinder  or  cylin- 
ders to  that  of  the  circulating  pump  : 

Description  of  Pump.  Description  of  Engine.  Ratio. 

Single-acting.  Expansive  1^  to  2  times.  13  to  16 

"  3     to  5    "  20  to  25 

Compound.  25  to  30 

Double    "  Expansive  1^  to  2  times.  25  to  30 

"  3     to  5    "  36  to  46 

Compound.  46  to  56 

The  ciear  area  through  the  valve-seats  and  past  the  valves  should  be  such 
that  the  mean  velocity  of  flow  does  not  exceed  450  feet  per  minute.  The 
flow  through  the  pipes  should  not  exceed  500  ft.  per  min.  in  small  pipes  and 
600  in  large  pipes. 

For  Centrifugal  Circulating -pumps,  the  velocity  of  flow  in  the  inlet  and 
outlet  pipes  should  not  exceed  400  ft.  per  min.  The  diameter  of  the  fan- wheel 
is  from  2%  to  3  times  the  diam.  of  the  pipe,  and  the  speed  at  its  periphery 
450  to  500  ft.  per  min.  If  W  =  quantity  of  water  per  minute,  in  American 
gallons,  d  —  diameter  of  pipes  in  inches,  R  =  revolutions  of  wheel  per  min., 

/    W  1700 

d  =  A/  — —  ;  diam.  of  fan-wheel  =  not  less  than  -=-.    Breadth  of  blade  at 


. 

tip  =  T^-T.    Diam.  of  cylinder  for  driving  the  fan  =  about  2.8  Vdiam.  of  pipe, 

and  its  stroke  -  0.28  X  diam.  of  fan. 

Feed-pumps  for  Marine  Engines.— With  surface-condensing 
engines  the  amount  of  water  to  be  fed  by  the  pump  is  the  amount  condensed 
from  the  main  engine  plus  what  may  be  needed  to  supply  auxiliary  engines 
arid  to  supply  leakage  and  waste.  Since  an  accident  may  happen  to  the 
surface-condenser,  requiring  the  use  of  jet-condensation,  the  pumps  of 
engines  fitted  with  surface-condensers  must  be  sufficiently  large  to  do  duty 
under  such  circumstances.  With  jet-condensers  and  boilers  using  salt  water 
the  dense  salt  water  in  the  boiler  must  be  blown  off  at  intervals  to  keep  the 
density  so  low  that  deposits  of  salt  will  not  be  formed.  Sea-water  contains 
about  1/^2  of  its  weight  of  solid  matter  in  solution.  The  boiler  of  a  surface- 
condensing  engine  may  be  worked  with  safety  when  the  quantity  of  salt  is 
four  times  that  in  sea-water.  If  Q  =  net  quantity  of  feed-water  required  in 
a  given  time  to  make  up  for  what  is  used  as  steam,  n  =  number  of  times  the 
saltness  of  the  water  in  the  boiler  is  to  that  of  sea-water,  then  the  gross  feed- 
water  = Q.  In  order  to  be  capable  of  filling  the  boiler  rapidly  each 

feed-pump  is  made  of  a  capacity  equal  to  twice  the  gross  feed- water.  Two 
feed-pumps  should  be  supplied,  so  that  one  may  be  kept  in  reserve  to  be 
used  while  the  other  is  out  of  repair.  If  Q  be  the  quantity  of  net  feed- water 
in  cubic  feet,  I  the  length  of  stroke  of  feed-pump  in  feet,  and  n  the  num- 
ber of  strokes  per  minute, 

Piameter  of  each  feed-pump  plunger  in  inches  : 


844 


THE   STEAM-ENGINE. 


If  Wbe  the  net  feed- water  in  pounds, 

/8  9"'X"  W^ 
Diameter  of  each  feed-pump  plunger  in  inches  =  A/  - — - — . 

y  ?l  X   >> 

Ail  Evaporative  Surface  Condenser  built  at  the  Virginia  Agri- 
cultural College  is  described  by  James  H.  Fitts  (Trans.  A.  S.  M.  E.,  xiv.  690). 
It  consists  of  two  rectangular  end  chambers  connected  by  a  series  of  hori- 
zontal rows  of  tubes,  each  row  of  tubes  immersed  in  a  pan  of  water. 
Through  the  spaces  between  the  surface  of  the  water  in  each  pan  and  the 
bottom  of  the  pan  above  air  is  drawn  by  means  of  an  exhaust -fan.  At  the 
top  of  one  of  the  end-chambers  is  an  inlet  for  steam,  and  a  horizontal  dia- 
phragm about  midway  causes  the  steam  to  traverse  the  upper  half  of  the 
tubes  and  back  through  the  lovyer.  An  outlet  at  the  bottom  leads  to  the  air- 
pump.  The  condenser,  exclusive  of  connection  to  the  exhaust  fan,  occupies 
a  floor  space  of  5'  4J4"  x  V  9-%",  and  4'  IJ/s"  high.  There  are  27  rows  of 
tubes,  8  in  some  and  7  in  others;  210  tubes  in  all.  The  tubes  are  of  brass, 
No.  20  B.W  G.,  94"  external  diameter  and  4'  9*4"  in  length.  The  cooling  sur- 
face (internal)  is  170.5  sq.  ft.  There  are  27  cooling  pans,  each  4'  9^6  "  X  V  9%", 
and  1  7/1 6"  deep.  These  pans  have  galvanized  iron  bottoms  "which  slide 
into  horizontal  grooves  W  wide  and  J4"  deep,  planed  into  the  tube-sheets. 
The  total  evaporating  surface  is  234.8  sq.  ft.  Water  is  fed  to  every  third  pan 
through  small  cocks,  and  overflow-pipes  feed  the  rest.  A  wood  casing  con- 
nects one  side  with  a  30"  Buff alo  Forge  Co.'s  disk-wheel.  This  wheel  is 
belted  to  a  3"  X  4"  vertical  engine  The  air-pump  is  5%"  diameter  with  a 
0"  stroke,  is  vertical  and  single-acting. 

The  action  of  this  condenser  is  as  follows:  The  passage  of  air  over  the 
water  surfaces  removes  the  vapor  as  it  rises  and  thus  hastens  evaporation. 
The  heat  necessary  to  produce  evaporation  is  obtained  from  the  steam  in  the 
tubes,  causing  the  steam  to  condense.  It  was  designed  to  condense  800  Ibs. 
steam  per  hour  and  give  a  vacuum  of  22  in.,  with  a  terminal  pressure  in  the 
cylinder  of  20  Ibs.  absolute. 

Results  of  tests  show  that  the  cooling- water  required  is  practically  equal  in 
amount  to  the  steam  used  by  the  engine.  And  since  consumption  of  steam 
is  reduced  by  the  application  of  a  condenser,  its  use  will  actually  reduce  the 
total  quantity  of  water  required.  From  a  curve  showing  the  rate  of  evapora- 
tion per  square  foot  of  surface  in  still  air.  and  also  one  show  ng  the  rate 
when  a  current  of  air  of  about  2300  ft.  per  min.  velocity  is  passed  ovar  its 
surface,  the  following  approximate  figures  are  taken: 


Temp. 
F. 

Evaporation,  Ibs.  per 
sq.  ft.  per  hour. 

Temp. 
F. 

Evaporation,  ]bs.  per 
sq.  ft.  per  hour. 

Still  Air. 

Current. 

Still  Air. 

Current. 

100° 
110 
120 
130 

0.2 

0.25 
0.4 
06 

1.1 
1.6 
2.5 
3.5 

140° 
150 
1GO 
170 

0.8 
1.1 
1.5 
2.0 

5.0 
6.7 
9.5 

Tlie  Continuous  Use  of  Condensing-water  is  described  in  a 
series  of  articles  in  Power,  Aug.-Dec.,  1892.  It  finds  its  application  in  situa- 
tions where  water  for  condensing  purposes  is  expensive  or  difficult  to  obtain. 

In  San  Francisco  J.  C.  H.  Stut  cools  the  water  after  it  has  left  the  hot- 
well  by  means  of  a  system  of  pans  upon  the  roof.  These  pans  are  shallow 
troughs  of  galvanized  iron  arranged  in  tiers,  on  a  slight  incline,  so  that  the 
water  flows  back  and  forth  for  1500  o*  ?000  ft.,  cooling  by  evaporation  and 
radiation  as  it  flows.  The  pans  are  about  5  ft.  in  width,  and  the  water  as  it 
flows  has  a  depth  of  about  half  an  inch,  the  temperature  being  reduced  from 
about  140°  to  90°.  The  water  from  the  hot- well  is  pumped  up  to  the  highest 
point  of  the  cooling  system  and  allowed  to  flow  as  above  described,  discharg- 
ing finally  into  the  main  tank  or  reservoir,  whence  it  again  flows  to  the  con- 
denser as  required.  As  the  water  in  the  reservoir  lowers  from  evaporation,  an 
auxiliary  feed  from  the  city  mains  to  the  condenser  is  operated,  thereby 
keeping  the  amount  of  water  in  circulation  practically  constant.  An  accu 
mulation  of  oil  from  the  engines,  with  dust  from  the  surrounding  streets, 
makes  a  cleaning  necessary  about  once  in  six  weeks  or  two  months.  It  is 
tound  by  comparative  trials,  running  condensing  and  non  condensing,  that 


CONDENSERS,  AIR-PUMPS,  ETC.  845 

about  50#  less  water  is  taken  from  the  city  mains  when  the  whole  apparatus 
is  in  use  than  when  the  engine  is  run  non-condensing.  22  to  23  in.  of  vacuum 
are  maintained.  A  better  vacuum  is  obtained  on  a  warm  day  with  a  brisk 
breeze  blowing  than  on  a  cold  day  with  but  a  slight  movement  of  the  air. 

In  another  plant  the  water  from  the  hot- well  is  sprayed  from  a  number  of 
fountains,  and  also  from  a  pipe  extending  around  its  border,  into  a  large 
pond,  the  exposure  cooling  it  sufficiently  for  the  obtaining  of  a  good  vacuum 
by  its  continuous  use . 

In  the  system  patented  by  Messrs.  See,  of  Lille,  France,  the  water  is  dis- 
charged from  a  pipe  laid  in  the  form  of  a  rectangle  and  elevated  above  a 
pond  through  a  series  of  special  nozzles,  by  which  it  is  projected  into  a  fine 
spray.  On  coming  into  contact  with  the  air  in  this  state  of  extreme  divi- 
sion'the  water  is  cooled  40°  to  50°,  with  a  loss  by  evaporation  of  only  one 
tenth  of  its  mass,  and  produces  an  excellent  vacuum.  A  3000-H.P.  cooler 
upon  this  system  has  been  erected  at  Lannoy,  one  of  *5GO  H  .P.  at  Madrid,  and 
one  of  1~00  H.P.  at  Liege,  as  well  as  others  at  Roubaix  and  Tourcoing.  The 
system  could  be  used  upon  a  roof  if  ground  space  were  limited. 

In  the  k'  self-cooling"  system  of  H.  R.  Worthington  the  injection- water  is 
taken  from  a  tank,  and  after  having  passed  through  the  condenser  is  dis- 
charged in  a  heated  condition  to  the  top  of  a  cooling  tower,  \\  here  it  is  scat- 
tered by  means  of  distributing-pipes  and  trickles  down  through  a  cellular 
structure  made  of  6-in.  terra-cotta  pipes,  2  ft.  long,  stood  on  end.  The 
water  is  cooled  by  a  blast  of  air  furnished  by  a  disk  fan  at  the  bottom  of  the 
tower  and  the  absorption  of  heat  caused  by  a  portion  of  the  water  being 
vaporized,  and  is  led  to  the  tank  to  be  again  started  on  its  circuit.  (Entfg 
News,  March  5,  1896.) 

In  the  evaporative  condenser  of  T.  Led  ward  &  Co.  of  Brockley,  London, 
the  water  trickles  over  the  pipes  of  the  large  condenser  or  radiator,  and  by 
evaporation  carries  away  the  heat  necessary  to  be  abstracted  to  condense 
the  steam  inside.  The  condensing  pipes  are  fitted  with  corrugations 
mounted  with  circular  ribs,  whereby  the  radiating  or  cooling  surface  is 
largely  increased.  The  pipes,  which  are  cast  in  sections  about  76  in.  long  by 
3J^>  in.  bore,  have  a  cooling  surface  of  26  sq.  ft.,  which  is  found  sufficient 
under  favorable  conditions  to  permit  of  the  condensation  of  20  to  30  Ibs. 
of  steam  per  hour  when  producing  a  vacuum  of  13  Ibs.  per  sq.  in.  In  a 
condenser  of  this  type  at  Rixdorf,  near  Berlin,  a  vacuum  ranging  from  24 
to  26  in.  of  mercury  was  constantly  maintained  during  the  hottest  weather 
of  August.  The  initial  temperature  of  the  cooling- water  used  in  the  appara- 
tus under  notice  ranged  from  80°  to  85°  F.,  and  the  temperature  in  the  sun, 
to  which  the  condenser  was  exposed,  varied  each  day  from  100°  to  115°  F. 
During  the  experiments  it  was  found  that  it  was  possible  to  run  one  engine 
under  a  load  of  100  horse-power  and  maintain  the  full  vacuum  without  the 
use  of  any  cooling-water  at  all  on  the  pipes,  radiation  afforded  by  the  pipes 
alone  sufficing  to  condense  the  steam  for  this  power. 

In  Klein's  condensing  water-cooler,  the  hot  water  coming  from  the  con- 
denser enters  at  the  top  of  a  wooden  structure  about  twenty  feet  in  height, 
and  is  conveyed  into  a  series  of  parallel  narrow  metal  tanks.  The  water 
overflowing  from  these  tanks  is  spread  as  a  thin  film  over  a  series  of  wooden 
partitions  suspended  vertically  about  3J/£  inches  apart  within  the  tower. 
The  upper  set  of  partitions,  corresponding  to  the  number  of  metal  tanks, 
reaches  half-way  down  the  tower.  From  there  down  to  the  well  is  sus- 
pended a  second  set  of  partitions  placed  at  right  angles  to  the  first  set.  This 
impedes  the  rapidity  of  the  downflow  of  the  water,  and  also  thoroughly 
mixes  the  water,  thus  affording  a  better  cooling.  A  fan-blower  at  the  base  of 
the  tower  drives  a  strong  current  of  air  with  a  velocity  of  about  twenty  feet 
per  second  against  the  thin  film  of  water  running  down  over  the  partitions. 
It  is  estimated  that  for  an  effectual  cooling  two  thousand  times  more  air 
than  water  must  be  forced  through  the  apparatus.  With  such  a  velocity 
the  air  absorbs  about  two  per  cent  of  aqueous  vapor.  The  action  of  the 
strong  air-current  is  twofold:  first,  it  absorbs  heat  from  the  hot  water  by 
being  itself  warmed  by  radiation;  and,  secondly,  it  increases  the  evapora- 
tion, which  process  absorbs  a  great  amount  of  heat.  These  two  cooling 
effects  are  different  during  the  different  seasons  of  the  year.  During  the 
winter  months  the  direct  cooling  effect  of  the  cold  air  is  greater,  while 
during  summer  the  heat  absorption  by  evaporation  is  the  more  important 
factor.  Taking  all  the  year  round,  the  effect  remains  very  much  the  same. 
The  evaporation  is  never  so  great  that  the  deficiency  of  water  would  not 
be  supplied  by  the  additional  amount  of  water  resulting  from  the  condensed 
steam,  while  in  very  cold  winter  months  it  may  be  necessary  to  occasionally 
rid  the  cistern  of  surplus  water.  It  was  found  that  the  vacuum  obtained  by 


846 


TfiE 


this  continual  use  of  the  same  condensing-water  varied  during  the  year 
between  27.5  and  28.7  inches.  The  great  saving  of  space  is  evident  from 
the  fact  that  only  the  five  -hundredth  part  of  the  floor-space  is  required  as 
if  cooling  tanks  or  ponds  were  used.  For  a  100-horse-power  engine  the 
floor-space  required  is  about  four  square  yards  by  a  height  of  twenty  feet. 
For  one  horse-power  3.6  square  yards  cooling-surface  is  necessary.  The 
vertical  suspension  of  the  partitions  is  very  essential.  With  a  ventilator  50 
inches  in  diameter  and  a  tower  6  by  7  feet  and  20  feet  high,  10,500  gallons  of 
water  per  hour  were  cooled  from  104°  F.  to  68°  F.  The  following  record 
was  made  at  Mannheim,  Germany:  Vacuum  in  condenser,  28.1  inches;  tem- 
perature of  condensing-water  entering  at  top  of  tower,  104°  to  108°  F.; 
temperature  of  water  leaving  the  cooler,  66.2°  to  71.6°  F.  The  engine  was 
of  the  Sulzer  compound  type,  of  120  horse-power.  The  amount  of  power 
necessary  for  the  arrangement  amounts  to  about  three  per  cent  of  the  total 
horse-power  of  the  engine  for  the  ventilator,  and  from  one  and  one  half  to 
three  per  cent  for  the  lifting  of  the  water  to  the  top  of  the  cooler,  the  total 
being  four  and  one  half  to  six  per  cent. 

A  novel  form  of  condenser  has  been  used  with  considerable  success  in 
Germany  and  other  parts  of  the  Continent.  The  exhaust-steam  from  the 
engine  passes  through  a  series  of  brass  pipes  immersed  in  water,  to  which 
it  gives  up  its  heat.  Between  each  section  of  tubes  a  number  of  galvanized 
disks  are  caused  to  rotate.  These  disks  are  cooled  by  a  current  of  *n'r 
supplied  by  a  fan  and  pass  down  into  the  water,  cooling  it  by  abstract- 
ing the  heat  given  out  by  the  exhaUst-steam  and  carrying  it  up  where  it  is 
driven  off  by  the  air-current.  The  disks  serve  also  to  agitate  the  water  and 
thus  aid  it  in  abstracting  the  heat  from  the  steam.  With  85  per  cent 
vacuum  the  temperature  of  the  cooling  water  was  about  130°  F.,  and  a 
consumption  of  water  for  condensing  is  guaranteed  to  be  less  than  a  pound 
for  each  pound  of  steam  condensed.  For  an  engine  40  in.  X  50  in.,  70  revo- 
lutions per  minute,  90  Ibs.  pressure,  there  is  about  1150  sq.  ft.  of  condensing- 
surface.  Another  condenser,  1600  sq.  ft.  of  condensing-surface,  is  used  for 
three  engines,  32  in.  X  48  in.,  27  in.  x  40  in.,  and  30  in.  X  40  in.,  respectively, 
—  The  Steamship. 

The  Increase  of  Power  that  may  be  obtained  by  adding  a  condenser 
giving  a  vacuum  of  26  inches  of  mercury  to  a  non-condensing  engine  may  be 
approximated  by  considering  it  to  be  equivalent  to  a  net  gain  of  12  pounds 
mean  effective  pressure  per  square  inch  of  piston  area.  If  A  —  area  of  piston 

12  4  S       A  S 
in  square  inches,  S  =  piston-speed  in  ft.  per  minute,  then  —  —  =  —  —  —  H.P. 

oo,UUU        2<5U 

made  available  by  the  vacuum.  If  the  vacuum  —  13.2  Ibs.  per  sq.  in.  =  27.9 
in.  of  mercury,  then  H.P.  =  AS  H-  2500. 

The  saving  of  steam  for  a  given  horse-power  will  be  represented  approxi- 
mately by  the  shortening  of  the  cut-off  when  the  engine  is  run  with  the 
condenser.  Clearance  should  be  included  in  the  calculation.  To  the  mean 
effective  pressure  non-condensing,  with  a  given  actual  cut-off,  clearance 
considered,  add  8  Ibs.  to  obtain  the  approximate  mean  total  pressure,  con- 
densing. From  tables  of  expansion  of  steam  find  what  actual  cut-off  will 
give  this  mean  total  pressure.  The  difference  between  this  and  the  original 
actual  cut-off,  divided  by  the  latter  and  by  100,  will  give  the  percentage  of 
saving. 

The  following  diagram  (from  catalogue  of  PI.  R.  Worthington)  shows  the 
percentage  of  power  that  may  be  gained  by  attaching  a  condenser  to  a  non- 
condensing  engine,  assuming  that  the  vacuum  is  12  Ibs.  per  sq.  in.  The  dia- 
gram also  shows  the  mean  pressure  in  the  cylinder  for  a  given  initial  pres- 
sure and  cut-off,  clearance  and  compression  not  considered. 

The  pressures  given  in  the  diagram  are  absolute  pressures  above  a  vacuum. 

To  find  the  mean  effective  pressure  produced  in  an  engine-cylinder  with  90 
Ibs.  gauge  (  =  105  Ibs.  absolute)  pressure,  cut-off  at  J4  stroke:  find  Kb  in  the 
left-hand  or  initial-pressure  column,  follow  the  horizontal  line  to  the  right 
until  it  intersects  the  oblique  line  that  corresponds  to  the  y±  cut-off,  and  read 
the  mean  total  pressure  from  the  row  of  figures  directly  above  the  point  of 
intersection,  which  in  this  case  is  63  Ibs.  From  this  subtract  the  mean  abso- 
lute back  pressure  (say  3  Ibs.  for  a  condensing  engine  and  15  Ibs  for  a  non- 
condensing  engine  exhausting  into  the  atmosphere)  to  obtain  the  mean  ef- 
fectiva  pressure,  which  in  this  case,  for  a  non-condensing  engine,  gives  48 
Ibs.  To  find  the  gain  of  power  by  the  use  of  a  condenser  with  this  engine, 
read  on  ilie  lower  scale  the  figures  lhat  correspond  in  position  to  48  ll>s.  in 
The  upper  row,  in  this  case  25$.  As  the  diagram  does  not  take  inio  consid- 
eration clearance  or  compression,  the  results  are  only  approximate. 


GAS,   PETROLEUM,   AND    HOT-AIR   ENGINES.         847 


//  /    /  ^bs'olu'te'Mean'Pressure  in  Pounds/        ~7        ///  / 
50    60 /TO    .80/90/100/110    120    130    140    150/160    HO    180  ..190/200 / 


120  60   40    30  Z4-   20    17     15    13    E    I      10 

Per  Cervt  of  Power  6 a  ned  by  Vacuum 


FIG.  151. 

Evaporators  and  Distillers  are  used  with  marine  engines  for  the 
purpose  of  providing  fresh  water  for  the  boilers  or  for  drinking  purposes. 

Weir's  Evaporator  consists  of  a  small  horizontal  boiler,  contrived  so  as 
to  be  easily  taken  to  pieces  and  cleaned.  The  water  in  it  is  evaporated  by 
the  steam  from  the  main  boilers  passing  through  a  set  of  tubes  placed  in  its 
bottom.  The  steam  generated  in  this  boiler  is  admitted  to  the  low- 
pressure  valve -box,  so  that  there  is  no  loss  of  energy,  and  the  water  con- 
densed in  it  is  returned  to  the  main  boilers. 

In  Weir's  Feed-heater  the  feed-water  before  entering  the  boiler  is  heated 
up  very  nearly  to  boiling-point  by  means  of  the  waste  water  and  steam 
from  the  low-pressure  valve-box  of  a  compound  engine. 

GAS,  PETROLEUM,  AND  HOT-AIR  ENGINES. 

Gas-engines.— For  theory  of  the  gas-engine,  see  paper  by  Dugald 
Clerk,  Proc.  Inst.  C.  E.  188-2,  vol.  Ixix.;  and  Van  Nostrand's  Science  Series, 
No.  62.  See  also  Wood's  Thermodynamics.  For  construction  of  gas-engines, 
see  Robinson's  Gas  and  Petroleum  Engines;  articles  by  Albert  Spies  in 
Gassier'1  s  Magazine,  1893;  also  Appleton's  Cyc.  of  Mechanics,  and  Modern 
Mechanism. 

In  the  ordinary  type  of  single-cylinder  gas-engine  (for  example  the  Otto) 
known  as  a  four-cycle  engine  one  ignition  of  gas  takes  place  iii  one  end  of 
the  cylinder  every  two  revolutions  of  the  fly-wheel,  or  every  two  double 
strokes.  The  following  sequence  of  operations  takes  place  during  four  con- 
secutive strokes :  (a)  inspiration  during  an  entire  stroke ;  (b)  compression 
during  the  second  (return)  stroke;  (c)  ignition  at  the  dead-point,  and  expan- 
sion during  the  third  stroke;  (d)  expulsion  of  the  burnt  gas  during  the  fourth 
(return)  stroke.  Beau  de  Rochas  in  1862  laid  down  the  law  that  there  are 


848        GAS,    PETROLEUM,    AND   HOT-AIR  ENGINES; 

four  conditions  necessary  to  realize  the  best  results  from  the  elastic  force 
of  gas:  (1)  The  cylinders  should  have  the  greatest  capacity  with  the  smallest 
circumferential  surface;  (2)  the  speed  should  be  as  high  as  possible;  (3)  the 
cut-off  should  be  as  early  as  possible;  (4)  the  initial  pressure  should  be  as 
high  as  possible.  In  modern  engines  it  is  customary  for  ignition  to  take 
place,  not  at  the  dead  point,  as  proposed  by  Beau  de  Rochas,  but  somewhat 
later,  when  the  piston  has  already  made  part  of  its  forward  stroke.  At  first 
sight  it  might  be  supposed  that  this  would  entail  a  loss  of  power,  but  experi- 
ence shows  that  though  the  area  of  the  diagram  is  diminished,  the  power 
registered  by  the  friction-brake  is  greater.  Stalling  is  also  made  easier  by 
this  method  of  working.  (The  Simplex  Engine,  Proc.  Inst.  M.  E.  1889.) 

In  the  Otto  engine  the  mixture  of  gas  and  air  is  compressed  to  about  3 
atmospheres.  When  explosion  takes  place  the  temperature  suddenly  rises 
to  somewhere  about  2900°  F.  (Robinson.) 

The  two  great  sources  of  waste  in  gas-engines  are:  1.  The  high  tempera- 
ture of  the  rejected  products  of  combustion ;  2.  Loss  of  heat  through  the 
cylinder  walls  to  the  water-jacket.  As  the  temperature  of  the  water-jacket 
is  increased  the  efficiency  of  the  engine  becomes  higher. 

With  ordinary  coal-gas  the  consumption  may  be  taken  at  20  cu.  ft.  per 
hour  per  I.H.P.,  or  24  cu.  ft.  per  brake  H.P.  The  consumption  will  vary  with 
the  quality  of  the  gas.  When  burning  Dowson  producer-gas  the  consump- 
tion of  anthracite  (Welsh)  coal  is  about  1.3  Ibs.  per  I.H.P.  per  hour  for 
ordinary  working.  With  large  twin  engines,  100  H.P.,  the  consumption  is 
reduced  to  about  1.1  Ib.  The  mechanical  efficiency  or  B.H.P.  •<-  I.H.P.  in 
ordinary  engines  is  about  85#;  the  friction  loss  is  less  in  larger  engines. 

Efficiency  of  the  Gas-engine.  (Thurston  on  Heat  as  a  Form  of 
Energy.) 

Heat  transferred  into  useful  work 17% 

to  the  jacket-water 52 

1     lost  in  the  exhaust-gas 16 

"       "    by  conduction  and  radiation 15 

-    83* 

This  represents  fairly  the  distribution  of  heat  in  the  best  forms  of  gas- 
engine.  The  consumption  of  gas  in  the  best  engines  ranges  from  a  mini- 
mum of  18  to  20  cu.  ft.  per  I.H.P.  per  hour  to  a  maximum  exceeding  in  the 
smaller  engines  25  cu.  ft.  or  30  cu.  ft.  In  small  engines  the  consumption  per 
brake  horse-power  is  one  third  greater  than  these  figures. 

The  report  of  a  test  of  a  170-H.P.  Crossley  (Otto)  gas-engine  in  England, 
1892,  using  producer-gas,  shows  a  consumption  of  but  .85  Ib.  of  coal  per  H.P. 
hour,  or  an  absolute  combined  efficiency  of  21.3*  for  the  engine  and  pro- 
ducer. The  efficiency  of  the  engine  alone  is  in  the  neighborhood  of  25*. 

The  Taylor  gas-producer  is  used  in  connection  with  the  Otto  gas-engine  at 
the  works  of  Schleicher,  Schumm  &  Co.,  of  Philadelphia.  The  only  loss  is  due 
to  radiation  through  the  walls  of  the  producer  and  a  small  amount  of  heat 
carried  off  in  the  water  from  the  scrubber.  Experiments  on  a  100-H.P. 
engine  show  a  consumption  of  97/100  Ib.  of  carbon  per  I.H.P.  per  hour.  This 
result  is  superior  to  any  ever  obtained  on  a  steam-engine.  (Iron  Age,  1893.) 

Tests  of  the  Simplex  Gas-engine.  (Proc.  Inst.  M.  E.'  1889.)— 
Cylinder  7%  X  15%  in.,  speed  160  revs,  per  min.  Trials  were  made  with  town 
gas  of  a  heating  value  of  607  heat-units  per  cubic  foot,  and  with  Dowson 
gas,  rich  in  CO,  of  about  150  heat -units  per  cubic  foot. 

Town  Gas.  Dowson  Gas. 

'  1.  2.  IT  17~            2.             IT 

Effective  H.P 6.70  8.67  9.28  7.12           3.61         5.26 

Gas  per  H.P.  per  hour,  cu.  ft..  21.55  20.12  20.73  88.03        114.85       97.88 

Water  per  H.P.  per  hour,  Ibs.  54.7  44.4  43.8  58.3 

Temp,  water  entering,  F 51°  51°  51°  48° 

"       effluent 135°  144°  172°  144° 

The  gas  volume  is  reduced  to  32°  F.  and  30  in  barometer.  A  50-H.P.  engine 
working  35  to  40  effective  H.P.  with  Dowson  generator  consumed  51  Ibs. 
English  anthracite  per  hour,  equal  to  1.48  to  1.3  Ibs.  per  effective  H.P.  A  16- 
H.P.  engine  working  12  H.P.  used  19.4  cu.  ft.  of  gas  per  effective  H.P. 

A  320-H.P.  Gas-engine.—  The  flour-mills  of  M.  Leblanc,  at  Pantin, 
France,  have  been  provided  with  a  320-horse-power  fuel-gas  engine  of  the 
Simplex  type.  With  coal-gas  the  machine  gives  450  horse-power.  There  is 
one  cylinder,  34.8 in.  diam. ;  the  piston-stroke  is 40 in.;  and  the  speed  100  revs. 


GAS-E^GISTES. 


849 


§er  min.  Special  arrangements  have  been  devised  in  order  to  keep  the 
ifferent  parts  of  the  machine  at  appropriate  temperatures.  The  coal  used 
is  0.812  )b.  per  indicated  or  1  .03  Ib.  per  brake  horse-power.  The  water  used 


s  8^4  gallons  per  brake  horse-power  per  hour. 
Test  of 


of  an  Otto  Gas-engine.  (Jour.  F.  J.,  Feb.  1890,  p.  115.)— En- 
gine 7  H.P.  nominal;  working  capacity  of  cylinder  .2594  cu.  ft.;  clearance 
space  .1796  cu.  ft. 

Per  cent 
of  Heat 


o  F 

Temperature  of  gas  supplied . .    62 . 2 

"    "    exhaust...  774.3 

"   entering  water    50.4 

"   exit  water ....     89.2 

Pressure  of  gas,  in.  of  water. .       3.06 

Revolution  per  min.,  av'ge 161.6 

Explosions  missed    per  min., 

average 6.8 

Mean   effective  pressure,   Ibs. 

per  sq.  in , 59. 

Horse-power,  indicated 4.94 

Work    per     explosion,    foot- 
pounds  2204. 

Explosions  per  minute 74. 

Gas  used  perl.H.P.  per  hour, 
cu.  ft .     23.4 


Heat-units. 

received. 

Transferred  into  work 22.84 

Taken  by  jacket- water 49 . 94 

"      *'    exhaust 27.22 

Composition  of  the  gas: 

By  Volume.    By  Weight. 

CO2 0.50$  1.923# 

C2H4 4.32  10.520 

0 1.00  2.797 

CO 5.33  15.419 

CH4 27.18  38.042 

H  51.57  9.021 

N 9.06  22.273 


99.995 


Temperature*  and  Pressures  developed  in  a  Gas-engine. 

(Clerk  on  the  Gas-engine.)— Mixtures  of  air  and  Oldham  coal-gas.     Temper- 
ature before  explosion,  17°  C. 


Air. 


Max.  Press 
above  Atmos., 
Ibs.  per  sq.  in. 

Temp,  of  Explo- 
sion calculated 
from  observed 
Pressure. 

Theoretical 
Temp,  of  Explo- 
sion if  all  Heat 
were  evolved. 

40. 

806°  C. 

1786°  C. 

51.5 

1033 

1912 

60. 

1202 

2058 

61. 

1220 

2228 

78. 

1557 

2670 

87. 

1733 

3334 

90. 

1792 

3808 

91. 

1812 

80. 

1595 

Test  of  the  Clerk  Gas-engine.  (Proc.  Inst.  C.  E.  1882,  vol.  Ixix.)— 
Cylinder  6  X  12  in.,  150  revs,  per  miu.;  mean  available  pressure  70.1  Ibs.,  9 
I.H.P.;  maximum  pressure,  220  Ibs.  per  sq.  in.  above  atmosphere;  pressure 
before  ignition,  41  Ibs.  above  atm.;  temperature  before  compression  60° 
F.,  after  compression,  313°  F.;  temperature  after  ignition  calculated  from 
pressure,  2800°  F. ;  gas  required  per  I. H.P.  per  hour,  22  cu,  ft. 

Combustion  of  the  Gas  in  the  Otto  Engine.— John  Imray,  in 
discussion  of  Mr.  Clerk's  paper  on  Theory  of  the  Gas-engine,  says:  The 
change  which  Mr.  Otto  introduced,  and  which  rendered  the  engine  a  success, 
was  that,  instead  of  burning  in  the  cylinder  an  explosive  mixture  of  gas  and 
air,  he  burned  it  in  company  with,  and  arranged  in  a  certain  way  in  respect 
of,  a  large  volume  of  incombustible  gas  which  was  heated  by  it,  and  which 
diminished  the  speed  of  combustion.  W.  R.  Bousfield,  in  the  same  discus- 
sion, says:  In  the  Otto  engine  the  charge  varied  from  a  charge  which  was 
an  explosive  mixture  at  the  point  of  ignition  to  a  charge  which  was  merely 
an  inert  fluid  near  the  piston.  When  ignition  took  place  there  was  n  explo- 
sion close  to  the  point  of  ignition  that  was  gradually  communicated  through- 
out the  mass  of  the  cylinder.  As  the  ignition  got  farther  away  from  the 
primary  point  of  ignition  the  rate  of  transmission  became  slower,  and  if  the 
engine  were  not  worked  too  fast  the  ignition  should  gradually  catch  up  to 
the  piston  during  its  travel,  all  the  combustible  gas  being  thus  consumed. 
This  theory  of  slow  combustion  is.  however,  disputed  by  Mr.  Clerk,  who 
holds  that  the  whole  quantity  of  combustible  gas  is  ignited  in  an  instant. 

Use   of  Carburet  ted   Air  in   Gas-engines.— Air  passed  over 


850        GAS,  PETROLEUM,  AKD   HOT-AIR  ENGINES. 


gasoline  or  volatile  petroleum  spirit  of  low  sp.  gr.,  0.65  to  0.70,  liberates 
some  of  the  gasoline,  and  the  air  thus  saturated  with  vapor  is  equal  in  heat- 
ing or  lighting  power  to  ordinary  coal-gas.  It  may  therefore  be  used  as  a 
fuel  for  gas-engines.  Since  the  vapor  is  given  off  at  ordinary  temperatures 
gasoline  is  very  explosive  and  dangerous,  and  should  be  kept  in  an  under- 
ground tank  out  of  doors.  A  defect  in  the  use  of  carburetted  air  for  gas- 
engines  is  that  the  more  volatile  products  are  given  off  first,  leaving  an  oily 
residue  which  is  often  useless.  Some  of  the  substances  in  the  oil  that  are 
taken  up  by  the  air  are  apt  to  form  troublesome  deposits  and  incrustations 
when  burned  in  the  engine  cylinder. 

The  Otto  Gasoline-engine.  (Eng'g  News,  May  4,  1893.)— It  is 
claimed  that  where  but  a  small  gasoline-engine  is  used  and  the  gasoline 
bought  at  retail  the  liquid  fuel  will  be  on  a  par  with  a  steam-engine  using  6 
Ibs.  of  coal  per  horse -power  per  hour,  and  coal  at  $3.50  per  ton,  and  will 
besides  save  all  the  handling  of  the  solid  fuel  and  ashes,  as  well  as  the  at- 
tendance for  the  boilers.  As  very  few  small  steam-engines  consume  less 
than  6  Ibs.  of  coal  per  hour,  this  is  an  exceptional  showing  for  economy.  At 
8  cts.  per  gallon  for  gasoline  and  1/10  gal.  required  per  H.P.  per  hour,  the 
cost  per  H.P.  per  hour  will  be  0.8  cent. 

Tne  Pries  till  an  Petroleum-engine,  (Jour.  Frank.  Inst.,  Feb. 
1893  )— The  following  is  a  description  of  the  operation  of  the  engine:  Any 
ordinary  high -test  (usually  150°  test)  oil  is  forced  under  air-pressure  to  an 
atomizer,  where  the  oil  is  met  by  a  current  of  air  and  broken  up  into  atoms 
and  sprayed  into  a  mixer,  where  it  is  mixed  with  the  proper  proportion  of 
supplementary  air  and  sufficiently  heated  by  the  exhaust  from  the  cylinder 
passing  around  this  chamber.  The  mixture  is  then  drawn  by  suction  into 
the  cylinder,  where  it  is  compressed  by  the  piston  and  ignited  by  an  electric 
spark,  a  governor  controlling  the  supply  of  oil  and  air  proportionately  to 
the  work  performed.  The  burnt  products  are  discharged  through  an  ex- 
haust-valve which  is  actuated  by  a  cam.  Part  of  the  air  supports  the  com- 
bustion of  the  oil,  and  the  heat  generated  by  the  combustion  of  the  oil 
expands  the  air  that  remains  and  the  products  resulting  from  the  explosion, 
and  thus  develops  its  power  from  air  that  it  takes  in  while  running.  In 
other  words,  the  engine  exerts  its  power  by  inhaling  air,  heating  that  air, 
and  expelling  the  products  of  combustion  when  done  with.  In  the  largest 
engines  only  the  1/250  part  of  a  pint  of  oil  is  used  at  any  one  time,  and  in 
the  smallest  sizes  the  fuel  is  prepared  in  correct  quantities  varying  from 
1/7000  of  a  pint  upward,  according  to  whether  the  engine  is  running  on  light 
or  full  duty.  The  cycle  of  operations  is  the  same  as  that  of  the  Otto  gas- 
engine. 

Trials  of  a  5-H.P.  Priestman  Petroleum-engine.  (Prof. 
W.  C.  Unwin,  Proc.  Inst.  C.  E.  1892.)— Cylinder,  8^  X  12  in.,  making  normally 
200  revs,  per  min.  Two  oils  were  used,  Russian  and  American.  The  more 
important  results  were  given  in  the  following  table: 


Trial  V. 
Full 
Power. 

Trial  I. 
Full 
Power. 

Trial  IV. 
Full 
Power. 

Trial  II. 
Half 
Power. 

Trial  III. 
Light. 

Oil  used                     .  .     •] 

Day- 

Russo- 

Russo- 

Russo- 

Russo- 

Brake  H  P 

light. 

7.722 

lene. 
6  765 

lene. 

6.882 

lene. 
3  62 

lerie. 

I  H  P 

9  369 

7  408 

8  332 

4  70 

0  889 

Mechanical  efficiency.  .  . 

0.824 

0.91 

0.876 

0.769 

Oil  used  per  brake  H.P. 
hour,  Ib  

0.842 

0.946 

0.988 

1.381 

Oil    used    per    indicated 
H.P  hour  Ib 

0  694 

0  864 

0  816 

1  063 

5  734 

Lb.  of  air  per  Ib.  of  oil.  . 
Mean  explosion  pressure, 
Ibs.  per  sq.  in  
Mean  compression  pres- 
sure, Ibs.  per  sq,  in  .. 
Mean  terminal  pressure, 
Ibs.  per  sq.  in  

33.4 
151.4 
35.0 
35.4 

31.7 
134.3 
27.6 

23.7 

43.2 

128.5 
26.0 
25.5 

21.7 
48.5 
14.8 
15.6 

10.1 
9.6 
6.0 

To  compare  the  fuel  consumption  with  that  of  a  steam-engine,  1   Ib.  of 
oil  might  be  taken  as  equivalent  to  1%  Ibs.  of  coal.    Then  the  consumption 


EFFICIEHCY  OF  LOCOMOTIVES.  851 

in  the  oil-engine  was  equivalent,  in  Trials  I.,  IV.,  and  V.,  to  1.42  Ibs.,  1.481bs., 
and  1. 20  Ibs.  of  coal  per  brake  horse-power  per  hour.  From  Trial  IV.  the 
following  values  of  the  expenditure  of  heat  were  obtained: 

Per  cent. 

Useful  work  at  brake 13.31 

Engine  friction 2.81 

Heat  shown  on  indicator-diagram 16.12 

Rejected  in  jacket- water  47.54 

"         in  exhaust -gases 26.72 

Radiation  and  unaccounted  for 9.61 


Total 


Naphtha-engines  are  in  use  to  some  extent  in  small  yachts  and 
launches.  The  naphtha  is  vaporized  in  a  boiler,  and  the  vapor  is  used  ex- 
pansively in  the  engine-cylinder,  as  steam  is  used;  it  is  then  condensed  and 
returned  to  the  boiler.  A  portion  of  the  naphtha  vapor  is  used  for  fuel  un- 
der the  boiler.  According  to  the  circular  of  the  builders,  the  Gas  Engine 
and  Power  Co.  of  New  York,  a  2-H.P.  engine  requires  from  3  to  4  quarts  of 
naphtha  per  hour,  and  a  4-H.P.  engine  from  4  to  6  quarts.  The  chief  advan- 
tages of  the  naphtha-engine  and  boiler  for  launches  are  the  saving  of  weight 
and  the  quickness  of  operation.  A.  2-H.P.  engine  weighs  200  Ibs.,  a  4-H.P.  300 
ibs.  It  takes  only  about  two  minutes  to  get  under  headway.  (Modern 
Mechanism,  p.  270.) 

Mot-air  (or  Calorie)  Engines. — Hot-air  engines  are  used  to  some 
extent,  but  their  bulk  is  enormous  compared  with  their  effective  power.  For 
an  account  of  the  largest  hot-air  engine  ever  built  (a  total  failure)  see 
Church's  Life  of  Ericsson.  For  theoretical  iuvestigaton,  see  Rankine's 
Steam-engine  and  Rontgen's  Thermodynamics.  For  description  of  con- 
structions, see  Appletorf  s  Cyc.  of  Mechanics  and  Modern  Mechanism,  and 
Babcock  on  Substitutes  for  Steam,  Trans.  A.  S.  M.  E.,  vii.,  p.  693. 

Test  of  a  Hot-air  Engine  (Robinson).— A  vertical  double-cylinder 
(Caloric  Engine  Co.'s)  12  nominal  H.P.  engine  gave  20.19  I.H.P.  in  the  work- 
ing cylinder  and  11.38  I.H.P.  in  the  pump,  leaving  8.81  net  I.H.P.;  while  the 
effective  brake  H.P.  was  5.9,  giving  a  mechanical  efficiency  of  67$.  Con- 
sumption of  coke,  3.7  Ibs.  per  brake  H.P.  per  hour.  Mean  pressure  on 
pistons  15.37  Ibs.  per  square  inch,  and  in  pumps  15.9  Ibs.,  the  area  of  working 
cylinders  being  twice  that  of  the  pumps.  The  hot  air  supplied  was  about 
1160°  F.  and  that  rejected  at  end  of  stroke  about  890°  F. 

The  b;'st  result  of  Stirling's  heft-engine  was  2.7  Ibs.  per  brake  H.P.  per 
hour.  Bailey's  hot-air  engine,  2  H.P.  nominal,  gave  4.2  I.H.P.,  2.6B.H.P.; 
mechanical  efficiency  62$;  estimated  temperature  at  highest  pressure  1500° 
F.,  and  at  atmospheric  pressure  700°  F.  Highest  pressure,  14  Ibs.  per  square 
inch  above  atmosphere.  Consumption  of  fuel,  7  Ibs.  per  hour  per  brake 
H.P.,  and  of  cooling  water,  30  Ibs. 


LOCOMOTIVES. 

Efficiency   of   Locomotives   and   Resistance   of  Trains. 

(George  R.  Henderson,  Proc.  Engrs.  Club  of  Phila.  1886.)—  The  efficiency  of 
locomotives  can  be  divided  into  two  principal  parts  :  the  first  depending 
upon  the  size  of  the  cylinders  and  wheels,  the  valve-gear,  boiler  and  steam- 
passages,  of  which  the  tractive  power  is  a  function;  and  the  second  upon 
the  speed,  grade,  curvature,  and  friction,  which  combine  to  produce  the 
resistance. 
The  tractive  power  may  be  determined  as  follows  : 

Let  P  =  tractive  power  ; 

p  =  average  effective  pressure  in  cylinder; 
tf  =  stroke  of  piston; 
d  =  diameter  of  cylinders; 
D  —  diameter  of  driving-wheels.    Then 


_ 

4irD 


LOCOMOTIVES. 


The  average  effective  pressure  can  be  obtained  from  an  indicator-dia- 
gram, or  by  calculation,  when  the  initial  pressure  and  ratio  of  expansion  are 
known,  together  with  the  other  properties  of  the  valve-motion.  The  sub- 
joined table  from  "  Auchincloss  "  gives  the  proportion  of  mean  effective 
pressure  to  boiler-pressure  above  atmosphere  for  various  proportions  of 
cut-off. 


Stroke,            ,*f'H- 
Cut  off  at-!    fffift). 

Stroke, 
Cut  off  at— 

(M.E.P. 
Boiler- 
pres.  =  1). 

Stroke, 
Cut  off  at— 

M.E.P. 
(Boiler- 
pres.  =  1). 

.1 

.15 

.333  =  \& 

•5=^2 

.625  =  % 

.79 

.125  =  M 

.2 

.375  =  % 

.55 

.666  =  % 

.82 

.15 

.24 

A 

.57 

.7 

.85 

.175 

.28 

.45 

.62 

.75  =  % 

.89 

.2 

.32 

.6  =  ^ 

.67 

.8 

.93 

.25  =  ^ 

.4 

.55 

.72 

.875  =  % 

.98 

.3                   <            =46 

These  values  were  deduced  from  experiments  with  an  English  locomotive 
by  Mr.  Gooch.  As  diagrams  vary  so  much  from  different  causes,  this  table 
will  only  fairly  represent  practical  cases.  It  is  evident  that  the  cut-off  must 
be  such  that  the  boiler  will  be  capable  of  supplying  sufficient  steam  at  the 
given  speed. 

In  the  following  calculations  it  is  assumed  that  the  adhesion  of  the  engine 
is  at  least  equal  to  the  tractive  power,  which  is  generally  the  case— if  the 
engine  be  well  designed— except  when  starting,  or  running  at  a  very  low 
rate  of  speed,  with  a  small  expansive  ratio.  When  running  faster,  economy, 
and  also  the  size  of  the  boiler,  necessitate  a  higher  ratio  of  expansion,  thus 
reducing  the  tractive  power  below  the  adhesion.  If  the  adhesion  be  less 
than  the  tractive  power,  substitute  it  for  the  latter  in  the  following  for- 
mulae. 

The  resistances  can  be  computed  in  the  following  manner,  first  consider- 
ing the  train: 

There  is  a  resistance  due  to  friction  of  the  journals,  pressure  of  wind,  etc., 
which  increases  with  the  speed.  Most  of  the  experiments  made  with  a  view 
of  determining  the  resistance  of  trains  have  been  with  European  rolling-stock 
and  on  European  railways.  The  few  trials  that  have  been  made  here  seem 
to  prove  that  with  American  systems  this  resistance  is  less. 

The  following  table  gives  the  resistance  at  different  speeds,  assumed  for 
American  practice  : 


Speed  in  miles  per  hour  : 
s  =      5         10          15        20 


40       45 


50 


55        60 


10.2     12.1    14.3     16.8    19.2 


25        30        35 

Resistance  in  pounds  per  ton  of  2240  Ibs.: 
y  =     3.1        3.4          4.        4.8      5.8       7.1        8.6 
Coefficient  of  resistance  in  terms  of  load  : 
I  =  .0015    .0017    .0020    .0024  .0029  .0035   .0043  .0051   .0060  .0071   .0084  .0096 

I  =  .0015  (l-fj—). 

The  resistance  due  to  curvature  is  about  .5  Ib.  per  ton  per  degree  of  cur- 
vature, or  the  coefficient  =  .00025c,  where  c  —  the  curvature  in  degrees. 

The  effect  of  grades  may  be  determined  by  the  theory  of  the  inclined 
plane. 

Consider  a  load  L  on  a  grade  of  m  feet  per  mile.  The  component  of  the 
weight  L  acting  in  the  line  of  traction,  or  parallel  to  the  track,  is 

L  sin  9  =  — ^  =  .00019Lw. 

To  combine  these  coefficients  in  one  equation  representing  the  resistance 
)f  the  train : 


of  the  train  : 

Let  L  =  weight  of  train,  exclusive  of  engine,  in  pounds; 
R  =  resistance  of  train,  in  pounds. 


R  =  resistance  of  train,  in  po 
«,  c,  and  m,  as  above.    Then 


R  = 


.00025c  ±  .00019m], 


INERTIA  AND  RESISTANCES  OF  RAILROAD  TRAINS.    853 

the  ±  sign  meaning  that  this  coefficient  is  positive  for  ascending  and  nega- 
tive for  descending  grades. 

To  find  a  grade  upon  which  a  train  would  descend  by  itself,  take  the  last 
coefficient  minus  and  make  R  =  O,  whence 


As  locomotives  usually  have  a  long  rigid  wheel-base,  the  coefficient  for 
curvature  had  better  be  doubled.  The  resistance  due  to  the  friction  of  the 
working  parts  will  be  considered  as  being  proportional  to  the  tractive  power, 
so  that  the  effective  tractive  power  will  be  represented  by  itP,  the  resistance 
being  (1  —  u)P. 

Combining  all  these  values,  there  results  the  equation  between  the  trac- 
tive power  and  the  weight  of  the  train»and  engine: 

Mp_  TF(.0005c  ±  .00019m)  =  LI  -f  .00025c  ±  .00019m, 

IF  being  weight  of  engine  and  tender,  and  u  being  probably  about  .8. 
Transforming,  we  have 

_  uP  -  TF(.0005c  ±  .00019m) 
I  _|_  .O0025c  ±  .00019m     ' 
and 

_  L(l  -f-  .00025C  ±  .00019m)  -f  TF(.0005c  ±  .00019m) 

u 

These  deductions,  says  Mr.  Henderson,  agree  well  with  railroad  practice. 
The  figures  given  above  for  resistances  are  very  much  less  than  those 
given  by  the  old  formulae  (which  were  certainly  wrongX  but  even  Mr.  Hen- 
derson's figures  for  high  speed  are  too  high,  according  to  a  diagram  given  by 
D.  L.  Barnes  in  Eng'g  Mag.,  June,  1894,  from  which  the  following  figures  are 
derived: 

Speed,  miles  per  hour  ..............     50       60       70       80       90       100 

Resistance,  pounds  per  gross  ton  ..     12      12.4    13.5      15        17        20 

Eng'g  News,  March  8,  1894,  gives  a  formula  which  for  high  speeds  gives 
figures  for  resistance  between  those  of  Mr.  Barnes  and  Mr.  Henderson.  See 
tests  reported  in  Eng'g  News  of  June  9,  1892.  The  formula  is,  resistance  in 
pounds  per  ton  =  J4  velocity  in  miles  per  hour  -[-  2.  This  gives  for 

Speed...      .5       10      15    20    25      30       35    40    45      50    60      70    80    90   100 
Resistance..  314    4.5    5%    7    8^4    9.5    10%  12  13>4  14.5  17    19.52224.527 

For  tables  showing  that  the  resistance  varies  with  the  area  exposed  to  the 
resistance  and  friction  of  the  air  per  ton  of  load,  see  Dashiell,  Trans.  A.  S. 
M.  E.,  vol.  xiii.  p.  371. 

Inertia  and  Resistances  of  Railroad  Trains  at  Increasing 
Speeds.—  A  series  of  tables  and  diagrams  is  given  in  R.  R.  Gaz.,  Oct.  31, 
1SHO,  to  show  the  resistances  due  to  inertia  in  starting  trains  and  accelerat- 
ing their  speeds. 

The  mechanical  principles  and  formulae  from  which  these  data  were  cal- 
culated are  as  follows: 

6*  =:  speed  in  miles  per  hour  to  be  acquired  at  the  end  of  a  mile. 

S  -T-  2  =  average  speed  in  miles  per  hour  during  the  first  mile  run. 

V  =  velocity  in  feet  per  second  at  the  end  of  a  mile;  then  FH-  2  =  aver- 
age velocity  in  feet  per  second  during  the  first  mile  run. 

5280  -s-  F/2  =  time  in  seconds  required  to  run  first  mile  =  10560  -f-  V. 

V-*-  (10560  -=-  V)  -  V*  ~  10560  =  .0000947F2  =  Constant  gain  in  velocity  or 
acceleration  in  feet  per  second  necessary  to  the  acquirement  of  a  velocity  V 
at  the  end  of  a  mile. 

g  =  acceleration  due  to  the  force  of  gravity,  i.e.,  32.2  feet  per  second. 

The  forces  required  to  accelerate  a  given  mass  in  a  given  time  to  different 
velocities  are  in  proportion  to  those  velocities.  The  weight  of  a  body  is  the 
measure  of  the  force  which  accelerates  it  in  the  case  of  gravity,  and  as  we 
are  considering  1  lb.,  or  the  unit  of  weight,  as  the  mass  to  be  accelerated, 
we  have  g:  (F2  -r-  10560)  :  :  1  is  to  the  force  required  to  accelerate  1  lb.  to  the 
velocity  Fat  the  end  of  a  mile  run,  or,  what  is  the  same,  to  accelerate  it  at 
the  rate  of  F2  -r-  10560  feet  per  second. 

From  this  the  pull  on  the  drawbar—  it  is  the  same  as  the  force  just  men- 
tioned, and  is  properly  termed  the  inertia  —  in  pounds  per  pound  of  train 
weight  is  F2  -,-  (10560  X  32.2),  which  equals  .00000294  F2, 


854  LOCOMOTIVES. 

This  last  formula  also  gives  the  grade  in  per  cent  which  will  give  a  resist- 
ance equal  to  the  inertia  due  to  acceleration. 

The  grade  in  feet  per  mile  is  .00000294  F2  X  5280  =  .01553 F2. 

The  resistance  offered  in  pounds  per  ton  is  2000  times  as  much  as  per 
pound,  or  .00588 F2. 

When  the  adhesion  of  locomotive  drivers  is  600  Ibs.  per  ton  of  weight 
thereon— this  is  about  the  maximum — then  the  tons  on  drivers  necessary  to 
overcome  the  inertia  of  each  ton  of  total  train  load  are  .00588F2  H-  600  = 
. 0000098 F2.  In  this  determination  of  resistances  no  account  has  been  taken 
of  the  rotative  energy  of  the  wheels. 

Efficiency  of  the  Mechanism  of  a  Locomotive.  —  Ihuitt 
Halpin  (Proc.  Inst.  M.  E.,  January,  1889,)  writes  as  follows,  concerning  the 
tractive  efficiency  of  locomotives;  With  simple  two-cylinder  engines,  hav- 
ing four  wheels  coupled,  experiments  have  been  made  by  the  late  locomo- 
tive superintendent  of  the  Eastern  Railway  of  Fiance,  M.  Regray,  with  the 
greatest  possible  care  and  with  the  best  apparatus,  and  the  result  arrived  at 
was  that  out  of  100  I.H.P  in  the  cylinders  43  H.P.  only  was  available  on  the 
draw-bar.  The  loss  of  57$  was  rather  a  high  price  to  pay  for  the  efficiency 
of  the  engine.  How  much  of  that  loss  was  due  to  coupling-rods  no  one 
could  yet  say;  but  a  considerable  amount  of  it  must  be  due  to  the  rods,  be- 
cause it  was  known  that  large  engines  with  a  single  pair  of  driving-wheels 
not  coupled  were  doing  their  work  more  economically,  while  advanced  loco- 
motive engineers  who  had  not  yet  gone  in  for  compounding  were  at  any  rate 
going  back  to  the  single  pair  of  driving-wheels.  Moreover,  that  astonishing 
loss  of  57$  had  been  confirmed  independently  on  the  Pennsylvania  Railroad, 
trials  made  with  an  engine  haying  18^4  X  24-in.  cylinders  and  6  ft.  6  in. 
wheels  four-coupled;  by  taking  indicator  diagrams  up  to  65  miles  an  hour, 
which  were  professed  to  be  taken  correctly,  the  power  on  the  draw-bar 
was  found  to  be  only  42$  of  that  in  the  cylinders,  or  only  1%  less  than  in  the 
French  experiments. 

The  Size  of  Locomotive  Cylinders  is  usually  taken  to  be  such 
that  the  engine  will  just  overcome  the  adhesion  of  its  wheels  to  the  rails  un- 
der favorable  circumstances. 

The  adhesion  of  the  wheel  is  about  one  third  the  weight  when  the  rail  is 
clean  and  sanded,  but  is  usually  assumed  at  0.25.  (Thurston.) 

A  committee  of  the  American  Association  of  Master  Mechanics,  after 
studying  the  performance  reports  of  the  best  engines,  proposes  the  follow- 
ing formula  for  weight  on  driving-wheels:  W  =  — — — — -  -  in  which  the 
mean  pressure  in  the  cylinder  is  taken  at  0.85  of  the  boiler-pressure  at 
starting,  C  is  a  numerical  coefficient  of  adhesion,  d  the  diameter  of  cylinder 
in  inches,  D  that  of  the  drivers  in  inches,  P  the  pressure  in  the  boiler  in 
pounds  per  square  inch,  S  the  stroke  of  piston  in  inches.  C  is  taken  as  0.25 
for  passenger  engines,  0.24  for  freight,  and  0.22  for  "  switching  "  engines. 

The  common  builder's  rule  for  determining  the  size  of  cylinders  for  the 
locomotive  is  the  following,  in  which  we  accept  Mr.  Forney's  assumption 
that  the  steam-pressure  at  the  engine  may  be  taken  as  nine  tenths  that  in 

the  boiler:    The  tractive  force  is,  approximately,  F  =  — ^-^ — * —  where 

C 

C  is  the  circumference  of  tires  of  driving-wheels,  S  =  the  stroke  in  inches, 
P!  =  the  initial  unbalanced  steam-pressure  in  the  cylinder  in  pounds  per 
square  inch,  and  A  =  the  area  of  one  cylinder  in  square  inches.  If  D  = 

diameter  of  driving  wheel  and  d  =  diameter  of  cylinder,  F  = 

Taking  the  adhesion  at  one  fourth  the  weight  IF, 

™      A  oKTjr       O.tyiX  A  X  48       O.Qp^S 
F=0.2W  =-       — _      -    =— -_  ; 

whence  the  area  of  each  piston  is 

0.25CIF 


A  =  -( 

The  above  formulae  give  the  maximum  tractive  force;  for  the  mean  trac- 
tive force  substitute  for  p^  in  the  formulae  the  mean  effective  pressure, 


BOILERS,    GRATE-SURFACE,    SMOKE-STACKS,    ETC.    855 

Von  Borries's  rule  for  the  diameter  of  the  low-pressure  cylinder  of  a  com- 
pound locomotive  is  d2  =  — — , 
ph 

where  d  =  diameter  of  l.p.  cylinder  in  inches; 
D  =  diameter  of  driving- wheel  in  inches; 
p  =  mean   effective  pressure  per  sq.  in.,    after  deducting   internal 

machine  friction; 
h  —  stroke  of  piston  in  inches; 
Z  —  tractive  force  required,  usually  0.14  to  0.16  of  the  adhesion. 

The  value  of  p  depends  on  the  relative  volume  of  the  two  cylinders,  and 
from  indicator  experiments  may  be  taken  as  follows: 

Pii««  nf  -Pncrinp     Ratio  of  Cylinder      p  in  percentage     p  for  Boiler-press 

Volumes.          of  Boiler-pressure.      ure  of  176  Ibs, 
Large-tender  eng's     1  :  2  or  1  :  2.05  42  74 

Tank-engines I:  2  or  1:2.2  40  71 

The  Size  of  Locomotive  Boilers.  (Forney's  Catechism  of  the 
Locomotive.)— They  should  be  proportioned  to  the  amount  of  adhesive 
weight  and  to  the  speed  at  which  the  locomotive  is  intended  to  work.  Thus 
a  locomotive  with  a  great  deal  of  weight  on  the  driving-wheels  could  pull  a 
heavier  load,  would  have  a  greater  cylinder  capacity  than  one  with  little  ad- 
hesive weight,  would  consume  more  steam,  and  therefore  should  have  a 
larger  boiler. 

The  weight  and  dimensions  of  locomotive  boilers  are  in  nearly  all  cases 
determined  by  the  limits  of  weight  and  space  to  which  they  are  necessarily 
confined.  It  may  be  stated  generally  that  within  these  limits  a  Locomotive 
boiler  cannot  be  made  too  large.  In  other  words,  boilers  for  locomotives 
should  always  be  made  as  large  as  is  possible  under  the  conditions  that  de 
term  inn  the  weight  and  dimensions  of  the  locomotives. 

Wootten's  Locomotive.  (Clark's  Steam-engine  ;  see  also  Jour. 
Frank.  lust.  1891,  and  Modern  Mechanism,  p.  485.)— J.  E.  Wool  ten  designed 
and  constructed  a  locomotive  boiler  for  the  combustion  of  anthracite  and 
lignite,  though  specially  for  the  utilization  as  fuel  of  the  waste  produced  in 
the  mining  and  preparation  of  anthracite.  The  special  feature  of  the  engine 
is^  the  fire-box,  which  is  made  of  great  length  and  breadth,  extending  clear 
over  the  wheels,  giving  a  grate-area  of  from  64  to  85  sq.  ft.  The  draught 
diffused  over  these  large  areas  is  so  gentle  as  not  to  lift  the  fine  pp~*icles  of 
the  fuel.  A  number  of  express-engines  having  this  type  of  boiler  are  engaged 
on  the  fast  trains  between  Philadelphia  and  Jersey  City.  The  fire-box  shell 
ir,  8  ft.  8  in.  wide  and  10  ft.  5  in.  long  ;  the  fire-box  is  8x9^  ft.,  making  76  sq. 
ft.  of  grate-area.  The  grate  is  composed  of  bars  and  water-tubes  alternately. 
The  regular  types  of  cast-iron  shaking  grates  are  also  used.  The  height  of 
the  fire-box  is  only  2  ft.  5  in.  above  the  grate.  The  grate  is  terminated  by 
a  bridge  of  fire-brick,  beyond  which  a  combustion-chamber,  27  in.  long, 
leads  to  the  flue-tubes,  about  184  in  number,  1%  in.  diam.  The  cylinders  are 
21  in.  diam.,  with  a  stroke  of  22  inches.  The  driving-wheels,  four-coupled, 
a,re  5  ft.  8  in.  diam.  The  engine  weighs  44  tons,  of  which  29  tons  are  on  driv- 
ing wheels.  The  heating-surface  of  the  fire-box  is  135  sq.  ft.,  that  of  the 
flue-tubes  is  982  sq.  ft.;  together,  1117  sq.  ft.,  or  14.7  times  the  grate-area. 
Hauling  15  passenger-cars,  weighing  with  passengers  360  tons,  at  an  average 
speed  of  42  miles  per  hour,  over  ruling  gradients  of  1  in  89,  the  engine  con- 
sumes 62  Ibs.  of  fuel  per  mile,  or  34^4  Ibs.  per  sq.  ft.  of  grate  per  hour. 

Qualities  Essential  for  a  Free-steaming  Locomotive. 
(From  a  paper  by  A.  E.  Mitchell,  read  before  the  N.  Y.  Railroad  Club; 
Eng'g  News,  Jan.  24,  1891.)— Square  feet  of  boiler-heating  surface  for  bitu- 
minous coal  should  not  be  less  than  4  times  the  square  of  the  diameter  in 
inches  of  a  cylinder  1  inch  larger  than  the  cylinder  to  be  used.  One  tenth 
of  this  should  be  in  the  fire-box.  On  anthracite  locomotives  more  heating- 
surface  is  required  in  the  fire-box,  on  account  of  the  larger  grate-area 
required,  but  the  heating-surface  of  the  flues  should  not  be  materially 
decreased. 

Grate-surface,  Smoke-stacks,  and  Exhaust-nozzles  for 
Locomotives.  (Am.  Mac/t.,  Jan.  8,  1891.) — For  grate-surface  for  anthra- 
cite coal:  Multiply  the  displacement  in  cubic  feet  of  one  piston  during  a 
stroke  by  8.5;  the  product  will  be  the  area  of  the  grate  in  square  feet. 

For  bituminous  coal :  Multiply  the  displacement  in  feet  of  one  piston 
during  a  stroke  by  6^;  the  product  will  be  the  grate-area  in  square  feet  for 
engines  with  cylinders  12  in.  in  diameter. and  upwards.  For  engines  with 


856 


LOCOMOTIVES. 


smaller  cylinders  the  ratio  of  grate-area  to  piston-displacement  should  be  ?J^ 
to  1,  or  even  more,  if  the  design  of  the  engine  will  admit  this  proportion. 

The  grate-areas  in  the  following  table  have  been  found  by  the  foregoing 
rules,  and  agree  very  closely  with  the  average  practice  : 

Smoke-stacks.— The  internal  area  of  the  smallest  cross-section  of  the  stack 
should  be  1/1?  of  the  area  of  the  grate  in  soft-coal-burning  engines. 

A.  E.  Mitchell,  Supt.  of  Motive  ?9wer  of  the  N.  Y.  L.  E.  &  W.  R.  R.,  says 
that  recent  practice  varies  from  this  rule.  Some  roads  use  the  same  size  of 
stack,  13^  in.  diam.  at  throat,  for  all  engines  up  to  20  in.  diam.  of  cylinder. 

The  area  of  the  orifices  in  the  exhaust-nozzles  depends  on  the  quantity  and 
quality  of  the  coal  burnt,  size  of  cylinder,  construction  of  stack,  and  the 
condition  of  the  outer  atmosphere.  It  is  therefore  impossible  to  give  rules 
for  computing  the  exact  diameter  of  the  orifices.  All  that  can  be  done  is  to 

five  a  rule  by  which  an  approximate  diameter  can  be  found.  The  exact 
iameter  can  only  be  found  by  trial.  Our  experience  leads  us  to  believe  that 
the  area  of  each  orifice  in  a  double  exhaust-nozzle  should  be  equal  to  1/400 
part  of  the  grate-surface,  and  for  single  nozzles  1/200  of  the  grate-surface. 
These  ratios  have  been  used  in  finding  the  diameters  of  the  nozzles  given  in 
the  following  table.  The  same  sizes  are  often  used  for  either  hard  or  soft 
coal-burners. 


Double 

Single 

Size  of 
Cylinders, 
in  inches. 

Grate-area 
for  Anthra- 
cite Coal,  in 
sq.  in. 

Grate-area 
for  Bitumin- 
ous Coal,  in 
sq.  in. 

Diameter 
of  Stacks, 
in  inches. 

Nozzles. 

Nozzles. 

Diam.  of 
Orifices,  in 

Diam.  of 
Orifices,  in 

inches. 

inches. 

12  X  20 

1591 

1217 

9^3 

2 

2  13/16 

13  X  20 

1873 

1432 

10^ 

&A 

3 

14  X  20 

2179 

1666 

ii£J 

2  5/16 

3^ 

15  X  22 

2742 

2097 

1»H 

2  9/16 

3  11/16 

16X24 

3415 

2611 

14 

2% 

4    1/16 

17  X  24 

3856 

2948 

15 

3  1/16 

4    5/16 

18X24 

4321 

3304 

15% 

m 

4% 

19  X  24 

4810 

3678 

i$Z 

3  7/16 

4  13/16 

20  X  24 

5337 

4081 

tfx 

3% 

5    1/16 

I^xhaust-nozzles  in  Locomotive  Boilers.— A  committee  of 
the  Am.  Ry.  Master  Mechanics1  Assn.  in  1890  reported  that  they  had,  after 
two  years  of  experiment  and  research,  come  to  the  conclusion  that,  owing 
to  the  great  diversity  in  the  relative  proportions  of  cylinders  and  boilers, 
together  with  the  difference  in  the  quality  of  fuel,  any  rule  which  does  not 
recognize  each  and  all  of  these  factors  would  be  worthless. 

The  committee  was  unable  to  devise  any  plan  to  determine  the  size  of  the 
exhaust-nozzle  in  proportion  to  any  other  part  of  the  engine  or  boiler,  and 
believes  that  the  best  practice  is  for  each  user  of  locomotives  to  adopt  a 
nozzle  that  will  make  steam  freely  and  fill  the  other  desired  conditions,  best 
determined  by  an  intelligent  use  of  the  indicator  and  a  check  on  the  fuel 
account.  The  conditions  desirable  are  :  That  it  must  create  draught  enough 
on  the  fire  to  make  steam,  and  at  the  same  time  impose  the  least  possible 
amount  of  work  on  the  pistons  in  the  shape  of  back  pressure.  It  should  be 
large  enough  to  prod  nee  a  nearly  uniform  blast  without  lifting  or  tearing 
the  fire,  and  be  economical  in  its  use  of  fuel. 

Fire-brick  Arches  in  Locomotive  Fire-boxes.— A  com- 
mittee of  the  Am.  Ry.  Master  Mechanics'  Assn.  in  1890  reported  strongly  in 
favor  of  the  use  of  brick  arches  in  locomotive  fire-boxes.  They  say  :  It  is 
the  unanimous  opinion  of  all  who  use  bituminous  coal  and  brick  arch,  that 
it  is.  most  efficient  in  consuming  the  various  gases  composing  black  smoke, 
and  by  impeding  and  delaying  their  passage  through  the  tubes,  and  ming- 
ling and  subjecting  them*  to  the  heat  of  the  furnace,  greatly  lessens  the 
volume  ejected,  and  intensifies  combustion,  and  does  not  in  the  least  check 
but  rather  augments  draught,  with  the  consequent  saving  of  fuel  and  in- 
creased steaming  capacity  that  might  be  expected  from  such  results.  This 
in  particular  when  used  in  connection  with  extension  front. 

Size,  Weight,  Tractive  Power,  etc.,  of  Different  Sizes  of 
locomotives.  (J.  G.  A.  Meyer,  Modern  Locomotive  Construction,  Am, 


SIZE,    WEIGHT,    TRACTIVE   POWER,    ETC. 


857 


Mach.,  Aug.  8,  1885.)— The  tractive  power  should  not  be  more  or  less  than 
the  adhesion.  In  column  3  of  each  table  the  adhesion  is  given,  and  since  the 
adhesion  and  tractive  power  are  expressed  by  the  same  number  of  pouuds, 
these  figures  are  obtained  by  finding  the  tractive  power  of  each  engine,  for 
this  purpose  always  using  the  small  diameter  of  driving-wheels  given  in 
column  2.  The  weight  on  drivers  is  shown  in  column  4,  which  is  obtained  by 
multiplying  the  adhesion  by  5  for  all  classes  of  engines.  Column  5  gives  the 
weights  on  the  trucks,  and  these  are  based  upon  observations.  Thus,  the 
weight  on  the  truck  for  an  eight-wheeled  engine  is  about  one  half  of  that 
placed  on  the  drivers. 

For  Mogul  engines  we  multiply  the  total  -weight  t>n  drivers  by  the  decimal 
.2,  and  the  product  will  be  the  weight  on  the  truck. 

For  ten-wheeled  engines  the  total  weight  on  the  drivers,  multiplied  by  the 
decimal  .32,  will  be  equal  to  the  weight  on  the  truck. 

And  lastly,  for  consolidation  engines,  the  total  weight  on  drivers  multi- 
plied by  the  decimal  .16,  will  determine  the  weight  on  the  truck. 

In  column  6  the  total  weight  of  each  engine  is  given,  which  is  obtained  by 
adding  the  weight  on  the  drivers  to  the  weight  on  the  truck.  Dividing  the 
adhesion  given  in  column  1  by  7^4  will  give  the  number  of  tons  of  2000  Ibs. 
that  the  engine  is  capable  of  hauling  on  a  straight  and  level  track,  column  7. 

The  weight  of  engines  given  in  these  tables  will  be  found  to  agree  gen- 
erally with  the  actual  weights  of  locomotives  recently  built,  although  it 
must  not  be  expected  that  these  weights  will  agree  in  every  case  with  the 
actual  weights,  because  the  different  builders  do  not  build  the  engines  alike. 

The  actual  weight  on  trucks  for  eight-wheeled  or  ten-wheeled  engines  will 
not  differ  much  from  those  given  in  the  tables,  because  these  weights  depend 
greatly  on  the  difference  between  the  total  and  rigid  wheel-base,  and  these 
are  not  often  changed  by  the  different  builders.  The  proportion  between 
the  rigid  and  total  wheel-base  is  generally  the  same. 

The  rule  for  finding  the  tractive  power  is  : 


j  Square  of  dia.  of  \ 
I  piston  in  inches    ' 


,  j  Mean  effect,  steam 
s  j  press,  per  sq.  in. 


Diameter  of  wheel  in  feet. 


j  stroke  \ 
1  in  feet  j 


=  tractive  power. 


EIGHT-WHEELED  LOCOMOTIVES. 

TEN-WHEELED  ENGINES. 

r 

fl  !fi 

£ 
® 

tjp 

rr 

l°fl_i 

|2 

fl 

q 

n  Driver 

i  Truck. 

i 

|fl| 

« 
1 
f 

S 

I 

fl 

i  Truck. 

1 

'o  fl"3 

fl 

o 

0 

® 

0 

0 

0 

If 

|1 

I 
3 

1 

1 

H 

^"3§H 
2  o>ti_i  ^ 

=  1 

|§ 

'53 
•O 

A 

.£? 
1* 

§ 

P 

!&! 

1 

i 

3 

4 

6 

6 

7 

1 

S 

8 

4 

5 

6 

t 

in. 

in. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

in. 

in. 

Ibs 

Ibs. 

Ibs 

Ibs. 

10x20 

45-51 

4000    20000 

10000 

30000 

533 

12X18 

39-431  5981 

29907 

9570 

39477 

797 

11x22 

45-51 

5324    26620 

13310 

39930 

709 

13x18 

41-45    6677 

33387 

L0683 

44070 

890 

12x22 

48-54 

5940    29700 

14850 

44550 

792 

14X20 

43-47 

8205 

41023  13127 

54150 

1093 

13x22 

49-57 

6828    34140 

17070 

51210 

910 

15X22 

45-50 

MOO 

49500  15840 

65340 

1320 

14x24 

55-61 

7697    38485 

19242 

57727 

1026 

16X24 

48-54  11520    57600  18432 

78032 

1536 

15X24 

55  60 

8836    44180 

66270 

1178 

17X24 

51-56  12240    61200  19584    80784 

1632 

16X24 

58-66 

9533    47605 

23832 

71497 

1271 

18X24 

51-56  13722 

68611  21955 

90566 

1829 

17x24 

60-66 

10404    52020 

2(5010 

78030 

1387 

19X24 

54-60  144-40 

72200  23104 

95304 

1925 

18X24 

61-66 

11472    57360 

28680 

86040 

1529 

1 

MOGUL  ENGINES. 


CONSOLIDATION  ENGINE 


in. 

in. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

in. 

in. 

Ibs. 

Ibs. 

Ibs. 

Ibs. 

11X16 

35-40 

4978 

:>I,S'.M 

4978 

29809 

663 

14x16 

36-38 

7840 

.•59200 

•i'.'7-J 

45172 

1045 

12X181  36-41 

6480 

.';•'}  oo 

6480 

3SS80 

864 

15x18 

36-38  10125 

501525 

8100 

nsr-r, 

1350 

13x18 

37-42 

7399 

::.i;*;»; 

7399 

44396 

986 

•JOX24 

48-50  18000 

'.rnooo 

14100 

mnoo 

2400 

14x20 

39-43 

90461  45230 

9046 

.M-.'TO 

1206 

J2X24 

50-52 

20909 

104644 

11727 

121271 

2787 

15  :<•.".' 

42-47 

106071  53035 

10607 

1414 

16X24 

45-51 

12288!  61440 

12288 

7:;;:;s 

1638 

17X24    49-54 

12739 

6301)7 

J27:!'.» 

1698 

18X24 

.")!   fji) 

13722 

68011 

13722 

w.;:;i; 

1829 

19X24    54-60 

14440    72200 

14440    86640 

1925 

858  LOCOMOTIVES. 

Leading  American  Types  of  Locomotive  for  Freight  and 
Passenger  Service. 

1.  The  eight-wheel  or  "American  "  passenger  type,  having  four  coupled 
driving-wheels  and  a  four-wheeled  truck  in  front. 

2.  The  "  ten- wheel "  type,  for  mixed  traffic,  having  six  coupled  drivers  and 
a  leading  four- wheel  truck. 

3.  The  "Mogul"  freight  type,  having  six  coupled  driving-wheels  and  a 
pony  or  two-wheel  truck  in  front. 

4.  The  "Consolidation'1'  type,  for  heavy  freight  service,  having  eight 
coupled  driving-wheels  and  a  pony  truck  in  front. 

Besides  these  there  is  a  great  variety  of  types  for  special  conditions  of 
service,  as  fo 


lese  there  is  a  great  variety  of  types  for  special  conditions  o 
our-wheel  and  six- wheel  switching-engines,  without  trucks;  th 


Steam-distribution  for  High-speed  Locomotives. 

(C.  H.  Quereau,  Eng'g  News,  March  8,  1894.) 

Balanced  Valves.— Mr.  Philip  Wallis,  in  1886,  when  Engineer  of  Tests  for 
the  C.,  B.  &  Q.  R.  R.,  reported  that  while  6  H.P.  was  required  to  work  un- 
balanced valves  at  40  miles  per  hour,  for  the  balanced  valves  2.2  H.P.  only 
was  necessary. 

Effect  of  Speed  on  Average  Cylinder-pressure. — Assume  that  a  locomotive 
has  a  train  in  motion,  the  reverse  lever  is  placed  in  the  running  notch,  and 
the  track  is  level;  by  what  is  the  maximum  speed  limited  ?  The  resistance 
of  the  train  and  the  load  increase,  and  the  power  of  the  locomotive  de •< 
creases  with  increasing  spewed  till  the  resistance  and  power  are  equal,  when 
the  speed  becomes  uniform.  The  power  of  the  engine  depends  on  th-3 
average  pressure  in  the  cylinders.  Even  though  the  cut-off  and  boiler- 
pressure  remain  the  same,  this  pressure  decreases  as  the  speed  increases; 
because  of  the  higher  piston-speed  and  more  rapid  valve-travel  the  stearn 
has  a  shorter  time  in  which  to  enter  the  cylinders  at  the  higher  speed.  The 
following  table,  from  indicator-cards  taken  from  a  locomotive  at  varying 
speeds,  shows  the  decrease  of  average  pressure  with  increasing  speed: 

Miles  per  hour.  ;     46  51  51        53  54        57       60  66 

Speed,  revolutions 224  248  248  258  263  277  292  321 

Average  pressure  per  sq.  in. : 

Actual 51.5  44.0  47.3  43.0  41.3  42.5  37.3  36.3 

Calculated 46.5  46.5  44.7  43.8  41.6  39.5  35.9 

The  "average  pressure  calculated"  was  figured  on  the  assumption  that 
the  mean  effective  pressure  would  decrease  in  the  same  ratio  that  the  speed 
increased.  The  main  difference  lies  in  the  higher  steam-line  at  the  lower 
speeds,  and  consequent  higher  expansion-line,  showing  that  more  steam 
entered  the  cylinder.  The  back  pressure  and  compression-lines  agree  quite 
closely  for  all  the  cards,  though  they  are  slightly  better  for  the  slower 
speeds.  That  the  difference  is  not  greater  may  safely  be  attributed  to  the 
large  exhaust-ports,  passages,  and  exhaust  tip,  which  is  5  in.  diameter. 
These  are  matters  of  great  importance  for  high  speeds. 

Boiler-pressure.— The  increase  of  train  resistance  with  increased  speed  is 
not  as  the  square  of  the  velocity,  as  is  commonly  supposed.  It  is  more  likely 
that  it  increases  as  the  speed  after  about  20  miles  an  hour  is  reached.  As- 
suming that  the  latter  is  true,  and  that  an  average  of  50  Ibs.  per  square  inch 
is  the  greatest  that  can  be  realized  in  the  cylinders  of  a  given  engine  at  40 
miles  an  hour,  and  that  this  pressure  furnishes  just  sufficient  power  to  keep 
the  train  at  this  speed,  it  follows  that,  to  increase  the  speed  to  50  miles,  the 
mean  effective  pressure  must  be  increased  in  the  same  proportion.  To  in- 
crease the  capacity  for  speed  of  any  locomotive  its  power  must  be  increased, 
and  at  least  by  as  much  as  the  speed  is  to  be  increased.  One  way  to  accom- 
plish this  is  to  increase  the  boiler-pressure.  That  this  is  generally  realized, 
is  shown  by  the  increase  in  boiler-pressure  in  the  last  ten  years.  For  twenty- 
three  single-expansion  locomotives  described  in  the  railway  journals  this 
year  the  steam-pressures  are  as  follows:  3,  160  Ibs.;  4,  165  Ibs. ;  2,  170  Ibs. ; 
13,  180  Ibs.;  1,  190  Ibs. 


SOME   LARGE   AMERICAH   LOCOMOTIVES,    1893.     859 

Valve-travel.  —  An  increased  average  cylinder-pressure  may  also  be 
obtained  by  increasing  the  valve-travel  without  raising  the  boiler-pressure, 
and  better  results  will  be  obtained  by  increasing  both.  The  longer  travel 
gives  a  higher  steam-pressure  in  the  cylinders,  a  later  exhaust-opening, 
later  exhaust-closure,  and  a  larger  exhaust-opening  —  all  necessary  for  high 
speeds  and  economy.  I  believe  that  a  20-in.  port  and  6^-in.  (or  even  ?-in.) 
travel  could  be  successfully  used  for  high-speed  engines,  and  that  frequently 
by  so  doing  the  cylinders  could  be  economically  reduced  and  the  counter- 
balance lightened.  Or,  better  still,  the  diameter  of  the  drivers  increased, 
securing  lighter  counterbalance  and  better  steam-distribution. 

Size  of  Drivers.  —  Economy  will  increase  with  increasing  diameter  of 
drivers,  provided  the  work  at  average  speed  does  not  necessitate  a  cut-off 
longer  than  one  fourth  the  stroke.  The  piston-speed  of  a  locomotive  with 
02-in.  drivers  at  55  miles  per  hour  is  the  same  as  that  of  one  with  68-in. 
drivers  at  61  miles  per  hour. 

Steam-ports.—  The  length  of  steam-ports  ranges  from  15  in.  to  23  in.,  and 
has  considerable  influence  on  the  power,  speed,  and  economy  of  the  loco- 
motive. In  cards  from  similar  engines  the  steam  -line  of  the  card  from  the 
engine  with  23-in.  ports  is  considerably  nearer  boiler-pressure  than  that  of 
the  card  from  the  engine  with  l?J4-in.  ports.  That  the  higher  steam-line  is 
due  to  the  greater  length  of  steam-port  there  is  little  room  for  doubt.  The 
23-in.  port  produced  531  H.P.  in  an  18^-in.  cylinder  at  a  cost  of  23.5  Ibs.  of 
indicated  water  per  I.  H.P.  per  hour.  The  17*4  in.  port,  424  H.P.,  at  the  rate 
of  22.9  Ibs.  of  water,  in  a  19-in.  cylinder. 

Allen  Valves.—  There  is  considerable  difference  of  opinion  as  to  the  advan- 
tage of  the  Allen  ported-  valve  (See  Eng.  News,  July  6,  1893.) 

Speed  of  Railway  Trains.—  In  1834  the  average  speed  of  trains  on 
the  Liverpool  and  Manchester  Railway  was  twenty  miles  an  hour;  in  1838  it 
was  twenty-five  miles  an  hour.  But  by  1840  there  were  engines  on  the  Great 
Western  Railway  capable  of  running  fifty  miles  an  hour  with  a  train,  and 
eighty  miles  an  hour  without.  A  speed  of  86  miles  per  hour  was  made  in 
England  with  the  T.  W.  Worsdell  compound  locomotive.  The  total  weight 
of  the  engine,  tender,  and  train  was  695,000  Ibs.;  indicator-cards  were  taken 
showing  1068.6  H.P.  on  the  level.  At  a  speed  of  75  miles  per  hour  on  a 
level,  and  the  same  train,  the  indicator-cards  showed  1040  H.P.  developed. 
(Trans.  A.  S.  M.  E.,  vol.  xiii.,  363.) 

The  limitation  to  the  increase  of  speed  of  heavy  locomotives  seems  at 
present  to  be  the  difficulty  of  counterbalancing  the  reciprocating  parts.  The 
unbalanced  vertical  component  of  the  reciprocating  parts  causes  the  pres- 
sure of  the  driver  on  the  rail  to  vary  with  every  revolution.  Whenever  the 
speed  is  high,  it  is  of  considerable  magnitude,  and  its  change  in  direction  is 
so  rapid  that  the  resulting  effect  upon  the  rail  is  not  inappropriately  called 
a  "hammer  blow.1"  Heavy  rails  have  been  kinked,  and  bridges  have  been 
shaken  to  their  fall  under  the  action  of  heavily  balanced  drivers  revolving 
at  high  speeds.  The  means  by  which  the  evil  is  to  be  overcome  has  not  yet 
been  made  clear.  See  paper  by  W.  F.  M.  Goss,  Trans.  A.  S.  M.  E..  vol.  xvi. 

Engine  No.  999  of  the  New  York  Central  Railroad  ran  a  mile  in  32  seconds, 
equal  to  112  miles  per  hour,  May  11,  1893. 

Speed  in  miles  I  _  circum.  of  driving-wheels  in  in.  X  no.  of  rev.  per  min.  X  60 
per  hour        f  -  360 


=  diam,  of  driving-wheels  in  in.  X  no.  of  rev.  per  min.  X  .003 
(approximate,  giving  result  8/10  of  1  per  cent  too  great). 

DIMENSIONS    OF    SOME    LARGE    AMERICAN 
LOCOMOTIVES,    1893. 

The  four  locomotives  described  below  were  exhibited  at  the  Chicago 
Exposition  in  1893.  The  dimensions  are  from  Engineering  News,  June,  1893. 
The  first,  or  Decapod  engine,  has  ten-coupled  driving-wheels.  It  is  one  of 
the  heaviest  and  most  powerful  engines  ever  built  for  freight  service.  The 
Philadelphia  &  Reading  engine  is  a  new  type  for  passenger  service,  with  four- 
coupled  drivers.  The  Rhode  Island  engin-e  has  six  drivers,  with  a  4-wheel 
leading  truck  and  a  2-wheel  trailing  truck.  These  three  engines  have  all 
compound  cylinders.  The  fourth  is  a  simple  engine,  of  the  standard  Ameri- 
can 8-wheel  type,  4  driving-wheels,  and  a  4-wheel  truck  in  front.  This 
engine  holds  the  world's  record  for  speed  (1893)  for  short  distances,  having 
run  a  mile  in  32  seconds. 


860 


LOCOMOTIVES. 


Baldwin. 
N.  Y.,  L.  E. 
& 
W.  R.  R. 
Decapod 
Freight. 

Baldwin. 
Phila. 
& 
Read.  R.  R. 
Express 
Passenger. 

Rhode  Isl. 
Locomotive 

Works. 
Heavy 
Express. 

N.  Y.  C.  & 
H.  R.  R. 

Empire 

State 
Express, 
No.  999. 

Running-gear  : 

Driving-wheels,  diam  
Truck          "           44     
Journals,  driving-axles... 
"          truck-       **     ... 
41          tender-     44     ... 
Wheel-base  : 
Driving.             

4  ft.  2  in. 

2  4t    6  4t 
9     xlOin. 
5     xlO  " 
4^x   9   " 

18ft.  10  in. 

6  ft.  6  in. 
4  44  0  44 
8V*>x  12  in. 
$1x10  " 
4y2  x   8  " 

6  ft.  10  in. 

6  ft.  6  in. 
2  "   9  " 
8     x  |894  in. 
5^x10      " 
4}4  x   8      " 

13  ft  6    in. 

7  ft.  2  in. 

3  "  4   " 
9     x  12^in. 
6^x10      " 
4^|x   8      " 

8  ft     6  in 

Total  engine  

27  "     3  " 

23  "     4  " 

29  4<  914  " 

23  "    11  tl 

44     tender 

16  44     8  " 

16  t4     0  ll 

15  "  0     '4 

15  ft  2^£  " 

"     engine  and  tender.  .. 
Wt.  in  working-order: 

On  drivers  
On  truck-wheels  

53  44     4  " 

170,000  Ibs. 
29,500    " 

47  "     3  4l 

82,700  Ibs. 
47,000  " 

50  "  6%  " 

88,500  Ibs. 

54,500  " 

47  "    8J^  '4 

84,000  Ibs. 
40,000    " 

Engine  total 

192,500   4* 

129  700  " 

143  000   " 

124  000    " 

1  1  7  500    '  ' 

80  573  " 

75  000  " 

80  000    " 

Engine  and  tender,  loaded 
Cylinders  : 
h.p  (2)     

310,000    " 
16x28  in. 

210,273  " 
13x24  in. 

218,000  " 
one  21  x  26 

204,000   " 
19x24  in 

l.p.  (2)  

27x28  " 

22  x  24  " 

one  31  x  ->6 

Distance  centre  to  centre. 
Piston-rod,  diam  .  .  . 

7ft.  5" 
4  in. 

7ft.  4^  in. 
3^  in. 

7  ft.  1  in. 
3>£  in 

6  ft.  5  in. 
3%  in. 

Connecting-rod,  length... 
Steam-ports  

9'  8  7/16" 
28^  x  2  in. 

8  ft.  OV6  in. 
24  x  \y>  in. 

10ft,  3^  in. 
11^x20  and 

8ft.  \y2  in. 
l^x  18  in. 

Exhaust-ports  

24x4^  " 

1^4  x  25 
3x20  in. 

Slide-valves,  out.  lap,  h.p. 
44         '        out.  lap,  l.p.. 

g\n- 

%  in. 

1  in!D' 

1  in. 

44                  in.  lap  h  p  .  . 

(neg.)  ^  in 

1/10  in 

in   lap  1  p 

None 

44                  max.  travel  . 
44                  lead,  h  p 

6  in. 
1/16  in. 

5  in. 

6y  in. 
3/32  " 

5J^  in. 

lead,  l.p  

5/16  *4 

a/  " 

Boiler—  Type  

Straight 

Straight 

Wagon  top 

Wagon  top 

Diam.  of  barrel  inside  — 
Thickness  of  barrel-plates 
Height  from  rail  to  centre 
line    
Length  of  smoke-  box  
Working  steam-pressure.. 
Firebox  —  type  

6  ft.  2%  in. 

8ft.  0    in. 

180  'ibs. 
Wootten 

4  ft.  8J4  in. 
%  in. 

'  '  180  ibs".  " 
Wootten 

5  ft.  2  in. 

8  ft.  11  in. 
6  "     1" 
200  Ibs. 
Radial  stay 

4  ft.  9  in. 

9/16  in. 

7ft.  1114  in. 
4  «    8       kl 
190  Ibs. 
Buchanan 

Length  inside  

10'  11  9/16" 

9  ft.  6    in. 

10  ft.  0    in. 

9ft.  6%  in. 

Width       "     

8  44  0}4  " 

3  "    4%  " 

Depth  at  front  
Thickness  of  side  plates  .  . 
44          "  back  plate.  .. 
Thickness  of  crown-sheet. 
4*          "  tube       " 
Grate-area  ... 

5/16  in. 
5/16   |4 

89  6  sq  ft 

3  44  2%  " 

5/16  in. 
5/16  " 
5/16  n 

H?" 

76  8  sq  ft 

6   "  10%  " 
5/1  6  in. 

28  sq  ft 

6  "    \Y4  " 
5/16  in. 
5/16  ^ 

30  7  ?q  ft. 

Stay-bolts,  diam.,  \%  in.  . 
Tubes  —  iron  .  . 

pitch,4>kin. 
354 

4  in. 
272 

4  in. 

268 

Pitch  

2%  in 

2  1/16  in 

2%  in 

Diam    outside 

2      " 

IVo  in 

2  in 

Length  betw'n  tube-plates 
Heating-surface  : 
Tubes,  exterior  
Fire-box  

11  ft.  11  in. 

2,208.8  ft. 
234  3  " 

10  ft.  0  in. 

1,262  sq.  ft. 
173    44     " 

12  ft.  8%  in. 

12  ft.  0  in. 

1  ,697  sq.  ft. 
233  "    " 

Miscellaneous  : 

Exhaust-nozzle,  diam  
Smokestack,smal'st  diam. 
"           height     from 
rail  to  top  

5  in. 
1  ft.  6  " 

15  "  6^  " 

5J/6  in. 
1  ft.  6  in. 

14  ft.  0%  in. 

i  ft.  3  in". 

15  4l   2  " 

3)4  in. 

1  ft.  314  in. 

14  u  10     " 

DIMENSIONS   OF   AMERICAN   LOCOMOTIVES-          861 


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862 


LOCOMOTIVES. 


Dimensions  of  Some  American  Locomotives.— The  table  on 
page  861   is  condensed  from  one  given  by  D.  L.  Barnes,   in  his  paper  on 
"  Distinctive  Features  and  Advantages  of  American  Locomotive  Practice," 
Trans.  A.S.C.E.,  1893.    The  formula  from  which  column  marked  ''Ratio  of 
cylinder-power  to  weight  available  for  adhesion1'  is  calculated  as  follows: 
2  X  cylinder  area  X  boiler-pressure  x  stroke 
Weight  on  drivers  X  diameter  of  driving-wheel' 

(Ratio  of  cylinder-power  of  compound  engines  cannot  be  compared  with 
that  of  the  single-expansion  engines.) 

Where  the  boiler-pressure  could  not  be  determined  from  the  description 
of  the  locomotives,  as  given  by  the  builders  and  operators  of  the  locomotives, 
it  has  been  assumed  to  be  160  Ibs.  per  sq.  in.  above  the  atmosphere. 

For  compound  locomotives  the  figures  in  the  last  column  of  ratios  are 
based  on  the  capacity  of  the  low-pressure  cylinders  only,  the  volume  of  the 
high-pressure  being  omitted.  This  has  been  done  for 'the  purpose  of  com- 
parison, and  because  there  is  no  accurate  simple  way  of  comparing  the 
cylinder-power  of  single-expansion  and  compound  locomotives. 

Dimensions   of  Standard   Locomotives   on  tlie  N.  \T.  €.  & 

H.  16.  R.  and  Penna.  R.  R.,  1882  and  1893. 
C.  H.  Quereau,  Eng*g  News,  March  8.  1894. 


N.  Y.  C.  &  H.  R.  R. 

Pennsylvania  R.  R. 

Through 
Passenger. 

Through 
Freight. 

Through 
Passenger. 

Through 
Freight. 

1882. 

1893. 

1882. 

1893. 

1882. 

1893. 

1882. 

1893. 

Grate  surface,  sq.  ft  
Heating  surface,  sq.  ft.. 
Boiler  diam    in 

17.87 
1353 
50 
70 
150 
17X24 

5*4 
1/16 

* 

n 

Am. 

27.3 
1821 
58 
78,  86 
180 
19X24 

5H 

1/16 
1 
0 

18 

1& 

Am. 

17.87 
1353 
50 
64 
150 
17X24 
5M 
1/16 

% 
1/1« 
15H 
1*4 

Am. 

29.8 
1763 
58 
67 
160 
19X26 
5% 
1/16 
% 
3/32Z 
18 

1*4 

Mog. 

17.6 
1057 
50 
62 
125 
17X24 
5 
1/16 

1 

16 

1M 

Am. 

33.2 

1583 
57 
78 
175 
18|X24 

f 

4 
***• 

Am. 

23. 

1260 
54 
50 
125 
20X24 
5 

\/m 

16 

iJ4 

Cons. 

31.5 
1498 
60 
50 
140 
20X24 
5 
1/16 

H 

1/322 
16 

m 

Cons. 

Driver,  diam.,  in  
Steam-  pressure,  Ibs. 
Cyliri.,  diam.  and  stroke. 
Valve-travel,  ins  
Lead  at  full  gear,  ins  
Outside  lap 

Inside  lap  or  clearance.  . 
Si  eam-ports,  length  
'4       width  
Type  of  engine  

Indicated  Water  Consumption  of  Single  and  Compound 
Locomotive  Engines  at  Varying  Speeds. 

C.  H.  Quereau,  Entfg  News,  March  8,  1894. 


Two-cylinder  Compound. 


Revolu- 
tions. 

Speed, 
miles  per 
hour. 

Water 
per  I.H.P. 
per  hour. 

Revolu- 
tions. 

Miles  per 
Hour. 

Water. 

100  to  150 
150  "  200 
200   "  250 
250  "  275 

21  to  31 
31   "  41 
41    "  51 
51   "  56 

18.33  Ibs. 
18.9      " 
19.7      " 
21.4      " 

151 
219 
253 
307 
321 

31 
45 
52 
63 
66 

21.70 
20.91 
20.52 
20.23 
20.01 

Single-expansion. 


per  hour. 

The  C.,  B.  &  Q.  two-cylinder  compound,  which  was  about  30#  less  eco- 
nomical than  simple  engines  of  the  same  class  when  tested  in  passenger 
service,  has  since  been  shown  to  be  15$  more  economical  in  freight  service 


ADVANTAGES   OF   COMPOUNDING.  863 

than  the  best  single-expansion  engine,  and  29$  more  economical  than  the 
average  record  of  40  simple  engines  of  the  same  class  on  the  same  division. 
Indicator-tests  of  a  Locomotive  at  High  Speed.  (Locomo- 
tive Eng'g,  June,  1893.)— Cards  were  taken  by  Mr.  Angus  Sinclair  on  the 
locomotive  drawing  the  Empire  State  Express. 

RESULTS  OF  INDICATOR-DIAGRAMS. 


Card  No. 

1 
2 
3 
4 
5 


Revs. 

per  hour. 

I.H.P. 

Card  No. 

Revs. 

Miles, 
per  hour. 

I.H.P. 

160 

37.1 

648.3 

7 

304 

70.5 

977 

260 

60.8 

728 

8 

296 

68.6 

972 

190 

44 

551 

9 

300 

69.6 

1,045 

250 

58 

891 

10 

304 

70.5 

1,059 

260 

60 

960 

11 

340 

78.9 

1,120 

298 

69 

983 

12 

310 

71.9 

1,026 

the  engine  was  first  lifting  the  train  into  speed  diagram  No.  1  was  taken,  iv 
shows  a  mean  cylinder-pressure  of  59  Ibs.  According  to  this,  the  power 
exerted  on  the  rails  to  move  the  train  is  6553  Ibs.,  or  24  Ibs.  per  ton.  The 
speed  is  37  miles  an  hour.  When  a  speed  of  nearly  60  miles  an  hour  was 
reached  the  average  cylinder-pressure  is  40.7  Ibs.,  representing  a  total 
traction  force  of  4520  Ibs.,  without  making  deductions  for  internal  friction. 
If  we  deduct  \Q%  for  friction,  it  leaves  15  Ibs.  per  ton  to  keep  the  train  going 
at  the  speed  named.  Cards  6,  7,  and  8  represent  the  work  of  keeping  the 
train  running  70  miles  an  hour.  They  were  taken  three  miles  apart,  when 
the  speed  was  almost  uniform.  The  average  cylinder-pressure  for  the  three 
cards  is  47.6  Ibs.  Deducting  10$  again  for  friction,  this  leaves  17.6  Ibs.  per 
ton  as  the  power  exerted  in  keeping  the  train  up  to  a  velocity  of  70  miles. 
Throughout  the  trip  7  Ibs.  of  water  were  evaporated  per  Ib.  of  coal.  The 
work  of  pulling  the  train  from  New  York  to  Albany  was  done  on  a  coal  con- 
sumption of  about  3J4  Ibs.  per  H.P.  per  hour.  The  highest  power  recorded 
»vas  at  the  rate  of  1120  H.P. 

Locomotive-testing  Apparatus  at  the  Laboratory  of 
Purdue  University.  (VV.  F.  M.  Goss,  Trans.  A.  S.  M.  E.,  vol.  xiv.  826.)— 
The  locomotive  is  mounted  with  its  drivers  upon  supporting  wheels  which 
are  carried  by  shafts  turning  in  fixed  bearings,  thus  allowing  the  engine  to 
be  run  without  changing  its  position  as  a  whole.  Load  is  supplied  by  four 
'notion-brakes  fitted  to  the  supporting  shafts  and  offering  resistance  to  the 
turning  of  the  supporting  wheels.  Traction  is  measured  by  a  dynamometer 
attached  to  the  draw-bar.  The  boiler  is  fired  in  the  usual  way,  and  an 
exhaust-blower  above  the  engine,  but  not  in  pipe  connection  with  it,  carries 
off  all  that  may  be  given  out  at  the  stack. 

A  Standard  Method  of  Conducting  Locomotive-tests  is  given  in  a  report 
by  a  Committee  of  the  A.  S.  M.  E.  in  vol.  xiv.  of  the  Transactions,  page  1312. 

Waste  of  Fuel  in  Locomotives.— In  American  practice  economy 
of  fuel  is  necessarily  sacrificed  to  obtain  greater  economy  due  to  heavy 
train-loads.  D.  L.  Barnes,  in  Eng.  Mag.,  June,  1894,  gives  a  diagram  showing 
the  reduction  of  efficiency  of  boilers  due  to  high  rates  of  combustion,  from 
which  the  following  figures  are  taken: 

Lbs.  of  coal  per  sq.  ft.  of  grate  per  hour 12      40      80      120      160      200 

Per  cent  efficiency  of  boiler 80      75      67       59       51 

A  rate  of  12  Ibs.  is  given  as  representing  stationary-boiler  practice,  40  Ibs. 
is  English  locomotive  practice,  120  Ibs.  average  American,  and  200  Ibs.  max- 
imum American,  locomotive  practice. 

Advantages  of  Compounding.— Report  of  a  Committee  of  the 
\mericanRailway  Master  Mechanics' Association  on  Compound  Locomotives 
(Am  Mack.,  July  3,  1890)  gives  the  following  summary  of  the  advantages 
gained  by  compounding:  (a)  It  has  achieved  a  saving  in  the  fuel  burnt 
averaging  18^  at  reasonable  boiler  -pressures,  with  encouraging  possibilities 


864  LOCOMOTIVES. 

of  further  improvement  in  pressure  and  in  fuel  and  water  economy,  (ft)  It 
has  lessened  the  amount  of  water  (dead  weight)  to  be  hauled,  so  that  (c)  the 
tender  and  its  load  are  materially  reduced  in  weight,  (d)  It  has  increased 
the  possibilities  of  speed  far  beyond  60  miles  per  hour,  without  unduly 
straining  the  motion,  frames,  axles,  or  axle-boxes  of  the  engine,  (e)  It  has 
increased  the  haulage-power  at  full  speed,  or,  in  other  words,  has  increased 
the  continuous  H.P.  developed,  per  given  weight  of  engine  and  boiler.  (/)  In 
some  classes  has  increased  the  starting-power.  (g)  It  has  materially  lessened 
the  slide-valve  friction  per  H.P.  developed.  (7i)  It  has  equalized  or  distrib- 
uted the  turning  force  on  the  crank-pin,  over  a  longer  portion  of  its  path, 
which,  of  course,  tends  to  lengthen  the  repair  life  of  the  engine,  (i)  In  the 
two-cylinder  type  it  has  decreased  the  oil  consumption,  and  has  even  done 
so  in  the  Woolf  four-cylinder  engine.  ( j)  Its  smoother  and  steadier  draught 
on  the  fire  is  favorable  to  the  combustion  of  all  kinds  of  soft  coal;  and  the 
sparks  thrown  being  smaller  and  less  in  number,  it  lessens  the  risk  to  prop- 
erty from  destruction  by  fire,  (k)  These  advantages  and  economies  are 
gained  without  having  to  improve  the  man  handling  the  engine,  less  being 
left  to  his  discretion  (or  careless  indifference)  than  in  the  simple  engine.  (I) 
Valve-motion,  of  every  locomotive  type,  can  be  used  in  its  best  working  and 
most  effective  position,  (m)  A  wider  elasticity  in  locomotive  design  is  per- 
mitted; as,  if  desired,  side-rods  can  be  dispensed  with,  or  articulated  engines 
of  100  tons  weight,  with  independent  trucks,  used  for  sharp  curves  on  moun- 
tain service,  as  suggested  by  Mallet  and  Brunner. 

Of  27  compound  locomotives  in  use  on  the  Phila.  and  Reading  Railroad  (in 
1892),  12  are  in  use  on  heavy  mountain  grades,  and  are  designed  to  be  the 
equivalent  of  22  X  24  in.  simple  consolidations;  10  are  in  somewhat  lighter 
service  and  correspond  to  20  X  24  in.  consolidations;  5  are  in  fast  passenger 
service.  The  monthly  coal  record  shows: 

Class  of  Engine.  No. 

Mountain  locomotives 12  25$  to  30$ 

Heavy  freight  service 10  12$  to  17$ 

Fast  passenger , 5  9$  to  11$ 

(Report  of  Com.  A.  R.  M.  M.  Assn.  1892.)  For  a  description  of  the  various 
types  of  compound  locomotive,  with  discussion  of  their  relative  merits,  see 
paper  by  A.  Von  Borries,  of  Germany,  The  Development  of  the  Compound 
Locomotive,  Trans.  A.  S.  M.  E.  1893,  vol.  xiv.,  p.  1172. 

Counterbalancing  locomotives.— The  following  rules,  adopted 
by  different  locomotive- builders,  are  quoted  in  a  paper  by  Prof.  Lanza 
(trans.  A.  S.  M.  E.,  x.  302): 

A.  "  For  the  main  drivers,  place  opposite  the  crank-pin  a  weight  equal  to 
one  half  the  weight  of  the  back  end  of  the  connecting-rod  plus  one  half  the 
weight  of  the  front  end  of  the  connecting-rod,  piston,  piston-rod,  and  cross- 
head.  For  balancing  the  coupled  wheels,  place  a  weight  opposite  the  crank- 
pin  equal  to  one  half  the  parallel  rod  plus  one  half  of  the  weights  of  the 
front  end  of  the  main-rod,  piston,  piston-rod,  and  cross-head.    The  centres 
of  gravity  of  the  above  weights  must  be  at  the  same  distance  from  the 
axles  as  the  crank-pin." 

B.  The  rule  given  by  D.  K.  Clark  :     "  Find  the  separate  revolving  weights 
of  crank-pin  boss,  coupling-rods,  and  connecting-rods  for  each  wheel,  also 
the  reciprocating  weight  of  the  piston  and  appendages,  and  one  half  the 
connecting-rod,  divide  the  reciprocating  weight  equally  between  each  wheel 
and  add  the  part  so  allotted  to  the  revolving  weight  on  each  wheel:  the 
sums  thus  obtained  are  the  weights  to  be  placed  opposite  the  crank-pin,  and 
at  the  same  distance  from  the  axis.    To  find  the  counterweight  to  be  used 
when  the  distance  of  its  centre  of  gravity  is  known,  multiply  the  above 
weight  by  the  length  of  the  crank  in  inches  and  divide  by  the  given  dis- 
tance.11   This  rule  differs  from  the  preceding  in  that  the  same  weight  is 
placed  in  each  wheel. 

Sx(w-j) 

C.  "  W ^ — J— ,  in  which  S  =  one  half  the  stroke,  G  =  distance 

from  centre  of  wheel  to  centre  of  gravity  in  counterbalance,  w  =>  weight  at 
crank-pin  to  be  balanced,  W  =  weight  in  counterbalance,  /  =  coefficient  of 
friction  so  called,  =  5  in  ordinary  practice.  The  reciprocating  weight  is 
found  by  adding  together  the  weights  of  the  piston,  piston-rod,  cross-head, 
and  one  half  of  the  main  rod.  The  revolving  weight  for  the  main  wheel  is 
found  by  adding  together  the  weights  of  the  crank-pin  hub,  crank-pin,  on© 


PETROLEUM-BURNING    LOCOMOTIVES.  865 

half  of  the  main  rod,  and  one  half  of  each  parallel-rod  connecting  to  this 
wheel;  to  this  add  the  reciprocating  weight  divided  by  the  number  of 
wheels.  The  revolving  weight  for  the  remainder  of  the  wheels  is  found  in 
the  same  manner  as  for  the  main  wheel,  except  one  half  of  the  main  rod  is 
not  added.  The  weight  of  the  crank-pin  hub  and  the  counterbalance  does 
not  include  the  weight  of  the  spokes,  but  of  the  metal  inclosing  them.  This 
calculation  is  based  for  one  cylinder  and  its  corresponding  wheels.1' 

D    "  Ascertain  as  nearly  as  possible  the  weights  of  crank-pin,  additional 
weight  of  wheel  boss   for  the  same,  add  side  rod,  and  main  connections, 


the  common  centre  of  gravity  of  the  counterweights,  is  taken  for  the  total 
counterweight  for  that  side  of  the  locomotive  which  is  to  be  divided  among 
the  wheels  on  that  side." 

E.  "  Balance  the  wheels  of  the  locomotive  with  a  weight  equal  to  the 
weights  of  crank-pin,  crank- pin  hub,  main  and  parallel  rods,  brasses,  etc., 
plus  two  thirds  of  the  weight  of  the  reciprocating  parts  (cross-head,  piston 
and  rod  and  packing).1' 

F.  "  Balance  the  weights  of  the  revolving  parts  which  are  attached  to 
each  wheel  with  exactness,  and  divide  equally  two  thirds  of  the  weights  of 
the  reciprocating  parts  between  all  the  wheels.    One  half  of  the  main  rod  is 
computed  as  reciprocating,  and  the  other  as  revolving  weight.11 

See  also  articles  on  Counterbalancing  Locomotives,  in  R.  R.  &  Eng.  Jour., 
March  and  April,  1890,  and  a  paper  by  W.  F.  M.  Goss,  in  Trans.  A.  S.  M.  E., 

VO]?JaViimnm    Safe    Load   for   Steel   Tires   on   Steel  Rails. 

(A  S.  M.  E.,  vii.,  p.  786.)— Mr.  Chanute's  experiments  led  to  the  deduction 
that  12,000  Ibs.  should  be  the  limit  of  load  for  any  one  driving-wheel.  Mr. 
Angus  Sinclair  objects  to  Mr.  Chanute's  figure  of  12,000  Ibs.,  and  says  that 
a  locomotive  tire  which  has  a  light  load  on  it  is  more  injurious  to  the  rail 
than  one  which  has  a  heavy  load.  In  English  practice  8  and  10  tons  are 
safely  used.  Mr.  Oberlin  Smith  has  used  steel  castings  for  cam-rollers  4  in. 
diam.  and  3  in.  face,  which  stood  well  under  loads  of  from  10,000  to  20,000 
Ibs.  Mr.  C.  Shaler  Smith  proposed  a  formula  for  the  rolls  of  a  pivot-bridge 
which  may  be  reduced  to  the  form  :  Load  =  1760  X  face  X  1/diam.,  all  in 
Ibs.  and  inches. 

See  dimensions  of  some  large  American  locomotives  on  pages  860  and  861. 
On  the  ''Decapod1'  the  load  on  each  driving-wheel  is  17,000  Ibs.,  and  on 
"No.  999,"  21. 000  Ibs. 

Narrow-gauge  Railways  in  Manufacturing  Works.-» 
A  tramway  of  18  inches  gauge,  several  rniies  in  length,  is  in  the  works  or 
the  Lancashire  and  Yorkshire  Railway.  Curves  of  13  feet  radius  are  used. 
The  locomotives  used  have  the  following  dimensions  (Proc.  Inst.  M.  E.,  July, 
1888)'  The  cylinders  were  5  in.  diameter  with  6  in.  stroke,  and  2  ft.  3J4  in. 
centre  to  centre.  The  wheels  were  16*4  in.  diameter,  the  wheel-base 

2  ft  9  in  ;  the  frame  7  ft.  4*4  in.  long,  and  the  extreme  width  of  the  engine 

3  feet.    The  boiler,  of  steel,  2  ft.  Sin.  outside  diameter  and  2  ft.  long  between 
tube-plates,  containing  55  tubes  of  \%  in.  outside  diameter;  the  fire-box,  of 
iron  and  cylindrical,  2  ft.  3  in.  long  and  17  in.  inside  diameter.    The  heating- 
surface  10  42  sq.  ft.  in  the  fire-box  and  36  12  in  the  tubes,  total  46.54  sq.  ft.; 
the  grate-area,  1.78  sq.  ft.;  capacity  of  tank,  26^  gallons;  working- pressure, 
170  Ibs.  per  sq.  in.;  tractive  power,  say,  1412  Ibs.,  or  9.22  Ibs.  per  Ib.  of  effec- 
tive pressure  per  sq.  in.  on  the  piston.    Weight,  when  empty,  2.80  tons; 
when  full  and  in  working  order,  3.19  tons. 

For  description  of  a  system  of  narrow-gauge  railways  for  manufactories, 
see  circular  of  the  C.  W.  Hunt  Co.,  New  York. 

Light  Locomotives.— For  dimensions  of  light  ocomotives  used  for. 
mining,  etc.,  and  for  much  valuable  information  concerning  them,  see  cata- 
logue of  H.  K.  Porter  &  Co.,  Pittsburgh. 

Petroleum-bnrning  Locomotives.  (From  Clark's  Steam-en- 
gine )— The  combustion  of  petroleum  refuse  in  locomotives  has  been  success 
fully  practised  by  Mr.  Thos.  Urquhart,  on  the  Grazi  and  Tsaritsin  Railway, 
Southeast  Russia.  Since  November,  1884,  the  whole  stock  of  143  locomotives 
under  his  superintendence  has  been  fired  with  petroleum  refuse.  The  oil  is 
injected  from  a  nozzle  through  a  tubular  opening  in  the  back  of  the  fire-box, 
by  means  of  a  jet  of  steam,  with  an  induced  current  of  air. 

A  brickwork  cavity  or  "regenerative  or  accumulative  combustion-cham- 
ber" is  formed  in  the  fire-box,  into  which  the  combined  current  breaks  as 


866  LOCOMOTIVES. 

spray  against  the  rugged  brickwork  slope.  In  this  arrangement  the  brick- 
work is  maintained  at  a  white  heat,  and  combustion  is  complete  and  smoke- 
less. The  form,  mass,  and  dimensions  of  the  brickwork  are  the  most  im- 
portant elements  in  such  a  combination. 

Compressed  air  was  tried  instead  of  steam  for  injection,  but  no  appreciable 
reduction  in  consumption  of  fuel  was  noticed. 

The  heating-power  of  petroleum  refuse  is  given  as  19,832  heat-units, 
equivalent  to  the  evaporation  of  20.53  Ibs.  of  water  from  and  at  212°  F.,  or  to 
17.1  Ibs.  at  8J4  atmospheres,  or  125  Ibs.  per  sq.  in.,  effective  pressure.  The 
highest  evaporative  duty  was  14  Ibs.  of  water  under  8^  atmospheres  per  Ib. 
of  the  fuel,  or  nearly  82$  efficiency. 

There  is  no  probability  of  any  extensive  use  of  petroleum  as  fuel  for  loco- 
motives in  the  United  States,  on  account  of  the  unlimited  supply  of  coal  and 
the  comparatively  limited  supply  of  petroleum. 

Fireless  Locomotive. — The  principle  of  the  Francq  locomotive  is 
that  it  depends  for  the  supply  of  steam  on  its  spontaneous  generation  from 
a  body  of  heated  water  in  a  reservoir.  As  steam  is  generated  and  drawn 
off  the  pressure  falls;  but  by  providing  a  sufficiently  large  volume  of  water 
heated  to  a  high  temperature,  at  a  pressure  correspondingly  high,  a  margin 
of  surplus  pressure  may  be  secured,  and  means  may  thus  be  provided  for 
supplying  the  required  quantity  of  steam  for  the  trip. 

The  fireless  locomotive  designed  for  the  service  of  the  Metropolitan  Rail- 
way of  Paris  has  a  cylindrical  reservoir  having  segmental  ends,  about  5  ft. 
Tin.  in  diameter,  26*4  ft.  in  length,  with  a  capacity  of  about  620  cubic  feet. 
Four  fifths  of  the  capacity  is  occupied  by  water,  which  is  heated  by  the  aid 
of  a  powerful  jet  of  steam  supplied  from  stationary  boilers.  The  water  is 
heated  until  equilibrium  is  established  between  the  boilers  and  the  reser- 
voir. The  temperature  is  raised  to  about  390°  F.,  corresponding  to  225  Ibs. 
per  sq.  in.  The  steam  from  the  reservoir  is  passed  through  a  reducing- 
valve,  by  which  the  steam  is  reduced  to  the  required  pressure.  It  is  then 
passed  through  a  tubular  superheater  situated  within  the  receiver  at  the 
upper  part,  and  thence  through  the  ordinary  regulator  to  the  cylinders. 
The  exhaust-steam  is  expanded  to  a  low  pressure,  in  order  to  obviate  noise 
of  escape.  In  certain  cases  the  exhaust-stearn  is  condensed  in  closed 
vessels,  which  are  only  in  part  filled  with  water.  In  the  upper  free  space  a 
pipe  is  placed,  into  which  the  steam  is  exhausted.  Within  this  pipe  another 
pipe  is  fixed,  perforated,  from  which  cold  water  is  projected  into  the  sur- 
rounding steam,  so  as  to  effect  the  condensation  as  completely  as  may  be. 
The  heated  water  falls  on  an  inclined  plane,  and  flows  off  without  mixing 
with  the  cold  water.  The  condensing  water  is  circulated  by  means  of  a 
centrifugal  pump  driven  by  a  small  three -cylinder  engine. 

In  working  off  the  steam  from  a  pressure  of  225  Ibs.  to  6?  Ibs.,  530  cubic 
feet  of  water  at  390°  F.Jis  sufficient  for  the  traction  of  the  trains,  for  working 
the  circulating-pump  for  the  condensers,  for  the  brakes,  and  for  electric- 
lighting  of  the  train.  At  the  stations  the  locomotive  takes  from  2200  to  3300 
Ibs.  of  steam— nearly  the  same  as  the  weight  of  steam  consumed  during  the 
run  between  two  consecutive  charging  stations.  There  is  210  cubic  feet  of 
condensing  water.  Taking  the  initial  temperature  at  60°  F.,  the  tempera- 
ture rises  to  about  180°  F.  after  the  longest  runs  underground. 

The  locomotive  has  ten  wheels,  on  a  base  24  ft.  long,  of  which  six  are 
coupled,  4^  ft.  in  diameter.  The  extreme  wheels  are  on  radial  axles.  The 
cylinders  are  23J4  in.  in  diameter,  with  a  stroke  of  23^  in. 

The  engine  weighs,  in  working  order,  53  tons,  of  which  36  tons  are  on  the 
coupled  wheels.  The  speed  varies  from  15  miles  to  25  miles  per  hour.  The 
trains  weigh  about  140  tons. 

Compressed-air  locomotives.— For  an  account  of  the  Mekarski 
system  of  compressed-air  locomotives  see  page  509,  ante. 


SHAFTING.  867 


SHAFTING. 

(See  also  TORSIONAL  STRENGTH;  also  SHAFTS  OF  STEAM-ENGINES.) 

For  diameters  of  shafts  to  resist  torsional  strains  only,  Molesworth  gives 

3/pT~ 
d  -  A/  — ,  in  which  d  =  diameter  in  inches,  P  =  twisting  force  in  pounds 

applied  at  the  end  of  a  lever-arm  whose  length  is  I  in  inches,  K  =  a  coeffi- 
cient whose  values  are,  for  cast  iron  1500,  wrought  iron  1700,  cast  steel  3200, 
gun-bronze  460,  brass  425,  copper  380,  tin  220,  lead  170.    The  value  given  for 
cast  steel  probably  applies  only  to  high-carbon  steel. 
Thurston  gives: 

For  head  shafts  well  J  ~  125  '      ~~  y         R 

supported        against-^  

springing:  H  p  =  dW.  d  =  */75H.P%  for  cold-rolled  iron. 


For      line      shafting,  , 
hangers  8  ft.  apart: 


H.P.  =  —  ;  d  =//^t£.\  for  cold-rolled  iron. 
55 


For  transmission  sim- 
y,  no  pulleys: 

H.P.  =  • 


H.P.  =  horse-power  transmitted,  d  =  diameter  of  shaft  in  inches,  R  =  rev- 
olutions per  minute. 


3  / 

J.  B.  Francis  gives  for  turned-iron  shafting  d  =  ju 


3  / 100  H.P. 


R 


Jones  and  Laughlins  give  the  same  formulae  as  Prof.  Thurston,  with  the 
following  exceptions:  For  line  shafting,  hangers  8  ft.  apart: 

cold-rolled  iron,  H.P.  =  ^,  d  =  j/-  -~. 

For  simply  transmitting  power  and  short  counters: 

d*R  VsOH.P.. 

turned  iron,  H.P.  =  -^-,  «  =  j/  —  ^  —  i 


cold-rolled  iron,  H.P.  =  ~ ,  d  =  j/3  R'  '. 

They  also  give  the  following  notes:  Receiving  and  transmitting  pulleys 
should  always  be  placed  as  close  to  bearings  as  possible;  and  it  is  good  prac- 
tice to  frame  short  "  headers  "  between  the  mam  tie-beams  of  a  mill  so  as 
TO  support  the  main  receivers,  carried  by  the  head  shafts  with  a  bearing 
close  to  each  side  as  is  contemplated  in  the  formulae  But  if  it  is  preferred, 
or  necessary,  for  the  shaft  to  span  the  full  width  of  the  "  bay  "  without  in- 


868 


SHAFTING. 


termediate  bearings,  or  for  the  pulley  to  be  placed  away  from  the  bearings 
towards  or  at  the  middle  of  the  bay,  the  size  of  the  shaft  must  be  largely 
increased  to  secure  the  stiffness  necessary  to  support  the  load  without  un- 
due deflection.  Shafts  may  not  deflect  more  than  1/80  of  an  inch  to  each 
foot  of  clear  length  with  safety. 

To  find  the  diameter  of  shaft  necessary  to  carry  safely  the  main  pulley  at, 
the  centre  of  a  bay:  Multiply  the  fourth' power  of  the  diameter  obtained  by 
above  formulae  by  the  length  of  the  "  bay,"  and  divide  this  product  by  the 
distance  from  centre  to  centre  of  the  bearings  when  the  shaft  is  supported 
as  required  by  the  formula.  The  fourth  root  of  this  quotient  will  be  the 
diameter  required. 

The  following  table,  computed  by  this  rule,  is  practically  correct  and  safe. 


im 

i-ja^ 
ii*N 

03^    >>r*    0> 
Q^-°Sffi 

in. 


Diameter  of  Shaft  necessary  to  carry  the  Load  at  the  Centre  of 
a  Bay,  which  is  from  'Centre  to  Centre  of  Bearings 


2^  ft. 


3ft. 


4ft. 


5  ft. 


6ft. 


f 


8ft. 


10  ft. 


As  the  strain  upon  a  shaft  from  a  load  upon  it  is  proportional  to  the 
product  of  the  parts  of  the  shaft  multiplied  into  each  other,  therefore, 
should  the  load  be  applied  near  one  end  of  the  span  or  bay  instead  of  at  the 
centre,  multiply  the  fourth  power  of  the  diameter  of  the  shaft  required  to 
carry  the  load  at  the  centre  of  the  span  or  bay  by  the  product  of  the  two 
parts  of  the  shaft  when  the  load  is  near  one  end,  and  divide  this  product  by 
the  product  of  the  two  parts  of  the  shaft  when  the  load  is  carried  at  the 
centre.  The  fourth  root  of  this  quotient  will  be  the  diameter  required. 

The  shaft  in  a  line  which  carries  a  receiving-pulley,  or  which  carries  a 
transmitting  -pulley  to  drive  another  line,  should  always  be  considered  a 
head  -shaft,  and  should  be  of  the  size  given  by  the  rules  for  shafts  carrying 
main  pulleys  or  gears. 

Deflection  of  Shafting*  (Pencoyd  Iron  Works.)—  As  the  deflection 
of  steel  and  iron  is  practically  alike  under  similar  conditions  of  dimensions 
and  loads,  and  as  shafting  is  usually  determined  by  its  transverse  stiffness 
rather  than  its  ultimate  strength,  nearly  the  same  dimensions  should  be 
used  for  steel  as  for  iron. 

For  continuous  line-shafting  it  is  considered  good  practice  to  limit  the 
deflection  to  a  maximum  of  1/100  of  an  inch  per  foot  of  length.  The  weight 
of  bare  shafting  in  pounds  =  2.6<i2L  =  W,  or  when  as  fully  loaded  with 
pulleys  as  is  customary  in  practice,  and  allowing  40  Ibs.  per  inch  of  width 
for  the  vertical  pull  of  the  belts,  experience  shows  the  load  in  pounds  to  be 
about  13rf2£  =  W.  Taking  the  modulus  of  transverse  elasticity  at  26,000,000 
Ibs.,  we  derive  from  authoritative  formulae  the  following: 


L  = 


TSd2,  d  =  A/ 
p/ 


—-,  for  bare  shafting; 

873 


L  =    V  175d*,  d  —  A/  -—,  for  shafting  carrying  pulleys/etc.  ; 

\    175 

Li  being  the  maximum  distance  in  feet  between  bearings  for  continuous 
shafHng  subjected  to  bending  stress  alone,  d  =  diam.  in  inches. 

The  torsional  stress  is  inverselv  proportional  to  the  velocity  of  rotation, 
while  the  bending  stress  will  not  be  reduced  in  the  same  ratio.  It  is  there- 
fore impossible  to  write  a  formula  covering  the  whole  problem  and  suffi- 


HORSE-POWER  AT   DIFFEREKT 


86ft 


ciently  simple  for  practical  application,  but  the  following  rules  are  correct 
within  the  range  of  velocities  usual  in  practice. 

For  continuous  shafting  so  proportioned  as  to  deflect  not  more  than  1/100 
of  an  inch  per  foot  of  length,  allowance  being  made  for  the  weakening 
effect  of  key-seats, 


d  = 


d  = 


=  r  720d2,  for  bare  shafts; 


140d2,  for  shafts  carrying  pulleys,  etc. 


d  =  diam.  in  inches,  L  =  length  in  feet,  R  =  revs,  per  min. 

The  following  table  (by  J.  B.  Francis)  gives  the  greatest  admissible  dis- 
tances between  the  bearings  of  continuous  shafts  subject  to  no  transverse 
strain  except  from  their  own  weight,  as  would  be  the  case  were  the  power 
given  off  from  the  shaft  equal  on  all  sides,  and  at  an  equal  distance  from 
the  hanger-bearings. 


Distance  between 
Bearings,  in  ft. 

Diam.  of  Shaft,  Wrought-iron    Steel 

in  inches.  Shafts.       Shafts. 

2  15.46  15.89 

3  17.70  18.19 

4  19.48  20.02 

5  2C.99  21.57 


Distance  between 
Bearings,  in  ft. 

Diam.of  Shaft,  ^Wrought-iron    Steel 
in  inches.  Shafts.       Shafts. 

6  22.30  22.92 

7  23.48  24.13 

8  24.55  25.23 

9  25.53  26.24 


These  conditions,  however,  do  not  usually  obtain  in  the  transmission  of 


by  belts  and  pulleys,  and  the  varying  circumstances  of  each  case 
it  impracticable  to  give  any  rule  which  would  be  of  value  for  univer- 


power 

render  i  _____  r__, 

sal  application. 

For  example,  the  theoretical  requirements  would  demand  that  the  bear- 
ings be  nearer  together  on  those  sections  of  shafting  where  most  power 
is  delivered  from  the  shaft,  while  considerations  as  to  the  location  and 
desired  contiguity  of  the  driven  machines  may  render  it  impracticable  to 
separate  the  driving-pulleys  by  the  intervention  of  a  hanger  at  the  theo- 
retically required  location.  (Joshua  Rose.) 


Horse-power   Transmitted  by  Turned   Iron  Shafting  at 
Different  Speeds. 

As  PRIME  MOVER  OR  HEAD  SHAFT  CARRYING  MAIN  DRIVING-PULLEY  OR  GEAR, 
WELL  SUPPORTED  BY  BEARINGS.    Formula  :  H.P.  =  d3R  •*-  125. 


Number  of  Revolutions  per  Minute. 


•2°£ 
ft  o5 

60 

80 

100 

125 

150 

175 

200 

225 

250 

275 

300 

Ins. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

1% 

2.6 

3.4 

4.3 

5.4 

6.4 

7.5 

8.6 

9.7 

10.7 

11.8 

1-2.9 

2 

3.8 

5.1 

6.4 

8 

9.6 

11.2 

12.8 

14.4 

16 

17.6 

19.2 

214 

5.4 

7.3 

8.1 

10 

12 

14 

16 

18 

20 

22 

24 

m 

7.5 

10- 

12.5 

15 

18 

22 

25 

28 

31 

34 

37 

2% 

10 

13 

16 

20 

24 

28 

32 

36 

40 

44 

48 

3 

13 

17 

20 

25 

30 

35 

40 

4Tj 

50 

55 

60 

3M 

16 

22 

27 

34 

40 

47 

54 

61 

67 

74 

81 

3»^ 

20 

27 

34 

42 

51 

59 

68 

76 

85 

93 

102 

m 

25 

33 

42 

52 

63 

73 

84 

94 

105 

115 

126 

4 

30 

41 

51 

64 

76 

89 

102 

115 

127 

140 

153 

4^ 

43 

58 

72 

90 

108 

126 

144 

162 

180 

198 

216 

5 

60 

80 

100 

125 

150 

175 

200 

225 

250 

275 

300 

Bfc 

80 

106 

133 

166 

199 

233 

266 

299 

333 

366 

400 

870 


SHAFTING. 


As  SECOND  MOVERS  OR  LINE-SHAFTING,  BEARINGS  8  FT.  APART. 
Formula  :  H.P.  =  d3R  +  90. 


Jq_|£ 
o  « 

a  to 

Number  of  Revolutions  per  Minute. 

100 

125 

150 

175 

200 

225 

250 

275 

300 

325 

350 

Ins. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

m 

6 

7.4 

8.9 

10.4 

11.9 

13.4 

14.9 

16.4 

17.9 

19.4 

20.9 

1% 

7.3 

9.1 

10.9 

12.7 

14.5 

16.3 

18.2 

20 

21.8 

23.6 

25.4 

2 

8.9 

11.1 

13.3 

15.5 

17.7 

20 

22.2 

^4.4 

26.0 

28.8 

31 

% 

10.6 

13.2 

15.9 

18.5 

21.2 

23.8 

26.5 

29.1 

31.8 

34.4 

37 

gix 

12.6 

15.8 

19 

22 

25 

28 

31 

35 

38 

41 

44 

~% 

15 

18 

22 

26 

29 

33 

37 

41 

44 

48 

52 

yi^ 

17 

21 

26 

30 

34 

39 

43 

47 

52 

56 

60 

2«M 

23 

29 

34 

40 

46 

52 

58 

64 

69 

75 

81 

3 

30 

37 

45 

52 

60 

67 

75 

82 

90 

97 

105 

3J4 

38 

47 

57 

66 

76 

85 

95 

104 

114 

123 

133 

31^ 

47 

59 

71 

83 

95 

107 

119 

131 

143 

155 

167 

3% 

58 

73 

88 

102 

117 

132 

146 

162 

176 

190 

205 

4 

71 

89 

107 

125 

142 

160 

178 

196 

213 

231 

249 

FOR  SIMPLY  TRANSMITTING  POWER. 
Formula  :  H.P.  =  d*R  -*-  50. 


S«w£ 
OS  0  J 

Q  to 

Number  of  Revolutions  per  Minute. 

100 

125 

150 

175 

200 

233 

267 

300 

333 

367 

400 

Ins. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

l/^ 

6.7 

8.4 

10.1 

11.8 

13.5 

15.7 

17.9 

20.3 

22.5 

24.8 

27.0 

1% 

8.6 

10.7 

12.8 

15 

17.1 

20 

22.8 

25.8 

28.6 

31.5 

34.3 

1% 

10.7 

13.4 

16 

18.7 

21.5 

25 

28 

32 

36 

39 

43 

1% 

13.2 

16.5 

19.7 

23 

26.4 

31 

35 

39 

44 

48 

52 

2 

16 

20 

24 

28 

32 

37 

42 

48 

53 

58 

64 

2^4 

19 

24 

29 

33 

38 

44 

51 

57 

63 

70 

76 

2/4 

22 

28 

34 

39 

45 

52 

60 

68 

75 

83 

90 

2&< 

27 

33 

40 

47 

53 

62 

70 

79 

88 

96 

105 

2^4) 

31 

39 

47 

54 

62 

73 

83 

93 

104 

114 

125 

2%. 

41 

52 

62 

73 

83 

97 

111 

125 

139 

153 

167 

3 

54 

67 

81 

94 

108 

126 

144 

162 

180 

198 

216 

3^4 

68 

86 

103 

120 

137 

160 

182 

205 

228 

250 

273 

*Yz 

85 

107 

128 

150 

171 

200 

228 

257 

285 

313 

342 

Horse-power  Transmitted  by  Cold-rolled  Iron  Shafting 
at  Different  Speeds. 

As   PRIME   MOVER   OR   HEAD   SHAFT  CARRYING  MAIN  DRIVING-PULLEY  OR 
GEAR,  WELL  SUPPORTED  BY  BEARINGS.     Formula  :  H.P.  =  d3B  -*-  75. 


Number  of  Revolutions  per  Minute. 

60 

80 

100 

125 

150 

175 

200 

225 

250 

275 

300 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

H.P. 

2.7 

3.6 

4.5 

5.6 

6.7 

7.9 

9.0 

10 

11 

12 

13 

4.3 

5.6 

7.1 

8.9 

10.6 

12.4 

14.2 

16 

.  18 

19 

21 

6.4 

8.5 

10.7 

13 

16 

19 

21 

24 

26 

29 

32 

9 

12 

15 

19 

23 

26 

30 

34 

38 

42 

46 

12 

17 

21 

26 

31 

36 

41 

47 

52 

57 

62 

16 

22 

27 

35 

41 

48 

55 

62 

70 

76 

82 

21 

29 

36 

45 

54 

63 

7'2 

81 

90 

98 

108 

27 

36 

45 

57 

68 

80 

91 

103 

114 

126 

136 

34 

45 

57 

71 

86 

100 

114 

129 

142 

157 

172 

42 

56 

70 

87 

105 

123 

140 

158 

174 

193 

210 

51 

69 

85 

106 

128 

149 

170 

192 

212 

244 

256 

73 

97 

121 

151 

182 

212 

243 

273 

302 

333 

364 

HORSE-POWER  AT   DIFFERENT   SPEEDS. 


871 


As  SECOND  MOVERS  OR  LINE-SHAFTING,  BEARINGS  8  FT.  APART. 
Formula  :  H.P.  =  d*R  -*-  50. 


r  +* 

Number  of  Revolutions  per  Minute. 

|o« 

ft   VI 

100 

125 

150 

175 

200 

225 

250 

275 

300 

325 

350 

Ins. 

m 
£ 

H.P. 
6.7 
8.6 
10.7 
13.2 
16 
19 

H.P. 

8.4 
10.7 
13.4 
16.5 
20 
24 

H.P. 
10.1 

12.8 
16 
19.7 
24 
29 

H.P. 

11.8 
15 
18.7 
23 
28 
33 

H.P. 
13.5 
17.1 
21.5 
26.4 
32 
38 

H.P. 
15.2 
19.3 
24.2 
29.6 
36 
43 

H.P. 

16.8 
21.5 
26.8 
32.9 
40 
48 

H.P. 
18.5 
23.6 
29.5 
36.2 
44 
52 

H.P. 
20.2 
25.7 
32.1 
39.5 
48 
57 

H.P. 
21.9 
28.9 
34.8 

42.8 
52 
62 

H.P. 
23.6 
31 
39 
46 
56 
67 

2^4 

93/ 

22 

28 
33 

34 

40 

39 

47 

45 
53 

50 
60 

56 
67 

61 
73 

68 

80 

74 
86 

80 
91 

31 

39 

47 

54 

62 

69 

78 

86 

93 

101 

109 

O^/ 

41 

52 

62 

73 

83 

93 

104 

114 

125 

135 

145 

3 

54 
68 
85 

67 
86 
107 

81 
103 
128 

94 
120 
150 

108 
137 
171 

121 
154 
192 

134 
172 
214 

148 
188 
235 

162 
205 
257 

175 
222 

278 

189 
240 
300 

FOR  SIMPLY  TRANSMITTING  POWER  AND  SHORT  COUNTERS. 
Formula:  H.P.  =  d*R  -s-  30. 


s  £ 

Number  of  Revolutions  per  Minute. 

100 

125 

150 

175 

200 

233 

267 

300 

333 

367 

400 

Ins. 

H.P. 
6  5 

H.P. 

8  1 

H.P. 
9.7 

H.P. 
11.3 

H.P. 

13 

HP. 
15.2 

H.P. 

17.4 

H.P. 
19.5 

H.P. 
21.7 

H.P. 
23.9 

H.P. 
26 

1»J 

8.5 
11.2 
14  2 

10.7 
14 

17  7 

12.8 
16.8 
21.2 

15 
19.6 

24.8 

17 
22.5 

28.4 

19.8 
26 
33 

22.7 
30 

38 

25.5 
33 

42 

28.4 
37 
47 

31 
41 
52 

34 
45 
57 

13/ 

18 

22 

27 

31 

35 

41 

47 

53 

59 

65 

71 

? 

22 
26 
32 

27 
33 
40 

33 

40 

47 

38 
46 
55 

44 
53 
63 

51 
62 
73 

58 
71 
84 

65 
80 
95 

88 
105 

79 
97 
116 

87 
106 
127 

1 

38 
44 
52 
69 
90 

47 
55 
65 
84 
112 

57 
66 
78 
99 
135 

66 
77 
91 
113 
157 

76 
88 
104 
138 
180 

89 
103 
121 
181 
210 

101 
118 
138 
184 
240 

114 
133 
155 
207 
270 

127 

148 
172 
231 
300 

139 
163 
190 
254 
330 

152 
178 
207 

277 
360 

SPEED  OF  SHAFTING.— Machine  shops 

Wood-working 

Cotton  and  woollen  mills 300  to  400 

There  are  in  some  factories  lines  1000  ft.  long,  the  power  being  applied  at 
the  middle. 

Hollow  Shafts.-Let  d  be  the  diameter  of  a  solid  shaft,  and  dtdz  the 
external and  internal  diameters  of  a  hollow  shaft  of  the  same jnatenal. 
Then  the  shafts  will  be  of  equal  torsional  strength  when  d*  =  *  ^  ••••*  . 
\  10-inch  hollow  shaft  with  internal  diameter  of  4  inches  will  weigh  16*  less 
than  a  solid  10-inch  shaft,  b  at  its  strength  will  be  only  2  56*  less  If  the  hole 
were  increased  to  5  inches  diameter  the  weight  would  be  25#  less  than  that 
of  the  solid  shaft,  and  the  strength  4.25$  less. 

Table  for  laying  Out  Shafting. -The  table  on  the  opposite  page 
(from  the  Stevens  IndKator,  April,  1892)  is  used  by  Wm.  Sellers  &  Co.  to 


u  show  the  position  of  the  hangers 

and  position  of  couplings,  either  for  the  case  of  extension  in  both  directions 
from L  a  central  head-shaft  or  extension  in  one  direction  from  that  head-shaft. 


fABLE   FOR   LAYING   OUT   SHAFTING. 


I 


CO 


ne- 
ing. 


Double 
vise  Co 


•saqoui 


•sui  'xog  ao  'Sm 


Nominal 
Size  of 
2d  Shaft. 


-iC^C^OJC-JWOOCO 


OS 

of 


1 
1 

B 


"c  G^'i'o  £  " 
ess  S£» ...  .KflQ 

53St8B)5 

*Jgf£ 

i  C^^D  5*otc^" 

C-Sgl^g^ 

|?'§ISi§^«^ 

•s!|||^| 
Bl^°?i 

:l!li^^ 

hj 

^o 

:  °. 


U 
olu 
f  t 


n  o  eg    . 

lass 

" 


cc  OJ-5  O)'1"1  4» 

fec^^-c^co 

111 lie 
•°s|^ 

» «     Ac 

•iic«<s««i 
"llbb 

'g  ^  p'S^  as 


.  or 
simil 
t  sha 
+  B 


. 
lumn,  under  the 
table,  marked 
be  coupled  to  i 
ded  to  the  lengt 
aring,  and  in  ca 
e  length  of  the 
ngth  ;  Fig.  2,  C  + 


)^54J-Q'C  e3 

8ss"S.a 


th 
len 


O   T->  00 

COCO  CO 


Tf  Tf<  iO  JO  SO 


i~<  T-H  CJ  C?  CO  00  TJ<  10 


Nfi» 

r-K 


>  r-  \er-»-e\ 

.^  00  O  1-1  0?  CO  ^t  0  CO  t~ 


PROPORTIONS  OF  PULLEYS. 


873 


PULLEYS. 

Proportions  of  Pulleys.    (See  also  Fly-wheels  pages  820  to  888.)- 

Let  n  -number  of  arms,  D  =  diameter  of  pul  ley  ,  S  =  thickness  .of  be  It,  *  = 
ffickness  of  rim  at  edge,  T  =  thickness  m  middle,  B  =  width  of  rim,  ft  = 
bell  /  -  breadth  of  arm  at  hub,  fc,  =  breadth  of  arm  at  rim,  e  = 
ofaraTat  Thub  e,  =  thickness  of  arm  at  rim,  c  =  amount  of  crown- 


ing;  dimensions  in  inches. 

Unwin. 

9/8  O  4-  0.4) 

Reuleaux. 

9/8/3  to  5/4J3 

/   -  thickness  at  edge  of  rim  .  .  . 

0  7S  4-  .005I> 

\  ^i5«k  °V/im') 

2t  -f-  c 

i    IA  to  >4 

h  =  breadth  of  arm  at  hub  
^              ti       «<    t<     4t   r|m  

JFor  single      A  /  _ 
belts  =  .6337|/ 
For    double    */ 
belts  =  .798|/  ' 

n     V4"      ^        ^ 
^D      4"       1        20n 

e  L  =  thickness  of  arm  at  hub.  .  . 
"          44*'"  rim  .  .  .  , 

0.4ft 

0.57i 
O.Sftj 

n=  number   of   arms,    for   a  ) 
single  set, 

'<notless!htj?5S, 

«(B  x  J-) 

)  F  for  sin.  -arm  pulleys. 

ftto^ft 

„  —  rwtwrnnp1  of  DlllleV  

1/24J5 

The  number  of  arms  is  really  arbitrary,  and  may  be  altered  if  necessary. 

TnWm;\  With  two  or  three  sets  of  arms  may  be  considered  as  two^or  three 
sepai 
shou 

EXA 
thick. 


Reuleaux  .....       4      5.0    4.0     2.5     2.0          1.25        16       5 
The  following  proportions  are  given  in  an  article  in  the  Amer.  Machinist, 


o£5Dt+  ^n.,  fcl  =  .04D  +  3125  in.,  e  =  .OBRD  +  .2  in.,  e,  =  .01«D  + 

^ThSj'e  ffive  for  the  above  example:  h  =  4.25  in.,  fe±  =  2.71  in    e  =  1.7  in., 
These  give  ror  i  *^  .n  all  cageg  js  takers  ellipticaJ. 

' 


formula  for  a  beam  of  elliptical  section  fP  =  .0982  -,-  ,  in  which  P  =  the 


of  the  arm  at  the  hub,  and  ,6  =  .=  =,0.4*.  the 

thickness.    We  then  have//>  =  10  X  ^  =  90o|  =  '   5^,  whence 

_  3  /900BD  _  fioo//^    Which  is  practically  the  same  as  the  value 
71  -  V    3535u'  -         \     n  ' 
reached  by  Unwin  from  a  different  set  of  assumptions. 


874 


PULLEYS. 


Convexity  of  Palleys.—  Authorities  differ.  Morin  gives  a  rise  equal 
to  1/10  of  the  face  ;  Molesworth,  1/24  ;  others  from  ^  to  1/96.  Scott  A. 
Smitli  says  the  crown  should  not  be  over  ^  inch  for  a  24-inch  face.  Pulleys 
for  shifting  belts  should  be  "  straight,11  that  is,  without  crowning. 

CONE  OR  STEP  PUI,I,EYS. 

To  find  the  diameters  for  the  several  steps  of  a  pair  of  cone-pulleys: 
1.  Crossed  Belts.—  Let  D  and  d  be  the  diameters  of  two  pulleys  con- 
nected  by  a  crossed  belt,  L  =  the  distance  between  their  centres,  and  /3  = 
the  angle  either  half  of  the  belt  makes  with  a  line  joining  the  centres  of  the 

pulleys  :   then  total   length  of  belt  =  (D  -f  d£  -f  (D  -f  d)~  +  2L  cos   ft. 

if  loO 


=  angle  whose  sine  is 


Cos  ft  =  A  /  L*  - 


The  length  of 


vhen  D  -{-  d  is  constant;  that  is,  in  a  pair  of  step- 

le  di£ 


the  belt  is  constant 

pulleys  the  belt  tension  will  be  uniform  when  the  sum  of  the  diameters  of 

each  opposite  pair  of  steps  is  constant.    Crossed  belts  are  seldom  used  for 

cone-pulleys,  on  account  of  the  friction  between  the  rubbing  parts  of  the 

belt. 

To  design  a  pair  of  tapering  speed-cones,  so  that  the  '  belt  may  fit 
equally  tight  in  all  positions  :  When  the  belt  is  crossed,  use  a  pair  of  equal 
and  similar  cones  tapering  opposite  ways. 

2.  Open  Belts.— When  the  belt  is  uncrossed,  use  a  pair  of  equal  and 
similar  conoids  tapering  opposite  ways,  and  bulging  in  the  middle,  accord- 
ing to  the  following  formula:  Let  L  denote  the  distance  between  the  axes 
of  the  conoids;  R  the  radius  of  the  larger  end  of  each;  r  the  radius  of  the 
smaller  end;  then  the  radius  in  the  middle,  rQ,  is  found  as  follows: 


Jg  +  r    ,    (R  -  r)8 
2       ^     6. 281,  ' 


(Rankine.) 


If  D9  =  the  diameter  of  equal  steps  of  a  pair  of  cone-pulleys,  D  and  d  — 
the  diameters  of   unequal  opposite  steps,  and  L  =  distance  between  the 

D  +  d    ,    (D  -d)« 
axes,  D.  =  -g-  +  -^j^. 

If  a  series  of  differences  of  radii  of  the  steps,  R  —  r,  be  assumed,  then 
for  each  pair  of  steps  —  ^—  =  ro  —  ~z^  ir-»  an(*  tne  radii  of  each  may  be 

2  0  .  6oJ^j 

computed  from  their  half  sum  and  half  difference,  as  follows  : 


p_. 


R  -r 


R  +  r 
~~ 


R-r 


A.  J.  Frith  (Trans.  A.  S.  M.  E.,  x.  298)  shows  the  following  application  of 
Rankine's  method:  If  we  had  a  set  of  cones  to  design,  the  extreme  diame- 
ters of  which,  including  thickness  of  belt,  were  40"  and  10",  and  the  ratio 
desired  4,  3,  2,  and  1,  we  would  make  a  table  as  follows,  L  being  100": 


Trial 
Sum  of 
D  +  d. 

Ratio. 

Trial  Diameters. 

Values  of 
(Z>-d)« 
12.56L~ 

Amount 
to  be 
Added. 

Corrected  Values. 

D 

d 

D 

d 

50 
50 
50 
50 

4 
3 
2 
1 

40 
37.5 
33.333 
25 

10 

12.5 
16.666 
25 

.7165 
.4975 
.2212 
.0000 

.0000 
.2190 
.4953 
.7165 

40 
37.2190 
33.8286 
25.7165 

10 
12.7190 
17.1619 
25.7165 

The  above  formulae  are  approximate,  and  they  do  not  give  satisfactory 
results  when  the  difference  of  diameters  of  opposite  steps  is  large  and  when 
the  axes  of  the  pulleys  are  near  together,  giving  a  large  belt-angle.  The 
following  more  accurate  solution  of  the  problem  is  given  by  C.  A.  Smith 
(Trans.  A.  S.  M.  E.,  x.  269)  (Fig  152): 

Lay  off  the  centre  distance  Cor  EF.  and  draw  the  circles  7),  and  d^  equal 
to  the  first  pair  of  pulleys,  which  are  always  previously  determined  by 
known  conditions.  Draw  HI  tangent  to  the  circles  D,  and  d^.  From  B, 
midway  between  E  and  -F,  erect  the  perpendicular  BG,  making  the  length 


COKE   OR   STEP   PULLEYS. 


875 


BG  —  .314C.  With  G  as  a  centre,  draw  a  circle  tangent  to  HI.  Generally 
this  circle  will  be  outside  of  the  belt-line,  as  in  the  cut,  but  when  C  is  short 
and  the  first  pulleys  D^  and  d±  are  large,  it  will  fall  on  the  inside  of  the  belt- 
line.  The  belt-line  of  any  other  pair  of  pulleys  must  be  tangent  to  the  cir- 
cle G]  hence  any  line,  as  JK or  LM,  drawn  tangent  to  the  circle  G,  will  give 


FIG.  152. 

the  diameters  D2,  d^  or  D3,  d3  of  the  pulleys  drawn  tangent  to  these  lines 
from  the  centres  E  and  F. 

The  above  method  is  to  be  used  when  the  belt-angle  A  does  not  exceed 
18°.  When  it  is  between  18°  and  30°  a  slight  modification  is  made.  In  that 
case,  in  addition  to  the  point  G,  locate  another  point  m  on  the  line  BG  .298  C 
above  B.  Draw  a  tangent  line  to  the  circle  G,  making  an  angle  of  18°  to  the 
line  of  centres  EF,  and  from  the  point  m  draw  an  arc  tangent  to  this  tan- 
gent line.  All  belt-lines  with  angles  greater,  than  18°  are  tangent  to  this  arc. 
The  following  is  the  summary  of  Mr.  Smith's  mathematical  method: 

A  =  angle  in  degrees  between  the  centre  line  and  the  belt  of  any  pair  of 

pulleys; 
a  =  .314  for  belt-angles  less  than  18°,  and  .298  for  angles  between  18° 

and  30° ; 
B°  =  an  angle  depending  on  the  velocity  ratio; 

C  =  the  centre  distance  of  the  two  pulleys; 

D,  d  =  diameters  of  the  larger  and  smaller  of  the  pair  of  pulleys; 
E°  —  an  angle  depending  on  B° ; 

L  =  the  length  of  the  belt  when  drawn  tight  around  the  pulleys; 
r  =  D  -s-  d,  or  the  velocity  ratio  (larger  divided  by  smaller). 


(1)  Sin  A  = 


D  - 
2C 


(2)  tan  B°  = 


2a(r  - 1). 
r  +  1 


(3)  Sin  E°  =  sin  5°  (cos  A  -  D ^  )  ? 
(4)  A  —  B°  —  E°  when  sin  E°  is  positive ;  =  B°  -f  E°  when  sin  E°  is  negative; 


(5)  d  = 


-  2C)  when  A  =  0  and  r  =  1; 


r-1    ' 

(6)  D  =  rd; 

(7)  L  =  2Ccos  A  -f  .01745d[180  +  (r  -  1)(90  -f  A)]. 

Equation  (1)  is  used  only  once  for  any  pair  of  cones  to  obtain  the  constant 
cos  A,  by  the  aid  of  tables  of  sines  and  cosines,  for  use  in  equation  (3), 


876  BELTING. 


BELTING. 

Theory  of  Belts  and  Bands.—  A  pulley  is  driven  by  a  belt  by 
means  of  the  friction  between  the  surfaces  in  contact.  Let  2\  be  the  tension 
on  the  driving  side  of  the  belt,  7'2  the  tension  on  the  loose  side;  then  S,  =  rl\ 
—  Ty  ,  is  the  total  friction  between  the  band  and  the  pulley,  which  is  equal  to 
the  tractive  or  driving  force.  Let  f  =  the  coefficient  of  friction,  9  the  ratio 
of  the  length  of  the  arc  of  contact  to  the  length  of  the  radius,  a  =  the  angle 
of  the  arc  of  contact  in  degrees,  e  =  the  base  of  the  Naperian  logarithms 
=  2.71828,  m  =  the  modulus  of  the  common  logarithms  =  0.434295.  The 
following  formulae  are  derived  by  calculus  (Rankine's  Mach'y  &  Millwork, 
p.  351  ;  Carpenter's  Exper.  Eng'g,  p.  173): 

-=  e/';   T2  =  A.;    T,  -  T,  =  T,  -  --  =  T,(l  -  e~fO). 


If  the  arc  of  contact  between  the  band  and  the  pulley  expressed  in  turns 
and  fractions  of  a  turn  =  n,  0  =  2mi;  e-t9  =  io2-7288/M;  that  is,  efe  is  the 
natural  number  corresponding  to  the  common  logarithm  2.7288/n, 

The  value  of  the  coefficient  of  friction  /  depends  on  the  state  and  material 
of  the  rubbing  surfaces.  ITor  leather  belts  on  iron  pulleys,  Morin  found 
f  =  .56  when  dry,  .36  when  wet,  .23  when  greasy,  and  .15  when  oily.  In  calcu- 
lating the  proper  mean  tension  for  a  belt,  the  smallest  value,  f  =  .15,  is 
to  be  taken  if  there  is  a  probability  of  the  belt  becoming  wet  with  oil.  The 
experiments  of  Henry  R.  Towne  and  Robert  Briggs,  however  (Jour.  Frnnk. 
Inst.,  1868).  show  that  such  a  state  of  lubrication  is  not  of  ordinary  occur- 
rence; and  that  in  designing  machinery  we  may  in  most  cases  safely  take 
/  =  0.42.  Reuleaux  takes/  =  0.25.  The  following  table  shows  the  values  of 
the  coefficient  2.72S8/,  by  which  n  is  multiplied  in  the  last  equation,  corre- 
sponding to  different  values  of  /;  also  the  corresponding  values  of  various 
ratios  among  the  forces,  when  the  arc  of  contact  is  half  a  circumference  : 

/=0.15  0.25  0.42  0.56 

2.7288/  =  0.41  0.68  0.15  1.53 

Let  9  =  TT  and  n  -  Y^  then 

T  H-  r2  =  1  603  2.188  3.758  5.821 

Tl  n-tf  =  2.66  1  84  1.36  1.21 

Ti-f  TV  +  28  =  2.16  1.34  0.86  0.71 

In  ordinary  practice  it  is  usual  to  assume  T2  =  $•  TI  =  2S;  Tl  -f  3Ta  -*- 
2S  =  1.5.  This  corresponds  to/  =0.22  nearly. 

For  a  wire  rope  on  cast  iron  /  maybe  taken  as  0.15  nearly;  and  if  the 
groove  of  the  pulley  is  bottomed  with  gutta-percha,  0.25.  (Kankine.) 

Centrifugal  Tension  of  Belts.—  When  a  belt  or  band  runs  at  a 
high  velocity,  centrifugal  force  produces  a  tension  in  addition  to  that  exist- 
ing when  the  belt  is  at  rest  or  moving  at  a  low  velocity.  This  centrifugal 
tension  diminishes  the  effective  driving  force. 

Rankine  says  :  If  an  endless  band,  of  any  figure  whatsoever,  runs  at  a 
given  speed,  the  centrifugal  force  produces  a  uniform  tension  at  each  cross- 
section  of  the  band,  equal  to  the  weight  of  a  piece  of  the  band  whose  length 
is  twice  the  height  from  which  a  heavy  body  must  fall,  in  order  to  acquire 
the  velocity  of  the  band.  (See  Cooper  on  Belting,  p.  101.) 

If  Tc  =  centrifugal  tension; 

V  =  velocity  in  feet  per  second  ; 
g  —  acceleration  due  to  gravity  =  32.2; 
W  —  weight  of  a  piece  of  the  belt  1  ft.  long  and  1  sq.  in.  sectional  area,— 

leather  weighing  56  Ibs.  per  cubic  foot  gives  W  =  56  -4-  144  =  .338. 


BELTING   PRACTICE.  8*5"? 

Belting  Practice.  Handy  Formulae  for  Belting.  —  Since 
in  the  practical  application  of  the  above  formulas  the  value  of  the  coefficient 
of  friction  must  be  assumed,  its  actual  value  varying  within  wide  limits  U6# 
to  135^),  and  since  the  values  of  rl\  and  jT2  also  are  fixed  arbitrarily  >  it  is  cus- 
tomary in  practice  to  substitute  for  these  theoretical  formulas  more  simple 
empirical  formulae  and  rules,  some  of  which  are  given  below. 

Let  d  =  diam.  of  pulley  in  inches;  nd  =  circumference; 

V  =  velocity  of  belt  in  ft.  per  second;  v  =  vel.  in  ft.  per  minute; 

a  =  angle  of  the  arc  of  contact; 

L  =  length  of  arc  of  contact  in  feet  =  irda  -4-  (12  X  360)  ; 

F  =  tractive  force  per  square  inch  of  sectional  area  of  belt; 

w  =  width  in  inches;  t  =  thickness; 

8  =  tractive  force  per  inch  of  width  =  F-i-  tf; 
rpin.  =  revs,  per  minute;  rps.  =  revs,  per  second  =  rpm.  •*•  60. 


v  ==  ~  X  rpm.;  =  MISd  x  rpm. 
Horse-power,  H.P. 

If  F  =  working  tension  per  square  inch  =  275  Ibs.,  and  t  —  7/32  inch,  S  = 
60  Ibs.  nearly,  then 


H.P.  -  S«  -  .mvw  =  .000476^  X  rpm.  =          ^. 
If  F  =  180  Ibs.  per  square  inch,  and  t  =  1/6  inch,  8  =  30  Ibs.,  then 


H.P.  =         =  .OUrw  =  .mmwd  X  rpm.  =  -  .    .    (2) 

If  the  working  strain  is  60  Ibs.  per  inch  of  width,  a  belt  1  inch  wide  travel- 
ling 550  ft.  per  minute  will  transmit  1  horse-power.  If  the  working  strain  is 
30  Ibs.  per  inch  of  width,  a  belt  1  inch  wide,  travelling  1100  ft.  per  minute, 
will  transmit  1  horse-power.  Numerous  rules  are  given  by  different  writers 
on  belting  which  vary  between  these  extremes.  A  rule  commonly  used  is  : 
1  inch  wide  travelling  1000  ft.  per  min.  =  I.H.P. 

.     .    (3) 


This  corresponds  to  a  working  strain  of  33  Ibs.  per  inch  of  width. 

Many  writers  give  as  safe  practice  for  single  belts  in  good  condition  a 
working  tension  of  45  Ibs.  per  inch  of  width.    This  gives 


,=  .  000357,^ 


For  double  belts  of  average  thickness,  some  writers  say  that  the  trans- 
mitting efficiency  is  to  that  of  single  belts  as  10  to  7,  which  would  give 

H.P.  of  double  belts  =  ^  =  .1169  Fw  =  .00051?^  X  rpm.  =  wd  XJfm'.   (5) 
51  o  .  I960 

Other  authorities,  however,  make  the  transmitting-power  of  double  belts 
twice  that  of  single  belts,  on  the  assumption  that  the  thickness  of  a  double- 
belt  is  twice  that  of  a  single  belt. 

Rules  for  horse-power  of  belts  are  sometimes  based  on  the  number  of 
square  feet  of  surface  of  the  belt  which  pass  over  the  pulley  in  a  minute. 
Sq.  ft.  per  min.  =  wv  -T-  12.  The  above  formulae  translated  into  this  form 
give: 

Cl)    For  8  =  60  Ibs.  per  inch  wide  ;  H.P.  =  46  sq.  ft.  per  minute. 

(2)  tl     S  =  30    "  "        H.P.  =  92 

(3)  "     8  =  33    "  "  "        H.P.  =  83       " 

(4)  '•     8  s=  45    "  "  •'        H.P.  =  61 

(5)  **    $«64.3"          "          "       H.P.  =43      "          "  (double  belt). 


878 


BELTING. 


The  above  formulae  are  all  based  on  the  supposition  that  the  arc  of  cori- 
tact  is  180°  For  other  arcs,  the  transmitting  power  is  approximately  pro- 
portional to  the  ratio  of  the  degrees  of  arc  to  180°. 

Some  rules  base  the  horse-power  on  the  length  of  the  arc  of  contact  in 

irda  ,  TT  ,..        Svw  Stv       red  a 

feet.    Smce  L  =  jj-^-  and  H.P.  =  ^  =  ^X  ^  X  rpm.  X  ^  we 

obtain  by  substitution  H.P.  =  -^555  X  I/  X  rpm.,  and  the  five  formulas  then 
take  the  following  form  for  the  several  values  of  S: 


wL  X  rpm. 
H'P-, 275~~   (1 

H.P.  (double  belt)  = 


ivL  X  rpm.  /ox      wL  X  rpm.  t 


ivL  X  rpm. 


550 

wL  X  rpm. 
257 


500 


(4); 


(5). 


None  of  the  handy  formulae  take  into  consideration  the  centrifugal  ten- 
sion of  belts  at  high  velocities.  When  the  velocity  is  over  3000  ft.  per  min- 
ute the  effect  of  this  tension  becomes  appreciable,  and  it  should  be  taken 
account  of  as  in  Mr.  Nagle's  formula,  which  is  given  below. 

Horse-power  of  a  Leather  Belt  One  Inch  wide.    (NAGLE.) 

Formula:  H.P.  =  CVtw(8  -  .012  F2)  -f  550. 

For  /  =  .40,  a  =  180°,  C  -  .715,  w  =  1. 


LACED  BELTS,  S  =  275. 

RIVETED  BELTS,  S  =  400. 

.S  o 

c  o 

D 

K 

Thickness  in  inches  =  t. 

si 

Thickness  in  inches  =  t. 

|& 

1/7 

1/6 

3/16 

7/32 

1/4 

5/16 

1/3 

|I 

7/32 

1/4 

5/16 

1/3 

3/8 

7/16 

1/2 

V  *j 
>& 

.143 

.167 

.187 

.219 

.250 

.312 

.333 

&  —  ' 

219 

.250 

.312 

.333 

.375 

.437 

.500 

10 

.51 

.59 

.63 

.73 

.84 

1.05 

1.18 

15 

1.69 

1.94 

2.42 

2.58 

2.91 

3.39 

3.87 

15 

.75 

.88 

1.00 

1.16 

1.32 

1.66 

1.77 

20 

2.24 

2.57 

3.21 

3.42 

3.85 

4.49 

5.13 

20 

1.00 

1.17 

1-32 

1.54 

1.75 

2  19 

2.34 

25 

2.79 

3.19 

3.98 

4.25 

4.78 

5.57 

6.37 

25 

1.23 

1.43 

1.61 

1.88 

2.16 

2.69 

2.86 

30 

3.31 

3.79 

4.74 

5.05 

5.67 

6.62 

7.58 

30 

1.47 

1.72 

1.93 

2.25 

2.58 

3.22 

3.44 

35 

3.82 

4.37 

5.46 

5.83 

6.56 

7.65 

8.75 

35 

1.69 

1.97 

2.22 

2.59 

2.96 

S.70 

3.94 

40 

4.33 

4.95 

6.19 

6.60 

7.42 

8.66 

9  90 

40 

1.90 

2.22 

2.49 

2.90 

3.32 

4.15 

4.44 

45 

4.85 

5  49 

6.86 

7.32 

8.43 

9  70 

10.98 

45 

2.09 

2.45 

2.75 

3.21 

3.67 

4.58 

4.89 

50 

5.26 

6.01 

7.51 

8.02 

9.02 

10.52;12.03 

50 

2.27 

2.65 

2.98 

3.48 

3.98 

4.97 

5.30 

55 

5.68 

6.50 

8.12 

8.66 

9.74 

n.se^is.oo 

55 

2.44 

2.84 

3.19 

3.72 

4.26 

5.32 

5.69 

60 

6.09 

6.C6 

8.70 

9.28 

10.43 

12.17)13.91 

60 

2.58 

3.01 

3.38 

3.95 

4.51 

5.64 

6.02 

65 

6.45 

7.37 

9.22 

9.83 

11.06 

12.90  14.75 

65 

2.71 

3.16 

3.55 

4.14 

4.74 

5  92 

0.32 

70 

6.78 

7.75 

9  69 

10.33 

11.62 

13.56  15.50 

70 

2.81 

3.27 

3.68 

4.29 

4.91 

e!i4 

6.54 

75 

7.09 

8.11 

10.13 

10.84 

12.16 

14.1816.21 

75 

2.89 

3.37 

3.79 

4.42 

5.05 

6.31 

6.73 

80 

7.36 

8.41 

10  51 

11.21 

12.61 

14.71:16.81 

80 

2.94 

3.43 

3.86 

4.50 

5.15 

6.44 

6.86 

85 

7.58 

8.66 

10.82 

11.55 

13.00 

15.16  17.32 

85 

2.97 

3.47 

3.90 

4.55 

5.20 

6.50 

6.93 

90 

7.74 

8.85 

11.06 

11.80 

13.27 

15.4817.69 

90 

2.97 

3.47 

3.90 

4.55 

5.20 

(5.50 

6.93 

100 

7.96 

9.10 

11.37 

12.13 

13  65 

15.92  18.20 

The  H.P.  becomes  a  maximum 

The  H.P.  becomes  a  maximum  at 

at  87.  41  ft.  per  sec,  =  5245  ft.  p.  min. 

105.4  ft.  per  sec.  =  6324  ft.  per  min. 

In  the  above  table  the  angle  of  sub  tension,  a,  is  taken  at  180°. 


Should  it  be I  90°|100° 

Multiply  above  values  by  |  .65  |  .70 


110° | 120° 
.75 


1 20° 1 130° j 140° 1 150° 1 160° 

.79|  .83  |  .87  |  .91  |  .94 


170°  [180°  (200° 
.971     1  11.05 


A.  F.  Nagle's  Formula  (Trans.  A.  S.  M.  E.,  vol.  ii.,  1881,  p.  91. 
Tables  published  in  1882.) 

H.P.  =  CFto.(i^E!); 


a  =  degrees  of  belt  contact; 
/  =  coefficient  of  friction; 
w  =  width  in  inches; 


t  —  thickness  in  inches; 
V  —  velocity  in  feet  per  second; 
S  =  stress  upon  btii  per  square  inch. 


\\IDTH    OF   BELT   FOR  A   GIVEN"   HORSE-POWER. 


Taking  fif  at  275  Ibs.  per  sq.  in.  for  laced  belts  and  400  Ibs.  per  sq  in.  for 
lapped  and  riveted  belts,  the  formula  becomes 

H  p  _  cVtw(M  —  .0000218F2)  for  laced  belts; 
H.P.  =  CVtw(.^21  -  .0000218F2)  for  riveted  belts. 

VALUES  OP  C  =  1  -  10  --00758/a.    (NAGLK.) 


•  «M   • 

Degrees  of  contact  =  a. 

H'l'l 

90° 

100° 

110° 

120° 

130° 

140° 

150° 

160° 

170° 

180* 

200° 

.15 
20 

.210 
.270 

.230 

.295 

.250 

.319 

.270 
.342 

.288 
.364 

.307 
.386 

.325 

.408 

.342 

.428 

.359 

.448 

.376 
.467 

.408 
.503 

25 

325 

354 

.381 

.407 

.432 

.457 

.480 

.503 

.524 

.544 

.582 

30 

376 

.408 

.438 

.467 

.494 

.520 

.544 

.567 

.590 

.610 

.649 

35 

.457 

.489 

.520 

.548 

.575 

.600 

.624 

.646 

.667 

.705 

40 

467 

.502 

.536 

.567 

.597 

.624 

.649 

.673 

.695 

.715 

.753 

.45 
55 

.507 

.578 

.544 
.617 

.579 
.652 

.610 

.684 

.640 
.713 

.667 
.739 

.692 
.763 

.715 
.785 

.737 
.805 

.757 
.822 

.792 

.853 

60 

610 

.649 

.684 

.715 

.744 

.769 

.792 

.813 

.832 

.848 

.877 

1.00 

.792 

.825 

.853 

.877 

.897 

.913 

.927 

.937 

.947 

.956 

.969 

The  following  table  gives  a  comparison  of  the  formulae  already  given  for 
the  case  of  a  belt  one  inch  wide,  with  arc  of  contact  180°. 
Horse-power  of  a  Belt  One  Inch  wide,  Arc  of  Contact  180°. 

COMPARISON  OP  DIFFERENT  FORMULAE. 


•-$ 

.Sc 
£5 

°f 

Form.  1 
HP   — 

Form.  2 
H.P.  - 

Form.  3 
H.P.  = 

Form.  4 
H.P.  = 

Form.  5 
dbl.belt 
HP   — 

Nagle's  Form. 
7/32'  'single  belt 

88, 

3* 

«M    p. 

wv 
"550" 

wv 

Hoo' 

wv 

iooo' 

wv 
"733" 

wv 

Laced. 

Riveted 

^ii 

>** 

CQ 

10 

600 

50 

1.09 

.55 

.60 

.82 

1.17 

.73 

1.14 

20 
30 
40 
50 
60 
70 
80 
90 
100 

1200 
1800 
2400 
3000 
3600 
4200 
4800 
5400 
6000 

fifiOft 

100 
150 
200 
250 
300 
350 
400 
450 
500 
550 

2.18 
3.27 
4.36 
5.45 
6.55 
7.63 
8.73 
9.82 
10.91 

3.09 
1.64 
2.18 
2.73 
3.27 
3.82 
4.36 
4.91 
5.45 

1.20 
1.80 
2.40 
3.00 
3.60 
4.20 
4.80 
5.40 
6.00 

1.64 
2.46 
3.27 
4.09 
4.91 
5.73 
6.55 
7.37 
8.18 

2.34 
3.51 
4.68 
5.85 
7.02 
8.19 
9.36 
10.53 
11.70 

1.54 
2.25 
2.90 
3.48 
3.95 
4.29 
4.50 
4.55 
4.41 
4.05 

2.24 
3.31 
4.33 
5.26 
6.09 
6.78 
7.36 
7.74 
7.96 
7.97 

120 

7800 

600 

3.49 

7.75 

Width  of  Belt  for  a  Given  Horse-power.— The  width  of  belt 
reouired  for  any  given  horse-power  may  be  obtained  by  transposing  the  for- 
mulse  for  horse-power  so  as  to  give  the  value  of  w.  Thus: 

550  H.P.       9. 17  H.P.       2101  H.P.        275  H.P. 
w  = — 


From  formula  (1), 
From  formula  (2), 
From  formula  (3), 
From  formula  (4), 

From  formula  (5),*  w  = 
*  For  double  belts. 


1100  H.P. 

v 
1000  H.P. 

v 
733  H.P. 


V 

18.33  H.P. 

V 
_  16.67  H.P. 

V 
12.22  H.P. 


513  H.P.       8.56  H.P. 


d  X  rpm. 

_  4202  H.P. 

~~  d  X  rpm. 

_  3820  HP. 

~  d  X  rpm. 

=   2800  H.P. 

"  d  X  rpm. 

I960  H.P.  = 

d  X  rpm.      L  x  rpm.' 


L  X  rpm. ' 
530  H.P. 
L  X  rpm.* 

-  50°  H>P- 
L  X  rpm.* 

860  H.P. 
"  L  x  rpm.* 
257  H.P. 


880 


BELTIHG. 


Many  authorities  use  formula  (1)  for  double  belts  and  formula  (2)  or  (81  for 
single  belts. 


550  H.P. 


or  divide 


To  obtain  the  width  by  Nagle's  formula,  w  =  y o 

the  given  horse-power  by  the  figure  in  the  table  corresponding  to  the  given 
thickness  of  belt  and  velocity  in  feet  per  second. 

The  formula  to  be  used  in  any  particular  case  is  largely  a 
matter  of  judgment.  A  single  belt  proportioned  according  to  formula  (1), 
if  tightly  stretched,  and  if  the  surface  is  in  good  condition,  will  transmit  the 
horse- power  calculated  by  the  formula,  but  one  so  proportioned  is  objec- 
tionable, first,  because  it  requires  so  great  an  initial  tension  that  it  is  apt  to 
stretch,  slip,  and  require  frequent  restretching  and  relacing;  and  second 
because  this  tension  will  cause  an  undue  pressure  on  the  pulley  -shaft,  and 
therefore  an  undue  loss  of  power  by  friction.  To  avoid  these  difficulties, 
formula  (2),  (3),  or  (4,)  or  Mr.  Nagle's  table,  should  be  used;  the  latter  espe- 
cially in  cases  in  which  the  velocity  exceeds  4000  ft.  per  min 

Taylor's  Rules  for  Belting.  -F.  W.  Taylor  (Trans.  A.  S.  M.  E., 
xv.  204)  describes  a  nine  years'  experiment  on  belting  in  a  machine-shop, 
giving  results  of  tests  of  42  belts  running  night  and  day.  Some  of  these 
belts  were  run  on  cone  pulleys  and  others  on  shifting,  or  fast-and-loose,  pul- 
leys. The  average  net  working  load  on  the  shifting  belts  was  only  4/10  of 
that  of  the  cone  belts. 

The  shifting  belts  varied  in  dimensions  from  39  ft.  7  in.  long,  3.5  in.  wide, 
.25  in.  thick,  to  51  ft.  5  in.  long,  6.5  in.  wide,  .37  in.  thick.  The  cone  belts 
varied  in  dimensions  from  24  ft.  7  in.  long,  2  in.  wide,  .25  in.  thick,  to  31  ft. 
10  in.  long,  4  in.  wide,  .37  in.  thick. 

Belt-clamps  were  used  having  spring-balances  between  the  two  pairs  of 
clamps,  so  that  the  exact  tension  to  which  the  belt  was  subjected  was 
accurately  weighed  when  the  belt  was  first  put  on,  and  each  time  it  was 
tightened. 

The  tension  under  which  each  belt  was  spliced  was  carefully  figured  so  as 
to  place  it  under  an  initial  strain— while  the  belt  was  at  rest  immediately 
after  tightening— of  71  Ibs.  per  inch  of  width  of  double  belts.  This  is  equiv- 
alent, in  the  case  of 

Oak  tanned  and  fulled  belts,  to  192  Ibs.  per  sq.  in.  section ; 
Oak  tanned,  not  fulled  belts,  to  229  "      "     "    "         '* 
Semi- raw-hide  belts,  to  253  "      "     **    "          " 

Raw-hide  belts,  to  284  "      *'     **    "         ** 

From  the  nine  years' experiment  Mr.  Taylor  draws  a  number  of  conclu- 
sions, some  of  which  are  given  in  an  abridged  form  below. 

In  using  belting  so  as  to  obtain  the  greatest  economy  and  the  most  satis- 
factory results,  the  following  rules  should  be  observed: 


Oak  Tanned 
and  Fulled 
Leather  Belts. 

Other  Types  of 
Leather  Belts 
and  6-  to  7-ply 
Rubber  Belts. 

A  double  belt,  having  an  arc  of  contact  of 
180°,  will  give  an  effective  pull  on  the  face 
of  a  pulley  per  inch  of  width  of  belt  of.  ... 
Or,  a  different  form  of  same  rule: 
The  number  of  sq.  ft.  of  double  Belt  passing 
around  a  pulley  per  minute  required  to 
transmit  one  horse  power  is 

35  Ibs. 
80  sq  ft 

30  Ibs. 
90  sq  ft 

Or  :  The  number  of  lineal  feet  of  double- 
belting  1  in.  wide  passing  around  a  pulley 
per  minute  required  to  transmit  one  horse- 
power is  

950ft 

1100ft 

Or  :  A  double  belt  6  in.  wide,  running  4000  to 
5000  ft.  per  min.,  will  transmit  

30  H.P. 

25  H.P. 

The  terms  "initial  tension,"  "  effective  pull,"  etc.,  are  thus  explained  by 
Mr.  Taylor  :  When  pulleys  upon  which  belts  are  tightened  are  at  rest,  both 
strands  of  the  belt  (the  upper  and  lower)  are  under  the  same  stress  per  in 
of  width.  By  "  tension,"  "  initial  tension,"  or  "  tension  while  at  rest,11  w» 


TAYLOR'S  RULES  FOR  BELTIKG.  881 

/soean  the  stress  per  in.  of  width,  or  sq,  in.  of  section,  to  which  one  of  the 
/strands  of  the  belt  is  tightened,  \\  hen  at  rest.  After  the  belts  are  in  motion 
and  transmitting  power,  the  stress  on  the  slack  side,  or  strand,  of  the  belt 
becomes  less,  while  that  on  the  tight  side— or  the  side  which  does  the  pull- 
ing— becomes  greater  than  when  the  belt  was  at  rest.  By  the  term  "  t€>tal 
load  "  we  mean  the  total  stress  per  in.  of  width,  or  sq.  in.  of  section,  on  the 
tight  side  of  belt  while  in  motion. 

The  difference  between  the  stress  on  the  tight  side  of  the  belt  and  its  slack 
side,  while  in  motion,  represents  the  effective  force  or  pull  which  is  trans- 
mitted from  one  pulley  to  another.  By  the  terms  "working  load,1'  "  net 
working  load,"  or  "effective  pull,11  we  mean  the  difference  in  the  tension 
of  the  tight  and  slack  sides  of  the  belt  per  in.  of  width,  or  sq.  in.  section, 
while  in  motion,  or  the  net  effective  force  that  is  transmitted  from  one  pul- 
ley to  another  per  in.  of  width  or  sq.  in.  of  section. 

The  discovery  of  Messrs.  Lewis  and  Bancroft  (Trans.  A.  S.  M.  E.,  vii.  749) 
that  the  "sum  of  the  tension  on  both  sides  of  the  belt  does  not  remain 
constant,1'  upsets  all  previous  theoretical  belting  formulae. 

The  belt  speed  for  maximum  economy  should  be  from  4000  to  4500  ft.  per 
minute. 

The  best  distance  from  centre  to  centre  of  shafts  is  from  20  to  25  ft. 

Idler  pulleys  work  most  satisfactorily  when  located  on  the  slack  side  of 
the  belt  about  one  quarter  waj7  from  the  driving-pulley. 

Belts  are  more  durable  and  work  more  satisfactorily  made  narrow  and 
thick,  rather  than  wide  and  thin. 

It  is  safe  and  advisable  to  use:  a  double  belt  on  a  pulley  12  in.  diameter  or 
larger;  a  triple  belt  on  a  pulley  20  in.  diameter  or  larger;  a  quadruple  belt 
on  a  pulley  30  in.  diameter  or  larger. 

As  belts  increase  in  width  they  should  also  be  made  thicker. 

The  ends  of  the  belt  should  be  fastene..  together  by  splicing  and  cement- 
ing, instead  of  lacing,  wiring,  or  using  hooks  or  clamps  of  any  kind. 

A  V-splice  should  be  used  on  triple  and  quadruple  belts  and  when  idlers 
are  used.  Stepped  splice,  coated  with  rubber  and  vulcanized  in  place,  is  best 
for  rubber  belts. 

For  double  belting  the  rule  works  well  of  making  the  splice  for  all  belts 
up  to  10  in.  wide,  10  in.  long;  from  10  in.  to  18  in.  wide  the  splice  should  be 
the  same  width  as  the  belt,  18  in.  being  the  greatest  length  of  splice  required 
for  double  belting. 

Belts  should  be  cleaned  and  greased  every  five  to  six  months. 

Double  leather  belts  will  last  well  when  repeatedly  tightened  under  a 
strain  (when  at  rest)  of  71  Ibs.  per  in.  of  width,  or  240  Ibs.  per  sq.  in.  section. 
They  will  not  maintain  this  tension  for  any  length  of  time,  however. 

Belt-clamps  having  spring- balances  between  the  two  pairs  of  clamps 
should  be  used  for  weighing  the  tension  of  the  belt  accurately  each  time  it 
is  tightened. 

The  stretch,  durability,  cost  of  maintenance,  etc.,  of  belts  proportioned 
(A)  according  to  the  ordinary  rules  of  a  total  load  of  111  Ibs.  per  inch  of 
width  corresponding  to  an  effective  pull  of  65  Ibs.  per  inch  of  width,  and  (B) 
according  to  a  more  economical  rule  of  a  total  load  of  54  Ibs.,  corresponding 
to  an  effective  pull  of  26  Ibs.  per  inch  of  width,  are  found  to  be  as  follows: 

When  it  is  impracticable  to  accurately  weigh  the  tension  of  a  belt  in  tight- 
ening it,  it  is  safe  to  shorten  a  double  belt  one  half  inch  for  every  10  ft.  of 
length  for  (A)  and  one  inch  for  every  10  ft.  for  (B),  if  it  requires  tightening. 

Double  leather  belts,  when  treated  with  great  care  and  run  night  and  day 
at  moderate  speed,  should  last  for  7  years  (A);  18  years  (B). 

The  cost  of  all  labor  and  materials  used  in  the  maintenance  and  repairs  of 
double  belts,  added  to  the  cost  of  renewals  as  they  give  out,  through  a  term 
of  years,  will  amount  on  an  average  per  year  to  37#  of  the  original  cost  of 
the  belts  (A);  14%  or  less  (B). 

In  figuring  the  total  expense  of  belting,  and  the  manufacturing  cost 
chargeable  to  this  account,  by  far  the  largest  item  is  the  time  lost  on  the 
machines  while  belts  are  being  relaced  and  repaired. 

The  total  stretch  of  leather  belting  exceeds  6$  of  the  original  length. 

The  stretch  during  the  first  six  months  of  the  life  of  belts  is  36$  of  their 
entire  stretch  (A);  15*  (B). 

A  double  belt  will  stretch  47/100  of  1%  of  its  length  before  requiring  to  be 
tightened  (A);  81/100  of  1%  (B). 

The  most  important  consideration  in  making  up  tables  and  rules  for  the 
use  and  care  of  belting  is  how  to  secure  the  minimum  of  interruptions  to 
manufacture  from  this  source. 


882  BELTING. 

The  average  double  belt  (A),  when  running  ni^ht  and  day  in  a  machine- 
shop,  will  cause  at  least  26  interruptions  to  manufacture  during  its  life,  or  5 
interruptions  per  year,  but  with  (B)  interruptions  to  manufacture  will  not 
average  oftener  for  each  belt  than  one  in  sixteen  months. 

The  oak-tanned  and  fulled  belts  showed  themselves  to  be  superior  in  all 
respects  except  the  coefficient  of  friction  to  either  the  oak-tanned  not  fulled, 
the  semi-raw-hide,  or  raw-hide  with  tanned  face. 

Belts  of  any  width  can  be  successfully  shifted  backward  and  forward  on 
tight  and  loose  pulleys.  Belts  running  between  5000  and  GOOD  ft.  per  min. 
and  driving  300  H.P.  are  now  being  daily  shifted  on  tight  and  loose  pulleys, 
to  throw  lines  of  shafting  in  and  out  of  use. 

The  best  form  of  belt-shifter  for  wide  belts  is  a  pair  of  rollers  twice  the 
width  of  belt,  either  of  which  can  be  pressed  onto  the  flat  surface  of  the 
belt  on  its  slack  side  close  to  the  driven  pulley,  the  axis  of  the  roller  making 
an  angle  of  75°  with  the  centre  line  of  the  belt. 

Remarks  on  Mr.  Taylor's  Rales.  (Trans.  A.  S.  M.  E.,  xv.,  242.) 
—The  most  notable  feature  in  Mr.  Taylor's  paper  is  the  great  difference  be- 
tween his  rules  for  proper  proportioning  of  belts  and  those  given  b}'  earlier 
writers.  A  very  commonly  used  rule  is,  one  horse-power  may  be  transmitted 
by  a  single  belt  1  in.  wide  running  x  ft.  per  min.,  substituting  for  x  various 
values,  according  to  the  ideas  of  different  engineers,  ranging  usually  from 
550  to  1100. 

The  practical  mechanic  of  the  old  school  is  apt  to  swear  by  the  figure 
600  as  being  thoroughly  reliable,  while  the  modern  engineer  is  more  apt  to 
use  the  figure  1000.  Mr.  Taylor,  however,  instead  of  using  a  figure  from  550 
to  1100  for  a  single  belt,  uses  950  to  1100  for  double  belts.  If  we  assume  that 
a  double  belt  is  twice  as  strong,  or  will  carry  twice  as  much  power,  as  a 
single  belt,  then  he  uses  a  figure  at  least  twice  as  large  as  that  used  in 
modern  practice,  and  would  make  the  cost  of  belting  for  a  given  shop  twice 
as  large  as  if  the  belting  were  proportioned  according  to  the  most  liberal  of 
the  customary  rules. 

This  great  difference  is  to  some  extent  explained  by  the  fact  that  the 
problem  which  Mr.  Taylor  undertakes  to  solve  is  quite  a  different  one  from 
that  which  is  solved  by  the  ordinary  rules  with  their  variations.  The  prob- 
lem of  the  latter  generally  is,  "How  wide  a  belt  must  be  used,  or  how  nar- 
row a  belt  may  be  used,  to  transmit  a  given  horse-power  ?"  Mr.  Taylor's 
problem  is:  '*  How  wide  a  belt  must  be  used  so  that  a  given  horse-power 
may  be  transmitted  with  the  minimum  cost  for  belt  repairs,  the  longest  life 
to  the  belt,  and  the  smallest  loss  and  inconvenience  from  stopping  the 
machine  while  the  belt  is  being  tightened  or  repaired  ?" 

The  difference  between  the  old  practical  mechanic's  rule  of  a  l-in.-wide 
single  belt,  600  ft.  per  min.,  transmits  one  horse-power,  and  the  rule  com- 
monly  used  by  engineers,  in  which  1000  is  substituted  for  600,  is  due  to  the 
belief  of  the  engineers,  not  that  a  horse-power  could  not  be  transmitted  by 
the  belt  proportioned  by  the  older  rule,  but  that  such  a  proportion  involved 
undue  strain  from  overtightening  to  prevent  slipping,  which  strain  entniled 
too  much  journal  friction,  necessitated  frequent  tightening,  and  decreased 
the  length  of  the  life  of  the  belt. 

Mr.  Taylor's  rule  substituting  1100  ft.  per  min.  and  doubling  the  belt  is  a 
further  step,  and  a  long  one,  in  the  same  direction.  Whether  it  will  be  taken 
in  any  case  by  engineers  will  depend  upon  whether  they  appreciate  the  ex- 
tent of  the  losses  due  to  slippage  of  belts  slackened  by  use  under  overstrain, 
and  the  loss  of  time  in  tightening  and  repairing  belts,  to  such  a  degree  as  to 
induce  them  to  allow  the  first  cost  of  the  belts  to  be  doubled  in  order  to 
avoid  these  losses. 

It  should  be  noted  that  Mr.  Taylor's  experiments  were  made  on  rather 
narrow  belts,  used  for  transmitting  power  from  shafting  to  machinery,  and 
his  conclusions  may  not  be  applicable  to  heavy  and  wide  belts,  such  as 
engine  fly-wheel  belts. 

MISCELLANEOUS  NOTES  ON  BELTING. 

Formulae  are  useful  for  proportioning  belts  and  pulleys,  but  they  furnish 
no  means  of  estimating  how  much  power  a  particular  belt  may  be  trans- 
mitting at  any  given  time,  any  more  than  the  size  of  the  engine  is  a  measure 
of  the  load  it  is  actually  drawing,  or  the  known  strength  of  a  horse  is  a 
measure  of  the  load  on  the  wagon.  The  only  reliable  means  of  determining 
the  power  actually  transmitted  is  some  form  of  dynamometer.  (See  Trans. 
A-  S.  M.  E.,  vol.  xii.  p.  707.) 


MISCELLANEOUS   NOTES   ON   BELTING.  8^3 

If  we  increase  the  thickness,  the  power  transmitted  ought  to  increaee  in 
proportion;  and  for  double  belts  we  should  have  half  the  width  required  for 
a  single  belt  under  the  same  conditions.  With  large  pulleys  and  moderate 
velocities  of  belt  it  is  probable  that  this  holds  good.  With  small  pulleys, 
however,  when  a  doable  belt  is  used,  there  is  not  such  perfect  contact 
between  the  pulley-face  and  the  belt,  due  to  the  rigidity  of  the  latter,  and 
more  work  is  necessary  to  bend  the  belt-fibres  than  when  a  thinner  and 
more  pliable  belt  is  used.  The  centrifugal  force  tending  to  throw  the  belt 
from  the  pulley  also  increases  with  the  thickness,  and  for  these  reasons  the 
width  of  a  double  belt  required  to  transmit  a  given  horse-power  when  used 
with  small  pulleys  is  generally  assumed  not  less  than  seven  tenths  the 
width  of  a  single  belt  to  transmit  the  same  power.  (Flather  on  "  Dynamom- 
eters and  Measurement  of  Power.") 

F.  W.  Taylor,  however,  finds  that  great  pliability  is  objectionable,  and 
favors  thick  belts  even  for  small  pulleys:  The  power  consumed  in  bending 
the  belt  around  the  pulley  he  considers  inappreciable.  According  to  Kan- 
kine's  formula  for  centrifugal  tension,  this  tension  is  proportional  to  the 
sectional  area  of  the  belt,  and  hence  it  does  not  increase  with  increase  of 
thickness  when  the  width  is  decreased  in  the  same  proportion,  the  sectional 
area  remaining  constant. 

Scott  A.  Smith  (Trans.  A.  S.  M.  E.,  x.  765)  says:  The  best  belts  are  made 
from  all  oak-tanned  leather,  ai'd  curried  with  the  use  of  cod  oil  and  tallow, 
all  to  be  of  superior  quality.  Such  belts  have  continued  in  use  thirty  to 
forty  years  when  used  as  simple  driving-belts,  driving  a  proper  amount  of 
power,  and  having  had  suitable  care.  The  flesh  side  should  not  be  run  to 
the  pulley-face,  for  the  reason  that  the  wear  from  contact  with  the  pulley 
should  come  on  the  grain  side,  as  that  surface  of  the  belt  is  much  weaker 
in  its  tensile  strength  than  the  flesh  side;  also  as  the  grain  is  hard  it  is  more 
enduring  for  the  wear  of  attrition;  further,  if  the  grain  is  actually  worn  off, 
then  the  belt  may  not  suffer  in  its  integrity  from  a  ready  tendency  of  the 
hard  grain  side  to  crack. 

The  most  intimate  contact  of  a  belt  with  a  pulley  comes,  first,  in  the 
smoothness  of  a  pulley -face,  including  freedom  from  ridges  and  hollows  left 
by  turning-tools;  second,  in  the  smoothness  of  the  surface  and  evenness  in 
the  texture  or  body  of  a  belt;  third, in  having  the  crown  of  the  driving  and  re- 
ceiving pulleys  exactly  alike, — as  nearly  so  as  is  practicable  in  a  commercial 
sense;  fourth,  in  having  the  crown  of  pulleys  not  over  J^"  for  a  24"  face,  tliat 
is  to  say,  that  the  pulley  is  not  to  be  over  y^"  larger  in  diameter  in  its  centre; 
fifth,  in  having  the  crown  other  than  two  planes  meeting  at  the  centre; 
sixth,  the  use  of  any  material  on  or  in  a  belt,  in  addition  to  those  necessarily 
used  in  the  currying  process,  to  keep  them  pliable  or  increase  their  tractive 
quality,  should  wholly  depend  upon  the  exigencies  arising  in  the  use  of 
belts:  non-use  is  safer  than  over-use;  seventh,  with  reference  to  the  lacing 
of  belts,  it  seems  to  be  a  good  practice  to  cut  the  ends  to  a  convex  shape  by 
using  a  former,  so  that  there  may  be  a  nearly  uniform  stress  on  the  lacing 
through  the  centre  as  compared  with  the  edges.  For  a  belt  10"  wide,  the 
centre  of  each  end  should  recede  1/10". 

Lacing  of  Belts.— In  punching  a  belt  for  lacing,  use  an  oval  punch, 
the  longer  diameter  of  the  punch  being  parallel  with  the  sides  of  the  belt. 
Punch  two  rows  of  holes  in  each  end,  placed  zigzag.  In  a  3-in.  belt  there 
should  be  four  holes  in  each  end— two  in  each  row.  In  a  6-inch  belt,  seven 
holes— four  in  the  row  nearest  the  end.  A  10-inch  telt  should  have  nine 
holes.  Theedge  of  the  holes  should  not  come  nearer  than  %  of  an  inch  from 
the  sides,  nor  %  of  an  inch  from  the  ends  of  the  belt.  The  second  row  should 
be  at  least  1^4  inches  from  the  end.  On  wide  belts  these  distances  should 
be  even  a  little  greater. 

Begin  to  lace  in  the  centre  of  the  belt  and  take  care  to  keep  the  ends 
exactly  in  line,  and  to  lace  both  sides  with  equal  tightness.  The  lacing 
should  not  be  crossed  on  the  side  of  the  belt  that  runs  next  the  pulley.  In 
taking  up  belts,  observe  the  same  rules  as  putting  on  new  ones. 

Setting  a  Belt  on  Quarter-twist.— A  belt  must  run  squarely  on  to 
the  pulley.  To  connect  with  a  belt  two  horizontal  shafts  at  right  angles 
with  each  other,  say  an  engine-shaft  near  the  floor  with  a  line  attached  to 
the  ceiling,  will  require  a  quarter-turn.  First,  ascertain  the  central  point 
on  the  face  of  each  pulley  at  the  extremity  of  the  horizontal  diameter  where 
the  belt,  will  leave  the  pulley,  and  then  set  that  point  on  the  driven  pulley 
plumb  over  the  corresponding  point  on  the  driver.  This  will  cause  the  belt 
to  run  squarely  on  to  each  pulley,  and  it  will  leave  at  an  angle  greater  or 
less,  according  to  the  size  of  the  pulleys  and  their  distance  from  each  otner. 


884 

In  quarter-twist  belts,  in  order  that  the  belt  may  remain  on  the  pulleys^ 
the  central  plane  on  each  pulley  must  pass  through  the  point  of  delivery  of 
the  other  pulley.  This  arrangement  does  not  admit  of  reversed  motion. 

To  find  the  Length  of  Belt  required  for  two  given 
Pulleys. — When  the  length  cannot  be  measured  directly  by  a  tape-line] 
the  following  approximate  rule  may  be  used  :  Add  the  diameter  of  the  twq 
pulleys  together,  divide  the  sum  by  2,  and  multiply  the  quotient  by  3*4,  and! 
add  the  product  to  twice  the  distance  between  the  centres  of  the  shafts] 
(See  accurate  formula  below.) 

To  find  the  Angle  of  the  Arc  of  Contact  of  a  Belt.— Divide 
the  difference  between  the  radii  of  the  two  pulleys  in  inches  by  the  distance 
between  their  centres,  also  in  inches,  and  in  a  table  of  natural  sines  find  thd 
angle  most  nearly  corresponding  with  the  quotient.  Multiply  this  angle  by 
2,  and  add  the  product  to  180°  for  the  angle  of  contact  with  the  larger 
pulley,  or  subtract  it  from  180°  for  the  smaller  pulley. 

Or,  let  R  =  radius  of  larger  pulley,  r  =  radius  of  smaller; 
L  —  distance  between  centres  of  the  pulleys; 
a  =  angle  whose  sine  is  (R  —  r)  -*-  L. 

Arc  of  contact  with  smaller  pulley  =  180°  —  2a; 
"    larger  pulley    =  180°  -f-  2a. 

To  find  the  Length  of  Belt  in  Contact  with  the  Pulley. 

For  the  larger  pulley,  multiply  the  angle  a,  found  as  above,  by  .0349,  to  tht 
product  add  3.1416,  and  multiply  the  sum  by  the  radius  of  the  pulley.  Oi 
length  of  belt  in  contact  with  the  pulley 

=  radius  X  (TT  -f-  .0349a)  =  radius  X  n(l  +Sj)« 

For  the  smaller  pulley,  length  =  radius  X  (7r-.0349a)=  radius  X  ir(l  -  |M  • 

The  above  rules  refer  to  Open  Belts.  The  accurate  formula  for  lengtl 
of  an  open  belt  is, 

Length  =,  »fl(l  +  ^)  +  »r(l  -  ^)  +  2L  cos  a 

=  R(n  +  .0349a)  +  r(n  -  .0349a)  +  2L  cos  a, 

in  which  R  =  radius  of  larger  pulley,  r  =  radius  of  smaller  pulley, 

L  =•  distance  between  centres  of  pulleys,  and  a  =  angle  whose  sine  is 

(R  -  r)  -s-  L  ;  cos  a  =   VL*  -  (R  -  r)2  -+-  L. 
For  Crossed  Belts  the  formula  is 

Length  of  belt  =-.  irR^l  +  ^)  +  *rr(l  +  ^)  +  2L  cos  /3, 
=  (R  -f  r)  X  (IT  +  .03490)  -f-  2L  cos  /3, 


in  which  0  =  angle  whose  sine  is  (R  -f-  r)  -f-  /-/;  cos  /3  =  |/L2  —  (R  -f-  r)2  -*-  L 

To  find  the  Length  of  Belt  when  Closely  Rolled.  The  sun: 
of  the  diameter  of  the  roll,  and  of  the  eye  in  inches,  X  the  number  of  turn: 
made  by  the  belt  and  by  .1309,  =  length  of  the  belt  in  feet 

To  find  the  Approximate  Weight  of  Belts  —Multiply  tin 
length  of  belt,  in  feet,  by  the  width  in  inches,  and  divide  the  product  by  If 
for  single,  and  8  for  double  belt. 

Relations  of  the  Size  and  Speeds  of  Driving  and  Driven 
Pulleys.— The  driving  pulley  is  called  the  driver,  D,  and  the  driven  pulley 
the  driven,  d.  If  the  number  of  teeth  in  gears  is  used  instead  of  diameter,  it 
these  calculations,  number  of  teeth  must  be  substituted  wherever  diainetei 
occurs.  R  =  revs,  per  inin.  of  driver,  r  —  revs,  per  min.  of  driven. 

D  =  dr-t-R, 
Diam.  of  driver  =  diam.  of  driven  x  revs,  of  driven  -*-  revs,  of  driver. 

d  =  DR  -5-  r; 
Diam.  of  driven  =  diam.  of  driver  X  revs,  of  driver  -*-  revs,  of  driven. 

R  =  dr-t-D\ 
Revs,  of  driver  =  revs,  of  driven  x  diam.  of  driven  -*-  diam.  of  driver. 


MISCELLANEOUS   NOTES   ON   BELTING. 


885 


Revs,  of  driven  =  revs,  of  driver  x  diam.  of  driver  -4-  diam.  of  driven. 

Kvils  of  Tight  Belts.  (Jones  and  Laughlins.)— Clamps  with  powerful 
screws  are  often  used  to  put  on  belts  with  extreme  tightness,  and  with  most 
injurious  strain  upon  the  leather.  They  should  be  very  judiciously  used  for 
horizontal  belts,  which  should  be  allowed  sufficient  slackness  to  move  with  a 
loose  undulating  vibration  on  the  returning  side,  as  a  test  that  they  have  no 
more  strain  imposed  than  is  necessary  simply  to  transmit  the  power. 

On  this  subject  a  New  England  cotton-mill  engineer  of  large  experience, 
savs'  I  believe  that  three  quarters  of  the  trouble  experienced  in  broken  pul- 
I  leys  'hot  boxes,  etc.,  can  be  Traced  to  the  fault  of  tight  belts.  The  enormous 
:  and  useless  pressure  thus  put  upon  pulleys  must  in  time  break  them,  if  they 
are  made  in  any  reasonable  proportions,  besides  wearing  out  the  whole  out- 
fit and  causing  heating  and  consequent  destruction  of  the  bearings.  Below 
are  some  figures  showing  the  power  it  takes  in  average  modern  mills  with 
first-class  shafting,  to  drive  the  shafting  alone  : 


Shafting  Alone. 

Shafting  Alone. 

Mill, 
No. 

Whole 
Load, 
H.P. 

Horse- 
power. 

Per  cent 
of  whole. 

Mill, 

No. 

Load, 
H.P. 

Horse- 
power. 

Per  cent 
of  whole. 

1 

199 

51 

25.6 

5 

759 

172.6 

22.7 

2 

472 

111.5 

23.6 

6 

235 

84.8 

36.1 

3 

486 

134 

27.5 

7 

670 

262.9 

39.2 

4 

677 

190 

28.1 

8 

677 

182 

26.8 

These  may  be  taken  as  a  fair  showing  of  the  power  that  is  required  in 
many  of  our  best  mills  to  drive  shafting.  It  is  unreasonable  to  think  that  all 
that 'power  is  consumed  by  a  legitimate  amount  of  friction  of  bearings 
and  belts.  I  know  of  no  cause  for  such  a  loss  of  power  but  tight  belts.  These, 
when  there  are  hundreds  or  thousands  in  a  mill,  easily  multiply  the  friction 
on  the  bearings,  and  would  account  for  the  figures. 

Sag  of  Belts.—  In  the  location  of  shafts  that  are  to  be  connected  with 
each  other  by  belts,  care  should  be  taken  to  secure  a  proper  distance  one 
from  the  other.  This  distance  should  be  such  as  to  allow  of  a  gentle  sag  to 
the  belt  when  in  motion. 

A  general  rule  may  be  stated  thus:  Where  narrow  belts  are  to  be  run  over 
small  pulleys  15  feet'is  a  good  average,  the  belt  having  a  sag  of  IV^to  2  inched. 

For  larger  belts,  working  on  larger  pulleys,  a  distance  of  20  to  25  feet  does 
well,  with  a  sag  of  2^  to  4  inches. 

For  main  belts  working  on  very  large  pulleys,  the  distance  should  be  25  to 
30  feet,  the  belts  working  well  with  a  sag  of  4  to  5  inches. 

If  too  great  a  distance  is  attempted,the  belt  will  have  an  unsteady  flapping 
motion,  which  will  destroy  both  the  belt  and  machinery. 

Arrangement  of  Belts  and  Pulleys.— If  possible  to  avoid  it,  con- 
nected shatts  should  never  be  placed  one  directly  over  the  other,  as  in  such 
case  the  belt  must  be  kept  very  tight  to  do  the  work.  For  this  purpose  belts 
should  be  carefully  selected  of  well-stretched  leather. 

It  is  desirable  that  the  angle  of  the  belt  with  the  floor  should  not  exceed 
45°  It  is  also  desirable  to  locate  the  shafting  and  machinery  so  that  belts 
should  run  off  from  each  shaft  in  opposite  directions,  as  this  arrangement 
will  relieve  the  bearings  from  the  friction  that  would  result  when  the  belts  all 
pull  one  way  on  the  shaft. 

In  arranging  the  belts  leading  from  the  main  line  of  shafting  to  the 
counters,  those  pulling  in  an  opposite  direction  should  be  placed  as  near 
each  other  as  practicable,  while  those  pulling  in  the  same  direction  should  be 
separated.  This  can  often  be  accomplished  by  changing  the  relative  posi- 
tions of  the  pulleys  on  the  counters.  By  this  procedure  much  of  the  friction 
on  the  journals  may  be  avoided. 

If  possible,  machinery  should  be  so  placed  that  the  direction  of  the  belt 
motion  shall  be  from  the  top  of  the  driving  to  the  top  of  the  driven  pulley, 
when  the  sag  will  increase  the  arc  of  contact. 

The  pulley  should  be  a  little  wider  than  the  belt  required  for  the  work. 


886  BELTING. 

The  motion  of  driving  should  run  with  and  not  against  the  laps  of  the  belts 

Tightening  or  guide  pulleys  should  be  applied  to  the  slack  side  of  belts  and 
near  the  smaller  pulley. 

Jones  &  Laughlins,  in  their  Useful  Information,  say:  The  diameter  of  the 
pulleys  should  be  as  large  as  can  be  admitted,  provided  they  will  not  pro- 
duce a  speed  of  more  than  3750  feet  of  belt  motion  per  minute. 

They  also  say:  It  is  better  to  gear  a  mill  with  small  pulleys  and  run  them 
at  a  high  velocity,  than  with  large  pulleys  and  to  run  them  slower.  A  mill 
thus  geared  costs  less  and  has  a  much  neater  appearance  than  with  laree 
heavy  pulleys. 

M.  Arthur  Achard  (Proc.  Inst.  M.  E.,  Jan.  1881,  p.  62)  says:  When  the  belt 
is  wide  a  partial  vacuum  is  formed  between  the  belt  and  the  pulley  at  a, 
high  velocity.  The  pressure  is  then  greater  than  that  computed  from  the 
tensions  in  the  belt,  and  ths  resistance  to  slipping  is  greater.  This  has  the 
advantage  of  permitting  a  greater  power  to  be  transmitted  by  a  given  belt, 
and  of  diminishing  the  strain  on  the  shafting. 

On  the  other  hand,  some  writers  claim  that  the  belt  entraps  air  between 
itself  and  the  pulley,  which  tends  to  diminish  the  friction,  and  reduce  the 
tractive  force.  On  this  theory  some  manufacturers  perforate  the  belt  with 
numerous  holes  to  let  the  air  escape. 

Care  of  Belts.— Leather  belts  should  be  well  protected  against  water 
and  even  loose  steam  and  other  moisture. 

Belts  of  coarse,  loose  leather  wiU  do  better  service  in  dry  warm  places-  for 
wet  or  moist  situations  the  finest  and  firmest  leather  should  be  used.  (J  B 
Hoyt  &  Co.) 

Do  not  allow  oil  to  drip  upon  the  belts.    Jt  destroys  the  life  of  the  leather. 

Leather  belting  cannot  safely  stand  above  110°  of  heat. 

Strength  ot  Belting.— The  ultimate  tensile  strength  of  belting  does 
not  generally  enter  as  a  factor  in  calculations  of  power  transmission. 

The  strength  of  the  solid  leather  in  belts  is  from  2000  to  5000  Ibs.  per  square 
inch;  at  the  lacings,  even  if  well  put  together,  only  about  1000  to  1500.  If 
riveted,  the  joint  should  have  half  the  strength  of  the  solid  belt.  The  work- 
ing strain  on  the  driving  side  is  generally  taken  at  not  over  one  third  of  the 
strength  of  the  lacing,  or  from  one  eighth  to  one  sixteenth  of  the  strength 
of  the  solid  belt.  Dr.  Hartig  found  that  the  tension  in  practice  varied  from 
30  to  532  Ibs.  per  square  inch,  averaging  273  Ibs. 

Adhesion  Independent  of  Diameter.  (Schultz  Belting  Co.)— 
1.  The  adhesion  of  the  belt  to  the  pulley  is  the  same— the  arc  or  number  of 
degrees  of  contact,  aggregate  tension  or  weight  being  the  same— without 
reference  to  width  of  belt  or  diameter  of  pulley. 

2.  A  belt  will  slip  just  as  readily  on  a  pulley  four  feet  in  diameter  as  it  will 
on  a  pulley  two  feet  in  diameter,  provided  the  conditions  of  the  faces  of  the 
pulleys,  the  arc  of  contact,  the  tension,  and  the  number  of  feet  the  belt 
travels  per  minute  are  the  same  in  both  cases. 

3.  A  belt  of  a  given  width,  and  making  any  given   number  of  feet  per 
minute,  will  transmit  as  much  power  running  on  pulleys  two  feet  in  diam 
eter  as  it  will  on  pulleys  four  feet  in  diameter,  provided  the  arc  of  contact, 
tension,  and  conditions  of  pulley  faces  are  the  same  in  both  cases 

4.  To  obtain  a  greater  amount  of  power  from  belts  the  pulleys  may  be 
covered  with  leather;  this  will  allow  the  belts  to  run  very  slack  and  give  25% 
more  durability. 

Endless  Belts.— If  the  belts  are  to  be  endless,  they  should  be  put  on 
and  drawn  together  by  "  belt  clamps  "  made  for  the  purpose.  If  the  belt  is 
made  endless  at  the  belt  factory,  it  should  never  be  run  on  to  the  pulleys,  lest 
the  irregular  strain  spring  the  belt.  Lift  out  one  shaft,  place  the  belt  on  the 
pulleys,  and  force  the  shaft  back  into  place. 

Belt  Data.— A  fly-wheel  at  the  Amoskeag  Mfg.  Co.,  Manchester,  N.  H., 
30  feet  diameter,  110  inches  face,  running  61  revolutions  per  minute,  carried 
two  heavy  double-leather  belts  40  inches  wide  each,  and  one  24  inches  wide 
The  engine  indicated  1950  H.P.,  of  which  probably  1850  H.P.  was  transmitted 
by  the  belts.  The  belts  were  considered  to  be  heavily  loaded,  but  not  over- 
taxed. 
30  X  3.14  X  104  X  61 

— jg50 —  =  323  feet  per  minute  for  1  H.P.  per  inch  of  width. 

Samuel  Webber  (Am.  Mo.ch.,  Feb.  22,  1894)  reports  a  case  of  a  belt  30 
inches  wide,  %  inch  thick,  running  for  six  years  at  a  velocity  of  3900  feet  per 
minute,  on  to  a  pulley  5  feet  diameter,  and  transmit  ting  556  H  P.  This  gives 
a  velocity  of  210  feet  per  minute  for  1  H.P.  per  inch  of  width.  By  Mr.  Nagle's 


TOOTHED-WHEEL    GEARING.  88? 

table  of  riveted  belts  this  belt  would  be  designed  for  332  H.P.  By  Mr.  Taylor's 
rule  it  would  be  used  to  transmit  only  123  H.P. 

The  above  may  be  taken  as  examples  of  what  a  belt  may  be  made  to  do, 
but  they  should  not  be  used  as  precedents  in  designing.  It  is  not  stated  how 
much  power  was  lost  by  the  journal  friction  due  to  over-tightening  of  these 
belts. 

Belt  Dressings.— We  advise,  when  the  belt  is  pliable,  and  only  dry  and 
husky,  the  application  of  blood-warm  tallow.  This  applied,  and  dried  in  by 
heat  of  fire  or  sun,  will  tend  to  keep  the  leather  in  good  working  condition. 
The  oil  of  the  tallow  passes  into  the  tallow  of  the  leather,  serving  to  soften 
it,  and  the  stearine  is  left  on  the  outside,  to  fill  the  pores  and  leave  a.  smooth 
surface.  The  addition  of  resin  to  the  tallow  for  belts,  if  used  in  wet  or  damp 
places,  will  be  of  service  and  help  preserve  their  strength.  Belts  which  have 
become  hard  and  dry  should  have  an  application  of  neat's-foot  or  liver  oil, 
mixed  with  a  small  quantity  of  resin.  This  prevents  the  oil  from  injuring  the 
belt  and  helps  to  preserve  it.  There  should  not  be  so  much  resin  as  to  leave 
the  belt  sticky.  ( J.  B.  Hoyt  &  Company.) 

Belts  should  not  be  soaked  in  water  before  oiling,  and  penetrating  oils 
should  but  seldom  be  used,  except  occasionally  when  a  belt  gets  very  dry 
and  husky  from  neglect.  It  may  then  be  moistened  a  little,  andjhave  neat's- 
foot  oil  applied.  Frequent  applications  of  such  oils  to  a  new  belt  render  the 
leather  soft  and  flabby,  thus  causing  it  to  stretch,  and  making  it  liable  to 
run  out  of  line.  A  composition  of  tallow  and  oil,  with  a  little  resin  or  bees- 
wax, is  better  to  use.  Prepared  castor-oil  dressing  is  good,  and  may  be 
applied  with  a  brush  or  rag  while  the  belt  is  running.  (Alexander  Bros.) 

Cement  for  Cloth  or  Leather.  (Moles worth. )—l 6  parts  gutta- 
percha,  4  india-rubber,  2  pitch,  1  shellac,  2  linseed-oil,  cut  small,  melted  to- 
gether and  well  mixed. 

Rubber  Belting.— The  advantages  claimed  for  rubber  belting  are 
perfect  uniformity  in  width  and  thickness;  it  will  endure  a  great  degree  of 
heat  and  cold  without  injury;  it  is  also  specially  adapted  for  use  in  damp  or 
wet  places,  or  where  exposed  to  the  action  of  steam;  it  is  very  durable,  and 
has  great  tensile  strength,  and  when  adjusted  for  service  it  has  the  most  per- 
fect hold  on  the  pulleys,  hence  is  less  liable  to  slip  than  leather. 

Never  use  animal  oil  or  grease  on  rubber  belts,  as  it  will  greatly  injure  and 
soon  destroy  them. 

Rubber  belts  will  be  improved,  and  their  durability  increased,  by  putting 
on  with  a  painter's  brush,  and  letting  it  dry,  a  composition  made  of  equal 
parts  of  red  lead,  black  lead,  French  yellow,  and  litharge,  mixed  with  boiled 
linseed-oil  and  japan  enough  to  make  it  dry  quickly.  The  effect  of  this  will 
be  to  produce  a  finely  polished  surface.  If,  from  dust  or  other  cause,  the 
belt  should  slip,  it  should  be  lightly  moistened  on  the  side  next  the  pulley 
with  boiled  linseed-oil.  (From  circulars  of  manufacturers.) 


GEARING. 

TOOTHED-WHEEL,  QEARING. 

Pitch,  Pitch-circle,  etc.— If  two  cylinders  with  parallel  axes  are 
pressed  together  and  one  of  them  is  rotated  on  its  axis,  it  will  drive  the  other 
by  means  of  the  friction  between  the  surfaces.  The  cylinders  may  be  con- 
sidered as  a  pair  of  spur-wheels  with  an  infinite  number  of  very  small  teeth. 
If  actual  teeth  are  formed  upon  the  cylinders,  making  alternate  elevations 
and  depressions  in  the  cylindrical  surfaces,  the  distance  between  the  axes 
remaining  the  same,  we  have  a  pair  of  gear-wheels  which  will  drive  one  an- 
other by  pressure  upon  the  faces  of  the  teeth,  if  the  teeth  are  properly 
shaped.  In  making  the  teeth  the  cylindrical  surface  may  entirely  disap- 
pear, but  the  position  it  occupied  may  still  be  considered  as  a  cylindrical 
surface,  which  is  called  the  "  pitch-surface,"  and  its  trace  on  the  end  of  the 
wheel,  or  on  a  plane  cutting  the  wheel  at  right  angles  to  its  axis,  is  called 
the  "  pitch-circle  "  or  *'  pitch-line."  The  diameter  of  this  circle  is  called  the 
pitch-diameter,  and  the  distance  from  the  face  of  one  tooth  to  the  corre- 
sponding face  of  the  next  tooth  on  the  same  wheel,  measured  on  an  arc  of 
the  pitch-circle,  is  called  the  "  pitch  of  the  tooth,"  or  the  circular  pitch. 

If  two  wheels  having  teeth  of  the  same  pitch  are  geared  together  so  that 
their  pitch-circles  touch,  it  is  a  property  of  the  pitch-circles  that  their  diam- 
eters are  proportional  to  the  number  of  teeth  in  the  wheels,  and  vice  verso,; 


888 


GEARING. 


thus,  if  one  wheel  is  twice  the  diameter  (measured  on  the  pitch-circle)  of  the 
other,  it  has  twice  as  many  teeth.  If  the  teeth  are  properly  shaped  the 
linear  velocity  of  the  two  wheels  are  equal,  and  the  angular  velocities,  or 
speeds  of  rotation,  are  inversely  proportional  to  the  number  of  teeth  and  to 
the  diameter.  Thus  the  wheel  that  has  twice  as  many  teeth  as  the  other 
will  revolve  just  half  as  many  times  in  a  minute. 

The  "pitch,"  or  distance  measured  on  an  arc  of  the  pitch-circle  from  the 
face  of  one  tooth  to  the  face  of  the  next,  consists  of  two  parts— the  "  thick- 
ness "  of  the  tooth  and  the  "space"  between  it  and  the  next  tooth.  The 
space  is  larger  than  the  thickness  by  a  small  amount  called  the  "  back- 
lash," which  is  allowed  for  imperfections  of  workmanship.  In  finely  cut 
gears  the  backlash  may  be  almost  nothing. 

The  length  of  a  tooth  in  the  direc- 
tion of  the  radius  of  the  wheel  is 
called  the  "depth,"  and  this  is  di- 
vided into  two  parts:  First,  the 
"addendum,"  the  height  of  the  tooth 
above  the  pitch  line;  second,  the 
"dedendum,"  the  depth  below  the 
pitch  line,  which  is  an  amount  equal 
to  the  addendum  of  the  mating  gear. 
The  depth  of  the  space  is  usually 
given  a  little  "clearance"  to  allow 
for  inaccuracies  of  workmanship, 
especially  in  cast  gears. 

Referring  to  Fig.  153,  pi,  pi  are  the 
pitch-lines,  al  the  addendum-line,  rl 
the  root-line  or  dedendum-line,  cl 
the  clearance-line,  and  b  the  back- 


FIG.  153. 


lash.    The  addendum  and  dedendum  are  usually  made  equal  to  each  other. 

No.  of  teeth  3.1416 

Diametral  pitch  =  - 


Circular  pitch  = 


diam.  of  pitch-circle  in  inches 
diam.  X  3.1416  3.1416 


circular  pitch' 


No.  of  teeth          diametral  pitch* 

Some    writers   use    the   term    diametral   pitch   to   mean 
circular  pitch 


diam. 


No.  of  teeth 
,  but  the  first  definition  is  the  more  common  and  the  more 


3.1416 

convenient.    A  wheel  of  12  in.  diam.  at  the  pitch-circle,  with  48  teeth  is  48/12 
=  4  diametral  pitch,  or  simply  4  pitch,    The  circular  pitch  of  the  same 

.     12  X  3.1416          ,..-„  3.1416         r.OK.  . 

wheel  is  —  -  =   .7854,  or  —    —  =  .7854  in. 

48  4 

Relation  of  Diametral  to  Circular  Pitch. 


Diama- 
tral 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

Circular 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

Circular 
Pitch. 

Diame- 
tral 
Pitch. 

1 

3.  142  in. 

11 

.286  in. 

3 

1.047 

15/16 

3  351 

ILj' 

2.094 

12 

.262 

2\r£ 

1.257 

% 

3.590 

2 

1.571 

14 

.224 

2 

1.571 

13/16 

3.867 

1.396 

16 

.196 

1% 

1.676 

34 

4.189 

2Vi> 

1.257 

18 

.175 

1% 

1.795 

11/16 

4.570 

03^ 

1.142 

20 

.157 

jG 

1.933 

% 

5.027 

3 

1.047 

22 

.143 

\\^ 

2.094 

9/16 

5.585 

31^ 

.898 

24 

.131 

1  7/16 

2.185 

& 

6.283 

4 

.785 

26 

.121 

1% 

2.285 

7/16 

7.181 

5 

.628 

28 

.112 

1  5/16 

2.394 

8.378 

6 

.524 

30 

.105 

\YA 

2.513 

5/16 

10.053 

7 

.449 

32 

.098 

1  3/16 

2.646 

M 

12.566 

8 

.393 

36 

.087 

\\fa 

2.793 

3/16 

16.755 

9 

.349      \      40 

.079 

1  1/16 

2.957 

Hi 

25.133 

10 

.314      |      48 

.065 

1 

3.142 

1/16 

50.266 

diam.  X  3.1416                      circ.  pitch  x  No.  of  teeth 
Since  circular  Ditch  —  —  -.  —  .    diam.  —  —  . 

No.  of  teeth    '  3.1416 

which  always  brings  out  the  diameter  as  a  number  with  an  inconvenient 


TOOTHED-WHEEL   GEARIKG. 


889 


fraction  if  the  pitch  is  in  even  inches  or  simple  fractions  of  an  inch.  By  the 
diametral-pitch  S3rstem  this  inconvenience  is  avoided.  The  diameter  may 
he  in  even  inches  or  convenient  fractions,  and  the  number  of  teeth  is  usually 
;ui  even  multiple  of  the  number  of  inches  in  the  diameter. 
Diameter  of  Pitch-line  of  Wheels  from  10  to  100  Teetli 
of  1  in.  Circular  Pitch. 


o| 

1= 

of 

la 

2  & 

Is 

o| 

Is 

of 

Is 

ll 

is 

H 

a 

HH 

Q 

5'" 

H 

P 

& 

p 

H 

5 

10 

3.183 

26 

8.276 

•41 

13.051 

56 

17.825 

71 

22.600 

86 

27.375 

11 

3.501 

27 

8.594 

42 

13.369 

57 

18.144 

72 

22.918 

87 

27.693 

12 

3.820 

28 

8.913 

43 

13.687 

58 

18.462 

73 

22.236 

88 

28.011 

13 

4.138 

29 

9.231 

44 

14.006 

59 

18.781 

74 

23.555 

89 

28.329 

14 

4.456 

30 

9.549 

45 

14.324 

60 

19.099 

75 

23.873 

90 

28.648 

15 

4.775 

31 

9.868 

46 

14.642 

61 

19.417 

76 

24.192 

91 

28.966 

16 

5.093 

32 

10.186 

47 

14.961 

62 

19.735 

77 

24.510 

92 

29.285 

17 

5.411 

33 

10.504 

48 

15.279 

63 

20.054 

78 

24.828 

93 

29.603 

IS 

5.730 

34 

10.823 

49 

15.597 

64 

20.372 

79 

25.146 

94 

29.921 

i'J  !     6.048 

35 

11.141 

50 

15.915 

65 

20.690 

80 

25.465 

95 

30.239 

20 

6.366 

36 

11.459 

51 

16.234 

66 

21.008 

81 

25.783 

96 

30.558 

21 

6.685 

37 

11.777 

52 

16.552 

67 

21.327 

82 

26.101 

97 

30.876 

22 

7.003 

38 

12.096 

53 

16.870 

68 

21.645 

83 

26.419 

98 

31.194 

23 

7.321 

39 

12  414 

54 

17.189 

69 

21.963 

84 

26.738 

99 

31.512 

24 

7.639 

40 

12.732 

55 

17.507 

70 

22.282 

85 

27.056 

100 

31.831 

25 

7.958 

For  diameter  of  wheels  of  any  other  pitch  than  1  in.,  multiply  the  figures 
in  the  table  by  the  pitch.  Given  the  diameter  and  the  pitch,  to  find  the  num- 
ber of  teeth.  Divide  the  diameter  by  the  pitch,  look  in  the  table  under 
diameter  for  the  figure  nearest  to  the  quotient,  and  the  number  of  teeth  will 
be  found  opposite. 

Proportions  of  Teeth.    Circular  Pitch  =  1. 


1. 

2. 

3. 

4. 

5. 

6. 

Depth  of  tooth  above  pitch-line.  .  . 
"      "      below  pitch-line... 
Working  depth  of  tooth  

.35 
.40 
.70 
.75 
.05 
.45 
.54 
.10 

.30 
.40 
.60 
.70 
.10 
.45 
.55 
.09 

.37 
.43 
.73 
.80 
.07 
.47 
.53 
.07 
.47 

.33 

!66 
.75 

A5 
.55 
.10 
.45 

.30 
.40 

!70 

.'475 
.525 
.05 
.70 

.30 
.35 

'.65 

!485 
.515 
.03 
.65 

Total  depth  of  tooth  

Clearance  at  root 

Thickness  of  tooth  

Width  of  space 

Backlash  

Thickness  of  rim 

7. 

8. 

9. 

10.* 
1-s-P 

1.157-r-P 

2-7-  P 
2.157-HP 
.157-i-P 
1.51-^-Pto 
1.57^-P 
1.57  -=-P  to 
1.63-*-P 
0  to  0.6-r-P 

Depth  of  tooth  above  pitch-line... 
"        "      "     below  pitch-line.  .. 
Working  depth  of  tooth 

.25  to  .33 
.35  to  .42 

.30 

.35+.  08" 

.318 
.369 
.637 
.687 
.04  to  .05 

.48  to  .5-j 

.52  to  .5-j 
.0   to  .04 

Total  depth  of  tooth  

.6   to  .75 

.65+  .08" 

Clearance  at  root          ... 

Thickness  of  tooth        

.48  to  .485 

.52  to  .515 
.04  to  .03 

.48-.  03" 

.52-f.03" 
.044-.  06" 

Width  of  space 

Backlash     

*  In  terms  of  diametral  pitch. 

AUTHORITIES.— 1.  Sir  Wm.  Fairbairn.  2,  3.  Clark,  R.  T.  D.;  "used  by  en- 
gineers in  good  practice.1'1  4.  Molesworth.  5,  6.  Coleinan  Sellers  :  5  for 
cast.  6  for  cut  wheels.  7, 8.  Unwin.  9,  10.  Leading  American  manufacturers 
of  cut  gears. 

The  Chorda!  Pitch  (erroneously  called  "  true  pitch "  by  some 
authors)  is  the  length  of  a  straight  line  or  chord  drawn  from  centre  to 
centre  of  two  adjacent  teeth.  The  term  is  now  but  little  used 


890 


Chordal  pitch  =  diam,  of  pitch-circle  X  sine  of 


180° 


— p.      Chordal 
No.  of  teeth 

pitch  of  a  wheel  of  10  in.  pitch  diameter  and  10  teeth,  10  X  sin  18°  =  3.0902 
in.  Circular  pitch  of  same  wheel  =  3.1416.  Chordal  pitch  is  used  with  chain 
or  sprocket  wheels,  to  conform  to  the  pitch  of  the  chain. 

Formulae  for  Determining  the  Dimensions  of  Small  Gears. 

(Brown  &  Sharpe  Mfg.  Co.) 

P  =  diametral   pitch,  or  the  number  of  teeth  to  one  inch  of  diameter  of 
pitch- circle; 


D'  =  diameter  of  pitch  circle. 

D  =  whole  diameter  

jV  =  number  of  teeth .   ... 

F  =  velocity  


df  =  diameter  of  pitch-circle , 

d  =  whole  diameter 

n  —  number  of  teeth  

v  —  velocity . 


'Larger 
Wheel. 


Smaller 
Wheel. 


These  wheels 

run 
together. 


a  —  distance  between  the  centres  of  the  two  wheels; 

b  —  number  of  teeth  in  both  wheels; 

t  —  thickness  of  tooth  or  cutter  on  pitch-circle; 

s  =  addendum ; 
J)"—  working  depth  of  tooth; 

/  =  amount   added  to  depth  of  tooth  for  rounding  the  corners  and  for 

clearance ; 
D"4-f  —  whole  depth  of  tooth; 

TT  =  3.1416. 

P'  =  circular  pitch,  or  the  distance  from  the  centre  of  one  tooth  to  the 
centre  of  the  next  measured  on  the  pitch-circle. 

Formulae  for  a  single  wheel: 


P  = 


_  N+2  t 
D     ' 


D'  = 


DX  N  . 

N+2  ' 


p=4; 


P'  — • 

"  P' 


»& 


D  = 


N 


D"  =  -|=2s; 

N      PD'; 
N  =  PD-  2; 

j&     ? 

s  =  ^  -  ^  =  .3183P'; 

_  jy      D 

N         N+2' 
'4V  =  ^(l+^)  =  .3685P' 

D-  D'+~ 


t- 


1.57 


Formulae  for  a  pair  of  wheels: 


b  =  2aP; 

AT  —    UV  • 

NV 

n  = ; 

v    ' 

bv 

-  v+V 
bV 


PD'V 


n 

NV 
; 

n 

nv  - 

N  ' 


D  = 


b 
2a(n  -f  2) 

—       ; 


-F+F1  -^7+F' 

The  following  proportions  of  gear  wheels  are  recommended  by  Prof.  Cole 

man  Sellers.    (Stevens  Indicator,  April,  1892.) 


TOOTHED-WHEEL   GEARING. 


891 


Proportions  of  Gear-wheels. 


Inside  of  Pitch-line. 

Width  of  Space. 

Diametra] 
Pitch. 

Circular 
Pitch. 

Outside  of 
Pitch-line. 
PX  .3 

For  Cast  or 
Cut  Bevels 
or  for  Cast 
Spurs. 

PX.4 

For  Cut 
Spurs. 
PX  .35 

For  Cast 
Spurs  or 
Bevels. 
P  X  .525 

For  Cut 
Bevels  or 
Spurs. 

Px  .01 

34 

.075 

.100 

.088 

.131 

.128 

12 

.2618 

.079 

.105 

.092 

.137 

.134 

10 

.31416 

.094 

.126 

.11 

.165 

.16 

% 

.113 

.150 

.131 

.197 

.191 

8 

.3927 

.118 

.157 

.137 

.206 

.2 

7 

.4477 

.134 

.179 

.157 

.235 

,228 

iz 

.15 

.20 

.175 

.263 

.255 

6 

.  5236    ' 

.157 

.209 

.183 

.275 

.267 

9/16 

.169 

.225 

.197 

.295 

.287 

% 

.188 

.25 

.219 

.328 

.319 

5 

.62832 

.188 

.251 

.22 

.33 

.32 

*H 

.225 

.3 

.263 

.394 

.383 

4 

.7854 

.236 

.314 

.275 

.412 

.401 

% 

.263 

.35 

.307 

.459 

.446 

1 

.3 

.4 

.35 

.525 

.51 

3 

1.0472 

.314 

.419 

.364 

.55 

.534 

\\^ 

.338 

.45 

.394 

.591 

.574 

2% 

1.1424 

.343 

.457 

.40 

.6 

.583 

i/4 

.375 

.5 

.438 

.656 

.638 

2V£ 

1.25661 

.377 

.503 

.44 

.66 

.641 

1% 

.413 

.55 

.481 

,722 

.701 

i  Jhlj 

.45 

.6 

.525 

.783 

.765 

2 

1.5708 

.471 

.628 

.55 

.825 

.801 

.525 

.7 

.613 

.919 

.893 

2  4 

.6 

.8 

.7 

.05 

1.02 

1V*> 

2.0944 

.628 

.838 

.733 

.1 

1.068 

' 

2/4 

.675 

.i) 

.788 

.181 

1.148 

gi/c 

.75 

1.0 

.875 

.313 

•-1.275 

2% 

.825 

1,1 

.963 

.444 

1.403 

3 

.9 

1.2 

1.05 

.575 

1.53 

1 

3.1416 

.942 

1,257 

1.1 

.649 

1.602 

3J4 

.975 

1.3 

1.138 

.706 

1.657 

3g 

1.05 

1.4 

1.225 

.838 

1.785 

Thickness  of  rim  below  root  =  depth  of  tooth. 

Width  of  Teeth.— The  widtl.  of  the  faces  of  teeth  is  generally  made 
from  2  to  3  times  tiie  circular  pitch  —  from  6.28  to  9.42  divided  by  the  diam- 
etral pitch.  There  is  no  standard  rule  for  vadth. 

The  following  sizes  arc  given  i:i  a  stock  list  of  cut  gears  in  "Grant's 
Gears:11 

Diametral  pitch 34  6  8  12  16 

Face,  inches 3  and  4    2^    1%  and  2    l^andl^   %  and  1    ^  and  % 

The  Walker  Mf;;.  Co.  give: 

Circular  pitch,  in'..  ^  %  %  ys  1  1^  2  2J^  3  4  5  G 
Face,  in \y±  1^  1^  2  2^  4^  6  7^  9  12  16  20 

Rules  for  Calculating  the  Speed  of  Ocars  and  Pulleys.  - 

The  relations  of  the  size  and  speed  of  driving  and  driven  gear  wheels  are 
the  same  as  those  of  belt  pulleys.  In  calculating  for  gears,  multiply  or 
divide  by  the  diameter  of  the  pitch-circle  or  by  the  number  of  teeth,  as 
may  be  required.  In  calculating  for  pulleys,  multiply  or  divide  by  their 
diameter  in  inches. 

If  D  =  dinm.  of  driving  wheel,  d  diam.  of  driven,  ft  —  revolutions  per 
minute  of  driver,  r  —  revs,  per  min.  of  drven. 

ft  =  rd  -f-  D;     r  -  RD  H-  d ;    D  ----=  dr  -*-  ft;    d  =  DR  H-  r. 

If  N      number  of  teeth  of  driver  and  n  «  number  of  teeth  of  driven, 
N  =  nr  -*-  ft;    n  —  IIP.  H-  r\    J?  =  rn  •*•  N\    r  =  ft  A"  -*-  n. 


892  GEARING. 

To  flnd  the  number  of  revolutions  of  the  last  wheel  at  the  end  of  a  train 
of  spur-wheels,  all  of  which  are  in  a  line  and  mesh  into  one  another,  when 
the  revolutions  of  the  first  wrheel  and  the  number  of  teeth  or  the  diameter 
of  the  first  and  last  are  given:  Multiply  the  revolutions  of  the  first  wheel  b.y 
its  number  of  teeth  or  its  diameter,  and  divide  the  product  by  the  number 
of  teeth  or  the  diameter  of  the  last  wheel. 

To  find  the  number  of  teeth  in  each  wheel  for  a  train  of  spur-wheels, 
each  to  have  a  given  velocity:  Multiply  the  number  of  revolutions  of  the 
driving-wheel  by  its  number  of  teeth,  and  divide  the  product  by  the  number 
of  revolutions  each  wheel  is  to  make. 

To  find  the  number  of  revolutions  of  the  last  wheel  in  a  train  of  wheels 
and  pinions,  when  the  revolutions  of  the  first  or  driver,  and  the  diameter, 
the  teeth,  or  the  circumference  of  all  the  drivers  and  pinions  are  given: 
Multiply  the  diameter,  the  circumference,  or  the  number  of  teeth  of  all  the 
driving-wheels  together,  and  this  continued  product  by  the  number  of  revo- 
lutions of  the  first  wheel,  and  divide  this  product  by  the  continued  product 
of  the  diameter,  the  circumference,  or  the  number  of  teetli  of  all  the  driven 
wheels,  and  the  quotient  will  be  the  number  of  revolutions  of  the  last  wheel. 

EXAMPLE.—  1.  A  train  of  wheels  consists  of  four  wheels  eadi  12  in.  diameter 
of  pitch-circle,  and  three  pinions  4,  4,  and  3  in.  diameter.  The  large  wheels 
are  the  drivers,  and  the  first  makes  36  revs,  per  min.  Required  the  speed 
of  the  last  wheel. 


2.  What  is  the  speed  of  the  first  large  wheel  if  the  pinions  are  the  drivers, 
the  3-in.  pinion  being  the  first  driver  and  making  36  revs,  per  min.  ? 

36  X  3  X  4  X  4 

- 


Milling  Cutters  for  Interchangeable  Gears.—  The  Pratt  & 
Whitney  Co.  make  a  series  of  cutters  for  cutting  epicycloidal  teeth.    The 
number  of  cutters  to  cut  from  a  pinion  of  12  teeth  to  a  rack  is  24  for  each 
pitch  coarser  than  10.    The  Brown  &  Sharpe  Mfg.  Co.  make  a  similar  series. 
and  also  a  series  for  involute  teeth,  in  which  eight  cutters  are  made  for 
each  pitch,  as  follows: 
No  .............          1.  2.  3.  4.  5.  6.  7.  8. 

Will  cut  from        135  55  35  26  21  17  14  12 

to  Rack       134  54  34  25  20  16  13 

FORMS  OF  THE  TKUTIff. 

In  order  that  the  teeth  of  wheels  and  pinions  may  run  together  smoothly 
and  with  a  constant  relative  velocity,  it  is  necessary  that  their  working 
faces  shall  be  formed  of  certain  curves  called  odontoid*.  The  essential 
property  of  these  curves  is  that  when  two  teeth  are  in  contact  the  common 
normal  to  the  tooth  curves  at  their  point  of  contact  must  pass  through  the 
pitch-point,  or  point  of  contact  of  the  two  pitch  circles.  Two  such  curves 
are  in  common  use  —  the  cyloid  and  the  involute. 

The  Cycloidal  Tooth,—  In  Fig.  154  let  PL  and  pi  be  the  pitch-circles 
of  two  gear-wheels;  (rC'and  yc  are  two  equal  gener&ting-circles,  whose  radii 
should  be  taken  as  not  greater  than  one  half  of  the  radius  of  the  smaller 
pitch-circle.  If  the  circle  gc  be  rolled  to  the  left  on  the  larger  pitch-circle 
PL,  the  point  O  will  describe  an  epicycloid,  oejgh.  It'  the  other  generating- 
circle  GO  be  rolled  to  the  right  on  PL,  the  point  O  will  describe  a  hypocy- 
cloid  oabcd.  These  two  curves,  which  are  tangent  at  O,  form  the  two  parts 
of  a  tooth  curve  for  a  gear  whose  pitch-circle  is  PL.  The  upper  part  oh  is 
called  the  face  and  the  lower  part  od  is  called  the  flank,  If  the  same  circles 
be  rolled  on  the  other  pitch-circle  pi,  they  will  describe  the  curve  for  a  tooth 
of  the  gearpZ,  which  will  work  properly  with  the  tooth  on  PL. 

The  cycloidal  curves  may  be  drawn  without  actually  rolling  the  generat- 
ing-circle,  as  follows:  On  the  line  PL,  from  O,  step  off  and  mark  equal  dis- 
tances, as  1,  2,  3,  4,  etc.  From  1,  2,  3,  etc.,  draw  radial  lines  toward  the  centre 
of  PL,  and  from  6,  7,  8,  etc.,  draw  radial  lines  from  the  same  centre,  but  be- 
yond PL.  With  the  radius  of  the  generating-circle,  and  with  centres  suc- 
cessively placed  on  these  radial  lines,  draw  arcs  of  circles  tangent  to  PL  at 
1  2  3,  6  7  8,  etc.  With  the  dividers  set  to  one  of  the  equal  divisions,  as  Olt 


FORMS   OF   THE   TEETH. 


893 


step  off  la  and  6e;  step  off  two  such  divisions  on  the  circle  from  2  to  b,  and 
from  7  io/;  three  such  divisions  from  3  to  c,  and  from  8  togr;  and  so  on,  thus 
locating  the  several  points  abcdH  and  efgk,  and  through  these  points  draw 
the  tooth  curves. 

The  curves  for  the  mating  tooth  on  the  other  wheel  may  be  found  in  like 
manner  by  drawing  arcs  of  the  generating-circle  tangent  at  equidistant 
points  on  the  pitch-  circle  pi. 

The  tooth  curve  of  the  face  oh  is  limited  by  the  addendum-line  r  or  rlt 


FIG.  154.  ? 

and  that  of  the  flank  oH  by  the  root  curve  R  or  R^.  R  and  r  represent  the 
root  and  addendum  curves  for  a  large  number  of  small  teeth,  and  R^r  the 
like  curves  for  a  small  number  of  large  teeth.  The  form  or  appearance  of 
the  tooth  therefore  varies  according  to  the  number  of  teeth,  while  the  pitch 
circle  and  the  generating-circle  may  remain  the  same. 

In  the  cycloidal  system,  in  order  that  a  set  of  wheels  of  different  diam- 
eters but  equal  pitches  shall  all  correctly  work  together,  it  is  necessary  that 
the  generating-circle  used  for  the  teeth  'of  all  the  wheels  shall  be  the  same, 
and  it  should  have  a  diameter  not  greater  than  half  the  diameter  of  the  pitch- 
line  of  the  smallest  wheel  of  the  set.  The  customary  standard  size  of  the 
generating-circle  of  the  cycloidal  system  is  one  having  a  diameter  equal  to 
the  radius  of  the  pitch-circle  of  a  wheel  having  12  teeth.  (Some  gear- 
makers  adopt  15  teeth.)  This  circle  gives  a  radial  flank  to  the  teeth  of  a 
wheel  having  12  teeth.  A  pinion  of  10  or  even  a  smaller  number  of  teeth 
can  be  made,  but  in  that  case  the  flanks  will  be  undercut,  and  the  tooth  will 
not  be  as  strong  as  a  tooth  with  radial  flanks.  If  in  any  case  the  describing 
circle  be  half  the  size  of  the  pitch-circle,  the  flanks  will  be  radial;  if  it  be 
less,  they  will  spread  out  toward  the  root  of  the  tooth,  giving  a  stronger 
form;  but  if  greater,  the  flanks  will  curve  in  toward  each  other,  whereby  the 
teeth  become  weaker  and  difficult  to  make. 

In  some  cases  cycloidal  teeth  for  a  pair  of  gears  are  made  with  the  gener- 
ating-circle of  each  gear,  having  a  radius  equal  to  half  the  radius  of  its  pitch- 
circle.  In  this  case  each  of  the  gears  will  have  radial  flanks.  This  method 
makes  a  smooth  working  gear,  but  a  disadvantage  is  that  the  wheels  are 
not  interchangeable  with  other  wheels  of  the  same  pitch  but  different  num- 
bers of  teeth. 


894 


GEARING. 


The  rack  in  the  cycloidal  system  is  equivalent  to  a  wheel  with  an  infinite 
number  of  teeth.  'The  pitch  is  equal  to  the  circular  pitch  of  the  mating 
gear.  Both  faces  and  flanks  are  cycloids  formed  by  rolling  the  generating- 
circle  of  the  mating  gear-wheel  on  each  side  of  the  straight  pitch-line  of 
the  rack. 


\ 


Another  method  of  drawing  the  cycloida*  curves  is  shown  in  Fig.  155.  It 
is  known  as  the  method  of  tangent  arcs.  The  generating-c  rles,  as  before, 
are  drawn  with  equal  radii,  tho  length  of  the  radius  being  less  than  half  the 
radius  of  pi,  the  smaller  pitch-circle.  Equal  divisions  1,  2,  3,  4,  etc.,  are 
marked  off  on  the  pitch-circles  and  divisions  of  the  same  length  stepped  off 
on  one  of  the  generating-circles,  as  oabc.  etc.  From  the  points  1,  2,  3, 4,  5  on 
the  line  po,  with  radii  successively  equal  to  the  chord  distances  oa,  ob,  oc, 
orf,  oe,  draw  the  five  small  arcs  F.  A  line  drawn  through  the  outer  edges  of 
these  small  arcs,  tangent  to  them  all,  will  be  the  hypocycloidal  curve  for  the 
flank  of  a  tooth  below  the  pitch-line  pi.  From  the  points  1,  2,  3,  etc.,  on  the 
line  oZ,  with  radii  as  before,  draw  the  small  arcs  G.  A  line  tangent  to  these 
arcs  will  be  the  epicycloid  for  the  face  of  the  same  tooth  for  which  the  flank 
curve  has  already  been  drawn.  In  the  same  way,  from  centres  on  the  line 
P0,  and  oL,  with  the  same  radii,  the  tangent  arcs  JaTand  Kmay  be  drawn, 
which  will  give  the  tooth  for  the  gear  whose  pitch-circle  i^  PL. 

If  the  generating-circle  had  a  radius  just  one  half  of  the  radius  of  pi,  the 
hypocycloid  F  would  be  a  straight  line,  and  the  flank  of  the  tooth  would 
have  been  radial. 

The  Involute  Tootli.—  In  drawing  the  involute  tooth  curve,  the 
angle  of  obliquity,  or  the  angle  which  a  common  tangent  to  the  teeth,  when 
they  are  in  contact  at  the  pitch-point,  makes  with  a  line  joining  the  centres 
of  the  wheels,  is  first  arbitrarily  determined.  It  is  customary  to  take  it  at  15° 
The  pitch-lines  pi  and  PL  being  drawn  in  contact  at  O,  the  line  of  obliquity 
A  B  is  drawn  through  O  normal  to  a  common  tangent  to  the  tooth  curves,  or 
at  the  given  angle  of  obliquity  to  a  common  tangent  to  the  pitch-circles.  In 


FORMS    OF   THE   TEETH. 


895 


the  cut  the  angle  is  20°.  From  the  centres  of  the  pitch-circles  draw  circles  c 
and  d  tangent,  to  the  line  AB.  These  circles  are  called  base-lines  or  base- 
circles,  from  which  the  involutes  jPand  K  are  drawn.  By  laying  off  conven- 
ient distances  0,  1,2,  3,  which  should  each  be  less  than  1/10  of  The  diameter 
of  the  base-circle,  small  arcs  can  be  drawn  with  successively  increasing- 
radii,  which  will  form  the  involute.  The  involute  extends  from  the  points  F 


P 


FIG.  156. 

and  K  down  to  their  respective  base-circles,  where  a  tangent  to  the  invo- 
lute becomes  a  raclir.s  of  the  circle,  and  the  remainders  of  the  tooth  curves, 
as  G  and  //,  are  radial  straight  lines. 

In  the  involute  system  the  customary  standard  form  of  tooth  is  one 
having  an  angle  of  obliquity  of  15°  (Brown  and  Sfaarpe  use  14^°),  an  adden- 
dum of  about  one  third  the  ciicular  pitch,  and  a  clearance  of  about  one 
eighth  of  the  addendum.  In  this  system  the  smallest  gear  of  a  set  has  12 
teeth,  this  being  the  smallest  number  of  teeth  that  will  gear  together  when 
made  \vith  this  angle  of  obliquity.  In  gears  with  less  than  30  teeth  the 
points  of  the  teeth  must  be  slightly  rounded  over  to  avoid  interference  (see 
Grant's  Teeth  of  Gears).  All  involute  teeth  of  the  same  pitch  and  with  the 
same  angle  of  obliquity  work  smoothly  together.  The  rack  to  gear  with  an 
involute-tootliod  wheel  has  straight  faces  on  its  teeth,  which  make  an  angle 
with  the  middle  line  of  the  tooth  equal  to  the  angle  of  obliquity,  or  in  the 
standard  form  the  fnces  are  inclined  at  an  angle  of  30°  with  each  other. 

To  draiv  the  teeth  of  a  rack  which  is  to  gear  with  an  involute  wheel  (Fig. 
157).— Let  AB  be  the  pitch-line  of  the  rack  and  AI-  II'=the  pitch.  Through 


FIG.  157. 


the  pitch 

line.  From  Id. aw  IK  perpendicular  to  AB  equal  to  the  greatest  addendum 
in  the  set  of  wheelc  of  t'io  given  pitch  and  obliquity  plus  an  allowance  for 
clearance  equal  to  y  of  the  addendum.  Through  K,  parallel  to  AB,  draw 
the  clearance-line.  ^ho  fronts  of  the  teeth  are  planes  perpendicular  to  EF, 
and  the  backs  are  planes  inclined  at  the  same  angle  to  AB  in  the  contrary 
direction  The  outer  half  of  the  working  face  AE  may  be  slightly  curved. 
Mr.  Grant  makes  it  a  circular  arc  drawn  from  a  centre  on  the  pitch-line 


896 


GEARING. 


with  a  radius  =  2.1  inches  divided  by  the  diametral  pitch,  or  .67  in.  X  cir- 
cular pitch. 

To  Draw  an  Angle  of  15°  without  using  a  Protractor.— From  C,  on  the 

line  AC,  with  radius  AC,  draw 
an  arc  AB,  and  from  A,  with 
the  same  radius,  cut  the  arc  at 
B.  Bisect  the  arc  BA  by  draw- 
ing small  arcs  at  D  from  A  and  B 
as  centres,  with  the  same  radius, 
which  must  be  greater  than  one 
half  of  AB.  Join  DC,  cutting  BA 
at  E.  The  angle  EGA  is  30°.  Bi- 
sect the  arc  AE  in  like  manner, 
and  the  angle  FCA  will  be  15°. 

A  property  of  involute-toothed 
wheels  is  that  the  distance  between 
the  axes  of  a  pair  of  gears  may  be 
altered  to  a  considerable  extent 
without  interfering  with  their  ac- 
tion. The  backlash  is  therefore 
variable  at  will,  and  may  be  ad- 


FIG.  158. 


justed  by  moving  the  wheels  farther  from  or  nearer  to  each  other,  and  may 
thus  be  adjusted  so  as  to  be  no  greater  than  is  necessary  to  prevent  jam- 
ming of  the  teeth. 

The  relative  merits  of  cycloidal  and  involute-shaped  teeth  are  still  a  sub- 
ject of  dispute,  but  there  is  an  increasing  tendency  to  adopt  the  involute 
tooth  for  all  purposes. 

Clark  (R.  T.  D.,  p.  734)  says  :  Involute  teeth  have  the  disadvantage  of 
being  too  much  inclined  to  the  radial  line,  by  which  an  undue  pressure  is 
exerted  on  the  bearings. 

Unwin  (Elements  of  Machine  Design,  8th  ed.,  p.  265)  says  :  The  obliquity 
of  action  is  ordinarily  alleged  as  a  serious  objection  to  involute  wheels.  Its 
importance  has  perhaps  been  overrated. 

George  B.  Grant  (Am.  Mack.,  Dec.  26,  1885)  says  : 

1.  The  work  done  by  the  friction  of  an  involute  tooth  is  always  less  than 
the  same  work  for  any  possible  epicycloidal  tooth. 

2.  With  respect  to  work  done  by  friction,  a  change  of  the  base  from  a 
gear  of  12  teeth  to  one  of  15  teeth  makes  an  improvement  for  the  epicycloid 
of  less  than  one  half  of  one  per  cent. 

3.  For  the  12  tooth  system  the  involute  has  an  advantage  of  1  1/5  per 
cent,  and  for  the  15-tooth  system  an  advantage  of  %  per  cent. 

4.  That  a  maximum  improvement  of  about  one  pe  r  cent  can  be  accom- 
plished by  the  adoption  of  any  possible  nori  -interchangeable  radial  flank 
tooth  in  preference  to  the  12-tooth  interchangeable  system. 

5.  That  for  gears  of  very  few  teeth  the  involute  has  a  decided  advantage. 

6.  That  the  common  opinion  among  millwrights  and  the  mechanical  i.<ul> 
lie  in  general  in  favor  of  the  epicycloid  is  a  prejudice  that  is  founded  on 
long-continued  custom,  and  not  on  an  intimate  knowledge  of  the  properties 
of  that  curve. 

Wilfred  Lewis  (Proc.  Engrs.  Club  of  Phila.,  vol.  x..  1893)  says  a  strong 
reaction  in  favor  of  the  involute  system  is  in  progress,  and  he  believes  thai 
an  involute  tooth  of  22^°  obliquity  will  finally  supplant  all  other  forms. 

Approximation  by  Circular  Arcs.— Having  found  the  form  oj 
the  actual  tooth-curve  on  the  drawing-board,  circular  arcs  maybe  found  bj 
trial  which  will  give  approximations  to  the  true  curves,  and  these  may  b*?» 


J59. 


FORMS   OF   THE   TEETH. 


897 


used  in  completing  the  drawing  and  the  pattern  of  the  gear-wheels.  The 
root  of  the  curve  is  connected  to  the  clearance  by  a  fillet,  which  should  be 
as  large  aspossible  to  give  increased  strength  to  the  tooth,  provided  it  is  non 
large  enough  to  cause  interference. 

Molesworth  gives  the  following  method  of  construction  by  circular  arcs  • 

From  the  radial  line  at  the  edge  of  the  tooth  on  the  pitch-line,  lay  off  the 
line  HKa,t  an  angle  of  75°  with  the  radial  line;  on  this  line  will  be  the  cen- 
tres of  the  root  AB  and  the  point  EF.  The  lines  struck  from  these  centres 
are  shown  in  thick  lines.  Circles  drawn  through  centres  thus  found  will 
give  the  lines  in  which  the  remaining  centres  will  be.  The  radius  DA  for 
striking  the  root  AB  is  =  pitch  -f-  the  thickness  of  the  tooth.  The  radius 
CE  for  striking  the  point  of  the  tooth  EF  =  the  pitch. 

George  B.  Grant  says  :  It  is  sometimes  attempted  to  construct  the  curve 
by  some  handy  method  or  empirical  rule,  but  such  methods  are  generally 
worthless. 

Stepped  Gears.  -  -Two  gears  of  the  same  pitch  and  diameter  mounted 
side  l>y  side  on  the  same  shaft  will  act  as  a  single  gear.  If  one  gear  is  keyed 
on  the  shaft  so  that  the  teeth  of  the  two  wheels  are  not  in  line,  but  the 
teeth  of  one  wheel  slightly  in  advance  of  the  other,  the  two  gears  form  a 
stepped  gear.  If  mated  with  a  similar  stepped  gear  on  a  parallel  shaft  the 
number  of  teeth  in  contact  will  be  twice  as  great  as  in  an  ordinary  gear, 
which  will  increase  the  strength  of  the  gear  and  its  smoothness  of  action. 

Twisted  Teeth..— If  a  great  number  of  very  thin  gears  were  placed 
together,  one  slightly  in  advance  of  the  other,  they  would  still  act  as  a 
stepped  gear.  Continuing  the  subdivision  until  the 


thickness  of  each  separate  gear  is  infinitesimal,  the 
faces  of  the  teeth  instead  of  being  in  steps  take  the 
form  of  a  spiral  or  twisted  surface,  and  we  have  a 
twisted  gear.  The  twist  may  take  any  shape,  and  if  it  is 
in  one  direction  for  half  the  width  of  the  gear  and  in  the 
opposite  direction  for  the  other  half,  we  have  what  is 
known  as  the  herring-bone  or  double  helical  tooth.  The 
obliquity  of  the  twisted  tooth  if  twisted  in  one  direction 
causes  an  end  thrust  on  the  shaft,  but  if  the  herring- 
bone twist  is  used,  the  opposite  obliquities  neutralize 
each  other.  This  form  of  tooth  is  much  used  in  heavy 
rolling-mill  practice,  where  great  strength  and  resistance 
to  shocks  are  necessary.  They  are  frequently  made  of 
steel  castings  (Fig.  160).  The  angle  of  the  tooth  with  a 
line  parallel  to  the  axis  of  the  gear  is  usually  30°.  FlG- 

Spiral  Gears.— If  a  twisted  gear  has  a  uniform  twist  it  becomes  a 
spiral  gear.  The  line  in  which  the  pitch-surface  intersects  the  face  of  the 
tooth  is  part  of  a  helix  drawn  on  the  pitch-surface.  A  spiral  wheel  may  be 
made  with  only  one  helical  tooth  wrapped  around  the  cylinder  several 
times,  in  which' it  becomes  a  screw  or  worm.  If  it  has  two  or  three  teeth 
so  wrapped,  it  is  a  double-  or  triple-threaded  screw  or  worm.  A  spiral-gear 
meshing  into  a  rack  is  used  to  drive  the  table  of  some  forms  of  planing- 
machine. 

Worm-gearing.— When  the  axes  of  two  spiral  gears  are  at  right 
angles,  and  a  wheel  of  one,  two,  or  three  threads  works  with  a  larger  wheel 
of  many  threads,  it  becomes  a  worm-gear,  or  endless  screw,  the  smaller 


FIG.  161. 

wheel  or  driver  being  called  the  worm,  and  the  larger,  or  driven  wheel,  the 
worm-wheel.  With  this  arrangement  a  high  velocity  ratio  may  be  obtained 
with  a  single  pair  of  wheels.  For  a  one-threaded  wheel  the  velocity  ratio  is 


898 


GEARING. 


the  number  of  teeth  in  the  worm-wheel.  The  worm  and  wheel  are  com- 
monly so  constructed  that  the  worm  will  drive  the  wheel,  but  the  wheel  will 
not  drive  the  worm. 

To  find  the  diameter  of  a  worm-wheel  at  the  throat,  number  of  teeth  and 
pitch  of  the  worm  being  given:  Add  2  to  the  number  of  teeth,  multiply  the 
sum  by  0.3183,  and  by  the  pitch  of  the  worm  in  inches. 

To  find  the  number  of  teeth,  diameter  at  throat  and  pitch  of  worm  being 
given:  Divide  3.1416  times  the  diameter  by  the  pitch,  and  subtract  2  from 
the  quotient. 

In  Fig.  161  ab  is  the  diam.  of  the  pitch-circle,  cd  is  the  diam.  at  the  throat. 
EXAMPLE.— Pitch  of  worm  *4  in.,  number  of  teeth  70,  required  the  diam. 
at  the  throat.    (70  f  2)  X  .3183  X  .25  =  5.73  in. 

Teeth  of  Oevel- wheels,  (Rankine's  Machinery  and  Millwork.)— 
The  teeth  of  a  bevel -wheel  have  acting  surfaces  of  the  conical  kind,  gen- 
erated by  the  motion  of  a  line  traversing  the  apex  of  the  conical  pitch- 
surface,  while  a  point  in  it  is  carried  round  the  traces  of  the  teeth  upon  a 
spherical  surface  described  about  that  apex. 

The  operations  of  drawing  the  traces  of  the  teeth  of  bevel-wheels  exactly, 
whether  by  involutes  or  by  rolling  curves,  are  in  every  respect  analogous  to 
those  for  drawing  the  traces  of  the  teeth  of  spur-wheels;  except  that  in  the 
case  of  bevel- wheels  all  those  operations  are  to  be  performed  on  the  surface 
of  a  sphere  described  about  the  apex,  instead  of  on  a  plane,  substituting 
poles  for  centres  and  great  circles  for  straight  lines. 

In  consideration  of  the  practical  difficulty,  especially  in  the  case  of  large 
wheels,  of  obtaining  an  accurate  spherical  surface,  and  of  drawing  upon  it 
when  obtained,  the  following  approximate  method,  proposed  originally  by 
Tredgold,  is  generally  used: 

Let  O,  Fig.  162,  be  the  common  apex  of  the  pitch-cones.  OBL  OB'I,  of  a 
pair  of  bevel- wheels;  OC,  OC',  the  axes  of  those  cones;  Ol  their  line  of  con- 
tact. Perpendicular  to  OI  draw 
AIA',  cutting  the  axes  in  A,  A'\ 
make  the  outer  rims  of  the  patterns 
and  of  the  wheels  portions  of  the 
cones  ABI,  A'B'I,  of  which  the  nar- 
row zones  occupied  by  the  teeth  will 
be  sufficiently  near  for  practical  pur- 
poses to  a  spherical  surface  described 
about  O.  As  the  cones  ABI,  A'B'I 
cut  the  pitch-cones  at  right  angles  in 
the  outer  pitch- circles  IB,  IB',  they 
may  be  called  the  normal  cones.  To 
find  the  traces  of  the  teeth  upon  the 
normal  cones,  draw  on  a  flat  surface 
circular  arcs,  ID,  ID',  with  the  radii 
AI,  A'l;  those  arcs  will  be  the  de- 
velopments of  arcs  of  the  pitch- 
circles  IB,  IB'  when  the  conical  sur- 
faces ABI,  A'B'I  are  spread  out  flat.  Describe  the  traces  of  teeth  for  the 
developed  arcs  as  for  a  pair  of  spur-wheels,  then  wrap  the  developed  arcs 
on  the  normal  cones,  so  as  to  make  them  coincide  with  the  pitch-circles,  and 
trace  the  teeth  on  the  conical  surfaces. 

For  formulas  and  instructions  for  designing  bevel-gears,  and  for  much  other 
valuable  information  on  the  subject  of  gearing,  see  "  Practical  Treatise  on 
Gearing,1"  and  "  Formulas  in  Gearing,'1  published  by  Brown  &  Sharpe  Mf  g 
Co.;  and  " Teeth  of  Gears,1'  by  George  B.  Grant,  Lexington,  Mass.  The 
student  may  also  consult  Rankine's  Machinery  and  Millwork,  Reuleaux's 
Constructor,  and  Unwinds  Elements  of  Machine  Design.  See  also  article  on 
Gearing,  by  C.  W.  MacCord  in  App.  Cyc.  Mech.,  vol.  ii. 

Annular  and  Differential  Gearing.  (S.  W.  Balch.,  Am.  Mfich., 
Aug.  24,  1893.)— In  internal  gears  the  sum  of  the  diameters  of  the  describing 
circles  for  faces  and  flanks  should  not  exceed  the  difference  in  the  pitch 
diameters  of  the  pinion  and  its  internal  gear.  The  sum  may  be  equal  to  this 
difference  or  it  may  be  less;  if  it  is  equal,  the  faces  of  the  teeth  of  each 
wheel  will  drive  the  faces  as  well  as  the  flanks  of  the  teeth  of  the  other 
wheel.  The  teeth  will  therefore  make  contact  with  each  other  at  two  points 
at  the  same  time. 

Cycloidal  tooth-curves  for  interchangeable  gears  are  formed  with  describ- 
ing circles  of  about  %  the  pitch  diameter  of  the  smallest  gear  of  the  series. 
To  admit  two  such  circles  between  the  pitch-circles  of  the  pinion  and  internal 


EFFICIENCY   OF   GEARING. 


899 


gear  th^  number  of  teeth  in  the  internal  gear  should  exceed  the  number  in 
the  pinion  by  12  or  more,  if  the  teeth  are  of  the  customary  proportions  and 
curvature  used  in  interchangeable  gearing. 

Very  often  a  less  difference  is  desirable,  and  the  teeth  may  be  modified  in 
several  ways  to  make  this  possible. 

First.  The  tooth  curves  resulting  from  smaller  describing  circles  may  be 
employed.  These  will  give  teeth  which  are  more  rounding  and  narrower  at 
their  tops,  and  therefore  not  as  desirable  as  the  regular  forms. 

Second.  The  tips  of  the  teeth  may  be  rounded  until  they  clear.  This  is  a 
cut-and-try  method  which  aims  at  modifying  the  teeth  to  such  outlines  as 
smaller  describing  circles  would  give. 

Third.  One  of  the  describing  circles  may  be  omitted  and  one  only  used, 
which  may  be  equal  to  the  difference  between  the  pitch -circles.  This  will 
permit  the  meshing  of  gears  differing  by  six  teeth.  It  will  usually  prove 
inexpedient  to  put  wheels  in  inside  gears  that  differ  ,by  much  less  than  12 
teeth. 

If  a  regular  diametral  pitch  and  standard  tooth  forms  are  determined  on, 
the  diameter  to  which  the  internal  gear-blank  is  to  be  bored  is  calculated  by 
subtracting  2  from  the  number  of  teeth,  and  dividing  the  remainder  by  the 
diametral  pitch. 

The  tooth  outlines  are  the  match  of  a  spur-gear  of  the  same  number  of 
teeth  and  diametral  pitch,  so  that  the  spur  gear  will  fit  the  internal  gear  as 
a  punch  fits  its  die,  except  that  the  teeth  of  each  should  fail  to  bottom  in 
the  tooth  spaces  of  the  other  by  the  customary  clearance  of  one  tenth  the 
thickness  of  the  tooth. 

Internal  gearing  is  particularly  valuable  when  employed  in  differential 
action.  This  is  a  mechanical  movement  in  which  one  of  the  wheels  is 
mounted  on  a  crank  so  that  its  centre  can  move  in  a  circle  about  the  centre 
of  the  other  wheel.  Means  are  added  to  the  device  which  restrain  the  wheel 
on  the  crank  from  turning  over  and  confine  it  to  the  revolution  of  the  crank. 

The  ratio  of  the  number  of  teeth  in  the  revolving  wheel  compared  with 
•die  difference  between  the  two  will  represent  the  ratio  between  the  revolv- 
ing wheel  and  the  crank-shaft  by  which  the  other  is  carried.  The  advan- 
tage in  accomplishing  the  change  of  speed  with  such  an  arrangement,  as 
L'omparecl  with  ordinary  spur-gearing,  lies  in  the  almost  entire  absence  of 
friction  and  consequent  wear  of  the  teeth. 

But  for  the  limitation  that  the  difference  between  the  wheels  must  not  be 
too  small,  the  possible  ratio  of  speed  might  be  increased  almost  indefinitely, 
and  one  pair  of  differential  gears  made  to  do  the  service  of  a  whole  train  of 
wheels.  If  the  problem  is  properly  worked  out  with  bevel-gears  this  limita- 
tion may  be  completely  set  aside,  and  external  and  internal  bevel-gears, 
differing  by  but  a  single  tooth  if  need  be,  made  to  mesh  perfectly  with  each 
other. 

Differential  bevel-gears  have  been  used  with  advantage  in  mowmg-ma- 
ohines.  A  description  of  their  construction  and  operation  is  given  by  Mr. 
Balcii  in  the  article  from  which  the  above  extracts  are  taken. 

EFFICIENCY  OF  GEARING. 

An  extensive  series  of  experiments  on  the  efficiency  of  gearing,  chiefly 
worm  and  spiral  gearing,  is  described  by  Wilfred  Lewis  in  Trans.  A.  S.  M.  E., 
vii.  273,  The  average  results  are  shown  in  a  diagram,  from  which  the  fol- 
lowing approximate  average  figures  are  taken  : 

EFFICIENCY  OP  SPUR,  SPIRAL,  AND  WORM  GEARING. 


Gearing. 

Pitch. 

Velocity  at  Pitch  line  in  feet  per  mm. 

3 

10 

40 

100 

200 

Spur  pinion  

45° 
30 
20 
15 

10 
7 
5 

.90 
.81 
.75 
.67 
.61 
.51 
.43 
.34 

.935 
.87 
.815 
.75 
.70 
.615 
.53 
.43 

.97 

.93 
.89 
.845 
.805 
.74 
.72 
.60 

.98 
.955 
.93 
.90 
.87 
.82 
.765 
.70 

.985 
.965 
.945 
.92 
.90 
.86 
.815 
.765 

Suirai  pinion 

44                     44 

44                     (4 

Spiral  pinion  or  worm  

900 


GEARIXG. 


The  experiments  showed  the  advantage  of  spur-gearing  over  all  other 
kinds  in  both  durability  and  efficiency.  The  variation  from  the  mean  results 
rarely  exceeded  5^  in  either  direction,  so  long  as  no  cutting  occurred,  but 
the  variation  became  much  greater  and  very  irregular  as  soon  as  cutting 
began.  The  loss  of  power  varies  with  the  speed,  the  pressure,  the  tempera- 
ture, and  the  condition  of  the  surfaces.  The  excessive  friction  of  worm  and 
spiral  gearing  is  largely  due  to  theend  thrust  on  the  collars  of  the  shaft. 
This  may  be  considerably  reduced  by  roller-bearings  for  the  collars. 

When  two  worms  with  opposite  spirals  run  iti  two  spiral  worm-gears  that 
also  work  with  each  other,  and  the  pressure  on  one  gear  is  opposite  that  on 
the  other,  there  is  no  thrust  on  the  shaft.  Even  with  light  loads  a  worm 
will  begin  to  heat  and  cut  if  run  at  too  high  a  speed,  the  limit  for  safe  work- 
ing being  a  velocity  of  the  rubbing  surfaces  of  200  to  300  ft.  per  minute,  the 
former  being  preferable  where  the  gearing  has  to  work  continuously.  The 
wheel  teeth  will  keep  cool,  as  they  form  part  of  a  casting  having  a  large 
radiating  surface;  but  the  worm  itself  is  so  small  that  its  heat  is  dissipated 
slowly.  Whenever  the  heat  generated  increases  faster  than  it  can  be  con- 
ducted and  radiated  away,  the  cutting  of  the  worm  may  be  expected  to  be- 
gin. A  low  efficiency  for  a  worm-gear  means  more  than  the  loss  of  power, 
since  the  power  which  is  lost  reappears  as  heat  and  may  cause  the  rapid 
destruction  of  the  worm. 

Unwin  (Elements  of  Machine  Design,  p.  294)  says  :  The  efficiency  is  greater 
the  less  the  radius  of  the  worm.  Generally  the  radius  of  the  worm  =  1.5  to 
3  times  the  pitch  of  the  thread  of  the  worm  or  the  circular  pitch  of  the 
worm-wheel.  For  a  one- threaded  worm  the  efficiency  is  only  2/5  to  J4; 
for  a  two-threaded  worm,  4/7  to  2/5;  for  a  three-threaded  worm,  %  to  y$>. 
Since  so  much  work  is  wasted  in  friction  it  is  not  surprising  that  the  wear 
is  excessive.  The  following  table  gives  the  calculated  efficiencies  of  worm- 
wheels  of  1,  2,  3,  and  4  threads  and  ratios  of  radius  of  worm  to  pitch  of  teeth 
of  from  1  to  6,  assuming  a  coefficient  of  friction  of  0.15  : 


No.  of 

Radius  of  Worm  -T-  Pitch. 

1 

m 

1^ 

1H 

2 

2^ 

3 

4 

6 

1 

.50 

.44 

.40 

.36 

.33 

.28 

.25 

.20 

.14 

2 

67 

.62 

.57 

.53 

.50 

.44 

.40 

.33 

.25 

3 

.75 

.70 

.67 

.63 

.60 

.55 

.50 

.43 

.33 

4 

.80 

.76 

.73 

.70 

.67 

.62 

.57 

.50 

.40 

STRENGTH  OF  GEAR-TEETH. 

The  strength  of  gear-teeth  and  the  horse-power  that  may  be  transmitted 
by  them  depend  upon  so  many  variable  and  uncertain  factors  that  it  is  not 
surprising  that  the  formulas  and  rules  given  by  different  writers  show  a 
wide  variation.  In  1879  John  H.  Cooper  (Jour.  Frank.  List.,  July,  1879) 
found  that  there  were  then  in  existence  about  48  well-established  rules  for 
horse-power  and  working  strength,  differing  from  each  other  in  extreme 
cases  about  500$.  In  1886  Prof.  Win.  Harkness  (Proc.  A.  A.  A.  S.  1886), 
from  an  examination  of  the  bibliography  of  the  subject,  beginning  in  1796, 
found  that  according  to  the  constants  and  formulae  used  by  various  authors 
there  were  differences  of  15  to  1  in  the  power  which  could  be  transmitted 
by  a  given  pair  of  geared  wheels.  The  various  elements  which  enter  into 
the  constitution  of  a  formula  to  represent  the  working  strength  of  a  toothed 
wheel  are  the  following:  1.  The  strength  of  the  metal,  usually  cast  iron,  which 
is  an  extremely  variable  quantity.  2.  The  shape  of  the  tooth,  and  espec- 
ially the  relation  of  its  thickness  at  the  root  or  point  of  least  strength  to  the 
pitch  and  to  the  length.  3.  The  point  at  which  the  load  is  taken  to  be  ap- 
plied, assumed  by  some  authors  to  be  at  the  pitch-line,  by  others  at  the 
extreme  end.  along  the  whole  face,  and  by  still  others  at  a  single  outer 
corner.  4.  The  consideration  of  whether  che  total  load  is  at  any  time  De- 
ceived by  a  single  tooth  or  whether  it  is  divided  between  two  teeth.  5.  The 
influence  of  velocity  in  causing  a  tendency  to  break  the  teeth  by  shock.  6. 
The  factor  of  safety  assumed  to  cover  all  the  uncertainties  of  the  other  ele- 
me nts  of  the  problem, 


STRENGTH   OF   GEAR-TEETH. 


901 


Prof.  Harkness,  as  a  result  of  his  investigation,  found  that  all  the  formulae 
on  the  subject  might  be  expressed  in  one  of  three  forms,  viz.: 

Horse-power  =  CVpJ,    or    CPp2,    or    CVp*f\ 

in  which  C  is  a  coefficient,  V  —  velocity  of  pitch-line  in  feet  per  second,  p  = 
pitch  in  inches,  and  /  —  face  of  tooth  in  inches. 

From  an  examination  of  precedents  he  proposed  the  following  formula 
for  cast-iron  wheels: 


H.P.  = 


He  found  that  the  teeth  of  chronometer  and  watch  movements  were  sub- 
ject to  stresses  four  times  as  great  as  those  which  any  engineer  would  dare 
to  use  in  like  prop'ortion  upon  cast-iron  wheels  of  large  size. 

It  appears  that  all  of  the  earlier  rules  for  the  strength  of  teeth  neglected 
the  consideration  of  the  variations  in  their  form;  the  breaking  strength,  as 
said  by  Mr.  Cooper,  being  based  upon  the  thickness  of  the  teeth  at  the  pitch- 
line  or  circle,  as  if  the  thickness  at  the  root  of  the  tooth  were  the  same  in 
all  cases  as  it  is  at  the  pitch-line. 

Wilfred  Lewis  (Proc.  Eug'rs  Club,  Phila.,  Jan.  1893;  Am.  Mach.,  June  22, 
1893)  seems  to  have  been  the  first  to  use  the  form  of  the  tooth  in  the  con- 
struction of  a  working  formula  and  table.  He  assumes  that  in  well-con- 
structed machinery  the  load  can  be  more  properly  taken  as  well  distributed 
across  the  tooth  than  as  concentrated  in  one  corner,  but  that  it  cannot  be 
safely  taken  as  concentrated  at  a  maximum  distance  from  the  root  less 
than  the  extreme  end  of  the  tooth.,  He  assumes  that  the  whole  loa,d  is 
taken  upon  one  tooth,  and  considers  the  tooth  as  a  beam  loaded  at  one  end, 
and  from  a  series  of  drawings  of  teeth  of  the  involute,  cycloiclal,  and  radial 
flank  systems,  determines  the  point  of  weakest  cross-section  of  each,  and 
the  ratio  of  the  thickness  at  that  section  to  the  pitch.  He  thereby  obtains 
the  general  formula, 

W=spfy; 

in  which  W  is  the  load  transmitted  by  the  teeth,  in  pounds;  s  is  the  safe 
working  stress  of  the  material,  taken  at  8000  Ibs.  for  cast  iron,  when  the 
working  speed  is  100  ft.  or  less  per  minute;  p  =  pitch; /  =  face,  in  inches; 
y  =  a  factor  depending  on  the  form  of  the  tooth,  whose  value  for  different 
cases  is  given  in  the  following  table: 


Factor  for  Strength,  y. 

Factor  for  Strength,  y. 

No.  of 

No  of 

Teeth. 

Involute 
20°  Obli- 
quity. 

Involute 
15°  and 
Cycloidal 

Radial 
Flanks. 

Teeth. 

Involute 
20°  Obli- 
quity. 

Involute 
15°  and 
Cycloidal 

Radial 
Flanks. 

12 

.078 

.067 

.052 

27 

.111 

.100 

.064 

13 

.083 

.070 

.053 

30 

.114 

102 

.065 

14 

.088 

.072 

.054 

34 

.118 

.104 

.066 

15 

.092 

.075 

.055 

38 

.122 

.107 

.067 

16 

.094 

.077 

.056 

43 

126 

.110 

.068 

17 

.096 

.080 

.057 

50 

;30 

.112 

.069 

18 

.098 

.083 

.058 

60 

134 

.114 

.070 

19 

.100 

.087 

.059 

75 

.138 

.116 

.071 

20 

.102 

.090 

.060 

100 

.142 

.118 

.072 

21 

.104 

.092 

.061 

150 

146 

.120 

.073 

28 

.106 

.094 

.062 

300 

.150 

122 

.074 

25 

.108 

.097 

.063 

Rack. 

.154 

.124 

.075 

SAFE  WORKING  STRESS,  s,  FOR  DIFFERENT  SPEEDS. 


Speed  of  Teeth  in 
ft.  per  minute. 

100  or 
less. 

SCO 

300 

600 

900 

1200 

1800 

2400 

Cast  iron 

8000 

6000 

4800 

4000 

3000 

2*00 

2000 

1700 

Steel  

20000 

15000 

12000 

10000 

7500 

6000 

5000 

4300 

902  GEARIKG. 

The  values  of  s  in  the  above  table  are  given  by  Mr.  Lewis  tentatively,  in 
the  absence  of  sufficient  data  upon  which  to  base  more  definite  values,  but 
they  have  been  found  to  give  satisfactory  results  in  practice. 

Mr.  Lewis  gives  the  following  example  to  illustrate  the  use  of  the  tables: 
Let  it  be  required  to  find  the  working  strength  of  a  12-  toothed  pinion  of  1- 
inch  pitch,  2J^-inch  face,  driving  a  wheel  of  60  teeth  at  100  feet  or  less  per 
minute,  and  let  the  teeth  be  of   the  20-degree  involute 
form.    In  the  formula  W  =  spfy  we  have  for  a  cast-iron 
pinion  s  =  8000,  pf  =  2  5,  and  y  =.078;  and  multiplying  these 
'  values  together,  we  have  W'—  1560  pounds.  For  'the  wheel 
we  have  y  =  .134  and  W  =  2680  pounds. 

The   cast-iron    pinion    is,    therefore,    the    measure    of 
strength;   but  if   a  steel  pinion  be  substituted   we  have 
s  =  20,000    and  W  =  3900    pounds,  in  which  combination 
the  wheel   is  the  weaker,  and  it  therefore  becomes  the 
,        /  measure  of  strength. 

^1=L/  \        For  bevel-wheels  Mr.  Lewis  gives  the  following,  rcfer- 

----  N    ring  to   Fjg    10e.     D  _  jarge    diameter    of    bevel;     d  = 
small  diameter  of  bevel;   p  —  pitch  at   large  diameter; 
n  =  actual  number  of  teeth;  /  =  face  of  bevel:  N=  for- 
FlG.  163.  mative  number  of  teeth  =  n  X  secant  a,  or  the  number 

corresponding  to  radius  R  ;  y  =  factor  depending  upon 
shape  of  teeth  and  formative  number  JV;  W  —  working  load  on  teeth. 

7)3  —  d3  d 

w  =  *Pfv  _  &)'•>   or,  more  simply,   W  =  spfy—< 


dH 
' 


which  gives  almost  identical  results  when  d  is  not  less  than  %  D,  as  is  the 
case  in  good  practice. 

In  Am.  Much.,  June  22,  1893,  Mr.  Lewis  gives  the  following  formulae  for 
the  working  strength  of  the  three  systems  of  gearing,  which  agree  very 
closely  with  those  obtained  by  use  of  the  table: 

For  involute,  20°  obliquity,          W  =  sp/(^.154  -  :—J  ; 

/  684  \ 

For  involute  15°,  and  cyc'oida1,  W  =  spf  ^  .124  --  —  J  ; 

For  radial  flank  system,  W  =  spf  (.075  -  —  )  ; 

in  which  the  factor  within  the  parenthesis  corresponds  to  y  in  the  general 
formula.     For  the  horse-power  transmitted,  Mr.  Lewis's  general  formula 

33.000  H.P.  spfi/v    . 

W  —  npfy,  =  —  —  ,  may  take  the  form  H.P.  =  -0;)'Ar.n,   in  which  v  = 

V  oo,UUU 

velocity  in  feet  per  minute;  or  since  v  =  dir  X  rpm.  -*•  12  =  .2618cZ  X  rpm.,in 
which  d  =  diameter  in  inches  and  rpm.  =  revolutions  per  minute, 


=  -000007933^  X  rp,n. 

It  must  be  borne  in  mind,  however,  that  in  the  case  of  machines  which 
consume  power  intermittently,  such  as  punching  and  shearing  machines, 
the  gearing  should  be  designed  with  reference  to  the  maximum  load  ir, 
which  can  be  brought  upon  the  teeth  at  any  time,  and  not  upon  the  average 
horse-power  transmitted 

Comparison  of  the  Harkness  and  L,ewis  Formulas.  - 
Take  an  average  case  in  whic.i  the  safe  working  strength  of  the  material, 
s  —  6000,  v  =  200  ft.  per  min.,  and  y  =  .100,  the  value  in  Mr.  Lewis's  table 
for  an  involute  tooth  of  15°  obliquity,  or  a  cycloidal  tooth,  the  number  of 
teeth  in  the  wheel  being  27. 


. 

if  Fis  taken  in  feet  per  second. 

Prof.  Harkness  gives  H.P.=  --.      If  the  V  in  the  denominator 

VI  4-  0.65  V 


STRENGTH    OF   GEAR-TEETH. 


90S 


oe  taken  at  200  - 

010 

and  H.P.=  H^ 

1. 


-  60  =  8^  feet  per  second,   4/1  +  0.65  V  ^  |7  3.167  =  1.78, 
/=  -571p/F,  or  about  52#  of  the  result  given  by  Mr.  Lewis's 


formula.  This  is  probably  as  close  an  agreement  as  can  be  expected,  since 
Prof.  Harkness  derived  his  formula  from  an  investigation  of  ancient  prece- 
dents and  rule-of-thumb  practice,  largely  with  common  cast  gears,  while 
Mr.  Lewis's  formula  was  derived  from  considerations  of  modern  practice 
with  machine  moulded  and  cut  gears. 

Mr.  Lewis  takes  into  consideration  the  reduction  in  working  strength  of  a 
tooth  due  to  increase  in  velocity  by  the  figures  in  his  table  of  the  values  of 
the  safe  working  stress  s  for  different  speeds.  Prof.  Harkness  gives  expres- 
sion to  the  same  reduction  by  means  of  the  denominator  of  his  formula, 
\  l  -f-  0.65F.  The  decrease  in  strength  as  computed  by  this  formula  is 
somewhat  less  than  that  given  in  Mr.  Lewis's  table,  and  as  the  figures  given 
in  the  table  are  riot  based  on  accurate  data,  a  mean  between  the  values  given 
by  the  formula  and  the  table  is  probably  as  near  to  the  true  value  as  may 
be  obtained  from  our  present  knowledge.  The  following  table  gives  the 
values  for  different  speeds  according  to  Mr.  Lewis's  table  and  Prof.  Hark- 
ness's  formula,  taking  for  a  basis  a  working  stress  s,  for  cast-iron  8000,  arid 
for  steel  20,000  Ibs.  at  speeds  of  100  ft.  per  minute  and  less: 


v  =  speed  of  teeth,  ft.  per  min  . 
F=  "      "   ft.  per  sec.. 

100 

1% 

8000 
1 
.6930 
1 
8000 
8000 
20000 
20000 

200 
3H 

300  600 
5  1  10 

900 
15 

1200 
20 

2400 
.3 

.2672 
.385 
3080 
2700 
0800 
6000 

1800 
30 

2400 
40 

1700 
.2125 
.1924 
.277 
2216 
2000 
4900 
4300 

Safe  stress  s,  cast-iron,  Lewis.  .. 
Relative  do.,  s  H-  8000  

6000 
.75 
.5621 
.811 
6438 
6200 
15500 
15000 

4800 
.6 
.4850 
.700 
5600 
5200 
13000 
12000 

4000 
.5 
.3650 
.526 

4208 
4100 
10300 
10000 

3000 
.375 
.3050 
.439 
3512 
3300 
8100 
7500 

2000 
.25 
.2208 
.318 
2544 
2300 
5700 
5000 

c  =  1  -M  1  4-0.65F  
Relative  val  c  -5-  693  

Si  —  8000  X  (c  •  693) 

Mean  of  s  and  slt  cast-iron  —  s2. 
••*   "   •'     for  steel  =  s3. 
Safe  stress  for  steel,  Lewis  

Comparing  the  two  formulae  for  the  case  of  s  —  8000,  corresponding  to  a 
speed  of  100  ft.  per  min.,  we  have 


Harkness:  H.P.  =  1 


I  -I-  0.65F  X  MQVpf  =  .695  X  .91  X  \%pf  =  1.051/>/' 


Lewis: 


H.P.  = 


in  which  y  varies  according  to  the  shape  and  number  of  the  teeth. 

For  radial-flank  gear  with  12  teeth  y  —  .052;  24.24pfy  =  1.2 

For  20°  involute,  19  teeth,  or  15°  inv.,  27  teeth  y  -  .100;  24.24p/*/  =  2.434p/; 
For  15°  involute,  300  teeth  y  =  .150;  24.24pjy  =  3.636p/. 

Thus  the  weakest  shaped  tooth,  according  to  Mr.  Lewis,  will  transmit  20 
per  cent  more  horse-power  than  is  given  by  Prof.  Harkness's  formula,  in 
which  the  shape  of  the  tooth  is  not  considered,  and  the  average-shaped 
tooth,  according  to  Mr.  Lewis,  will  transmit  more  than  double  the  horse- 
power given  by  Prof.  Harkness's  formula. 

Comparison  of  Other  Formulae.—  Mr.  Cooper,  in  summing  up 
his  examination,  selected  an  old  English  rule,  which  Mr.  Lewis  considers  as 
a  passably  correct  expression  of  good  general  averages,  viz.  :  X  —  2000p/, 
X  =  breaking  load  of  tooth  in  pounds,  p  —  pitch.  /  =  face.  If  a  factor  of 
safety  of  10  be  taken,  this  would  give  for  safe  working  load  W  =  200/>/. 

George  B.  Grant,  in  his  Teeth  of  Gears,  page  33.  takes  the  breaking  load 
at  SSOOpA  and.  with  a  factor  of  safety  of  10,  gives  W  =  350p/. 

Nystrpm's  Pocket-Book,  20th  ed.,  1891,  says  :  "  The  strength  and  durability 
of  cast-iron  teeth  require  that  the.y  shall  transmit  a  force  of  80  Ibs.  per  inch 
of  pitch  and  per  inch  breadth  of  face."  This  is  equivalent  to  W  =  80p/,  or 
only  40$  of  that  given  by  the  English  rule. 

F.  A.  Halsey  (Clark's  Pocket  Book)  gives  a  table  calculated  from  the 
formula  H.P.  =  pfd  X  rpm.  -*-  850. 

Jones  &  Laughlins  give  H.P.  —  pfd  X  rpm.  -r-  550. 

These  formulae  transformed  give  W=  128p/and  W  =  218p/,  respectively 


;  Kl\/f ' 


904  GEARIKG. 

Unwin,  on  the  assumption  that  the  load  acts  oh  the  corners  of  the  teeth, 
derives  a  formula  p  =  K  V~W,  in  which  K  is  a  coefficient  derived  from  ex- 
isting wheels,  its  values  being  :  for  slowly  moving  gearing  not  subject  to 
much  vibration  or  shock  K  —  .04;  in  ordinary  mill-gearing,  running  at 
greater  speed  arid  subject  to  considerable  vibration,  K  =  .05;  and  in  wheels 
subjected  to  excessive  vibration  and  shock,  and  in  mortise  gearing,  K=  .06. 
Reduced  to  the  forrri  W=  Cpf,  assuming  that/  =  2/>,  these  values  of  K  give 
W  =  262p/,  200p/,  and  139p/,  respectively. 

Unwin  also  gives  the  following  formula,  based  on  the  assumption  that  the 

pressure  is  distributed  along  the  edge  of  the  tooth  :    p  : 

where  KI  —  about  .0707  for  iron  wheels  and  .0848  for  mortise  wheels  when 
the  breadth  of  face  is  not  less  than  twice  the  pitch.  For  the  case  of  /  =  2p 
and  the  given  values  of  Kt  this  reduces  to  W  =  200p/  and  W  =  189p/, 
respectively. 

Box,  in  his  Treatise  on  Mill  Gearing,  gives  H.P.  =         '         n,  in  which  n 

=  number  of  revolutions  per  minute.  This  formula  differs  from  the  more 
modern  formulae  in  making  the  H.P.  vary  as  p2/,  instead  of  as  p/,  and  in 
this  respect  it  is  no  doubt  incorrect. 

Making  the  H.P.  vary  as  \/.dn  or  as  1/v,  instead  of  directly  as  v,  makes 
the  velocity  a  factor  of  the  working  strength^  as  in  the  Harkness  and  Lewis 

formulae,  the  relative  strength  varying  as ,  or  as   , /-  ,  which  for  different 

velocities  is  as  follows  : 

Speed  of  teeth  in  ft.  per  min.,D  =  100  200  300  600  900  1200  1800  2400 
Relative  strength  =  1  .707  .574  .408  .333  .289  .236  .204 

Showing  a  somewhat  more  rapid  reduction  than  is  given  by  Mr.  Lewis. 

For  the  purpose  of  comparing  different  formulae  they  may  in  general  be 
reduced  to  either  of  the  following  forms  : 

H.P.  =  Cpfv,       H.P.  =  dpfd  X  rpm.,        W  =  cpf, 

in  which  p  =  pitch,  /  =  face,  d  =  diameter,  all  in  inches  ;  v  =  velocity  in 
feet  per  minute,  rpm.  revolutions  per  minute,  and  C,  (7,  and  c  coefficients. 
The  formulae  for  transformation  are  as  follows  : 

HP  -    Wv    -  W  X  d  X  rpm>  • 
~~  33000  "          126,050 

Tr  =  38-°°OH-P-  =12rf6'05°H-P-  =  88.000Q,/ ;  ff=*£.  =        °-P"        =  ?. 
v  dX  rpm.  Cv       Cid  X  rpm.       c 

<7x  =  . 2618(7;    c  =  33,000(7;    C  =  3.82<7i ,  =  =5?^;    c  =  126,050C?i. 

oo,OU(J 

In  the  Lewis  formula  C  varies  with  the  form  of  the  tooth  and  with  the 
speed,  and  is  equal  to  sy  -4-  33,000,  in  which  y  and  s  are  the  values  taken  from 
the  table,  and  c  =  sy. 

910 

In  the  Harkness  formula  C  varies  with  the  speed  and  is  equal  to  ^-        77— 

(V  being  in  feet  per  second),  =  — '    '' 

1/1  +  .Ollv. 
In  the  Box  formula  C  varies  with  the  pitch  and  also  with  the  velocity 


and  equals  12p     d*  rpm"  =  .02345  ^    c  =  33,OOOC  =  774  -*- 

V'v  \/v 

For  v  =  100  ft.  per  min.  C  —  77.4p  ;    for  v  =  600  ft.  per  minute  c  =31.6p>. 

In  the  other  formulae  considered  (7,  d  ,  and  c  are  constants.     Reducing 
the  several  formulae  to  the  form  W  —  cpf,  we  have  the  following  : 


PBICTIOKAL   GEARING.  905 

COMPARISON  OF  DIFFERENT  FORMULAE  FOR  STRENGTH  OF  GEAR-TEETH. 

Safe  working  pressure  per  inch  pitch  and  per  inch  of  face,  or  value  of  c  in 
formula  W  =  cpf: 

v=100ft.      v  =  600ft. 
per  min.         per  min. 

Lewis:  Weak  form  of  tooth,  radial  flank,  12  teeth. . .  c  =    416  208 

Medium  tooth,  inv.  15°,  or  cycloid,  27  teeth.,  c  —    800  400 

Strong  form  of  tooth,  or  cycloid,  300  teeth. . .  c  =  1200  600 

Harkness:  Average  tooth c=    347  184 

Box:  Tooth  of  1  inch  pitch c=     77 A  31.6 

"      "  3  inches  pitch c  =    232  95 

Various,  in  which  c  is  independent  of  form  and  speed:  Old  English 
rule,  c  =  200;  Grant,  c  =  350;  Nystrom,  c  =  80;  Halsey,  c  =  128;  Jones  & 
Laughlins,  c  =  218;  Unwin,  c  =  262,  200,  or  139,  according  to  speed,  shock, 
and  vibration. 

The  value  given  by  Nystrom  and  those  given  by  Box  for  teeth  of  small 
pitch  are  so  much  smaller  than  those  given  by  the  other  authorities  that  they 
may  be  rejected  as  having  an  entirely  unnecessary  surplus  of  strength.  The 
values  given  by  Mr.  Lewis  seem  to  rest  on  the  most  logical  basis,  the  form  of 
the  teeth  as  well  as  the  velocity  being  considered;  and  since  they  are  said  to 
have  proven  satisfactory  in  an  extended  machine  practice,  they  may  be  con- 
sidered reliable  for  gears  that  are  so  well  made  that  the  pressure  bears 
along  the  face  of  the  teeth  instead  of  upon  the  corners.  For  rough  ordi- 
nary work  the  old  English  rule  W  =  200p/  is  probably  as  good  as  any,  ex 
cept  that  the  figure  200  may  be  too  high  for  weak  forms  of  tooth  and  for 
high  speeds. 

The  formula   W=  200p/ is  equivalent  to  H.P.  =  pfd  ^Qrpm'  =  ^-,  or 

H.P.  =  .0015873p/d  X  rpm.  =  .006063p/v. 

Maximum  Speed  of  Gearing.— A.  Towler,  Eng'g,  April  19,  1889, 
p.  388,  gives  the  maximum  speeds  at  which  it  was  possible  under  favorable 
conditions  to  run  toothed  gearing  safely  as  follows: 

Ft,  per  min. 

Ordinary  cast-iron  wheels 1800 

Helical        "        "         "      2400 

Mortise       "        "         " 2400 

Ordinary  cast-steel  wheels 2600 

Helical        "        "         " 3000 

Special  case-iron  machine-cut  wheels 3000 

Prof.  Coleman  Sellers  (Stevens  Indicator,  April,  1892)  recommends  that 
gearing  be  not  run  over  1200  ft.  per  minute,  to  avoid  great  noise.  The 
Walker  Mfg.  Co.,  Cleveland,  O.,  say  that  2200  ft.  per  min.  for  iron  gears  and 
3000  ft.  for  wood  and  iron  (mortise  gears)  are  excessive,  and  should  be 
avoided  if  possible.  The  Corliss  engine  at  The  Philadelphia  Exhibition  (1876) 
had  a  fly-wheel  30  ft.  in  diameter  running  35  rpm.  geared  into  a  pinion  12  ft. 
cliam.  The  speed  of  the  pitch-line  was  3800  ft.  per  min. 

A  Heavy  Machine-cut  Spur-gear  was  made  in  1891  by  the 
Walker  Mfg.  Co.,  Cleveland,  O.,  for  a  diamond  mine  in  South  Africa,  with 
dimensions  as  follows:  Number  of  teeth,  192;  pitch  diameter,  30'  6.66";  face, 
30";  pitch,  6":  bore,  27";  diameter  of  hub,  9'  2";  weight  of  hub,  15  tons;  and 
total  weight  of  gear,  66%  tons.  The  rim  was  made  ic  12  segments,  the  joints 
of  the  segments  being  fastened  with  two  bolts  each.  The  spokes  were  bolted 
to  the  middle  of  the  segments  and  to  the  hub  with  four  bolts  in  each  end. 

Frictional  GeariMg.— In  f fictional  gearing  the  wheels  are  toothless, 
and  one  wheel  drives  rhe  other  by  means  of  the  friction  between  the  two 
surfaces  which  are  pressed  together.  They  may  be  used  where  the  power 
to  be  transmitted  is  not  very  great;  when  the  speed  is  so  high  that  toothed 
wheels  would  be  noisy;  when  the  shafts  require  to  be  frequently  put  into 
and  out  of  gear  or  to  have  their  relative  direction  of  motion  reversed;  or 
when  it  is  desired  to  change  the  velocity-ratio  while  the  machinery  is  in  mo- 
tion, as  it)  the  case  of  disk  friction-wheels  for  changing  the  feed  in  machine 
tools. 

Let  P  =  the  normal  pressure  in  pounds  at  the  line  of  contact  by  which 
two  wheels  are  pressed  together,  T  =  tangential  resistance  of  the  driven 
wheel  at  the  line  of  contact,  /  =  the  coefficient  of  friction,  V  =  the  velocity 
of  the  pitch-surface  in  feet  per  second,  and  H.P.  =  horse-power ;  then 
T  may  be  equal  to  or  less  than  fP;  H.P.  =  TV -%-  550.  The  value  of/  for 


906 


HOISTING. 


metal  on  metal  may  be  taken  at  .15  to  .20;  for  wood  on  metal,  .25  to  .30;  and 
for  wood  on  compressed  paper,  .20.  The  tangential  driving  force  T  may  he 
as  high  as  80  Ibs.  per  inch  width  of  face  of  the  driving  surface,  but  this  is  ac- 
companied by  great  pressure  and  friction  on  the  journal-bearings. 

In  •  frictional  grooved  gearing  circumferential  wedge-shaped  grooves  are 
cut  in  the  faces  of  two  wheels  in  contact.  If  p  =  the  force  pressing  the 
wheels  together,  and  N  =  the  normal  pressure  on  all  the  grooves,  P  =  N 
(sin  a  -}- /cos  a),  in  which  2a  =  the  inclination  of  the  sides  of  the  grooves, 
and  the  maximum  tangential  available  force  T  —  fN.  The  inclination  of  the 
sides  of  the  grooves  to  a  plane  at  right  angles  to  the  axis  is  usually  30°. 

Frictioiial  Grooved  Gearing.— A  set  of  friction  -gears  for  trans- 
mitting 150  H.F.  is  on  a  steam-dredge  described  in  Proc.  lust.  M.  E.,  July, 
1888.  Two  grooved  pinions  of  54  in.  diam.,  with  9  grooves  of  1%  in.  pitch  and 
an^le  of  40°  cut  on  their  face,  are  geared  into  two  wheels  of  127^  in  diarn. 
similarly  grooved.  The  wheels  can  be  thrown  in  and  out  of  gear^by  levers 
operating  eccentric  bushes  on  the  large  wheel-shaft.  The  circumferential 
speed  of  the  wheels  is  about  500  ft.  per  min.  Allowing  for  engine-friction, 
if  halt'  the  power  is  transmitted  through  each  set  of  gears  the  tangential 
force  at  the  rims  is  about  3960  Ibs.,  requiring,  if  the  angle  is  40°  and  the  co- 
efficient of  friction  0  18,  a  pressure  of  7524  Ibs.  between  the  wheels  and 
pinion  to  prevent  slipping. 

The  wear  of  the  wheels  proving  excessive,  the  gears  were  replaced  by  spur- 
gear  wheels  and  brake-wheels  with  steel  brake-bands,  which  arrangement 
has  proven  more  durable  than  the  grooved  wheels.  Mr.  Daniel  Adamson 
states  that  if  the  frictional  wheels  had  been  run  at  a  higher  speed  the  results 
would  have  been  better,  and  says  they  should  run  at  least  30  ft.  per  second. 


HOISTING. 

Approximate  Weight  and  Strength   of  Cordage. 

and  jjockport  Block  Co.)— See  also  pages  339  to  345. 


(Boston 


Size  in 
Circum- 
ference. 

Size  in 
Diam- 
eter. 

Weightof 
100ft. 
Manila, 
in  Ibs. 

Strength 
of  Manila 
Rope, 
in  Ibs. 

Size  in 
Circum- 
ference. 

Size  in 
Diam- 
eter. 

Weight  of 
100  ft. 
Manila, 
in  Ibs. 

Strength 
of  Manila 
Rope, 
in  Ibs. 

inch. 

inch. 

inch. 

inch. 

2 

% 

13 

4,000 

&A 

1  9/16 

72 

22,500 

2H 

M 

16 

5,000 

5 

1% 

80 

25,000 

2i^j 

13/16 

20 

6,250 

5^ 

1% 

97 

30,250 

2% 

% 

24 

7,500 

6 

2 

113 

36,000 

3 

1 

28 

9,000 

6^ 

2^ 

133 

42,250 

3*4 

1  1/16 

33 

10,500 

7 

m 

153 

49,000 

31*12 

IH 

38 

12,250 

7^ 

% 

184 

56.250 

3% 

m 

45 

14,000 

8 

2% 

211 

64,000 

4 

\  5/16 

51 

16,000 

8^ 

2% 

236 

72,250 

4/4 

1% 

58 

18,062 

9 

3 

262 

81,000 

4V£ 

1^£ 

65 

20,250 

•Working  Strength  of  Blocks.    (B.  &  L.  Block  Co.) 
Regular  Mortise-blocks  Single  and    Wide    Mortise    and    Extra 


Double,  or  Two  Double  Iron- 
strapped  Blocks,  will  hoist  about— 


inch. 


10 
12 

14 


Ibs. 

250 

350 

600 

1,200 

2,000 

4,000 

10.000 

16,000 


Single  and  Double,  or  Two  Double, 

Iron-strapped  Blocks,  will    hoist 
about— 

inch.  Ibs. 

8  2,000 

10  6,000 

12  12,000 

14  24,000 

16  36,000 

18  50.000 

20  90,000 


Where  a  double  and  triple  block  are  used  together,  a  certain  extra  propor- 
tioned amount  of  weight  can  be  safely  hoisted,  as  larger  hooks  are  usecl. 


PKOPOKTIONS   OF   HOOKS. 


907 


Comparative  Efficiency  in  Chain-blocks  both  in 
Hoisting  and  Lowering. 

(Tests  by  Prof.  R.  H.  Thurston,  Hoist  iny,  March,  1892.) 


WORK  OF  HOISTING. 
Load  of  2000  Ibs. 

WORK  OF  LOWERING. 
Load  of  2000  Ibs.,  lowered  7  ft.  in  each  case. 

1 
« 

o 

o 

.53^ 

e 

.2 

Exclusive  of  Factor  of  Time. 

Inclusive  of 
Time. 

fl   CO 

"-".a" 

rn 

!£,- 

a 

c 

£  g 

£$ 

0)  ° 

>  *- 

^ 

08  .0 

2j  . 

«  . 
^  s  » 

S 

£  0 

£> 

II 

!§  a 

Sjj 
rf"S 

1 

§-s 

sS| 

UTS  ^ 

>  0  55 

p  ¥  o, 

a 

|1 

s 

to 

fV* 

Oi 

"""  5^ 

J  c3 

s  'w 

cs  S*o 

s 

P3  ^S 

£ 

o 

**" 

ig 

W 

ft 

^« 

S 

1 

20.50 

79.50 

1.00 

32.50 

8.00 

227. 

1,816 

1.00 

0.75 

1.000 

68.00 

32.00 

.40 

62.44 

14.00 

436. 

6,104 

3.3S 

1.20 

.186 

3 

69.  00 

31.00 

.39 

30.00 

92.30 

196. 

18,090 

10.00 

1.50 

.050 

4 

71.20 

28.80 

.36 

28.00 

92.60 

168. 

15,556 

8.60 

2.50 

.035 

5 

73.96 

26.04 

.33 

48.00 

73.30 

17.5 

1,282 

0.71 

2.80 

.380 

6 

75.66 

24.34 

.31 

53.00 

56.60 

370. 

20,942 

11.60 

1.80 

.036 

7 

77.00 

23.00 

.29 

44.30 

55.00 

310. 

17,050 

9.40 

2.75 

.029 

8 

81.03 

18.97 

.24 

61.00 

48.50 

426. 

20,000 

11.60 

3'.75 

.018 

No.  1  was  Weston's  triplex  block;  No.  3,  Weston's  differential;  No.  4, 
Western's  imported.  The  others  were  from  different  makers,  whose  names 
are  not  given.  All  the  blocks  were  of  one-ton  capacity. 

Proportions  of  Hooks.— The  following  formulae  are  given  by 
Henry  K.  Towne,  in  his  Treatise  on  Cranes,  as  a  result  of  an  extensive 
experimental  and  mathematical  investi- 
gation. They  apply  to  hooks  of  capaci- 
ties from  250  Ibs.  to  20,000  Ibs.  Each  size 
of  hook  is  made  from  some  C9mmercial 
size  of  round  iron.  The  basis  in  each 
case  is,  therefore,  the  size  of  iron  of 
which  the  hook  is  to  be  made,  indicated 
by  A  in  the  diagram.  The  dimension  D 
is  arbitrarily  assumed.  The  other  di- 
mensions, as  given  by  the  formulae,  are 
those  which,  while  preserving  a  proper 
bearing-face  on  the  interior  of  the  hook 
for  the  ropes  or  chains  which  may  be 
passed  through  it,  give  the  greatest  re- 
sistance to  spreading  and  to  ultimate 
rupture,  which  the  amount  of  material 
in  the  original  bar  admits  of.  The  sym- 
bol A  is  used  to  indicate  the  nominal  ca- 
pacity of  the  hook  in  tons  of  ^000  Ibs. 
The  formulas  which  determine  the  lines 
of  the  other  parts  of  the  hooks  of  the 
several  sizes  are  as  follows,  the  measure- 
ments being  all  expressed  in  inches: 


FIG.  164. 


D  =  .5  A  -f-  1.25 
&  =  .64  A  -f  1.60 
F  =  .33  A  4-  -85 


G  =  .75  D. 

O  =  .363  A  +    .66 

Q  =  .64    A  +  1.60 


H=  1.08.4 
7=1.33,1 
J=  1.20A 

K  =  1.13A 


L  =  1.05  A 
M  =  .5QA 
N=  .855  -  .16 


The  dimensions  A  are  necessarily  based  upon  the  ordinary  merchant  sizes 
of  round  iron.    The  sizes  which  it  has  been  found  best   to  select  are  the 
following: 
Capacity  of  hook: 

ys         y±       Yz  1         1^       234568         10  tons. 

Dimension  A: 

%      11/16      %      11/16      1J4      \%      m      2      2M      2^      2%      S^in, 


908  HOISTIKG. 

Experiment  has  shown  that  hooks  made  according  to  the  above  formulae 
will  give  way  first  by  opening  of  the  jaw,  which,  however,  will  not  occur 
except  with  a  load  much  in  excess  of  the  nominal  capacity  of  the  hook. 
This  yielding  of  the  hook  when  overloaded  becomes  a  source  of  safety,  as  it 
constitutes  a  signal  of  danger  which  cannot  easily  be  overlooked,  and  which 
must  proceed  to  a  considerable  length  before  rupture  will  occur  and  the 
load  be  dropped. 

POWER  OF  HOISTING-ENGINES. 

Horse-power     required    to    raise    a    Load    at    a    Given 

Gross  weight  in  Ibs 
Speed.  —  H.P.  =  —      —  ^JQQ  —      "'  x  speed  in  ft.  per  rnin.    To  this  add 


. 

To  find  the  load  which  a  given  pair  of  engines  ivill  start.—  Let  A  =  area 
oP  cylinder  in  square  inches,  or  total  area  of  both  cylinders,  if  there  are  two; 
P  =  mean  effective  pressure  in  cylinder  in  Ibs.  per  sq.  in.;  8  =  stroke  of 
cylinder  in  inches;  C  =  circumference  of  hoisting-drum  in  inches;  L  =  load 
lifted  by  hoisting-  rope  in  Ibs.  ;  F=  friction,  expressed  as  a  diminution  of 

A  pOO 


the  load.    Then  L  =  ^F  -  F. 

L> 

An  example  in  CoWy  Engr.,  July,  1891,  is  a  pair  of  hoisting-engines  24"  X 
40",  drum  13  ft.  diam.,  average  steam-pressure  in  cylinder  =  59.5  Ibs.;  A  = 
904.8;  P=  59.5;  S  =  40;  C  =  453.4.  Theoretical  load,  not  allowing  for  friction, 
A  P28  +C=  9589  Ibs.  The  actual  load  that  could  just  be  lifted  on  trial  was  79W: 
Ibs.,  making  friction  loss  F  =  1(301  Ibs.,  or  20  -f-  per  cent  of  the  actual  load 
lifted,  or  16%$  of  the  theoretical  load. 

The  above'  rule  takes  no  account  of  the  resistance  due  to  inertia  of  the 
load,  but  for  all  ordinary  cases  in  which  the  acceleration  of  speed  of  the 
cage  is  moderate,  it  is  covered  by  the  allowance  for  friction,  etc.  The  re- 
sistance due  to  inertia  is  equal  to  the  force  required  to  give  the  load  the 
velocity  acquired  in  a  given  time,  or,  as  shown  in  Mechanics,  equal  to  the 

WV 
product  of  the  mass  by  the  acceleration,  or  R  =  —  —  ,  in  which  R  =  resist- 

ance in  Ibs.  due  to  inertia;  W  =  weight  of  load  in  Ibs.  ;  V—  maximum  veloc- 
ity in  feet  per  second;  T  =  time  in  seconds  taken  to  acquire  the  velocity  V\ 
g  =  32.16. 

Effect  of  Slack  Rope  upon  Strain  in  Hoisting.  —  A  series  of 
tests  with  a  dynamometer  a1  e  published  by  the  Trenton  Iron  Co.,  which 
show  that  a  dangerous  extra  strain  may  be  caused  by  a  few  inches  of  slack 
rope  In  one  case  the  cage  and  full  tubs  weighed  11,300  Ibs.  ;  the  strain  when 
the  load  was  lifted  gently  was  11,525  Ibs.;  with  3  in.  of  slack  chain  it  was 
19.0-25  Ibs  ,  with  6  in.  slack  25.750  Ibs.,  and  with  9  in.  slack  37,950  Ibs. 

Limit  of  Depth  for  Hoisting.—  Taking  the  weight  of  a  cast-steel 
hoisting-rope  of  1^  inches  diameter  at,  3  Ibs.  per  running  foot,  and  its  break- 
ing strength  at  84,000  Ibs.,  it  should,  theoretically,  sustain  itself  until  42,00(1 
feet  long  before  breaking  from  its  own  weight.  But  taking  the  usual  factor 
of  safety  of  7,  then  the  safe  working  length  of  such  a  rope  would  be  only 
6000  feet.  If  a  weight  of  3  tons  is  now  hung  to  the  rope,  which  is  equivalent 
to  that  of  a  cage  of  moderate  capacity  with  its  loaded  cars,  the  maximum 
length  at  which  such  a  rope  could  be  used,  with  the  factor  of  safety  of  7,  is 
3000  feet,  or 

2x  -f-  6000  =  §4,000  ;         .-.x  =  3000  feet. 

This  limit  may  be  greatly  increased  by  using  special  steel  rope  of  higher 
strength,  by  using  a  smaller  factor  of  safety,  and  by  using  taper  ropes. 
(See  paper  by  H.  A.  Wheeler,  Trans.  A.  I.  M.  E.,  xix.  107.) 

Large  Hoisting  Records.—  At  a  colliery  in  North  Derbyshire  dur- 
ing the  first  week  in  June,  1890,  6309  tons  were  raised  from  a  depth  of  509 
yards,  the  time  of  winding  being  from  7  a.m.  to  3.30  p.m. 

At  two  other  Derbyshire  pits,  170  and  140  yards  in  depth  the  speed  of 
winding  and  changing  has  been  brought  to  such  perfection  that  tubs  are 
drawn  and  changed  three  times  in  one  minute.  (Froc,  Inst,  M.  E.,  1890.} 


POWER   OP    HOISTING-ENGINES.  909 

At  the  Nottingham  Colliery  near  Wilkesbarre,  Pa.,  in  Oct.  1891,  70,152  tons 
were  shipped  in  24.15  days,  the  average  hoist  per  day  being  1318  mine  cars. 

The  depth  of  hoist  was  470  feet,  and  all  coal  came  from  one  opening.  The 
engines  were  fast  motion,  22  X  48  inches,  conical  drums  4  feet  1  inch  long.  7 
feet  diameter  at  small  end  and  9  feet  at  large  end.  (Eng'g  News,  Nov.  1891 .) 

Pneumatic  Hoisting.  (H.  A.  Wheeler,  Trans.  A.  I.  M.  E.,  xix.  107.)- 
A  pneumatic  hoist  was  installed  in  1876  at  Epinac,  France,  consisting  of  two 
continuous  air-tight  iron  cylinders  extending  from  the  bottom  to  the  top  of 
the  shaft.  Within  the  cylinder  moved  a  piston  from  which  was  hung  the 
cage.  It  was  operated  by  exhausting  the  air  from, above  the  piston,  the 
lower  side  being  open  to  the  atmosphere.  Its  use  vas  discontinued  on  ac- 
count of  the  failure  of  the  mine.  Mr.  Wheeler  gives  a  description  of  the  sys- 
tem, but  criticises  it  as  not  being  equal  on  the  whole  to  hoisting  by  steel  ropes. 

Pneumatic  hoisting-cylinders  using  compressed  air  have  beeH  used  at 
blast-furnaces,  the  weighted  piston  counterbalancing  the  weight  of  tliecnge, 
and  the  two  being  connected  by  a  wire  rope  passing  over  a  pulley-sheave 
above  the  top  of  the  cylinder.  In  the  more  modern  furnaces  steam-engine 
hoists  are  generally  used. 

Counterbalancing  of  Winding-engines.  (H.  W.  Hughes,  Co- 
lumbia Coll.  (Jly.) — Engines  running  unbalanced  are  subject  to  enormous 
variations  in  the  load;  for  Jet  W  —  weight  of  cage  and  empty  tubs,  say  6270 
Ihs.;  c  =  weight  of  coal,  say  4480  Ibs.,;  r  =  weight  of  hoisting  rope,  say  6000 
Ibs. ;  r'  =  weight  of  counterbalance  rope  hanging  down  pit,  say  6000  Ibs.  The 
weight  to  be  lifted  will  be: 

If  weight  of  rope  is  unbalanced.         If  weight  of  rope  is  balanced. 

At  beginning  of  lift:  1 

W -\-c-\-r-  W  or  10, 480  Ibs.  W+c  +  r  -  (W~+r'), 

At  middle  of  lift:  or 

)or  4480  Ibs.    TF+c  +    +      -^++'  ° 


Ibs. 

A.t  end  of  lift: 
W+c  -  (W+r)  or  minus  1520  Ibs.  W+c  +  r'  —  (W-\-  r),         J 

That  counterbalancing  materially  affects  the  size  of  winding-engines  is 
jhown  by  a  formula  given  by  Mr.  Robert  Wilson,  which  is  based  on  the  fact 
that  the  greatest  work  a  winding-engine  has  to  do  is  to  get  a  given  mass  into 
ft  certain  velocity  uniformly  accelerated  from  rest,  and  to  raise  a  load  the 
distance  passed  over  during  the  time  this  velocity  is  being  obtained. 

Let  W  =  the  weight  to  be  set  in  motion:  one  cage,  coal,  number  of  empty 
tubs  on  cage,  one  winding  rope  from  pit  head-gear  to  bottom, 
and  one  rope  from  banking  level  to  bottom. 

v  =  greatest  velocity  attained,  uniformly  accelerated  from  rest; 

g  =  gravity  =  32.2; 

t  =  time  in  seconds  during  which  v  is  obtained; 

L  =  unbalanced  load  on  engine; 

R  —  ratio  of  diameter  of  drum  and  crank  circles; 

P  —  average  pressure  of  steam  in  cylinders; 

N  =  number  of  cylinders; 

$  =  space  passed  over  by  crank-pin  during  time  t ; 

C  =  %,  constant  to  reduce  angular  space  passed  through  by  crank,  to 
the  distance  passed  through  by  the  piston  during  the  time  £; 

A  —  area  of  one  cylinder,  without  margin  for  friction.  To  this  an  ad- 
dition for  friction,  etc.,  of  engine  is  to  be  made,  varying  from  10 
to  30fe  of  A. 

1st.  Where  load  is  balanced, 


PNtiC. 

2d.  Where  load  is  unbalanced: 

The  formula  is  the  same,  with  the  addition  of  another  term  to  allow  for 
the  variation  in  the  lengths  of  the  ascending  and  descending  ropes.  In  this 
case 


916 


HOISTIHG. 


hi  —  reduced  length  of  rope  in  t  attached  to  ascending  cage; 
7i2  =  increased  length  of  rope  iri  t  attached  to  descending  cage; 
w  —  weight  of  rope  per  foot  in  pounds.    Then 


PNSC. 

Applying  the  above  formula  when  designing  new  engines,  Mr.  Wilson 
found  that  30  inches  diameter  of  cylinders  would  produce  equal  results,  when 
balanced,  to  those  of  the  36-inch  cylinder  in  use,  the  latter  being  unbal- 
anced. 

Counterbalancing  may  be  employed  in  the  following  methods  : 

(a)  Tapering  Rope.—  At  the  initial  stage  the  tapering  rope  enables  us  to 
wind  from  greater  depths  than  is  possible  with  ropes  of  uniform  section, 
The  thickness  of  such  a  rope  at  any  point  should  only  be  such  as  to  safely 
bear  the  load  on  it  at  that  point. 

With  tapering  ropes  we  obtain  a  smaller  difference  between  the  initial  and 
final  load,  but  the  difference  is  still  considerable,  and  for  perfect  equaliza- 
tion of  the  load  we  must  rely  on  some  other  resource.  The  theory  of  taper 
ropes  is  to  obtain  a  rope  of  uniform  strength,  thinner  at  the  cage  end  where 
the  weight  is  least,  and  thicker  at  the  drum  end  where  it  is  greatest. 

(b)  The  Counterpoise  System  consists  of  a  heavy  chain  working  up  and 
down  a  staple  pit,  the  motion  being  obtained  by  means  of  a  special  small 
drum  placed  on  the  same  axis  as  the  winding  drum.    It  is  so  arranged  that 
the  chain  hangs  in  full  length  down  the  staple  pit  at  the  commencement  of 
the  winding;  in  the  centre  of  the  run  the  whole  of  the  chain  rests  on  the 
bottom  of  the  pit,  and,  finally,  at  the  end  of  the  winding  the  counterpoise 
has  been  rewound  upon  the  small  drum,  and  is  in  the  same  condition  as  it 
was  at  the  commencement. 

(c)  Loaded-wagon  System.  —  A  plan,  formerly  much  employed,  was  to 
have  a  loaded  wagon  running  on  a  short  incline  in  place  of  this  heavy  chain; 
the  rope  actuating  this  wagon  being  connected  in  the  same  manner  as  the 
above  to  a  subsidiary  drum.    The  incline  was  constructed  steep  at  the  com- 
mencement, the  inclination  gradually  decreasing  to  nothing.     At  the  begin- 
ning of  a  wind  the  wagon  was  at  the  top  of  the  incline,  and  during  a  portion 
of  the  run  gradually  passed  down  it  till,  at  the  meet  of  cages,  no  jpull  was 
exerted  on  the  engine—  the  wagon  by  this  time  being  at  the  bottom.    In  the 
latter  part  of  the  wind  the  resistance  was  all  against  the  engine,  owing  to 
its  having  to  pull  the  wagon  up  the  incline,  and  this  resistance  increased 
from  nothing  at  the  meet  of  cages  to  its  greatest  quantity  at  the  conclusion 
of  the  lift. 

(d)  The  Endless-rope  System  is  preferable  to  all  others,  if  there  is  suffi 
cient  sump  room  and  the  shaft  is  free  from  tubes,  cross  timbers,  and  other 
impediments.     It  consists  in  placing  beneath  the  cages  a  tail  rope,  similar 
in  diameter  to  the  winding  rope,  and,  after  conveying  this  down  the  pit,  it  ii; 
attached  beneath  the  other  cage. 

(e)  Flat  Ropes  Coiling  on  Reels  —  This  means  of  winding  allows  of  a  cer- 
tain equalization,  for  the  radius  of  the  coil  of  fascending  rope  continues  to 
increase,  while  that  of  the  descending  one  continues  to  diminish.    Conse- 
quently, as  the  resistance  decreases  in  the  ascending  load  the  leverage 
increases,  and  as  the  power  increases  in  the  other,  the  leverage  diminishes. 
The  variation  in  the  leverage  is  a  constant  quantity,  and  is  equal  to  the 
thickness  of  the  rope  where  it  is  wound  on  the  drum. 

By  the  above  means  a  remarkable  uniformity  in  the  load  may  be  ob- 
tained, the  only  objection  being  the  use  of  flat  ropes,  which  weigh  heavier 
and  only  last  about  two  thirds  the  time  of  round  ones. 

(/)  Conical  Drums.  —  Results  analogous  to  the  preceding  may  be  obtained 
by  using  round  ropes  coiling  on  conical  drums,  which  may  either  be  smooth, 
with  the  successive  coils  lying  side  by  side,  or  they  may  be  provided  with  a 
spiral  groove.  The  objection  to  these  forms  is,  that  perfect  equalization  is 
not  obtained  with  the  conical  drums  unless  the  sides  are  very  steep,  and  con- 
sequently there  is  great  risk  of  the  rope  slipping;  to  obviate  this,  scroll 
drums  were  proposed.  They  are,  however,  very  expensive,  and  the  lateral 
displacement  of  the  winding  rope  from  the  centre  line  of  pulley  becomes 
very  great,  owing  to  their  necessary  large  width. 

(g)  The  Koepe  System  of  Winding.—  An  iron  pulley  with  a  single  circular 
groove  takes  the  place  of  the  ordinary  drum.  The  winding  rope  passes 
from  one  cage,  over  its  head-gear  pulley,  round  the  drum,  and,  after  pass 


CRAKES.  911 

ing  over  the  other  head-gear  pulley,  is  connected  with  the  second  cage.  The 
winding  rope  thus  encircles  about  half  the  periphery  of  the  drum  in  the 
same  manner  as  a  driving-belt  on  an  ordinary  pulley.  There  is  a  balance 
rope  beneath  the  cages,  passing  round  a  pulley  in  the  sump;  the  arrange- 
in  -nt  may  be  likened  to  an  endless  rope,  the  two  cages  being  simply  points 
of  attachment. 

BELT-CONVEYORS. 

Grain-elevators.  —  American  Grain-elevators  are  described  in  a 
paper  by  E.  Lee  Heidenreich,  read  at  the  International  Engineering  Con- 
gress at  Chicago  (Trans.  A.  S.  C.  E.  1893).  See  also  Trans.  A.  S.  M.  E.  vii,  660. 

Bands  for  carrying  firain.  — Flexible-rubber  bands  are  exten- 
sively used  for  carrying  grain  in  and  around  elevators  and  warehouses.  An 
article  on  the  grain-storage  warehouses  of  the  Alexandria  Dock,  Liverpool 
(Froc.  Inst.  M.  E.,  July,  1891),  describes  the  performance  of  these  bands, 
aggregating  three  miles  in  length.  A  band  16^  inches  wide,  1270  feet  long, 
running  9  to  10  feet  per  second  has  a  carrying  capacity  of  50  tons  per  hour. 
See  also  paper  on  Belts  as  Grain  Conveyors,  by  T.  W.  Hugo,  Trans.  A.  S. 
M.  E..  vi.  400. 

Carrying-bands  or  Belts  are  used  for  the  purpose  both  of  sorting 
coal  anci  of  removing  impurities.  These  carrying-bands  may  be  said  to  be 
confined  to  two  descriptions,  namely,  the  wire  belt,  which  consists  of  an 
endless  length  of  woven  wire;  and  the  steel-plate  belt,  which  consists  of 
two  or  three  endless  chains,  carrying  steel  plates  varying  in  width  from  6 
inches  to  14  inches.  (Proc.  Inst.  M.  E.,  July,  1890.) 

CRANES. 
Classification  of  Cranes.    (Henry  R.  Towne,  Trans.  A.  S.  M.  E.,  iv. 

288.    Revised  in  Hoisting,  published  by  The  Yale  &  Towne  Mfg.  Co.) 

A  Hoist  is  a  machine  for  raising  and  lowering  weights.  A  Crane  is  a 
hoist  with  the  added  capacity  of  moving  the  load  in  a  horizontal  or  lateral 
direction. 

Cranes  are  divided  into  two  classes,  as  to  their  motions,  viz.,  Rotary  and 
Rectilinear,  and  into  four  groups,  as  to  their  source  of  motive  power,  viz.: 

Hand.— When  operated  by  manual  power. 

Power. — When  driven  by  power  derived  from  line  shafting. 

Steam,  Electric,  Hydraulic,  or  Pneumatic.— When  driven  by  an  engine  or 
motor  attached  to  the  crane,  and  operated  by  steam,  electricity,  water,  or 
air  transmitted  to  the  crane  from  a  fixed  source  of  supply. 

Locomotive. — When  the  crane  is  provided  with  its  own  boiler  or  other 
generator  of  power,  and  is  self-propelling  ;  usually  being  capable  of  both 
rotary  and  rectilinear  motions. 

Rotary  and  Rectilinear  Cranes  are  thus  subdivided : 

ROTARY  CRANES. 

(1)  Swing-cranes.— Having  rotation,  but  no  trolley  motion. 

(2)  Jib-cranes.— Having  rotation,  and  a  trolley  travelling  on  the  jib. 

(3)  Column-cranes.— Identical  with  the  jib-cranes,  but  rotating  around  a 
fixed  column  (which  usually  supports  a  floor  above). 

(4)  Pillar-cranes.—  Having  rotation  only;  the  pillar  or  column  being  sup- 
ported entirely  from  the  foundation. 

(5)  Pillar  Jib-cranes.— Identical  with  the  last,  except  in  having  a  jib  and 
trolley  motion. 

(6)  Derrick-cranes.— Identical  with  jib-cranes,  except  that  the  head  of  the 
mast  is  held  in  position  by  guy- rods,  instead  of  by  attachment  to  a  roof  or 
ceiling. 

(7)  Walking-cranes. — Consisting  of  a  pillar  or  jib-crane  mounted  on  wheels 
and  arranged  to  travel  longitudinally  upon  one  or  more  rails. 

(8)  Locomotive-cranes. — Consisting  of  a  pillar  crane  mounted  on  a  truck, 
and  provided  with  a  steam-engine  capable  of  propelling  and  rotating  the 
crane,  and  of  hoisting  and  lowering  the  load. 

RECTILINEAR  CRANES. 

(9)  Bridge-cranes.— Having  a  fixed  bridge  spanning  an  opening,  and  a 
trolley  moving  across  the  bridge. 

(10)  Tram-cranes. — Consisting  of  a  truck,  or  short  bridge,  travelling  lon- 
gitudinally on  overhead  rails,  and  without  trolley  motion. 

(11)  Travelling-cranes.— Consisting  of  a  bridge  moving  longitudinally  on 
overhead  tracks,  and  a  trolley  moving  transversely  on  the  bridge. 


912  HOISTING. 

(12)  Gantries.— Consisting  of  an  overhead  bridge,  carried  at  each  end  by  a 
trestle  travelling  on  longitudinal  tracks  on  the  ground,  and  having  a  trolley 
moving  transversely  on  the  bridge. 

(13)  Rotary  Bridge-cranes.— Combining  rotary  and  rectilinear  movements 
and  consisting  of  a  bridge  pivoted  at  one  end  to  a  central  pier  or  post, 
and  supported  at  the  other  end  on  a  circular  track  ;  provided  with  a  trolley 
moving  transversely  on  the  bridge. 

For  descriptions  of  these  several  forms  of  cranes  see  Towne's  "Treatise 
on  Cranes." 

Stresses  in  Cranes. — See  Stresses  in  Framed  Structures,  p.  440,  ante. 

Position  of  the  Inclined  Brace  in  a  Jib-crane.— The  most 
economical  arrangement  is  that  in  which  the  inclined  brace  intersects  the 
jib  at  a  distance  from  the  mast  equal  to  four  fifths  the  effective  radius  of 
the  crane.  (Hoisting.) 

A  Large  Travelling-crane,  designed  and  built  by  the  Morgan 
Engineering  Co.,  Alliance,  O..  for  the  12-inch-gnn  shop  at  the  Washington 
Navy  Yard,  is  described  in  American  Machinist,  June  12,  1890.  Capacity, 
150  net  tons;  distance  between  centres  of  inside  rails,  59  ft.  6  in.;  maximum 
cross  travel,  44  ft.  2  in.;  effective  lift,  40  ft.;  four  speeds  for  main  hoist,  1,  2, 
4,  and  8  ft.  per  min.;  loads  for  these  speeds,  150,  75,  37^,  and  18%  tons  respec- 
tively ;  traversing  speeds  of  trolley  on  bridge,  25  and  50  ft.  per  minute  ; 
speeds  of  bridge  on  main  track,  30  and  60  ft.  per  minute.  Square  shafts  are 
employed  for  driving. 

A  1 50-ton  Pillar-crane  was  erected  in  1893  on  Finnieston  Quay, 
Glasgow.  The  jib  is  formed  of  two  steel  tubes,  each  39  in.  diam.  and  90  ft. 
long.  The  radius  of  sweep  for  heavy  lifts  is  65  ft.  The  jib  and  its  load  are 
counterbalanced  by  a  balance-box  weighted  with  100  tons  of  iron  and  steel 
punchings.  In  a  test  a  130-ton  load  was  lifted  at  the  rate  of  4  ft.  per  minute, 
and  a  complete  revolution  made  with  this  load  in  5  minutes.  Eng'g  News, 
July  20,  1893. 

Compressed-air  Travelling-cranes.— Compressed-air  overhead 
travelling-cranes  have  been  built  by  the  Lane  &  Bodley  Co.,  of  Cincinnati. 
They  are  of  20  tons  nominal  capacity,  each  about  50  ft.  span  and  400  ft.  length 
of  travel,  and  are  of  the  triple-motor  type,  a  pair  of  simple  reversing-engines 
being  used  for  each  of  the  necessary  operations,  the  pair  of  engines  for  the 
bridge  and  the  pair  for  the  trolley  travel  being  each  5-inch  bore  by  7-inch 
stroke,  while  the  pair  for  hoisting  is  7-inch  bore  by  9-inch  stroke.  Air  is 
furnished  by  a  compressor  having  steam  and  air  cylinders  each  10-in.  diam. 
and  12-in.  stroke,  which  with  a  boiler-pressure  of  about  80  pounds  gives  an  air- 
pressure  when  required  of  somewhat  over  100  pounds.  The  air -compressor 
is  allowed  to  run  continuously  without  a  governor,  the  speed  being  regulated 
by  the  resistance  of  the  air  in  a  receiver.  From  a  pipe  extending  from  the 
receiver  along  one  of  the  supporting  trusses  communication  is  continuously 
maintained  with  an  auxiliary  receiver  on  each  traveller  by  means  of  a  one- 
inch  hose,  the  object  of  the  auxiliary  receiver  being  to  provide  a  supply  of 
air  near  the  engines  for  immediate  demands  and  independent  of  the  hose 
connection,  which  may  thus  be  of  small  dimension.  Some  of  the  advantages 
said  to  be  possessed  by  this  type  of  crane  are:  simplicity;  absence  of  all  mov- 
ing parts,  excepting  those  required  for  a  particular  motion  when  that  motion 
is  in  use;  no  danger  from  fire,  leakage,  electric  shocks,  or  freezing;  ease  of 
repair;  variable  speeds  and  reversal  without  gearing;  almost  entire  absence 
of  noise;  and  moderate  cost. 

Quay-cranes.— An  illustrated  description  of  several  varieties  of  sta- 
tionary and  travelling  cranes,  with  results  of  experiments,  is  given  in  a 
paper  on  Quay-cranes  in  the  Port  of  Hamburg  by  Chas.  Nehls,  Trans.  A.  S. 
C.  E..  Chicago  Meeting,  1893. 

Hydraulic  Cranes,  Accumulators,  etc.— See  Hydraulic  Press^ 
ure  Transmission,  page  616,  ante. 

Electric  Cranes.— Travelling-cranes  driven  by  electric  motors  have 
largely  supplanted  cranes  driven  by  square  shafts  or  flying-ropes.  Each  of 
the  three  motions,  viz.,  longitudinal,  traversing  and  hoisting,  is  usually  ac- 
complished by  a  separate  motor  carried  upon  the  crane. 

WIRE-ROPE  HAULAGE. 

Methods  for  transporting  coal  and  other  products  by  means  of  wire  rope, 
though  varying  from  each  other  in  detail,  may  be  grouped  in  five  classes: 
I.  The  Self-acting  or  Gravity  Inclined  Plane. 
II.  The  Simple  Engine -plane. 


WIBE-KOPE  HAULAGE.  913 

III.  The  Tail-rope  System. 

IV.  The  Endless-rope  System. 
V.  The  Cable  Tramway. 

The  following  brief  description  of  these  systems  is  abridged  from  a 
pamphlet  on  Wire-rope  Haulage,  by  Wm.  Hildenbrand,  C.E.,  published  by 
John  A.  Roeblinar's  Sons  Co.,  Trenton,  N.  J. 

I.  The  Self-acting  Inclined  Plane.— The  motive  power  for  the 
self-acting  inclined  plane  is  gravity;  consequently  this  mode  of  transport- 
ing coal  finds  application  only  in  places  where  the  coal  is  conveyed  from  a 
higher  to  a  lower  point  and  where  the  plane  has  sufficient  grade  for  the 
loaded  descending  cars  to  raise  the  empty  cars  to  an  upper  level. 

At  the  head  of  the  plane  there  is  a  drum,  which  is  generally  constructed 
of  wood,  having  a  diameter  of  seven  to  ten  feet.  It  is  placed  high  enough 
to  allow  men  and  cars  to  pass  under  it.  Loaded  cars  coming  from  the  pit 
are  either  singly  or  in  sets  of  two  or  three  switched  on  the  track  of  the 
plane,  and  their  speed  in  descending  is  regulated  by  a  brake  on  the  drum. 

Supporting  rollers,  to  prevent  the  rope  dragging  on  the  ground,  are 
generally  of  wood,  5  to  6  inches  in  diameter  and  18  to  24  inches  long,  with 
'Y\-  to  %-inch  iron  axles.  The  distance  between  the  rollers  varies  from  15  to 
30  feet,  steeper  planes  requiring  less  rollers  than  those  with  easy  grades. 
Considering  only  the  reduction  of  friction  and  what  is  best  for  the  preserva- 
tion of  rope,  a  general  rule  may  be  given  to  use  rollers  of  the  greatest 
possible  diameter,  and  to  place  them  as  close  as  economy  will  permit. 

The  smallest  angle  of  inclination  at  which  a  plane  can  be  made  self-acting 
will  be  when  the  motive  and  resisting  forces  balance  each  other.  The 
motive  forces  are  the  weights  of  the  loaded  car  and  of  the  descending  rope. 
The  resisting  forces  consist  of  the  weight  of  the  empty  car  and  ascending 
rope,  of  the  rolling  and  axle  friction  of  the  cars,  and  of  the  axle  friction  of 
the  supporting  rollers.  The  friction  of  the  drum,  stiffness  of  rope,  and 
resistance  of  air  may  be  neglected.  A  general  rule  cannot  be  given,  because 
a  change  in  the  length  of  the  plane  or  in  the  weight  of  the  cars  changes  the 
proportion  of  the  forces;  also,  because  the  coefficient  of  friction,  depending 
on  the  condition  of  the  road,  construction  of  the  cars,  etc.,  is  a  very  uncer- 
tain factor. 

For  working  a  plane  with  a  %-inch  steel  rope  and  lowering  from  one  to 
four  pit  cars  weighing  empty  1400  Ibs.  and  loaded  4000  Ibs.,  the  rise  in  100 
feet  necessary  to  make  the  plane  self-acting  will  be  from  about  5  to  10  feet, 
decreasing  as  the  number  of  cars  increase,  and  increasing  as  the  length  of 
plane  increases. 

A  gravity  inclined  plane  should  be  slightly  concave,  steeper  at  the  top 
than  at  the  bottom.  The  maximum  deflection  of  the  curve  should  be  at  an 
inclination  of  45  degrees,  and  diminish  for  smaller  as  well  as  for  steeper 
inclinations. 

II.  The    Simple    Engine-plane.— The  name  "  Engine-plane  "  is 
given  to  a  plane  on  which  a  load  is  raised  or  lowered  by  means  of  a  single 
wire  rope  and  stationary  steam-engine.    It  is  a  cheap  and  simple  method  of 
conveying  coal  underground,  and  therefore  is  applied  wherever  circum- 
stances permit  it. 

Under  ordinary  conditions  such  as  prevail  in  the  Pennsylvania  mine 
region,  a  train  of  twenty-five  to  thirty  loaded  cars  will  descend,  with  reason- 
able velocity,  a  straight  plane  5000  feet  long  on  a  grade  of  1%  feet  in  100, 
while  it  would  appear  that  2J4  feet  in  100  is  necessary  for  the  same  number 
of  empty  cars.  For  roads  longer  than  5000  feet,  or'when  containing  sharp 
curves,  the  grade  should  be  correspondingly  larger. 

III.  The  Tail-rope  System.— Of  all  methods  for  conveying  coal 
underground  by  wire  rope,  the  tail-rope  system  has  found  the  most  applica- 
tion    It  can  be   applied  under  almost  any  condition.    The  road  may  be 
straight  or  curved,  level  or  undulating,  in  one  continuous  line  or  with  side 
branches. .  In  general  principle  a  tail-rope  plane  is  the  same  as  an  engine- 
plane  worked  in  both  directions  with  two  ropes.  One  rope,  called  the  "  main 
rope,"  serves  for  drawing  the  set  of  full  cars  outward;  the  other,  called 
the  "tail-rope,"  is  necessary  to  take  back  the  empty  set,  which  on  a  level 
or  undulating  road  cannot  return  by  gravity.    The  two  drums  may  be 
located  at  the  opposite  ends  of  the  road,  and  driven  by  separate  engines, 
but  more  frequently  they  are  on  the  same  shaft  at  one  end  of  the  plane. 
In  the  first  case  each  rope  would  require  the  length  of  the  plane,  but  in  the 
second  case  the  tail  rope  must  be  twice  as  long,  being  led  from  the  drum 
around  a  sheave  at  the  other  end  of  the  plane  and  back  again  to  its  starting- 


914 


UOISTIHG. 


point.  When  the  main  rope  draws  a  set  of  full  cars  out,  the  tail-rope  drum 
runs  loose  on  the  shaft,  and  the  rope,  being  attached  to  the  rear  car.  un- 
winds itself  steadily.  Going  in,  the  reverse  takes  place.  Each  drum  is 
provided  with  a  brake  to  check  the  speed  of  the  train  on  a  down  grade  and 
prevent  its  overrunning  the  forward  rope.  As  a  rule,  the  tail  rope  is 
strained  less  than  the  main  rope,  but  in  cases  of  heavy  grades  dipping  out- 
ward it  is  possible  that  the  strain  in  the  former  may  become  as  large,  or 
even  larger,  than  in  the  latter,  and  in  the  selection  of  the  sizes  reference 
should  be  had  to  this  circumstance. 

IV.  The  Endless-rope  System.— The  principal  features  of  this 
system  are  as  follows: 

1.  The  rope,  as  the  name  indicates,  is  endless. 

2.  Motion  is  given  to  the  rope  by  a  single  wheel  or  drum,  and  friction  is 
obtained  either  by  a  grip-wheel  or  by  passing  the  rope  several  times  around 
the  wheel. 

3.  The  rope  must  be  kept  constantly  tight,  the  tension  to  be  produced  by 
artificial  means.    It  is  done  in  placing  either  the  return-wheel  or  an  extra 
tension  wheel  on  a  carriage  and  connecting  it  with  a  weight  hanging  over  a 
pulley,  or  attaching  it  to  a  fixed  post  by  a  screw  which  occasionally  can  be 
shortened. 

4.  The  cars  are  attached  to  the  rope  by  a  grip  or  clutch,  which  can  take 
hold  at  any  place  and  let  go  again,  starting  and  stopping  the  train  at  will, 
without  stopping  the  engine  or  the  motion  of  the  rope. 

5.  On  a  single-track  road  the  rope  works  forward  and  backward,  but  on  a 
double  track  it  is  possible  to  run  it  always  in  the  same  direction,  the  full 
cars  going  on  one  track  and  the  empty  cars  on  the  other. 

This  method  of  conveying  coal,  as  a  rule,  has  not  found  as  general  an  in- 
troduction as  the  tail-rope  system,  probably  because  its  efficacy  is  not  so 
apparent  and  the  opposing  difficulties  require  greater  mechanical  skill  and 
more  complicated  appliances.  Its  advantages  are,  first,  that  it  require? 
one  third  less  rope  than  the  tail-rope  system.  This  advantage,  however, 
is  partially  counterbalanced  by  the  circumstance  that  the  extra  tension  in 
the  rope  requires  a  heavier  size  to  move  the  same  load  than  when  a  main 
and  tail  rope  are  used.  The  second  and  principal  advantage  is  that  it  is 
possible  to  start  and  stop  trains  at  will  without  signalling  to  the  engineer. 
On  the  other  hand,  it  is  more  difficult  to  work  curves  with  the  endless  sys- 
tem, and  still  more  so  to  work  different  branches,  and  the  constant  stretch 
of  the  rope  under  tension  or  its  elongation  under  changes  of  temperature 
frequently  causes  the  rope  to  slip  on  the  wheel,  in  spite  of  every  attention, 
causing  delay  in  the  transportation  and  injury  to  the  rope. 

V.  Wire-rope  Tramways.— The  methods  of  conveying  products  on 
a  suspended  rope  tramway  find  especial  application  in  places  where  a  mine 
is  located  on  one  side  of  a  river  or  deep  ravine  and  the  loading  station  on 
the  other.    A.  wire  rope  suspended  between  the  two  stations  forms  the  track 
on  which  material  in  properly  constructed  ''carriages"  or  "buggies'1  is 
transported.    It  saves  the  construction  of  a  bridge  or  trestlework,  and  is 
practical  for  a  distance  of  2000  feet  without  an  intermediate  support. 

There  are  two  distinct  classes  of  rope  tramways: 

1.  The  rope  is  stationary,  forming  the  track  on  which  a  bucket  holding 
the  material  moves  forward  and  backward,  pulled  by  a  smaller  endless 
wire  rope. 

2.  The  rope  is  movable,  forming  itself  an  endless  line,  which  serves  at 
the  same  time  as  supporting  track  and  as  pulling  rope. 

Of  these  two  the  first  method  has  found  more  general  application,  and  is 
especially  adapted  for  long  spans,  steep  inclinations,  and  heavy  loads.  The 
second  method  is  used  for  long  distances,  divided  into  short  spans,  and  is 
only  applicable  for  light  loads  which  are  to  be  delivered  at  regular  intervals. 

For  detailed  descriptions  of  the  several  systems  of  wire-rope  transporta- 
tion, see  circulars  of  John  A.  Roebliag's  Sons  Co.,  The  Trenton  Iron  Co.,  and 
other  wire-rope  manufacturers.  See  also  paper  on  Two-rope  Haulage 
Systems,  by  R.  Van  A.  Norris,  Trans.  A.  S.  M.  E.,  xii.  6v6. 

In  the  JBleichert  System  of  wire-rope  tramways,  in  which  the  track  rope  is 
stationary,  loads  of  1000  pounds  each  and  upward  are  carried.  While  the 
average  spans  on  a  level  are  from  150  to  200  feet,  in  cro-sing  rivers,  ravines, 
etc.,  spans  up  to  1500  feet  are  frequently  adopted.  In  a  tramway  on  this 
system  at  Granite,  Montana,  the  total  length  of  the  line  is  9750  feet,  with  a 
fall  of  1225  feet.  The  descending  loads,  amounting  to  a  constant  weight  of 
about  11  tons,  develop  over  14  horse-power,  which  is  sufficient  to  haul  the 
empty  buckets  as  well  as  about  50  tons  of  supplies  per  day  up  the  line,  and 


SUSPENSION   CABLEWAYS   OR  CABLE   HOISTS.       915 


also  to  run  the  ore  crusher  and  elevator.    It  is  capable  of  delivering  250 
tons  of  material  in  10  hours. 

SUSPENSION   CAUSEWAYS  OR  CABLE  HOISTS. 

(Trenton  Iron  Co.) 

In  quarrying,  rock-cutting,  stripping,  piling,  dam- building,  and  many 
other  operations  where  it  is  necessary  to  hoist  and  convey  large  individual 
loads  economically,  it  frequently  happens  that  the  application  of  a  system 
of  derricks  is  impracticable,  by  reason  of  the  limited  area  of  their  efficiency 
and  the  room  which  they  occupy. 

To  meet  such  conditions  cable-hoists  are  adapted,  as  they  can  be  efficiently 
operated  In  clear  spans  up  to  1500  feet,  and  in  lifting  individual  loads  up  to 
15  tons.  Two  types  are  made— one  in  which  the  hoisting  and  conveying  are 
done  by  separate  running  ropes,  and  the  other  applicable  only  to  inclines, 
in  which  the  carriage  descends  by  gravity,  and  but  one  running  rope  is  re- 
quired. The  moving  of  the  carriage  in  the  former  is  effected  by  means  of 
an  endless  rope,  and  these  are  commonly  known  as  "  endless  -rope  "  cable- 
hoists  to  distinguish  them  from  the  latter,  which  are  termed  "inclined'1 
cable-hoists. 

The  general  arrangement  of  the  endless-rope  cable-hoists  consists  of  a 
main  cable  passing  over  towers,  A  frames  or  masts,  as  may  be  most  conve- 
nient, and  anchored  firmly  to  the  ground  at  each  end,  the  requisite  tension 
in  the  cable  being  maintained  by  a  turnbuckle  at  one  anchorage. 

Upon  this  cable  travels  the  carriage,  which  is  moved  back  and  forth  over 
the  line  by  means  of  the  endless  rope.  The  hoisting  is  done  by  a  separate 
rope,  both  ropes  being  operated  by  an  engine  specially  designed  for  the 
purpose,  which  may  be  located  at  either  end  of  the  line,  and  is  constructed 
in  such  a  way  that  the  hoisting-rope  is  coiled  up  or  paid  out  automatically 
as  the  carriage  is  moved  in  and  out.  Loads  may  be  picked  up  or  discharged 
at  any  point  along  the  line.  Where  sufficient  inclination  can  be  obtained  in 
the  main  cable  for  the  carriage  to  descend  by  gravity,  and  the  loading  and 
unloading  is  done  at  fixed  points,  the  endless  rope  can  be  dispensed  with. 
The  carriage,  which  is  similar  in  construction  to  the  carriage  used  in  the 
endless-rope  cableways,  is  arrested  in  its  descent  by  a  stop-block,  which 
may  be  clamped  to  the  main  cable  at  any  desired  point,  the  speed  of  the 
descending  carriage  being  under  control  of  a  brake  on  the  engine-drum. 

Stress  in  Hoisting-ropes  on  Inclined  Planes. 

(Trenton  Iron  Co.) 


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140 

55 

28°  49' 

1003 

110 

47°  44' 

1516 

10 

5°  43' 

240 

60 

30°  58' 

1067 

120 

50°  12' 

1573 

15 

8°  32' 

336 

65 

33°  02' 

1128 

130 

52°  267 

1620 

20 

11°  10' 

432 

70 

35°  00' 

1185 

140 

54°  28' 

1663 

25 

14°  03' 

527 

75 

36°  53' 

1238 

150 

56°  19' 

1699 

30 

16°  42' 

613 

80 

38°  40' 

1287 

160 

58°  00' 

1730 

35 

1  9°  18' 

700 

85 

40°  22' 

1332 

170 

59°  33' 

1'58 

40 

21°  49' 

782 

90 

42°  00' 

1375 

180 

60°  57' 

1782 

45 

24°  14' 

860 

95 

43°  32' 

1415 

190 

62°  15' 

1804 

50 

26°  34' 

933 

100 

45°  00' 

1450 

200 

63°  277 

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The  above  table  is  based  on  an  allowance  of  40  Ibs.  per  ton  for  rolling  fric- 
tion, but  an  additional  allowance  must  be  made  for  stress  due  to  the  weight 
of  the  rope  proportional  to  the  length  of  the  plane.  A  factor  of  safety  of  5 
to  7  should  be  taken. 

In  hoisting  the  slack-rope  should  be  taken  up  gently  before  beginning  the 
lift,  otherwise  a  severe  extra  strain  will  be  brought  on  the  rope. 

The  best  rope  for  inclined  planes  is  composed  of  six  strands  of  seven  wires 
each,  laid  about  a  hempen  centre.  The  wires  are  much  coarser  than  those 
of  the  114-wire  rope  of  the  same  diameter,  and  for  this  reason  the  42-wire 
rope  is  better  adapted  to  withstand  the  rough  usage  and  surface  wear 
encountered  upon  inclined  planes. 

A  Double-suspension  Cableivay,  carrying  loads  of  26  tons,  erected  near 


HOtSTttfG. 


carriage  sup'ported  on  four  wheels  and  moved  by  an  endless  cable  1  inch  in 
diam.  The  load  consists  of  a  cage  carrying  a  railroad-car  loaded  with  lum- 
ber, the  latter  weighing  about  12  tons.  The  power  is  furnished  by  a  50-H.P. 
engine,  and  the  trip  across  the  river  is  made  in  about  three  minutes. 

A  hoisting  cableway  on  the  endless-rope  system,  erected  by  the  Lidger- 
wood  Mfg.  Co.,  at  the  Austin  Dam,  Texas,  had  a  single  span  1350  ft.  in 
length,  with  main  cable  2^  in.  diam.,  and  hoisting-rope  1^  in.  diam.  Loads 
of  7  to  8  tons  were  handled  at  a  speed  of  600  to  800  ft.  per  minute. 

Tension  required  to  Prevent  Slipping  of  Wire  on  Drum. 
(Trenton  Iron  Co.) — The  amount  of  artificial  tension  to  be  applied  in  an 
endless  rope  to  prevent  slipping  on  the  driving-drum  depends  on  the  char- 
acter of  the  drum,  the  condition  of  the  rope  and  number  of  laps  which  it 
makes.  If  Tand  S  represent  respectively  the  tensions  in  the  taut  and  slack 
lines  of  the  rope;  W,  the  necessary  weight  to  be  applied  to  the  tail-sheave; 
R,  the  resistance  of  the  cars  and  rope,  allowing  for  friction;  n,  the  number 
of  half-laps  of  the  rope  on  the  driving-drum;  and  /,  the  coefficient  of  fric- 
tion, the  following  relations  must  exist  to  prevent  slipping: 

T=  Sefnir,     W  =  T+  S,    and    R  =  T  -  S; 


from  which  we  obtain 


in  which  e  =  2.71828,  the  base  of  the  Naperian  system  of  logarithms. 
The  following  are  some  of  the  values  off : 

Dry.        Wet.        Greasy. 

Rope  on  a  grooved  iron  drum 120         .085  .070 

Rope  on  wood-filled  sheaves 235          .170  .140 

Rope  on  rubber  and  leather  filling 495          .400  .205 

efnir  i   | 

The  values  of  the  coefficient  —  ,  corresponding  to  the  above  values 

efnir  -  1 

of  /,  for  one  up  to  six  half-laps  of  the  rope  on  the  driving-drum  or  sheaves, 
are  as  follows: 


n  —  Number  of  Half-laps  on  Driving-wheel. 


1 

2 

3 

4 

5 

6 

.070 

9.130 

4.623 

3.141 

2.418 

1.999 

.729 

.085 

7.536 

3.833 

2.629 

2.047 

1.714 

.505 

.120 

5.345 

2.777 

1.953 

1.570 

1.358 

.232 

.140 

4.623 

2.418 

1.729 

1.416 

1.249 

.154 

.170 

3.833 

2.047 

1.505 

1.268 

1.149 

.085 

.205 

3.212 

1.762 

1.338 

1.165 

1.083 

.043 

.235 

2.831 

1.592 

1.245 

1.110 

1.051 

.024 

.400 

1.795 

1.176 

1.047 

1.013 

1.004 

.001 

.495 

1.538 

1.093 

1.019 

1.004 

1.001 

The  importance  of  keeping  the  rope  dry  is  evident  from  these  figures. 

When  the  rope  is  at  rest  the  tension  is  distributed  equally  on  the  two  lines 
of  the  rope,  but  when  running  there  will  be  a  difference  in  the  tensions  of 
the  taut  and  slack  lines  equal  to  the  resistance,  and  the  values  of  T  and  S 
mav  be  readily  computed  from  the  foregoing  formulas. 

Taper  Ropes  of  Uniform  Tensile  Strength.— Prof.  A.  S. 
Herschel  in  The  Engineer,  April,  1880,  p..  267,  gives  an  elaborate  mathe- 
matical investigation'  of  the  problem  of  making  a  taper  hoisting-rope  of 
uniform  tensile  strength  at  every  point  in  its  length.  Mr.  Charles  D.  West, 
commenting  on  Prof*.  Herschefs  paper,  gives  a  similar  solution,  and  derives 
therefrom  the  following  formula,  based  on  a  breaking  strain  of  80,000  Ibs. 
per  sq.  in.  of  the  rope,  core  included,  with  a  factor  of  safety  of  10: 

F  =  3680[log  G  -  log  g] ;    log  G  =  ^  +  log  g; 

in  which  F  =  length  in  fathoms,  and  G  and  g  the  girth  in  inches  at  any  two 
sections  F  fathoms  apart. 


WIRE-HOPE   TRANSMISSION. 


EXAMPLE.— Let  it  be  required  to  find  the  dimensions  of  a  steel-wire  rope  to 
draw  6720  Ibs.— cage,  trams,  and  coal— from  a  depth  of  400  fathoms. 

Area  of  section  at  lower  end  =  6720  -*-  8000  =  .84  sq.  in.;  therefore  girth  = 
314  in.  at  bottom. 

Log  G  =  400  -H  3680  +  log  3.25  =  .10869  -f  .51188  =  .62057; 

therefore  G  =  4.174,  or,  say,  4  3/16  in.  girth  at  top. 

The  equations  show  that  the  true  form  of  rope  is  not  a  regular  taper  or 
truncated  cone,  but  follows  a  logarithmic  curve,  the  girth  rapidly  increas- 
ing towards  the  upper  end. 

Relative  Effect  of  Various-sized  Sheaves  or  Drums  on  the 
Life  of  Wire  Ropes. 

(Thos.  E.  Hughes,  ColVy  Eng.,  April,  1893.) 

CAST-STEEL  ROPES  FOR  INCLINES. 
Made  of  6  strands,  of  7  wires  each,  laid  around  a  hemp  core. 


Diam.  of 
Rope  in 

Diameters  of  Sheaves  or  Drums  in  feet,  showing  percent- 
ages of  life  for  various  diameters. 

inches. 

lOOfc. 

90^. 

80^. 

75#. 

60*. 

50^. 

25*. 

l^j 

16 

14 

12 

11 

9 

7 

4.75 

1% 

14 

12 

10 

8.5 

7 

6 

4.5 

114 

12 

10 

8 

7.25 

6.5 

5.5 

4.25 

1^ 

10 

8.5 

7.75 

7 

6 

5 

4 

1 

8.5 

7.75 

6.75 

6 

5 

4.5 

3.75 

% 

7.75 

7 

6.25 

5.75 

4.5 

3.75 

3.25 

•M 

7 

6.25 

5.5 

5 

4.25 

3.5 

2.75 

% 

6 

5.25 

4.5 

4 

3.25 

3 

2.5 

X 

5 

4.5 

4 

3.5 

2.75 

2.25 

1.75 

The  use  of  iron  ropes  for  inclines  has  been  generally  abandoned,  steel 
ropes  being  more  satisfactory  and  economical. 

CAST-STEEL  HOISTING-ROPES. 
Made  of  6  strands,  of  19  wires  each,  laid  around  a  hemp  core. 


Diam.  of 
Rope  in 

j-/io/iiictci  o  UL  cuiceivcs  ui    \ji  uma  ill  xcrt,  »iiuwiiig   JJCHJCIIL- 

ages  of  life  for  various  diameters. 

inches. 

100*. 

90£. 

80fo. 

75$. 

60#. 

50#. 

25#. 

/4 

14 

12 

10 

8.5 

7 

6 

4.5 

% 

12 

10 

8 

7 

6 

5.25 

4.25 

% 

10 

8.5 

7.5 

6.75 

5.5 

5 

4 

/^ 

9 

7.5 

6.5 

6 

5 

4.5 

3.75 

8 

7 

6 

5.5 

4.5 

4 

3.50 

% 

7.5 

6.75 

5.75 

5 

4.25 

3.5 

3 

§ 

5.5 

4.5 

4 

3.75 

3.25 

3 

2.25 

% 

4.5 

4 

3.75 

3.25 

3 

2.5 

2 

4 

3 

3 

2.75 

2.25 

2 

1.5 

% 

3 

2 

1.5 

WIRE-ROPE  TRANSMISSION. 

The  following  data  and  formulae  are  taken  from  a  paper  by  Wm.  Hewitt, 
of  the  Trenton  Iron  Co.,  1890.  (See  also  circulars  of  John  A.  Roebling's 
Sons  Co.,  Trenton,  N.  J.;  ''Transmission  of  Power  by  Wire  Ropes,1'  by  A. 
W.  Stahl,  Van  NostrancPs  Science  Series  No.  28;  and  Reuleaux's  Constructor.) 

The  Section  of  Wire  Rope  best  suited,  under  ordinary  conditions, 
for  the  transmission  of  power  is  composed  of  6  strands  of  7  wires  each, laid 
together  about  a  hempen  centre.  Ropes  of  12  and  19  wires  to  the  strand  are 
also  used.  They  are  more  flexible,  and  may  be  applied  with  advantage  un- 
der conditions  which  do  not  allow  the  use  of  large  transmission  wheels,  but 
admit  of  high  speed.  They  are  not  as  well  adapted  to  stand  surface  wear, 
however,  on  account  of  the  smaller  sige  of  the  wires. 


918 


WIKE-ROPE   TRANSMISSION. 


The  Driving- wheels  (Fig.  165)  are  usually  of  cast  iron,  and  are 
made  as  light  as  possible  consistent  with  the  requisite  strength.  Various 
materials  have  been  used  for  filling  the  bot 
torn  of  the  groove,  such  as  tawed  oakum, 
jute  yarn,  hard  wood,  India-rubber  and  leather. 
The  filling  which  gives  the  best  satisfaction, 
however,  consists  of  segments  of  leather  and 
blocks  of  India-rubber,  soaked  in  tar  and 
packed  alternately  in  the  groove,  and  then 
turned  to  a  true  surface. 

In  long  spans,  intermediate  supporting 
wheels  are  frequently  used,  and  it  is  usually 
sufficient  to  support  only  the  slack  or  follow 
ing  side  of  the  rope;  but  whatever  the  distance 
that  the  power  is  transmitted,  the  driving  side 
of  the  rope  will  require  a  less  number  of  sup- 
ports than  the  slack  side.  The  sheaves  sup- 
porting the  driving  side,  however,  should  in 
all  cases  be  of  equal  diameter  with  the  driving- 
wheels.  With  the  slack  side  smaller  wheels 
may  be  used,  but  their  diameter  should  not  be  less  than  one  half  that  of  the 
driving-sheaves. 

The  system  of  carrying  sheaves  may  generally  be  replaced  to  advantage 
by  that'  of  intermediate  stations.  The  rope  thus,  instead  of  running  the 
whole  length  of  the  transmission,  runs  only  from  one  station  to  the  other;  and 
it  is  advisable  to  make  the  stations  equidistant,  so  that  a  rope  may  be  kept 
on  hand,  ready  spliced,  to  put  on  the  wheels  of  any  span,  should  its  rope 
give  out.  This  method  is  to  be  preferred  where  there  is  sometimes  a  jerking 
motion  to  the  rope,  as  it  prevents  sudden  movements  of  this  kind  from  be- 
ing transmitted  over  the  entire  line. 

Gross  horse-power  transmitted  =  JV0  =  .0003702Z)2v  (Jc  -TFr>/>    m    which 

D  =  diameter  of  rope  in  inches  (=  9  times  diameter  of  single  wire);  v  = 
velocity  of  rope  in  feet  per  second;  k  =  safe  stress  per  square  inch  on  wires 
=  for  iron  25,700  Ibs.;  E  =  modulus  of  elasticity  -  28,500,000  for  iron;  R  ~ 

ED 
radius  of  driving- wheels  in  inches.    The  term  — r^  =  the  stress  per  square 

inch  due  to  bending  of  wires  around  sheaves. 

Loss  due  to  centrifugal  force  =  Nl  =  .0000424ZW; 

Loss  due  to  journal  friction  of  driving-wheels  =  2Va  =  .0000045  ( 1 6502V0 -f  tov); 

"          "  intermediate-wheels  =  .0000045(  W+  iu)v\ 
in  which  W  =  total  weight  of  rope;  w  =  weight  of  wheel  and  axle. 

Net  horse-power  transmitted, 


N  =  N0  -  Nt  -  Ny  = 


[.0003675(fc  -  y^)-  .0000424v]  -  .1 


For  a  maximum  value  of  JV'the  diameter  of  the  wheels  should  be  approxi- 
mately from  185  to  192  times  the  diameter  of  the  rope,  and  for  the  latter 
ratio  of  diameters  an  approximate  formula  for  the  actual  horse-power 
transmitted  is  N  =  3  0148D3F,  in  which  V.  —  number  of  revolutions  of 
wheels  per  minute. 

The  proper  deflections  when  the  rope  is  at  rest  are  obtained  from  the  for- 
mula Deflection  =  .00005765  span2,  and  are  as  follows: 

Span  in  feet..      50     JOO       150         200         250         300         350        400        450 
Deflection....     1%"    7"  V  '$&'  2' 3%"  3'  7*4"  5'  2^"  7'%"   9' 2%"  11  >8" 

It  has  been  found  in  practice  that  when  the  deflection  of  the  rope  at  rest 
is  less  than  3  inches  the  transmission  cannot  be  effected  with  satisfaction, 
and  shafting  or  belting  is  to  be  preferred.  This  deflection  corresponds  to  a 
span  of  about  54  feet.  It  is  customary  to  make  the  under  side  of  the  rope 
the  driving  side.  The  maximum  limit  of  span  is  determined  by  the  maxi- 
mum deflection  that  may  be  given  to  the  upper  side  of  the  rope  when  in 
motion.  Assuming  that  the  clearance  between  the  upper  and  lower  sides  of 
the  rope  should  not  lie  less  than  two  feet,  and  that  the  wheels  are  at  least  10 
feet  in  diameter,  we  have  a  maximum  deflection  of  the  upper  side  of  8  feet, 
which  corresponds  to  a  span  of  about  370  feet. 

Much  greater  spans  than  this  are  practicable,  in  cases  where  the  contour 
Of  the  ground  is  such  that  the  upper  side  of  the  rope  may  be  made  the 


WIRE-ROPE   TRANSMISSION. 


919 


driver,  as  in  crossing  gullies  or  valleys,  and  there  is  nothing  to  interfere  with 
obtaining  the  proper  deflections.  Some  very  long  transmissions  of  power 
have  been  effected  in  this  way  without  an  intervening  support.  There  is  one 
at  Lockport,  N.  Y.,  for  instance,  with  a  clear  span  of  about  1700  feet. 

In  a  later  circular  of  the  Trenton  Iron  Co.  (1892)  the  above  figures  are 
somewhat  modified,  giving  lower  values  for  the  power  transmitted  by  a  given 
rope,  as  follows: 

The  proper  ratio  between  the  diameters  of  rope  and  sheaves  is  that  which 
will  permit  the  maximum  working  tension  to  be  obtained  without  overstrain- 
ing the  wires  in  bending.  For  rope  of  7-wire  strands  this  ratio  is  about 
1  : 150;  for  rope  of  12-wire  strands,  1  :  115;  and  for  rope  of  19-wire  strands, 
1:  90;  which  gives  the  following  minimum  diameter  of  sheaves,  in  inches, 
corresponding  to  maximum  efficiency. 


Diam.  rope,  in  inches. 

M 

5/16 

% 

7/16 

K 

9/16 

% 

11/16 

H 

% 

1 

IK 

7-wire  strands.  ...... 

12    '•           "     .   ., 

37 

47 

36 

56 
43 

66 
50 

75 
57 

84 
65 

94 
72 

103 

78 

112 
86 

ioi 

115 

19    "            "      

34 

39 

45 

51 

56 

62 

68 

79 

90 

101 

Assuming  the  sheaves  are  of  equal  diameter,  and  not  smaller  than  con- 
sistent with  maximum  efficiency  as  determined  by  the  preceding  table,  the 
actual  horse-power  transmitted  approximately  equals  3.1  times  the  square 
of  the  diameter  of  the  rope  in  inches  multiplied  by  the  velocity  in  feet  per 
second. 

From  this  rule  we  deduce  the  following: 

Horse-power  of  Wire-rope  Transmission. 


Velocity,  in  feet  | 
per  second.       \ 

20 

30 

40 

50 

60 

70 

80 

Diam.  Rope,  in 
inches. 

Horse-power  Transmitted. 

1/4 

4 

6 

8 

10 

12 

14 

16 

5/16 

6 

9 

12 

15 

18 

21 

24 

3/8 

9 

13 

17 

22 

26 

31 

35 

7/16 

12 

18 

24 

30 

36 

42 

47 

1/2 

16 

23 

31 

39 

47 

54 

62 

9/16 

20 

29 

39 

49 

59 

69 

78 

5/8 

24 

36 

48 

61 

73 

85 

97 

11/16 

29 

44 

59 

73 

88 

103 

117 

3/4 

35 

52 

70 

87 

105 

122 

140 

7/8 

48 

71 

95 

119 

142 

166 

190 

1 

62 

93 

124 

155 

186 

217 

248 

The  proper  deflection  to  give  the  rope  in  order  to  secure  the  necessary 
tension  is 

h  =  .0000695S2. 

//  =  the  deflection  with  the  rope  at  rest,  and  S  =  the  span,  both  in  feet. 

Durability  of  Wire  Ropes.— At  the  Risdon  Iron  Works,  San  Fran- 
cisco, a  steel  wire  rope  2J4  inches  in  circumference  running  over  10-foot 
sheaves  at  5000  ft.  per  minute  lias  transmitted  40  H.P.  for  six  years  without 
renewing  the  rope.  At  the  wire-mills  a  steel  wire  rope  2*4  in.  in  circumfer- 
ence running  over  8-foot  sheaves  has  been  running  steadily  for  a  period  of 
three  years  at  a  velocity  of  4500  ft.  per  minute,  transmitting  80  H.P. 

In  Inclined  Transmissions,  when  the  angle  of  inclination  is 
great,  the  proper  deflections  cannot  be  readily  determined,  and  the  rope  be- 
comes more  sensitive  to  the  ordinary  variations  in  the  deflections,  so  that 
tightening  sheaves  must  be  resorted  to  for  producing  the  requisite  tension, 
as  in  the  case  of  very  short  spans.  When  the  horizontal  distance  between 
the  two  wheels  is  less  than  60  ft.,  or  when  the  angle  of  inclination  exceeds 
30  to  45  degrees,  it  will  be  found  desirable  to  use  tightening  sheaves. 

Tightening  pulleys  should  be  placed  on  the  slack  side  of  the  rope. 

The  Wire-rope  Catenary.  (From  an  article  on  Wire-rope 
Transmission,  by  M.  Arthur  Achard,  Proc.  Inst.  M.  E.,  Jan.  1881.)- The 
wires  have  to  bear  two  distinct  molecular  straias  :  First,  the  tension  -S' 


920  WIRE-ROPE   TRANSMISSION. 

resulting  from  the  maximum  tension  T  necessary  to  transmit  the  motion, 
whose  value  in  pounds  per  square  inch  is  8  =  t.  ,,.,  d  being  the  diameter 

Y^nCi^l 

of  the  wires  and  i  their  number ;  second,  the  strain  produced  by  flexure 
upon  the  pulley,  which  is  approximately  Z  -  E—,  R  being  the  radius  of 

the  pulley  and  E  the  modulus  of  elasticity  of  the  metal.  The  approximate 
values  allowed  in  practice  for  iron-wire  ropes  are  S  =  14,220  Ibs.  per  square 
inch,  and  Z  =  11,380  Ibs.  per  square  inch.  S  -f-  Z  should  not  exceed  say  11 
tons  (24,640  Ibs.)  per  square  inch. 

The  curve  in  which  the  rope  hangs  is  a  catenary;  and  it  is  upon  the  form 
of  the  particular  catenary  in  which  it  hangs,  whether  more  or  less  deep,  as 
well  as  upon  its  lineal  weight,  that  the  tension  to  which  it  is  subjected  de- 
pends. By  fixing  the  weight  of  the  rope  and  its  length,  the  forms  which  its 
two  spans  assume  in  common,  when  at  rest,  is  determined,  and  consequently 
their  common  tension  ;  which  latter  must  be  such  as  to  produce  in  running 
the  two  unequal  tensions,  T  and  t,  necessary  for  the  transmission  of  the 
power.  The  driving  force  =  T  —  t . 

Moreover,  the  tension  in  either  span  is  not  the  same  throughout  its  whole 
length;  it  is  a  minimum  at  the  lowest  point  of  the  curve  and  goes  on  increas- 
ing towards  the  two  extremities.  The  calculation  of  the  tension  at  the  low- 
est point  is  very  complicated  if  based  upon  the  true  form  of  the  catenary; 
but  by  substituting  a  parabola  for  the  catenary,  which  is  allowable  in  almost 
all  cases,  the  calculation  becomes  simple.  If  the  two  pulleys  are  on  the 
same  level,  the  lowest  point  is  midway  between  them,  and  the  tension  at 

this  point  is  S0  =  —-,  p  being  the  lineal  weight,  or  pounds  per  foot,  of  the 

rope,  I  its  horizontal  projection,  which  is  approximately  equal  to  the  distance 
between  the  centres  of  the  pulleys,  and  h  the  deflection  in  the  middle.  The 
catenary  possesses  the  remarkable  mechanical  property  that  the  difference 
between  the  tensions  at  any  two  points  is  equal  to  the  weight  of  a  length  of 
rope  corresponding  to  the  difference  in  level  between  the  two  points.  The 

tensions  therefore  at  the  two  ends  will  be  St  =  S0  -f  ph  =  ^-  -f  ph.     By 

substituting  for  St  in  the  above  equation  the  required  values  of  Tand  t,  and 
solving  it  with  relation  to  ft,  the  deflections  7i,  and  7i2  of  the  driving  and 
trailing  spans  will  be  obtained.  The  deflection  7i0  ,  common  to  the  two  spans 
at  rest,  is  given  by  the  equation  h0  =  |/V^ia  -f  l/2/i22-  If  w  =  the  sectional 
area  of  the  iron  portion  of  the  rope,  and  S  the  unit  strain  which  the  maximum 

tension  T  produces  on  it,  we  havemS  =  T  =  ^-\-ph^.  Taking  the  sectional 

area  w  of  the  rope  in  square  inches,  and  its  weight  p  in  pounds  per  foot  run, 
the  ratio  w  -*-  p  differs  little  from  a  mean  value  of  0.24.  The  safe  limit  of 
working  tension  usually  assigned  for  iron-wire  ropes  is  S  =  14,220  Ibs.  per 
square  inch.  Hence  ws  -*•  p  =  0.24  X  14,220  =  3410;  and  we  have  the  approx- 

imate  equation  ^-  -f-  hi  =  3410,  which  is  useful  as  giving  a  relation  between 

the  length  I  and  deflection  ft,  for  the  driving-span  of  a  rope.  In  the  case  of 
leather,  w  H-  p  =  2.53  approximately,  and  it  is  impossible  to  give  S  a  higher 
value  than  about  355  Ibs.  per  square  inch;  the  relation  obtained  would  be 

^j—  +  hi  =  900,  which  with  equal  deflections  would  give  much  shorter  spans. 

If  the  working  tension  S  were  reduced  to  the  American  limit  of  185  Ibs.  per 
square  inch  for  leather  belts,  the  above  figure  900  would  be  reduced  to  470, 
which  would  further  shorten  the  span  one  half. 

It  is  therefore  owing  to  the  great  strength  which  iron- wire  ropes  possess 
in  proportion  to  their  weight  that  they  admit  of  long  spans,  with  a  smaller 
number  of  supports,  and  consequently  smaller  loss  of  power  by  friction. 
They  may  therefore  be  expected  to  yield  a  high  efficiency,  The  experiments 
of  M.  Ziegler  on  the  transmission  of  power  at  Oberusel  give  for  the  mean 
efficiency  of  a  single  relay  =  96.2  per  cent.  The  efficiency  of  transmission 
by  relays,  including  m  intermediate  stations,  is  approximately  obtained  by 

raising  the  efficiency  of  a  single  relay  to  the  power  of  m  ~£~  2. 

It  often  happens  that  the  two  pulleys  of  a  single  relay  are  at  different 
levels,  in  which  case  neither  span  of  the  rope  has  the  same  tension  at  its 


WIRE-ROPE   TRANSMISSION. 


921 


hlnoS8foVmu]a  for  the  tension  at  the  ends  of  a  catenary  (assuming  it  to 
e  a  parabola)  is  S,  =  ~  V(W  +  (W,  in  which  S  =  the  tension  in  Ibs  ; 


•» 

8267 


Si 


Kji"to»^   e-~-          -,       11 

Double  groove,  Ibs.. 
Table  of  Transmission  of  Power  by  Wire  Ropes. 

(J.  A.  Roebling's  Sons  Co.,  1886.) 


•§  £ 

l§" 

Diameter  < 
of  Rope. 

i  u 

cc  U 

II 

cw  S 

mimoer 
of  Revo- 
lutions. 

ill 

it 

ft  o 

I! 

3 
3 
3 
3 
4 

80 
100 
120 
140 
80 

23 
23 
23 
23 
23 

i 

3 

|< 

8 
8 
8 
8 

140 
80 
100 
120 
140 

20 
19 
19 
19 
19 

9/16 

35 

26 
32 

39 
45 

47 

4 

100 

23 

% 

5 

9 

80 

(  20 
119 

[  9/16  YS 

i  48 

4 

120 

23 

% 

6 

9 

100 

J20 

119 

\  9/16  % 

j  58 
1  60 

4 

140 

23 

% 

7 

9 

120 

j20 
119 

\  9/16  % 

j  69 
1  73 

5 

80 

22 

7/16 

9 

9 

140 

J20 
119 

j-  9/16  % 

j  82 
1  84 

5 

100 

22 

7/16 

11 

10 

80 

U9 

118 

\  %  H/16 

j 

J  64 
1  68 

19 

\ 

j  80 

5 

120 

22 

7/16 

13 

10 

100 

118 

>•  %  11/16 
) 

1  85 

5 

140 

22 

7/16 

15 

10 

120 

J19 
118 

j-  %  H/16 

j  96 
1102 

6 

80 

21 

y2 

14 

10 

140 

J19 

118 

i  %  11/16 

j  112 
1119 

6 

100 

21 

¥> 

17 

12 

80 

18 
117 

[  11/16  % 

j  93 
1  99 

6 

120 

21 

y* 

20 

12 

100 

j  18 

1  11/16  M 

J116 
1124 

6 

140 

21 

¥2 

23 

12 

120 

j  18 
117 

j-  11/16  % 

]  140 
1149 

7 

80 

20 

9/16 

20 

12 

120 

16 

<  8 

> 

173 

(  141 

7 

100 

20 

9/16 

25 

14 

80 

j-  1  1^ 

1148 

i  8 

j  176 

7 

120 

20 

9/16 

30 

14 

100 

1  7 

\  1  1H 

1185 

HOPE-DRIVING. 


YYi-icic;  an<*i£j  duties  utjuui    111    LJIC  iiuc,  uuwcvci,  siicctvcs  must   uc 

size  corresponding  to  the  safe  limit  of  tension  due  to  bending.  The  rope 
run  under  a  high  working  tension,  far  in  excess  of  what  in  the  ordinary' 
system  would  cause  the  rope  to  slip  on  the  sheaves.  The  working  tension* 
may  be  four  or  five  times  as  great  as  the  tension  in  the  slack  portion  of  the- 
rope,  and  in  order  to  prevent  slipping,  the  rope  is  wrapped  several  times 
about  grooved  drums,  or  a  series  of  sheaves  at  each  end  of  the  line.  To 
provide  for  the  slack  due  to  the  stretch  of  the  rope,  one  of  the  sheaves  is 
placed  on  a  slide  worked  by  long-threaded  bolts,  or,  better  still,  on  a  car- 
riage provided  with  counterweights,  which  runs  back  and  forth  on  a  track, 
The  latter  preserves  a  uniform  tension  in  the  slack  portion  of  the  rope, 
which  is  very  important. 

Wire-rope  tramways  are  practically  transmissions  of  power  of  this  kind, 
in  which  the  load,  however,  instead  of  being  concentrated  at  one  terminal, 
is  distributed  uniformly  over  the  entire  line.  Cable  railways  are  also  trans- 
missions of  this  class.  The  amount  of  horse-power  transmitted  is  given  by 
the  formula 

N  ^[4.755Z)2  -  .000006  (TF-f  g  -f  gj]v\ 

in  which  D  =  diameter  of  the  rope  in  inches;  v  =  velocity  in  ft.  per  second; 
W  —  weight  of  the  rope;  g  —  weight  of  the  terminal  sheaves  and  axles,  and 
02  =  weight  of  the  intermediate  sheaves  and  axles. 


ROPE-DRIVINGL 

The  transmission  of  power  by  cotton  or  manila  ropes  promises  to  become 
a  formidable  competitor  with  gearing  and  leather  belting  for  use  where  the 
amount  of  power  is  large,  or  the  distance  between  the  power  and  the  work 
is  comparatively  great.  The  following  is  condensed  from  a  paper  by  Charles 
W.  Hunt,  Trans.  A.  S.  M.  E.,  vol.  xii.  p.  230: 

But  few  accurate  data  are  available,  on  account  of  the  long  period  re- 
quired in  each  experiment,  a  rope  lasting  from  three  to  six  years.  In  many 
of  the  early  applications  so  great  a  strain  was  put  upon  the  rope  that  the 
wear  was  rapid,  and  success  only  came  when  the  work  required  of  the  rope 
was  greatly  reduced.  The  strain  upon  the  rope  has  been  decreased  until  it 
is  approximately  known  what  it  should  be  to  secure  reasonable  durability. 
Installations  which  have  been  successful,  as  well  as  those  in  which  the  wear 
of  the  rope  was  destructive,  indicate  that  200  Ibs.  on  a  rope  one  inch  in  diam- 
eter is  a  safe  and  economical  working  strain.  When  the  strain  is  materially 
increased,  the  wear  is  rapid. 

In  the  following  equations 

C  =  circumference  of  rope  in  inches;       g  =  gravity: 

D  =  sag  of  the  rope  in  inches;  H=  horse-power; 

F  =  centrifugal  force  in  pounds;  L  =  distance  between  pulleys  in  ft0 

P  =  pounds  per  foot  cf  rope;  w  =  working  strain  in  pounds; 

R  —  force  in  pounds  doing  useful  work; 

S  =  strain  in  pounds  on  the  rope  at  the  pulley; 

T  —  tension  in  pounds  of  driving  side  of  the  rope; 

t  =  tension  in  pouuds  on  slack  side  of  the  rope; 

v  =  velocity  of  the  rope  in  feet  per  second; 
W  =  ultimate  breaking  strain  in  pounds. 

W  =  720C2;       P  =  .032C";       w  =  20C2. 

This  makes  the  normal  working  strain  equal  to  1/36  of  the  breaking 
strength,  and  about  1/35  of  the  strength  at  the  splice.  The  actual  strains  are 
ordinarily  much  greater,  owing  to  the  vibrations  in  running,  as  well  as  from 
imperfectly  adjusted  tension  mechanism. 

For  this  investigation  we  assume  that  the  strain  on  the  driving  side  of  a 
rope  is  equal  to  200  Ibs.  on  a  rope  one  inch  in  diameter,  and  an  equivalent 
strain  for  other  sizes,  and  that  the  rope  is  in  motion  at  various  velocities  of 
from  10  to  140  ft.  per  second. 

The  centrifugal  force  of  the  rope  in  running  over  the  pulley  will  reduce 


KOPE-DRIVIKG.  923 

the  amount  of  force  available  for  the  transmission  of  power.  The  centrifu- 
gal force  F  =  Pv*  -f-  g. 

At  a  speed  of  about  80  ft.  per  second,  the  centrifugal  force  increases  faster 
than  the  power  from  increased  velocity  of  the  rope,  and  at  about  140  ft.  per 
second  equals  the  assumed  allowable  tension  of  the  rope.  Computing  this 
force  at  various  speeds  and  then  subtracting  it  from  the  assumed  maximum 
tension,  we  have  the  force  available  for  the  transmission  of  power.  The 
whole  of  this  force  cannot  be  used,  because  a  certain  amount  of  tension  on 
the  slack  side  of  the  rope  is  needed  to  give  adhesion  to  the  pulley.  What 
tension  should  be  given  to  the  rope  for  this  pin-pose  is  uncertain,  as  there 
are  no  experiments  which  give  accurate  data.  It  is  known  from  considerable 
experience  that  when  the  rope  runs  in  a  groove  whose  sides  are  inclined 
toward  each  other  at  an  angle  of  45°  there  is  sufficient  adhesion  when  the 
ratio  of  the  tensions  T-t-  1  =  2. 

For  the  present  purpose,  T  can  be  divided  into  three  parts:  1.  Tension 
doing  useful  work;  2.  Tension  from  centrifugal  force;  3.  Tension  to  balance 
the  strain  for  adhesion. 

The  tension  t  can  be  divided  into  two  parts:  1.  Tension  for  adhesion; 
2.  Tension  from  centrifugal  force. 

It  is  evident,  however,  that  the  tension  required  to  do  a  given  work  should 
not  be  materially  exceeded  during  the  life  of  the  rope. 

There  are  two  methods  of  putting  ropes  on  the  pulleys;  one  in  which  the 
ropes  are  single  and  spliced  on,  being  made  very  taut  at  first,  and  less  so  as 
the  rope  lengthens,  stretching  until  it  slips,  when  it  is  respliced.  The  other 
method  is  to  wind  a  single  rope  over  the  pulley  as  many  turns  as  needed  to 
obtain  the  necessary  horse-power  and  put  a  tension  pulley  to  give  the  neces- 
sary adhesion  and  also  take  up  the  wear.  The  tension  t  required  to  trans- 
mit the  normal  horse-power  for  tiie  ordinary  speeds  and  sizes  of  rope  is  com- 
puted by  formula  (1).  below.  The  total  tension  T  on  the  driving  side  of  the 
rope  is  assumed  to  be  the  same  at  all  speeds.  The  centrifugal  force,  as  well 
as  an  amount  equal  to  the  tension  for  adhesion  on  the  slack  side  of  the  rope, 
must  be  taken  from  the  total  tension  T  to  ascertain  the  amount  of  force 
available  for  the  transmission  of  power. 

It  is  assumed  that  the  tension  on  the  slack  side  necessary  for  giving 
adhesion  is  equal  to  one  half  the  force  doing  useful  work  on  the  driving  side 

of  the  rope;  hence  the  force  for  useful  work  is  R  —  —  —  -  -  •  ;  and  the  ten- 

o 
sion  on  the  slack  side  to  give  the  required  adhesion  is  Y^T  —  F).    Hence 


The  sum  of  the  tensions  T  and  t  is  not  the  same  at  different  speeds,  as  the 
equation  (1)  indicates. 

As  F  varies  as  the  square  of  the  velocity,  there  is,  with  an  increasing 
speed  of  the  rope,  a  decreasing  useful  force,  and  an  increasing  total  tension, 
/,  on  the  slack  side. 

With  these  assumptions  of  allowable  strains  the  horse-power  will  be 


Transmission  ropes  are  usually  from  1  to  1%  inches  in  diameter.  A  com- 
putation of  the  horse-power  for  four  sizes  at  various  speeds  and  under 
ordinary  conditions,  based  on  a  maximum  strain  equivalent  to  200  Ibs.  for  a 
rope  one  inch  in  diameter,  is  given  in  Fig.  166.  The  horse-power  of  other 
sizes  is  readily  obtained  from  these.  The  maximum  power  is  transmitted, 
under  the  assumed  conditions,  at  a  speed  of  about  80  feet  per  second. 

The  wear  of  the  rope  is  both  internal  and  external;  the  internal  is  caused 
by  the  movement  of  the  fibres  on  each  other,  under  pressure  in  bending 
over  the  sheaves,  and  the  external  is  caused  by  the  slipping  and  the  wedg- 
ing in  the  grooves  of  the  pulley.  Both  of  these  causes  of  wear  are,  within 
the  limits  of  ordinary  practice,  assumed  to  be  directly  proportional  to  the 
speed.  Hence,  if  we  assume  the  coefficient  of  the  wear  to  be  &,  the  wear 
will  be  kv,  in  which  the  wear  increases  directly  as  the  velocity,  but  the 
horse-power  that  can  be  transmitted,  as  equation  (2)  shows,  will  not  vary  at 
the  same  rate. 

The  rope  is  supposed  to  have  the  strain  T  constant  at  all  speeds  on  the 
driving  side,  and  in  direct  proportion  to  the  area  of  the  cross-section;  hence 


924 


ROPE-DRIVIM. 


the  catenary  of  the  driving  side  is  not  affected  by  the  speed  or  by  the  diam- 
eter of  the  rope. 

The  deflection  of  the  rope  between  the  pulleys  on  the  slack  side  varies 
with  each  change  of  the  load  or  change  of  the  speed,  as  the  tension  equation 
(1)  indicates. 

The  deflection  of  the  rope  is  computed  for  the  assumed  value  of  T  and  t 


ROPE     DRIVING. 

Horse  Power  of  manill 
rope  at  various  speed 


Velocity  oTDrving  .Kope  in  fee.t  per  second. 
FIG.  166. 

PL2 
by  the  parabolic  formula  S  =  -^=-  -f-  -PA  S  being  the  assumed  strain  T  on 

oJJ 

the  driving  side,  and  t,  calculated  by  equation  (1),  on  the  slack  side.    The 
tension  t  varies  with  the  speed. 

Horse-power  of  Transmission  Rope  at  Various  Speeds. 

Computed  from  formula  (2),  given  above. 


"o 

II 

Speed  of  the  Rope  in  feet  per  minute. 

"ao5©  »  ™ 
v    .  frA 
S  c  «  o 

e6  CS  C 
g  «  S  •- 

Sa*.s 

1500 

2000 

2500 

3000 

3500 

4000 

4500 

5000 

6000 

7000 

2.2 
3.4 

4.9 
6.9 

8.8 
13.8 
19.8 
27.6 
35.2 

8000 

1M 
iy> 
1% 

2 

1.45 
2.3 
3.3 
4.5 
5.8 
9.2 
13.1 
18 
23.2 

1.9 
3.2 
4.3 
5.9 

7.7 
12.1 
17.4 
23.7 
30.8 

2.3 
3.6 
5.2 
7.0 
9.2 
14.3 
20.7 
28.2 
36.8 

2.7 
4.2 
5.8 
8.2 
10.7 
16.8 
23.1 
32.8 
42.8 

3 

4.6 
6.7 
9.1 
11.9 
18.6 
26.8 
36.4 
47.6 

3.2 
5.0 

7.2 
9.8 
12.8 
20.0 
28.8 
39.2 
51.2 

3.4 
5.3 

7.7 
10.8 
13.6 
21.2 
30.6 
41.5 
54.4 

3.4 
5.3 

i?  ff 

w'.s 

13.7 
21.4 
30.8 
41.8 

54.8 

3.1 
4.9 

7.1 
9.3 
12.5 
19.5 
28.2 
37.4 
50 

0 
0 
0 
0 
0 
0 
0 
0 
0 

20 
24 
30 
36 
42 
54 
60 
72 
84 

The  following  notes  are  from  the  circular  of  the  C.  W.  Hunt  Co.,  New 
York  : 

For  a  temporary  installation,  when  the  rope  is  not  to  be  long  in  use,  it 
might  be  advisable  to  increase  the  work  to  double  that  given  in  the  table. 

For  convenience  in  estimating  the  necessary  clearance  on  the  driving  and 
on  the  slack  sides,  we  insert  a  table  showing  the  sag  of  the  rope  at  different 
speeds  when  transmitting  the  horse-power  given  in  the  preceding  table. 
When  at  rest  the  sag  is  not  the  same  as  when  running,  being  greater  on  the 
driving  and  less  on  the  slack  sides  of  the  rope.  The  sag  of  the  driving  side 
when  transmitting  the  normal  horse-power  is  the  same  no  matter  what  size 
of  rope  is  used  or  what  the  speed  driven  at,  because  the  assumption  is  that 
the  strain  on  the  rope  shall  be  the  same  at  all  speeds  when  transmitting  the 


SAG   OF   THE   ROPE   BETWEEN   PULLEYS. 


925 


assumed  horse -power,  but  on  the  slack  side  the  strains,  and  consequently 
the  sag,  vary  with  the  speed  of  the  rope  and  also  with  the  horse -power. 
The  table  gives  the  sag  for  three  speeds.  If  the  actual  sag  is  less  than  given 
in  the  table,  the  rope  is  strained  more  than  the  work  requires. 

This  table  is  only  approximate,  and  is  exact  only  when  the  rope  is  running 
at  its  normal  speed,  transmitting  its  full  load  and  strained  to  the  assumed 
amount.  All  of  these  conditions  are  varying  in  actual  work,  and  the  table 
must  be  used  as  a  guide  only. 

Sag  of  the  Rope  between  iPulleys. 


Distance 
between 
Pulleys 
in  feet. 

Driving  Side. 

Slack  Side  of  Rope. 

All  Speeds. 

80  ft.  per  sec. 

60  ft.  per  sec. 

40  ft.  per  sec. 

40 
60 
80 
100 
120 
140 
160 

0  feet  4  inches 
0    "    10      " 

Ofeet 

1    " 

7  inches 

5      " 

Ofeet  9  inches 

1    "      8      »' 

Ofeet  11  inches 
1    "    11      " 

3           3 

5    **      2 

(i 

9    "      9 

14    "      0 

5    "      1       " 

7   " 
9    " 

3      " 

8    "      9      " 
11    "      3      " 

The  size  of  the  pulleys  has  an  important  effect  on  the  wear  of  the  rope—- 
the larger  the  sheaves^  the  less  the  fibres  of  the  rope  slide  on  each  other,  and 
consequently  there  is  less  internal  wear  of  the  rope.  The  pulleys  should  not 
be  less  than  forty  times  the  diameter  of  the  rope  for  economical  wear,  and 
as  much  larger  as  it  is  possible  to  make  them.  This  rule  applies  also  to  the 
idle  and  tension  pulleys  as  well  as  to  the  main  driving-pulley. 

The  angle  of  the  sides  of  the  grooves  in  which  the  rope  runs  varies,  with 
different  engineers,  from  45°  to  60°.  It  is  very  important  that  the  sides  of 
these  grooves  should  be  carefully  polished,  as  the  fibres  of  the  rope  rubbing 
on  the  metal  as  it  comes  from  the  lathe  tools  will  gradually  break  fibre  by 
fibre,  and  so  give  the  rope  a  short  life.  It  is  also  necessary  to  carefully  avoid 
all  sand  or  blow  holes,  as  they  will  cut  the  rope  out  with  surprising  rapidity. 

Much  depends  also  upon  the  arrangement  of  the  rope  on  the  pulleys,  es- 
pecially where  a  tension  weight  is  used.  Experience  shows  that  the 
increased  wear  on  the  rope  from  bending  the  rope  first  in  one  direction  and 
then  in  the  other  is  similar  to  that  of  wire  rope.  At  mines  where  two  cages 
are  used,  one  being  hoisted  and  one  lowered  by  the  same  engine  doing  the 
same  work,  the  wire  ropes,  cut  from  the  same  coil,  are  usually  arranged  so 
that  one  rope  is  bent  continuously  in  one  direction  and  the  other  rope  is  bent 
first  in  one  direction  and  then  in  the  other,  in  winding  on  the  drum  of  the 
engine.  The  rope  having  the  opposite  bends  wears  much  more  rapidly  than 
the  other,  lasting  about  three  quarters  as  long  as  its  mate.  This  difference 
in  wear  shows  in  mauila  rope,  both  in  transmission  of  power  and  in  coal- 
hoisting.  The  pulleys  should  be  arranged,  as  far  as  possible,  to  bend  the 
rope  in  one  direction. 

The  wear  of  the  rope  is  independent  of  the  distance  apart  of  the  shafts, 
since  the  wear  takes  place  only  on  the  pulleys;  hence  in  transmitting  power 
any  distance  within  the  limits  of  rope-driving,  the  life  of  the  rope  will  be 
the  same  whether  the  distance  is  small  or  great,  but  the  first  cost  will  be  in 
proportion  to  the  distance. 

TENSION  ON  THE  SLACK  PART  OF  THE  ROPE. 


Speed  of 
Rope,  in  feet 
per  second. 

Diameter  of  the  Rope  and  Pounds  Tension  on  the  Slack  Rope. 

y* 

Ys 

H 

Ys 

1 

1J4 

m 

m 

2 

20 

10 

27 

40 

54 

71 

110 

162 

216 

283 

30 

14 

29 

42 

56 

74 

115 

170 

226 

296 

40 

15 

31 

45 

60 

79 

123 

181 

240 

315 

50 

16 

33 

49 

65 

85 

132 

195 

259 

339 

60 

18 

36 

53 

71 

93 

145 

214 

285 

373 

70 

19 

39 

59 

78 

101 

158 

236 

310 

406 

80 

21 

43 

64 

85 

111 

173 

255 

340 

445 

90 

24 

48 

70 

93 

122 

190 

279 

372 

487 

926 


ROPE-DRIVING. 


For  large  amounts  of  power  it  is  common  to  use  a  number  of  ropes  lying 
side  by  side  in  grooves,  each  spliced  separately.  For  lighter  drives  some 
engineers  use  one  rope  wrapped  as  many  times  around  the  pulleys  as  is 
necessary  to  get  the  horse-power  required,  with  a  tension  pulley  to  take  up 
the  slack  as  the  rope  wears  when  first  put  in  use.  The  weight  put  upon  this 
tension  pulley  should  be  carefully  adjusted,  as  the  overstraining  of  the  rope 
from  this  cause  is  one  of  the  most  common  errors  in  rope  driving.  We 
therefore  give  a  table  showing  the  proper  strain  on  the  rope  for  the  various 
sizes,  from  which  the  tension  weight  to  transmit  the  horse-power  in  the 
tables  is  easilj7  deduced.  This  strain  can  be  still  further  reduced  if  the 
horse-power  transmitted  is  usually  less  than  the  nominal  work  which  the 
rope  was  proportioned  to  do,  or  if  the  angle  of  groove  in  the  pulleys  is 
acute. 

DIAMETER  OP  PULLEYS  AND  WEIGHT  OP  ROPE. 


Diameter  of 
Rope, 
in  inches. 

Smallest  Diameter 
of  Pulleys,  in 
inches. 

Length  of  Rope  to 
allow  for  Splicing, 
in  feet. 

Approximate 
Weight,  in  Ibs.  per 
foot  of  rope. 

^ 

20 

6 

.12 

% 

24 

6 

.18 

% 

30 

7 

.24 

so 

36 

8 

.32 

1 

42 

9 

.49 

\\^ 

54 

10 

,60 

1^ 

60 

12 

.83 

1% 

72 

13 

1.10 

2 

84 

14 

1.40 

'"  ]%" 

1L£" 

1^6" 

1%" 

1%" 

2" 

\    .6 

.72 

.844 

.98 

1.125 

1.3 

t   53 

44 

38 

33 

28 

25 

9   121 

145 

170 

193 

228 

256 

3   360 

430 

500 

600 

675 

780 

)   36 

43 

50 

60 

67 

78 

9   203 

242 

280 

347 

380 

446 

1   28 

34 

41 

49 

54 

63 

With  a  given  velocity  of  the  driving-rope,  the  weight  of  rope  required  for 
transmitting  a  given  horse-power  is  the  same,  no  matter  what  size  rope  is 
adopted.  The  smaller  rope  will  require  more  parts,  but  the  weight  will  be 
the  same. 

-Miscellaneous  Notes  on  Rope-driving.— WT.  H.  Booth  coniinu- 
nrcaresto  the  Anter.  Machinist  the  following  data  from  English  practice  with 
cotton  ropes.  The  calculated  figures  are  based  on  a  total  allowable  tension 
on  a  1%-inch  rope  of  600  Ibs.,  and  an  initial  tension  of  1/10  the  total  allowed 
stress,  which  corresponds  fairly  with  practice. 

Diameter  of  rope 1/4" 

Weight  per  foot,  Ibs 5 

Centrifugal  tension  =  F2  divided  by    64 
for  V=  80  ft.  per  sec.,  Ibs.  100 

Total  tension  allowable 300 

Initial  tension 30 

Net  working  tension  at  80  ft. velocity  170 
Horse-power  per  rope     **        *'  24 

The  most  usual  practice  in  Lancashire  is  summed  up  roughly  in  the  fol- 
lowing figures:  1%-inch  cotton  ropes  at  5000  ft.  per  minute  velocity  =  50  H. P. 
per  rope.  The  most  common  sizes  of  rope  now  used  are  1%  and  \%  in.  The 
maximum  horse-power  for  a  given  rope  is  obtained  at  about  80  to  83  feet 
per  second.  Above  that  speed  the  power  is  reduced  by  centrifugal  tension. 
At  a  speed  of  2500  ft.  per  minute  four  ropes  will  do  about  the  same  work  as 
three  at  5000  ft.  per  min. 

Cotton  ropes  do  not  require  much  lubrication  in  the  sense  that  it  is  re- 
quired by  ropes  made  of  the  rough  fibre  of  manila  hemp.  Merely  a  slight 
surface  dressing  is  all  that  is  required.  For  small  ropes,  common  in  spin- 
ning machinery,  from  ^  to  §4  inch  diameter,  it  is  the  custom  to  prevent  the 
fluffing  of  tlie  ropes  on  the  surface  by  a  light  application  of  a  mixture  of 
black-lead  and  molasses, — but  only  enough  should  be  used  to  lay  the  fibres, — 
put  upon  one  of  the  pulleys  in  a  series  of  light  dabs. 

Reuleaux's  Constructor  gives  as  the  "  specific  capacity  "  of  hemp  rope  in 
actual  practice,  that  is,  the  horse-power  transmitted  per  square  inch  of 
cross-section  for  each  foot  of  linear  velocity  per  minute,  .004  to  .002,  the 
cross-section  being  taken  as  that  due  to  the  full  outside  diameter  of  the 
rope.  For  a  1%-in.  rope,  with  a  cross-section  of  2.405sq.  in.,  at  a  velocity  of 
5000  ft.  per  min.,  this  gives  a  horse-power  of  from  24  to  48,  as  against  '41.8 
by  Mr.  Hunt's  table  and  49  by  Mr.  Booth's. 


MISCELLANEOUS  NOTES  OK   ROPE-DRIVING.        927 


lack  of  experimen  . 

power  due  to  journal  friction  =  4*,  to  stiffness  7.8*,  and  to  creep  of,  or  16.W 
i  a  al  loss. 


H1M?  limits  formula,  Tension  of  driving  side  of  rope  -*-  tension  of  slack 
side  of  'rope  =  2,  imp  ies  a  coefficient  of  friction  of  only  .10.     But  I  have 


nume  ou    a  g 

ion  although  we  hear  a  great  deal  about  the  loss  of  power  on  this  account 
I  am  singly  in  favor  of  using  the  continuous-rope  system,  and  also  of 


plovs  5/16-  n  nian  .  , 

naje     Rather  than  use  large  ropes  I  think  it  wiser  to  replace  small  ones 

of  tlner,  f  or  by  so  doing  a  great  gain  may  be  made  in  efficiency,  thus  saving 

flA  large  majority  of  failures  in  the  continuous-rope  plan  have  occurred 
where  the  driving  and  driven  sheaves  were  of  widely  different  diameters  as 
for  elample  driving  dynamos,  or  driving  a  line-shaft  from  an  engine  fly- 
wheel As  ord  narifv  installed  the  ropes  will  not  pull  alike,  and  by  calcula- 
tion or  by  experiment  we  may  find  one  rope  pulling  twice  or  three  times  as 

employs  an  engine-driving  sheave 


Plltnheas°bfeen  observed  that  in  sheaves  of  the  same  diameter  by  the  use  of  a 


aseen  oserv 

proper  tension  weight,  the  ropes  may  all  pull  alike;  while  where  the  sheaves 
are  of  unequal  diameter,  the  pull  is  unequal.  The  only  difference  of  condi- 
tions in  the  two  cases  lies  in  the  different  arc  of  contact  ot  the  ^ope  on  the 
two  sheaves,  which  leads  to  a  greater  fnctional  hold  of  the  rope  on  the  large 
sheave  To  equalize  the  f  notional  hold  on  the  two  sheaves  we  may  sharpen 
thlangle  of  the  small  sheave  or  increase  the  angle  of  the  large  sheave. 

The  Walker  Mf  e  Co  adopts  a  curved  form  of  groove  instead  of  one  with 
straight  sidefinclfned  to  each  other  at  45°.  The  curves,  are  concave  to  the 
rope  The  rope  rests  on  the  sides  of  the  groove  in  driving  and  driven  pul- 
E£r  Tn  Mler  pullevs  the  rope  rests  on  the  bottom  of  the  groove,  which  is 
Scircu  ar  The  wllker  Mf  g  Co.  also  uses  a  "  differential  "  drum  for  heavy 
m?e  drives  in  L  which  the  grooves  are  contained  each  in  a  separate  ring 
which  ta  free  to  "slide  on  the  turned  surface  of  the  drum  in  case  one  rope 

PUAhea°vy  %£&£%  the  separate,  or  English  rope  *£^*gS$& 

n* 

rion 


928 


FRICTION   AKD    LUBRICATIOK. 


to  the  amount  of  power  required  upon  the  several  floors.  Lambeth  cottonf 
ropes  are  used.  (For  much  other  information  on  this  subject  see  "  RopeH 
Driving,1'  by  J.  J.  Flather,  John  Wiley  &  Sons,  1895.) 

FRICTION  AND  LUBRICATION. 

Friction  is  defined  by  Rankine  as  that  force  which  acts  between  two 
bodies  at  their  surface  of  contact  so  as  to  resist  their  sliding  on  each  other^ 
and  which  depends  on  the  force  with  which  the  bodies  are  pressed  together  j 

Coefficient  of  Friction.— The  ratio  of  the  force  required  to  slide  a; 
body  alon^  a  horizontal  plane  surface  to  the  weight  of  the  body  is  called  the! 
coefficient  of  friction.  It  is  equivalent  to  the  tangent  of  the  angle  of  repose^ 
which  is  the  angle  of  inclination  to  the  horizontal  of  an  inclined  plane  or^ 
which  the  body  will  just  overcome  its  tendency  to  slide.  The  angle  is  usually 
denoted  by  0.  and  the  coefficient  by  f.f—  tan  0. 

Friction  of  Rest  and  of 'Motion.— The  force  required  to  start  a 
body  sliding  is  called  the  friction  of  rest,  and  the  force  required  to  continue 
its  sliding-  after  having:  started  is  called  the  friction  of  motion. 

Rolling  Friction  is  the  force  required  to  roll  a  cylindrical  or  spheri- 
cal body  on  a  plane  or  on  a  curved  surface.  It  depends  on  the  nature  of  the 
surfaces  and  on  the  force  with  which  they  are  pressed  together,  but  ia 
essentially  different  from  ordinary,  or  sliding,  friction. 

Friction  of  Solids.— Rennie's  experiments  (1839)  on  friction  of  solids, 
usually  un lubricated  and  dry,  led  to  the  following  conclusions: 

1.  The  laws  of  sliding  friction  differ  with  the  character  of  the  bodies 
rubbing  together. 

2.  The  friction  of  fibrous  material   is  increased  by  increased  extent  of 
surface  and  by  time  of  contact,  and  is  diminished  by  pressure  and  speed. 

3.  With  wood,  metal,  and  stones,  within  the  limit  of  abrasion,  friction 
varies  only  with  the  pressure,  and  is  independent  of  the  extent  of  surface, 
time  of  contact  and  velocity. 

4.  The  limit  of  abrasion  is  determined  by  the  hardness  of  the  softer  of  the 
two  rubbing  parts. 

5.  Friction  is  greatest  with  soft  and  least  with  hard  materials. 

6.  The  friction  of  lubricated  surfaces  is  determined  by  the  nature  of  the 
lubricant  rather  than  by  that  of  the  solids  themselves. 

Friction  of  Rest.    (Rennie.) 


Pressure, 
Ibs. 
per  square 
inch. 

Values  of/. 

Wrought  iron  on 
Wrought  Iron. 

Wrought  on 
Cast  Iron. 

Steel  on 
Cast  Iron. 

Brass  on 
Cast  Iron. 

187 
224 
336 
448 
560 
672 
784 

.25 

.27 
.31 
.38 
.41 
Abraded 

.28 
.29 
.33 
.37 
.37 
.38 
Abraded 

.30 
.33 
.35 

.35 
.36 
.40 
Abraded 

.23 
.22 
.21 
.21 
.23 
.23 
.23 

Law  of  Unlubricated  Friction.— A.  M.  Wellington,  Encfg  Neivs, 
April  7,  1888,  states  that  the  most  important  and  the  best  determined  of  all 
the  laws  of  unlubricated  friction  may  be  thus  expressed: 

The  coefficient  of  unlubricated  friction  decreases  materially  with  velocity 
is  very  much  greater  at  minute  velocities  of  0  +,  falls  very  rapidly  with 
minute  increases  of  such  velocities,  and  continues  to  fall  much  less  rapidly 
with  higher  velocities  up  to  a  certain  varying  point,  following  closely  the 
laws  which  obtain  with  lubricated  friction.' 

Friction  of  Steel  Tires  Sliding  on  Steel  Rails.  (Westing 
house  &  Galton.) 

Speed,  miles  per  hour 10        15        25        38       45        50 

Coefficient  of  friction 0.110     .087     .080     .051     .047    .040 

Adhesion,  Ibs.  per  ton  (2240  Ibs.)      246      195      179      128     114      90 


FRIC 


929 


Rolling  Friction  is  a  consequence  of  tne  irregularities  of  form  and 
the  roughnt-ss  of  surface  of  bodies  rolling  one  over  the  other.  Its  laws 
are  not  yet  definitely  established  in  consequence  of  the  uncertainty  which 
exists  in  experiment  as  to  how  much  of  the  resistance  is  due  to  roughness  of 
surface,  how  much  to  original  and  permanent  irregularity  of  form,  and  how 
much  to  distortion  under  the  load.  (Thurston.) 

Coefficients  of  Rolling  Friction.— If  R  =  resistance  applied  at 
the  circumference  of  the  wheel,  W  —  total  weight,  r  =  radius  of  the  wheel, 
and  /  =  a  coefficient,  R  —  fW-%-  r.  f  is  very  variable.  Coulomb  gives  .06 
for  wood,  .005  for  metal,  where  W  is  in  pounds  and  r  in  feet.  Tredgold 
made  the  value  of /for  iron  on  iron  .002. 

For  wagons  on  soft  soil  Morin  found/  =  .065,  and  on  hard  smooth  roads 
.0*. 

A  Committee  of  the  Society  of  Arts  (Clark,  R.  T.  D.)  reported  a  loaded 
omnibus  to  exhibit  a  resistance  on  various  loads  as  below: 


Pavement 


Speed  per  hour.    Coefficient. 


Granite     

Asphalt 

Wood  

Macadam,  gravelled 

granite,  new.. 


2.87  miles. 
3.56     " 
3.34     " 
3.45     " 
3.51      " 


.007 
.0121 
.0185 
.0199 
.0451 


Resistance. 
17.41  per  ton. 
27.14        " 
41.60 

44.48        " 
101.09        " 


Thurston  gives  the  value  of /for  ordinary  railroads,  .003,  well-laid  railroad 
track,  .002;  best  possible  railroad  track,  .001. 

The  few  experiments  that  have  been  made  upon  the  coefficients  of  rolling 
friction,  apart  from  axle  friction,  are  too  incomplete  to  serve  as  a  basis  for 
practical  rules.  (Trautwine). 

Laws  of  Fluid  Friction.  -For  all  fluids,  whether  liquid  or  gaseous, 
the  resistance  is  (1)  independent  of  the  pressure  between  the  masses  in 
contact;  (2)  directly  proportional  to  the  area  of  rubbing -surf  ace;  (3)  pro- 

r»rf-i/-»nal   t.r\  tlit»  cnnnro  f\f  t.li«-»  ivalfltivft  Vf»lr»r»if.v  fl t  mnrlprat.A  flriH   Viio-Vi   crk»^/le 


- 
tion as  the  journal  is  run  dry,  and  to  that  of  fluid  friction  as  it  is  flooded 


Angles  of  Repose  and   Coefficients   of  Friction  of  Build- 
ing Materials.    (From  Rankine's  Applied  Mechanics.) 


0. 

/  =  tan  0. 

1 
tan  0* 

Dry  masonry  and  brickwork.  . 
Masonry  and  brickwork  with 
damp  mortar  

31°  to  35° 
361/4° 

.6  to  .7 
74 

1.67  to  1.4 
1  35 

°6i 

about   4 

2  5 

35°  to  16%° 

7  to    3 

1  43  to  3  3 

Timber  on  timber  

26^j°  to  11H° 

.5  to    2 

2  to  5 

*'        "  metals 

31°  to  11^° 

6  to    2 

1  67  to  5 

Metals  on  metals      

14°  to  8U° 

.25  to    15 

4  to  6  67 

Masonry  on  dry  clay 

27° 

51 

1  96 

"          u  moist  clay  
Earth  on  earth  

18^° 
14°  to  45° 

.33 
.25  to  1.0 

3. 
4  to  I 

*'       "    dry  sand,  clay, 
and  mixed  earth.  
Earth  on  earth,  damp  clay  
wet  clay  
"      "      "        shingle   and 
gravel  

21°  to  37° 
45° 
17° 

39°  to  48° 

.38  to  .75 
1.0 
.31 

.81 

2.63  to  1.33 
1 
3.23 

1.23  to  0.9 

Friction  of  Motion.— The  following  is  a  table  of  the  angle  of  repose 
0,  the  coefficient  of  friction  /  =  tan  0,  and  its  reciprocal,  1  -r-/,  for  the  ma- 
terials of  mechanism— condensed  from  the  tables  of  General  Morin  (1831), 
and  other  sources,  as  given  by  Kankine: 


930 


FBICTIOtf   AND   LUBBICATION. 


No. 

Surfaces. 

0.  • 

/. 

I-/. 

1 
2 
3 

4 

Wood  on  wood,  dry  .  .   .  . 
"       "        "     soaped.. 
Metals  on  oak,  dry  
"        "     "     wet 

14°  to  26^° 
11^°  to  2° 
26J40  to  31° 
1-3^6°  to  14° 

.25  to  .5 
.2    to  .04 
.5  to  .6 
24  to    26 

4  to  2 
5  to  25 
2  to  1.67 
4  17  to  3  85 

5 

6 

"        "     "     soapy..  . 
"   elm,  dry  
Hemp  on  oak,  dry  

H^° 
11^°  to  14° 

28° 

.2 

.2  to  .25 
.53 

5 
5  to  4 
1  89 

8 

"       4*    "      wet 

18i^0 

33 

3 

9 

Leather  on  oak  

15°  to  19U° 

27  to  .38 

3.7  to  2  86 

10 
11 

13 
14 
15 
16 

"         "  metals,  dry.. 
"        "        "       wet.. 
1     greasy 
"        "        "     oily... 
Metals  on  metals,  dry.  .. 
'"       "        **         wet... 
Smooth    surfaces,  occa- 
siotially  creased 

mp- 

20° 
13° 

w 

8^°  toll0 
16#> 

4°  to  4^° 

.56 
.36 
.23 
.15 
.15  to  .2 
.3 

07  to   08 

1.79 
2.78 
4.35 
6.67 
6.67  to  5 
3.33 

14  3  to  12  5 

17 
18 

Smooth     surfaces,    con- 
tinuously greased  
Smooth    surfaces,    best 
results  

3° 
1%°  to  2° 

.05 
03  to  .036 

20 

19 

Bronze  ou  lignum  vitae, 
constantly  wet  

3°  ? 

.05  ? 

Coefficients  of  Friction  of  Journals.    (Morin.) 


Material. 

Unguent. 

Lubrication. 

Intermittent. 

Continuous. 

Cast  iron  on  cast  iron  .  .  ..  •! 

Cast  iron  on  bronze  j 

Cast  iron  on  lignum  vitae  .  . 
Wrought  iron  on  cast  iron  I 
"     "  bronze.,  f 

Iron  on  lignum  vitae  -j 
Bronze  on  bronze       .       •{ 

Oil,  lard  tallow. 
Unctuous  and  wet. 
Oil,  lard,  tallow. 
Unctuous  and  wet. 
Oil,  lard. 

Oil,  lard,  tallow. 

Oil,  lard. 
Unctuous. 
Olive-oil. 
Lard. 

.07  to  .08 
.14 
.07  to  .08 
.16 

.03  to  .054 
.03  to  .054 

.09 
.03  to  .054 

.07  to  .08 

.11 
.19 

.10 
.09 

Prof.  Thurston  says  concerning  the  above  figures  that  much  better  results 
are  probably  obtained  in  good  practice  with  ordinary  machinery.  Those 
here  given  are  so  greatly  modified  by;variations  of  speed,  pressure,  and  tem- 
perature, that  they  cannot  be  taken  as  correct  for  general  purposes. 

Average  Coefficients  of  Friction.  Journal  of  cast  iron  in  bronze 
bearing;  velocity  720  feet  per  minute;  temperature  70°  F. ;  intermittent 
feed  through  an  oil-hole.  (Thurston  on  Friction  and  Lost  Work.) 


Pressures,  pounds  per  square  inch. 


U11S. 

8 

16 

32 

48 

Sperm,  lard,  neat's-foot,etc. 

.159 

to 

.250 

.138 

to 

.192 

.086 

to 

.141 

.077  to 

.144 

Olive,  cotton  -seed,  rape,  etc. 

.160 

'* 

.283 

.107 

M 

.245 

.101 

k* 

.168 

.079   " 

.131 

Cod  and  menhaden  
Mineral  lubricating-oils.   .  .  . 

.248 
.154 

- 

.278 
.261 

.124 
.145 

- 

.167 
.233 

.097 
.086 

« 

.102    081    " 
.178i  .094   " 

.122 
.222 

With  fine  steel  journals  running  in  bronze  bearings  and  continuous  lubri- 
cation, coefficients  far  below  those  above  given  are  obtained.  Thus  with 
sperm-oil  the  coefficient  with  50  Ibs.  per  square  inch  pressure  was  .0034;  with 
200  Ibs.,  .0051;  with  300  Ibs.,  .0057. 


FRICTION.  931 

For  very  low  pressures,  as  in  spindles,  the  coefficients  are  much  higher 
Thus  Mr.  Woodbury  found,  at  a  temperature  of  100°  and  a  velocity  ot  600 


. 
feet  per  minute, 


Pressures,  Ibs.  per  sq.  in 1  2  3  4  5 

Coefficient....   ...   38        .27        .22        .18        .17 

These  high  coefficients,  however,  and  the  great  decrease  in  the  coefficient 
at  increased  pressures  are  limited  as  a  practical  matter  only  to  the  smaller 
pressures  which  exist  especially  in  spinning  machinery  where  the  pressure 
is  so  light  and  the  film  of  oil  so  thick  that  the  viscosity  of  the  oil  is  an  import- 


Oil- bath,   (reported    by   the    Committee   on   Friction,    I' roc.   lust.  ME., 
Nov   18S3)  show  that  the  absolute  friction,  that  is,  the  absolute  tangential 

l^uv.   J.CKXJ;    o»*v^  _^..,;,,«-   « V>,»  +  /irwl£k»i/-»ir  /->f  tlit»  V»rnc« 


nper 

The  -journal  was  of  steel,  4  inches  diameter  and  6  inches  long,  and  a  gun- 
metal  brass,  embracing  somewhat  less  than  half  the  circumference  of  the 
iournal  rested  on  its  upeer  side,  on  which  the  load  was  applied.  When  the 
bottom  of  the  journal  was  immersed  in  oil,  and  the  oil  therefore  earned 
under  the  brass  by  rotation  of  the  journal,  the  greatest  load  carried  with 
rape-oil  was  573  Ibs.  per  square  inch,  and  with  mineral  oil  625  Ibs. 

In  experiments  with  ordinary  lubrication,  the  oil  being  fed  in  at  the  cen- 
tre of  the  top  of  the  brass,  and  a  distributing  groove  being  cut  in  the  brass 


to  be  satisfactory,  but  the  bearing  seized  with  380  Ibs.  per  square  inch. 

When  the  oil  was  introduced  through  two  oil-holes,  one  near  each  end  ot 
the  brass,  and  each  connected  with  a  curved  groove,  the  brass  refused  t< 
take  its  oil  or  run  cool,  and  seized  with  a  load  of  only  200  Ibs.  per  square 

111  With  an  oil-pad  under  the  journal  feeding  rape-oil,  the  bearing  fairly  car- 
ried 551  Ibs.  Mr.  Tower's  conclusion  from  these  experiments  is  that  the 
friction  depends  on  the  quantity  and  uniformity  of  distribution  of  the  oil, 
and  mav  be  anything  between  the  oil-bath  results  and  seizing,  according  to 
the  perfection  or  imperfection  of  the  lubrication.  The  lubrication  may  be 
very  small,  giving  a  coefficient  of  1/100;  but  it  appeared  as  though  it  could 
not  be  diminished  and  the  friction  increased  much  beyond  this  point  witt 
out  imminent  risk  of  heating  and  seizing.  The  oil-bath  probably  represents 


or  from  luu  to  2uu  reec  per  minute,    u.y  prvj>oii.y  v^>  i  " 

surface  to  the  load,  it  is  possible  to  reduce  the  coefficient  of  friction  to  as  low 
as  1/1000.    A  coefficient  of  1/1500  is  easily  attainable,  and  probably  is  fre- 
quently attained,  in  ordinary  engine-bearings  in  which  the  direction  c 
force  is  rapidlv  alternating  and  the  oil  given  an  opportunity  to  get  between 
the  surfaces,  while  the  duration  of  the  force  in  one  direction  is  not  sufficient 


t 


to  allow  time  for  the  oil  film  to  be  squeezed  out. 

Observations  on  the  behavior  of  the  apparatus  gave  reason  to  be lieve  that 
with  perfect  lubrication  the  speed  of  minimum  friction  was  from  100  to  1; 
feet  per  minute,  and  that  this  speed  of  minimum  friction  tends  to  be  highei 
with  an  increase  of  load,  and  also  with  less  perfect  lubrication.  By  the 
sp«e-l  of  minimum  friction  is  meant  that  speed  in  approaching  which  trom 
rest  the  friction  diminishes,  and  above  which  the  friction  increases. 


932 


FRICTION   AKD   LUBRICATION. 


Coefficients  of  Friction   of  Journal  with  Oil-bath.— Ab< 

stract  of  results  of  Tower's  experiments  <»n  friction  (Proc.  Inst.  M.  E.,  Nov. 
1883).     Journal,  4  in.  diani.,  6  in.  long;  temperature,  90°  F. 


Lubricant  in  Bath. 

Nominal  Load,  in  pounds  per  square  inch. 

625 

520 

415 

310 

205 

153  |  100 

Lard-oil  : 
157  ft.  per  min  

Coefficients  of  Friction. 

.0009 
.0017 

.0014 
.0022 

seiz'd 

.0012 
.0021 

.0016 
.0027 

.0015 
.0021 

.0009 
.0016 

.0012 
.002 

.0014 
.0029 

.0022 
.004 

.0011 
.0019 

.0008 
.0016 

.0014 
.0024 

.0056 
.0068 

.0020 
.0042 

.0034 
.0066 

.0016 
.0027 

.0014 
.0024 

.0021 
.00:35 

.0098 
.0077 

.0027 
.0052 

.0038 
.0083 

.0019 
0037' 

.002 
.004 

.0042 
.009 

.0076 
.0151 

.003 
.0064 

.004 
.007 

.004 

.007 

.0125 
.0152 

.0099 
.0133 

471      "           "  

Mineral  grease  : 
157ft  per  min           .... 

.001 
.002 

471      "           "  

Sperm-oil  : 
157  ft.  per  min  

471      'k           "   

Rape-oil  : 
157  ft  per  min  

(573  Ib.) 
.001 

.001 
.0015 

.0012 
.0018 

471      "          "  

Mineral-oil  : 
157ft.  per  min  „  
471      "          "  

.OC13 

Rape-oilfed  by  syphon  lubricator: 
157  ft.  per  min  
314     "          "   

Rape-oil,  pad  under  journal: 
157  ft.  per  min  , 

.0099 

0105 

314     "          "   

.0099 

.0078 

Comparative  friction  of  different  lubricants  under  same  circumstances, 
temperature  90°,  oil-bath: 

Lard. 


Sperm-oil 100  per  cent. 

Rape-oil 106 

Mineral  oil 129 


Olive-oil 135 

Mineral  grease 21 


135  per  cent. 


With  sperm 07 

With  lard .07 


Coefficients  of  Friction  of  Motion  and  of  Rest  of  a 
Journal. — A  cast-iron  journal  in  steel  boxes,  tested  by  Prof.  Thurston  at 
a  speed  of  rubbing  of  150  feet  per  minute,  with  lard  and  with  sperm  oil, 
gave  the  following: 

Pressures  per  sq.  in.,  Ibs 50  100  250  500  750        1000 

Coeff.,  with  sperm 013         .008         .005          .004         .0043       .009 

..»'•     lard 02         .0137        .0085        .0053        .0066       .0125 

The  coefficients  at  starting  were: 

.135          .14  .15          .185          .18 

.11  .11  .10          .12  .12 

The  coefficient  at  a  speed  of  150  feet  per  minute  decreases  with  increase 
of  pressure  until  500  Ibs.  per  sq.  in.  is  reached;  above  this  it  increases.  The 
coefficient  at  rest  or  at  starting  increases  with  the  pressure  throughout  the 
ranere  of  the  tests. 

Value  of  Anti-friction  Metals.  (Denton.)— The  various  white 
metals  available  for  lining  brasses  do  not  afford  coefficients  of  friction 
lower  than  can  be  obtained  with  bare  brass,  but  they  are  less  liable  to 
"overheating,1'  because  of  the  superiority  of  such  material  over  bronze  in 
ability  to  permit  of  abrasion  or  crushing,  without  excessive  increase  of 
friction. 

Thurston  (Friction  and  Lost  Work)  says  that  gun-bronze,  Btbbitt,  and 
other  soft  white  alloys  have  substantially' the  same  friction;  in  other  words, 
the  friction  is  determined  by  the  nature  of  the  unguent  and  not  by  that  of 
the  rubbing- surfaces,  when  the  latter  are  in  good  order.  The  soft  metals 
run  at  higher  temperatures  than  the  bronze.  This,  however,  does  not  nec- 
essarily indicate  a  serious  defect,  but  simply  deficient  conductivity.  The 
value  of  the  white  alloys  for  bearings  lies  mainly  in  their  ready  reduction 
to  a  smooth  surface  after  any  local  or  general  injury  by  alteration  of  either 
surface  or  form, 


MORIN'S  LAWS  OF  FRICTION*.  933 

Cast-iron  for  Bearings.  (Joshua  Rose.)-Cast  iron  appears  to  be  an 
exception  to  the  general  rule,  that  the  harder  the  metal  the  greater  the 
resistance  to  wear,  because  cast  iron  is  softer  in  its  texture  and  easier  to 
cut  with  steel  tools  than  steel  or  wrought  iron,  but  in  some  situations  it  is 
far  more  durable  than  hardened  steel;  thus  when  surrounded  by  steam  it 
will  wear  better  than  will  any  other  metal.  Thus,  for  instance,  experience 
has  demonstrated  that  piston-rings  of  cast  iron  will  wear  smoother,  better, 
and  equally  as  long  as  those  of  steel,  and  longer  than  those  of  either 
wrought  iron  or  brass,  whether  the  cylinder  in  which  it  works  be  composed 
of  brass,  steel,  wrought  iron,  or  cast  iron;  the  latter  being  the  more  note- 
worthy, since  two  surfaces  of  the  same  metal  do  not,  as  a  rule,  wear  or 
work  well  together.  So  also  slide-valves  of  brass  are  not  found  to  wear  so 
long  or  so  smoothly  as  those  of  cast  iron,  let  the  metal  of  which  the  seating 
is  composed  be  whatever  it  may;  while,  on  the  other  hand,  a  cast  iron  slide- 
valve  will  wear  longer  of  itself  and  cause  less  wear  to  its  seat,  if  the  latter 
is  of  cast  iron,  than  if  of  steel,  wrought  iron,  or  brass. 

Friction  of  Metals  under  Steam-pressure.— The  friction  of 
brass  upon  iron  under  steam -pressure  is  double  that  of  iron  upon  iron. 
(G.  H.  Babcock,  Trans.  A.  S.  M.  E..  i.  151.) 

Moriii*s  "I^aws  of  Friction."—!.  The  friction  between  two  bodies 
is  directly  proportioned  to  the  pressure;  i.e.,  the  coefficient  is  constant  for 
all  pressures. 

2.  The  coefficient  and  amount  of  friction,  pressure  being  the  same,  is  in- 
dependent of  the  areas  in  contact. 

3  The  coefficient  of  friction  is  independent  of  velocity,  although  static 
friction  (friction  of  rest)  is  greater  than  the  friction  of  motion. 

Eng'g  News,  April  7,  1888,  comments  on  these  "laws"  as  follows  :  From 
1831  till  about  1876  there  was  no  attempt  worth  speaking  of  to  enlarge  our 
knowledge  of  the  laws  of  friction,  which  during  all  that  period  was  assumed 
to  be  complete,  although  it  was  really  worse  than  nothing,  since  it  was  for 
the  most  part  wholly  false.  In  the  year  first  mentioned  Morin  began  a  se- 
ries of  experiments  which  extended  over  two  or  three  years,  and  whick 
resulted  in  the  enunciation  of  these  three  "  fundamental  laws  of  friction," 
no  one  of  which  is  even  approximately  true. 

For  fifty  years  these  laws  were  accepted  as  axiomatic,  and  were  quoted  as 
such  without  question  in  every  scientific  work  published  during  that  whole 
period.  Now  that  they  are  so  thoroughly  discredited  it  has  been  attempted 
to  explain  away  their  defects  on  the  ground  that  they  cover  only  a  very  lim- 
ited range  of  pressures,  areas,  velocities,  etc.,  and  that  Morin  himself  only 
announced  them  as  true  within  the  range  of  his  conditions.  It  is  now  clearly 
established  that  there  are  no  limits  or  conditions  within  which  any  one  of 
them  even  approximates  to  exactitude,  and  that  there  are  many  conditions 
under  which  they  lead  to  the  wildest  kind  of  error,  while  many  of  the  con- 
stants were  as  inaccurate  as  the  laws.  For  example,  in  MorhYs  "  Table  of 
Coefficients  of  Moving  Friction  of  Smooth  Plane  Surfaces,  perfectly  lubri- 
cated/' which  may  be  found  in  hundreds  of  text-books  now  in  use.  the  coeffi- 
cient of  wrought  iron  on  brass  is  given  as  .075  to  .103,  which  would  make  the 
rolling  friction  of  railway  trains  35  to  20  Ibs.  per  ton  instead  of  the  3  to  G  Ibs. 
which  it  actually  is. 

General  Morin,  in  a  letter  to  the  Secretary  of  the  Institution  of  Mechanical 
Engineers,  dated  March  15, 1879,  writes  as  follows  concerning  his  experiments 
on  friction  made  more  than  forty  years  before:  "  The  results  furnished  by  my 
experiments  as  to  the  relations  between  pressure,  surface,  and  speed  on  the 
one  hand,  and  sliding  friction  on  the  other,  have  always  been  regarded  by 
myself,  not  as  mathematical  laws,  but  as  close  approximations  to  the  truth, 
within  the  limits  of  the  data  of  the  experiments  themselves.  The  same  holds, 
in  my  opinion,  for  many  other  laws  of  practical  mechanics,  such  as  those  of 
rolling  resistance,  fluid  resistance,  etc." 

Prof.  J.  E.  Denton  (titevens  Indicator,  July,  1890)  says:  It  has  been  gen- 
erally assumed  that  friction  between  lubricated  surfaces  follows  the  simple 
law  that  the  amount  of  the  friction  is  some  fixed  fraction  of  the  pressure  be- 
tween the  surfaces,  such  fraction  being  independent  of  the  intensity  of  the 
pressure  per  square  inch  and  the  velocity  of  rubbing,  between  certain  limits 
of  practice,  and  that  the  fixed  fraction  referred  to  is  represented  by  the  co- 
efficients of  friction  given  by  tb  -  experiments  of  Morin  or  obtained  from  ex- 
perimental data  wrhich  represent  conditions  of  practical  lubrication,  such  as 
those  given  in  Webber's  Manual  of  Power. 

By  the  experiments  of  Thurston,  Woodbury,  Tower,  etc.,  however,  it 
appears  that  the  friction  between  lubricated  metallic  surfaces,  such  as  ina- 


934  FRICTION   AXD   LUBRICATION. 

chine  bearings,  is  not  directly  proportional  to  the  pressure,  is  not  indepen- 
dent of  the  speed,  and  that  the  coefficients  of  Morin  and  Webber  are  about 
tenfold  too  great  for  modern  journals. 

Prof.  Denton  offers  an  explanation  of  this  apparent  contradiction  of  au- 
thorities by  showing,  with  laboratory  testing  machine  data,  that  Morin 's 
laws  hold  for  bearings  lubricated  by  a  restricted  feed  of  lubricant,  such  as 
is  afforded  by  the  oil-cups  common  to  machinery;  whereas  the  modern  ex- 
periments have  been  made  with  a  surplus  feed  or  superabundance  of  lubri- 
cant, such  as  is  provided  only  in  railroad -car  journals,  and  a  few  special 
cases  of  practice- 
That  the  low  coefficients  of  friction  obtained  under  the  latter  conditions 
are  realized  in  the  case  of  car  journals,  is  proved  by  the  fact  that  the  tem- 
perature of  car- boxes  remains  at  100°  at  high  velocities;  arid  experiment  shows 
that  this  temperature  is  consistent  only  with  a  coefficient  of  friction  of  a 
traction  of  one  per  cent.  Deductions  from  experiments  on  train  resistance 
also  indicate  the  same  low  degree  of  friction.  But  these  low  co -efficients  dt 
not  account  for  the  internal  friction  of  steam-engines  as  well  as  do  the  co 
efficients  of  Morin  and  Webber. 

In  American  Machinist,  Oct.  23,  1890,  Prof.  Denton  says:  Mqrin's  measure- 
ment of  friction  of  lubricated  journals  did  not  extend  to  light  pressures. 
They  apply  only  to  the  conditions  of  general  shafting  and  engine  work. 

He  clearly  understood  that  there  was  a  frictional  resistance,  due  solely  to 
the  viscosfty  of  the  oil,  and  that  therefore,  for  very  light  pressures,  the  laws 
which  he  enunciated  did  not  prevail. 

He  applied  his  dynamometers  to  ordinary  shaft-journals  without  special 
preparation  of  the  rubbing- surf  aces,  and  without  resorting  to  artificial 
methods  of  supplying  the  oil. 

Later  experimenters  have  with  few  exceptions  devoted  themselves  exclu- 
sively to  the  measurement  of  resistance  pra-erically  due  to  viscosity  alone. 
They  have  eliminated  the  resistance  to  which  Morin  confined  his  measure- 
ments, namely,  the  friction  due  to  such  contact  of  the  rubbing-surfaces  as 
prevail  with  a  very  thin  film  of  lubricant  between  comparatively  rough  sur- 
faces. 

Prof.  Denton  also  says  (Trans.  A.  S.  M.  E.,  x.  518):  "  I  do  not  believe  there 
is  a  particle  of  proof  in  any  investigation  of  friction  ever  made,  that  Morin 's 
laws  do  not  hold  for  ordinary  practical  oil-cups  or  restricted  rates  of  feed.1' 

Laws  of  Friction  of  well-lubricated  Journals.  — John 
Goodman  (Trans.  Inst.  C.  E.  188G,  Eny^y  A'ems,  Apr.  7  and  14,  1888;,  review- 
ing the  results  obtained  from  the  testing-machines  of  Thurston,  Tower,  and 
Stroudley,  arrives  at  the  following  laws: 

LAWS  OF  FRICTION:  WELL- LUBRICATED  SURFACES. 
(Oil-bath.) 

1.  The  coefficient  of  friction  with  the  surfaces  efficiently  lubricated  is  from 
1/6  to  1/10  that  for  dry  or  scantily  lubricated  surfaces. 

2.  The  coefficient  of  friction  for  moderate  pressures  and  speeds  varies  ap- 
proximately inversely  as  the  normal  pressure:  the  frictional  resistance  va- 
ries as  the  area  in  contact,  the  normal  pressure  remaining  constant. 

3  At  very  low  journal  speeds  the  coefficient  of  friction  is  abnormally 
high;  but  as  the  speed  of  sliding  increases  from  about  10  to  100  ft.  per  min'. 
the  friction  diminishes,  and  again  rises  when  that  speed  is  exceeded,  varying 
approximately  as  the  square  root  of  the  speed. 

4.  The  coefficient  of  friction  varies  approximately  inversely  as  the  temper- 
ature, within  certain  limits,  namely,  just  before  abrasion  tnkes  place. 

The  evidence  upon  which  these  laws  are  based  is  taken  from  various  mod- 
ern experiments.  That  relating  to  Law  1  is  derived  from  the  "First  Report 
on  Friction  Experiments,1'  by  Mr.  Beauchamp  Tower. 


Method  of  Lubrication. 

Coefficient  of 
Friction. 

Comparative 
Friction. 

Oil-bath                  

.00139 

1.00 

.0098 

7.06 

Pad  under  journal  

.0090 

6.48 

With  a  load  of  293  Ibs  per  sq.  in.  and  a  journal  speed  of  314  ft.  per  min. 
Mr.  Tower  found  the  coefficient  of  friction  to  be  .0016  with  an  oil-bath,  «nd 


LAWS  OF 


935 


.0097,  or  six  times  as  much,  with  a  pad.  The  very  low  coefficients  ob- 
tained by  Mr.  Tower  will  be  accounted  for  by  Law  2,  as  he  found  that  the 
frictional  resistance  per  square  inch  under  varying  loads  is  nearly  constant, 
as  below: 

Load  in  Ibs.  per  sq.  in 529      468      415      363      310      258      205      153    100 

Frictional  resist,  persq.  in.  .416     .514     .498     .472     .464    .438    .43      .458  .45 

The  frictional  resistance  per  square  inch  is  the  product  of  the  coefficient 
of  friction  into  the  load  per  square  inch  on  horizontal  sections  of  the  brass. 
Hence,  it'  this  product  be  a  constant,  the  one  factor  must  vary  inversely  as 
the  Other,  or  a  high  load  will  give  a  low  coefficient,  and  vice  versa. 

For  ordinary  lubrication,  the  coefficient  is  more  constant  under  varying 
loads;  the  frictional  resistance  then  varies  directly  as  the  load,  as  shown  by 
Mr.  Tower  in  Table  VIII  of  his  report  (Proc.  Inst.  M.  E.  1883). 

With  respect  to  Law  3,  A.  M.  Wellington  (Trans.  A.  S.  0.  E.  1884).  in  ex- 
periments on  journals  revolving  at  very  low  velocities,  found  that  the  friction 
was  then  very  great,  and  nearly  constant  under  varying  conditions  of  the 
lubrication,  load,  and  temperature.  But  as  the  speed  increased  the  friction 
fell  slowly  and  regularly,  and  again  returned  to  the  original  amount  when 
the  velocity  was  reduced  to  the  same  rate.  This  is  shown  in  the  following 
table: 
Speed,  feet  per  minute: 

0-f      2.16      3.33      4.86 
Coefficient  of  friction: 

.118   .094   .070   .069 


8.82   21.42   35.37   53.01   89.28   106.02 


.055   .047    .040    .035 


.026 


It  was  also  found  by  Prof.  Kimball  that  when  the  journal  velocity  was  in- 
creased from  6  to  110  ft.  per  minute,  the  friction  was  reduced  70$;  in  another 
case  the  friction  was  reduced  67$  when  the  velocity  was  increased  from  1  to 
100ft.  per  minute;  but  after  that  point  was  reached  the  coefficient  varied 
approximately  with  the  square  root  of  the  velocity. 

The  following  results  were  obtained  by  Mr.  Tower: 


Feet  per  minute.  .. 

209 

262 

314 

366 

419 

471 

Nominal  Load 
per  sq.  in. 

Coeff  .  of  friction  .  . 

.0010 
.0013 
.0014 

.0012 
.0014 
.0015 

.0013 
.0015 
.0017 

.0014 
.0017 
.0019 

.0015 
.0018 
.0021 

.0017 
.002 
.0024 

520  Ibs. 

468    " 
415    " 

The  variation  of  friction  with  temperature  is  approximately  in  the  inverse 
ratio,  Law  4.    Take,  for  example,  Mr.  Tower's  results,  at  262  ft.  per  minute: 


Temp.  F. 

110° 

100° 

90° 

80° 

70° 

60° 

Observed  
Calculated  

.0044 
.00451 

.0051 
.00518 

.006 
.00608 

.0073 
.00733 

.0092 
.00964 

.0119 
.01252 

Thi 
efficie 

Serature 
as  bee 

per  Sq     iu.        J.ui»  10  auuwu  iu   i/iic  juju 

experiments  with  a  pad  of  rape  oil: 


e,  but  on  a  gradually  decreasing  scale,  until  the  normal  temperature 
jn  reached;  this  normal  temperature  increases  directly  as  the  load 
in.  This  is  shown  in  the  following  table  taken  from  Mr.  Stroudley's 


Temp  F    .. 

105° 

110° 

115° 

120° 

125° 

130° 

135° 

140° 

145° 

Coefficient  
Decrease  of  coeff.. 

.022 

.0180 
.0040 

.0160 
.0020 

.0140 
0020 

.0125 
.0015 

.0115 
.0010 

.0110 
.0005 

.0106 
.0004 

.0102 
.0002 

In  the  Gral ton -Westinghouse  experiments  it  was  found  that  with  velocities 
below  100  ft.  per  min.,  and  with  low  pressures,  the  frictional  resistance 
varied  directly  as  the  normal  pressure;  but  when  a  velocity  of  100  ft.  per 
min.  was  exceeded,  the  coefficient  of  friction  greatly  diminished;  from  the 
same  experiments  Prof.  Kennedy  found  that  the  coefficient  of  friction  for 
high  pressures  was  sensibly  less  than  for  low. 

Allowable  Pressures  on  Bearing-surfaces.  (Proc.  Inst.  M.  E., 
May,  1888.)— The  Committee  on  Friction  experimented  with  a  steel  ring  of 


936  FKICTIOH  AKD   LtTBUICATIOK. 

rectangular  section,  pressed  between  two  cast-iron  disks,  the  annular  bear- 
ing-surfaces of  which  were  covered  with  gun-metal,  and  were  12  in.  inside 
diameter  and  14  in.  outside.  The  two  disks  were  rotated  together,  and  the 
steel  ring  was  prevented  from  rotating  by  means  of  a  lever,  the  holding 
force  of  which  was  measured.  When  oiled  through  grooves  cut  in  each  face 
of  the  ring  and  tested  at  from  50  to  130  revs,  per  min.,  it  was  found  that  a 
pressure  of  75  Ibs.  per  sq.  in.  of  bearing-surface  was  as  much  as  it  would 
bear  safely  at  the  highest  speed  without  seizing,  although  it  carried  90  Ibs. 
per  sq.  in.  at  the  lowest  speed.  The  coefficient  of  friction  is  also  much 
higher  than  for  a  cylindrical  bearing,  and  the  friction  follows  the  law  of  the 
friction  of  solids  much  more  nearly  than  that  of  liquids.  This  is  doubtless 
due  to  the  much  less  perfect  lubrication  applicable  to  this  form  of  bearing 
compared  with  a  cylindrical  one.  The  coefficient  of  friction  appears  to  be 
about  the  same  with  the  same  load  at  all  speeds,  or,  in  other  words,  to  be 
independent  of  the  speed;  but  it  seems  to  diminish  somewhat  as  the  load  is 
increased,  and  may  be  stated  approximately  as  1/20  at  15  Ibs.  per  sq.  in., 
diminishing  to  1/30  at  75  Ibs.  per  sq.  in. 

The  high  coefficients  of  friction  are  explained  by  the  difficulty  of  lubricat- 
ing a  collar-bearing.  It  is  similar  to  the  slide-block  of  an  engine,  which  can 
carry  only  about  one  tenth  the  load  per  sq.  in.  that  can  be  carried  by  the 
crank-pins. 

In  experiments  on  cylindrical  journals  it  has  been  shown  that  when  a 
cylindrical  journal  was  lubricated  from  the  side  on  which  the  pressure  bore, 
100 Ibs.  per  sq  in.  was  the  limit  of  pressure  that  it  would  carry;  hut  when  it 
came  to  be  lubricated  on  the  lower  side  and  was  allowed  to  drag  the  oil  in 
with  it,  600  Ibs  per  sq  in.  was  reached  with  impunity;  and  if  the  600  Ibs.  per 
sq.  in.,  which  was  reckoned  upon  the  full  diameter  of  the  bearing,  came  to 
be  reckoned  on  the  sixth  part  of  the  circle  that  was  taking  the  greater  pro- 
portion of  the  load,  it  followed  that  the  pressure  upon  that  part  of  the  circle 
amounted  to  about  1:300  Ibs.  per  sq.  in. 

In  connection  with  these  experiments  Mr.  Wicksteed  states  that  in  drill- 
ing-machines the  pressure  on  the  collars  is  frequently  as  high  as  336  Ibs.  per 
sq.  in.,  but  the  speed  of  rubbing  in  this  case  is  lower  than  it  was  in  any  of 
the  experiments  of  the  Research  Committee.  In  machines  working  very 
slowly  and  intermittently,  as  in  testing-machines,  very  much  higher  pres- 
sures are  admissible. 

Mr.  Adamson  mentions  the  case  of  a  heavy  upright  shaft  carried  upon  a 
small  footstep-beariujr,  where  a  weight  of  at  least  $20  tons  was  carried  on  a 
shaft  of  5  in.  diameter,  or,  say,  20  sq.  in.  area,  giving  a  pressure  of  1  ton  per 
sq.  in.  The  speed  was  190  to  200  revs  per  min.  It  was  necessary  to  force  1he 
oil  under  the  bearing  by  means  of  a  pump.  For  heavy  horizontal  shafts, 
such  as  a  fly-wheel  shaft,  carrying  100  tons  on  two  journals,  his  practice  for 
getting  oil' into  the  bearings  was  to  flatten  the  journal  along  one  side 
throughout  its  whole  length  to  the  extent  of  about  an  eighth  of  an  inch  in 
width  for  each  inch  in  diameter  up  to  8  in.  diameter;  above  that  size  rather 
less  flat  in  proportion  to  the  diameter.  At  first  sight  it  appeared  alarming 
to  get  a  continuous  flat  place  coming  round  in  every  revolution  of  a  heavily 
loaded  shaft;  yet  it  carried  the  oil  effectually  into  the  bearing,  which  ran 
much  better  in  consequence  than  a  truly  cylindrical  journal  without  a  flat 
side. 

In  thrust-bearings  on  torpedo-boats  Mr.  Thornycroft  allows  a  pressure  of 
never  more  than  50  Ibs.  per  sq.  in. 

Prof.  Thurston  (Friction  and  Lost  Work,  p.  240)  says  7000  to  9000  Ibs. 
pressure  per  square  inch  is  reached  on  the  slow-working  and  rarely  moved 
pivots  of  swing  bridges. 

Mr.  Tower  says  (Proc.  Inst  M  E.,  Jan.  1884):  In  eccentric-pins  of  punch- 
ing and  shearing-machines  very  high  pressures  are  sometimes  used  without 
seizing.  In  addition  to  the  alternation  in  the  direction,  the  pressure  is  ap* 
plied  for  only  a  very  short  space  of  time  in  these  machines,  so  that  the  oil 
has  no  time  to  be  squeezed  out. 

In  the  discussion  on  Mr.  Tower's  paper  (Proc.  Inst.  M.  E.  1885)  it  was 
stated  that  it  is  well  known  from  practical  experience  that  with  a  constant 
load  on  an  ordinary  journal  it  is  difficult  and  almost  impossible  to  have  more 
than  200  Ibs.  per  square  inch,  otherwise  the  bearing  would  get  hot  and  the 
oil  go  out  of  it;  bat  when  the  motion  was  reciprocating,  so  that  the  load  was 
alternately  relieved  from  the  journal,  as  with  crank-pins  and  similar  jour- 
nals, much  higher  loads  might  he  applied  than  even  700  or  800  Ibs.  per  square 
inch. 


FRICTION   OF   CAR-JOURNAL   BRASSES.  937 

Mr  Goodman  (Proc.  lust.  C.  E.  1886)  found  that  the  total  frictional  re- 
sistance is  materially  reduced  by  diminishing  the  width  of  the  brass 

The  lubrication  is  most  efficient  in  reducing  the  friction  when  the  brass 
subtends  an  angle  of  from  1^0°  to  60°.  The  film  is  probably  at  its  best  be- 
bween  the  angles  80°  and  110°. 

In  the  case  of  a  brass  of  a  railway  axle-bearing  where  an  oil-groove  is  cut 
alono-  its  crown  and  an  oil-hole  is  drilled  through  the  top  of  the  brass  into  it, 
the  wear  is  invariably  on  the  off  side,  which  is  probably  due  to  the  oil  escap- 
ing as  soon  as  it  reaches  the  crown  of  the  brass,  and  so  leaving  the  off  side 
almost  dry,  where  the  wear  consequently  ensues. 

In  railway  axles  the  brass  wears  always  on  the  forward  side  The  same  ob- 
servation has  been  made  in  marine  engine  journals,  which  always  wear  in 
exactly  the  reverse  way  to  what  they  might  be  expected.  Mr.  Strpudley 
thinks  this  peculiarity  is  due  to  a  film  of  lubricant  being  drawn  iin  from  the  un- 
der side  of  the  journal  to  the  aft  part  of  the  brass,  which  effectually  lubri- 
cates and  prevents  wear  on  that  side;  and  that  when  the  lubricant  reaches 
the  forward  side  of  the  brass  it  is  so  attenuated  down  to  a  wedge  shape  that 
there  is  insufficient  lubrication,  and  greater  wear  consequently  follows. 

Prof  J  E  Denton  (Am.  Mack..  Oct.  30,  1890)  says:  Regarding  the  pres- 
sure to  which  oil  is  subjected  in  railroad  car-service,  it  is  probably  more  severe 
than  in  anv  other  class  of  practice.  Car  brasses,  when  used  bare,  are  so  im- 
perfectly fitted  to  the  journal,  that  during  the  early  stages  ot  their  use  the 
are  a  of  bearing  may  be  but  about  one  square  inch.  In  this  case  the  pressure 
Ser  square  inch  is  upwards  of  6000  Ibs.  But  at  the  slowest  speeds  ot  freight 
service  the  wear  of  a  brass  is  so  rapid  that,  within  about  thirty  minutes  the 
area  is  either  increased  to  about  three  inches,  and  is  thereby  able  to  relieve 
the  oil  so  that  the  latter  can  successfully  prevent  overheating  of  the  oournal, 
or  else  overhearing  takes  place  with  aim  oil.  and  measures  of  relief  must  be 
tak-n  which  eliminate  the  question  of  differences  of  lubricating  power 
among  the  different  lubricants  available.  A  brass  which  has  been  run  about 
fifty  miles  under  5000  Ibs.  load  may  have  extended  the  area  of  bearing-surface 
tc  about  three  square  inches.  The  pressure  is  then  about  1700  Ibs.  per  square 
inch  It  may  be  assumed  that  this  is  an  average  minimum  area  for  car-ser- 
vice where  no  violent  and  un  manageable  overheating  has  occurred  during  the 
use  of  a  brass  for  a  short  time.  This  area  will  very  slowly  increase  with  any 
lubricant  Feb  Igg8)  Qne  of  the  raost  vital  points  of  an  en- 

gine for  electrical  service  is  that  of  main  bearings.  They  should  have  a  sur- 
See  velocfty  -of  not  exceeding  350  feet  per  minute,  with  a  mean  beanng- 
oressure  per  square  inch  of  projected  area  of  journal  ot  not  more  than  80 
Fbs  ThisPis  considerably  within  the  safe  limit  of  cool  performance  ;  and  easy 
operation  If  the  bearings  are  designed  in  this  way,  it  would  admit  the  ui 
of  grease  on  all  the  main  wearing-surface,  which  in  a  large  type  of  engines 
for  this  class  of  work  we  think  advisable.  ,_  _  , 

Oil-prelsur^  Hi  a  Bearing.  -Mr  Beauchamp  Tower  (Pronto* 
ME  ,  Jan.  1885)  made  experiments  with  a  brass  bearing  4  inches  diameter 
by  6  inches  Ion-,  to  determine  the  pressure  of  the  oil  between  the  :  brass  and 
the  iournal  The  bearing  was  half  immersed  in  oil,  and  had  a  total  load  ot 
SOOS  Ibs  uDon  it  The  Iournal  rotated  150  revolutions  per  minute.  The 
pressure  ot  the  oil  was  determined  by  drilling  small  holes  in  the  bearing  at 
different  points  ard  connecting  them  by  tubes  to  a  Bourdon  gauge 
foundThat  the  pressure  varied  from  310  to  625  Ibs.  per  square  inch  the  great- 
est pressure  being  a  little  to  the  "  off  "  side  of  the  centre  line  ot  the  top  of 
the  bearing,  in  the  direction  of  motion  of  the  journal.  The  sum  of  ^the  up- 
ward force  exerted  by  these  pressures  for  the  whole  lubricated  are 
Larly  equal  !o  the  total  pressure  on  the  bearing.  The  speed  was  reduced 
olutions,  but  the  oil-pressure  remained  the  same,  sh  £  K  ing 

^ 


The  nominal  load  per  square  inch  is  the  total  load  divided  by  the  product  of 
^he  diameter  and  length  of  the  journal.  At  the  same  low  speed  of  30  revo- 
l^ionsp^  minute  itVas  increased  to  676  Ibs.  per  square  inch  without  any 

Si^ic«onn|f  Ca?fogurnal  Brakes.    (J.  E  Denton,  Trans  AS  ,  M- 
13    xii  405  "A  new  brass  dressed  with  an  emery-wheel,  loaded  with  5000  Ibs 
m^nave  an  actual  bearing-surface  on  the  journal,  as  shown  by  the  polish 


938  FRICTION   AKD   LUBRICATION. 

of  a  portion  of  the  surface,  of  only  1  square  inch.  With  this  pressure  of  5000 
Ibs.  per  square  inch,  the  coefficient  of  friction  may  he  6*,  and  the  brass  may 
be  overheated,  scarred  and  cut  but,  on  the  contrary,  it  may  wear  down  event  v 
to  a  smooth  bearing  giving  a  highly  polished  area  of  intact  of  ?squae 
inches,  or  more,  inside  of  two  hours  of  running  gradually  decreasing  the 
pressure  per  square  inch  of  contact,  and  a  coefficient  of  friction  of  less  than 
0.5^  A  reciprocating  motion  in  the  direction  of  the  axis  is  of  importance 
m  A»?cm*me'  fricH°n-.  With  such  Pushed  surfaces  any  oil  will  lubricate 
and  the  coefficient  of  friction  then  depends  on  the  viscosity  of  the  oil  With 
a  pressure  of  1000  Ibs  per  square  inch  revolutions  from  170  to  320  per  minute 
and  temperatures  of  76°  to  113°  F.  with  both  sperm  and  parmffiToite  a  co- 
bf  a  raid  ^  aS  S  obtataed,  the  oil  being  fed  continuously 

Experiments  on  Overiieating  of  Bearings.  -Hot  ROAO* 
(Denton.)-Tests  with  car  brasses  loaded  from  1  1  00  to*4500  Ibs  ?peF  squire 
inch  gave  .cases  of  overheating  out  of  32  trials.  The  tests  show  bow  purely 
a  matter  of  chance  is  the  overheating,  as  a  brass  which  ran  hot  at  5000  Ibs 
load  on  one  day  would  run  cool  on  a  later  date  at  the  same  or  higher  me? 
f£  rf  '^  e  e*PlaT1:*tion  of.  th*s  apparently  arbitrary  difference  of  behavior  is 
that  the  accidental  variations  of  the  smoothness  of  the  surfaces,  almost  in- 
finitesimal in  their  magnitude,  cause  variations  of  friction  which  are  alwavs 
tending  to  produce  overheating,  and  it  is  solely  a  matter  of  chance  vv  hen 
these  tendencies  preponderate  over  the  lubricating  influence  of  the  oil 
There  is  no  appreciable  advantage  shown  by  sperm-oil,  when  there  is  no  ten- 
dency to  overheat-that  is,  paraffine  can  lubricate  under  the  highest  pres- 
sures which  occur,  as  well  as  sperm,  when  the  surfaces  are  wnhin  he  cS 
tions  affording  the  minimum  coefficients  of  friction 

Sperm  and  other  oils  of  high  heat-resisting  qualities,  like  vegetable  oil  and 
li^leUr?fiCylmd^  S.tocl5s1'.only  d^r  from  the  more  volatile  lubrfcant^ 
like  paraffine,  in  their  ability  to  reduce  the  chances  of  the  continual  acci- 
dental infinitesimal  abrasion  producing  overheating 

beaHngf  'bus  eTplafned  ?***  ^  BUb8tanoe  in  redUCing  overheating  of  a 
The  effect  of  the  emery  upon  the  surfaces  of  the  bearings  is  to  cover  the 
latter  with  a  series  ot  parallel  grooves,  and  appareotlv  after  such  grooves 
overmtahielhe  pretsenfc?h°f  ,thfe  emery  does  not  pmctically  increase  the  faction 
over  the  amount  of  the  latter  when  pure  oil  only  is  between  the  surfaces 
The  infinite  number  of  grooves  constitute  a  very  perfect  means  of  insuring 
a  uniform  oil  supply  at  every  point  of  the  bearings.  As  long  as  grooves  in 
the  journal  match  with  those  in  the  brasses  the  friction  appears  to  amount 
to  only  about  1W  to  15*  of  the  pressure.  But  if  a  smooth^ourifal  is  p  aced 
between  a  set  of  brasses  which  are  grooved,  and  pressure  be  applied,  the 
K  fir™8  £S  -the  Shoves  and  becomes  brazed  or  coated  with  brass,  and 
then  the  coefficient  ot  friction  becomes  upward  of  40#  If  then  emerv  K 
applied,  the  friction  is  made  very  mucb  less  by  its  presence  because  the 
grooves  are  made  to  match  each  other,  and  a  uniform  oil  supply  prevails  at 
every  point  of  the  bearings,  whereas  before  the  application  of  the  T  emery 
many  spots  of  the  latter  receive  no  oil  between  them  y 

Moment  of  Frietion  and  Work    of  Friction  of  Sli<Iin<>- 
surfaces,  etc. 


Flat  surfaces . 


Moment  of  Fric-        Energy  lost  by  Friction 
tion,  inch-lbs.  in  ft.-lbs.  per  miii. 


fWS 


Shafts  and  journals  ............     KfWd"  .2618/TFdn 

Flatpivots  ....................     MfWr  A745fWrn 


Collar-bearing 


Conical  pivot. .   ....     2/3fWr  cosec  a  .1745/fFm  cosec  a 

Conical  journal %fWrseca  A74SfWrn  sec  a 


*  ^  ~ 


Truncated-cone  pivot %fW'  ¥Y 

r*  sin  a  J       rz  sin  a 

Hemispherical  pivot fWr  2618fPTr 

Tractrix,    or   Schiele's    "  anti- 
friction "  pivot '       fWr  .2618/TTr. 


PIVOT-BEARIKGS.  939 

|ta  the  above    /  =  coefficient  of  friction; 

W  =  weight  on  journal  or  pivot  in  pounds; 
r  —  radius,  d  =  diameter,  iii  inches; 
S  =  space  in  feet  through  which  sliding  takes  place; 
r2  —  outer  radius,    rj  =  inner  radius; 
n  =.  number  of  revolutions  per  minute; 
a  —  the  half-angle  of  the  cone,  i.e.,  the  angle  of  the  slope 
with  the  axis. 

To  obtain  the  horse-power,  divide  the  quantities  in  the  last  column  by 
^3,000.  Horse-power  absorbed  by  friction  of  a  shaft  =  ^6050' 

The  formula  for  energy  lost  by  shafts  and  journals  is  approximately  true 
for  loosely  fitted  bearings.  Prof.  Thurston  shows  that  the  correct  formula 
varies  according  to  the  character  of  fit  of  the  bearing;  thus  for  loosely 
fitted  journals,  if  U  =  the  energy  lost, 


Wn  inch-pounds  =  -m*fW**  foot_lbs. 


Vi  -f/2 

For  perfectly  fitted  journals    U  =  2.54/nrTFn-  inch-lbs.  =  .3325/TTdu,  ft.-lbs. 

For  a  bearing  in  which  the  journal  is  so  grasped  as  to  give  a  uniform 
pressure  throughout,  U  -  fir*rWn  inch-lbs.  -  AUZfWdn,  ft.-lbs. 

Resistance  of  railway  trains  and  wagons  due  to  friction  of  trains: 

f  X  2^40 

Pull  on  draw-bar  =  J  —  ^—  pounds  per  gross  ton, 
K 

in  which  R  is  the  ratio  of  the  radius  of  the  wheel  to  the  radius  of  journal. 

A  cylindrical  journal,  perfectly  fitted  into  a  bearing,  and  carrying  a  total 
»oad,  distributes  the  pressure  due  to  this  load  unequally  on  the  bearing,  the 
maximum  pressure  being  at  the  extremity  of  the  vertical  radius,  while  at 
the*  extremities  of  the  horizontal  diameter  the  pressure  is  zero.  At  any 
point  of  the  bearing-  surf  ace  at  the  extremity  of  a  radius  which  makes  an 
angle  0  with  the  vertical  radius  the  normal  pressure  is  proportional  to  cos  0. 
jf  p  —  normal  pressure  on  a  unit  of  surface,  w  =  total  load  on  a  unit  of 
length  of  the  journal,  and  r  =  radius  of  journal, 

w  cos  d 
w  cos  0  =  1.57rp,     p  -    1  57r  . 

PIVOT-BEARINGS. 

The  Sclilele  Curve.  —  W.  H.  Harrison,  in  a  letter  to  the  Am.  Machin- 

ist 1891  says  the  Schiele  curve  is  not  as  good  a  form  for  a  bearing  as  the 
segment  of  a  sphere.  He  says:  A  mill  stone  weighing  a  ton  frequently 
bears  its  whole  weight  upon  the  flat  end  of  a  hard-steel  pivot  1J£"  diameter, 
or  one  square  inch  area  of  bearing;  but  to  carry  a  weight  of  3000  Ibs.  he 
advises  an  end  bearing  about  4  inches  diameter,  made  in  the  form  of  a  seg- 
ment of  a  sphere  about  ^  inch  in  height.  The  die  or  fixed  bearing  should 
be  dished  to  fit  the  pivot.  T  'is  form  gives  a  chance  for  the  bearing  to 
adjust  itself,  which  it  does  not  have  when  made  flat,  or  when  made  with  the 
Schiele  curve  If  a  side  bearing  is  necessary  it  can  be  arranged  farther  up 
the  shaft.  The  pivot  and  die  should  be  of  steel,  hardened;  cross-gutters 
should  be  in  the  die  to  allow  oil  to  flow,  and  a  central  oil-hole  should  be 
made  in  the  shaft. 

The  advantage  claimed  for  the  Schiele  bearing  is  that  the  pressure  is  uni- 
formly distributed  over  its  surface,  and  that  it  therefore  wears  uniformly. 
Wilfred  Lewis  (Am.  Mach  ,  April  19,  1894)  says  that  its  merits  as  a  thrust- 
bearing  have  been  vastly  overestimated;  that  the  term  "anti-friction 
applied  to  it  is  a  misnomer,  since  its  friction  is  greater  than  that  of  a  flat 
step  or  collar  of  the  same  diameter.  He  advises  that  flat  thrust-bearing; 
should  always  be  annular  in  form,  having  an  inside  diameter  one  half  of 
the  external  diameter 

Friction  of  a  Flat  Pivot-bearing.  -The  Research  Committee 
on  Friction  (Proc.  Inst.  M.  E.  1S01)  experimented  on  a  step-bearing,  flat- 
ended  3  in  diam.,  the  oil  being  forced  into  the  bearing  through  a  hole  in 
its  centre  and  distributed  through  two  radial  grooves,  insuring  thorough 
lubrication  The  step  was  of  steel  and  the  bearing  of  manganese-bronze, 


940  FRICTIOK  AND   LUBRICATION. 

At  revolutions  per  min 50  128  194  290         353 

The  coefficient  of  friction  varied  j          .0181        .0053        .0051        .0044      .0053 

between  I  and  .0221        .0113        .0102        .0178      .0167 

Wilh  a  white-metal  bearing  at  128  revolutions  the  coefficient  of  friction 
was  a  little  larger  than  with  the  manganese-bronze.  At  the  higher  speeds 
the  coefficient  of  friction  was  less,  owing  to  the  more  perfect  lubrication,  as 
shown  by  the  more  rapid  circulation  of  the  oil.  At  128  revolutions  the 
bronze  bearing  heated  and  seized  on  one  occasion  with  a  load  of  260  pounds 
and  on  another  occasion  with  300  pounds  per  square  inch.  The  white-metal 
bearing  under  similar  conditions  heated  and  seized  with  a  load  of  240 
pounds  per  square  inch.  The  steel  footstep  on  manganese-bronze  was  after- 
wards tried,  lubricating  with  three  and  with  four  radial  grooves;  but  the 
friction  was  from  one  and  a  half  tin.es  to  twice  as  great  as  writh  only  the  two 
groovi  s.  (See  also  Allowable  Pressures,  page  936.) 

Mercury-bath  Pivot.  -A  nearly  frictipnless  step-bearing  may  be 
obtained  by  floating  the  bearing  with  its  superincumbent  weight  upon  mer- 
cury. Such  an  apparatus  is  used  in  the  lighthouses  of  La  Heve,  Havre.  It 
is  thus  described  in  Eng'g,  July  14,  1893,  p.  41: 

The  optical  apparatus,  weighing  about  1  ton,  rests  on  a  circular  cast-iron 
table,  which  is  supported  by  a  vertical  shaft  of  wrought  iron  2.36  in. 
diameter. 

Tin's  is  kept  in  position  at  the  top  by  a  bronze  ring  and  outer  iron  support, 
and  at  the  bottom  in  the  same  way,  while  it  rotates  on  a  removable  steel 
pivot  resting  in  a  steel  socket,  which  is  fitted  to  the  base  of  the  support.  To 
the  vertical  shaft  there  is  rigidly  fixed  a  floating  cast-iron  ring  17.1  in.  diam- 
eter ami  11.8  in.  in  depth,  which  is  plunged  into  and  rotates  in  a  mercury 
bath  contained  in  a  fixed  outer  drum  or  tank,  the  clearance  between  the 
vertical  surfaces  of  the  drum  and  ring  being  only  0.2  in.,  so  as  to  reduce  as 
much  as  possible  the  volume  of  mercury  (about  220  Ibs.),  while  the  horizon- 
tal clearance  at  the  bottom  is  0.4  in. 

BALL-BEARINGS,  FRICTION  ROLLERS,  ETC. 

A.  H.  Tyler  (Entfg,  Oct.  20,  1893,  p.  483),  after  experiments  and  com- 
parison with  experiments  of  others  arrives  at  the  following  conclusions: 

That  each  ball  must  have  two  points  of  contact  only. 

The  balls  and  race  must  be  of  glass  hardness,  and  of  absolute  truth. 

The  balls  should  be  of  the  largest  possible  diameter  which  the  space  at 
disposal  will  admit  of. 

Anyone  ball  should  be  capable  of  carrying  the  total  load  upon  the  bearing. 

Two  rows  of  balls  are  always  sufficient. 

A  ball-bearing  requires  no  oil,  and  has  no  tendency  to  heat  unless  over- 
loaded. 

Until  the  crushing  strength  of  the  balls  is  being  neared,  the  frictional  re- 
sistance is  proportional  to  the  load. 

The  frictional  resistance  is  inversely  proportional  to  the  diameter  of  the 
balls,  but  in  what  exact  proportion  Mr.  Tyler  is  unable  to  say.  Probably  it 
varies  with  the  square. 

The  resistance  is  independent  of  the  number  of  balls  and  of  the  speed. 

No  rubbing  action  will  take  place  between  the  balls,  and  devices  to  guard 
against  it  are  unnecessary,  and  usually  injurious. 

The  above  will  show  that  the  ball-bearing  is  most  suitable  for  high  speeds 
and  light  loads.  On  the  spindles  of  wood-carving  machines  some  make  as 
much  as  30.000  revolutions  per  minute.  They  run  perfectly  cool,  and  never 
have  any  oil  upon  them.  For  heavy  loads  the  balls  should  not  be  less  than 
two  thirds  the  diameter  of  the  shaft,  and  are  better  if  made  equal  to  it. 

Ball-bearings  have  not  been  found  satisfactory  for  thrust-blocks,  for 
the  reason  apparently  that  the  tables  crowd  together.  Better  results  have 
been  obtained  from  coned  rollers.  A  combined  system  of  rollers  and  balls 
is  described  in  EIIQ'O.  Oct.  6,  1893,  p.  429. 

Friction-rollers.  —If  a  journal  instead  of  revolving  on  ordinary 
bearings  be  supported  on  friction -rollers  the  force  required  to  make  the  jour- 
nal revolve  will  be  reduced  in  nearly  the  same  proportion  that  the  diameter 
of  the  axles  of  the  rollers  is  less  than  the  diameter  of  the  rollers  themselves. 
In  experiments  by  A.  M.  Wellington  with  a  journal  3J/2  in.  diam.  supported 
on  rollers  8  in.  diam.,  whose  axles  were  1%  m-  diam.,  the  friction  in  starting 
from  rest  was  *4  the  friction  of  an  ordinary  3^-in.  bearing,  but  at  a  car 
speed  of  10  miles  per  hour  it  was  ^  that  of  the  ordinary  bearing.  The  ratio 
of  the  diam,  of  the  axle  to  diam.  of  roller  was  1^4: 8,  or  as  1  to  4.6, 


FRICTION  OF   STEAM-EHGIHES. 

Bearings  for  Very  High  Rotative  Speeds.  (Proc.  Inst  ME., 
Occ  1S8S  p  48'-'  )— In  the  Parsons  steam-turbine,  which  has  a  speed  of  as 
hie-h  as  18  000  rev.  per  min.,  as  it  is  impossible  to  secure  absolute  accuracy 
of  balance  the  bearings  are  of  special  construction  so  as  to  allow  of  a  certain 
very  small  amount  of  lateral  freedom.  For  this  purpose  the  bearing  is  sur- 
roundel  bv  two  sets  of  steel  washers  1/16  inch  thick  and  of  different  diam- 
eters, the  larger  fitting  close  in  the  casing  and  about  1/32  inch  clear  of  the 
bearing,  and  the  smaller  fitting  close  on  the  bearing  and  about  1/32  inch 
clear  of  the  casing.  These  are  arranged  alternately,  and  are  pressed 
together  by  a  spiral  spring.  Consequently  any  lateral  movement  of  the 
bearing  causes  them  to  slide  mutually  against  one  another,  and  by  their 
friction  to  check  or  damp  any  vibrations  that  may  be  set  up  in  the  spindle. 
The  tendency  of  the  spindle  is  then  to  rotate  about  its  axis  of  mass,  or  prm- 
bipal  axis  as  it  is  called;  and  the  bearings  are  thereby  relieved  from  exces- 
:  sive  pressure,  and  the  machine  from  undue  vibration.  The  finding  of  the 
centre  of  gyration,  or  rather  allowing  the  turbine  itself  to  find  its  own 
centre  of  gyration,  is  a  well-known  device  in  other  branches  of  mechanics: 
as  in  the  instance  of  the  centrifugal  hydro-extractor,  where  a  mass  very 
much  ou^,  of  balance  is  allowed  to  find  its  own  centre  of  gyration;  the  faster 
it  ran  the  more  steadily  did  it  revolve  and  the  less  was  the  vibration.  An- 
other illustration  is  to  be  found  in  the  spindles  of  spinning  machinery, 
which  run  at  about  10,000  or  11,000  revolutions  per  minute:  they  are  made 
of  hardened  and  tempered  steel,  and  although  of  very  small  dimensions,  the 
outside  diameter  of  the  largest  portion  or  driving  whorl  being  perhaps  not 
more  than  1  YA  in.,  it  is  found  impracticable  to  run  them  at  that  speed  m 
what  might  be  called  a  hard-and-fast  bearing.  They  are  therefore  run  with 
some  elastic  substance  surrounding  the  bearing,  such  as  steel  springs,  hemp. 
or  cork.  Any  elastic  substance  is  sufficient  to  absorb  the  vibration,  and 
permit  of  absolutely  steady  running. 

FRICTION  OF  STEAM-ENGINES. 

Distribution  of  tiie  Friction  of  Engines.— Prof .  Thurston  in 
His  "  Friction  and  Lost  Work,"  gives  the  following: 

1.  2.  3. 

Mainbearings 47.0 

Piston  and  rod 32.9 

Crank-pin 5.11  13  0 

Cross-head  and  wrist-pin 4.1 

Valveandrod 2.5  26. 4{  22<0 

Eccentric  strap 9  01 


Link  and  eccentric 
Total 


100.0  100.0  100.0 


Jrror     inurSlOU  »  l>e»i»  oil  a/  uu.m.uc:i   w*  UIIAJ-^'  v^i.iu  avj  *«-i  <3 ii    1 —  xi 

that  the  friction   of  any  engine  is  practically  constant  under  all  loads. 
(Trans.  A.  S.  M.  E.,  viii.  86;  ix.  74.) 


being  only  2.6  H.P.,  or  about  5*^  ^^  ^  Q  ^  ^  ^^  R  p  ^  ^ 


In  a  compound  condensing-engine,  tested  trom  u  i     lus.o  orane  n.r.,  K»V 
I  H  P.  from  14.92  to  117.8  H.P.,  the  friction  H.P.  varying  only  from  14.92  to 
17  42.     At  the  maximum  load  the  friction  was  15.2  H.P.,  or  12.9*. 

The  friction  increases  with  increase  of  the  boiler-pressure  from  30  to  70 
Ibs.,  and  then  becomes  constant.  The  friction  generally  increases  with  in- 
crease of  speed,  but  there  are  exceptions  to  this  rule. 

Prof.  Denton    (Stevens  Indicator,  July,  1890),  comparing  the  calcula 


for  the  friction  of  pisuuus,  jsuuiuiis-uuA.cn,  cm*.*  .n,*.^.  -•-  -.-- 
Pawtucket  Dumping-engine,  estimating  the  friction  of  the  external  bearings 
with a  coefficient  of  friction  of  6^  and  that  of  the  pistons,  valves  and  stuff- 
ing-boxes as  in  the  case  of  the  ice-machine,  we  have  the  total  faction 
distributed  as  follows : 


942 


fc&ICTION   ASTD   LUBRICATION. 


Horse-  Per  cent 

power,  of  Whole, 

Crank-pins  and  effect  of  piston-thrust  on  main  shaft..    0.71  11.4 

Weight  of  fly-wheel  and  main  shaft 1.95  32.4 

Steam-valves 0.23  3.7 

Eccentric 0.07  1.2 

Pistons 0.43  7.2 

Stuffing-boxes,  six  altogether  0.72  11.3 

Air-pump 2. 10  32 . 8 

Total  friction  of  engine  with  load 6.21          100.0 

Total  friction  per  cent  of  indicated  power  ...     4.27 

The  friction  of  this  engine,  though  very  low  in  proportion  to  the  indicated 
power,  is  satisfactorily  accounted  for  by  Morin1s  law  used  with  a  coefficient 
of  friction  of  5$.  In  both  cases  the  main  items  of  friction  are  those  due  to 
the  weight  of  the  fly-wheel  and  main  shaft  and  to  the  piston-thrust  on 
crank-pins  and  main-shaft  bearings.  In  the  ice-machine  the  latter  items 
are  the  larger  owing  to  the  extra  crank  pin  to  work  the  pumps,  while 
in  the  Pawtucket  engine  the  former  preponderates,  as  the  crank-thrusts  are 
partly  absorbed  by  the  pump-pistons,  and  only  the  surplus  effect  acts  on 
the  crank -shaft. 

Prof.  Denton  describes  in  Trans.  A.  S.  M.  E.,  x.  392,  an  apparatus  by 
which  he  measured  the  friction  of  a  piston  packing-ring.  When  the  parts 
of  the  piston  were  thoroughly  devoid  of  lubricant,  the  coefficient  of  friction 
was  found  to  be  about  7*4$;  with  an  oil-feed  of  one  drop  in  two  minutes  the 
coefficient  was  about  5$;  with  one  drop  per  minute  it  was  about  3$.  These 
rates  of  feed  gave  unsatisfactory  lubrication,  the  piston  groaning  at  the 
ends  of  the  stroke  when  run  slowly,  and  the  flow  of  oil  left  upon  the  surfaces 
was  found  by  analysis  to  contain  about  50£  of  iron.  A  feed  of  two  drops  per 
minute  reduced  the  coefficient  of  friction  to  about  1$,  and  gave  practically 
perfect  lubrication,  the  oil  retaining  its  natural  color  and  purity. 

LUBRICATION. 

Measurement  of  the  Durability  of  Lubricants.  •  (J.  E.  Den- 
ton,  Trans.  A.  S.  M.^E.,  xi.  1013.)— Practical  differences  of  durability  of  lubri- 
cants depend  not  on  any  differences  of  inherent  ability  to  resist  being  "worn 
out"  by  rubbing,  but  upon  the  rate  at  which  they  flow  through  and  away 
from  the  bearing-surfaces.  The  conditions  which  control  this  flow  are  so 
delicate  in  their  influence  that  all  attempts  thus  far  made  to  measure  dura- 
bility of  lubricants  may  be  said  to  have  failed  to  make  distinctions  of  lubri- 
cating valuehaving  any  practical  significance.  In  some  kinds  of  service  the 
limit  to  the  consumption  of  oil  dependsupon  the  extent,  to  which  dust  or  other 
refuse  becomes  mixed  with  it,  as  in  railroad-car  lubrication  and  in  the  case 
of  agricultural  machinery.  The  economy  of  one  oil  over  another,  so  far  as 
the  quality  used  is  concerned — that  is.  so  far  as  durability  is  concerned— is 
simply  proportional  to  the  rate  at  which  it  can  insinuate  itself  into  and  flow 
out  of  minute  orifices  or  cracks.  Oils  will  differ  in  their  ability  to  do  tin's, 
first,  in  proportion  to  their  viscosity,  and,  second,  in  proportion  to  the  ca- 
pillary properties  which  they  may  possess  by  virtue  of  the  particular  ingre- 
dients used  in  their  composition.  Where  the  thickness  of  film  between  rub- 
bing-surfaces must  be  so  great  that  large  amounts  of  oil  pass  through 
bearings  in  a  given  time,  and  the  surroundings  are  such  as  to  permit  oil  tc 
be  fed  at  high  temperatures  or  applied  by  a  method  not  requiring  a  perfect 
fluidity,  it  is  probable  that  the  least  amount  of  oil  will  be  used  when  the  vis- 
cosity is  as  great  as  in  the  petroleum  cylinder  stocks.  When,  however,  the 
oil  must  flow  freely  at  ordinary  temperatures  and  the  feed  of  oil  is 
restricted,  as  in  the  case  of  crank-pin  bearings,  it  is  not  practicable  to  feed 
such  heavy  oils  in  a  satisfactory  manner.  Oils  of  less  viscosity  or  of  a 
fluidity  approximating  to  lard-oil  must  then  be  used. 

Relative  Value  of  Lubricants.  (J.  E. Denton,  Am.  Mach.,  Oct.  30, 
1890.) — The  three  elements  which  determine  the  value  of  a  lubricant  are  the 
cost  due  to  consumption  of  lubricants,  the  cost  spent  for  coal  to  overcome 
the  fiictional  resistance  caused  by  use  of  the  lubricant,  and  the  cost  due  to 
the  metallic  wear  on  the  journal 'and  the  brasses.  In  cotton-mills  the  cost 
of  the  power  is  alone  to  be  considered;  in  rolling-mills  and  marine  engines 
the  cost  of  the  quantity  of  lubricant  used  is  the  only  important  factor;  but 
in  railroads  not  only  do  both  these  elements  enter  the  problem  as  tangible 


LUBRICATION.  943 

factors,  but  the  cost  of  the  wearing  away  of  the  metallic  parts  enters  in  ad- 
dition. and  furthermore,  the  latter  is  the  greatest  element  of  cost  in  the  case 
The  Qualification*  of  a  Good  Lubricant,  as  laid  down  by 
W.  H.  Bailey,  in  Proc  Inst.  C.  E.,  vol.  xlv.,  p.  372,  are:  1.  Sufficient  body 
to  keep  the  surfaces  free  from  contact  under  maximum  pressure  2  The 
greatest  possible  fluidity  consistent  with  the  foregoing  condition!  3!  The 
lowest  possible  coefficient  of  friction,  which  in  bath  lubrication  would  be  for 
fluid  friction  approximately.  4.  The  greatest  capacity  for  storing  and 
carry  ing  away  heat.  5.  A  high  temperature  of  decomposition.  6.  Power 
to  resist  oxidation  or  the  action  of  the  atmosphere.  7.  Freedom  from  cor- 
rosive action  on  the  metals  upon  which  used. 

Best  Lubricants  for  Different  Purposes.    (Thurston.) 

Low  temperatures,  as  in  rock-drills    (  r  .  ,  , 
driven  by  compressed  air:  }  LlSht  mineral  lubncating-oils. 

Very  great  pressures,  slow  speed.  ..  J  GraPh.ite»  soapstone,  and  other  solid 

(     lubricants. 

Heavy  pressures,  with  slow  speed.  .  .  j  ^e^f'  a"d  lard'  tallow'  and  other 
Heavy  pressures  and  high  speed.  .  .  .  -  S^™'  castor-oil>  and  heavy  ™™~ 


- 

Light  pressures  and  high  speed  .....  -j  S^™^S?ad  petroleum'  olive'  raPe' 

Orvlhiflrv  maohinprv  1  Lard-oil,  tallow-oil,  heavy  mineral  oils. 

iery  ................  ")     and  the  heavier  vegetable  oils. 

Steam-cylinders  .......................  Heavy  mineral  oils,  lard,  tallow. 


Watches  and  other  delicate 

For  mixture  with  mineral  oils,  sperm  is  best;  lard  is  much  used:  olive  and 
cotton-seed  are  good. 

Amount  of  Oil  needed  to  Run  an  Engine.—  The  Vacuum  Oil 
Co.  in  1892,  in  response  to  an  inquiry  as  to  cost  of  oil  to  run  a  1000-H.P. 
Corliss  engine,  wrote:  The  cost  of  running  two  engines  of  equal  size  of  the 
same  make  is  not  always  the  same.  Therefore  while  we  could  furnish 
figures  showing  what  it  is  costing  some  of  our  customers  having  Corliss 
engines  of  1000  H.P.,  we  could  only  give  a  general  idea,  which  in  itself 
might  be  considerably  out  of  the  way  as  to  the  probable  cost  of  cylinder- 
and  engine-oils  per  year  for  a  particular  engine.  Such  an  engine  ought  to 
run  readily  on  less  than  8  drops  of  600  W  oil  per  minute.  If  3000  drops  are 
figured  to  the  quart,  and  8  drops  used  per  minute,  it  would  take  about 
two  and  one  half  barrels  (52.5  gallons)  of  600  W  cylinder-  oil,  at  65  cents  per 
gallon,  or  about  $85  for  cylinder-oil  per  year,  running  6  days  a  week  and  10 
hours  a  day.  Engine-oil  would  be  even  more  difficult  to  guess  at  what  the 
cost  would  be,  because  it  would  depend  upon  the  number  of  cups  required 
on  the  engine,  which  varies  somewhat  according  to  the  style  of  the  engine. 
It  would  doubtless  be  safe,  however,  to  calculate  at  the  outside  that  not 
more  than  twice  as  much  engine-oil  would  be  required  as  of  cylinder-  oil. 

The  Vacuum  Oil  Co.  in  1892  published  the  following  results  of  practice 
with  "  600  W  "  cylinder-  oil: 

Porliw  pomnonnd  engine  -!  20  and  33  X  48'  83  rev8'  Per   min'  '    l  dr°P   °f   oil 
orliss  compound  engine,  -j     per  mm  to  l  drop  in  two  minutes 

"       triple  exp.       "          20,  33,  and  46  X  48;  1  drop  every  2  minutes. 
p     ,      A1.  „       j  20  and  36  X  36:  143  revs,  per  min.  ;  2  drops  of  oil 

1     per  min.,  reduced  afterwards  to  1  drop  per  min. 

n   n  u       J  15  X  25  X  16;  240  revs,  per  min.;  1  drop  every  4 

1     minutes. 

Results  of  tests  on  ocean-steamers  communicated  to  the  author  by  Prof. 
Denton  in  1892  gave:  for  1200-H.P.  marine  engine,  5  to  6  English  gallons  (6  to 
7.2  U.  S.  gals.)  of  engine-oil  per  24  hours  for  external  lubrication;  and  for  a 
1500-H.P.  marine  engine,  triple  expansion,  running  75  revs,  per  min.,  6  to  7 
English  gals,  per  24  hours.  The  cylinder-oil  consumption  is  exceedingly 
variable,—  from  1  to  4  gals,  per  day  on  different  engines,  including  cylinder- 
oil  used  to  swab  the  piston-rods. 

Quantity  of  Oil  used  on  a  locomotive  Crank-pin.—  Prof. 
Denton,  Trans.  A.  S.  M.  E.,  xi.  1020,  says:  A  very  economical  case  of  practical 
oil-consumption  is  when  a  locomotive  main  crank-pin  consumes  about  six 


944  FRICTION   AND   LUBRICATIOK. 

cubic  inches  of  oil  in  a  thousand  miles  of  service.  This  is  equivalent  to  a 
consumption  of  one  milligram  to  seventy  square  inches  of  surface  rubbed 
over. 

The  Examination  of  Lubricating-oils.  (Prof.  Thos.  B.  Still- 
man,  Stevens  Indicator,  July,  1890.)— The  generally  accepted  conditions  of 
a  good  lubricant  are  as  follows: 

1.  "  Body  "  enough  to  prevent  the  surfaces,  to  which  it  is  applied,  from 
corning  in  contact  with  each  other.     (Viscosity.) 

2.  Freedom  from  corrosive  acid,  either  of  mineral  or  animal  origin. 

3.  As  fluid  as  possible  consistent  with  "  body." 

4.  A  minimum  coefficient  of  friction. 

5.  High  "flash1'  and  burning  points. 

6.  Freedom  from  all  materials  liable  to  produce  oxidation  or  "  gumming." 
The  examinations  to  be  made  to  verify  the  above  are  both  chemical  and 

mechanical,  and  are  usually  arranged  in  the  following  order  : 

1.  Identification  of  the  oil,  whether  a  simple  mineral  oil,  or  animal  oil,  or 
a  mixture.  2.  Density.  3.  Viscosity.  4.  Flash-point.  5.  Burning -point. 
6.  Acidity.  7.  Coefficient  of  friction.  8.  Cold  test. 

Detailed  directions  for  making  all  of  the  above  tests  are  given  in  Prof. 
Stillnian's  article. 

Weights  of  Oil  per  Gallon.— The  following  are  approximately  the 
weights  per  gallon  of  different  kinds  of  oil  (Penn.  R.  R.  Specifications): 

Lard-oil,  tallow-oil,  neat's-foot  oil,  bone-oil,  colza-oil,  mustard-seed  oil, 
rape-seed  oil,  paraffine-oil,  500°  fire-test  oil,  engine-oil,  and  cylinder  lubricant, 
7}4  pounds  per  gallon. 

Well-oil  and  passenger-car  oil,  7.4  pounds  per  gallon;  navy  sperm-oil,  7.2 
pounds  per  gallon;  signal-oil,  7.1  pounds  per  gallon;  300°  burning-oil,  6.9 
pounds  per  gallon;  and  150°  burning-oil,  6.6  pounds  per  gallon. 

Penna.  R.  R.  Specifications  for  Petroleum  Products. 
1889.— Five  different  grades  of  petroleum  products  will  be  used. 

The  materials  desired  under  this  specification  are  the  products  of  the  dis- 
tillation and  refining  of  petroleum  unmixed  with  any  other  substances. 

150°  Fire-test  Oil.—  This  grade  of  oil  will  not  be  accepted  if  sample  (1)  is 
not  "water-white"  in  color;  (2)  flashes  below  130°  Fahrenheit;  (3)  burns 
below  151°  Fahrenheit;  (4)  is  cloudy  or  shipment  has  cloudy  barrels  when 
received,  from  the  presence  of  glue  or  suspended  matter;  (5)  becomes 
opaque  or  shows  cloud  when  the  sample  has  been  10  minutes  at  a  temper- 
ature of  0°  Fahrenheit. 

The  flashing  and  burning  points  are  determined  by  heating  the  oil  in  an 
open  vessel,  not  less  than  12°  per  minute,  and  applying  the  test  flame  every 
7°,  beginning  at  123°  Fahrenheit.  The  cold  test  may  be  conveniently  made 
by  having  an  ounce  of  the  oil,  in  a  four-ounce  sample  bottle,  with 'a  ther- 
mometer suspended  in  the  oil,  and  exposing  this  to  a  freezing  mixture  of 
ice  and  salt.  It  is  advisable  to  stir  with  the  thermometer  while  the  oil  is 
cooling.  The  oil  must  remain  transparent  in  the  freezing  mixture  ten 
minutes  after  it  has  cooled  to  zero. 

300°  Fire-test  Oil.—  This  grade  of  oil  will  not  be  accepted  if  sample  (1)  is 
not  "water  white  "  in  color;  (2)  flashes  below  249°  Fahrenheit;  (3)  burns 
below  298°  Fahrenheit;  (4)  is  cloudy  or  shipment  has  cloudy  barrels  when 
received,  from  the  presence  of  glue  or  suspended  matter;  (5)  becomes 
opaque  or  shows  cloud  when  the  sample  has  been  10  minutes  at  a.  temper- 
ature of  32°  Fahrenheit. 

The  flashing  and  burning  points  are  determined  the  same  as  for  150°  fire- 
test  oil,  except  that  the  oil  is  heated  15°  per  minute,  test-flame  being  applied 
first  at  242°  Fahrenheit.  The  cold  test  is  made  the  same  as  above,  except 
that  ice  and  water  are  used. 

Paraffine-oil.—  This  grade  of  oil  will  not  be  accepted  if  the  sample  (1)  is 
other  than  pale-lemon  color;  (2)  flashes  below  249°  Fahrenheit;  (3)  shows 
viscosity  less  than  40  seconds  or  more  than  65  seconds  when  tested  as 
described  under  "  Well  Oil "  at  100°  Fahrenheit  throughout  the  year;  (4)  has 
gravity  at  60°  Fahrenheit,  below  24°  Baume\  or  above  29°  BauinS;  (5)  from 
October  1st  to  May  1st  has  a  cold  test  above  10°  Fahrenheit. 

The  flashing-point  is  determined  same  as  for  300°  fire-test  oil.  The  cold 
test  is  determined  as  follows:  A  couple  of  ounces  of  oil  is  put  in  a  four-ounce 
sample  bottle,  and  a  thermometer  placed  in  it.  The  oil  is  then  frozen,  a 
freezing  mixture  of  ice  and  salt  being  used  if  necessary.  When  the  oil  has 
become  hard,  the  bottle  is  removed  from  the  freezing  mixture  and  the 
frozen  oil  allowed  to  soften,  being  stirred  and  thoroughly  mixed  at  the  same 
time  by  means  of  the  thermometer,  until  the  mass  will  run  from  one  end  of 


SOLID   LUBRICANTS.  945 

the  bottle  to  the  other.    The  reading  of  the  thermometer  when  this  is  the 
case  is  regarded  as  the  cold  test  of  the  oil. 

Well  Oil— This  grade  of  oil  will  not  be  accepted  if  the  sample  (1)  flashes 
from  May  1st  to  October  1st,  below  249°  Fahrenheit,  or  from  October  1st  to 
May  1st  below  200°  Fahrenheit;  (2)  has  a  gravity,  at  60°  Fahrenheit  below 
28°  Baume,  or  above  30°;  (3)  from  October  1st  to  May  1st  has  a  cold  test 
above  10°  Fahrenheit;  (4)  shows  any  precipitation  in  10  minutes  when  5 
cubic  centimetres  are  mixed  with  95  cubic  centimetres  of  88°  gasoline;  (5) 
shows  a  viscosity  less  than  55  seconds,  or  more  than  100  seconds,  when  tested 
as  described  below.  From  October  1st  to  May  1st  the  test  must  be  made 
at  100°  Fahrenheit,  and  from  May  1st  to  October  1st  at  110°  Fahrenheit. 

For  summer  oil  the  flashing-point  is  determined  the  same  as  f or  paraffine- 
oil;  and  for  winter  oil  the  same,  except  that  the  test-flame  is  applied  first 
at  193°  Fahrenheit.  The  cold  test  is  made  the  same  as  for  paraffine-oil. 

The  precipitation  test  is  to  exclude  tarry  and  suspended  matter.  It  is 
easiest  made  by  putting  5  cubic  centimetres  of  the  oil  in  a  100-cubic -cen- 
timetre graduate,  then  filling  to  the  mark  with  gasoline,  and  thoroughly 
shaking. 

The  viscosity  test  is  made  as  follows:  A 100  cubic -centimetre  pipette  of  the 
long  bulb  form  is  regraduated  to  hold  just  100  cubic  centimetres  to  the  bottom 
of  the  bulb.  The  size  of  the  aperture  at  the  bottom  is  then  made  such  that 
100  cubic  centimetres  of  water  at  100°  Fahrenheit  will  run  out  the  pipette 
down  to  the  bottom  of  the  bulb  in  34  seconds.  Pipettes  with  bulbs  varying 
from  \%  inches  to  \y2  inches  in  diameter  outside,  and  about  4^  inches  long 
give  almost  exactly  the  same  results,  provided  the  aperture  at  the  bottom 
is  the  proper  size.  The  pipette  being  obtained,  the  oil  sample  is  heated  to 
the  required  temperature,  care  being  taken  to  have  it  uniformly  heated,  and 
then  is  drawn  up  into  tbe  pipette  to  the  proper  marK.  The  time  occupied 
by  tbe  oil  in  running  out,  down  to  the  bottom  of  the  bulb,  gives  the  test 
figures. 

500°  Fire-test  Oil—  This  grade  of  oil  will  not  be  accepted  if  sample  (1) 
flashes  below  445°  Fahrenheit;  (2)  shows  precipitation  with  gasoline  when 
tested  as  described  for  well  oil. 

The  flashing -point  is  determined  the  same  as  for  well-oil,  except  that  the 
test  flame  is  applied  first  at  438°  Fahrenheit. 

SOLID    LUBRICANTS. 

Graphite  in  a  condition  of  powder  and  used  as  a  solid  lubricant,  so 
called,  to  distinguish  it  from  a  liquid  lubricant,  has  been  found  to  do  well 
where  the  latter  has  failed. 

Rennie,  in  1829,  says:  "Graphite  lessened  friction  in  all  cases  where  it 
was  used."  General  Morin,  at  a  later  date,  concluded  from  experiments 
that  it  could  be  used  with  advantage  under  heavy  pressures;  and  Prof. 
Thurston  found  it  well  adapted  for  use  under  both  light  and  heavy  pressures 
when  mixed  with  certain  oils.  It  is  especially  valuable  to  prevent  abrasion 
and  cutting  under  heavv  loads  and  at  low  velocities. 

Soapstone,  also  called  talc  and  steatite,  in  the  form  of  powder  and 
mixed  with  oil  or  fat,  is  sometimes  used  as  a  lubricant.  Graphite  or  soap- 
stone,  mixed  with  soap,  is  used  on  surfaces  of  wood  working  against  either 
iron  or  wood. 

Fibre-graphite.— A  new  self-lubricating  bearing  known  as  fibre- 
graphite  is  described  by  John  H.  Cooper  in  Trans.  A.  S.  M.  E.,  xiii.  374,  as 
the  invention  of  P.  H.  Holmes,  of  Gardiner,  Me.  This  bearing  material  is 


^*~., ~~~ — ^  .~ ous  proportions,  ace „  „          F..-F... 

be  served,  and  then  solidified  by  pressure  in  specially  prepared  moulds  ; 
after  removal  from  which  the  bearings  are  first  thoroughly  dried,  then  satu- 
rated with  a  drying  oil,  and  finally  subjected  to  a  current  of  hot,  dry  air  for 
the  purpose  of  oxidizing  the  oil,  and  hardening  the  mass.  When  finished, 
they  may  be  "  machined  "  to  size  or  shape  with  the  same  facility  and  means 
employed  on  metals. 

Metaline  is  a  solid  compound,  usually  containing  graphite,  made  in  the 
form  of  small  cylinders  which  are  fitted  permanently  into  holes  drilled  m 
the  surface  of  the  bearing.  The  bearing  thus  fitted  runs  without  any  other 
lubrication. 


946  THE   FOUNDED. 


THE    FOUNDRY. 

CUPOLA  PRACTICE. 

The  following  notes,  with  the  accompanying  table,  are  taken  from  an 
article  by  Simpson  Bolland  in  American  Machinist,  June  30, 1892.  The  table 
shows  heights,  depth  of  bottom,  quantity  of  fuel  on  bed,  proportion  of  fuel 
and  iron  in  charges,  diameter  of  main  blast-pipes,  number  of  tuyeres,  blast - 
pressure,  sizes  of  blowers  and  power  of  engines,  and  melting  capacit}7  per 
hour,  of  cupolas  from  24  inches  to  84  inches  in  diameter. 

Capacity  of  Cupola. — The  accompanying  table  will  be  of  service  in  deter- 
mining the  capacity  of  cupola  needed  for  the  production  of  a  given  quantity 
of  iron  in  a  specified  time. 

First,  ascertain  the  amount  of  iron  which  is  likely  to  be  needed  at  each 
cast,  and  the  length  of  time  which  can  be  devoted  profitably  to  its  disposal; 
and  supposing  that  two  hours  is  all  that  can  be  spared  for  that  purpose,  and 
that  ten  tons  is  the  amount  which  must  be  melted,  find  in  the  column,  Melt- 
ing Capacity  per  hour  in  Pounds,  the  nearest  figure  to  five  tons  per  hour, 
which  is  found  to  be  10,760  pounds  per  hour,  opposite  to  which  in  the  column 
Diameter  of  Cupolas,  Inside  Lining,  will  be  found  48  inches  ;  this  will  be  the 
size  of  cupola  required  to  furnish  ten  tons  of  molten  iron  in  two  hours. 

Or  suppose  that  the  heats  were  likely  to  average  6  tons,  with  an  occasional 
increase  up  to  ten,  then  it  might  not  be  thought  wise  to  incur  the  extra  ex- 
pense consequent  on  working  a  48-inch  cupola,  in  which  case,  by  following 
the  directions  given,  it  will  be  found  that  a  40-inch  cupola  would  answer  the 
purpose  for  6  tons,  but  would  require  an  additional  hour's  time  for  melting 
whenever  the  10  ton  heat  came  along. 

The  quotations  in  the  table  are  not  supposed  to  be  all  that  can  be  melted 
in  the  hour  by  some  of  the  very  best  cupolas,  but  are  simply  the  amounts 
which  a  common  cupola  under  ordinary  circumstances  may  be  expected  to 
melt  in  the  time  specified. 

Height  of  Cupola.— By  height  of  cupola  is  meant  the  distance  from  the 
base  to  the  bottom  side  of  the  charging  hole. 

Depth  of  Bottom  of  Cupola.— Depth  of  bottom  is  the  distance  from  the 
sand-bed,  after  it  has  been  formed  at  the  bottom  of  the  cupola,  up  to  the 
under  side  of  the  tuyeres. 

All  the  amounts  for  fuel  are  based  upon  a  bottom  of  10  inches  deep,  and 
any  departure  from  this  depth  must  be  met  by  a  corresponding  change  in 
the  quantity  of  fuel  used  on  the  bed  ;  more  in  proportion  as  the  depth  is 
increased,  and  less  when  it  is  made  shallower. 

Amount  of  Fuel  Required  on  the  Bed. — The  column  "  Amount  of  Fuel  re- 
quired on  Bed.  in  Pounds"  is  based  on  the  supposition  that  the  cupola  is  a 
straight  one  all  through,  and  that  the  bottom  is  10  inches  deep.  If  the  bot- 
tom be  more,  as  in  those  of  the  Colliau  type,  then  additional  fuel  will  be 
needed. 

The  amounts  being  given  in  pounds,  answer  for  both  coal  and  coke,  for, 
should  coal  be  used,  it  would  reach  about  15  inches  above  the  tuyeres  ;  the 
same  weight  of  coke  would  bring  it  up  to  about  22  inches  above  the  tuyeres, 
which  is  a  reliable  amount  to  stock  with. 

First  Charge  of  Iron.— The  amounts  given  in  this  column  of  the  table  are 
safe  figures  to  work  upon  in  every  instance,  yet  it  will  always  be  in  order. 
after  proving  the  ability  of  the  bed  to  carry  the  load  quoted,  to  make  a  slow 
and  gradual  increase  of  the  load  until  it  is  fully  demonstrated  just  how  mucH 
burden  the  bed  will  carry. 

Succeeding  Charges  of  Fuel  and  Iron.— In  the  columns  relating  to  succeed- 
ing charges 'of  fuel  and  iron,  it  will  be  seen  that  the  highest  proportions  are 
not  favored,  for  the  simple  reason  that  successful  melting  with  any  greater 
proportion  of  iron  to  fuel  is  not  the  rule,  but,  rather,  the  exception.  When- 
ever we  see  that  iron  has  been  melted  in  prime  condition  in  the  proportion 
of  13  pounds  of  iron  to  one  of  fuel,  we  may  reasonably  expect  that  the  talent, 
material,  and  cupola  have  all  been  up  to  the  highest  degree  of  excellence. 

Diameter  of  Main  Blast-pipe.— The  table  gives  the  diameters  of  main 
blast-pipes  for  all  cupolas  from  24  to  84  inches  diameter.  The  sizes  given 
opposite  each  cupola  are  of  sufficient  area  for  all  lengths  up  to  100  feet. 


CUPOLA   PRACTICE. 


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948  THE 

Tuyeres  for  Cupola.— Two  columns  are  devoted  to  the  number  and  sizes  of 
tuyeres  requisite  for  the  successful  working  of  each  cupola  ;  one  gives  the 
number  of  pipes  6  inches  diameter,  and  the  other  gives  the  number  and 
dimensions  of  rectangular  tuyeres  which  are  their  equivalent  in  area. 

From  these  two  columns  any  other  arrangement  or  disposition  of  tuyeres 
may  be  made,  which  shall  answer  in  their  totality  to  the  areas  given  in  the 
table. 

When  cupolas  exceed  60  inches  in  diameter,  the  increase  in  diameter 
should  begin  somewhere  above  the  tuyeres.  This  method  is  necessary  in  all 
common  cupolas  above  60  inches,  because  it  is  not  possible  to  force  the  blast 
to  the  middle  of  the  stock,  effectively,  at  any  greater  diameter. 

On  no  consideration  must  the  tuyere  area  be  reduced;  thus,  an  84-inch 
cupola  must  have  tuyere  area  equal  to  31  pipes  6  inches  diameter,  or  16  flat 
tuyeres  16  inches  by  13}^  inches. 

if  it  is  found  that  the  given  number  of  flat  tuyeres  exceed  in  circumference 
that  of  the  diminished  part  of  the  cupola,  they  can  be  shortened,  allowing 
the  decreased  length  to  be  added  to  the  depth,  or  they  may  be  built  in  on 
end;  by  so  doing,  we  arrive  at  a  modified  form  of  the  Blakeney  cupola. 

Another  important  point  in  this  connection  is  to  arrange  the  tuyeres  in 
such  a  manner  as  will  concentrate  the  fire  at  the  melting-point  into  the 
smallest  possible  compass,  so  that  the  metal  in  fusion  will  have  less  space 
to  traverse  while  exposed  to  the  oxidizing  influence  of  the  blast. 

To  accomplish  this,  recourse  has  been  had  to  the  placing  of  additional 
rows  of  tuyeres  in  some  instances— the  "Stewart  rapid  cupola"  having 
three  rows, 'and  the  "Colliau  cupola  furnace"  having  two  rows,  of  tuyeres. 

Blast-pressure. — Experiments  show  that  about  30,000  cubic  feet  of  air  are 
consumed  in  melting  a  ton  of  iron,  which  would  weigh  about  2400  pounds, 
or  more  than  both  iron  and  fn-Jl.  When  the  proper  quantity  of  air  is  sup- 
plied, the  combustion  of  the  fuel  ; ;  perfect,  and  carbonic-acid  gas  is  the 
result.  When  the  supply  of  air  is  insufficient,  the  combustion  is  imperfect, 
and  carbonic-oxide  gas  is  the  result.  .The  amount  of  heat  evolved  in  these 
two  cases  is  as  15  to  4^£  showing  ..  loss  of  over  two  thirds  of  the  heat  by  im- 
perfect combustion. 

It  is  not  always  true  that  we  obtain  the  most  rapid  melting  when  we  are 
forcing  into  the  cupola  the  J  rgest  quantity  of  air.  Some  time  is  required 
to  elevate  the  temperature  of  the  air  supplied  to  the  point  that  it  will  enter 
into  combustion.  If  more  air  than  this  is  supplied,  it  rapidly  absorbs  heat, 
reduces  the  temperature,  and  retards  combustion,  and  the  fire  in  the  cupola 
may  be  extinguished  with  too  mu  h  blast. 

Slag  in  Cupolas. — A  certain  amount  of  slag  is  necessary  to  protect  the 
molten  iron  which  has  fallen  to  tue  bottom  from  the  action  of  the  blast  ;  if 
it  was  not  there,  the  iron  would  suffer  from  decarbonization. 

When  slag  from  any  cause  forms  in  too  great  abundance,  it  should  be  led 
away  by  inserting  a  hole  a  little  below  the  tuyeres,  through  which  it  will 
find  its  way  as  the  iron  rises  in  the  bottom. 

In  the  event  of  clean  iron  and  fuel,  slag  seldom  forms  to  any  appreciable 
extent  in  small  heats  ;  this  renders  any  preparation  for  its  withdrawal  un- 
necessary, but  when  the  cupola  is  to  be  taxed  to  its  utmost  capacity  it  is 
then  incumbent  on  the  melter  to  flux  the  charges  all  through  the  heat,  car- 
rying it  away  in  the  manner  directed. 

The  best  flux  for  this  purpose  is  the  chips  from  a  white  marble  yard. 
Abnut  6  pounds  to  the  ton  of  iron  will  give  good  results  when  all  is  clean. 

When  fuel  is  bad,  or  iron  is  dirty,  or  both  together,  it  becomes  imperative 
that  the  slag  be  kept  running  all  the  time. 

Fuel  for  Cupolas. — The  best  fuel  for  melting  iron  is  coke,  because  it  re- 
quires less  blast,  makes  hotter  iron,  and  melts  faster  than  coal.  When  coal 
must  be  used,  care  should  be  exercised  in  its  selection.  All  anthracites 
which  are  bright,  black,  hard,  and  free  from  slare,  will  melt  iron  admirably. 
The  size  of  the  coal  used  affects  the  melting  to  an  appreciable  extent,  and, 
for  the  best  results,  small  cupolas  should  be  charged  with  the  size  called 
"egg, "a  still  larger  grade  for  medium-sized  cupolas,  and  what  is  called 
"lump"  will  answer  for  all  large  cupolas,  when  care  is  taken  to  pack  it 
carefully  on  the  charges. 

Charging  a  Cupola.— Ohas.  A.  Smith  (Am.  Mnch.,  Feb.  12, 1891)  gives 
the  following:  A  28-in.  cupola  should  have  from  300  to  400  pounds  of  coke 
on  bottom  bed:  a  36-in.  cupola,  700  to  800  pounds;  a  48-in.  cupola,  1500  Ibs. ; 
and  a  60-in.  cupola  should  have  one  ton  of  fuel  on  bottom  bed.  To  every 
pound  of  fuel  on  the  bed,  three,  and  sometimes  four  pounds  of  metal  can  be 
added  with  safety,  if  the  cupola  has  proper  blast;  in  after-charges,  to  every 


CUPOLA   PKACTICE. 


949 


pound  of  fuel  add  8  to  10  pounds  of  metal;  any  well-constructed  cupola  will 
stand  ten. 

F.  P.  Wolcott  (Am.  Mach.,  Mar.  5,  1891)  gives  the  following  as  the  practice 
of  the  Col  well  Iron-works,  Carteret,  N.  J.:  "  We  melt  dailv  from  twenty  to 
forty  tons  of  iron,  with  an  average  of  11.2  pounds  of  iron  to  one  of  fuel.  In 
a  36-in.  cupola  seven  to  nine  pounds  is  good  melting,  but  in  a  cupola  that 
lines  up  48  to  60  inches,  anything  less  than  nine  pounds  shows  a  defect  in 


reports  in 
ag  from  Maine  to 
Oregon. 

Cupola  Charges  Ici  Stove-foundries.  (Iron  Age,  April  14,  1892.) 
No  two  cupolas  are  charged  exactly  the  same.  The  amount  of  fuel  on  the 
bed  or  between  the  charges  differs,  while  varying  amounts  of  iron  are  used 
in  the  charges.  Below  will  be  found  charging-lists  from  some  of  the  prom- 
inent stove-foundries  in  the  country  : 


Ibs. 
A—  Bed  of  fuel,  coke  ..........  1,500 

First  charge  of  iron  ......  5,000 

All  other  charges  of  iron  .  .  1,000 
First  and  second  charges 
of  coke,  each  ............      200 


Ibs. 
Four  next  charges  of  coke, 

each 150 

Six  next  charges  of  coke,  each  120 
Nineteen  next  charges  of  coke, 

each 100 


Thus  for  a  melt  of  18  tons  there  would  be  5120  Ibs.  of  coke  used,  giving  a 
ratio  of  7  to  1  .  Increase  the  amount  of  iron  melted  to  24  tons,  and  a  ratio  of 
8  pounds  of  iron  to  1  of  coal  is  obtained. 


Ibs. 
Second  and  third  charges  of 

fuel 130 

All  other  charges  of  fuel,  each     100 


Ibs. 

B  -Bed  of  fuel,  coke  1,600 

First  charge  of  iron 1,800 

First  charge  of  fuel 150 

All  other  charges  of  iron, 
each 1,000 

For  an  18-ton  melt  5060  Ibs.  of  coke  would  be  necessary,  giving  a  ratio  of 
7.1  Ibs.  of  iron  to  1  pound  of  coke. 
Ibs. 

C— Bed  of  fuel,  coke  1,600 

First  charge  of  iron 4,000 


First  and  second  charges 
of  coke 


200 


All  other  charges  of  iron 

All  other  charges  of  coke. . . . 


Ibs. 

2,000 

150 


In  a  melt  of  18  tons  4100  Ibs.  of  coke  would  be  used,  or  a  ratio  of  8.5  to  1. 
Ibs.    I  Ibs. 

1>— Bed  of  fuel,  coke 1,800       All  charges  of  coke,  each 200 

First  charge  of  iron 5,600    j    All  other  charges  of  iron 2,900 

In  a  melt  of  18  tons,  3900  Ibs.  of  fuel  would  be  used,  giving  a  ratio  of  9.4 
pounds  of  iron  to  1  of  coke.    Very  high,  indeed,  for  stove-plate. 


Ibs. 

All  other  charges  of  iron,  each  2,000 
All  other  charges  of  coal,  each     175 


Ibs. 

E— Bed  of  fuel,  coal 1 ,900 

First  charge  of  iron 5,000 

First  charge  of  coal 200 

In  a  melt  of  18  tons  4700  Ibs.  of  coal  would  be  used,  giving  a  ratio  of  7.7 
Ibs.  of  iron  to  1  Ib.  of  coal. 

These  are  sufficient  to  demonstrate  the  varying  practices  existing  among 
different  stove-foundries.  In  all  these  places  the  iron  was  proper  for  stove- 
plate  purposes,  and  apparently  there  was  little  or  no  difference  in  the  kind 
of  work  in  the  sand  at  the  different  foundries. 

Results  of  Increased  driving.  (Erie  City  Iron-works,  1891.)- 
May— Dec.  1890:  60-in.  cupola,  100  tons  clean  castings  a  week,  melting  8  tons 
per  hour:  iron  per  pound  of  fuel,  7^>  Ibs. ;  percent  weight  of  good  castings  to 
iron  charged,  75%.  Jan.-May,  1891:  Increased  rate  of  melting  to  11)6  tons  per 
hour;  iron  per  Ib.  fuel,  9^;  per  cent  weight  of  good  castings,  75;  one  week, 
13*4  tons  per  hour,  10.3  Ibs.  iron  per  Ib.  fuel;  per  cent  weight  of  good  cast- 
ings, 75.3.  The  increase  was  made  by  putting  in  an  additional  row  of  tuyeres 
and  using  stronger  blast,  14  ounces.  Coke  was  used  as  fuel.  (W.  Q.  Webber, 
Trans.  A.  S.  M.  F,-  xii.  1045.) 


950 


THE   FOUND R 


Buffalo  Steel  Pressure-blower*.    Speeds  and  Capacities 
as  applied  to  Cupolas. 


1  P»J  • 

t. 

-b  '-     !•- 

b 

'55  *** 

i 

<g  „, 

'3  a 

<*« 

-—  0) 

g 

g 

^  C  «D 

"Sft 

*-  S 

CD 

1 

o 

•s.3 

.s 

•  C§ 

§4 

0  ft 

^ts 

i 

a 

6-2^ 

&¥ 

o  a 

C^ 

s 

3 

S| 

£ 

ils 

ttg  . 

lli 

""«  s 

SL-g 

g 

55^.5 

go  u 

!§! 

i"3 

05  C4 

B 

d 

go 
Jo 

1 

•»*•&, 

|?o 

if! 

i  ^ 

2s 

o  a1 

1 

|ll 

'|  c| 

Ill 

-  CJ 

M^ 

02 

Iz; 

5 

h 

02 

g 

0  "  ' 

n 

£ 

y2 

S 

5  ~ 

4 

4 

20 

8 

4793 

1545 

412 

1.0 

9 

5095 

164? 

438 

1  3 

6 

5 

25 

8 

3911 

2321 

619 

1.2 

10 

4509 

2600 

694 

2.  '2 

8 

6 

30 

8 

3-156 

3093 

825 

2.05 

10 

3974 

3671 

926 

3.1 

11 

7 

35 

8 

3092 

4218 

1125 

3.1 

10 

3476 

4777 

1274 

4.25 

14 

8 

40 

8 

2702 

5425 

1444 

3.9 

10 

3034 

6082 

1622 

5.52 

18 

9 

45 

10 

2617 

7818 

2085 

7.1 

12 

2916 

8598 

2293 

9.36 

26 

10 

55 

10 

2139 

11295 

3012 

10.2 

12 

2353 

12378 

3301 

12. 

46 

11 

73 

12 

1639 

21978 

5861 

23.9 

14 

1777 

238:58 

6357 

30.3 

08 

12 

88 

12 

1639 

32395 

8636 

35.2 

14 

1777 

35190 

9384 

43.7 

In  the  table  are  given  two  different  speeds  and  pressures  for  each  size  of 
blower,  and  the  quantity  of  iron  that  may  be  melted,  per  hour,  with  each. 
In  all  cases  it  is  recommended  to  use  the  lowest  pressure  of  blast  that  will  do 
the  work.  Run  up  to  the  speed  given  for  that  pressure,  and  regulate  quan- 
tity of  air  by  the  blast-gate.  The  tuyere  area  should  be  at  least  one  ninth 
of  the  area  of  cupola  in  square  inches,  with  not  less  than  four  tuyeres  at 
equal  distances  around  cupola,  so  as  to  equalize  the  blast  throughput.  Va- 
riations in  temperature  affect  the  working  of  cupolas  materially,  hot 
weather  requiring  increase  in  volume  of  air. 
(For  tables  of  the  Sturtevant  blower  see  pages  519  and  520.) 
Loss  in  Melting  Iron  in  Cupolas.— G.  O.  Vair,  Am.  Mack., 
March  5,  1891,  gives  a  record  of  a  45-in.  Colliau  cupola  as  follows: 

Ratio  of  fuel  to  iron,  1  to  7.42. 

Good  castings  21,314  Ibs. 

New  scrap 3,005  " 

Millings 200  " 

Loss  of  metal 1,481  " 


Amount  melted 26,000  Ibs. 

Loss  of  metal,  5.69#.    Ratio  of  loss,  1  to  17.55. 

Use  of  Softeners  in  Foundry  Practice.  (W.  Graham,  Iron  Age, 
June  27.  1889.)— In  the  foundry  the  problem  is  to  have  the  right  proportions 
of  combined  and  graphitic  carbon  in  the  resulting  casting;  rhis  is  done  by 
getting  the  proper  proportion  of  silicon.  The  variations  in  the  proportions 
of  silicon  afford  a  reliable  and  inexpensive  means  of  producing  a  cast  iron 
of  any  required  mechanical  character  which  is  possible  with  the  material 
employed.  In  this  way,  by  mixing  suitable  irons  in  the  right  proportions, 
a  required  grade  of  casting  can  be  made  more  cheaply  than  by  using  irons 
in  which  the  necessary  proportions  are  already  found. 

If  a  strong  machine  casting  were  required,  it  would  be  necessary  to  keep 
the  phosphorus,  sulphur,  and  manganese  within  certain  limits.  Professor 
Turner  found  that  cast  iron  which  possessed  the  maximum  of  the  desired 
qualities  contained,  graphite,  2.59^;  silicon,  1.42#;  phosphorus,  0.39^;  sul- 
phur, 0.06$;  manganese,  0.58$. 

A  strong  casting  could  not  be  made  if  there  was  much  increase  in  the 
amount  of  phosphorus,  sulphur,  or  manganese.  Irons  of  the  above  percent- 
ages of  phosphorus,  sulphur,  and  manganese  would  be  most  suitable  for  this 
purpose,  but  they  could  be  of  different  grades,  having  different  percentages 
of  silicon,  com hined  and  graphitic  carbon.  Thus  hard  irons,  mottled  and 
white  irons,  and  even  steel  scrap,  all  containing  low  percentages  of  silicon 
and  high  percentages  of  combined  carbon,  could  be  employed  if  an  iron 
having  a  large  amount  of  silicon  were  mixed  with  them  in  sufficient  amount. 
This  would  bring  the  silicon  to  the  proper  proportion  and  would  cause  the 
Qombhied  carbon  to  be  forced  into  the  graphitic  state,  and  the  resulting 


SHRINKAGE   OF  CASTINGS. 


951 


casting  would  be  soft.    High-silicon  irons  used  in  this  way  are  called  "  soft- 
eners.'1 
The  following  are  typical  analyses  of  softeners: 


Ferro-silicon. 

Softeners,  American. 

Scotch 
Irons,  No.  1. 

Foreign. 

American. 

Well- 
ston. 

Globe 

Belle- 
fonte. 

Eg- 
1  in  ton 

Colt- 
ness. 

2.59 

Silicon  
Combined  C.. 
Graphitic  C.. 
Manganese  .  . 
Phosphorus.  . 
Sulphur  

10.55 
1.84 

0.52 
3.86 
0.04 
0.03 

9.80 
0.69 
1.12 
1.95 
0.21 
0.04 

12.08 
0.06 
1.52 
0.76 
0.48 
Trace 

10.34 
0.07 
1.92 
0.52 
0.45 
Trace 

6.67 
2!57 

0^50 
Trace 

5.89 
0.30 
2.85 
1.00 
1.10 
0.02 

3  to  6 
0.25 
3. 
0.53 
0.35 
0.03 

2.15 
0.21 
3.76 
2.80 
0.62 
0.03 

1.70 
0.85 
0.01 

(For  other  analyses,  see  pages  371  to  373.) 

Ferro-silicons  contain  a  low  percentage  of  total  carbon  &nd  a  high  per- 
centage of  combined  carbon.  Carbon  is  the  most  important  constituent  of 
cast  iron,  and  there  should  be  about  3.4#  total  carbon  present.  By  adding 
ferro  silicon  which  contains  only  2%  of  carbon  the  amount  of  carbon  in  the 
resulting  mixture  is  lessened. 

Mr.  Keep  found  that  more  silicon  is  lost  during  the  remelting  of  pig  of 
over  lOfe  silicon  than  in  remelting  pig  iron  of  lower  percentages  of  silicon. 
He  also  points  out  the  possible  disadvantage  of  using  ferro-sil  icons  contain- 
ing as  high  a  percentage  of  combined  carbon  as  0.70$  to  overcome  the  bad 
effects  of  combined  carbon  in  other  irons. 

The  Scotch  irons  generally  contain  much  more  phosphorus  than  is  desired 
in  irons  to  be  employed  in  making  the  strongest  castings.  It  is  a  mistake  to 
mix  with  strong  low -phosphorus  irons  an  iron  that  would  increase  the 
amount  of  phosphorus  for  the  sake  of  adding  softening  qualities,  when  soft- 
ness can  be  produced  by  mixing  irons  of  the  same  low  phosphorus. 

(For  further  discussion  of  the  influence  of  silicon  see  page  365.) 

Shrinkage  of  Castings.— The  allowance  necessary  for  shrinkage 
varies  for  different  kinds  of  metal,  and  the  different  conditions  under  which 
they  are  cast.  For  castings  where  the  thickness  runs  about  one  inch,  cast 
under  ordinary  conditions,  the  following  allowance  can  be  made: 


For  cast-iron,  J^  inch  per  foot. 
"    brass,        3/16     "       "       " 
"    steel,         J4 
"    inal.  iron,  ^|         "      "      " 


For  zinc,  5/16  inch  per  foot. 

"    tin,  1/12    "       "      " 

"    aluminum,  3/16    "       "      " 
"    Britannia,   1/32    "       "      " 


Thicker  castings,  under  the  same  conditions,  will  shrink  less,  and  thinner 
ones  more,  than  this  standard.  The  quality  of  the  material  and  the  manner 
of  moulding  and  cooling  will  also  make  a  difference. 

Numerous  experiments  by  W.  J.  Keep  (see  Trans.  A.  S.  M.  E.,  vol.  xvi.) 
showed  that  the  shrinkage  of  cast-  iron  of  a  given  section  decreases  as  the 
percentage  of  silicon  increases,  while  for  a  given  percentage  of  silicon  the 
shrinkage  decreases  as  the  section  is  increased.  Mr.  Keep  gives  the  follow- 
ing table  showing  the  approximate  relation  of  shrinkage  to  size  and  per- 
centage of  silicon: 


Sectional  Area  of  Casting. 


Percentage 
of 
Silicon. 

fc*o 

1"    D 

1"  X  2" 

2"  p 

3"  n 

4"  n 

Shrinkage  in  Decimals  of  an  inch  per  foot  of  Length. 

1. 
1.5 
2. 
2.5 
3. 
3.5 

.183 
.171 
.159 
.147 
.135 
.123 

.158 
.145 
.133 
.121 
.108 
.095 

.146 
.133 
.121 
.108 
.095 
.082 

.130 
.117 
.104 
.092 
.077 
.065 

.113 
.098 
.085 
.073 
.059 
.046 

.102 
.087 
.074 
.060 
.045 
.032 

952 


THE   FOUNDRY. 


Mr.  Keep  also  gives  the  following  "  approximate  key  for  regulating  foun- 
dry mixtures"  so  as  to  produce  a  shrinkage  of  y§  in.  per  ft.  in  castings  of 
different  sections: 

Size  of  casting %  1  2  3  4      in.  sq. 

Silicon  required,  per  cent 3.25       2.75       2.25        1.75        1.25  percent. 

Shrinkage  of  a  \fc\ u.  test-bar.     .125        .135        .145        .155        .165  in.  per  ft. 

Weight  of  Castings  determined   from  Weight  of  Pattern. 

(Rose's  Pattern-maker's  Assistant.) 

Will  weigh  when  cast  in 


A.  .rauern  weignmg  <jne  rouna, 
made  of  — 

Cast 
Iron. 

Zinc. 

Copper. 

Yellow 
Brass. 

Gun- 
metal. 

Mahogan  y  —  Nassau 

Ibs. 

10  *7 

Ibs. 

10  A. 

Ibs. 

19  8 

Ibs. 

199 

Ibs. 

1  o   K 

**           Honduras. 

12  9 

12  7 

15  3 

14.  fi 

1  £\ 

"           Spanish  

8  5 

8  2 

10  1 

9   7 

a  Q 

Pine,  red  

1°  5 

12  1 

14  9 

14  2 

14  6 

"    white       

16  7 

16  1 

19  8 

19  0 

1Q  ^ 

"    yellow  

14  1 

13  6 

16  7 

16  0 

16  5 

Moulding  Sand.  (From  a  paper  on  "The  Mechanical  Treatment  of 
Moulding  Sand."  by  Walter  Bagshaw,  Proc.  Inst.  M.  E.  1891.) — The  chemical 
composition  of  sand  will  affect  the  nature  of  the  casting,  no  matter  what 
treatment  it  undergoes.  Stated  generally,  good  sand  is  composed  of  94  parts 
silica,  5  parts  alumina,  and  traces  of  magnesia  and  oxide  of  iron.  Sand  con- 
taining much  of  the  metallic  oxides,  and  especially  lime,  is  to  be  avoided. 
Geographical  position  is  the  chief  factor  governing  the  selection  of  sand; 
and  whether  weak  or  strong,  its  deficiencies  are  made  up  for  by  the  skill  of 
the  moulder.  For  this  reason  the  same  sand  is  often  used  for  both  heavy  and 
light  castings,  the  proportion  of  coal  varying1  according  to  the  nature  of  the 
casting.  A  common  mixture  of  facing-sand  consists  of  six  parts  by  weight 
of  old  sand,  four  of  new  sand,  and  one  of  coal-dust.  Floor-sand  requires 
only  half  the  above  proportions  of  new  sand  and  coal-dust  to  renew  it.  Ger- 
man founders  adopt  one  part  by  measure  of  new  sand  to  two  of  old  sand; 
to  which  is  added  coal-dust  in  the  proportion  of  one  tenth  of  the  bulk  for 
large  castings,  and  one  twentieth  for  small  castings.  A  few  founders  mix 
street-sweepings  with  the  coal  in  order  to  get  porosity  when  the  metal  in 
the  mould  is  likely  to  be  a  long  time  before  setting.  Plumbago  is  effective  in 
preventing  destruction  of  the  sand;  but  owing  to  its  refractory  nature,  it 
must  not  be  dusted  on  in  such  quantities  as  to  close  the  pores  and  prevent 
free  exit  of  the  gases.  Powdered  French  chalk,  soapstone,  and  other  sub- 
stances are  sometimes  used  for  facing  the  mould;  but  next  to  plumbago,  oak 
charcoal  takes  the  best  place,  notwithstanding  its  liability  to  float  occasion- 
ally and  give  a  rough  casting. 

For  the  treatment  of  sand  in  the  moulding-shop  the  most  primitive  method 
is  that  of  hand-riddling  and  treading.  Here  the  materials  are  roughly  pro- 
portioned by  volume,  and  riddled  over  an  iron  plate  in  a  flat  heap,  where 
the  mixture  is  trodden  into  a  cake  by  stamping  with  the  feet;  it  is  turned 
over  with  the  shovel,  and  the  process  repeated.  Tough  sand  can  be  obtained 
in  this  manner,  its  toughness  being  usually  tested  by  squeezing  a  handful 
into  a  ball  and  then  breaking  it;  but  the  process  is  slow  and  tedious.  Other 
things  being  equal,  the  chief  characteristics  of  a  good  moulding-sand  are 
toughness  and  porosity,  qualities  that  depend  on  the  manner  of  mixing  as 
well  as  on  uniform  ramming. 

Toughness  of  Sand.— In  order  to  test  the  relative  toughness,  sand 
mixed  in  various  ways  was  pressed  under  a  uniform  load  into  bars  1  in.  sq. 
and  about  12  in.  long,  and  each  bar  was  made  to  project  further  and 
further  over  the  edge  of  a  table  until  its  end  broke  off  by  its  own  weight. 
Old  sand  from  the  shop  floor  had  very  irregular  cohesion,  breaking  at  all 
lengths  of  projections  from  ^  in.  to  1^  in.  New  sand  in  its  natural  state 
held  together  until  an  overhang  of  2%  in.  was  reached.  A  mixture  of  old 
sand,  new  sand,  and  coal-dust 

Mixed  under  rollers broke  at  2     to  2*4  in-  of  overhang. 

in  the  centrifugal  machine "       "  2      "2*4"    "          " 

M       through  a  riddle "       "  1%  "  2%  "    "         « 


SPEED   OF  CUTTIHG-TOOLS  1ST  LATHES,    ETC.       953 


Showing  as  a  mean  of  the  tests  only  slight  differences  between  the  last 
three  methods,  but  in  favor  of  machine-work.  In  many  instances  the  frac- 
tures were  so  uneven  that  minute  measurements  were  not  taken. 

Dimension*  of  Foundry  Ladles.— The  following  table  gives  the 
dimens  QMS.  inside  tiie  lining,  of  ladles  from  25  Ibs.  to  16  tons  capacity.  All 
the  ladles  are  supposed  to  have  straight  sides.  (Am.  Mach.,  Aug.  4,  1892.) 


Capacity. 

Diam. 

Depth. 

Capacity. 

Diam. 

Depth. 

16  tons  

in. 
54 

in. 

56 

%ton  

in. 
20 

in. 

20 

14      "         

52 

53 

17 

17 

12      "     

49 

50 

£4    ** 

13/4 

13}/£ 

10     "       
8     "        

46 
43 

48 
44 

300    pounds  .  .  . 
250         " 

11V6 
loa^ 

ttS 

1] 

6     "     
4      "     . 
3     "     
2     "         

39 
34 
31 

27 

40 

35 
32 

28 

200          " 
150          " 

100          " 
75          " 

10' 

9 
8 

7 

9V£ 

ll/2  •*      

24X> 

25 

50          " 

6^£ 

fil/ 

1       " 

22 

22 

35          '• 

5V6 

g 

THE    MACHINE-SHOP. 


SPEED    OF    CUTTING-TOOLS    IN    LATHES,     MILLING 

MACHINES,  ETC. 

Relation  of  diameter  of  rotating  tool  or  piece,  number  of  revolutions, 
and  cutting-speed  : 

Let  d  -  diain.  of  rotating  piece  in  inches,  n  =  No.  of  revs,  per  min.; 
/S  —  speed  of  circumference  in  feet  per  minute; 


3.828 
d 


d 


3.82S 


Approximate  rule  :  No.  of  revs,  per  min.  =  4  X  speed  in  ft.  per  min.  -*- 
diatn.  in  inches. 

Speed  of  Cwt-for  Lathes  and  Planers.  (Prof.  Coleman  Sellers, 
Stevens  Indicator,  April,  1892.)— Brass  may  be  turned  at  high  speed  like 
wood. 

Bronze.— A  speed  of  18  feet  per  minute  can  be  used  with  the  soft  alloys- 
say  8  to  1,  while  for  hard  mixtures  a  slow  speed  is  required— say  6  feet  per 
minute. 

Wrought  Iron  can  be  turned  at  40  feet  per  minute,  but  planing-machines 
that  are  used  for  both  cast  and  forged  iron  are  operated  at  18  feet  per 
minute. 

Machinery  Steel.— Ordinary,  14  feet  per  minute;  car-axles,  etc.,  9  feet  per 
minute. 

Wheel  Tires.— Q  feet  per  minute;  the  tool  stands  well,  but  many  prefer 
to  run  faster,  say  8  to  10  feet,  and  grind  the  tool  more  frequently. 

Lathes.— The  speeds  obtainable  by  means  of  the  cone-pulley  and  the  back 
gearing  a.re  in  geometrical  progression  from  the  slowest  to  the  fastest, 
a  well-proportioned  machine  the  speeds  hold  the  same  relation  through  all 
the  steps.    Many  lathes  have  the  same  speed  on  the  slowest  of  the  cone  and 
the  fastest  of  the  back-gear  speeds. 

The  Speed  of  Counter-shaft  of  the  lathe  is  determined  by  an  assumption 
of  a  slow  speed  with  the  back  gear,  say  6  feet  per  minute,  on  the  largest 
diameter  that  the  lathe  will  swing. 


J.U  luiiHUi;    ui     {jiaijuiji,,  J.L    LUC   vjut'Lujg-o^v^u    ^AV/^^«    v.«    ..»•.  f~~  ' 

much  heat  will  be  produced  that  the  temper  will  be  drawn  from  the  tool 


in  cutting  niuu  steei,  wim  a  traverse  01  ?g  in.  ptu 

with  a  shaving  about  %  in.  thick,  the  speed  of  cutting  must  be  reduced  to 

about  8  ft.  per  minute.    A  good  average  cutting-speed  for  wrought  or  cast 


954 


THE   MA  CHINE- SHOP. 


iron  is  20  ft.  per  minute,  whether  for  the  lathe,  planing,  shaping,  or  slotting 
machine.    (Proc.  Inst.  M.  E.,  April,  1883,  p.  248.) 

Table  of  Cutting-speeds. 


Diameter, 
inches. 


I 


7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
18 
20 
22 
24 
26 
28 
30 
36 
42 
48 
54 
60 


Feet  per  minute. 

5 

10 

15 

20 

25 

30 

35    | 

40 

45 

50 

Revolutions  per  minute. 

76.4 

152.8    229.2 

305.6 

382.0    458.4 

534.8 

611.2 

687.6 

764.0 

50.9 

101.9 

153.8 

203.7 

254.6 

305.6 

356.5 

407.4 

458.3 

509.3 

38.2 

7G.4 

114.6 

152.8 

191.0 

229.2 

267.4 

305.6 

343.8 

382.0 

30.6 

61.1 

91.7 

122.2 

152.8 

183.4 

213.9 

244.5    275.0 

305.6 

25.5 

50.9 

76.4 

101.8 

127.3 

152.8 

178.2 

203.7    229.1 

254.6 

21.8 

43.7 

65.5 

87.3 

109.1 

130.9 

152.8 

174.6    196.4 

218.3 

19.1 

38.2 

57.3 

7(5.4 

95.5 

114.6 

153.  7 

152.8 

171.9 

191.0 

17.0 

34.0 

50.9 

67.9 

84.9 

101.8 

118.8 

135.8 

152.8 

169.7 

15.3 

30.6 

45.8 

61.1 

76.4 

91.7 

106.9 

122.2 

137.5 

152.8 

18  .9 

27.  8 

41.7 

55.6 

69.5 

83.3 

97.2 

111.1 

125.0 

138.9 

12.7 

25.5 

38.2 

50.9 

63.6 

76.4 

89.1 

101.8 

114.5 

127.2 

10.9 

21.8 

32.7 

43.7 

54.6 

65.5 

76.4 

87.3 

98.2 

109.2 

9.6 

19.1 

28.7 

38.2 

47.8 

57.3 

66.9 

76.4 

86.0 

95.5 

8.5 

17.0 

25.5 

34.0 

42.5 

50.9 

59.4 

67.9 

76.4 

84.9 

7.6 

15.3 

22  9 

30.6 

38.2 

45.8 

53.5 

61.1 

68.8 

76.4 

6.9 

13.9 

20.8 

27.8 

34.7 

41.7 

48.6 

55.6 

62.5 

69.5 

6.4 

12.7 

19.1 

25.5 

31.8 

38.2 

44.6 

50.9 

57.3 

63.'J 

5.5 

10.9 

16.4 

21.8 

27.3 

32.7 

38.2 

43.7 

49.1 

54.6 

4.8 

9.6 

14.3 

19.1 

23.9 

28.7 

33.4 

38  2 

43.0 

47.8 

4.2 

8.5 

12.7 

17.0 

21.2 

25.5 

29.7 

34.0 

38.2 

42.5 

3.8 

7.6 

11.5 

15.3 

19.1 

22.9 

26.7 

30.6 

34.4 

38.1 

3.5 

6.9 

10.4 

13.9 

17.4 

20.8 

24.3 

27.8 

31.2 

34.7 

3.2 

6.4 

9.5 

12.7 

15.9 

19.1 

22.3 

25.5 

28.6 

31.8 

2.7 

5.5 

8.2 

10.9 

13.6 

16.4 

19.1 

21.8 

24.6 

27.3 

2.4 

4.8 

7.~ 

9.6 

11.9 

14.3 

16.7 

19.1 

21.5 

23.9 

2.1 

4.2 

6.4 

8.5 

10.6 

12.7 

14.8 

17.0 

19.1 

21.2 

.9 

3.8 

5.7 

7.6 

9.6 

11.5 

13.3 

15.3 

17.  '2 

19.1 

.7 

3.5 

5.2 

6.9 

8.7 

10.4 

12.2 

13.9 

15.6 

17.4 

.6 

3.2 

4.8 

6.4 

8.0 

9.5 

11.1 

12.7 

14.3 

15.9 

.5 

2.9 

4.4 

5.9 

7.3 

8.8 

10.3 

11.8 

13.2 

14.7 

.4 

2.7 

4.1 

5.5 

6.8 

8.2 

9.5 

10.9 

12.3 

13.6 

.3 

2.5 

3.8 

5.1 

6.4 

7.6 

8.9 

10.2 

11.5 

12.7 

.2 

2.4 

3.6 

4.8 

6.0 

7.2 

8.4 

9.5 

10.7 

11.9 

.1 

2.1 

3.2 

4.2 

5.3 

6.4 

7.4 

8.5 

9.5 

10.6 

.0 

:  .9 

2.9 

3.8 

4.8 

5.7 

6.7 

7.6 

8.6 

9.6 

.9 

2.6 

3.5 

4.3 

5.2 

6.1 

6.9 

7.8 

8.7 

.8 

!e 

2.4 

3.2 

4.0 

4.8 

5.6 

6.4 

7.2 

8.0 

.7 

.5 

2.2 

2.9 

3.7 

4.4 

5.1 

5.9 

6.6 

7.3 

.7 

.4 

2.0 

2  7 

3.4 

4.1 

4.8 

5.5 

6.1 

6.8 

.6 

.3 

1.9 

2'.5 

3.2 

3.8 

4.5 

5.1 

5  7 

6.4 

.5 

1.1 

1.6 

2.1 

2.7 

3.2 

3.7 

4.2 

4.8 

5.3 

.5 

.9 

1.4 

1.8 

2.3 

2.7 

3.2 

3.6 

4.1 

4.5 

.4 

.8 

1.2 

1.6 

2.0 

2.4 

2.8 

3.2 

3.6 

4.C 

.4 

.7 

1.1 

1.4 

1.8       2.1 

2.5 

2.8 

3.2 

3.r 

.3 

.6       1.0 

1.3 

1.6        1.9 

2.2 

2.5 

2.9 

3.X 

Speed  of  Cutting  with  Turret  loathes.— Jones  &  Lamson  Ma 
chine  Co.  give  the  following  cutting-speeds  for  use  with  their  flat  turret 
lathe: 

Ft.  per  minute, 

(  Tool  steel  and  taper  on  tubing. 10 

Threading  •<  Machinery. 15 

(  Very  soft  steel 20 

Tiirnino-     f  Cut  which  reduces  the  stock  to  y%  of  its  original  diam . .        20 
mnnhirwarir  J  Cut  which  reduces  the  stock  to  %  of  its  original  diam. .        25 
eJUS i       I  Cnt  which  reduces  the  stock  to  %  of  its  original  diam . .  30  to  & 
I  Cut  which  reduces  the  stock  to  15/16  of  its  original  diam.  40  to  4£ 
Turning  very  soft  machinery  steel,  light  cut  and  cool  work 50  to  6( 


GEARING   OF  LATHES.  955 

Forms  of  Metal-cutting  Tools.— "  Hutte,"  the  German  Engi- 
neers1  Pocket-book,  gives  the  following  cutting-angles  for  using  least  power: 

Top  Rake,       Angle  of  Cutting-edge. 

Wroughtiron 3°  51° 

Castiron 4°  51° 

Bronze 4°  66° 

The  American  Machinist  comments  on  these  figures  as  follows  :  We  are 
not  able  to  give  the  best  nor  even  the  generally  used  angles  for  tools, 
because  these  vary  so  much  to  suit  different  circumstances,  such  as  degree 
of  hardness  of  the  metal  being  cut,  quality  of  steel  of  which  the  tool  is 
made,  depth  of  cut,  kind  of  finish  desired,  etc.  The  angles  that  cut  with 
the  least  expenditure  of  power  are  easily  determined  by  a  few  experiments, 
but  the  best  angles  must  be  determined  by  good  judgment.,  guided  by  expe- 
rience. In  nearly  all  cases,  however,  we  think  the  best  practical  angles  are 
greater  than  those  given. 

For  illustrations  and  descriptions  of  various  forms  of  cutting-tools,  see 
articles  on  Lathe  Tools  in  App.  Cyc.  App.  Mech.,  vol.  ii.,  and  in  Modern 
Mechanism. 

Cold  Chisels.—  Angle  of  cutting-faces  (Joshua  Rose):  For  cast  steel, 
about  60  degrees;  for  gun-metal  or  brass,  about  50  degrees;  for  copper  and 
soft  metals,  about  30  to  35  degrees. 

Rule  for  Gearing  Lathes  for  Screw-cutting.  (Garvin  Ma- 
chine Co.) — Read  from  Hie  lathe  index  the  number  of  threads  per  inch  cut 
by  equal  gears,  and  multiply  it  by  any  number  that  will  give  for  a  product 
a  gear  on  the  index;  put  this  gear  upon  the  stud,  then  multiply  the  number 
of  threads  per  inch  to  be  cut  by  the  same  number,  and  put  the  resulting  gear 
upon  the  screw. 

EXAMPLE. — To  cut  1 1*4  threads  per  inch.  We  find  on  the  index  that  48  into 
48  cuts  6  threads  per  inch,  then  0  X  4  =  24,  gear  on  stud,  and  11-;  '_,  X  4  =  46, 
gear  on  screw.  Any  multiplier  may  be  used  so  long  as  the  products  include 
gears  that  belong  with  the  lathe.  For  instance,  instead  of  4  as  a  multiplier 
we  may  use  6.  Thus,  6  X  6  =  36,  gear  upon  stud,  and  11^  X  6  =  69,  gear 
upon  screw. 

Rules  for  Calculating  Simple  and  Compound  Gearing 
-where  tliere  is  no  Index.  (Am  Mac/?..)— If  the  lathe  is  simple- 
geared,  and  tiie  stud  runs  at  the  same  speed  as  the  spindle,  select  some  gear 
for  the  screw,  and  multiply  its  number  of  teeth  by  the  number  of  threads 
per  inch  in  the  lead-screw,  and  divide  this  result  by  the  number  of  threads 
per  inch  to  be  cut.  This  will  give  tha  number  of  teeth  in  the  gear  for  the 
stud.  If  this  result  is  a  fractional  number,  or  a  number  which  is  not  among 
the  gears  on  hand,  then  try  some  other  gear  for  the  screw.  Or,  select  the 
gear  for  the  stud  first,  then  multiply  its  number  of  teeth  by  the  number  of 
threads  per  inch  to  be  cut,  and  divide  by  the  number  of  threads  per  inch  on 
the  lead-screw.  This  will  give  the  number  of  teeth  for  the  g^ar  on  the 
screw.  If  the  lathe  is  compound,  select  at  random  all  the  driving-gears, 
multiply  the  numbers  of  their  teeth  together,  and  this  product  by  the  num- 
ber of  threads  to  be  cut.  Then  select  at  random  all  the  driven  gears  except 
one;  multiply  the  numbers  of  their  teeth  together,  and  this  product  by  the 
number  of  threads  per  inch  in  the  lead-screw.  Now  divide  the  first  result  by 
the  second,  to  obtain  the  number  of  teeth  in  the  remaining  driven  gear.  Or, 
select  at  random  all  the  driven  gears.  Multiply  the  numbers  of  their  teeth 
together,  and  this  product  by  the  number  of  threads  per  inch  in  the  lead- 
screw.  Then  select  at  random  all  the  driving-gears  except  one.  Multiply 
the  numbers  of  their  teeth  together,  and  this  result  by  the  number  of  threads 
per  inch  of  the  screw  to  be  cut.  Divide  the  first  result  by  the  last,  to  obtain 
the  number  of  teeth  in  the  remaining  driver.  When  the  gears  on  the  com- 
pounding smcl  are  fast  together,  and  cannot  be  changed,  then  the  driven  one 
has  usually  twice  as  many  teeth  as  the  other,  or  driver,  in  which  case  in  the 
calculations  consider  the 'lead-screw  to  have  twice  as  many  threads  per  inch 
as  it  actually  has  and  then  ignore  the  compounding  entirely.  Some  lathes 
are  so  constructed  that  the  stud  on  which  the  first  driver  is  placed  revolves 
only  half  as  fast  as  the  spindle.  This  can  be  ignored  in  the  calculations  by 
doubling  the  number  of  threads  of  the  lead-screw.  If  both  the  last  condi- 
tions are  present  ignore  them  in  the  calculations  by  multiplying  the  number 
of  threads  per  inch  in  the  lead-screw  by  four.  If  the  thread  to  be  cut  is  a 
fractional  one,  or  if  the  pitch  of  the  lead-screw  is  fractional,  or  if  both  are 
fractional,  then  reduce  the  fractions  to  a  common  denominator,  and  use 
the  numerators  of  these  fractions  as  if  they  equalled  the  pitch  of  the  screw 


956 


THE  MACHIKE-SHOP. 


to  be  cut,  and  of  the  lead-screw,  respectively.  Then  use  that  part  of  the  rule 
given  above  which  applies  to  the  lathe  in  question.  For  instance,  suppose 
it  is  desired  to  cut  a  thread  of  25/32-inch  pitch,  and  the  lead-screw  has  4 
threads  per  inch  Then  the  pitch  of  the  lead-screw  will  be  M  inch,  which  is 
equal  to  8/32  icch.  We  now  have  two  fraction,  25/d2  and  8/32,  and  the  two 
screws  will  be  in  the  proportion  of  25  to  8,  and  the  gears  can  be  figured  by 
the  above  rule,  assuming  the  number  of  threads  to  be  cut  to  be  8  per  inch, 
and  those  on  the  lead-screw  to  be  25  per  inch.  But  this  latter  number  may 
be  further  modified  by  conditions  named  above,  such  as  a  reduced  speed  of 
the  stud,  or  fixed  compound  gears.  In  the  instance  given,  if  the  lead-screw 
had  been  2}&  threads  per  inch,  then  its  pitch  being  4/10  inch,  we  have  the 
fractions  4/10  and  25/32,  which,  reduced  to  a  common  denominator,  are 
64/160  and  125/160,  and  the  gears  wall  be  the  same  as  if  the  lead-screw  had  12E 
threads  per  inch,  and  the  screw  to  be  cut  64  threads  per  inch. 

On  this  subject  consult  also  "  Formulas  in  Gearing,"  published  by  Brown 
&  Sharpe  Mfg.  Co..  and  Jamieson's  Applied  Mechanics. 

Change-gears  for  Screw-cutting  loathes.— There  is  a  lack  of 
uniformity  among  lathe-builders  as  to  the  change-gears  provided  for  screw- 
cutting.  W.  R.  Macdonald,  in  Am.  Mach.,  April  7,  1892,  proposes  the  follow- 
ing series,  by  which  33  whole  threads  (not  fractional)  may  be  cut  by  changes 
of  only  nine  gears: 


i 

Spindle. 

2 

_i_i_ 

Whole  Threads. 

£ 

20 

aG 

40 

50 

60 

70 

110 

120 

130 

20 

8 

6 

4  4/5 

4 

3  3/7 

2  2/11 

2 

1  11/13 

2 

11 

22 

44 

ao 

18 

9 

7  1/5 

6 

5  1/7 

3  3/11 

3 

2  10/13 

3 

12 

24 

48 

40 

24 

16 

12 

9  3/5 

8 

6  6/7 

4  4/11 

4 

3  9/13 

4 

13 

26 

52 

50 

30 

20 

15 

10 

8  4/7 

5  5/11 

5 

4  8/13 

5 

14 

28 

66 

60 

36 

24 

18 

14  2/5 

10  2/7 

6  6/11 

6 

5  7/13 

6 

15 

30 

72 

70 

42 

28 

21 

16  4/5 

14 

7  7/11 

7 

6  6/13 

7 

16 

33 

78 

110 

66 

44 

33 

26  2/5 

22 

18  6/7 

11 

10  2/13 

8 

18 

36 

120 

72 

48 

36 

28  4/5 

24 

20  4/7 

13  1/11 

11  1/13 

9 

20 

39 

130 

78 

39 

31  1/5 

26 

22  3/7 

14  2/11 

13 

10 

21 

42 

Ten  gears  are  sufficient  to  cut  all  the  usual  threads,  with  the  exception  of 
perhaps  11^,  the  standard  pipe-thread;  in  ordinary  practice  any  fractional 
thread  between  11  and  12  will  be  near  enough  for  the  customary  short  pipe- 
thread;  if  not,  the  addition  of  a  single  gear  will  give  it. 

In  this  table  the  pitch  of  the  lead-screw  is  12,  and  it  may  be  objected  to  as 
too  fine  for  the  purpose.  This  may  be  rectified  by  making  the  real  pitch  6 
or  any  other  desirable  pitch,  and  establishing  the  proper  ratio  between  the 
lathe  spindle  and  the  gear-stud. 

Metric  Screw  -threads  may  be  cut  on  lathes  with  inch-divided  lead- 
ing-set ews.  bv  the  use  of  a  change-wheel  with  127  teeth;  for  127  millimetres 
equnl  5  inches  (127  X  .03937  =  4.99999  in.). 

Rule  lor  Setting  the  Taper  in  a  Lathe.  (Am.  Mach.}— No 
rule  can  be  given  which  will  produce  exact  results,  owing  to  the  fact  that 
the  cent  res  enter  the  work  an  indefinite  distance.  If  it  were  not  for  this  cir- 
cumstance the  following  would  be  an  exact  rule,  and  it  is  an  approximation 
as  it  is.  To  find  the  distance  to  set  the  centre  over:  Divide  the  difference  in 
the  diameters  of  the  large  and  small  end  of  the  taper  by  2,  and  multiply  this 
quotient  by  the  ratio  which  the  total  length  of  the  shaft  bears  to  the  length 
of  the  tapered  portion.  Example:  Suppose  a  shaft  three  feet  long  is  to  have 
a  taper  turned  on  the  end  one  foot  long,  the  large  end  of  the  ta.per  being  two 

2—1       3 
inches  and  the  small  end  one  inch  diameter.    •  X  -  =  l/£  inches. 

Electric  Brilling-mac  nines  -Speed  of  Drilling  Holes  in 
Steel  Plates.  (Froc.  Inst.  M.  E.,  Aug.  1887,  p.  329.)— In  drilling  holes  in 
the  shell  of  the  S.S.  "Albania,"  after  a  very  small  amount  of  practice  the 
men  working  the  machines  drilled  the  %-inch  holes  in  the  shell  with  great 
rapidity,  doing  the  work  at  the  rate  of  one  hole  every  69  seconds,  inclusive  of 
the  time  occupied  in  altering  the  position  of  the  machines  by  means  of  differ- 
ential pulley-blocks,  which  were  not  conveniently  arranged  as  slings  for 
this  purpose.  Repeated  trials  of  these  drilling-machines  have  also  shown 
that,  when  using  electrical  energy  in  both  holding-on  magnets  and  motor 


MILLING-CUTTERS. 


957 


amounting  to  about  %  H.P.,  they  have  drilled  holes  of  1  inch  diameter 
through  11^  inch  thickness  of  solid  wrought  iron,  or  through  \%  inch  of  mild 
steel  in  two  plates  of  13/16  inch  each,  taking  exactly  1^4  minutes  for  each 
hole. 

Speed  of  Twist-drills.— The  cutting-speeds  and  rates  of  feed  recom- 
mended by  the  Morse  Twist -drill  and  Machine  Company  are  given  in  the 
following  table. 

Revolutions  per  minute  for  drills  1/16  in.  to  2  in.  diam.,  as  usually  applied: 


Diameter 
of 
Drills. 

Speed 
for 
Steel. 

Speed 
for 
Iron. 

Speed 
for 
Brass. 

Diameter 
of 
Drills. 

Speed 
for 
Steel. 

Speed 
for 
Iron. 

Speed 
for 
Brass. 

inch. 

inch. 

1/16 

940 

1280 

1560 

1  1/16 

54 

75 

95 

Vs 

460 

660 

785 

IX 

52 

70 

90 

3/16 

316 

420 

540 

1  3/16             49 

66 

85 

y* 

230 

320 

400 

114              46 

62 

80 

5/16 

190 

260 

320 

1  5/16 

44 

60 

75 

H 

150 

220 

260 

1% 

42 

58 

72 

7/16 

130 

185 

230 

1  7/16 

40 

56 

69 

X 

115 

160 

200 

*M 

39 

54 

66 

9/16 

100 

140 

180 

1  9/16 

37 

51 

63 

% 

95 

130 

160 

1% 

36 

49 

60 

11/16 

85 

115 

145 

1  11/16 

34 

47 

58 

A 

75 
70 

105 
100 

130 
120 

m 

1  13/16 

33 
32 

45 
43 

56 
54 

% 

65 

90 

115 

1% 

31 

41 

52 

15/J6 

62 

85 

110 

1  15/16 

30 

40 

51 

1 

58 

80 

100 

2 

29 

39 

49 

To  drill  one  inch  in  soft  cast  iron  will  usually  require:  For  J4-in.  drill,  125 
revolutions;  for  ^g-in.  drill,  120  revolutions;  for  %-in.  drill,  100  revolutions; 
for  1-in.  drill,  95  revolutions. 

The  rates  of  feed  for  twist  drills  are  thus  given  by  the  same  company: 
Diameter  of  drill 1/16       J4  %       ^  %  1  1^ 

Revs,  per  inch  depth  of  hole.  125       125       120  to  140        1  inch  feed  per  min. 
MILLING-CUTTERS. 

George  Addy.  (Proc.  Inst.  M.  E.,  Oct.  1890,  p.  537),  gives  the  following: 
Analyses   of  Steel.— The  following  are  analyses  of   milling-cutter 
blanks,  made  from  best  quality  crucible  cast  steel  and  from  self -hardening 
"  Ivanhoe  "  steel : 

Crucible  Cast  Steel, 
per  cent. 
1.2 


Carbon . 

Silicon 0.112 

Phosphorus    0.018 

Manganese .  0.36 

Sulphur 0.02 

Tungsten 

Iron,  by  difference, 98.29 


Ivanhoe  Steel, 

per  cent. 

1.67 


0.252 
0.051 
2.557 
0.01 
4.65 
90.81 

100.000 


100.000 

The  first  analysis  is  of  a  cutter  14  in.  diam.,  1  in.  wide,  which  gave  very 
good  service  at 'a  cutting-speed  of  60  ft.  per  min.  Large  milling-cutters  are 
sometimes  built  up.  the  cutting-edges  only  being  of  tool  steel.  A  cutter  22  in. 
diam.  by  514  in.  wide  has  been  made  in  this  way,  the  teeth  being  clamped 
between  two  cast-iron  flanges.  Mr.  Addy  recommends  for  this  form  of 
tooth  one  with  a  cutting-angle  of  70°.  the  face  of  the  tooth  being  set  10°  back 
of  a  radial  line  on.  the  cutter,  the  clearance -angle  being  thus  10°.  At  the 
Clarence  Iron -works,  Leeds,  the  face  of  the  tooth  is  set  10°  back  of  the  radial 
line  for  cutting  wrought  iron  and  20°  for  steel. 

Pitch  of  Teetli.— For  obtaining  a  suitable  pitch  of  teeth  for  milling- 
cutters  of  various  diameters  there  exists  no  standard  rule,  the  pitch  being 
usually  decided  in  an  arbitrary  manner  according  to  individual  taste. 


958  THE   MACHIKE-SHOP. 

For  estimating  the  pitch  of  teeth  in  a  cutter  of  any  diameter  from  4  in.  to  15 
in.,  Mr.  Addy  has  worked  out  the  following  rule,  which  he  has  found  capa- 
ble of  giving  good  results  in  practice: 


Pitch  in  inches  =  |/(diam.  in  inches  X  8)  X  0.0625  =  .177  1/diam. 

J.  M.  Gray  gives  a  rule  for  pitch  as  follows:  The  number  of  teeth  in  a 
milling-cutter  ought  to  be  100  times  the  pitch  in  inches;  that  is,  if  there 
were  27  teeth,  the  pitch  ought  to  be  0.27  in.  The  rules  are  practically  the 
same,  for  if  d  =  diam.,  n  =  No.  of  teeth,  p  =  pitch,  c  =  circumference,  c  = 

pn:    d  =  -—  =  — —  =  31.83»2;    p  =  V.0314d  =  .177  ty'd:    No.  of  teeth,  n,  — 

It  TT 

3  \4d  -»-  p. 

Number  of  Teeth  in  Mills  or  Cutters.  (Joshua  Rose.)— The  teetii 
of  cutters  must  obviously  be  spaced  wide  enough  apart  to  ad  niit  of  the  emery  - 
wheel  grinding  one  tooth  without  touching  the  next  one,  and  the  front  faces 
of  the  teeth  are  always  made  in  the  plane  of  a  line  radiating  from  the  axis  of 
the  cutler.  In  cutters  up  to  3  in.  in  diam.  it  is  good  practice  to  provide  8 
teetii  per  in.  of  diam.,  while  in  cutters  above  that  diameter  the  spacing 
may  be  coarser,  as  follows: 

Diameter  of  cutter,  6  in. ;  number  of  teeth  in  cutter,  40 

7  "  "          "      "      "       tk        45 

8  "  "          "      "      "       "        50 

§peed  of  Cutters.— The  cutting  speed  for  milling  was  originally  fixed 
very  low;  but  experience  has  shown  that  with  the  improvements  now  in 
use' it  may  with  advantage  be  considerably  increased,  especially  with  cutters 
of  large  diameter.  The  following  are  recommended  as  safe  speeds  for  cut- 
ters of  6  in.  and  upwards,  provided  there  is  not  any  great  depth  of  material 
to  cut  away: 

Steel.      Wrought  iron.  Cast  iron.        Brass. 
Feet  per  minute..  ,..      36  48  60  120 

Feed,  inch  per  min. ..      14  1  1%  *7^ 

Should  it  be  desired  to  remove  any  large  quantity  of  material,  the  same 
cutting-speeds  are  still  recommended,  but  with  a  finer  feed.  A  simp!-,  r.ile 
for  cutting-speed  is:  Number  of  revolutions  per  minute  which  the  cutter 
spindle  should  make  when  working  on  cast  iron  —  240,  divided  by  the  diam- 
eter of  the  cutter  in  inches. 

Speed  of  Milling-cutters.  (Proc.  Inst.  M.  E.,  April.  1883,  p.  248.)— 
The  cutting-speed  which  can  be  employed  in  milling  is  much  greater  than 
that  which  can  be  used  in  any  of  the  ordinary  operations  of  turning  in  the 
lathe,  or  of  planing,  shaping,  or  slotting.  A  milling-cutter  with  a  plentiful 
supply  of  oil,  or  soap  and  water,  can  be  run  at  from  80  to  100  ft.  per  min., 
when  cutting  wrought  iron.  The  same  metal  can  only  bs  turned  in  a  lathe, 
with  a  tool-holder  having  a  good  cutter,  at  the  rate  of  30  ft.  per  min.,  or  at 
about  one  third  the  speed  of  milling.  A  milling-cutter  will  cut  cast  stee:l  at 
the  rate  of  25  to  30  ft.  per  min. 

The  following  extracts  are  taken  from  an  article  on  speed  and  feed  of 
milling-cutters  in  Evg'g,  Oct.  22,  1891:  Milling-cutters  are  successfully  em- 
ployed on  cast  iron  at  a  speed  of  250  ft.  per  min.;  on  wrought  iron  at  fiom 
80  ft.  to  100  ft.  per  min.  The  latter  materials  need  a  copious  supply  of  good 
lubricant,  such  as  oil  or  soapy  water.  These  rates  of  speed  are  not  ap- 
proached by  other  tools.  The  usual  cutting-speeds  on  the  lathe,  planing. 
shaping,  and  slotting  machines  rarely  exceed  about  one  third  of  those  given 
above,  and  frequently  average  about  a  fifth,  the  time  lost  in  back  strokes  not 
being  reckoned. 

The  feed  in  the  direction  of  cutting  is  said  by  one  writer  to  vary,  in  ordi- 
nary work,  from  40  to  70  revs,  of  a  4-in.  cutter  per  in.  of  feed.  It  must  ahva y- 
to  an  extent  depend  on  the  character  of  the  work  done,  but  the  above  give* 
shavings  of  extreme  thinness.  For  example,  the  circumference  of  a  4  in! 
cutter  being,  say,  12^  in.,  and  having,  say,  60  teeth,  the  advance  corre- 
sponding to  the  passage  of  one  cutting-tooth  over  the  surface,  in  the  coars-.'i 
of  the  above-named  feed-motions,  is'l/40  X  1/60  =  1/2400  in.:  the  finer  tVed 
gives  an  advance  for  each  tooth  of  only  1/70  X  1/60  =  1/4200  in.  Such  fin^ 
feeds  as  these  are  used  only  for  light  finishing  cuts,  and  the  same  author- 
-  ity  recommends,  also  for  finishing,  a  cutter  about  i)  in.  in  circumference,  01 
nearly  3  in.  in  diameter,  which  should  be  run  at  about  60  revs,  per  min.  i< 
cut  tough  wrought  steel,  120  for  ordinary  cast  iron,  about  80  for  wrought 


MILLISTG-MACHINES.  959 

Iron  and  from  140  to  160  for  the  various  qualtities  of  grun-metal  and  brass 
With  cutters  smaller  or  larger  the  rates  of  revolution  are  increased  or 
diminished  to  accord  with  the  following  table,  which  gives  these  rates  of 
cutting-speeds  and  shows  the  lineal  speed  of  the  cutting-edge: 

Steel.    Wrought  Iron.    Cast  Iron.    Gun-metal     Brass 
Feet  per  minute...        45  60  90  105  120  ' 

These  speeds  are  intended  for  very  light  finishing  cuts,  and  they  must  be 
reduced  to  about  one  half  for  heavy  cutting. 

The  following  results  have  been  found  to  be  the  highest  that  could  be  at- 
tained in  ordinary  workshop  routine,  having  due  consideration  to  economy 
and  the  time  taken  to  change  and  grind  the  cutters  when  they  become  dull' 
Wrought  iron— 36  ft.  to  40  ft.  per  min.;  depth  of  cut.  1  in.;  feed,  %  in  per 
inin.  Soft,  mild  steel— About  30  ft.  per  min.;  depth  of  cut,  J4  in  ;  t'eecl  % 
in.  per  min.  Tough  gun-metal— 80  ft.  per  min. ;  depth  of  cut,  y.  in.';  feed,  % 
in.  per  min.  Cast-iron  gear-wheels— 26J^  ft.  per  min.;  depth  of  cut,  V»  in  • 
feed,  %  in.  per  min.  Hard,  close-grained  cast  iron— 30  ft.  per  min.;  depth 
of  cut,  2^j  in.;  feed,  5/16  in.  per  min.  Gun-metal  joints,  53  ft.  per  min  • 
depth  of  cut,  \%  in.;  feed,  %  in.  per  min.  Steel-bars— 21  ft.  per  min  :  depth 
of  cut,  1/32  in.;  feed,  %  in.  per  min. 

A  stepped  milling-cutter,  4  in.  in  diam.  and  12  in.  wide,  tested  under  two 
conditions  of  speed  in  the  same  machine,  gave  the  following  results:  The 
cutter  in  both  instances  was  worked  up  to  its  maximum  speed  before  it  gave 
way,  the  object  being  to  ascertain  definitely  the  relative  amount  of  work 
done  by  a  high  speed  and  a  light  feed,  as  compared  with  a  low  speed  and  a 
heavy  cut.  The  machine  was  used  single-geared  and  double-geared,  and  in 
both  cases  the  width  of  cut  was  10J4  in. 

Single-gear,  42  ft.  per  min.;  5/16  in.  depth  of  cut;  feed,  1.3  in.  per  min.  — 
4.16  cu.  in.  per  min.  Double-gear,  19  ft.  per  min.;  %in.  depth  of  cut;  feed, 
%  in.  per  min.  =  2.40  cu.  in.  per  min. 

Extreme  Results  with  Milling-macliiiies.  —Horace  L. 
Arnold  (Am.  Macli.,  Dec.  28,  1893)  gives  the  following  results  in  flat-surface 
milling,  obtained  in  a  Pratt  &  Whitney  milling-machine  :  The  mills  for  the 
flat  cut  were  5"  diam.,  12  teeth,  40  to  50  revs,  and  4%"  feed  per  min.  One 
.single  cut  was  run  over  this  piece  at  a  feed  of  9"  per  ruin.,  but  the  mills 
showed  plainly  at  the  end  that  this  rate  was  greater  than  they  could  endure. 
At  50  revs,  for  these  mills  the  figures  are  as  follows,  with  4%"  feed:  Surface 
speed,  64  ft.,  nearly;  feed  per  tooth,  0.00812":  cuts  per  inch,  123.  And  with 
9"  feed  per  min.:  Surface  speed,  64  ft.  per  min. ;  feed  per  tooth,  0.015";  cuts 
per  inch,  66%. 

At  a  feed  of  4%"  per  min.  the  mills  stood  up  well  in  this  job  of  cast-iron 
surfacing,  while  with  a  9"  feed  they  required  grinding  after  surfacing  one 
piece;  in  other  words,  it  did  not  damage  the  mill-teeth  to  do  this  job  with 
123  cuts  per  in.  of  surface  finished,  but  they  would  not  endure  66%  cuts  per 
inch.  In  this  cast-iron  milling  the  surface  speed  of  the  mills  does  not  seem 
to  be  the  factor  of  mill  destruction:  it  is  the  increase  of  feed  per  tooth  that 
prohibits  increased  production  of  finished  surface.  This  is  precisely  the  re- 
verse of  the  action  of  single-pointed  lathe  and  planer  tools  in  general:  with 
such  tools  there  is  a  surface-speed  limit  which  cannot  be  economically  ex- 
ceeded for  dry  cuts,  and  so  long  as  this  surface-speed  limit  is  not  reached, 
the  cut  per  tooth  or  feed  can  be  made  anything  up  to  the  limit  of  the  driv- 
ing power  of  the  lathe  or  planer,  or  to  the  safe  strain  on  the  work  itself, 
which  can  in  many  cases  be  easily  broken  by  a  too  great  feed. 

In  wrought  metal  extreme  figures  were  obtained  in  one  experiment  made 
in  cutting  keyways  5/16"  wide  by  *?&"  deep  in  a  bank  of  8  shafts  1*4"  diam. 
at  once,  on  a  Pratt  &  Whitney  No.  3  column  milling-machine.  The  8  mills 
were  successfully  operated  with  45  ft.  surface  speed  and  19^  in.  per  min. 
feed;  the  cutters  were  5"  diam.,  with  28  teeth,  giving  the  following  figures, 
in  steel:  Surface  speed,  45  ft.  per  min.;  feed  per  tooth.  0.02024";  cuts  per 
inch,  50,  nearly.  Fed  with  the  revolution  of  mill.  Flooded  with  oil,  that  is, 
a  large  stream  of  oil  running  constantly  over  each  mill.  Face  of  tooth 
radial.  The  resulting  keyway  was  described  as  having  a  heavy  wave  or 
cutter-mark  in  the  bottom,  and  it  was  said  to  have  shown  no  signs  of  being 
heavy  work  on  the  cutters  or  on  the  machine.  As  a  result  of  the  experiment 
it  was  decided  for  economical  steady  work  to  run  at  17  revs.,  with  a  feed  of 
4"  per  min.,  flooded  cut,  work  fed  with  mill  revolution,  giving  the  following 
figures:  Surface  speed,  22*4  ft.  per  min.;  feed  per  tooth,  0,0084";  cuts  pet- 
inch,  119, 


960  THE   MACHINE-SHOP. 

An  experiment  in  milling  a  wrought  iron  connecting-rod  of  a  locomotive 
on  a  Pratt  &  Whitney  double-head  milling-machine  is  described  in  the  Iron 
Age,  Aug.  27,  1891.    The  amount  of  metal  removed  at  one  cut  measured  3%    j 
in.  wide  by  1  3/16  in.  deep  in  the  groove,  and  across  the  top  %  in.  deep  by  4% 
in.  wide.    This  represented  a  section  of  nearly  4^  sq.  in.    This  was  done  at 
the  rate  of  1%  in.  per  min.    Nearly  8  cu.  in.  of  metal  were  cut  up  into  chips    ! 
every  minute.    The  surface  left  by  the  cutter  was  very  perfect.    The  cutter   i 
moved  in  a  direction  contrary  to  that  of  ordinary  practice;  that  is,  it  cut   J 
down  from  the  upper  surface  instead  of  up  from  the  bottom. 

Milling  "with"  or  " against"  the  Feed.— Tests  made  with  | 
the  Brown  &  Sharpe  No.  5  milling-machine  (described  by  H.  L.  Arnold,  in 
Am.  Mach.,  Oct.  18,   1894)  to  determine  the  relative  advantage  of  running 
the  milling-cutter  with  or  against  the  feed — "  with  the  feed  "  meaning  that 
the  teeth  of  the  cutter  strike  on  the  top  surface  or  "scale"  of  cast-iron  ! 
work  in  process  of  being  milled,  and  "against  the  feed  "  meaning  that  the 
teeth  begin  to  cut  in  the  clean,  newly  cut  surface  of  the  work  and  cut  up-  i 
wards  toward  the  scale— showed  a  decided  advantage  in  favor  of  running 
the  cutter  against  the  feed.    The  result  is  directly  opposite  to  that  obtained 
in  tests  of  a  Pratt  &  Whitney  machine,  by  experts  of  the  P.  &  W.  Co. 

In  the  tests  with  the  Brown  &  Sharpe  machine  the  cutters  used  were  6 
inches  face  bj7  4^  and  3  inches  diameter  respectively,  15  teeth  in  each  mill, 
42  revolutions  per  minute  in  each  case,  or  nearly  50  feet  per  minute  surface 
speed  for  the  4^-inch  and  33  feet  per  minute  for  the  3-inch  mill.  The  revo- 
lution marks  were  6  to  the  inch,  giving  a  feed  of  7  inches  per  minute,  and  a 
cut  per  tooth  of  .011".  When  the  machine  was  forced  to  the  limit  of  its 
driving  the  depth  of  cut  was  11/32  inch  when  the  cutter  ran  in  the  "  old  " 
way,  or  against  the  feed,  and  only  ^  inch  when  it  ran  in  the  "  new  "  way, 
or  with  the  feed.  The  endurance  of  the  milling-cutters  was  much  greater 
when  they  were  run  in  the  "  old  "  way. 

Spiral  Milling-cutters.— There  is  no  rule  for  finding  the  angle  of 
the  spiral;  from  10°  to  15°  is  usually  considered  sufficient;  if  much  greater 
the  end  thrust  on  the  spindle  will  be  increased  to  an  extent  not  desirable  for 
some  machines. 

Milling-cutters  with.  Inserted  Teeth.— When  it  is  required  to 
use  milling- cutters  of  a  greater  diameter  than  about  8  in.,  it  is  preferable  to 
insert  the  teeth  in  a  disk  or  head,  so  as  to  avoid  the  expense  of  making 
solid  cutters  and  the  difficulty  of  hardening  them,  not  merely  because  of. 
the  risk  of  breakage  in  hardening  them,  but  also  on  account  of  the  difficulty 
in  obtaining  a  uniform  degree  of  hardness  or  temper. 

Milling  -  machine  versus  Planer. —  For  comparative  data  of 
work  done  by  each  see  paper  by  J.  J.  Grant,  Trans.  A.  S.  M.  E.,  ix.  259.  He 
says :  The  advantages  of  the  milling  machine  over  the  planer  are  many, 
among  which  are  the  following  :  Exact  duplication  of  work;  rapidity  of  pro- 
duction —  the  cutting  being  continuous;  cost  of  production,  as  several 
machines  can  be  operated  by  one  workman,  and  he  not  a  skilled  mechanic; 
and  cost  of  tools  for  producing  a  given  amount  of  work. 

POWER  REQUIRED  FOR  MACHINE:  TOOLS. 

Resistance  Overcome  in  Cutting  Metal.  (Trans.  A.  S.  M.  E., 
viii.  308.) — Some  experiments  made  at  the  wrorks  of  William  Sellers  &  Co. 
showed  that  the  resistance  in  cutting  steel  in  a  lathe  would  vary  from 
180,000  to  700,000  pounds  per  square  inch  of  section  removed,  while  for 
cast  iron  the  resistance  is  about  one  third  as  much.  The  power  required  to 
remove  a  given  amount  of  metal  depends  on  the  shape  of  the  cut  and  on 
the  shape  and  the  sharpness  of  the  tool  used.  If  the  cut  is  nearly  square  in 
section,  the  power  required  is  a  minimum;  if  wide  and  thin,  a  maximum. 
The  dulness  of  a  tool  affects  but  little  the  power  required  for  a  heavy  cut. 

Heavy  Work  on  a  Planer.— Wm.  Sellers  &  Co.  write  as  follows 
to  the  American  Machinist :  The  120''  planer  table  is  geared  to  run  18  ft.  per 
minute  under  cut,  and  72  feet  per  minute  on  the  return,  which  is  equivalent, 
without  allowance  for  time  lost  in  reversing,  to  continuous  cut  of  14.4  feet 
per  minute.  Assuming  the  work  to  be  28  feet  long,  we  may  take  14  feet  as 
the  continuous  cutting  speed  per  minute,  the  .8  of  a  foot  being  much  more 
than  sufficient  to  cover  time  loss  in  reversing  and  feeding.  The  machine 
carries  four  tools.  At  }£"  feed  per  tool,  the  surface  planed  per  hour  would 
be  35  square  feet.  The  section  of  metal  cut  at  %"  depth  would  be  .75"  X 
,125"  X  4  =  .375  square  inch,  which  would  require  approximately  30,000  Ibs, 


POWER   REQUIRED   FOR   MACHINE   TOOLS. 


961 


pressure  to  remove  it.  The  weight  of  metal  removed  per  hour  would  be 
14  X  12  X  .375  X  .26  X  60  =  1082.8  Ibs.  Our  earlier  form  of  36"  planer  has 
removed  with  one  tool  on  %'  cut  on  work  200  Ibs.  of  metal  per  hour,  and 
the  120"  machine  has  more  than  five  times  its  capacity.  The  total  pulling 
power  of  the  planer  is  45,000  ibs. 

Horse-power  Required  to  Run  Lathes.  (J.  J.  Flather,  Am,. 
Mack.,  April  23,  1891.)— The  power  required  to  do  useful  work  varies  with 
the  depth  and  breadth  of  chip,  with  the  shape  of  tool,  and  with  the  nature 
and  density  of  metal  operated  upon ;  and  the  power  required  to  run  a  ma- 
chine empty  is  often  a  variable  quantity. 

For  instance,  when  the  machine  is  new,  and  the  working  parts  have  not 
become  worn  or  fitted  to  each  other  as  they  will  be  after  running  a  few 
months,  the  power  required  will  be  greater  than  will  be  the  case  after  the 
running  parts  have  become  better  fitted. 

Another  cause  of  variation  of  the  power  absorbed  is  the  driving-belt;  a 
tight  belt  will  increase  the  friction,  hence  to  obtain  the  greatest  efficiency 
of  a  machine  we  should  use  wide  belts,  and  run  them  just  tight  enough  to 
prevent  slip.  The  belts  should  also  be  soft  and  pliable,  otherwise  power  is 
consumed  in  bending  them  to  the  curvature  of  the  pulleys. 

A  third  cause  is  the  variation  of  journal-friction,  due  to  slacking  up  or 
tightening  the  cap-screws,  and  also  the  end-thrust  bearing  screw. 

Hartig's  investigations  show  that  it  requires  less  total  power  to  turn  off  a 
given  weight  of  metal  in  a  given  time  than  it  does  to  plane  off  the  same 
amount;  and  also  that  the  power  is  less  for  large  than  for  small  diameters. 

The  following  table  gives  the  actual  horse-power  required  to  drive  a  lathe 
empty  at  varying  numbers  of  revolutions  of  main  spindle. 

HORSE-POWER  FOR  SMALL  LATHES. 


Without  Back  Gears. 

With  Back  Gears. 

Remarks. 

Revs,  of 
Spindle 
per  min*. 

H.P. 
required 
to  drive 
empty. 

Revs,  ot 

Spindle 
per  min. 

H.P. 
required 
to  drive 
empty. 

132.72 

219.08 
365.00 

.145 
.197 
.310 

14.6 
24.33 
38.42 

.126 
.141 
.274 

20"  Fitchburg  lathe. 

47.4 
125.0 
188 

.159 
.259 
.339 

4.84 
12.8 
19  2 

.132 

.187 
.230 

Smallla  the  (13L£"),  Chem- 
nitz.   Germany.      New 
machine. 

54.6 
122 
183 

.206 
.339 
.455 

6.61 
14.8 
22.1 

.157 
.206 
.249 

17^"   lathe  do.     New 
machine. 

18.8 
54.6 
82.2 

.086 
.210 
.326 

2.31 
6.72    • 
10.8 

.035 
.063 
.087 

26"  lathe  do. 

If  H.P.o  =  horse-power  necessary  to  drive  lathe  empty,  and  N=  number 
of  revolutions  per  minute,  then  the  equation  for  average  small  lathes  is 
H.P.o  =  0.095  +  0.0012AT. 

For  the  power  necessary  to  drive  the  lathes  empty  when  the  back  gears 
are  in,  an  average  equation  for  lathes  under  20"  swing  is 

H.P.o  =  0.10  +  0.006^. 

The  larger  lathes  vary  so  much  in  construction  and  detail  that  no  general 
rule  can  be  obtained  which  will  give,  even  approximately,  the  power  re- 
quired to  run  them,  and  although  the  average  formula  shows  that  at  least 
0.095  horse-power  is  needed  to  start  the  small  lathes,  there  are  many  Amer- 
ican lathes  under  20"  swing  working  on  a  consumption  of  less  than  .05 
horse-power. 


962 


THE   MACHINE-SHOP. 


The  amount  of  power  required  to  remove  metal  in  a  machine  is  determin- 
able  within  more  accurate  limits. 

Referring  to  Dr.  Hartig's  researches,  H.P.j  =  CW,  where  C  is  a  constant, 
and  Wthe  weight  of  chips  removed  per  hour. 

Average  values  of  C  are  .030  for  cast-iron,  .032  for  wrought-iron,  .047  for 
steel. 

The  size  of  lathe,  and,  therefore,  the  diameter  of  work,  has  no  apparent 
effect  on  the  cutting  power.  If  the  lathe  be  heavy,  the  cut  can  be  increased, 
and  consequently  the  weight  of  chips  increased,  but  the  value  of  C  appears 
to  be  about  the  same  for  a  given  metal  through  several  varying  sizes  of 
lathes. 

HORSE-POWER  REQUIRED  TO  REMOVE  CAST  IRON  IN  A  20-INCH  LATHE. 
(J.  J.  Hobart.) 


. 

•  '-> 

c 

£«5 

i  > 

«5fcj 

i* 

"a? 

a  ft 

•^ja 

EO 

^  o 

8 

o 

fc 

"C 
H 

5$ 

3  <U 

3 

go 

|| 

i 

Descriptive 

Number  of 

Tool  used. 

IP 

>  03  £ 

x:J3 

I1 

Average  B 
of  Cut  in  i 

Average  H 
quired  to  i 
Metal. 

Ji£ 

Value  of  Co 

a 

1 

99 

Side  tool 

37.90 

125 

015 

342 

13  30 

0°5 

9 

15 

Diamond  

30.50 

.125 

.015 

218 

10  70 

0°0 

17 

Round  nose 

42  61 

125 

015 

352 

14  95 

023 

4 

2 

Left  -  hand    round 

nose 

26.29 

125 

.015 

237 

9  22 

026 

5 

4 

Square  -faced  tool 

i^j"  broad 

25.82 

015 

125 

255 

9  06 

028 

6 

1 

25.27 

.048 

.048 

16.89 

.018 

7 

1 

" 

25.64 

.125 

.015 

.246 

8.99 

.027 

The  above  table  shows  that  an  average  of  .26  horse-power  is  required  to 
turn  off  10  pounds  of  cast-iron  per  hour,  from  which  we  obtain  the  average 
value  of  the  constant  C  =  .024. 

Most  of  the  cuts  were  taken  so  that  the  metal  would  be  reduced  *4"  in 
diameter;  with  a  broad  surface  cut  and  a  coarse  feed,  as  in  No.  5,  the  power 
required  per  pound  of  chips  removed  in  a  given  time  was  a  maximum;  the 
least  power  per  unit  of  weight  removed  being  required  when  the  chip  was 
square,  as  in  No.  6. 

HORSE-POWER  REQUIRED  TO  REMOVE  METAL  IN  A  29-iNCH  LATHE. 
(R.  H.  Smith.) 


W 

«jjj 

s 

1 

*#;. 

c  > 

o| 

Metal. 

5,8 

CO  t-> 

3 
O 

(f-     ^ 

U.- 

"S 

S    r" 

Mp, 

*o 

fcC-*^" 

*  2* 

fcJD—  O 

TZ 

£& 

s  . 

a 

§5 

g'|| 

§1*2 

1 

3 

& 

O 

Q 

^ 

<j  ^  ' 

<4 

4 

Cast  iron 

12.7 

.05 

.046 

.105 

5.49 

.019 

4 

Cast  iron 

11.1 

.135 

.046 

.217 

12.96 

.017 

2 

Cast  iron 

12.85 

.04 

.038 

.098 

3.66 

.027 

4 

Wrought  iron 

9.6 

.03 

.046 

.059 

2.49 

.023 

4 

Wrought  iron 

9.1 

.06 

.046 

.138 

4.72 

.029 

4 

Wrought  iron 

7.9 

.14 

.046 

.186 

9.56 

.019 

2 

Wrought  iron 

9.35 

.045 

.038 

.092 

2.99 

.031 

4 

Steel 

6.00 

.02 

.046 

.043 

1.03 

.042 

4 

Steel 

5.8 

.04 

.046 

.085 

2.00 

.042 

4 

Steel 

5.1 

.06 

.046 

.108 

2.64 

.040 

POWER   REQUIRED    FOR   MACHINE   TOOLS.  963 


le  small  values  of  C,  .017  and  .019,  obtained  for  cast  iron  are  probably 
to  two  reasons :  the  iron  was  soft  and  of  fine  quality  known  as  pulley 
al,  requiring  less  power  to  cut;  and,  as  Prof.  Smith  remarks,  a  lower 


The  $ 

due  to 

cutting-speed  also  takes  less  horse-power. 

Hardness  of  metals  and  forms  of  tools  vary,  otherwise  the  amount  of 
chips  turned  out  per  hour  per  horse-power  would  be  practically  constant  the 
higher  cutting-speeds  decreasing  but  slightly  the  visible  work  done. 

Taking  into  account  these  variations,  the  weight  of  metal  removed  per 
hour,  multiplied  by  a  certain  constant,  is  equal  to  the  power  necessary  to  do 
the  work. 

This  constant,  according  to  the  above  tests,  is  as  follows : 

Cast  Iron.  Wrought  Iron.  Steel. 

Hartig 030  .032  .047 

Smith 023  .028  042 

Hobart 024 

Average 026  .030  .044 

The  power  necessary  to  run  the  lathe  empty  will  vary  from  about  .05  to  .3 
H.P.,  which  should  be  ascertained  and  added  to  the  useful  horse-power,  to 
obtain  the  total  power  expended. 

Power  used  by  Machine-tools.  (R.  E.  Dinsmore,  from  the  Elec- 
trical World.) 

\.  Shop  shafting  2  3/16"  X  180  ft.  at  160  revs.,  carrying  26  pulleys 
from  6"  diam.  to  36",  and  running  20  Idle  machine  belts 1.32  H.P. 

2.  Lodge  Davis  upright  back-geared  drill-press  with  table,  28" 
swing,  drilling  %"  hole  in  cast  iron,  with  a  feed  of  1  in.  per 

minute 0.78  H.P. 

3.  Morse  twist-drill  grinder  No.  ^,  carrying  2"  x  0"  wheels  at  3200 

revs 0.29  H.P. 

4.  Pease  planer  30"  X  36",  table  6  ft.,  planing  cast  iron,  cut  14" 

deep,  planing  6  sq.  in.  per  minute,  at  9  reversals. . .     1.06  H.P. 

5.  Shaping-machine  22"  stroke,  cutting  steel  die,  6"  stroke,  ^" 

deep,  shaping  at  rate  of  1.7  square  inch  per  minute 0.37  H.P. 

6.  Engine-lathe  17"  swing,  turning  steel  shaft  2%"  diam.,  cut  3/16 

deep,  feeding  7.92  inch  per  minute 0.43  H.P. 

7.  Engine-lathe  81"  swing,  boring  cast-iron  hole  5"  diam.,  cut  3/16 

diam.,  feeding  0.3"  per  minute 0.23  H.P. 

8.  Sturtevant  No.  2,  monogram  blower  at  1800  revs,  per  minute, 

no  piping 0.8  H.P. 

9.  Heavy  planer  28"  X  28"  X  14  ft.  bed,  stroke  8",  cutting  steel, 

22  reversals  per  minute 3.2  H.P. 

The  table  on  the  next  page  compiled  from  various  sources,  principally 
from  Hartig's  researches,  by  Prof.  J.  J.  Flather  (Am.  Mach.,  April  12,  1894), 
may  be  used  as  a  guide  in  estimating  the  power  required  to  run  a  given 
machine;  but  it  must  be  understood  that  these  values,  although  determined 
by  dynamometric  measurements  for  the  individual  machines  designated, 
are  not  necessarily  representative,  as  the  power  required  to  drive  a  machine 
itself  is  dependent  largely  on  its  particular  design  and  construction.  The 
character  of  the  work  to  be  done  may  also  affect  the  power  required  to 
operate;  thus  a  machine  to  be  used  exclusively  for  brass  work  may  be 
speeded  from  10$  to  15$  higher  than  if  it  were  to  be  used  for  iron  work  of 
similar  size,  and  the  power  required  will  be  proportionately  greater. 

Where  power  is  to  be  transmitted  to  the  machines  by  means  of  shafting 
and  countershafts,  an  additional  amount,  varying  from  30$  to  50$  of  the  total 
power  absorbed  by  the  machines,  will  be  necessary  to  overcome  the  friction 
of  the  shafting. 

Horse-power  required  to  drive  Shafting.— Samuel  Webber, 
in  his  "  Manual  of  Power  "  gives  among  numerous  tables  of  power  required 
to  drive  textile  machinery,  a  table  of  results  of  tests  of  shafting.  A  line  of 
2J4"  shafting,  342  ft.  long,  weighing  4098  Ibs.,  with  pulleys  weighing  5331  Ibs., 
or  a  total  of  9429  Ibs.,  supported  on  47  bearings,  216  revolutions  per  minute, 
required  1.858  H.P.  to  drive  it.  This  gives  a  coefficient  of  friction  of  5.5^. 
In  seventeen  tests  the  coefficient  ranged  from  3.34$  to  11.4$,  averaging 
5.73$. 


964 


THE   MACHINE-SHOP. 


Horse-power  Required  to  »rive  Machinery. 


Name  of  Machine. 

Observed  Horse-power. 

Total 
Work. 

Running  Light. 

Small  screw-cutting  lathe  13}4"  swing,  B.  G  
Screw-cutting  lathe  17^",  B.  G 

0.41 
0.867 
0.47 
0.462 
0.53 
0.91 

0.16 
0.24 
0.63 
1.14 
0.24 
0  84 
1.47 
0.62 
0.41 
1.33 
1.24 
0.53 
0.67 
1.08 
0.28 
0.44 
0.95 
0.28 
0.66 

0.18 
0.28 

0  93 

1.52 
7.12 

4.41 
0.79 
4.12 
2.70 
4.24 
3.03 
4.63 
5.00 
3.20 
6.91 
3.23 
5.64 
0.96 
0.49 

3.68 
2.11 
2.73 
2.25 
2.00 
2.45 

1.55 
3.11 
0.56 

0.18;0.15*-0.34t 
0.207;  0.16-0.466 
0.12;  0.12  to  0.31 
0.05;  0.03  to  0.33 
0.187;0.12to0.66 
0.37;  0.39  to  0.81 
0.23  to  3.  4.0 
0.086  to  0.26 
0.07;  0.07  to  0.1  2 
0.21;  0.01  to  0.47 
0.26;  0.15  to  0.73 
OJ2;  0.12  to  0.40 
0.27 
0.60 
0.39 
0.15;  0.15  toO.43 
0.62 
0.62 
0.44:  0.1*-0.44t 
0.30;  0.  12*-  0.801- 
0.46 
0.09;  0.05  to  o.25 
0.22;  0.15  to  0.65 
0.57;  0.43  to  09^ 
0.01;  0.003-0.  13 
0.26;  0.26  to  0.55 

0.10 
0.11 
0.12;  0.10-0.12*; 
0.10to0.25t 
0  37 
0.67 

1.00 
0.16 
0.61 
.54 
3.35 
1  42 
1.25 
0.74t-0.17§ 
1.45 
4.18 
0.70 
1.16 
0.19 
0.34 

1.67;  0.65  to  2.0 
1.42 
0.61 
2.17 
1.30 
2.00 

0.32 
0.24 
0.40 

Screw-cutting  lathe  20/r^Fitchburg),  B.  G  

Screw-cutting  lathe  26",  B.  G               .     . 

Lathe,  80"  face  plate,  will  swing  108",  T.  G  

Large  facing  lathe,  will  swing  68",  T  G  . 

Wheel  lathe  60"  swing  

Small  shaper  (stroke  4",  traverse  11") 

Small  shaper,  Richards  (9J^"  x  22")  

Shaper  (15"  stroke  Gould  &  Eberhardt) 

Large  shaper,  Richards  (29"  X  91")..  .   . 

Crank  planer  (capacity  23"  x  27"  X  28^"  stroke).  . 
Planer  (capacity  36''  X  36"  X  11  feet)  
Large  planer  (capacity  76"  X  76"  X  57  feet  

Small  drill  press  

Upright  slot  drilling  mach.  (will  drill  2^"  diam.)..  .  . 
Medium  drill  press  

Large  drill  press  

Radial  drill  6  feet  swing  

Radial  drill  8^  feet  swing  

Radial  drill  press  

Slotter  (8"  stroke)  

Slotter  (9J4"  stroke)  .   .   . 

Slotter  (15"  stroke)  ... 

Universal  milling  mach   (Brown  &  Sharpe  No.  1)..  .  . 
Milling  machine  (13"  cutter-head,  12  cutters)  
Small  head  traversing  milling  machine  (cutter-head 
11"  diameter,  16  cutters)  

Gear  cutter  will  cut  20"  diameter 

Horizontal  boring  machine  for  iron,  22^"  swing  
Hydraulic  shearing  machine  

Large  plate  shears—  knives  28"  long,  3"  stroke  
Large  punch  press,  over-reach  28",  3"  stroke,  1^" 
stock  can  be  punched  

Small  punch  and  shear  comb'd,  7*4"  knives.  1J£''  str. 
Circular  saw  for  hot  iron  (30V£"  diameter  of  saw).  .  . 
Plate-bending  rolls,  diam.  of  rolls  13",  length  9i-£  ft. 
Wood  planer  13^"  (rotary  knives,  2  hor'l  2  vert.".  .  . 
Wood  planer  24"  (rotary  knives)   

Wood  planer  17^"  (rotary  knives).        .   . 

Wrood  planer  28"  (rotary  knives)  

Wood  planer  28"  (Daniel's  pattern)  

Wood  planer  and  matcher  (capacity  14J^  X  4%").  .  . 
Circular  saw  for  wood  (23"  diameter  of  saw)  
Circular  saw  for  wood  (35"  diameter  of  saw)  
Bnnd  saw  for  wood  (34"  band  wheel)  

Wood-mortising  and  boring  machine 

Hor'l  wood-boring  and  mortising  machine,  drill  4" 
diam.,  mortise  8%  deep  x  ll^j"  long  
Tenon  and  mortising  machine  

Tenon  and  mortising  machine.   .  . 

Tenon  and  mortising  machine  

Edge-molder  and  shaper.     (Vertical  spindle)  
Wood-molding  mach.  (cap.  7^  x  2^).     Hor.  spindle 
Grindstone  for  tools,  31"  diam.,  6"  face.    Velocity 
680  ft.  per  minute  

Grindstone  for  stock,  42"xl2".    Vel.  1680  ft.  per  min. 
Emery  wheel  ll^j"  diameter  X  J4"-     Saw  grinder. 

*  With  back  gears,    t  Without  back  gears,    i  For  surface  cutters.    §  With 
side  cutters.    B.  G.,  back-geared.    T.  G.,  triple-geared. 


ABRASIVE    PROCESSES. 


Horse-power;  Friction;  m en  Employed 


Name  of  Firm. 

Kind 
of 
Work. 

Horse-power. 

G 
0) 

1 

132 

300 
1600 
150 
230 
4100 

300 
432 
725 
900 
700 
90 
30 
130 
3500 
1500 
80 
250 
400 

08 
O 
H 

&. 

-P- 
6 

o 

<D 

o" 

fc 

3.53 
5.24 

8.82 

8.20 

4.87 
4.11 

10.25 
3.75 

1.73 
0.83 

H 

•£ 

is 

'S   . 
11 

r 

!i 

G  03 
u 

Lane  &  Bodley 

E.  &W.  W. 
W.  W. 
E.,M.  M. 
M.  E.,  etc. 
E. 
L. 

H.  M. 
M.  T. 

C.  &  L. 
P.  &D. 
P.  &  S. 
H   F. 
S.JI. 

M.S. 
F. 

58 
100 
400 
25 
95 
2500 

102 
180 
120 
230 
135 
35 
12 
150 
1300 
350 
40 
400 
350 

15 
95 

8 

2000 

41 
75 

67 
11 

75 
100 

85 
305 
17 

500 

61 
105 

68 
24 

75 
300 

15 
23 
32 

80 

40 
41 

49 
31 

50 
25 

2.27 

3.00 
4.00 
6.00 
2  42 
1^64 

2.93 
2.40 
6.04 
3.91 
5.11 
2.57 
2.50 
.86 
2.69 
4.28 
2.00 
0.62 
1.14 

J.  A.  Fay  &  Co  

Union  Iron  Works  
Frontier  Iron  &  Brass  W'ks 
Taylor  Mfg.  Co  

Baldwin  Loco.  Works  . 

W.  Sellers  &  Co.  (one  de- 
partment) . 

Pond  Machine  Tool  Co  ... 
Pratt  &  Whitney  Co  
Brown  &  Sharpe  Co  

Yale  &  Towne  Co 

Ferracute  Machine  Co  
T  B  Wood's  Sons 

Bridgeport  Forge  Co  
Singer  Mfg.  Co  
Howe  Mfg.  Co.  
Worcester  Mach.  Screw  Co 
Hartford         " 
Nicholson  File  Co  

Averages  

346.4 

38.6$ 

818.3 

2.96 

5.13 

Abbreviations:  E.,  engine;  W.W.,  wood-working  machinery;  M.  M.,  min- 
ing machinery;  M.  E.,  marine  engines;  L.,  locomotives;  H.  M.,  heavy  ma- 
chinery; M.  T.,  machine  tools;  C.  &  L.,  cranes  and  locks;  P.  &  D.,  presses 
and  dies;  P.  &  S.,  pulleys  and  shafting;  H.  F.,  heavy  forgings;  S.  M.,  sewing- 
machines;  M.  S.,  machine-screws:  F.,  files. 

J.  T.  Henthorn  states  (Trans.  A.  S.  M.  E.,  vi.  462)  that  in  print-mills  which 
he  examined  the  friction  of  the  shafting  and  engine  was  in  7  cases  below 
20$  and  in  35  cases  between  20^  and  30&  in  11  cases  from  30#  to  35$  and  in  2 
cases  above  35$,  the  average  being  25. 9$.  Mr.  Barrus  in  eight  cotton-mills 
found  the  range  to  be  between  18$  and  25.7$,  the  average  being  22$.  Mr. 
Flather  believes  that  for  shops  using  heavy  machinery  the  percentage  of 
power  required  to  drive  the  shafting  will  average  from  40$  to  50$  of  the  total 
power  expended.  This  presupposes  that  under  the  head  of  shafting  are 
included  elevators,  fans,  and  blowers. 

ABRASIVE:  PROCESSES. 

Abrasive  cutting  is  performed  by  means  of  stowes,  sand,  emery,  glass, 
corundum,  carborundum,  crocus,  rouge,  chilled  globules  of  iron,  and  in  some 
cases  by  soft,  friable  iron  alone.  (See  paper  by  John  Richards,  read  before 
the  Technical  Society  of  the  Pacific  Coast,  Am.  Mach.,  Aug.  20,  1891,  and 
Enci.  &  M.  Jour.,  July  25  and  Aug.  15,  1891.) 


066  tfcE  MACfctKfe-SHOK 


The  **Cold  Saw.»—  For  sawing  any  section  of  iron  x\iuie  cold  the 

cold  sa\\  is  sometimes  used.  This  consists  simply  of  a  plain  soft  steel  01' 
iron  disk  \\ithout  tooth.  about  -1?  inches  diameter  ami  3  Id  inch  thick.  Tho 
xelocity  of  ilu>  circumference  is  about  ir>.iHX)  foot  per  uuiiuto.  One  of  those 
saws  \v  ill  saw  through  an  ordinary  stool  rail  cold  in  about  0110  luinuto  In 
this  saxx  tho  slot"!  or  iro-n  is  ground  oft"  by  tlio  friction  of  tho  disk.  and  is  not 
i-ut  as  xx  ith  tlu1  tooth  of  an  ordinary  saw.  It  has  generally  boon  found  more 
profitable.  ho\\  ox  or.  to  saw  iron  \x  ith  disks  or  baud-saws  tit  tod  witli  euttini; 
teeth,  \x  hioh  run  at  moderate  speeds.  and  out  tho  motal  as  tio  the  tooth  of  a 
nulling:  -cutter. 

KOONC^N  FliNliig-iliMk.  Reese's  fusing  disk  is  an  application  of  the 
oold  s.'uv  to  cutting  iron  or  stool  in  tho  form  of  bars,  tubes,  cy  luulors.  etc 
iu  xvliioh  tho  piece  to  bo  out  is  uiado  to  rovolvo  at  a  slower  "rate-  of  speed 
than  tho  saxv.  l>y  this  means  only  a  small  surfaoo  of  the  bar  to  bo  out  is 
presented  at  a  time  to  the  circumference  of  the  saxv.  The  saw  is  about  tho 
samo  si/.o  as  tho  ooid  saw  above  described,  and  is  rotated  at  a  velocity  of 
about  'Jo.  000  foot  per  minute.  The  heat  tronerated  by  the  frietionof  this  saxv 
against  the  small  surface  of  the  bar  rotated  against  it  is  so  great  that  the 
particles  of  iron  or  steel  in  (ho  bar  are  actually  fused,  and  ihe  "saxv  dust  " 
x\  elds  as  it  falls  iutoa  solid  mass.  Thisiiisk  xvill  cut  either  east  iron,  \\  rought 
iron,  or  Steel.  It  will  CUt  a  bar  of  Steel  1:*s  iueh  diameter  in  one  minute,  in 
eluding  the  time  of  set  tint:  it  in  the  machine,  the  bar  being  rotated  about 
•Jo'O  turns  per  muiuttv 

1  uf  Itiii;  Stone  \\  ilh  \Vire.  A  plan  of  culling  stone  by  means  of  a 
x\ii>-  cord  has  been  tried  in  Kurope.  While  retaining  sand  as  the  cutting 
agent.  M.  rauhn  Uax  .  of  Marseilles,  has  suoi'ctHled  in  applying  it  by  median 
ical  means,  and  as  continuously  as  formerly  tho  sand-blast  and  band  -saw, 
with  both  of  xx  Inch  appliance's  hs  system  that  of  the  "  helicoidal  wire 
cord"  lias  considerable  analogy.  An  engine  puts  in  motion  a  continuous 
x\  ire  cord  o'iit'.vin^  from  tive  to  seven  thirty-secoiuis  of  an  inch  in  diameter. 
according  to  the  xvork  .  composed  of  three  mild-steel  wires  txvisted  at  a  v-or 
tain  pitch,  that  is  found  to  give  the  best  results  in  practice,  at  a  speed  of 
from  i:>  to  I?  feet  per  second. 

Tlie  Saml-blaKf.  li;  the  sand  blast,  invented  by  IV  F  Tilghumn.  of 
Philadt  iplua.  aiiii  tirst  exhibittnl  at  the  American  Institute  Fair.  No\\  YiM-k, 
in  1ST!,  common  sand,  pox\dtxnvtl  i]iiart/..  emery,  or  any  sharp  i-uttmg  matt- 
rial  is  bloxvn  by  a  jet  of  air  or  >team  on  giass.  metal,  or  other  comparatively 
brittle  substance,  by  xvluch  means  the  latter  is  cut.  drilled,  or  engraved. 
To  protect  those  portions  of  the  surface  which  it  is  tit  sired  shall  not  ho 
abraded  it  is  only  necessary  to  oo\or  them  \\ith  a  soft  or  tough  material, 
such  as  lead,  rubber,  leather,  paper.  xva\.  or  rubber  paint.  (See  description 
in  App.  Cyc,  Meoh.;  also  U.S.  report  of  Vienna  Exhibition,  1878.  vol.  iii.  3u'O 

A  "  jo:  ot  sand  "  impelled  by  steam  of  moderate  pressure,  or  oxen  by  tho 
blast  of  an  ordinary  fan,  depolishes  glass  in  a  fexv  stViMuls:  xvood  is  cut  quite 
rapidly;  and  metals  are  ^iveii  the  so-called  "frosted"  surface  xx  ith  groat 
rapidity.  With  a  jet,  issuing  from  under  ;>00  pounds  pressure,  a  hole  was 
out  through  a  piece  of  oorundrum  lUj  inches  thick  in  Of>  minutes. 

The  sand  blast  has  been  applied  to  tlu>  cleaning  of  nu^tal  castings  and 
sheet  metal,  tho  graining  of  /inc  plates  for  lithographic  purposes,  the  frost 
mg  of  silx  tirwart\  tlu>  cutting  of  ticures  tin  stone  aiul  glass,  and  the  cutting 
of  devices  on  monuments  or  tombstones,  the  room  ling  of  tiles,  etc.  The 
lime  required  to  sharpen  a  worn-out  H-inch  bastard  tile  is  about  four 
minutes.  About  one  pint  of  sand,  passed  through  a  No.  100  sieve,  ami  four 
horse-power  of  tiO-lb.  stoam  are  required  for  tho  operation.  For  cleaning 
castings  compressed  air  at  from  S  to  10  pounds  pressure  per  square  inch  is 
employed.  Chilled  iron  globules  instead  of  quart/,  or  flint  sand  are  used 
with  good  results,  both  as  to  speed  of  xxorking  and  cost  of  material,  xvhen 
tlu1  operation  can  be  carried  on  under  proper  conditions.  With  the  expen- 
diture of  0  horse  poxx  or  in  compressing  air,  0  square  feet  of  ordinary 
scale  on  the  surface  of  steel  and  iron  plates  can  be  remox-ed  per  minute. 
The  surface  thus  prepared  is  ready  for  tinning,  calx  -ani/.ing.  plating,  bron/- 
mg.  painting,  etc  By  continuing  the  operation  the  hard  skin  on  the  surface 
of  castings,  xvhich  is  so  destructive  to  the  cutting  edges  of  milling  and 
other  tools,  can  I  e  removed.  Small  castings  are  placed  in  a  sort  of  slowly 
rotating  barrel,  open  at  one  or  both  ends,  through  xvhieh  the  blast  is 
directed  doxvmvard  against  them  as  they  tumble  over  and  over.  No  portion 
of  the  surface  escapes  the  action  of  the  sand.  Plain  cored  xvork,  such  as 
valve-bodies,  can  bo  cleaned  perfectly  both  inside  and  out.  100  Ibs.  of  oast- 
ings  can  be  cleaned  in  from  10  to  !."•>  minutes  xx  ith  a  blast  created  by  0  horse- 


I:MI;I;Y-\VHI;KLS 


ame  weight  of  small  forcings  and  stampings  can  be  scaled  in 

from  20  to  -'{0  minutes,      /run.  .!'/>',  .March  S,  IH'Jl. 

B   »n;ic  v  -\v  in  i  j.v  AND  «.ici  M»SI  OM  s. 

Tli«'  S«l«M-.lloii  ol"  linn  I  > -vv  h«  •  Is.  A  pamphlet  entitled  "  Emery- 
u  heels,  their  Selection  and  1,'se,  '  published  by  t  he  Hrown  <V.  Sharpe  Mfg. 
( '.).,  at  lei  railing  attention  to  the  fact  that  too  much  should  not  be  expected 
<*l  one  wheel,  and  romment.ing  upon  the  importance  of  selecting  the  proper 

wheel  for  the  work  to  be  done,  says  : 

Wheels  are  numbered  from  coarse  to  fine;  that  Is,  a  wheel  made  of  No. 
00  emery  is  coarser  than  one  made  of  No.  100.  Within  certain  limits,  and 
other  t.hings  being  equal,  a  coarse  wheel  is  less  liable  to  change  the  tem- 
perat  me  of  the  work  arid  less  liable  to  gla/e  than  a  fine  wheel.  As  a  rule, 
the  harder-  the  stock  the  coarser  the  wheel  required  to  produce  a  given 
finish.  For  example,  coarser  wheels  are  required  to  produce  a  given  sur- 
l;ice  upon  hardened  steel  than  upon  soft,  steel,  while  finer  wheels  an- re 
quired  to  produce  this  surface  upon  brass  or  copper  than  upon  either 
hardened  or  soft  steel. 

Wheels  are  graded  from  soft  to  hard,  and  the  grade  is  denoted  by  tli e 
letters  of  the  alphabet,  A  denoting  the  softest  grade.  Awheel  is  soft  or 
hard  chiefly  on  account  of  t  he  amount  and  character  of  the  material  com- 
bined in  its  manufacture-  with  emery  or  corundum.  But  other  character- 
istics bem^  equal,  a  wheel  that  is  composed  of  flue  emery  is  more  compact 
and  harder  than  one  made  of  coarser  emery.  For  instance,  a  wheel  of  No. 
100  emery,  grade  B,  will  be  harder  than  orie'of  No.  00  emery,  same  grade. 

The  soft  ness  of  a  wheel  is  generally  its  most  important  characteristic.  A 
soft  wheel  is  less  apt  to  cause  a  change  of  temperature  in  the  work,  or  to 
become  glazed,  than  a  harder  one.  It  is  best  for  grinding  hardened  steel, 
cast,  iron,  brass,  copper,  and*  rubber,  while  a  harder  or  more  compact  wheel 
is  better  for  grinding  soft,  steel  and  wrought  iron.  As  a  rule,  other  things 
being  equal,  the  harder  the  stock  the  softer  the  wheel  required  to  produce 
a  given  finish. 

(Generally  speaking,  a  wheel  should  be  softer  as  the  surface  in  contact 
with  the  work  is  increased.  For  example,  a  wheel  1/10-inch  face  should  be 
harder  than  one  ]/,  inch  face.  If  a  wheel  is  hard  and  heats  or  chatters,  it 
can  often  be  made  somewhat  more  effective  by  turning  off  a  part  of  its 
cutting  surface;  but  it  should  be  clearly  understood  that  while  this  will 
sometimes  prevent  a  hard  wheel  from  heating  or  chattering  the  work,  such 
a  wheel  will  not  prove  as  economical  as  one  of  the  full  width  and  proper 
grade,  for  it,  should  be  borne  in  mind  that  the  grade  should  always  bear  the 
proper  relation  to  the  width.  (See  the  pamphlet  referred  to  for  other  in- 
formation. See  also  lecture  by  T.  iJunkin  1'aret,  I'reti't  of  The  Tanite  Co., 
on  Kmery-wheels,  Jour.  Frank.  Inst.,  March,  1890.) 

S|M-«'«i  ol  Hmery-wlieel*.  The  following  speeds  are  recommended 
by  different  makers  : 


ll 

i—  «' 

1^ 
3  ~ 

4 

5 
0 

7 
H 
9 

Revolutions  per  minute. 

tl 

i 

10 

14 

10 
18 
20 
22 
24 
20 
30 
30 

Revolutions  per  minute. 

jN 

% 

19,000 
12,600 

7f«oo 

0,400 

4,800 
8,800 

3,200 
2,700 
2,400 
2,150 

The 
Tauite  Co. 

^ 

t. 

1,950 
1,000 
1,400 
1,200 
1.050 
950 
875 
800 
750 
075 
550 

_J_ 

2,100 
1,800 
1,570 
1,350 
1,222 
1,080 
1,000 
917 

°Jj|_ 

2,200 
1,800 
1,000 
1,400 
1,250 
1,100 
1,000 
925 
000 
500 
400 

|3 

2,200~" 
1,850 
1,000 
1,400 
1,250 
1,100 
1,000 
916 
825 
735 
550 

14,400 
10,800 
8.010 
7,200 
5.400 
4,320 
3,000 
8,060 
2,700 
2,400 

12,000 

10.000 
8,500 
7,100 
5,450 
4,400 
3,000 
3,150 
2,700 
2,450 

7,400 
5,400 
4,400 
8,600 
8,200 
2,700 

;3,  100 

733 
011 

"  We  advise,  the  regular  speed  of  5500  feet  per  minute.11    (Detroit  Emery- 
wheel  Co.) 
"Experience  has  demonstrated  that  there  is  no  advantage  in  running 


968 


THE   MACHINE-SHOP. 


solid  emery-wheels  at  a  higher  rate  than  5500  feet  per  minute  peripheral 
speed."    (Springfield  E.  W.  Mfg.  Co.) 

u  Although  there  is  no  exactly  defined  limit  at  which  a  wheel  must  be  run 
to  render  it  effective,  experience  has  demonstrated  that,  taking  into  account 
safety,  durability,  and  liability  to  heat,  5500  feet  per  minute  at  the  periphery 
gives  the  best  results.  All  first-class  wheels  have  the  number  of  revolutions 
necessary  to  give  this  rate  marked  on  their  labels,  and  a  column  of  figures 
in  the  price-list  gives  a  corresponding  rate.  Above  this  speed  all  wheels 
are  unsafe.  If  run  much  below  it  they  wear  away  rapidly  in  proportion  to 
what  they  accomplish."  (Northampton  E.  W.  Co.) 

Grades  of  Emery.— The  numbers  representing  the  grades  of  emery 
run  from  8  to  120,  and  the  degree  cf  smoothness  of  surface  they  leave  may 
,  be  compared  to  that  left  by  files  as  follows: 

8  and    10  represent  the  cut  of  a  wood  rasp. 


16 
24 
36 
46 
70 
90 


20 
30 
40 
60 
80 
100 


''  a  coarse  rough  file. 
"  an  ordinary  rough  file. 
"  a  bastard  file. 
"  a  second-cut  file. 
"  a  smooth          " 
"  a  superfine      " 
"  a  dead-smooth  file. 


120  F  and  FF      " 

Speed  of  Polish i  tig- wheels. 

Wood  covered  with  leather,  about 7000  ft,  per  mfnute 

"     a  hair  brush,  about 2500  revs,  for  largest 

"        \Yd'  to  8"  diarn.,  hair  I"  to  \W  long,  ab.  4500    "       "  smallest 

Walrus-hide  wheels,  about 8000-  ft.  per  minute 

Rag-wheels,  4  to  8  in.  diameter,  about 7000  "     "          " 

Safe  Speeds  for  Grindstones  and  Emery-wheels.— G.  D. 
Hiscox  (Iron  Aye,  April  7,  1892),  b'y  an  application  of  the  form  u  la  for  centrif- 
ugal force  in  fly-wheels  (see  Fty- wheels),  obtains  the  figures  for  strains  in 
grindstones  and  emery-wheels  which  are  given  in  the  tables  below.  His 
formulae  are: 

Stress  per  sq.  in.  of  section  of  a  grindstone       =  (.7071 D  X  N)*  X  .0000795 
"    "     "    "         "        "  an  emery-wheel  =  (.7071D  X  JV)«  X   00010226 

D  =  diameter  in  feet,  N  —  revolutions  per  minute. 

He  takes  the  weight  of  sandstone  at  .078  Ib.  per  cubic  inch,  and  that  of  an 
emery-wheel  at  0.1  Ib.  per  cubic  inch;  Ohio  stone  weighs  about  .081  Ib.  and 
Huron  stone  about  .089  Ib.  per  cubic  inch.  The  Ohio  stone  will  bear  a  speed 
at  the  periphery  of  2500  to  3000  ft.  per  min.,  which  latter  should  never  be 
exceeded.  The  Huron  stone  can  be  trusted  up  to  4000  ft.,  when  properly 
clamped  between  flanges  and  not  excessively  wedged  in  setting.  Apart 
from  the  speed  of  grindstones  as  a  cause  of  bursting,  probably  the  majority 
of  accidents  have  really  been  caused  by  wedging  them  on  the  shaft  and  over- 
wedging  to  true  them.  The  holes  being  square,  the  excessive  driving  of. 
wedges  to  true  the  stones  starts  cracks  in  the  corners  that  eventually  run 
out  until  the  centrifugal  strain  becomes  greater  than  the  tenacity  of  the 
remaining  solid  stone.  Hence  the  necessity  of  great  caution  in  the  use  of 
wedges,  as  well  as  the  holding  of  large  quick-running  stones  between  large 
flanges  and  leather  washers. 

Strains  in  Grindstones. 

LIMIT  OF  VELOCITY  AND  APPROXIMATE  ACTUAL  STRAIN  PER  SQUARE  INCH  OF 
SECTIONAL  AREA  FOR  GRINDSTONES  OF  MEDIUM  TENSILE  STRENGTH. 


Diam- 
eter. 

Revolutions  per  minute. 

100 

150 

200 

250 

300 

350 

400 

feet. 
2 

V 

8» 
£ 

6 

7 

Ibs. 
1.58 
2.47 
3.57 
4.86 
6.35 
8.04 
9.93 
14.30 
19.44 

Ibs. 
3.57 
5.57 
8.04 
10.93 
14.30 
18.08 
22.34 
32.17 

Ibs. 
6.35 
9.88 
14.28 
19.44 
27  37 

Ibs. 
9.93 
15.49 
22.34 
30.38 

Ibs. 
14.30 
22.29 
32,16, 

Ibs. 
18.36 
28.64 

Ibs. 
25.42 
39.75 

32.16 

Approximate  breaking  strain  ter 
times  the  strain   for  size  opposite 
the  bottom  figure  in  each  column. 

•EMERY-WHEELS  AND  GRINDSTONES. 


9G9 


The  figures  at  the  bottom  of  columns  designate  the  limit  cf  velocity  (in 
revolutions  pec  minute),  at  the  head  of  the  columns  for  stones  of  ihe  diam- 
eter in  the  first  column  opposite  the  designating  figure. 

A  general  rule  of  safety  for  any  size  grindstone  that  has  a  compact  and 
strong  grain  is  to  limit  the  peripheral  velocity  to  4?  feet  per  second 

There  is  a  large  variation  in  the  listed  speeds  of  emery-wheels  by  different 
makers— 4000  as  a  minimum  and  5600  maximum  feet  per  minute  while 
others  claim  a  maximum  speed  of  10,000  feet  per  minute  as  the  safe  speed 
of  their  best  emery-wheels.  Rim  wheels  and  iron  centre  wheels  are  special- 
ties that  require  the  maker's  guarantee  and  assignment  of  speed. 

Strains  In  Emery-wheels. 
ACTUAL  STRAIN  PER  SQUARE  INCH  OF  SECTION  IN  EMERY-WHEELS  AT  THE 

VELOCITIES  AT  HEAD  OF  COLUMNS  FOR  SIZES  IN  FIRST  COLUMN. 


Jo 
Q.2 

Revolutions  per  minute. 

600 

800 

1000 

1200 

1400 

1600 

1800 

2000 

2200 

2400 

2600 

4 
6 
8 
10 
12 
14 
16 
18 
20 
22 
24 
26 
30 
36 

22.67 
51.13 
90.71 
141.90 

27.43 
61.86 
109.76 
171.71 

32.64 
73.62 
130.62 

38.31 
86.40 
153.30 

22.67 
35.47 
51.12 
68.70 
90.24 
115.03 
141.22 
171.23 

32  65 
51.08 
73.02 
99.21 
130.31 
165.65 

44.45 
69.51 
100.21 
134.65 
177.80 

58.05 
90.81 
130.88 
175.60 

73.47 
114.94 
165.65 

18.40 
24.80 
32.57 
41.41 
50.98 
61.81 
73.62 
86.36 
115.04 
165.64 

32.72 
43.90 
57.65 
73.62 
90.23 
109.41 
130.88 
152.85 

Diatn 

Revs,  per 
min. 

in. 

2800 

3000 

0004k. 

44.43 
100.21 
177.80 

51.12 
115.03 

Joshua  Rose  (Modern  Machine-shop  Practice)  says:  The  average  speed  of 
grindstones  in  workshops  may  be  given  as  follows: 

Circumferential  Speed  of  Stone. 

For  grinding  machinists'  tools,  about  900  feet  per  minute. 

"        carpenters1     '"         "      600    "     4l         " 

The  speeds  of  stones  for  file-grinding,  and  other  similar  rapid  grinding  is 
thus  given  in  the  "Grinders1  List.'1 

Diam.  ft 8       7^        7       6^       6       5^       5       4J4        4      3U       3 

Revs,  per  min.  135  144  154  106  180  196"  216  240  270  308  360 
The  following  table,  from  the  Mechanical  World,  is  for  the  diameter  of 
stones  and  the  number  of  revolutions  they  should  run  per  minute  (not  to  be 
exceeded),  with  the  diameter  of  change  of  shift-pulleys  required,  varying 
each  shift  or  change  ^  inches,  2J4  inches,  or  2  inches  in  diameter  for  each 
reduction  of  6  inches  in  the  diameter  of  the  stone. 


Diameter 

Revolutions 

Shift  of  Pulleys,  in  inches. 

of  Stone. 

per  minute. 

2^ 

2M 

2 

ft      in 

8       0 

135 

40 

36 

32 

7       6 

144 

37Va 

3334 

30 

7       0 

154 

35 

31^| 

28 

6       6 

166 

32L£ 

29^4 

26 

6        0 

180 

30 

27 

24 

5       6 

196 

27^ 

24% 

22 

5       0 

216 

25 

22^£ 

20 

4        6 
4        0 

240 
270 

If 

20»4 
18 

18 
16 

3       6 

308 

17^o 

15% 

14 

3        0 

360 

15 

13H 

12 

1 

2 

3 

4 

5 

970 


THE   MACHINE-SHOP. 


Columns  3,  4,  and  5  are  given  to  show  that  if  we  start  an  8-foot  stone  with, 
say.  a  countershaft  pulley  driving  a  40-inch  pulley  on  the  grindstone  spindle, 
and  the  stone  makes  the  right  number  (135)  of  revolutions  per  minute,  the 
reduction  in  the  diameter  of  the  pulley  on  the  grinding-stone  spindle,  when 
the  stone  has  been  reduced  6  inches  in  diameter,  will  require  to  be  also  re- 
duced 2}^  inches  in  diameter,  or  to  shift  from  40  inches  to  37^  inches,  and  so 
on  similarly  for  columns  4  and  5.  Any  other  suitable  dimensions  of  pulley 
may  be  used  for  the  stone  when  eight  feet  in  diameter,  but  the  number  of 
inches  in  each  shift  named,  in  order  to  be  correct,  will  have  to  be  propor- 
tional to  the  numbers  of  revolutions  the  stone  should  run,  as  given  in  column 
2  of  the  table. 

Varieties  of  Grindstones. 

(Joshua  Rose.) 

FOR  GRINDING  MACHINISTS'  TOOLS. 


Name  of  Stone. 

Kind  of  Grit. 

Texture  of  Stone. 

Color  of  Stone. 

Nova  Scotia, 

Bay  Chaleur  (New  \ 
Brunswick),           ) 
Liverpool  or  Melling. 

All  kinds,  from 
finest  to  coarsest 

Medium  to  finest 
Medium  to  fine 

All  kinds,  from 
hardest  to  softest 

Soft  and  sharp 

Soft,  with  sharp 
grit 

Blue  or  yellowish 
gray 
Uniformly    light 
blue 
Reddish} 

FOR  WOOD-WORKING  TOOLS. 

Wickersley 

Medium  to  fine 
Medium  to  fine  •! 

Medium  to  finest 
Fine 

Very  soft 
Soft,  with  sharp 
grit 

Soft  and  sharp 
Soft  and  sharp 

Grayish  yellow 
Reddish 

Uniform  light  blue 
Uniform  light  blue 

Liverpool  or  Melling. 

Bay  Chaleur  (New  1 
Brunswick),            f 
Huron,  Michigan  .  .  . 

FOR  GRINDING  BROAD  SURFACES,  AS  SAWS  OR  IRON  PLATES. 


Newcastle..        

Coarse  to  med'm 

The  hard  ones 

Yellow 

Independence. 

Coarse 

Hard  to  medium 

Grayish  white 

Massillon  

Coarse 

Hard  to  medium 

Yellowish  white 

TAP  DRILLS. 

Taps  for  Machine-screws.    (The  Pratt  &  Whitney  Co.) 


Approx. 

Approx. 

Diameter, 

Wire 

No.  of  Threads 

Diameter, 

Wire 

No.  of  Threads 

fractions 

Gauge. 

to  inch. 

fractions 

Gauge. 

to  inch. 

of  an  inch. 

of  an  inch. 

No.  1 

60,  72 

No.  13 

20,24 

2 

48,  56,  64 

Y4 

14 

16,  18,  20,  22,  24 

3 

40,  48,  56 

15 

18,  20,  24 

7/64 

4 

32,  36,  40 

17/64 

16 

16,  18,  20,  22 

5 

30,  32,  36,  40 

9/32 

18 

16,  18,  20 

9/64 

6 

30,  32,  36,  40 

19 

16,  18,  20 

7 

24,  30,  32 

5/16 

20 

16,  18,  20 

5/32 

8 

24,  30.  32,  36,  40 

22 

16,  18 

9 

24,  28,  30,  32 

% 

24 

14,  16,  18 

3/16 

10 

20,  22,  24,  30,  32 

26 

16 

11 

22,  24 

28 

16 

7/32 

12 

20.  22,  24 

30 

16 

The  Morse  Twist  Drill  and  Machine  Co.  gives  the  following  table  showing 
the  different  sizes  of  drills  that  should  be  used  when  a  full  thread  is  10  be 
tapped  \n  a  hole.  The  sizes  given  are  practically  correct, 


TAP   DRILLS. 


971 


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n 

0 

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6          £-3         OOOOQOQO iooioo    •    i   •    ioooo 

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ft     £  02 

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«3  t 

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972 


THE    MACHINE-SHOP. 


TAPER  BOLTS,  PINS,  REAMERS,  ETC. 


Taper  Bolts  for  Locomotives.—  Bolt-threads,  American  stan- 
dard, except  stay-bolts  and  boiler-studs,  V  threads,  12  per  inch;  valves, 
cocks,  and  plugs,  V  threads,  14  per  inch,  and  J^-inch  taper  per  1  inch. 
Standard  bolt  taper  1/16  inch  per  foot. 

Taper  Reamers.—  The  Pratt  &  Whitney  Co.  makes  standard  taper 
reamers  for  locomotive  work  taper  1/16  inch  per  foot  from  14  inch  diam.; 
7  in.  length  of  flute  to  1%  inch  diam.;  16  in.  length  of  flute,  diameters  ad- 
vancing by  16ths.  P.  &  W.  Co.'s  standard  taper  pin  reamers  taper  %  in. 
per  foot,  are  made  in  14  sizes  of  diameters,  0.135  to  1.009  in.;  length  of  flute 
1  5/16  in.  to  12  in. 

DIMENSIONS  OF  THE  PRATT  &  WHITNEY  COMPANY'S  REAMERS  FOR  MORSE 
STANDARD-TAPER  SOCKET. 


No. 

Diameter 
Small  End, 
inches. 

Diameter 
Large  End, 
inches. 

Gauge 
Diam.,la'ge 
end,  inches 

Gauge 
L'ngth, 
inches. 

Length 
Flute, 
inches. 

Total 
L'ngth. 

Taper 
per  foot 
inches. 

1 
2 
3 

4 
5 
6 

0.374 
0.574 
0.783 
1.027 
1.484 
2.117 

0.525 
0.749 
0.982 
1.283 
1.796 
2.566 

0.481 
0.699 
0.950 
1.232 
1.746 
2.500 

2^1 

35/16 
4 
5 

7M 

3 
3^ 
4 

5 
6 

8^ 

10  4 

12^ 

0.605 
0.600 
0.605 
0.615 
0.625 
0.634 

Standard   Steel    Taper-pins.— The  following  sizes  are  made  bj 
the  Pratt  &  Whitney  Co.: 
Number: 

0  123456789          10 

Diameter  large  end: 

.156    .172   .193  .219  .250  . 


Approximate  fractional  sizes: 

5/32        11/64    3/16    7/32 
Lengths  from 


.289   .341   .409  .492  .591   .706 
19/64  11/32  13/32   ^   19/32  23/32 


i 


1 


Diameter  small  end  of  standard  taper-reamer :t 

.125         .146      .162     .183     .208      .240       .279       .331 


.398     .482      .581 


Standard  Steel  Mandrels.  (The  Pratt  &  Whitney  Co.)— These 
mandrels  are  made  of  tool-steel,  hardened,  and  ground  true  on  their  cen 
tres.  The  ends  are  of  a  form  best  adapted  to  resist  injury  likely  to  be 
caused  by  driving.  They  are  slightly  taper.  Sizes,  *4  in.  diameter  by  3^ 
in.  long  to  3  in.  diam.  by  14^  in.  long,  diameters  advancing  by  16ths. 

PUNCHES  AND  DIES,  PRESSES,  ETC. 

Clearance  between  Punch  and  Die.  —For  computing  the  amoun 
of  clearance  that  a  die  should  have,  or,  in  other  words,  the  difference  ii 
size  between  die  and  punch,  the  general  rule  is  to  make  the  diameter  oJ 
die-hole  equal  to  the  diameter  of  the  punch,  plus  2/10  the  thickness  of  tht 
plate.  Or,  D  =  d  +  -'Zt,  in  which  D  =  diameter  of  die-hole,  d  =  diameter  01 
punch,  and  t  =  thickness  of  plate.  For  very  thick  plates  some  mechanic! 
prefer  to  make  the  die-hole  a  little  smaller  than  called  for  by  the  above  rule 
For  ordinary  boiler-work  the  die  is  made  from  1/10  to  3/10'of  the  thickness 
of  the  plate  larger  than  the  diameter  of  the  punch;  and  some  boiler-makers 
advocate  making  the  punch  fit  the  die  accurately.  For  punching  nuts,  th< 
punch  fits  in  the  die.  (Am.  Machinist.} 

Kennedy's  Spiral  Punch.  (The  Pratt  &  Whitney  Co.)— B.  Martell 
Chief  Surveyor  of  Lloyd's  Register,  reported  tests  of  Kennedy's  spira 
punches  in  which  a  %-incli  spiral  punch  penetrated  a  %-inch  plate  at  a  pres 
sure  of  22  to  25  tons,  while  a  flat  punch  required  33  to  35  tons.  Steel  boiler 
plates  punched  with  a  flat  punch  gave  an  average  tensile  strength  of  58,57! 

*  Taken  \Q'  from  extreme  end,  each  size  overlaps  smaller  one  about  %" 
Taper  *4"  to  the  foot,  t  Lengths  vary  by  y^"  each  size. 


AND   SHRINKING   FITS.  973 

Ibs.  per  square  inch,  and  an  elongation  in  two  inches  across  the  hole  of  5.2$, 
while  plates  punched  with  a  spiral  punch  gave  63,929  Ibs.,  and  10.6$  elonga- 
tion. 

The  spiral  shear  form  is  not  recommended  for  punches  for  use  in  metal  of 
a  thickness  greater  than  the  diameter  of  the  punch.  This  form  is  of  great- 
est benefit  when  the  thickness  of  metal  worked  is  less  than  two  thirds  the 
diameter  of  punch. 

Size  of  Blanks  used  in  the  Drawing-press.  Oberlin  Smith 
(Jour.  Frank.  Inst.,  Nov.  1886;  gives  three  methods  of  finding  the  size  of 
blanks.  The  first  is  a  tentative  method,  and  consists  simply  in  a  series  of 
experiments  with  various  blanks,  until  the  proper  one  is  found.  This  is  for 
use  mainly  in  complicated  cases,  and  when  the  cutting  portions  of  the  die 
and  punch  can  be  finally  sized  after  the  other  work  is  done.  The  second 
method  is  by  weighing  the  sample  piece,  and  then,  knowing  the  weight  of 
the  sheet  metal  per  square  inch,  computing  the  diameter  of  a  piece  having 
the  required  area  to  equal  the  sample  in  weight.  The  third  method  is  by 
computation,  and  the  formula  is  x  =  Vd*  -f  4dh  for  sharp-cornered  cup, 
where  x  =  diameter  of  blank,  d  =  diameter  of  cup,  h  =  height  of  cup.  For 
round-cornered  cup  where  the  corner  is  small,  say  radius  of  corner  less  than 
14  height  of  cup,  the  formula  is  x  =  (  1/d2  +  4dh)  -  r,  about;  r  being  the 
radius  of  the  corner.  This  is  based  upon  the  assumption  that  the  thickness 
of  the  meial  is  not  to  be  altered  by  the  drawing  operation. 

Pressure  attainable  by  the  Use  of  the  Drop-press.  (R.  H. 
Thiirston,  Trans.  A.  S.  M.  E.,  v.  53.)— A  set  of  copper  cylinders  was  prepared, 
of  pure  Lake  Superior  copper;  they  were  subjected  to  the  action  of  presses 
of  different  weights  and  of  different  heights  of  fall.  Companion  specimens 
of  copper  were  compressed  to  exactly  the  same  amount,  and  measures  were 
obtained  of  the  loads  producing  compression,  and  of  the  amount  of  work 
done  in  producing  the  compression  by  the  drop.  Comparing  one  with  the 
other  it  was  found  that  the  work  done  with  the  hammer  was  90$  of  the  work 
which  should  have  been  done  with  perfect  efficiency.  That  is  to  say,  90$  of 
the  work  done  in  the  testing-machine  was  equal  to  that  due  the  weight  of 
the  drop  falling  the  given  distance. 

Weight  of  drop  X  fall  x  efficiency 

Formula:  Mean  pressure  in  pounds  =  -  compression.  ~ 

For  pressures  per  square  inch,  divide  by  the  mean  area  opposed  to  crush- 
ing action  during  the  operation. 

Flow  of  Metals.  (David  Townsend,  Jour.  Frank.  Inst.,  March,  1878.) 
--In  punching  holes  7/16  inch  diameter  through  iron  blocks  1?4  inches  thick, 
it  was  found  that  the  core  punched  out  was  only  1  1/16  inch  thick,  and  its 
volume  was  only  about  32$  of  the  volume  of  the  hole.  Therefore,  68$  of  the 
metal  displaced  by  punching  the  hole  flowed  into  the  block  itself,  increasing 
its  dimensions. 

FORCING  AND  SHRINKING  FITS. 

Forcing  Fits  of  Pins  and  Axles  by  Hydraulic  Pressure. 

— A  4-inch  axle  is  turned  .015  inch  diameter  larger  than  the  hole  into  which 
it  is  to  be  fitted.  They  are  pressed  on  by  a  pressure  of  30  to  35  tons.  (Lec- 
ture by  Coleinan  Sellers,  1872.) 

For  forcing  the  crank-pin  into  a  locomotive  driving-wheel,  when  the  pin- 
hole  is  perfectly  true  and  smooth,  the  pin  should  be  pressed  in  with  a  pres- 
sure of  6  tons  for  every  inch  of  diameter  of  the  wheel  fit.  When  the  hole  is 
not  perfectly  true,  which  may  be  the  result  of  shrinking  the  tire  on  the 
wheel  centre  after  the  hole  for' the  crank-pin  has  been  bored,  or  if  the  hole  is 
not  perfectly  smooth,  the  pressure  may  have  to  be  increased  to  9  tons  for 
every  inch  of  diameter  of  the  wheel-fit.  (Am.  Machinist.) 

Shrinkage  Fits.— In  1886  the  American  Railway  Master  Mechanics1 
Association  recommended  the  following  shrinkage  allowances  for  tires  of 
standard  locomotives.  The  tires  are  uniformly  heated  by  gas-flames,  slipped 
over  the  cast-iron  centres,  and  allowed  to  cool.  The  centres  are  turned  to 
the  standard  sizes  given  below,  and  the  tires  are  bored  smaller  by  the 
amount  of  the  shrinkage  designated  for  each  : 

Diameter  of  centre,  in   . .          38        44        50        56        62        66 
Shrinkage  allowance,  in..     .040     .047     .053     .060    .066     .070 

This  shrinkage  allowance  is  approximately  I/SO  inch  per  foot,  or  1/960.  A 
common  allowance  is  1/1000  Taking  the  modulus  of  elasticity  of  sieel  at 


974  THti  MACHINE-SHOP. 

30,000,000,  the<strain  caused  by  shrinkage  would  be  30,000  Ibs.  per  square  inch, 
which  is  well  within  the  elastic  limit  of  machinery  steel. 

SCREWS,  SCREW-THREADS,  ETC.* 

Efficiency  of  a  Screw.—  Let  a  —  angle  of  the  thread,  that  is,  the 
angle  whose  tangent  is  the  pitch  of  the  screw  divided  by  the  circumference 
of  a  circle  whose  diameter  is  the  mean  of  the  diameters  at  the  top  and 
bottom  of  the  thread.  Then  for  a  square  thread 

1  —  /  tan  a 

Efficiency  -  ,    .    /  —  -  -  , 
1  +  /  cotan  a 

in  which  /  is  tlie  coefficient  of  friction.  (For  demonstration,  see  Cotterill  and 
Slade,  Applied  Mechanics,  p.  146.)  Since  cotan  =  1  -*-  tan,  we  may  substitute 
for  cotan  a  the  reciprocal  of  the  tangent,  or  if  p  =  pitch,  and  c  =  mean  cir- 
cumference of  the  screw, 


Efficiency  = 


EXAMPLE.— -Efficiency  of  square- threaded  screws  of  ^  in.  pitch. 


Diameter  at  bottom  of  thread,  in  ....      1                 2                  3 
"    top         "       "         "  .-...     1^              2^                3^ 
Mean  circumference"      "         "....3.927           7.069            10.21 
Cotangent  a  —  c  -^  p  —7.854         14.14              20.42 

A 

26.  7C 

Tangent  a  —  p  -*~  c               .       .       —    1273           .0661             .0490 

.037.' 

Efficiency  if  /—  .10  —  553$           41.2$             32.7$ 

27.  2?, 

44           "/—  .15  -    45%             31.  7$             24.4$ 

19.9^ 

The  efficiency  thus  increases  with  the  steepness  of  the  pitch. 
The  above  formulae  and  examples  are  for  square-threaded  screvvi 

5,  and 

*f    *V>,, 

consider  the  friction  of  the  screw-thread  only,  and  not  the  friction  of  the 
collar  or  step  by  which  end  thrust  is  resisted,  and  which  further  reduces  tht 
efficiency.  The  efficiency  is  also  further  reduced  by  giving  an  inclination  tc 
the  side  of  the  thread,  as  in  the  V-threaded  screw.  For  discussion  of  this 
subject,  see  paper  by  Wilfred  Lewis,  Jour.  Frank.  Inst.  1880;  also  Trans. 
A.  S.  M.  E.,  vol.  xii.  784. 

Efficiency  of  Screw-bolts.—  Mr.  Lewis  gives  the  following  approx- 
imate formula  for  ordinary  screw-bolts  (V  threads,  with  collars):  p  = 
pitch  of  screw,  d  =  outside  diameter  of  screw,  F  =  force  applied  at  circuni 
rerence  to  lift  a  unit  of  weight,  E  =  efficiency  of  screw.  For  an  average 
case,  in  which  the  coefficient  of  friction  may  be  assumed  at  .15, 


=, 

3d 

For  bolts  of  the  dimensions  given  above,  J^-in.  pitch,  and  outside  diam 
eters  1^,  2^,  3^,  and  4^  in.,  the  efficiencies  according  to  this  formula 
would  be,  respectively,  .25,  .167,  .125,  and  .10. 

James  McBride  (Trans.  A.  S.  M.  E.,  xii.  781)  describes  an  experiment  with 
an  ordinary  2-in.  screw-bolt,  with  a  V  thread,  4^  threads  per  inch,  raising 
a  weight  of  7500  Ibs.,  the  force  being  applied  by  turning  the  nut.  Of  the 
power  applied  89.8$  was  absorbed  by  friction  of  the  nut  on  its  supporting 
washer  and  of  the  threads  of  the  bolt  in  the  nut.  The  nut  was  not  faced, 
and  had  the  flat  side  to  the  washer. 

Prof.  Ball  in  his  "  Experimental  Mechanics  "  says:  "Experiments  showed 
in  two  cases  respectively  about  %  and  M  of  the  power  was  lost.11 

Trautwine  says:  "  In  practice  the  friction  of  the  screw  (which  under 
heavy  loads  becomes  very  great)  make  the  theoretical  calculations  of  but 
little  value." 

Weisbach  says:  "  The  efficiency  is  from  19$  to  30$." 

Efficiency  of  a  Differential  Screw.—  A  correspondent  of  the 
American  Machinist  describes  an  experiment  with  a  differential  screw- 
punch,  consisting  of  an  outer  screw  2  in.  diam.,  3  threads  per  in.,  and  an 
inner  screw  \%  in.  diam.,  3J4  threads  per  inch.  The  pitch  of  the  outer  screw 


*  For  U.  S.  Standard  Screw-threads,  see  page  204. 


KEYS.  975 

being  %  in.  and  that  of  the  inner  screw  2/7  in.,  the  punch  would  ad- 
vance in  one  revolution  ^  -  2/7  =  1/21  in.  Experiments  were  made  10  de- 
termine the  force  required  to  punch  an  11/16-in.  hole  in  iron  y*  in  thick  the 
force  being  applied  at  the  end  of  a  lever-arrn  of  47%  in.  The  leverage  would 
be  47%  X  27r  x  21  =  6300.  The  mean  force  applied  at  the  end  of  the  lever 
was  95  Ibs.,  and  the  force  at  the  punch,  if  there  was  no  friction,  would  be 
6300  X  95  =  598,500  Ibs.  The  force  required  to  punch  the  iron  assuming  a 
shearing  resistance  of  50,000  Ibs.  per  sq.  in.,  would  be  50,000  X  11/16  X  TT  X 
J4  =  27,000  Ibs.,  and  the  efficiency  of  the  punch  would  be  27,000  -4-  598,500  = 
only  4.5$.  With  the  larger  screw  only  used  as  a  punch  the  mean  force  at 
the  end  of  the  lever  was  only  82  Ibs.  The  leverage  in  this  case  was  47  M  X 
2ir  x  3  =  900,  the  total  force  referred  to  the  punch,  including  friction  900  x 
82  =  73,800,  and  the  efficiency  27,000  -i-  73,800  =  36. 7#.  The  screws  were  of 
tool -steel,  well  fitted,  and  lubricated  with  lard-oil  and  plumbago. 

Powell's  New  Screw-thread.— A.  M.  Powell  (Am.  Mach.,  Jan.  24, 
1895)  has  designed  a  new  screw-thread  to  replace  the  square  form  of  thread, 
giving  the  advantages  of  greater  ease  in  making  fits,  and  provision  for  "  take 
up  "  in  case  of  wear.  The  dimensions  are  the  same  as  those  of  square- 
thread  screws,  with  the  exception  that  the  sides  of  the  thread,  instead  of 
being  perpendicular  to  the  axis  of  the  screw,  are  inclined  14^°  to  such  per- 
pendicular; that  is,  the  two  sides  of  a  thread  are  inclined  29°  to  each  other. 
The  formulae  for  dimensions  of  the  thread  are  the  following:  Depth  of 
thread  =  ^  -f-  pitch;  width  of  top  of  thread  =  width  of  space  at  bottom  = 
.3707  -7-  pitch;  thickness  at  root  of  thread  =  width  of  space  at  top  =  .6293  -*- 
pitch.  The  term  pitch  is  the  number  of  threads  to  the  inch. 

PROPORTIONING  PARTS  OF  MACHINES  IN  A  SERIES 

OF  SIZES. 
(Stevens  Indicator,  April,  1892.) 

The  following  method  was  used  by  Coleman  Sellers  while  at  William  Sellers 
&  Co/s  to  get  the  proportions  of  the  parts  of  machines,  based  upon  the 
size  obtained  in  building  a  large  machine  and  a  small  one  to  any  series  of 
machines.  This  formula  is  used  in  getting  up  the  proportion-book  and  ar- 
ranging the  set  of  proportions  from  which  any  machine  can  be  constructed 
of  intermediate  size  between  the  largest  and  smallest  of  the  series. 

Rule  to  Establish  Construction  Formulae.— Take  difference 
between  the  nominal  sizes  of  the  largest  and  the  smallest  machines  that 
have  been  designed  of  the  same  construction.  Take  also  the  difference  be- 
tween the  sizes  of  similar  parts  on  the  largest  and  smallest  machines  se- 
lected. Divide  the  latter  by  the  former,  and  the  result  obtained  will  be  a 
"factor,11  which,  multiplied  by  the  nominal  capacity  of  the  intermediate 
machine,  and  increased  or  diminished  by  a  constant  "  increment,'1  will  give 
the  size  of  the  part  required.  To  find  the  "  increment :"  Multiply  the  nomi- 
nal capacity  of  some  known  size  by  the  factor  obtained,  and  subtract  the 
result  from  the  size  of  the  part  belonging  to  the  machine  of  nominal  ca- 
pacity selected. 

EXAMPLE.— Suppose  the  size  of  a  part  of  a  72-in.  machine  is  3  in.,  and  the 
corresponding  part  of  a  42-in.  machine  is  1%,  or  1.875  in.:  then  72  -  42  = 
30,  and  3  in.  -  1%  in.  -  \V%  in.  =  1.125.  1.125  -r-  30  =  .0375  =  the  "  factor," 
and  .0375  X  42  =  1.575.  Then  1.875  -  1.575  =  .3  =  the  "increment11  to  bo 
added.  Let  D  =  nominal  capacity;  then  the  formula  will  read:  x  = 
D  X  .0375  4-  .3. 

Proof:  42  x  .0375  -f-  .3  =  1.875,  or  1%.  the  size  of  one  of  the  selected  parts. 

Some  prefer  the  formula:  aD  -f  c  =  x,  in  which  D  =  nominal  capacity  in 
inches  or  in  pounds,  c  is  a  constant  increment,  a  is  the  factor,  and  x  =  the 
part  to  be  found. 

KEYS. 

Sizes  of  Keys  for  Mill-gearing.    (Trans.  A.  S.  M.  E.,  xiii.  229.)-E. 

G.  Parkhurst's  rule  :  Width  of  key  =  %  diam.  of  shaft,  depth  =  1/9  diam.  of 
Shaft ;  taper  %  in.  to  the  foot. 

Custom  in  Michigan  saw-mills  :  Keys  of  square  section,  side  =  *4  diam.  of 
shaft,  or  as  nearly  as  may  be  in  even  sixteenths  of  an  inch. 

J.  T.  Hawkins's  rule  :  Width  =  ^  diam.  of  hole;  depth  of  side  abutment 
in  shaft  =  >£  diam.  of  hole. 

W.  S.  Huson's  rule  :  J^-inch  key  for  1  to  1*4  in.  shafts,  5/16  key  for  114  to 
1*6  in.  shafts,  %  in.  key  for  1^  to  1%  in.  shafts,  and  so  on.  Taper  %  in.  to 
the  foot.  Total  thickness  at  large  end  of  splice,  4/5  width  of  key. 


976  THE    MACHINE-SHOP. 

Unvvin  (Elements  of  Machine  Design)  gives  :  Width  =  y^d  -f  %  in.  Thick- 
ness =  %d  -f  H  in-.  in  which  d  —  diam.  of  shaft  in  inches.  When  wheels  or 
pulleys  transmitting  only  a  small  amount  of  power  are  keyed  on  large  shafts, 
he  says,  these  dimensions  are  excessive.  In  that  case,  if  H.P.  =  horse- 
power transmitted  by  the  wheel  or  pulley,  N  —  revs,  per  ruin,  P  =  force 
acting  at  the  circumference,  in  IDS.,  and  R  =  radius  of  pulley  in  inches,  take 


3/100  H.P.  a/PR 

=  Y        N         or    V    630 ' 


Prof.  Coleman  Sellers  (Stevens  Indicator,  April,  1892)  gives  the  following  : 
The  size  of  keys,  both  for  shafting  and  for  machine  tools,  are  the  propor- 
tions adopted 'by  William  Sellers  &  Co.,  and  rigidly  adhered  to  during  a  pe- 
riod of  nearly  forty  years.  Their  practice  in  making  keys  and  fitting  them 
is,  that  the  keys  shall  always  bind  tight  sidewise,  but  not  top  and  bottom; 
that  is,  not  necessarily  touch  either  at  the  bottom  of  the.  key-seat  in  the 
shaft  or  touch  the  top  of  the  slot  cut  in  the  gear-wheel  that  is  fastened  to 
the  shaft  ;  but  in  practice  keys  used  in  this  manner  depend  upon  the  fit  of 
the  wheel  upon  the  shaft  being  a  forcing  fit,  or  a  fit  that  is  so  tight  as  to  re 
quire  screw-pressure  to  put  the  wheel  in  place  upon  the  shaft. 

Size  of  Keys  for  Shafting. 

Diameter  of  Shaft,. in.  Size  of  Key,  in. 

1^4  1  7/16      1  11/16 5/16  x  % 

115/16    23/16 7/16  x  ^ 

27/16 9/16  x  % 

211/16    215/16    33/16      37/16 ll/16x  % 

3  15/16    4  7/16      4  15/16 13/16  x   % 

57/16      515/16    67/16.. 15/16x1 

6  15/16    7  7/16      7  15/16    8  7/16    8  15/16..  1  1/16x1^ 
Length  of  key-seat  for  coupling  =  \y%  X  nominal  diameter  of  shaft. 

Size  of  Keys  for  Machine  Tools. 


Diam.  of  Shaft,  in.       ^f^ej, 

15/16    and  under ^ 

1      tol  3/1(5 3/16 


to  1  7/16 

^2  to  1  11/16. 5/16 

94  to  2  3/16 7/16 

^  to  2  11/16 9/16 

%  to  3  15/16 11/16 


Diam.  of  Shaft,  in.        Size  °f  £ey' 

4   to  5  7/16 13/16 

5U  to  6  15/16 15/16 

7      to    8  15/16 1  1/16 

9      to  10  15/16 1  3/16 

11      to  12  15/16 1  5/16 

13      to  14  15/16  1  7/16 


John  Richards,  in  an  article  in  Gassier' s  Magazine, writes  as  follows:  There 
are  two  kinds  or  system  of  keys,  both  proper  and  necessary,  but  widely  dif- 
ferent in  nature.  1.  The  common  fastening  key,  usually  made  in  width  one 
fourth  of  the  shaft's  diameter,  and  the  depth  five  eighths  to  one  third  the 
width.  These  keys  are  tapered  and  fit  on  all  sides,  or,  as  it  is  commonly  de- 
scribed, "  bear  all  over."  They  perform  the  double  function  in  most  cases 
of  driving  or  transmitting  and  fastening  the  keyed-on  member  againsr 
movement  endwise  on  the  shaft.  Such  keys,  when  properly  made,  drive 
as  a  strut,  diagonally  from  corner  to  corner. 

i.  The  other  kind  or  class  of  keys  are  not  tapered  and  fit  on  their  sides 
only,  a  slight  clearance  being  left  on  the  back  to  insure  against  wedge  action 
or  radial  strain.  These  keys  drive  by  shearing  strain. 

For  fixed  work  where  there  is  no  sliding  movement,  such  keys  are  com- 
monly made  of  square  section,  the  sides  only  being  planed,  so  the  depth  is 
more  than  the  width  by  so  much  as  is  cut  away  in  finishing  or  fitting. 

For  sliding  bearings,  as  in  the  case  of  drilling-machine  spindles,  the  depth 
should  be  increased,  ami  in  cases  where  there  is  heavy  strain  there  should 
be  two  keys  or  feathers  instead  of  one. 

The  following  tables  are  taken  from  proportions  adopted  in  practical  use. 

Flat  keys,  as  in  the  first  tabl^,  are  employed  for  fixed  wprk  when  the 
parts  are 'to  be  held  not  only  against  torsional 'strain,  but  also  against  move- 
ment endwise  ;  and  in  case  of  heavy  strain  the  strut  principle  being  the 
strongest  and  most  secure  against  movement  when  there  is  strain  each  way, 
as  in  the  case  of  engine  cranks  and  first  movers  generally.  The  objections 


HOLDIKG-POWER  OF   KEYS   AKD    SET-SCREWS.      971 


to  the  system  for  general  use  are,  straining  the  work  out  of  truth  the  care 
and  expense  required  in  fitting,  and  destroying  the  evidence  of  good  or  bad 
fitting  of  the  keyed  joint.  When  a  wheel  or  other  part  is  fastened  with  a 
tapering  key  of  this  kind  there  is  no  means  of  knowing  whether  the  work  is 
well  fitted  or  not.  For  this  reason  such  keys  are  not  employed  by  machine- 
tool-makers,  and  in  the  case  of  accurate  work  of  any  kind,  indeed,  cannot 
be,  because  of  the  wedging  strain,  and  also  the  difficulty  of  inspecting  com- 
pleted work. 

I.  DIMENSIONS  OF  FLAT  KEYS,  IN  INCHES. 


Diam.  of  shaft.... 
Breadth  of  keys 
Depth  of  keys . . . , 


'32  3/ 


1M 

5/16 
"'16 


7/1 
Y4  9/32  5/16 


7/16 


%  11/16  13/16 


II.  DIMENSIONS  OF  SQUARE  KEYS,  IN  INCHES. 


Diam.  of  shaft  
Breadth  of  keys..  . 
Depth  of  keys  

1 

5/32 
3/16 

W4 

7/32 

% 

*9/32 
5/16 

Tt/32 
% 

2 

13/32 
7/16 

2^ 

15/32 

fc 

3 

17/32 
9/16 

V/2 
9/16 

% 

4 
11/16 
H 

III.  DIMENSIONS  OF  SLIDING  FEATHER-KEYS,  IN  INCHES. 


Diam.  of  shaft.... 
Breadth  of  keys. . 
Depth  of  keys 


5/16 

7/16 


5/16 
7/16 


9/16 


P.  Pryibil  furnishes  the  following  table  of  dimensions  to  the  Am.  Machin- 
ist. He  says :  On  special  heavy  work  and  very  short  hubs  we  put  in  two 
keys  in  one  shaft  90°  apart.  With  special  long  hubs,  where  we  cannot  use 
keys  with  noses,  the  keys  should  be  thicker  than  the  standard. 


Diameter  of  Shafts, 
inches. 

Width, 
inches. 

Thick- 
ness, in. 

Diameter  of  Shafts, 
inches. 

Width, 
inches. 

Thick- 
ness,in. 

%         to  1  1/16 

3/16 

3/16 

3  7/16    to  3  11/16 

Vs 

% 

\YS         to  1  5/16 
1  7/16    tol  11/16 
1  15/16  to  2  3/16 

5/16 

&e 

3  15/16  to  4  3/16 
4  7/16    to  4  11/16 

l 

11/16 
15/16 

2  7/16    to  2  11/16 

% 

\& 

5%         to  6% 

i^ 

1 

2  15/16  to  3  3/16 

M 

9/16 

6%         to  7% 

1% 

1^ 

Keys  longer  than  10  inches,  say  14  to  16",  1/16"  thicker;  keys  longer  than 
10  inches,  say  18  to  20",  W  thicker;  and  so  on.  Special  short  hubs  to  have 
two  keys. 

For  description  of  the  Woodruff  system  of  keying,  see  circular  of  the 
Pratt  &  Whitney  Co.;  also  Modern  Mechanism,  page  455. 

HOL,DHVCi-POWER  OF  KEYS  AND  SET-SCREWS. 

Tests    of  the  Holding-power   of  Set-screws  in  Pulleys. 

(G.  Lanza,  Trans.  A.  S.  M.  12.,  x.  230.)— These  tests  were  made  by  using  a 
pulley  fastened  to  the  shaft  by  two  set-screws  with  the  shaft  keyed  to  the 
holders;  then  the  load  required  at  the  rim  of  the  pulley  to  cause  it  to  slip 
was  determined,  and  this  being  multiplied  by  the  number  6.037  (obtained  by 
adding  to  the  radius  of  the  pulley  one-half  the  diameter  of  the  wire  rope, 
and  dividing  the  sum  by  twice  the'radiufi  of  the  shaft,  since  there  were  two 
set-screws  in  action  at  a  time)  gives  the  holding-power  of  the  set-screws. 
The  set-screws  used  were  of  wrought-iron,  %  of  an  inch  in  diameter,  and  ten 
threads  to  the  inch;  the  shaft  used  was  of  steel  and  rather  hard,  the  set- 
screws  making  but  little  impression  upon  it.  They  were  set  up  with  a 
force  of  75  Ibs.  at  the  end  of  a  ten-inch  monkey-wrench.  The  set-screws 
used  were  of  four  kinds,  marked  respectively  A,  B,  C,  and  D.  The  results 
were  as  follows : 


978  DYNAMOMETERS. 

A,  ends  perfectly  flat,  9/16-in.  diameter,      1412  to  2294  Ibs. ;  average  2664. 

B,  radius  of  rounded  ends  about  ^  inch,  2747  "  3079    "  "        2910. 

C,  "       "          "  "  "      Y±    "        1902  "  3079    "  "        2573. 
D  ends  cup-shaped  and  case-hardened,      1962  "  2958    "  2470. 

REMARKS. — A.  The  set-screws  were  not  entirely  normal  to  the  shaft ;  hence 
they  bore  less  in  the  earlier  trials,  before  they  had  become  flattened  by 
wear. 

B.  The  ends  of  these  set-screws,  after  the  first  two  trials,  were  found  to 
be  flattened,  the  flattened  area  having  a  diameter  of  about  J4  inch. 

C.  The  ends  were  found,  after  the  first  two  trials,  to  be  flattened,  as  in  B. 

D.  The  first  test  held  well  because  the  edges  were  sharp,  then  the  holding- 
power  fell  off  till  they  had  become  flattened  in  a  manner  similar  to  B,  when 
the  holding-power  increased  again. 

Tests  of  the  Holding-power  of  Keys.  (Lanza.)— The  load 
was  applied  as  in  the  tests  of  set-screws,  the  shaft  being  firmly  keyed  to  the 
holders.  The  load  required  at  the  rim  of  the  pulley  to  shear  the  keys  was 
determined,  and  this,  multiplied  by  a  suitable  constant,  determined  in  a  sim- 
ilar way  to  that  used  in  the  case  of  set-screws,  gives  us  the  shearing  strength 
per  square  inch  of  the  keys. 

The  keys  tested  were  of  eight  kinds,  denoted,  respectively,  by  the  letters 
A,  B,  C,  D,  E,  F,  G  and  H,  and  the  results  were  as  follows  :  A,  B,  D  and  F, 
each  4  tests;  E,  3  tests  ;  C,  G,  and  H,  each  2  tests. 

A,  Norway  iron,  2"  X  H"  X  15/32",  40,184  to   47,760 Ibs.;  average,  42,726. 

B,  refined  iron,  2"  X  J4"  X  15/32",  36,482  lt    39,254;  "         38,059. 

C,  tool  steel,  1"  X  W  X  15/32",  '  91,344  &  100,056. 

D,  machinery  steel,  2"  X  V\"  X  15/32",  64,630  to   70,186;  "         66,875. 

E,  Norway  iron,  1^"  X  %"  X  7/16",  36,850  "    37,222;  "         37,036. 

F,  cast-iron,  2"  X  W  X  15/3.2",  30,278  "    36,944;  "         33,034. 

G,  cast-iron,  W  X  %"  X  7/16",  37,222  &    38,700. 
H,  cast-iron,  1"  X  J4"  X  7/16",  29,814  &    38,978. 

In  A  and  B  some  crushing  took  place  before  shearing.  In  E,  the  keys  be* 
ing  only  7/16  in.  deep,  tipped  slightly  in  the  key-way.  Ill  H,  in  the  first  test, 
there  was  a  defect  in  the  key-way  of  the  pulley. 


DYNAMOMETERS. 

Dynamometers  are  instruments  used  for  measuring  power.  They  are  of 
several  classes,  as :  1.  Traction  dynamometers,  used  for  determining  the 
power  required  to  pull  a  car  or  other  vehicle,  or  a  plough  or  harrow. 
2.  Brake  or  absorption  dynamometers,  in  which  the  power  of  a  rotating 
shaft  or  wheel  is  absorbed  or  converted  into  heat  by  the  friction  of  a  brake; 
and,  3.  Transmission  dynamometers,  in  which  the  power  in  a  rotating  shaft 
is  measured  during  its  transmission  through  a  belt  or  other  connection  to 
another  shaft,  without  being  absorbed. 

Traction  Dynamometers  generally  contain  two  principal  parts: 
(1)  A  spring  or  series  of  springs,  through  which  the  pull  is  exerted,  the  exten- 
sion of  the  spring  measuring  the  amount  of  the  pulling  force;  and  (2)  a  paper- 
covered  drum,  rotated  either  at  a  uniform  speed  by  clockwork,  or  at  a  speed 
proportional  to  the  speed  of  the  traction,  through  gearing,  on  which  the  ex- 
tension of  the  spring  is  registered  by  a  pencil.  From  the  average  height  of 
the  diagram  drawn  by  the  pencil  above  the  zero-line  the  average  pulling 
force  in  pounds  is  obtained,  and  this  multiplied  by  the  distance  traversed, 
in  feet,  gives  the  work  done,  in  foot-pounds.  The  product  divided  by  the 
time  in  minutes  and  by  33,000  gives  the  horse-power. 

The  Prony  brake  is  the  typical  form  of  absorption  dynamometer. 
(See  Fig.  167,  from  Fiather  on  Dynamometers  and  the  Measurement  of 
Power.) 

Primarily  this  consists  of  a  lever  connected  to  a  revolving  shaft  or  pulley 
in  such  a  manner  that  the  friction  induced  between  the  surfaces  in  contact 
will  tend  to  rotate  the  arm  in  the  direction  in  which  the  shaft  revolves.  This 
rotation  is  counterbalanced  by  weights  P,  hung  in  the  scale-pan  at  the  end 
of  the  lever.  In  order  to  measure  the  power  for  a  given  number  of  revolu- 
tions of  pulley,  we  add  weights  to  the  scale-pan  and  screw  up  on  bolts  bb, 
until  the  friction  induced  balances  the  weights  and  the  lever  is  maintained 


ALDEK   ABSORPTIOtf-DtNAMOMETfcft.          9t9 

in  its  horizontal  position  while  the  revolutions  of  shaft  per  minute  remain 
constant. 

For  stiiall  powers  the  beam  is  generally  omitted — the  friction  being  mea- 
sured by  weighting  a  band  or  strap  thrown  over  the  pulley.  Ropes  or  cords 
are  often  used  for  the  same  purpose. 

Instead  of  hanging  weights  in  a  scale-pan,  as  in  Fig.  167,  the  friction  may  be 
weighed  on  a  platform-scale;  in  this 
case,  the  direction  of  rotation  being 
the  same,  the  lever-arm  will  be  on  the 
opposite  side  of  the  shaft. 

In  a  modification  of  this  brake,  the 
brake- wheel  is  keyed  to  the  shaft, 
and  its  rim  is  provided  with  inner 
flanges  which  form  an  annular  trough 
for  the  retention  of  water  to  keep  the 
pulley  from  heating.  A  small  stream 
of  water  constantly  discharges  into 
the  trough  and  revolves  with  the  PIQ  ic* 

pulley— the  centrifugal  force  of  the 

particles  of  water  overcoming  the  action  of  gravity;  a  waste-pipe  with  its 
end  flattened  is  so  placed  in  the  trough  that  it  acts  as  a  scoop,  and  removes 
all  surplus  water.  The  brake  consists  of  a  flexible  strap  to  which  are  fitted 
blocks  of  wood  forming  the  rubbing-surface;  the  ends  of  the  strap  are  con- 
nected by  an  adjustable  bolt-clamp,  by  means  of  which  any  desired  tension 
may  be  obtained. 

The  horse-power  or  work  of  the  shaft  is  determined  from  the  following: 

Let  W  —  work  of  shaft,  equals  power  absorbed,  per  minute; 

P  —  unbalanced  pressure  or  weight  in  pounds,  acting  on  lever-arm 

at  distance  L; 

L  =  length  of  lever-arm  in  feet  from  centre  of  shaft ; 
V  =  velocity  of  a  point  in  feet  per  minute  at  distance  I/,  if  arm  were 

allowed  to  rotate  at  the  speed  of  the  shaft; 
N  —  number  of  revolutions  per  minute; 
H.P.  =  horse-power. 

Then  will  W  =  PV  =  2*LNP. 

Since  H.P.  =  PP-f-  33,000,  we  have  H.P.  =  2irLN£  -s-  33,000. 

33  7VP 

If  L  =  — ,  we  obtain  H.P.  =  -^-.   33  +  2*  is  practically  5  ft.  3  in.,  a  value 

&tr  1000 

often  used  in  practice  for  the  length  of  arm. 

If  the  rubbing-surface  be  too  small,  the  resulting  friction  will  show  great 
irregularity— probably  on  account  of  insufficient  lubrication— the  jaws  be- 
<ng  allowed  to  seize  the  pulley,  thus  producing  shocks  and  sudden  vibra- 
tions of  the  lever-arm. 

Soft  woods,  such  as  bass,  plane-tree,  beech,  poplar,  or  maple  are  all  to  be 
preferred  to  the  harder  woods  for  brake-blocks.  The  rubbing^surface  should 
be  well  lubricated  with  a  heavy  grease. 

Tne  Alden  Absorption-dynamometer.  (G.  I.  Alden,  Trans. 
A.  S.  M.  E.,  vol.  xi.  958;  also  xii,  TOO  and  xiii.  429.)—  This  dynamometer  is  a 
friction-brake,  which  is  capable  in  quite  moderate  sizes  of  absorbing  large 
powers  with  unusual  steadiness  and  complete  regulation.  A  smooth  cast- 
iron  disk  is  keyed  on  the  rotating  shaft.  This  is  enclosed  in  a  cast-iron 
shell,  formed  of  two  disks  and  a  ring  at  their  circumference,  which  is  free 
to  revolve  on  the  shaft.  To  the  interior  of  each  of  the  sides  of  the  shell  is 
fitted  a  copper  plate,  enclosing  between  itself  and  the  side  a  water-tight 
space.  Water  under  pressure  from  the  city  pipes  is  admitted  into  each  of 
these  spaces,  forcing  the  copper  plate  against  the  central  disk.  The 
chamber  enclosing  the  disk  is  filled  with  oil.  To  the  outer  shell  is  fixed  a 
weighted  arm,  which  resists  the  tendency  of  the  shell  to  rotate  with  the 
shaft,  caused  by  the  friction  of  the  plates  against  the  central  disk.  Four 
brakes  of  this  type,  56  in.  diam.,  were  used  in  testing  the  experimental 
locomotive  at  Purdue  University  (Trans.  A.  S.  M.E.,  xiii.  429).  Each  was 
designed  for  a  maximum  moment  of  10,500  foot-pounds  with  a  water-press- 
ure of  40  Ibs.  per  sq.  in. 

The  area  in  effective  contact  with  the  copper  plates  on  either  side  is  rep- 
resented by  an  annular  surface  having  its  outer  radius  equal  to  28  inches, 
and  its  inner  radius  equal  to  10  inches.  The  apparent  coefficient  of  friction 
between  the  plates  and  the  disk  wa 


980 


DYKAMOMETti&S. 


W.  W.  Beaumont  (Proc.  Inst.  C.  E.  1889)  has  deduced  a  formula  by  means 
of  which  the  relative  capacity  of  brakes  can  be  compared,  judging  from  the 
amount  of  horse-power  ascertained  by  their  use. 

If  W—  width  of  rubbing -surf  ace  on  brake-wheel  in  inches;  V  —  vel.  of 
point  on  circum.  of  wheel  in  feet  per  minute;  K  —  coefficient;  then 

K  =  WV  -H  H.P. 

Capacity  of  Friction-brakes.— Prof.  Flather  obtains  the  values 
of  K  given  in  the  last  column  of  the  subjoined  table  : 


Horse-power. 

1 

PQ 

^ 

*! 
« 

Brake- 
pulley. 

Length  of  Arm. 

Design  of  Brake. 

Value  of  K. 

28 

,J=5 
$>  O 

&~ 

~7~ 
7 
7 
10.5 
10.5 
10 
12 
24 
24 

24 
13 

1  Diameter, 

it  »f».  -lUTCssDworcncjtm  in  feet. 

21 
19 
20 
40 
33 
150 
24 
180 
475 
125| 
250  f 
40  \ 
125  f 

150 
148.5 
146 
180 
150 
150 
142 
100 
76.2 
2901 
250  f 
322  / 
290  f 

33" 
33.38" 
32.19" 
32" 
32" 

38.  3i" 
126.1" 
191" 

63" 
27%" 

Royal  Ag.  SOc.,  compensating 

785 
858 
802 
741 
749 
282 
1385 
209 
84.7 

465 

847 

McLaren,  compensating  

'  '          water-cooled  and  comp  
Garrett,                                       '     

Schoenheyder,  water-cooled... 

Balk.     .   . 

Gately  &  Kletsch,  water-cooled 

Webber,  water-cooled  

Westinghouse   water-cooled 

The  above  calculations  for  eleven  brakes  give  values  of  K  varying  from 
84.7  to  1385  for  actual  horse-powers  tested,  the  average  being  K  =  655. 

Instead  of  assuming  an  average  coefficient,  Prof.  Flather  proposes  the 
following : 

Water-cooled  brake,  non-compensating,  K  =  400;  W  —  400  H.P.  -*-  V. 

Water-cooled  brake,  compensating,  K  =  750;  W  =  750  H.P.  -*-  V. 

Non-cooling  brake,  with  or  without  compensating  device,  K  =  900; 
W  =  900  H.P.  -i-  V. 

Transmission  Dynamometers  are  of  various  forms,  as  the 
Batchelder  dynamometer,  in  which  the  power  is  transmitted  through  a 
"  train-arm  "  of  bevel  gearing,  with  its  modifications,  as  the  one  described 
by  the  author  in  Trans.  A.  I.  M.  E.,  viii.  177,  and  the  one  described  by 
Samuel  Webber  in  Trans.  A.  S.  M.  E.,  x.  514;  belt  dynamometers,  as  the 
Tatham;  the  Van  Winkle  dynamometer,  in  which  the  power  is  transmitted 
from  a  revolving  shaft  to  another  in  line  with  it,  the  two  almost  touching, 
through  the  medium  of  coiled  springs  fastened  to  arms  or  disks  keyed  to 
the  shafts;  the  Brackett  and  the  Webb  cradle  dynamometers,  used  for 
measuring  the  power  required  to  run  dynamo-electric  machines.  Descrip- 
tions of  the  four  last  named  are  given  in  Flather  on  Dynamometers. 

Much  information  on  various  forms  of  dynamometers  will  be  found  in 
Trans.  A.  S.  M.  E.,  vol.  vii.  to  xv.,  inclusive,  indexed  under  Dynamometers. 


OPERATIONS   OF   A   REFR1GERATIXG-MACHINE.      981 


ICE-MAKING  OB  REFRIGERATING  MACHINES. 

References.— An  elaborate  discussion  of  the  thermodynamic  theory  of 
the  action  of  the  various  fluids  used  in  the  production  of  cold  was  published  by 
M.  Ledotix  in  theAnnales  dex  Mines,  and  translated  in  Van  Nostrand's  Maga- 
zine in  1879.  This  work,  revised  and  additions  made  in  the  light  of  recent  ex- 
perience by  Professors  Denton,  Jacobus,  and  Riesenberger,  was  reprinted  in 
1893.  (Van  Nostrand's  Science  Series,  No.  46.)  The  work  is  largely  mathe- 
matical, but  it  also  contains  much  information  of  immediate  practical  value, 
from  which  some  of  the  matter  given  below  is  taken.  Other  references  are 


11  and  Dec.  4,  1891 ;  May  6  and  July  8,  1892.  For  properties  of  Ammonia  and 
Sulphur  Dioxide,  see  papers  by  Professors  Wood  and  Jacobus,  Trans.  A.  S. 
M.  E.,  vols.  x.  and  xii. 

For  illustrated  articles  describing  refrigerating-machines,  see  Am.  Mach., 
May  29  and  June  26.  1890,  and  Mfrs.  Record,  Oct.  ?,  1892;  also  catalogues  of 
builders,  as  Frick  &  Co.,  Waynesboro,  Pa.;  De  La  Vergne Ref rigerating-ma- 
chine  Co  ,  New  York;  and  others. 

Operations  of  a  Refrlgerating-maehine.— Apparatus  designed 
for  refrigerating  is  based  upon  the  following  series  of  operations: 

Compress  a  gas  or  vapor  by  means  of  some  external  force,  then  relieve  it 
of  its  heat  so  as  to  diminish  ifs  volume;  next,  cause  this  compressed  gas  or 
vapor  to  expand  so  as  to  produce  mechanical  work,  and  thus  lower  its  tem- 
perature. The  absorption  of  heat  at  this  stage  by  the  gas,  in  resuming  its 
original  condition,  constitutes  the  refrigerating  effect  of  the  apparatus. 

A  refrigerating-macbine  is  a  heat-engine  reversed. 

From  this  similarity  between  heat-motors  and  freezing-machines  it  results 
that  all  the  equations  deduced  from  the  mechanical  theory  of  heat  to  deter- 
mine the  performance  of  the  first,  apply  equally  to  the  second. 

The  efficiency  depends  upon  the  difference  between  the  extremes  of  tem- 
perature. 

The  useful  effect  of  a  refrigerating-machine  depends  upon  the  ratio 
between  the  heat-units  eliminated  and  the  work  expended  in  compressing 
and  expanding. 

This  result  is  independent  of  the  nature  of  the  body  employed. 

Unlike  the  heat-motors,  the  freezing-machine  possesses  the  greatest  effi- 
ciency when  the  range  of  temperature  is  small,  and  when  the  final  tempera- 
ture is  elevated. 

If  the  temperatures  are  the  same,  there  is  no  theoretical  advantage  in  em- 
ploying a  gas  rather  than  a  vapor  in  order  to  produce  cold. 

The  choice  of  the  intermediate  body  would  be  determined  by  practical 
considerations  based  on  the  physical  characteristics  of  the  body,  such  as  the 
greater  or  less  facility  for  manipulating  it,  the  extreme  pressures  required 
for  the  best  effects,  etc. 

Air  offers  the  double  advantage  that  it  is  everywhere  obtainable,  and  that 
we  can  vary  at  will  the  higher  pressures,  independent  of  the  temperature  of 
the  refrigerant.  But  to  produce  a  given  useful  effect  the  apparatus  must 
be  of  larger  dimensions  than  that  required  by  liquefiable  vapors. 

The  maximum  pressure  is  determined  by  the  temperature  of  the  con- 
denser and  the  nature  of  the  volatile  liquid:  this  pressure  is  often  very  high. 

When  a  change  of  volume  of  a  saturated  vapor  is  made  under  constant 
pressure,  the  temperature  remains  constant.  The  addition  or  subtraction  of 
heat,  which  produces  the  change  of  volume,  is  represented  by  an  increase  or 
a  diminution  of  the  quantity  of  liquid  mixed  with  the  vapor. 

On  the  other  hand,  when  Vapors,  even  if  saturated,  are  no  longer  in  con- 
tact with  their  liquids,  and  receive  an  addition  of  heat  either  through  com- 
pression by  a  mechanical  force,  or  from  some  external  source  of  heat,  they 
comport  themselves  nearly  in  the  same  way  as  permanent  gases,  and  be- 
come superheated. 

It  results  from  this  property,  that  refrigerating-machines  using  a  liquefi- 
able gas  will  afford  results  differing  according  to  the  method  of  working, 


982       ICE-MAKING    OR   REFRIGERATING    MACHINES. 


and  depending  upon  the  state  of  the  gas,  whether  it  remains  constantly  sat- 
urated, or  is  superheated  during  a  part  of  the  cycle  of  working. 

The  temperature  of  the  condenser  is  determined  by  local  conditions.  The 
interior  \\ill  exceed  by  9°  to  18°  the  temperature  of  the  water  furnished  to 
the  exterior.  This  latter  will  vary  from  about  52°  F.,  the  temperature  of 
water  from  considerable  depth  below  the  surface,  to  about  95°  F.,  the  tem- 
perature of  surface-water  in  hot  climates.  The  volatile  liquid  employed  in 
the  machine  ought  not  at  this  temperature  to  have  a  tension  above  that 
which  can  be  readily  managed  by  the  apparatus. 

On  the  other  hand,  if  the  tension  of  the  gas  at  the  minimum  temperature 
is  too  low,  it  becomes  necessary  to  give  to  the  compression-cylinder  large 
dimensions,  in  order  that  the  weight  of  vapor  compressed  by  a  single  stroke 
of  the  piston  shall  be  sufficient  to  produce  a  notably  useful  effect. 

These  two  conditions,  to  which  may  be  added  others,  such  as  those  de- 
pending upon  the  greater  or  less  facility  of  obtaining  the  liquid,  upon  the 
dangers  incurred  in  its  use,  either  from  its  inflammability  or  unhealthful- 
ness,  and  finally  upon  its  action  upon  the  metals,  limit  the  choice  to  a  small 
number  of  substances. 

The  gases  or  vapors  generally  available  are:  sulphuric  ether,  sulphurous 
oxide,  ammonia,  methylic  ether,  and  carbonic  acid. 

The  following  table,  derived  from  Regnault,  shows  the  tensions  of  the 
vapors  of  these  substances  at  different  temperatures  between  —  22°  and  4- 
104°. 

Pressures  and  Boiling-points  of  Liquids  available  for 
Use  in  Itefrigerating-machines. 


Temp,  of 
Ebullition. 

Tension  of  Vapor,  in  Ibs.  per  sq.  in.,  above  Zero. 

Deg. 
Fahr. 

Sul- 
phuric 
Ether. 

Sulphur 
Dioxide. 

Ammonia. 

Methylic 
Ether. 

Carbonic 
Acid. 

Pictet 
Fluid. 

—  40 

10  22 

—  31 

13.23 

—  22 

5  56 

16  95 

11  15 

13 

7  23 

21  51 

13  85 

251  6 

-    4 

1.30 

9.27 

27.04 

17.06 

292.9 

13.5 

5 

1.70 

11.76 

33.67 

20.84 

340.1 

16.2 

14 

2.19 

14.75 

41.58 

25.27 

393.4 

19.3 

23 

2.79 

18.31 

50.91 

30.41 

453.4 

,°2.9 

32 

3.55 

22.53 

61.85 

36.34 

520.4 

26.9 

41 

4.45 

27.48 

74.55 

43.13 

594.8 

31.2 

50 

5.54 

33.26 

89.21 

50.84 

676.9 

36.2 

59 

6.84 

39.93 

105.99 

59  56 

766.9 

41.7 

68 

8.38 

47.62 

1-25.08 

69.35 

864.9 

48.1 

77 

10.19 

56.39 

146.64 

80.28 

971.1 

55.6 

86 

12.31 

66.37 

170.83 

92.41 

1085.6 

64.  1 

95 

14  76 

77.64 

197  83 

1207  9 

73  2 

104 

17.59 

90.32 

227.76 

1338.2 

82.9 

The  table  shows  that  the  use  of  ether  does  not  readily  lead  to  the  produc- 
tion of  low  temperatures,  because  its  pressure  becomes  then  very  feeble. 

Ammonia,  on  the  contrary,  is  well  adapted  to  the  production  of  low  tem- 
peratures. 

Methylic  ether  yields  low  temperatures  without  attaining  too  great  pres- 
sures at  the  temperature  of  the  condenser.  Sulphur  dioxide  readily  affords 
temperatures  of  —  14  to  —  5,  while  its  pressure  is  only  3  to  4  atmospheres 
at  the  ordinary  temperature  of  the  condenser.  These  latter  substances  then 
lend  themselves  conveniently  for  the  production  of  cold  by  means  of 
mechanical  force. 

The  "Pictet  fluid"  is  a  mixture  of  97$  sulphur  dioxide  and  3$  carbonic 
acid.  At  atmospheric  pressure  it  affords  a  temperature  14°  lower  than 
sulphur  dioxide. 

Carbonic  acid  is  as  yet  (1895)  in  use  but  to  a  limited  extent,  but  the  rela- 
tively greater  compactness  of  compressor  that  it  requires,  and  its  inoffensive 


THE    AMMONIA    ABSORPTION-MACHINE.  983 

character,  are  leading  to  its  recommendation  for  service  on  shipboard,  where 
economy  of  space  is  important. 

Certain  ammonia  plants  are  operated  with  a  surplus  of  liquid  present  dur- 
ing compression,  so  that  superheating  is  prevented.  This  practice  is  known 
as  the  "  cold  system  "  of  compression. 

Nothing  definite  is  known  regarding  the  application  of  methylic  ether  or 
of  the  petroleum  product  chymogene  in  practical  refrigerating  service.  The 
inflammability  of  the  latter  and  the  cumbrousness  of  the  compressor 
required  are  objections  to  its  use. 

"  Ice-melting  Effect."— It  is  agreed  that  the  term  "ice-melting 
effect1'  means  the  cold  produced  in  an  insulated  bath  of  brine,  on  the  as- 
sumption that  each  142.2  B.T.U.*  represents  one  pound  of  ice,  this  being  the 
latent  heat  of  fusion  of  ice,  or  the  heat  required  to  melt  a  pound  of  ice  at 
32°  to  water  at  the  same  temperature. 

The  performance  of  a  machine,  expressed  in  pounds  or  tons  of  "  ice-melt- 
ing capacity,"  does  not  mean  that  the  refrigerating-macbine  would  make 
the  same  amount  of  actual  ice,  but  that  the  cold  produced  is  equivalent  to 
the  effect  of  the  melting  of  ice  at  32°  to  water  of  the  same  temperature. 

In  making  artificial  ice  the  water  frozen  is  generally  about  70°  F.  when  sub- 
mitted to  the  refrigerating  effect  of  a  machine ;  second,  the  ice  is  chilled  from 
1'2°  to  20°  below  its  freezing-point;  third,  there  is  a  dissipation  of  cold,  from 
the  exposure  of  the  brine  tank  and  the  manipulation  of  the  ice-cans:  there- 
fore the  weight  of  actual  ice  made,  multiplied  by  its  latent  heat  of  fusion, 
142.2  thermal  units,  represents  only  about  three  fourths  of  the  cold  produced 
in  the  brine  by  the  refrigerating  fluid  per  I.H.P.  of  the  engine  driving  the 
compressing-pumps.  Again,  there  is  considerable  fuel  consumed  to  operate 
the  brine-circulating  pump,  the  condensing-water  and  feed-pumps,  and  to 
reboil,  or  purify,  the  condensed  steam  from  which  the  ice  is  frozen.  This 
fuel,  together  with  that  wasted  in  leakage  and  drip  water,  amounts  to  about 
one  half  that  required  to  drive  the  main  steam-engine.  Hence  the  pounds 
of  actual  ice  manufactured  from  distilled  water  is  just  about  half  the  equiv- 
alent of  the  refrigerating  effect  produced  in  the  brine  per  indicated  horse- 
power of  the  steam-cylinders. 

When  ice  is  made  directly  from  natural  water  by  means  of  the  "plate 
system,1'  about  half  of  the  fuel,  used  with  distilled  water,  is  saved  by  avoid- 
ing the  reboil  ing,  and  using  steam  expansively  in  a  compound  engine. 

Ether-machines5  used  in  India,  are  said  to  have  produced  about  6 
Ibs.  of  actual  ice  per  pound  of  fuel  consumed. 

The  ether  machine  is  obsolete,  because  the  density  of  the  vapor  of  ether, 
at  the  necessary  working-pressure,  requires  that  the  compressing-cylinder 
shall  be  about  6  times  larger  than  for  sulphur  dioxide,  and  17  times  larger 
than  for  ammonia. 

Air-machines  require  about  1.2  times  greater  capacity  of  compress- 
ing cylinder,  and  are,  as  a  whole,  more  cumbersome  than  ether  machines, 
but  they  remain  in  use  on  ship-board.  In  using  air  the  expansion  must  take 
place  in  a  cylinder  doing  work,  instead  of  through  a  simple  expansion-cock 
which  is  used  with  vapor  machines.  The  work  done  in  the  expansion-cylin- 
der is  utilized  in  assisting  the  compressor. 

Ammonia  Compression-machines.— "CoZd  "  vs.  "Dry  "  Systems 
of  Compression. — In  the  "  cold  "  system  or  ''humid1'  system  some  of  the 
ammonia  entering  the  compression-cylinder  is  liquid,  so  that  the  heat  de- 
veloped in  the  cylinder  is  absorbed  by  the  liquid  and  the  temperature  of  the 
ammonia  thereby  confined  to  the  boiling-point  due  to  the  condenser-pres- 
sure. No  jacket  is  therefore  required  about  the  cylinder. 

In  the  "  dry'1  or  "  hot"  system  all  ammonia  entering  the  compressor  is 
gaseous,  and  the  temperature  becomes  by  compression  several  hundred  de- 
grees greater  than  the  boiling-point  due  to  the  condenser-pressure.  A  water- 
jacket  is  therefore  necessary  to  permit  the  cylinder  to  be  properly  lubri- 
cated. 

Relative  Performance  of  Ammonia  Compression-  and 
Absorption-machines,  assuming  no  Water  to  DC  En- 
trained \vith  the  Ammonia-gas  in  the  Condenser.  (Deuton 
and  Jacobus,  Trans.  A.  S.  M.  E.,  xiii.)— It  is  assumed  in  the  calculation  for 
both  machines  that  1  Ib.  of  coal  imparts  10,000  B.T.U.  to  the  boiler.  The 

*  The  latent  heat  of  fusion  of  ice  is  144  thermal  units  (Phil.  Mag.,  1871, 
xli  182);  but  it  is  customary  to  use  142.  (Prof.  Wood.  Trans.  A.  S.  M.  E., 
yi.  834.) 


984       ICE-MAKING   OR   REFRIGERATING   MACHINES. 


condensed  steam  from  the  generator  of  the  absorption-machine  is  assumed 
to  be  returned  to  the  boiler  at  the  temperature  of  the  steam  entering  the 
generator.  The  engine  of  the  compression-machine  is  assumed  to  exhaust 
through  a  feed-water  heater  that  heats  the  feed-water  to  21 2°  F.  The  engine 
is  assumed  to  consume  26*4  Ibs.  of  water  per  hour  per  horse-power.  The 
figures  for  the  compression- machine  include  the  effect  of  friction,  which  is 
taken  at  15%  of  the  net  work  of  compression. 


Condenser. 

Refrigerat- 
ing Coils. 

fe* 

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per  Ib.  of  Coal. 

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969 

59.0 

106.0 

5 

33.7 

59.0 

39.8 

74.6 

38.3 

33.9 

967 

59.0 

106.0 

5 

33.7 

130.0 

39.8 

74.6 

39.8 

35.1 

931 

59.0 

106.0 

-22 

16.9 

59.0 

23  4 

43.9 

36.3 

31.5 

1000 

86.0 

170.8 

5 

33.7 

86.0 

25.0 

46.9 

35.4 

28.6 

988 

86.0 

170.8 

5 

33.7 

130.0 

25.0 

46.9 

36.2 

29.2 

966 

86.0 

170.8 

-22 

16.9 

86.0 

16.5 

30.8 

33.3 

26.5 

1025 

86.0 

170.8 

-22 

16.9 

130.0 

16.5 

30.8 

34.1 

27.0 

1002 

104  0 

227.7 

5 

33.7 

104.0 

19.6 

36.8 

33.4 

25.1 

1002 

104.0 

227.7 

-22 

16.9 

104.0 

13.5 

25.3 

31.4 

23.4 

1041 

The  A  in  tn  on  ia  Absorption-machine  comprises  a  generator 
which  contains  a  concentrated  solution  of  ammonia  in  water;  this  gener- 
ator is  heated  either  directly  by  a  fire,  or  indirectly  by  pipes  leading  from  a 
steam-boiler.  The  condenser  communicates  with  the  upper  part  of  the  gen- 
erator by  a  tube;  it  is  cooled  externally  by  a  current  of  cold  water.  The 
cooler  or  brine-tank  is  so  constructed  as  ro  utilize  the  cold  produced;  the  up- 
per part  of  it  is  in  communication  with  the  lower  part  of  the  condenser. 

An  absorption-chamber  is  filled  with  a  weak  solution  of  ammonia;  a  tube 
puts  this  chamber  in  communication  with  the  cooling-tank. 

The  absorption-chamber  communicates  with  the  boiler  by  two  tubes:  one 
leads  from  the  bottom  of  the  generator  to  the  top  of  the  chamber,  the  other 
leads  from  the  bottom  of  the  chamber  to  the  top  of  the  generator.  Upon 
the  latter  is  mounted  a  pump,  to  force  the  liquid  from  the  absorption-cham- 
ber, where  the  pressure  is  maintained  at  about  one  atmosphere,  into  the  gen- 
erator, where  the  pressure  is  from  8  to  12  atmospheres. 

To  work  the  apparatus  the  ammonia  solution  in  the  generator  is  first 
heated.  This  releases  the  gas  from  the  solution,  and  the  pressure  rises. 
When  it  reaches  the  tension  of  the  saturated  gas  at  the  temperature  of  the 
condenser  there  is  a  liquefaction  of  the  gas,  and  also  of  a  small  amount  of 
steam.  By  means  of  a  cock  the  flow  of  the  liquefied  gas  into  the  refrigerat- 
ing coils  contained  in  the  cooler  is  regulated.  It  is  here  vaporized  by  ab- 
sorbing the  heat  from  the  substance  placed  there  to  be  cooled.  As  fast  as  it 
is  vaporized  it  is  absorbed  by  the  weak  solution  in  the  absorbing-chamber. 

Under  the  influence  of  the  heat  in  the  boiler  the  solution  is  unequally  sat- 
urated, the  stronger  solution  being  uppermost. 

The  weaker  portion  is  conveyed  by  the  pipe  entering  the  top  of  the  absorb- 
ing-chamber, the  flow  being  regulated  by  a  cock,  while  the  pump  sends  an 
equal  quantity  of  strong  solution  from  the  chamber  back  to  the  boiler. 

*  5$  of  water  entrained  in  the  ammonia  will  lower  the  economy  of  the  ab- 
sorption-machine about  15$  to  20$  below  the  figures  given  in  the  table, 


SULPHUR-DIOXIDE   MACHINES. 


985 


The  working  of  the  apparatus  depends  upon  the  adjustment  and  regula- 
tion of  the  flow  of  the  gas  and  liquid;  by  these  means  the  pressure  is  varied, 
and  consequently  the  temperature  in  the  cooler  may  be  controlled. 

The  working  is  similar  to  that  of  compression-machines.  The  absorption- 
chamber  fills  the  office  of  aspirator,  and  the  generator  plays  the  part  of 
compressor. 

The  mechanical  force  producing  exhaustion  is  here  replaced  by  the  affinity 
of  water  for  ammonia  gas;  and  the  mechanical  force  required  for  compres- 
sion is  replaced  by  the  heat  which  severs  this  affinity  and  sets  the  gas  at 
liberty. 

(For  discussion  of  the  efficiency  of  the  absorption  system,  see  Ledoux's 
work;  paper  by  Prof.  Linde,  and  discussion  on  the  same  by  Prof.  Jacobus, 
Trans.  A.  S.  M.  E.,  xiv.  1416,  1436;  and  papers  by  Denton  and  Jacobus 
Trans.  A.  S.  M.  E.  x.  792;  xiii.  507. 

Sulphur-Dioxide  Machines.— Results  of  theoretical  calculations 
are  given  in  a  table  by  Ledoux  showing  an  ice-melting  capacity  per 
hour  per  horse-power  ranging  from  134  to  63  Ibs.,  and  per  pound  of  coal 
ranging  from  44.7  to  21.1  Ibs.,  as  the  temperature  corresponding  to  the 
pressure  of  the  vapor  in  the  condenser  rises  from.  59°  to  104°  F.  The  theo- 
retical results  do  not  represent  the  actual.  It  is  necessary  to  take  into  ac- 
count the  loss  occasioned  by  the  pipes,  the  waste  spaces  in  the  cylinder,  loss 
of  time  in  opening  of  the  valves,  the  leakage  around  the  piston  and  valves, 
the  reheating  by  the  external  air,  and  finally,  when  the  ice  is  being  made, 
the  quantity  of  the  ice  melted  in  removing  the  blocks  from  their  moulds. 
Manufacturers  estimate  that  practically  the  sulphur-dioxide  apparatus  using 
water  at  55°  or  60°  F.  produces  56  Ibs.  of  ice,  or  about  1 0,000  heat-units,  per 
hour  per  horse-power,  measured  on  the  driving-shaft,  which  is  about  55$  of 
the  theoretical  useful  effect.  In  the  commercial  manufacture  of  ice  about 
7  Ibs.  are  produced  per  pound  of  coal.  This  includes  the  fuel  used  for  re- 
boiling  the  water,  which,  together  with  that  wasted  by  the  pumps  and  lost 
oy  radiation,  amounts  to  a  considerable  portion  of  that  used  by  the  engine. 

Prof.  Denton  says  concerning  Ledoux's  theoretical  results:  The  figures 
given  are  higher  than  those  obtained  in  practice,  because  the  effect  of 
superheating  of  the  gas  during  admission  to  the  cylinder  is  not  considered. 
This  superheating  may  cause  an  increase  of  work  of  about  25$.  There  are 
other  losses  due  to  superheating  the  gas  at  the  brine- tank,  and  in  the  pipe 
leading  from  the  brine-tank  to  the  compressor,  so  that  in  actual  practice  a 
sulphur-dioxide  machine,  working  under  the  conditions  of  an  absolute 
'pressure  in  the  condenser  of  56  Ibs.  per  sq.  in.  and  the  corresponding  tem- 
perature of  77°  F.,  will  give  about  22  Ibs.  of  ice-melting  capacity  per  pound 
of  coal,  which  is  about  60$  of  the  theoretical  amount  neglecting  friction,  or 
70$  including  friction.  The  following  tests,  selected  from  those  made  by 
Prof.  Schroter  on  a  Pictet  ice-machine  having  a  compression-cylinder  11.3 
In.  bore  and  24.4  in.  stroke,  show  the  relation  between  the  theoretical  and 
actual  ice-melting  capacity. 


No.  of 
Test. 

1  Tern  p.  in  degrees  Fahr. 
corresponding  to 
pressure  of  vapor. 

Ice-melting  capacity  per  pound  of  coal, 
assuming  3  Ibs.  per  hour  per  H.P. 

Condenser. 

Suction. 

Theoretical 
friction 
included.* 

Actual. 

Per  cent  loss  due  to 
cylinder  super- 
h  eating,  or  differ- 
ence  between 
cols.  4  and  5. 

tl 
12 
13 

14 

76  !2 
75.2 

80.6 

28.5 
14.4 

-2.5 
-15.9 

41.3 
31.2 
23.0 
16.6 

33.1 
24.1 
17.5 
10.1 

19.9 
22.8 
23.9 
39.2 

The  Refrigerating  Coils  of  a  Pi-ctet  ice-macfiine  described  l.y 
Ledoux  had  79  sq.  ft.  of  surface  for  each  100.000  theoretic  negative  heat-units 
produced  per  hour.  The  temperature  corresponding  to  the  pressure  of  the 
dioxide  in  the  coils  is  10.4°  F.,  and  that  of  the  bath  (calcium  chloride  solu- 


*  Friction  taken -at  figure  observed  in  the  test,  which  ranged  from  2?,$  to 
6#  of  the  work  of  the  steam-cylinder. 


086       ICE-MAKIHG   Oil  BEFRiGERATlNG   MACHINES. 


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AMMONIA   COMPRESSION-MACHINES. 


988      ICE-MAKING   OR   REFRIGERATING   MACHINES. 

The  following  is  a  comparison  of  the  theoretical  ice-melting  capacity  of  an 
ammonia  compression  machine  with  that  obtained  in  some  of  Prof. 
Schroter's  tests  on  a  Linde  machine  having  a  compression-cylinder  9.9-in. 
bore  and  16.5  in.  stroke,  and  also  in  tests  by  Prof.  Denton  on  a  machine 
having  two  single-acting  compression  cylinders  12  in.  x  30  in.: 


Temp,  in  Degrees  F. 
Corresponding  to 

Ice-melting  Capacity  per  Ib.  of  Coal, 
assuming  3  Ibs  per  hour  per 

No. 

Pressure  of  Vapor. 

Horse-power. 

of 
Test. 

Condenser. 

Suction. 

Theoretical, 
Frictfon  *  in- 
cluded. 

Actual. 

Per  Cent 
of  Loss  Due  to 
Cylinder 
Superheating. 

&  f  1 

72.3 

26.6 

50.4 

40.6 

19.4 

1  J    2 

70.5 

14.3 

37.6 

30.0 

20.2 

f  1    3 

69.2 

0.5 

29.4 

22.0 

25.2 

&  (  4 

68.5 

-11.8 

22,8 

16.1 

29.4 

§  (24 

84.2 

15.0 

27.4 

24.2 

11.7 

S]26 

82.7 

-  3.2 

21.6 

17.5 

19.0 

||25 

84.6 

-10.8 

18.8 

14.5 

22.9 

Refrigerating  Machines  using  Vapor  of  Water.  (Ledoux.) 
— In  these  machines,  sometimes  called  vacuum  machines,  water,  at  ordi- 
nary temperatures,  is  injected  into,  or  placed  in  connection  with,  a  chamber 
in  which  a  strong  vacuum  is  maintained.  A  portion  of  the  water  vaporizes, 
the  heat  to  cause  the  vaporization  being  supplied  from  the  water  not  vapor- 
ized, so  that  the  latter  is  chilled  or  frozen  to  ice.  If  brine  is  used  instead  of 
pure  water,  its  temperature  may  be  reduced  below  the  freezing-point  of 
water.  The  water  vapor  is  compressed  from,  say,  a  pressure  of  one  tenth 
of  a  pound  per  square  inch  to  one  and  one  half  pounds,  and  discharged  into 
a  condenser.  It  is  then  condensed  and  removed  by  means  of  an  ordinary 
air-pump.  The  principle  of  action  of  such  a  machine  is  the  same  as  that 
of  volatile-vapor  machines. 

A  theoretical  calculation  for  ice-making,  assuming  a  lower  temperature 
of  32°  F.,  a  pressure  in  the  condenser  of  1^  Ibs.  per  square  inch,  and  a  coal 
consumption  of  3  Ibs.  per  I.H.P.  per  hour,  gives  an  ice-melting  effect  of  34.5 
Ibs.  per  pound  of  coal,  neglecting  friction.  Ammonia  for  ice-making  condi- 
tions gives  40.9  Ibs.  The  volume  of  the  compressing  cylinder  is  about  150 
times  the  theoretical  volume  for  an  ammonia  machine  for  these  conditions. 

Relative  Efficiency  of  a  Refrigerating  Machine.  —The  effi- 
ciency of  a  refrigerating  machine  is  sometimes  expressed  as  the  quotient  of 
the  quantity  of  heat  received  by  the  ammonia  from  the  brine,  that  is,  the 
quantity  of  useful  work  done,  divided  by  the  heat  equivalent  of  the  mechan- 
ical work  done  in  the  compressor.  Thus  in  column  1  of  the  table  of  perform- 
ance of  the  75-ton  machine  (page  D98)  the  heat  given  by  the  brine  to  the 
ammonia  per  minute  is  14,776  B.T.U.  The  horse-power  of  the  ammonia  cylin- 
der is  65.7,  and  its  heat  equivalent  =  65.7  X  33,000  -s-  778  =  2786  B.T.U.  Then 
14,776  -T-  2786  =  5.304,  efficiency.  The  apparent  paradox  that  the  efficiency 
is  greater  than  unity,  which  is  impossible  in  any  machine,  is  thus  explained. 
The  working  fluid,  as  ammonia,  receives  heat  from  the  brine  and  rejects 
heat  into  the  condenser.  (If  the  compressor  is  jacketed,  a  portion  is  rejected 
into  the  jacket-water.)  The  heat  rejected  into  the  condenser  is  greater  than 
that  received  from  the  brine;  the  difference  (plus  or  minus  a  small  difference 
radiated  to  or  from  the  atmosphere)  is  heat  received  by  the  ammonia  from 
the  compressor.  The  work  to  be  done  by  the  compressor  is  not  the  mechan- 
ical equivalent  of  the  refrigeration  of  the  brine,  but  only  that  necessary  to 
supply  the  difference  between  the  heat  rejected  by  the  ammonia  into  the  con- 
denser and  that  received  from  the  brine.  If  cooling  water  colder  than  the 
brine  were  available,  the  brine  might  transfer  its  heat  directly  into  the  cool- 
ing water,  and  there  wrould  be  no  need  of  ammonia  or  of  a  compressor;  but 


*  Friction  taken  at  figures  observed  in  the  tests,  which  range  from  \\%  to 
20$  of  the  work  of  the  steam-cylinder. 


EFFICIENCY    OF    KEFKIGERATISG-MACHINES.        989 


since  such  cold  water  is  not  available,  the  brine  rejects  its  heat  into  tho 
colder  ammonia,  and  then  the  compressor  is  required  to  heat  the  ammonia 
to  such  a  temperature  that  it  may  reject  heat  into  the  cooling  water. 

The  efficiency  of  a  refrigerating  plant  referred  to  the  amount  of  fuel 
consumed  is 


i  Pounds  circulated  per  hour  ) 
X  specific  heat  x  range  \ 
of  temperature  \ 


Ice-melting    capacity  )    = 
per  pound  of  fuel.      J 


142.2  X  pounds  of  fuel  used  per  hour. 
The  ice -melting  capacity  is  expressed  as  follows: 


Tons  (of  2000  Ibs.) 
ice-melting  ca- 
pacity per  24  1 


s.)       ) 
i-       y  = 
tiours  ) 


[  24  x  pounds  ) 

X  specific  heat      >-  of  brine  circulated  per  hour. 
X  range  of  temp.  ) 

142.2  X  2000 


The  analogy  between  a  heat-engine  and  a  refrigerating -machine  is  as  fol- 
lows: A  steam-engine  receives  heat  from  the  boiler,  converts  a  part  of  it 


lows:  A  sieaiu  c»  ncciu  uuiii  LUC  uoiier,  converts  a 

into  mechanical  work  in  the  cylinder,  and  throws  away  the  difference  into 
the  condenser.  The  ammonia  in  a  compression  refrigerating  machine  re- 
ceives heat  from  the  brine-tank  or  cold-room,  receives  an  additional  amount 
of  heat  from  the  mechanical  work  done  in  the  compression -cylinder,  and 
throws  away  the  sum  into  the  condenser.  The  efficiency  of  the  steam-engine 
=:  work  done  -*-  heat  received  from  boiler.  The  efficiency  of  the  refrigerat- 
ing-machine  =  heat  received  from  the  brine-tank  or  cold-room  -*-  heat  re- 
quired to  produce  the  work  in  the  compression-cylinder.  In  the  ammonia 


I  I   r 


Compress 


Oo  Brine  Outlet 


209°             239 

^10°                         3° 

Brine  Tank 

Condenser 

82°                           v 

64° 

Ammonia 
Coils 

I  1    • 


Heat  received 
from  compression. 


Warm  Water  from  compression.  Heat  received 

Heat  rejected  from  brine 

DIAGRAM    OF   AMMONIA    COMPRESSION    MACHINE. 


/ 

Ji_ 

f 

Brine  Tank 

Cold 
Room 

^"21° 

272° 

Gener- 
ator 

j? 

1                     ^ 

80°|| 

i  s 

^B=§ 

3     Absorber 

I      I     80  °  "Force  Pump 

DIAGRAM    OF   AMMONIA   ABSORPTION    MACHINE. 


990       ICE- MAKING   OR   REFRIGERATING   MACHINES. 

TEST-TRIADS  OF  REFRIGERATUVG-MACHINES. 

(G.  Linde,  Trans.  A.  S.  M.  E.,  xiv.  1414.) 

The  purpose  of  the  test  is  to  determine  the  ratio  of  consumption  and  pro- 
duction, so  that  there  will  have  to  be  measured  both  the  refrigerative  effect 
and  the  heat  (or  mechanical  work)  consumed,  also  the  cooling  water.  The 
refrigerative  effect  is  the  product  of  the  number  of  heat-units  (Q)  abstracted 

from  the  body  to  be  cooled,  and  the  quotient  c  ~  ;  in  which  Tc  =  abso- 
lute temperature  at  which  heat  is  transmitted  to  the  cooling  water,  and  T  = 
absolute  temperature  at  which  heat  is  taken  from  the  body  to  he  cooled. 

The  determination  of  the  quantity  of  cold  will  be  possible  with  the  proper 
exactness  only  when  the  machine  is  employed  during  the  test  to  refrigerate 
a  liquid;  and  if  the  cold  be  found  from  the  quantity  of  liquid  circulated  per 
unit  of  time,  from  its  range  of  refrigeration,  and  from  its  specific  heat. 
Sufficient  exactness  cannot  be  obtained  by  the  refrigeration  of  a  current  of 
circulating  air,  nor  from  the  manufacture  of  a  certain  quantity  of  ice,  nor 
from  a  calculation  of  the  fluid  circulating  within  the  machine  (for  instance, 
the  quantity  of  ammonia  circulated  by  the  compressor).  Thus  the  refrig- 
eration of  brine  will  generally  form  the  basis  for  tests  making  any  pretension 
to  accuracy.  The  degree  of  refrigeration  should  not  be  greater  than  neces- 
sary for  allowing  the  range  of  temperature  to  be  measured  with  the  neces- 
sary exactness;  a  range  of  temperature  of  from  5°  to  6°  Fahr.  will  suffice. 
The  condense!-  measurements  for  cooling  water  and  its  temperatures  will 
be  possible  with  sufficient  accuracy  only  with  submerged  condensers. 

The  measurement  of  the  quantity  of  brine  circulated,  and  of  the  cooling 
water,  is  usually  effected  by  water-meters  inserted  into  the  conduits.  If  the 
necessary  precautions  are  observed,  this  method  is  admissible.  For  quite 
precise  tests,  however,  the  use  of  two  accurately  gauged  tanks  must  be  ad 
vised,  which  are  alternately  filled  and  emptied. 

To  measure  the  temperatures  of  brine  and  cooling  water  at  the  entrance 
and  exit  of  refrigerator  and  condenser  respectively,  the  employment  of 
specially  constructed  and  frequently  standardized  thermometers  is  indis- 
pensable; no  less  important  is  the  precaution  of  using  at  each  spot  simul- 
taneously two  thermometers,  and  of  changing  the  position  of  one  such 
thermometer  series  from  inlet  to  outlet  (and  vice  versa)  after  the  expiration 
of  one  half  of  the  test,  in  order  that  possible  errors  may  be  compensated. 

It  is  important  to  determine  the  specific  heat  of  the  brine  used  in  each 
instance  for  its  corresponding  temperature  range,  as  small  differences  in  the 
composition  and  the  concentration  may  cause  considerable  variations. 

As  regards  the  measurement  of  consumption,  the  programme  will  not  have 
any  special  rules  in  cases  where  only  the  measurement  of  steam  and  cooling 
water  is  undertaken,  as  will  be  mainly  the  case  for  trials  of  absorption-ma 
chines  For  compression-machines  the  steam  consumption  depends  both 
on  the'quality  of.  the  steam-engine  and  on  that  of  the  refrigerating-machine 
while  it  is  evidently  desirable  to  know  the  consumption  of  the  former  sep- 
arately from  that  of  the  latter.  As  a  rule  steam-engine  and  compressor  art 
coupled  directly  together,  thus  rendering  a  direct  measurement  of  the  powei 
absorbed  by  the  refrigerating-machine  impossible,  and  it  will  have  to  suffice 
to  ascertain  the  indicated  work  both  of  steam-engine  and  compressor.  Bj 
further  measuring  the  work  for  the  engine  running  empty,  and  by  compar 
ing  the  differences  in  power  between  steam-engine  and  compressor  resulting 
for  wide  variations  of  condenser-pressures,  the  effective  consumption  o: 
work  Le  for  the  refrigerating-machine  can  be  found  very  closely.  In  gen 
eral  it  will  suffice  to  use  the  indicated  work  found  in  the  steam-cylinder 
especially  as  from  this  observation  the  expenditure  of  heat  can  be  directli 
determined.  Ordinarily  the  use  of  the  indicated  work  in  the  compressor 
cylinder,  for  purposes  of  comparison,  should  be  avoided;  firstly,  because 
there  are  usually  certain  accessory  apparatus  to  be  driven  (agitators,  etc.) 
belonging  to  the  refrigerating-machine  proper;  and  secondly,  because  th< 
external  friction  would  be  excluded. 

Heat  Balance.— We  possess  an  important  aid  for  checking  the  cor 
rectness  of  the  results  found  in  each  trial  by  forming  the  balance  m  eacl 
case  for  the  heat  received  and  rejected.  Only  such  tests  should  be  re 
warded  as  correct  beyond  doubt  which  show  a  sufficient  conformity  in  th< 
heat  balance.  It  is  true  that  in  certain  instances  it  may  not  be  easy  t« 
account  fully  for  the  transmission  of  heat  between  the  several  parts  of  th 
machine  and  its  environment  by  radiation  and  convection,  but  generall; 


TEMPERATURE   RANGE.  991 

: 

'particularly  for  compression  -machines)  it  will  be  possible  to  obtain  for  the 
ueat  received  and  rejected  a  balance  exhibiting  small  discrepancies  only. 

Report  of  Test.— Reports  intended  to  be  used  for  comparison  with 
Lhe  figures  found  for  other  machines  will  therefore  have  to  embrace  at  least 
Mie  following  observations  : 
Refrigerator: 

Quantity  of  brine  circulated  per  hour 

Brine  temperature  at  inlet  to  refrigerator 

Brine  temperature  at  outlet  of  refrigerator t 

Specific  gravity  of  brine  (at  64°  Fahr.)    

Specific  heat  of  brine  

Heat  abstracted  (cold  produced) Qe 

Absolute  pressure  in  the  refrigerator 

Condenser : 

Quantity  of  cooling  water  per  hour 

Temperature  at  inlet  to  condenser 

Temperature  at  outlet  of  condenser t 

Heat  abstracted , $t 

Absolute  pressure  in  the  condenser 

Temperature  of  gases  entering  the  condenser 


A  BSORPTI  ON  -  MACHINE. 

Still  : 

Steam  consumed  per  hour 

Abs.  pressure  of  heating  steam. 

Temperature  of  condensed 
steam  at  outlet 

Heat  imparted  to  still ......  Q'e 

Absorber  : 

Quantity  of  cooling  water  per 


hour 


Temperature  at  inlet 

Temperature  at  outlet 

Heat  removed  Qa 

Pump  for  Ammonia  Liquor: 
Indicated  work  of  steam-engine 
Steam-consumption  for  pump.. 
Thermal  equivalent  for  work  of 


COMPRESSION-MACHINE. 
Compressor : 

Indicated  work Lt 

Temperature  of  gases  at  inlet.. 
Temperature  of  gases  at  exit. . 
Steam-engine  : 

Feed- water  per  hour 

Temperature  of  feed-water 

Absolute  steam-pressure  before 

steam-engine 

Indicated  work  of  steam-engine 
Le 

Condensing  water  per  hour 

Temperature  of  da 

Total  sum  of  losses  by  radiation 

and  convection ±  Q9 

Heat  Balance  : 
Qe  +  ALc  =  <2i  ±  Qs> 


pump ALp 

Total  sum  of  losses  by  radiation 

and  convection ±  Q3 

Heat  Balance  : 

Qe  +  Q'e  =  Q,  +  Q2  ±  Q3. 

For  the  calculation  of  efficiency  and  for  comparison  of  various  tests,  the 

actual  efficiencies  must  be  compared  with  the  theoretical  maximum  of  effi- 

/  O   \                      T 
ciency  ( -y-J  max.  —  — —  corresponding  to  the  temperature  range, 

Temperature  Range.  —  As  temperatures  (T  and  Tc)  at  which  the 
heat  is  abstracted  in  the  refrigerator  and  imparted  to  the  condenser,it  is  cor- 
rect to  select  the  temperature  of  the  brine  leaving  the  refrigerator  and  that 
of  the  cooling  water  leaving  the  condenser,  because  it  is  in  principle  impos- 
sible to  keep  the  refrigerator  pressure  higher  than  would  correspond  to  the 
lowest  brine  temperature,  or  to  reduce  the  condenser  pressure  below  that 
corresponding  to  the  outlet  temperature  of  the  cooling  water. 

Prof.  Linde  shows  that  the  maximum  theoretical  efficiency  of  a  com- 
pression-machine may  be  expressed  by  the  formula 

Q  T 

AL   ~  Tc  -  T' 

in  which  Q  —  quantity  of  heat  abstracted  (cold  produced); 

AL  =  thermal  equivalent  of  the  mechanical  work  expended; 
L  =  the  mechanical  work,  and  A  —  1  -r-  778; 
T  =  absolute  temperature  of  heat  abstraction  (refrigerator) ; 
Tc  =        "  "      "      rejection  (condenser). 

If  u  =  ratio  between  the  heat  equivalent  of  the  mechanical  work  AL,  and 
the  quantity  of  heat  Q'  which  must  be  imparted  to  the  motor  to  produce 
the  work  Z/,  then 


992       ICE-MAKING    Oil   REFRIGERATING   MACHINES. 


AL 


=  u,  and   ^-  = 


91  -  Tc  ~  T 


uT 


It  follows  that  the  expenditure  of  heat  Q'  necessary  for  the  production  of 
the  quantity  of  cold  Q  in  a  compression -machine  will  be  the  smaller,  the 
smaller  the  difference  of  temperature  Tc.  -  T. 

Metering  tfee  Ammonia.-For  a  complete  test  of  an  ammonia  re- 
frigerating-machine  it  is  advisable  to  measure  the  quantity  of  ammonia  cir- 
culated, as  was  done  in  the  test  of  the  75-ton  machine  described  by  Prof. 
Denton.'  (Trans.  A.  S.  M.  E.,  xii.  326.) 

PROPERTIES  OF  SULPHUR  DIOXIDE  AND 

|f     Ledoux's  Table  for  Saturated  Sulphur-dioxide  Gas. 

Heat-units  expressed  in  B.T.U.  per  pound  of  sulphur  dioxide. 


a 

i 

•2 

Ofl 

in 

•-  , 

>  be 

JD  .2 

D 

fa 

7      ^ 

~cS 

^       ' 

•  ^j 

3  O 

=  =  c^ 

£5.53! 

S'Sw 

j'B™ 

M? 

|w|  £ 

ij  S 

WL 

"2$.^.* 

|j?  £•*» 

Is  #+ 

W§g-< 

*O  ?"d  * 

"c  §* 

^2^^ 

c  -^ 

Ifci 

§o  «^ 

H 

!§&."< 

|2I 

0>  !-><*-! 

ill 

11 

a 

i^i 

5  ftO 

Deg.  F. 

Lbs. 

B.T.U. 

B.T.U. 

B.T.U. 

B.T.U. 

B.T.U. 

Cu.  ft. 

Lbs. 

—22 

5.56 

157.43 

-19.56 

176.99 

13.59 

163.39 

13.17 

.076 

—13 

7.23 

158.64 

—16.30 

174.95 

13.83 

161.12 

10.27 

.097 

—  4 

9.27 

159.84 

-13.05 

172.89 

14.05 

158.84 

8.12 

.123 

5 

11.76 

161.03 

-  9.79 

170.82 

14.26 

156.56 

6.50 

.153 

14 

14.74 

162.20 

-  6.53 

168.73 

14.46 

154.27 

5.25 

.190 

*      S3 
32 

18.31 
22.53 

163.36 
161.51 

-  3.27 
0.00 

166.63 
164.51 

14.66 

14.84 

151.97 
149.68 

4.29 
3.54 

.232 

.282 

41 

27.48 

165.65 

3.27 

162.38 

15.01 

147.37 

2.93 

.340 

50 

33.25 

166.78 

6.55 

160.23 

15.17 

145.06 

2.45 

.407 

59 

39.93 

167.90 

9.83 

158.07 

15.32 

142.75 

2.07 

.483 

68 

47.61 

168.99 

13.11 

155.89 

15.46 

140.43 

1.75 

.570 

77 

56.39 

170.09 

16.39 

153.70 

15.59 

138.11 

1.49 

.669 

86 

66.36 

171.17 

19.69 

151.49 

15.71 

135.78 

1.27 

.780 

95 

77.64 

172.24 

22.98 

149.26 

15.82 

133.45 

1.09 

.906 

104 

90.31 

173.30 

26.28 

147.02 

15.91 

181.11 

91 

1.046 

(D'Andreff,  Trans.  A.  S.  M.  E 


5 
41 


10 

50 

.6230 


15 

59 

.6160 


2( 
61 

.60! 


Density  of  Liquid  Ammonia. 

x.  641.) 

At  temperature  C —  10 

Density *'.'.'.'.'..    1s492      .6429      .6364 

These  may  be  expressed  very  nearly  by 

8  =  0.6364  -  0. 00142°  Centigrade; 
S  =  0.6502  -  0. 000777 T°  Fahr. 

Latent  Heat  of  Eva{  oration  of  Ammonia.  (Wood,  Tran 
A.  S.  M.  E.,x.  641.) 

he  =  555.5    -0.613T   -  0.0002192^  (in  B.T.U.,  Fahr.  deg.); 

Ledoux  found  he  =  583.33  -  0.5499T  -  0,00011782*. 

For  experimental  values  at  different  temperatures  determined  by  Prc 
Denton,  see  Trans.  A.  S.  M.  E.,  xii.  356.  For  calculated  values,  s 
vol  x  646 

Density  of  Ammonia  Gas.-Theoretical,  0.5894;  experiments 
0.596.  Regnault  (Trans.  A.  S.  M.  E..  x.  633) 

Specific  Heat  of  Liquid  Ammonia.    (Wood,  Trans.  A  S.  M.  I 
x  645  )— The  specific  heat  is  nearly  constant  at  different  temperatures,  ai 
about  equal  to  that  of  water,  or  unity.    From  0°  to  100°  F.,  it  is 
c  =  1.096  -  .0012T,  nearly. 

Inalater  paper  by  Prof.  Wood  (Trans,  A.S,  M.  E.,  xii.  136)  he  gives  a  high 
value,  viz.,  c  =  1.12136  +  0.000438 T. 


PROPERTIES   OF   AMMONIA   VAPOR. 


993 


Dr.  Von  Strombeck,  in  1890,  found  from  the  mean  of  eight  experiments 
at  a  temperature  about  80°  F.,  c  -  1.82876,—  about  G#  greater  than  that  cal- 
culated from  this  formula. 

In  Prof.  Wood's  Thermodynamics  (edition  of  1894)  in  addition  to  the  above 
figures  lie  gives  the  mean  of  six  determinations  by  Ludeking  and  Starr,  0.886. 
This,  says  Prof.  Wood,  leaves  the  correct  result  in  doubt,  and  one  may  con- 
sider it  as  unity  until  determined  by  further  experiments. 

Properties  of  the  Saturated  Vapor  of  Ammonia. 

(Wood's  Thermodynamics.) 


Temperature. 

Pressure, 
Absolute. 

Heat  of 
Vaporiza- 

Volume 
of  Vapor 

Volume 
of  Liquid 

Weight 
of  a  cu. 

Degs. 

Abso- 
lute, F. 

Lbs.per 

sq.  ft. 

Lbs.per 
sq.  in. 

tion,  ther- 
mal units. 

per  lb., 
cu.  ft. 

per  lb., 
cu.  ft. 

ft.  of 
Vapor, 
Ibs. 

-    40 

420.66 

1540.7 

10.69 

579.67 

24  .  372 

.0234 

.0410 

-    35 

425.66 

1773.6 

12.31 

576.69 

21.319 

.0236 

.0468 

-    30 

430.66 

2035.8 

14.13 

573.69 

18.697 

.0237 

.0535 

~    25 

435.66 

2329.5 

16.17 

570.68 

16.445 

.0238 

.0608 

-    20 

440.66 

2657.5 

18.45 

567.67 

14.507 

.0240 

.0689 

-    15 

445.66 

3022.5 

20.99 

564.64 

12.834 

.0242 

.0779 

-    10 

450.66 

3428.0 

23.80 

561.61 

11.384 

.0243 

.0878 

—     5 

455.66 

3877.2 

26.93 

558.56 

10.125 

.0244 

.0988 

0 

460.66 

4373.5 

30.37 

555.50 

9.027 

.0246 

.1108 

4    5 

465.66 

4920.5 

34.17 

552.43 

8.069 

.0247 

.1239 

+    10 

470.66 

5522.2 

38.84 

549.35 

7.229 

.0249 

.1383 

+    15 

475.66 

6182.4 

42.93 

546.26 

6.492 

.0250 

.1544 

+   20 

480.66 

6905.3 

47.95 

543.15 

5.842 

.0252 

.1712 

+   25 

485.66 

7695.2 

53.43 

540.03 

5.269 

.0253 

.1898 

+  30 

490.66 

8556.6 

59.41 

536.92 

4.763 

.0254 

.2100 

+   35 

495.66 

9493.9 

65.93 

533.78 

4.313 

.0256 

.2319 

+   40 

500.66 

10512 

73.00 

530.63 

3.914 

.0257 

.2555 

+   45 

505.66 

11616 

80.66 

527.47 

3.559 

.0259 

.2809 

+   50 

510.66 

12811 

88.96 

524.30 

3.242 

.0261 

.3085 

4    55 

515.66 

14102 

97.93 

521.12 

2.958 

.0263 

.3381 

+    60 

520.66 

15494 

107.60 

517.93 

2.704 

.0265 

.3698 

+    65 

525.66 

16993 

118.03 

514.73 

2.476 

.0266 

.4039 

+    70 

530.66 

18605 

129.21 

511.52 

2.271 

.0268 

.4403 

+   76 

535.66 

20336 

141  .25 

508.29 

2.087 

.0270 

.4793 

+  80 

540.66 

22192 

154.11 

505.05 

.920 

.0272 

.5208 

+   85 

545.66 

24178 

167.86 

501.81 

.770 

.0273 

.5650 

+  90 

550.66 

26300 

182.8 

498.11 

.632 

.0274 

.6128 

+   95 

555.66 

28565 

198.37 

495.29 

.510 

.0277 

.6623 

+  100 

560.66 

30980 

215.14 

492.01 

.398 

.0279 

.7153 

+  105 

565.  66 

33550 

232.98 

488.72 

.296 

.0281 

.7716 

+  110 

570.66 

36284 

251.97 

485.42 

.203 

.0283 

.8312 

+  115 

575.66 

39188 

272.14 

482.41 

.119 

.0285 

.8937 

+  120 

580.66 

42267 

293.49 

478.79 

.045 

.0287 

.9569 

+  125 

585.66 

45528 

316.16 

475.45 

0.970 

.0289 

.0309 

+  150 

590  66 

48978 

340.42 

472.11 

0.905 

.0291 

.1049 

+  135 

595.66 

52626 

365.16 

468.75 

0.845 

.0293 

.1834 

+  140 

600.66 

56483 

392  22 

465.39 

0.791 

.0295 

.2642 

+  145 

605.66 

60550 

420.49 

462.01 

0.741 

.0297 

.3495 

+  150 

610.66 

64833 

450.20 

458.62 

0.695 

.0299 

.438R 

+  155 

615.66 

69341 

481.54 

455.22 

0.652 

.0302 

.5337 

+  160 

6-20.66 

74086 

514.40 

451.81 

0.613 

.0304 

.6343 

4-165 

625.66 

79071 

549.04 

448.39 

0.577 

.0306 

.7333 

Specific  Heat  of  Ammonia  Vapor  at  the  Saturation 
Point,  (Wood,  Trans.  A.  S.  M.^E  .  x.  644.)— For  the  range  of  temperatures 
ordinarily  used  in  engineeering  practice,  the  specific  heat  of  saturated  am- 
monia is  negative,  and  the  saturated  vapor  will  condense  with  adiabatic  ex- 
pansion, and  the  liquid  will  evaporate  with  the  compression  of  the  vapor, 
and  when  all  is  vaporized  will  superheat. 

Regnault  (Rel.  des.  Exp.,  ii.  162)  gives  for  specific  heat  of  ammonia-gas 
0.50836.  (Wood,  Trans.  A.  S.  M.  E.,  xii.  133.) 


994       ICK-MAKIXG    OR    REFRIGERATING    MACHINES. 


Properties  of  Brine  used  to  absorb  Refrigerating  Effect 
of  Ammonia.  (J.  E.  Denton,  Trans.  A.  S.  M.  E  ,  x.  799.)— A  solution  of 
Liverpool  salt  in  well-water  having  a  specific  gravity  of  1.17,  or  a  weight 
per  cubic  foot  of  73  Ibs.,  will  not  sensibly  thicken  or  congeal  at  0°  Fahren- 
heit. (It  is  reported  that  brine  of  1.17  gravity,  made  with  American  salt, 
begins  to  congeal  at  about  24°  Fahr.) 

The  mean  specific  heat  between  39°  and  16°  Fahr.  was  found  by  Denton  to 
be  0.805.  Brine  of  the  same  specific  gravity  has  a  specific  heat  of  0.805  at 
65°  Fahr.,  according  to  Naumann. 

Naumann's  values  are  as  follows  (Lehr-  und  Handbuch  der  Thermochemie, 
1882): 

Specific  heat 791       .805*      .863      .895      .931       .962      .978 

Specific  gravity.     1.187    1.170      1.103    1.072    1.044    1.023    1.012 
*  Interpolated. 

Chloride-of-calcium  solution  has  been  used  instead  of  brine.  Ac- 
cording to  Naumann,  a  solution  of  1.0255  sp.  gr.  has  a  specific  heat  of  .957. 
A  solution  of  1.163  sp.  gr.  in  the  test  reported  in  Eng'g,  July  22,  1887,  gave  a 
specific  heat  of  .827. 

ACTUAL   PERFORMANCES  OF  ICE-MAKINQ 
MACHINES. 

The  table  given  on  page  996  is  abridged  from  Denton,  Jacobus,  and  Riesen- 
berger's  translation  of  Ledoux  on  Ice-making  Machines.  The  following 
shows  the  class  and  size  of  the  machines  tested,  referred  to  by  letters  in  the 
table,  with  the  names  of  the  authorities: 


Class  of  Machines. 

Authority. 

Dimensions    of    Compres- 
sion-cylinder in  inches. 

Bore. 

Stroke. 

A.  Ammonia  cold-compression.. 
B.  Pictet  fluid  dry  -compression. 
C  Bell-Coleman  air 

Schroter. 

j  Ren  wick  & 
\   Jacobus. 
Denton. 

9.9 
11.3 
28.0 

10. 
12.0 

16.5 
24.4 
23.8 

18.0 
30.0 

I)  Closed  cycle  air  

E.  Ammonia  dry-compression  .  . 
F.  Ammonia  absorption  

Performance  of  a  75-ton  Ammonia  Compression- 
macliiiie.  (J.  E.  Denton,  Trans.  A.  S.  M.  E.,  xii,  326.)— The  machine  had 
two  single-acting  compression  cylinders  12"  X  30",  and  one  Corliss  steam - 
cylinder,  double-acting,  18"  X  36".  It  was  rated  by  the  manufacturers  as  a 
50-ton  machine,  but  it  showed  75  tons  of  ice- refrigerating  effect  per  24  hours 
during  the  test. 

The  most  probable  figures  of  performance  in  eight  trials  are  as  follows  : 


ca  .  ;* 

«w  «w   ,  •  V, 

a^  "  as 

F-H  «M  .1 

, 

Ammonia 

Brine 

o^ 

®  °  j§  5 

g    °  -~Q 

3  °'§ 

_i 

Pressures, 

Tempera- 

j§,o'~'rd 

5  ';  S^ 

0^    . 

•r 

Ibs.  above 

tures, 

^  ^  ft 

•""  w  t<    . 

CC—   £   O 

•<$     .2 

H 

Atmosphere. 

Degrees  F. 

£j>-  jfi 

=>  ft^^K 

S  Sas   . 

v    a3Sb 

'o  ?lj 

CM 
O 

O 

6 

Con- 
densing 

Suc- 
tion. 

Inlet. 

Outlet. 

!*W.c 

|llll 

tf  .2  >•  *  * 
£**' 

w 

I1 

1 

151 

28 

36.76 

28.86 

70.3 

22.60 

0.80 

10 

1.0 

8 

161 

2T.5 

36.36 

28.45 

70.1 

22.27 

1.09 

1.0 

1.0 

7 

147 

13.0 

14.29 

2.29 

42.0 

16.27 

0.83 

1.70 

1.66 

4 

152 

8.2 

6.27 

2.03 

36.43 

14.10 

1.1 

1.93 

1.92 

6 

105 

7.6 

6.40 

—2.22 

37.20 

17.00 

2.00 

1.91 

1.88 

2 

135 

15.7 

4.62 

3.22 

27.2 

13.20 

1.25 

2.59 

2  57 

The  principal  results  in  four  tests  are  given  in  the  table  on  page  998.  The 
fuel  economy  under  different  conditions  of  operation  is  shown  in  the  fol- 
lowing table : 


PERFORMANCES   OF   ICE-MAKING   MACHINES.       995 


Condensing  Press- 
ure, Ibs. 

bion-pressure, 
Ibs. 

Pounds  of  Ice-melting  Effect  with 
Engines  — 

B.T.U.  per  Ib.  of  Steam 
witli  Engines— 

Non-con- 
densing. 

Non- 

POU1K 

dens 

com- 
Con- 
,ing. 

Compound 
Con- 
densing. 

Non-condens- 
ing. 

Condensing. 

it 
H 

66 

pd^l 

oS 

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,riS 

iO^ 

oS 

CO 

IS 

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|8 

fH  £> 

&z 

IS 

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150 
150 

105 
105 

28 

7 
28 

24 
14 
34.5 
22 

2.90 
1.69 
4.16 
2.65 

30 
17.5 
43 
27.5 

3.61 
2.11 

5.18 
3.31 

37.5 
21.5 
54 
34.5 

4.51 
2.58 
6.50 
4.16 

393 
240 
591 
376 

513 
300 
725 
470 

640 
366 
923 
591 

The  non -condensing  engine  is  assumed  to  require  25  Ibs.  of  steam  per 
horse-power  per  hour,  the  non-compound  condensing  20  Ibs.,  and  the  com- 
densing  16  Ibs.,  and  the  boiler  efficiency  is  assumed  at  8.3  Ibs.  of  water  per 
Ib.  coal  under  working  conditions.  The  following  conclusions  were  derived 
from  the  investigation  : 

1.  The  capacity  of  the  machine  is  proportional,  almost  entirely,  to  the 
weight  of  ammonia  circulated.      This   weight  depends   on   the    suction- 
pressure  and  the  displacement  of  the  compressor-pumps.    The  practical 
suction-pressures  range  from  7  Ibs.  above  the  atmosphere,  with  which  a 
temperature  of  0°  F.  can  be  produced,  to  28  Ibs.  above  the  atmosphere,  \\ith 
which  the  temperatures  of  refrige ration  are  confined  to  about  28°  F.    At  the 
lower  pressure  only  about  one  half  as  much  weight  of  ammonia  can  be  cir- 
culated as  at  the  upper  pressure,  the  proportion  being  about  in  accordance 
with  the  ratios  of  the  absolute  pressures,  22  and  42  Ibs.  respectively.   For  each 
cubic  foot  of  piston-displacement  per  minute  a  capacity  of  about  one  sixth 
of  a  ton  of  "  refrigerating  effect  "  per  24  hours  can  be  produced  at  the  lower 
pressure,  and  of  about  one  third  of  a  ton  at  the  upper  pressure.    No  other 
elements  practically  affect  the  capacity  of  a  machine,  provided  the  cooling- 
surface  in  the  brine-tank  or  other  space  to  be  cooled  is  equal  to  about 
36  sq.  ft.  per  ton  of  capacity  at  28  Ibs.  back  pressure.    For  example,  a  differ- 
ence of  100$  in  the  rate  of  circulation  of  brine,  while  producing  a  propor- 
tional difference  in  the  range  of  temperature  of  the  latter,  made  no  practical 
difference  in  capacity. 

The  brine-tank  was  10^  X  13  X  19%  ft.,  and  contained  8000  lineal  feet  of 
1-in.  pipe  as  cooling-surface.  The  condensing-tank  WHS  12  X  10  X  10  ft.,  and 
contained  5000  lineal  feet  of  1-in.  pipe  as  cooling-surface. 

2.  The  economy  in  coal-consumption  depends  mainly  upon  both  the  suc- 
tion-pressures and  condensing-pressures.    Maximum  economy,  with  a  given 
type  of  engine,  where  water  must  be  bought  at  average  city  prices,  is 
obtained  at  28  Ibs.  suction-pressure  and  about  150  Ibs.  condensing-pressure. 
Under  these  conditions,  for  a  non-condensing  steam-engine,  consuming  coal 
at  the  rate  of  3  Ibs.  per  hour  per  I.H.P.  of  steam-cylinders,  24  Ibs.  of  ice- 
refrigerating  effect  are  obtained  per  Ib.  of  coal  consumed.    For  the  same 
condensing-pressure,  and  with  7  Ibs.  suction-pressure,  which  affords  tem- 
peratures of  0°  F.,  the  possible  economy  falls  to  about  14  Ibs.  of  "  refrigerat- 
ing effect "  per  Ib.  of  coal  consumed.    The  condensing-pressure  is  determined 
by  the  amount  of  condensing-water  supplied  to  liquefy  the  ammonia  in  the 
condenser.    If  the  latter  is  about  1  gallon  per  minute  per  ton  of  refrigerating 
effect  per  24  hours,  a  condensing-pressure  of  150  Ibs.  results,  if  the  initial  tem- 
perature of  the  water  is  about  56°  F.     Twenty-five  per  cent  less  water  causes 


11.5  at  7  Ibs.  If,  on  the  other' hand,  the  supply  of  water  is  made  3  gallons 
per  minute,  the  condensiug-pressure  may  be  confined  to  about  105  Ibs.  The 
work  of  compression  is  thereby  reduced  about  25#  .and  a  proportional  increase 
of  economy  results.  Minor  alterations  of  economy  depend  on  the  initial 
temperature  of  the  condensing-water  and  variations  of  latent  heat,  but  these 
are  confined  within  about  5$  of  the  gross  result,  the  main  element  of  control 
being  the  work  of  compression,  as  affected  by  the  back  pressure  and  con- 
h.  If  the  steam  engine  supplying  the  motive  power 


densing-pressure,  or  bot 
may  use  a  condenser  to 
available  over  the  above  figures,  making  the 


may  usVa  condenser  to  secure  a  vacuum,  an  increase  of  economy  of  25#  is 

1     Ibs.  of  "  ice  effect "  per  Ib.  of 


996      ICE-MAKING    OR   REFRIGERATING   MACHINES. 


coal  for  150  Ibs.  condensing-pressure  and  28  Ibs.  suction -pressure  30.0,  and 
for  7  Ibs.  suction-pressure,  17.5.  It  is,  however,  impracticable  to  use  a  con- 
denser in  cities  where  water  is  bought.  The  latter  must  be  practically 
free  of  cost  to  be  available  for  this  purpose.  In  this  case  it  may  be  assumed 
that  water  will  also  be  available  for  condensing  the  ammonia  tp^obtain  as 
low 
ei'i 

of  coal,  "if  a"compouml  condensing-engine  can  be  used  with  a  steam-cori- 
sumption  per  hour  per  horse-power  of  16  Ibs.  of  water,  the  economy  of  the 
refrigerating-machine  may  be  25$  higher  than  the  figures  last  named,  mak- 
ing for  28  Ibs.  back  pressure  a  refrigerating  effect  of  54.0  Ibs.  per  Ib.  of  coal, 
and  for  7  Ibs.  back  pressure  a  refrigerating  effect  of  34.0  Ibs.  per  Ib.  of  coal. 
Actual  Performance  of  Ice-making  Machines. 


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*  Temperatura  of  air  at  entrance  and  exit  of  expansion-cylinder. 

t  On  a  basis  of  3  Ibs.  of  coal  per  hour  per  H.P.  of  steam-cylinder  of  com- 
pression-machine and  an  evaporation  of  11.1  Ibs.  of  water  per  pound  of 
combustible  from  and  at  212°  F.  in  the  absorption-machine. 

t  Per  cent  of  theoretical  with  no  friction. 

§Loss  due  to  he  iting  during  aspiration  of  gas  in  the  compression-cylinder 
and  to  radiation  and  superheating  at  brine-tank. 

||  Actual,  including  resistance  due  to  inlet  and  exit  valves. 


PERFOILMAXCKS    OF    ICE-MAKIKG    MACHINES.        997 

In  class  A,  a  German  machine,  the  ice-melting  capacity  ranges  from  46.29 
to  10.14  Ibs.  of  ice  per  pound  of  coal,  according  as  the  suction  pressure 
varies  from  about  45  to  8  Ibs.  above  the  atmosphere,  this  pressure  being  the 
condition  which  mainly  controls  the  economy  of  compression-machines. 
These  results  are  equivalent  to  realizing  from  72$  to  \X%  of  theoretically  per- 
fect performances.  The  higher  per  cents  appear  to  occur  with  ihe  higher 
suction-pressures,  indicating  a  greater  loss  from  cylinder-heating  (a  phe- 
nomenon the  reverse  of  cylinder  condensation  in  steam-engines),  as  -the 
range  of  the  temperature  of  the  gas  in  the  compression -cylinder  is 
greater. 

In  E,  an  American  compression-machine,  operating  on  the  u  dry  system,1' 
the  percentage  of  theoretical  effect  realized  ranges  from  69.5$  to  62. 6#. 
The  friction  losses  are  higher  for  the  American  machine.  The  latter's  higher 
efficiency  may  be  attributed,  therefore,  to  more  perfect  displacement. 

The  largest  "  ice-melting  capacity  "  in  the  American  machine  is  24.16  Ibs. 
This  corresponds  to  the  highest  suction-pressures  used  in  American  practice 
for  such  refrigeration  as  is  required  in  beer-storage  cellars  using  the  direct- 
expansion  system.  The  conditions  most  nearly  corresponding  to  American 
brewery  practice  in  the  German  tests  are  those  in  line  5,  which  give  an  "  ice- 
melting  capacity  "  of  19.07  Ibs. 

For  the  manufacture  of  artificial  ice,  the  conditions  of  practice  are  those 
of  lines  3  and  4,  and  lines  25  and  26.  In  the  former  the  condensing  pressure 
used  requires  more  expense  for  cooling  water  than  is  common  in  American 
practice.  The  ice-melting  capacity  is  therefore  greater  in  the  German  ma- 
chine, being  22.03  and  16.14  Ibs.  against  17.55  and  14.52  for  the  American 
apparatus. 

CLASS  B.  Sulphur  Dioxide  or  Pictet  Machines.— No  records  are  available 
for  determination  of  the  "ice-melting  capacity"  of  machines  using  pure 
sulphur  dioxide.  This  fluid  is  in  use  in  American  machines,  but  in  Europe 
it  has  given -way  to  the  "  Pictet  fluid,1'  a  mixture  of  about  97$  of  sulphur 
dioxide  and  3#  of  carbonic  acid.  The  presence  of  the  carbonic  acid  affords 
a  temperature  about  14  Fahr.  degrees  lower  than  is  obtained  with  pure  sul- 
phur dioxide  at  atmospheric  pressure.  The  latent  heat  of  this  mixture  has 
never  been  determined,  but  is  assumed  to  be  equal  to  that  of  pure  sulphur 
dioxide. 

For  brewery  refrigerating  conditions,  line  17,  we  have  26.24  Ibs.  "ice- 
melting  capacity,"  and  for  ice-making  conditions,  line  13,  the  "ice-melt- 
ing capacity  "  is  17.47  Ibs.  These  figures  are  practically  as  economical 
as  those  for  ammonia,  the  per  cent  of  theoretical  effect  realized  ranging 
from  65.4  to  57.8.  At  extremely  low  temperatures,  —15°  Fahr.,  lines  14  and 
18,  the  per  cent  realized  is  as  low  as  42.5. 

Cylinder-heating. — In  compression-machines  employing  volatile 
vapors  the  principal  cause  of  the  difference  between  the  theoretical  and  the 
practical  result  is  the  heating  of  the  ammonia,  by  the  warm  cylinder  walls, 
during  its  entrance  into  the  compressor,  thereby  expanding  it,  so  that  to 
compress  a  pound  of  ammonia  a  greater  number  of  revolutions  must  be 
made  by  the  cornpressing-pumps  than  corresponds  to  the  density  of  the 
ammonia-gas  as  it  issues  from  the  brine-tank. 

Tests  of  Ammonia  Absorption-machine  used  in  storage-ware 
houses  under  approaches  to  the  New  York  and  Brooklyn  Bridge.  (Kng'ffi 
July  22,  1887.)— The  circulated  fluid  consisted  of  a  solution  of  chloride  of  cal- 
cium of  1  163  sp.  gr.  Its  specific  heat  was  found  to  be  .827. 

The  efficiency  of  the  apparatus  for  24  hours  was  found  by  taking  the 
product  of  the  cubic  feet  of  brine  circulating  through  the  pipes  by  the  aver- 
age difference  in  temperature  in  the  ingoing  and  outgoing  currents,  as 
observed  at  frequent  intervals  by  ihe  specific  heat  of  the  brine  (  827)  and  its 
weight  per  cubic  foot  (73.48).  The  final  product,  applying  all  allowances  for 
corrections  from  various  causes,  amounted  to  6,218,816  heat-units  as  the 
amount  abstracted  in  24  hours,  equal  to  the  melting  of  43,565  Ibs.  of  ice  in 
the  same  time. 

The  theoretical  heating-power  of  the  coal  used  in  24  hours  was  27.000,000 
heat-units;  hence  the  efficiency  of  the  apparatus  was  23*.  This  is  equivalent 
to  an  ice -melting  effect  of  16.1  Ibs.  per  Ib.  of  coal  having  a  heating  value  of 
10,000  B.T.U.  perlb. 

A  test  of  1.1  35-fou  absorption -machine  in  New  Haven,  Conn.,  by  Prof. 
Denton  (Trans.  A.  S.  M.  E.,  x.  792),  gave  an  ice-melting  effect  of  20.1  Ibs.  per 
H>.  of  coal  on  a  basis  of  boiler  economy  equivalent  to  3  Ibs.  of  steam  per 
I.H.P.  in  a  good  non-condensing  steam-engine.  The  ammonia  was  worked 
between  138  and  23  Ibs.  pressure  above  the  atmosphere. 


098      ICE-MAKING   OR    REFRIGERATING   MACHINES. 
Performance  of  a  75-ton  Refrigerating-macliine. 


11 

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Av.  high  ammonia  press,  above  atmos  
Av.  back  ammonia  press,  above  atmos  
A  v.  temperature  brine  inlet      

151  Ibs. 

28  " 
36.76° 

152  Ibs. 

8.2  " 
6.27° 

147  Ibs. 
13  " 
14.29° 

161  Ibs. 
27.5  " 

Av  temperature  brine  outlet                .  . 

28.86°       2.03° 

2.29° 

28.45° 

79°         4  24° 

12  00° 

7  91° 

Lbs.  of  brine  circulated  per  minute  

2281     i     2173 

943 

2374 

Av.  temp,  condensing-water  at  inlet  

44.65° 

56.65° 

46.9° 

54.00° 

Av.  temp,  condensing-water  at  outlet  

83.66° 

85.4° 

85.46° 

82.86° 

Av.  range  of  temperature  

39.01° 

28.75° 

38.56° 

28.80° 

Lbs.  water  circulated  p.  min.  thro1  cond'ser 

442 

315 

257           601.5 

Lbs.  water  per  min.  through  jackets  

25 

44 

40             14 

Range  of  temperature  in  jackets  

24.0° 

16.2° 

16.4° 

29.1° 

Lbs.  ammonia  circulated  per  min  

*28.17 

14.68 

16.67 

28.32 

Probable  temperature  of  liquid  ammonia, 

entrance  to  brine-tank  

*71.3° 

*68° 

*63.7° 

76.7° 

Temp,  of  amm.  corresp.  to  av.  back  press. 

+14° 

-  8° 

-  5° 

14° 

Av.  temperature  of  gas  leaving  brine-tanks 

34.2° 

14.7° 

3  0° 

29.2° 

Temperature  of  gas  entering  compressor 

*39° 

25° 

10.13° 

34° 

Av.  temperature  of  gas  leaving  compressor 

213° 

263° 

239° 

221° 

Av.  temp,  of  gas  entering  condenser...   .  . 

200° 

218° 

209° 

168° 

Temperature  due  to  condensing  pressure.. 

84.5° 

84.0° 

82.5° 

88.0° 

Heat  given  ammonia: 

By  brine,  B  T.U.  per  rniniute  

14776 

7186 

8824 

14647 

By  compressor,  B.T.U.  per  minute  

2786 

2320 

2518 

3020 

By  atmosphere,  B  T.U.  per  minute.  .  .  . 
Total  heat  rec.  by  amm.,  B.T.U.  per  min. 

140 
17702 

147 
9653 

167 
11409 

141 
17704 

Heat  taken  from  ammonia: 

By  condenser  B  T  U  per  min 

17242 

9056 

9910 

17359 

By  jackets  B  T  U   per  min  

608 

712 

656 

406 

By  atmosphere,  B.T.U.  per  min  

182 

338 

250 

252 

Total  heat  rej.  by  arnm.,  B.T  U.  per  min.  .  . 
Dif.  of  heat  rec'd  and  rej.,  B.T.U.  per  min. 

18032 
330 

10106 
453 

10816 
407 

18017 
309 

%  work  of  compression  removed  by  jackets. 
Av.  revolutions  per  min  

58.09 

81* 

57.7 

26fc 
57.88 

58.89 

Mean  eff.  press,  steam-cyl.,  Ibs.  per  sq.  in  .  . 

32.5 

27.17 

27.83 

32.97 

Mean  eff.  press,  amm.-cyl.,  Ibs.  per  sq.  in  .  . 

65.9 

53.3 

59.86 

70.54 

Av.  H.  P.  steam-cylinder  

85.00 

71.7 

73.6 

88.63 

A.V  H  P  ammonia-cylinder 

65.7 

54  7 

59.37 

71.20 

Friction  in  per  cent  of  steam  HP          

23.0 

24.0 

20.0 

19.67 

Total  cooling  water,  gallons  per  min.  per 

ton  per  24  hours 

0  75 

1  185 

0.797 

0.990 

Tons  ice-melting  capacity  per  24  hours  
Lbs    ice-  refrigerating  eff.  per  Ib.  coal  at  3 

74.8 

36.43 

44.64 

74.56 

Ibs.  per  H.P.  per  hour  

24.1 

14  .1 

17.27 

23.37 

Cost  coal  per  ton  of  ice-refrigerating  effect 
at  $4  per  ton     .... 

$0.166 

$0.283 

$0.231 

$0.170 

Cost  water  per  ton  of  ice-refrigerating  effect 
at  $1  per  1000  cu.  ft  

$0.128 

$0.200 

$0.136 

$0.109 

Total  cost  of  1  ton  of  ice-refrigerating  eff... 

$0.294 

$0.483 

$0.467 

$0.339 

Figures  marked  thus  (*)  are  obtained  by  calculation:  all  other  figures  are 
obtained  from  experimental  data  ;  temperatures  are  in  Fahrenheit  degrees. 


ARTIFICIAL   ICE-MANUFACTUKK. 


999 


Ammonia  Compression-machine. 

ACTUAL  RESULTS  OBTAINED  AT  THE  MUNICH  TESTS. 
(Prof.  Linde,  Trans.  A.  S.  M.  E.,  xiv.  1419.) 


No.  of  Test  

1 

2 

3 

4 

5 

Temp,  of  refrig-  }  Inlet,  deg.  F  

43  194 

28  344 

13  952 

—  0  2*~9 

28  251 

erated  brine     f  Outlet,  t  deg.  F.  .  . 

37.054 

22.885 

8.771 

-5.879 

23.072 

Specific  heat  of  brine  

0.861 

0.851      0.843 

0.83? 

0.851 

Quantity  of  brine  circ.  per  h.,  cu.  ft. 

1,039.38 

908.84    633.89 

414.98 

800.93 

Cold  produced,  B.T.U.  per  hour  
Quau  t.  of  cooling  water  per  h.,  c.  ft. 

342,909 
338.76 

263,950 
260.83 

172,776 
187.506 

121,474 
139.99 

220,284 
97.76 

l.H.P.  in  steam-engine  cy  linder  (7>). 

15.80 

16.47 

15.28 

14.24 

21.61 

Cold    pro-  1  Per  l.H.P.  in  comp.-cyl. 
duced  per  >Per  l.H.P.  in  steam-cyl. 
h.,  B.T.U.  (  Per  Ib.  of  steam  

24,813 
21.703 
1,100.8 

18,471 
16,026 
785.  6 

12,770 
11,307 
564.9 

10,140 
8,530 
435.82 

11,151 
10,194 
512.12 

Means  for  Applying  the  Cold.  (M.  C.  Bannister,  Liverpool 
Eng'g  !Soc'y»  1890.; — The  most  useful  means  for  applying  the  cold  to  various 
uses  is  a  saturated  solution  of  brine  or  chloride  of  magnesium,  which 
remains  liquid  at  5°  Fahr.  The  brine  is  first  cooled  by  being  circulated  in 
contact  with  the  refrigerator-tubes,  and  then  distributed  through  coils  of 
pipes,  arranged  either  in  the  substances  requiring  a  reduction  of  tempera- 
ture, or  in  the  cold  stores  or  rooms  prepared  for  them ;  the  air  coming  in 
contact  with  the  cold  tubes  is  immediately  chilled,  and  the  moisture  in  the 
air  deposited  on  the  pipes.  It  then  falls,  making  room  for  warmer  air,  and 
so  circulates  until  the  whole  room  is  at  the  temperature  of  the  brine  in  the 
pipes. 

lu  a  recent  arrangement  for  refrigerating  made  by  the  Linde  British  Re- 
1  rigeration  Co.,  the  cold  brine  is  circulated  through  a  shallow  trough,  in 
which  revolve  a  number  of  shafts,  each  geared  together,  and  driven  by  me- 
chanical means.  On  the  shafts  are  fixed  a  number  of  wrought -iron  disks, 
partly  immersed  in  the  brine,  which  cool  them  down  to  the  brine  tempera- 
ture as  they  revolve;  over  these  disks  a  rapid  circulation  of  air  is  passed  by 
a  fan,  being  cooled  by  contact  with  the  plates;  then  it  is  led  into  the  cham- 
bers requiring  refrigeration,  from  which  it  is  again  drawn  by  the  same  fan; 
thus  all  moisture  and  impurities  are  removed  from  the  chambers,  and  de- 
posited in  the  brine,  producing  the  most  perfect  antiseptic  atmosphere  yet 
invented  for  cold  storing;  while  the  maximum  efficiency  of  the  brine  tem- 
perature was  always  available,  the  brine  being  periodically  concentrated  by 
suitable  arrangements. 

Air  has  also  been  used  as  the  circulating  medium.  The  ammonia-pipes 
refrigerate  the  air  in  a  cooling-chamber,  and  large  wooden  conduits  are  used 
to  convey  it  to  and  return  it  from  the  rooms  to  be  cooled.  An  advantage  of 
this  system  is  that  by  it  a  room  may  be  refrigerated  more  quickly  than  by 
brine-coils.  The  returning  air  deposits  its  moisture  in  the  form  of  snow  on 
the  ammonia-pipes,  which  is  removed  by  mechanical  brushes. 

ARTIFICIAL  ICE-MANUFACTURE. 

Under  summer  conditions,  with  condensing  water  at  70°,  artificial  ice-ma- 
chines use  ammonia  at  about  190  Ibs.  above  the  atmosphere  condenser- 
pressure,  and  15  Ibs.  suction-pressure. 

In  a  compression  type  of  machine  the  useful  circulation  of  ammonia, 
allowing  for  the  effect  of  cylinder- heating,  is  about,  13  Ibs.  per  hour  per  in- 
dicated horse-power  of  the  steam -cylinder.  This  weight  of  ammonia  pro- 
duces about  32  Ibs.  of  ice  at  15°  from  water  at  70°.  If  the  ice  is  made  from 
distilled  water,  as  in  the  "can  system,"  the  amount  of  the  latter  supplied 
by  the  boilers  is  about  38#  greater  than  the  weight  of  ice  obtained.  This 
excess  represents  steam  escaping  to  the  atmosphere,  from  the  re- boiler  and 
steam-condenser,  to  purify  the  distilled  water,  or  free  it  from  air;  also,  the 
Joss  through  leaks  and  drips,  and  loss  by  melting  of  the  ice  in  extracting  it 
from  the  cans.  The  total  steam  consumed  per  horse-power  is,  therefore, 
about  32  X  1.33  =  43.0  Ibs.  About  7.0  Ibs.  of  this  covers  the  steam -consump- 
tion of  the  steam-engines  driving  the  brine  circulating-pumps,  the  several 


1000  ICE-MAKING  OR  REFRIGERATING  MACHINES. 

cold-water  pumps,  and  leakage,  drips,  etc.  Consequently,  the  main  steam- 
engine  must  consume  36  Ibs.  of  steam  per  hour  per  I.H.P.,  or  else  live  steam 
must  be  condensed  to  supply  the  required  amount  of  distilled  water.  There 
is,  therefore,  nothing  to  be  gained  by  using  steam  at  high  rates  of  expansion 
in  the  steam-engines,  in  making  artificial  ice  from  distilled  water.  If  the 
cooling  water  for  the  ammonia-coils  and  steam-condenser  is  not  too  hard  for 
use  in  the  boilers,  it  may  enter  the  latter  at  about  175°  F.,  by  restricting  the 

Suantity  to  1^  gallons  per  minute  per  ton  of  ice.     With  good  coal  8%  Ibs.  of 
eed -water  may  then  be  evaporated,  on  the  average,  per  Ib.  of  coal. 

The  ice  made  per  pound  of  coal  will  then  be  32  -*•  -^-  —  6.0  Ibs.    This  cor- 

o.o 
responds  with  the  results  of  average  practice. 

If  ice  is  manufactured  by  the  "plate  system,"  no  distilled  water  is  used 
for  freezing.  Hence  the  water  evaporated  by  the  boilers  may  be  reduced  to 
the  amount  which  will  drive  the  steam-motors,  and  the  latter  may  use  steam 
expansively  to  any  extent,  consistent  with  the  power  required  to  compress 
the  ammonia,  operate  the  feed  and  filter  pumps,  and  the  hoisting  machinery. 
The  latter  may  require  about  15#  of  the  power  needed  for  compressing  the 
ammonia. 

If  a  compound  condensing  steam-engine  is  used  for  driving  the  com- 
pressors, the  steam  per  indicated  steam  horse-power,  or  per  32  Ibs.  of  net 
ice,  may  be  14  Ibs.  per  hour.  The  other  motors  at  50  Ibs.  of  steam  per  horse- 
power will  use  7.5  Ibs.  per  hour,  making  the  total  consumption  per  steam 
horse  power  of  the  compressor  21.5  Ibs.  Taking  the  evaporation  at  8  Ibs.., 
the  feed-water  temperature  being  limited  to  about  110°,  the  coal  per  horse- 
power is  2.7  Ibs.  per  hour.  The  net  ice  per  Ib.  of  coal  is  then  about  3^5  -r-  2.7  — 
11.8  Ibs.  The  best  results  with  "plate-system"  plants,  using  a  compound 
steam-engine,  have  thus  far  afforded  about  10^  Ibs.  of  ice  per  Ib.  of  coal. 

In  the  "  plate  system  "  the  ice  gradually  forms,  in  from  9  to  14  days,  to  a 
thickness  of  about  14  inches,  on  hollow  plates  10  X  14  feet  in  area,  in  which 
the  cooling  fluid  circulates. 

In  the  "can  system  "  the  water  is  frozen  in  blocks  weighing  about  300  Ibs. 
each,  and  the  freezing  is  completed  in  from  50  to  60  hours.  The  freezing- 
tank  area  occupied  by  the  "plate  system11  is,  therefore,  about  four  times, 
and  the  cubic  contents  about  twelve  times,  as  much  as  is  required  in  the 
"can  system." 

The  investment  for  the  "  plate  "  is  about  one  third  greater  than  for  the- 
"can  "  system.  In  the  latter  system  ice  is  being  drawn  throughout  the  24 
hours,  and  the  hoisting  is  done  by  hand  tackle.  In  the  "  plate  system  "  the 
entire  daily  product  is  drawn,  cut,  and  stored  in  a  few  hours,  the  hoisting 
being  performed  by  power.  The  distribution  of  cost  is  as  follows  for  the 
two  systems,  taking  the  cost  for  the  "can  "  or  distilled- water  system  as  100, 
which  represents  an  actual  cost  of  about  $1.25  per  net  ton: 

Can  System.    Plate  System. 

Hoisting  and  storing  ice 14.2  2.8 

Engineers,  firemen,  and  coal-passer 15.0  13.9 

Coal  at  $3.50  per  gross  ton 42.2  20.0 

Water  pumped  directly  from  a  natural  source 

at  5  cts.  per  1000  cubic  feet 1.8  2.6 

In terest  and  depreciation  at  10%. 24.6  32.7 

Rppairs 3.4 

100.00  75.4 

A  compound  condensing  engine  is  assumed  to  be  used  by  the  "  plate  sys. 
tern." 
Test  of  the    New  York:  Hygeia  Ice-making   Plant.— (By 

Messrs.  Hupfel,  Griswold,  and  Mackenzie;  Stevens  Indicator,  Jan.  1891.) 
The  final  results  of  the  tests  were  as  follows: 

Net  ice  made  per  pound  of  coal,  in  pounds 7.12 

Pounds  of  net  ice  per  hour  per  horse-power 37.8 

Net  ice  manufactured  per  day  (12  hours)  in  tons 97 

A  v.  pressure  of  ammonia-gas  at  condenser,  Ibs.  per  sq.  in.  ab.  atmos.  135.2 

Average  back  pressure  of  amm.-gas,  Ibs.  per  sq.  in.  above  atmos.. .  15.8 

Average  temperature  of  brine  in  freezing-tanks,  degrees  F ...  197 

Total  number  of  cans  filled  per  week   4389 

Ratio  of  cooling-surface  of  coils  in  brine-tank  to  can-surface 7  to  10= 


MARINE    ENGINEERING.  100  L 

Ratio  of  brine  in  tanks  to  water  in  cans 1  to  1  2 

Ratio  of  circulating'  water  at  condensers  to  distilled  water. ......    .'.   26  to  1 

rounds  of  water  evaporated  at  boilers  per  pound  of  coal 8.085 

Total  horse-power  developed  by  compressor-engines '.'.      444 

Percentage  of  ice  lost  in  removing  from  cans ".'.!!!!        2.2 

APPROXIMATE  DIVISION   OF  STEAM  IN  PER  CENTS  OF  TOTAL  AMOUNT. 

Compressor-engines go  j 

Live  steam  admitted  directly  to  condensers 19.7 

Steam  for  pumps,  agitator,  and  elevator  engines , '.        7.6 

Live  steam  for  rebelling  distilled  water 6*5 

Steam  for  blowers  furnishing  draught  at  boilers ....        5^6 

Sprinklers  for  removing  ice  from  cans 0.5 

The  precautions  taken  to  insure  the  purity  of  the  ice  are  thus  described: 
The  water  which  finally  leaves  the  condenser  is  the  accumulation  of  the 
exhausts  from  the  various  pumps  and  engines,  together  with  an  amount  of 
live  steam  injected  into  it  directly  from  the  boilers.  This  last  quantity  is 
used  to  make  up  any  deficit  in  the  amount  of  water  necessary  to  supply  the 
ice-cans.  This  water  on  leaving  the  condensers  is  violently  reboiled,  and 
afterwards  cooled  by  running  through  a  coil  surface-cooler.  It  then  passes 
through  an  oil-separator,  after  which  it  runs  through  three  charcoal-filters 
and  deodorizers,  placed  in  series  and  containing  28  feet  of  charcoal.  It  next 
passes  into  the  supply-tank  in  which  there  is  an  electrical  attachment  for 
detecting  salt-.  Nitrate-of-silver  tests  are  also  made  for  salt  daily.  From 
this  tank  it  is  fed  to  the  ice-cans,  which  are  carefully  covered  so  the,t  the 
water  cannot  possibly  receive  any  impurities. 

MARINE  ENGINEERING-. 

Rules  for  Measuring  Dimension*  and  Obtaining  Ton- 
nage of  Vessels.  (Record  of  American  &  Foreign  Shipping.  American 
Shipmasters'-  Assn.,  N.  Y.  1890.)— The  dimensions  to  be  measured  as  follows: 

I.  Length.  L. — From  the  fore  side  of  stem  to  the  after  side  of  stern-post 
measured  at  middle  line  on  the  upper  deck  of  all  vessels,  except  those  hav- 
ing a  continuous  hurricane-deck  extending  right  fore  and  aft.  in  which  the 
length  is  to  be  measured  on  the  range  of  deck  immediately  below  the  hurri- 
cane-deck. 

Vessels  having  clipper  heads,  raking  forward,  or  receding  stems,  or  rak- 
ing stern-posts,  the  length  to  be  the  distance  of  the  fore  side  of  stem  from 
aft-side  of  stern-post  at  the  deep-load  water-line  measured  at  middle  line. 
^The  inner  or  propeller-post  to  be  taken  as  stern-post  in  screw-steamers. 

II.  Breadth,  B.—  To  be  measured  over  the  widest  frame  at  its  widest  part; 
in  other  words,  the  moulded  breadth. 

III.  Depth,  D.—  To  be  measured  at  the  dead-flat  frame  and  at  middle  line 
of  vessel.    It  shall  be  the  distance  from  the  top  of  floor-plate  to  the  upper 
side  of  upper  deck-beam  in  all  vessels  except  those  having  a  continuous 
ihurricane-deck,  extending    right  fore  and  aft,   and  not  intended   for  the 
American  coasting  trade,  in  which  the  depth  is  to  be  the  distance  from  top 
of  floor-plate  to  midway  between  top  of  hurricane  deck-beam  and  the  top 
of  deck-beam  of  the  deck  immediately  below  hurricane-deck. 

In  vessels  fitted  with  a  continuous  hurricane  deck,  extending  right  fore 
and  aft.  and  intended  for  the  American  coasting  trade,  the  depth  is  to  be 
the  distance  from  top  of  floor-plate  to  top  of  deck-beam  of  deck  immedi- 
ately below  hurricane-deck. 

Rule  for  Obtaining  Tonnage.— Multiply  together  the  length, 
breadth,  and  depth,  and  their  product  by  .75;  divide  the  last  product  by  100; 

the  quotient  will  be  the  tonnage.     L  X  B  ^  =  tonnage. 

The  IT.  s.  Custom-house  Tonnage  Law,  May  6,  1864,  provides 
thnt  "the  register  tonnage  of  a  vessel  shall  be  her  entire  internal  cubic 
capacity  in  tons  of  100  cubic  feet  each.'1  This  measurement  includes  all  the 
spare  between  upper  decks,  however  many  there  may  be.  Explicit  direc- 
tions for  making  the  measurements  are  given  in  the  law. 

The  Displacement  of  a  Vessel  (measured  in  tons  of  2240  Ibs.)  is 
the  weight  of  the  volume  of  water  which  it  displaces.  For  sea-water  it  is 
equal  to  the  volume  of  the  vessel  beneath  the  water-line,  in  cubic  feet, 
divided  by  35,  which  figure  is  the  number  of  cubic  feet  of  sea-water  at  60° 


1002  MARINE    ENGINEERING. 

F.  in  a  ton  of  2240  Ibs.  For  fresh  water  the  divisor  is  35.93.  The  U.  S.  reg- 
ister tonnage  will  equal  the  displacement  when  the  entire  internal  cubic 
capacity  bears  to  the  displacement  the  ratio  of  100  to  35. 

The  displacement  or  gross  tonnage  is  sometimes  approximately  estimated 
as  follows:  Let  L  denote  the  length  in  feet  of  the  boat,  B  its  extreme 
breadth  in  feet,  and  D  the  mean  draught  in  feet;  the  product  of  these  three 
dimensions  will  give  the  volume  of  a  parallelopipedon  in  cubic  feet.  Put- 
ting V  for  this  volume,  we  have  V  =  L  X  B  X  D. 

The  volume  of  displacement  may  then  be  expressed  as  a  percentage  of 
the  volume  V,  known  as  the  "  block  coefficient.'"  This  percentage  varies  for 
different  classes  of  ships.  In  racing  yachts  "with  very  deep  keels  it  varies 
from  22  to  33;  in  modern  merchantmen  from  55  to  75;  for  ordinary  small 
boats  probably  50  will  give  a  fair  estimate.  The  volume  of  displacement  in 
cubic  feet  divided  by  35  gives  the  displacement  in  tons. 

Coefficient  of  Fineness.  —  A  term  used  to  express  the  relation  be- 
tween the  displacement  of  a  ship  and  the  volume  of  a  rectangular  prism  or 
box  whose  lineal  dimensions  are  the  length,  breadth,  and  draught  of  the 
ship. 

Coefficient  of  fineness  =  ,  .,  *  ^  W7;  D  being  the  displacement  in  tons 

Li  X  -t>  X    vv 

of  35  cubic  feet  of  sea-  water  to  the  ton,  I/the  length  between  perpendiculars, 
B  the  extreme  breadth  of  beam,  and  W  the  mean  draught  of  water,  all  in 
feet. 

Coefficient  of  "Water-lines.—  An  expression  of  the  relation  of  the 
displacement  to  the  volume  of  the  prism  whose  section  equals  the  midship 
section  of  the  ship,  and  length  equal  to  the  length  of  the  ship. 

Coefficient  of  Water-lines  =  area  Of  immers^wTter  section  x  L'  Seat°n 
gives  the  following  values: 

Coefficient  Coefficient  of 

of  Fineness.  Water-lines. 

Finely-shaped  ships  ......  .......................           0.55  0.63 

Fairly-shaped  ships  -----  ........................           0.61  0.67 

Ordinary  merchant  steamers  for  speeds  of  10  to 

11  knots  .....   ..................  ............           0.65  0.72 

Cargo  steamers,  9  to  10  knots  ...................           0.70  0.76 

Modern  cargo  steamers  of  large  size  ............           0.78  0.83 

Resistance  of  Ships.—  The  resistance  of  a  ship  passing  through 
water  may  vary  from  a  number  of  causes,  as  speed,  form  of  body,  displace- 
ment, midship  dimensions,  character  of  wetted  surface,  fineness  of  lines, 
etc.  The  resistance  of  the  water  is  twofold  :  1st.  That  due  to  the  displace- 
ment of  the  water  at  the  bow  and  its  replacement  at  the  stern,  with  the 
consequent  formation  of  waves.  2d.  The  friction  between  the  wetted  sur- 
face of  the  ship  and  the  water,  known  as  skin  resistance.  A  common  ap- 
proximate formula  for  resistance  of  vessels  is 

Resistance  =  speed2  X  /^/displacement2  x  a  constant,  or   R  =  S*D%  X  C. 

If  D  =  displacement  in  pounds,  S  =  speed  in  feet  per  minute,  R  =  resist- 

ance in  foot-pounds  per  minute,  R  =  CS8Z)i.    The  work  done  in  overcom- 


ing the  resistance  through  a  distance  equal  to  S  is  R  x  S  =  CSSD^;   and 
if  E  is  the  efficiency  of  the  propeller  and  machinery  combined,  the  indicated 


horse-power  I.H.P.  =  -- 


If  S  =  speed  in  knots,  D  =  displacement  in  tons,  and  C  a  constant  which 
includes  all  the  constants  for  form  of  vessel,  efficiency  of  mechanism,  etc., 


. 

The  wetted  surface  varies  as  the  cube  root  of  the  square  of  the  displace- 
ment; thus,  let  L  be  the  length  of  edge  of  a  cube  just  immersed,  whose  dis- 
placement is  D  and  wetted  surface  W.  Then  D  —  L3  or  L  =  y'D,  and 
W  ~  5  X  L2  =  5  X(  |/Z>)a.  That  is,  W  varies  as  Z>§, 


MARINE   ENGINEERING. 
Another  approximate  formula  is 


1003 


P  _  area  of  immersed  midship  section  X 
K. 


The  usefulness  of  these  two  formulae  depends  upon  the  accuracy  of  the 
so-called  "constants  "  Cand  K,  which  vary  with  the  size  and  form  of  the 
ship,  and  probably  also  with  the  speed.  Seaton  gives  the  following  which 
may  be  taken  roughly  as  the  values  of  C  and  Sunder  the  conditions  ex- 
pressed  : 


General  Description  of  Ship. 

Speed, 
knots. 

Value 
of  C. 

Value 
of  K. 

Ships  over  400  feet  long,  finely  shaped  .  .  . 

15  to  17 

240 

6^0 

300                                              

15       17 

190 

500 

13        15 

240 

650 

t(                                             It                                                « 

11        13 

260 

700 

Ships  over  300  feet  long,  fairly  shaped  

11        13 

240 

650 

9        11 

260 

700 

Ships  over  250  feet  long,  finely  shaped  

13        15 

200 

580 

11        13 

240 

660 

it          -          *t                     it 

9        11 

260 

700 

Ships  over  250  feet  long,  fairly  shaped  

11        13 

220 

690 

9       11 

250 

680 

Ships  over  200  feet  long,  finely  shaped  

11        12 

220 

600 

9       11 

240 

640 

Ships  over  200  feet  long,  fairly  shaped  

9       11 

220 

620 

Ships  under  200  feet  long,  finely  shaped  

11        12 
10       11 

200 
210 

550 

580 

<t                 K                       tt 

9    '  10 

230 

620 

Ships  under  200  feet  long,  fairly  shaped  

9    '  10 

200 

600 

Coefficient  of  Performance  of  Vessels.  -The  quotient 


^/(displacement)2  x  (speed  in  knots)3 
tons  of  coal  in  24  hours 

gives  a  quotient  of  performance  which  represents  the  comparative  cost  of 
propulsion  in  coal  expended.  Sixteen  vessels  with  three-stage  expansion- 
engines  in  1890  gave  an  average  coefficient  of  14,810,  the  range  being  from 
12,150  to  16,700. 

In  1881  seventeen  vessels  with  two-stage  expansion-engines  gave  an  aver- 
age coefficient  of  11.710.  In  1881  the  length  of  the  vessels  tested  ranged  from 
260  to  320,  and  in  1890  from  295  to  400.  The  speed  in  knots  divided  by  the 
square  root  of  the  length  in  feet  in  1881  averaged  0.539;  and  in  1890,  0.579; 
ranging  from  0.520  to  0.641.  (Proc.  lust.  M  E.,  July,  1891,  p.  329.) 

Defects  of  the  Common  Formula  for  Resistance.— Modern 
experiments  throw  doubt  upon  the  truth  of  the  statement  that  the  resistance 
varies  as  the  square  of  the  speed.  (See  liobt.  Mansel's  letters  in  Engineer- 
ing,  1891 ;  also  his  paper  on  The  Mechanical  Theory  of  Steamship  Propulsion, 
read  before  Section  G  of  the  Engineering  Congress,  Chicago,  1893.) 

Seaton  says:  In  small  steamers  the  chief  resistance  is  the  skin  resistance. 
In  very  fine  steamers  at  high  speeds  the  amount  of  power  required  seems 
excessive  when  compared  with  that  of  ordinary  steamers  at  ordinary  speeds. 

In  torpedo-launches  at  certain  high  speeds  the  resistance  increases  at  a 
lower  rate  than  the  square  of  the  speed. 

In  ordinary  sea-going  and  river  steamers  the  reverse  seems  to  be  the  case. 

Rankine's  Formula  for  total  resistance  of  vessels  of  the  "wave- 
line  "  type  is: 


B  =  ALBV*(1  +  4  sin2  0  +  sin*  0), 


of  the  stream- 


in  which  equation  9  is  the  mean  angle  of  greatest  obliquity  of  

lines,  A  is  a  constant  multiplier.  B  the  mean  wetted  girth  of  the  surface  ex- 
posed to  friction,  L  the  length  in  feet,  and  V  the  speed  in  knots.  The  power 
demanded  to  impel  a  ship  is  thus  the  product  of  a  constant  to  be  determined 
by  experiment,  the  area  of  the  wetted  surface,  the  cube  of  the  speed,  and  the 


1004 


MARINE    ENGINEERING. 


quantity  in  the  parenthesis,  which  is  known  as  the  "coefficient  of  augmen- 
tation.1' The  last  term  of  the  coefficient  may  he  neglected  in  calculating  the 
resistance  of  ships  as  too  small  to  be  practically  important.  In  applying  the 
formula,  the  mean  of  the  squares  of  the  sines  of  the  angles  of  maximum 
obliquity  of  the  water-lines  is  to  be  taken  for  sin2  0,  and  the  rule  will  then 
read  thus: 

To  obtain  the  resistance  of  a  ship  of  good  form,  in  pounds,  multiply  the 
length  in  feet  by  the  mean  immersed  girth  and  by  the  coefficient  of  augmen- 
tation, and  then  take  the  product  of  this  "augmented  surface,11  as  Rankine 
termed  it,  by  the  square  of  the  speed  in  knots,  and  by  the  proper  constant 
coefficient  selected  from  the  following: 

For  clean  painted  vessels,  iron  hulls  .......  .  A  —  .01 

For  clean  coppered  vessels  .............  ____  A  =  .009  to  .008 

For  moderately  rough  iron  vessels  .........  A  =  .011  -f 

The  net,  or  effective,  horse  -power  demanded  will  be  quite  closely  obtained 
by  multiplying  the  resistance  calculated,  as  above,  by  the  speed  in  knots  and 
dividing  by  326.  The  gross,  or  indicated,  power  is  obtained  by  multiplying 
the  last  quantity  by  the  reciprocal  of  the  efficiency  of  the  machinery  and 
propeller,  which  usually  should  be  about  0.6.  Rankine  uses  as  a  divisor  in 
this  case  200  to  260. 

The  form  of  the  vessel,  even  when  designed  by  skilful  and  experienced 
naval  architects,  will  often  vary  to  such  an  extent  as  to  cause  the  above  con- 
stant coefficients  to  vary  somewhat;  and  the  range  of  variation  with  good 
forms  is  found  to  be  from  0.8  to  1.5  the  figures  given. 

For  well-shaped  iron  vessels,  an  approximate  formula  for  the  horse-power 


required  is  H.P.  =  ;jY7nh'  m  wn*cn  ^  *s  ^ 
SV3 


"augmented  surface."    The  ex- 


pression  ==-=-  has  been  called  by  Rankine  the  coefficient  of  propulsion.    In 

Xl.i  . 

the  Hudson  River  steamer  "  Mary  Powell,11  according  to  Thurston,  this 
coefficient  was  as  high  as  23,500. 


The  expression 


== 

Jti.Jr. 


has  been  called  the  locomotive  performance.    (See 


Rankine's  Treatise  on  Shipbuilding,  1864;  Thurston^  Manual  of  the  Steam- 
engine,  part  ii.  p.  16;  also  paper  by  F.  T.  Bowles,  U.S.N.,  Proc.  U.  S.  Naval 
Institute,  1883.) 

Rankine's  method  for  calculating  the  resistance  is  said  by  Seaton  to  give 
more  accurate  and  reliable  results  than  those  obtained  by  the  older  rules, 
but  it  is  criticised  as  being  difficult  and  inconvenient  of  application. 

I>r,  Kirk's  Method.  —  This  method  is  generally  used  on  the  Clyde. 

The  general  idea  proposed  by  Dr.  Kirk  is  to  reduce  all  ships  to  so  definite 
and  simple  a  form  that  they  may  be  easily  compared;  and  the  magnitude  of 
certain  features  of  this  form  shall  determine  the  suitability  of  the  ship  for 
speed,  etc. 

The  form  consists  of  a  middle  body,  which  is  a  rectangular  parallelepiped, 
and  fore  body  and  after  body,  prisms  having  isosceles  triangles  for  bases, 
as  shown  in  Fig.  168. 


FIG.  168. 

This  is  called  a  block  model,  and  is  such  that  its  length  is  equal  to  that  of 
the  ship,  the  depth  is  equal  to  the  mean  draught,  the  capacity  equal  to  the 
displacement  volume,  and  its  area  of  section  equal  to  the  area  of  im- 


MABINE   ENGINEERING.  1005 

liiersed  midship  section.  The  dimensions  of  the  block  model  may  be  obtained 
as  follows: 

Let  A3  =  HB  =  length  of  fore-  or  after-body  =  F; 
GH  =  length  of  middle  body  =  M\ 

KL  =  mean  draught  =  H\ 

_,T-.       area  of  immersed  midship  section 
*K  =  ~  KL  ~  =  B' 

Volume  of  block  =  (F+  M )  X  B  X  H\ 

Midship  section  =  B  X  H; 

Displacement  in  tons  =  volume  in  cubic  ft.  -*-  35. 

AH  =  AG  -f-  GH  =  F+  M  =  displacement  X  35  •*•  (B  X  H). 

'Uie  wetted  surface  of  the  block  is  nearly  equal  to  that  of  the  ship  of  the 
s*-,me  length,  beam  and  draught;  usually  2%  to  5%  greater.  In  exceedingly 
fine  hollow-line  ships  it  may  be  8$  greater. 

Area  of  bottom  of  block  =  (F+M)  X  B\ 
Area  of  sides  =  2M  X  H. 


Area  of  sides  of  ends  =  4|/  F*  -f  (— J   x  H\ 

1/7?  R 

Tangent  of  half  angle  of  entrance  =  <-~-  =  — . 

From  this,  by  a  table  of  natural  tangents,  the  angle  of  entrance  may  be 
obtained: 

Angle  of  Entrance     Fore-body  in 
of  the  Block  Model,  parts  of  length. 
Ocean-going  steamers,  14  knots  and  upward.      18°  to  15°  .3   to  .36 

"  12  to  14  knots 21    to  18  .26  to  .3 

"  cargo  steamers,  10  to  12  knots..      30    to  22  .22  to  .26 

K.  R.  Mumford's  Met  hod  of  Calculating  Wetted  Surfaces 

is  given  iu  a  paper  by  Archibald  Denny,  Eng'g,  Sept.  21,  1894.  The  following 
is  his  formula,  which  gives  closely  accurate  results  for  medium  draughts, 
beams,  and  finenesses: 

S=(LXDX  1.7)  -f  (L  X  B  X  C), 

in  which  S  =  wetted  surface  in  square  feet; 

L  =  length  between  perpendiculars  in  feet; 
D  =  middle  draught  in  feet: 
B  =  beam  in  feet; 
C  =  block  coefficient. 

The  formula  may  also  be  expressed  in  the  form  S  =  L(1.7D  -f-  BC). 

Iu  the  case  of  twin-screw  ships  having  projecting  shaft-casings,  or  in  the 
case  of  a  ship  having  a  deep  keel  or  bilge  keels,  an  addition  must  be  made 
for  such  projections.  The  formula  gives  results  which  are  in  general  much 
more  accurate  than  those  obtained  by  Kirk's  method.  It  underestimates 
i  he  surface  when  the  beam,  draught,  or  block  coefficients  are  excessive;  but 
the  error  is  small  except  in  the  case  of  abnormal  forms,  such  as  stern-wheel 
steamers  having  very  excessive  beams  (nearly  one  fourth  the  length),  and 
also  very  full  block  coefficients.  The  formula  gives  a  surface  about  6^  too 
small  for  such  forms. 

To  Find  tlie  Indicated  Horse-power  from  tne  Wetted 
Surface.  (Seatou.)— In  ordinary  cases  the  horse-power  per  100  feet  of 
wetted  surface  may  be  found  by  assuming  that  the  rate  for  a  speed  of  10 
knots  is  5,  and  that  the  quantity  varies  as  the  cube  of  the  speed.  For  exam- 
ple: To  find  the  uumoer  of  I.ILP.  necessary  to  drive  a  ship  at  a  speed  of  15 
knots,  having  a  wetted  skin  of  block  model  of  16,200  square  feet: 

The  rate  per  100  feet  =  (15/10)3  x  5  =  16.875. 
Then  I.H.P.  required  =  16.875  X  162  =  2734. 


1006 


MA  HIKE   ENGINEERING. 


When  the  ship  is  exceptionally  well-proportioned,  the  bottom  quite  clean, 
and  the  efficiency  of  the  machinery  high,  as  low  a  rate  as  4  I.H.P.  per  100 
feet  of  wetted  skin  of  block  model  may  be  allowed 

The  gross  indicated  horse-power  includes  the  power  necessary  to  over- 
come the  friction  and  other  resistance  of  the  engine  itself  and  the  shafting, 
and  also  the  power  lost  in  the  propellor.  In  other  words,  I.H.P.  is  no  meas- 
ure of  the  resistance  of  the  ship,  and  can  only  be  relied  on  as  a  means  of 
deciding  the  size  of  engines  for  speed,  so  long  as  the  efficiency  of  the  engine 
and  propellor  is  known  definitely,  or  so  long  as  similar  engines  and  propellers 
are  employed  in  ships  to  be  compared.  The  former  is  difficult  to  obtain, 
and  it  is  nearly  impossible  in  practice  to  know  how  much  of  the  power  shown 
in  the  cylinders  is  employed  usefully  in  overcoming  the  resistance  of  the 
ship.  The  following  example  is  given  to  show  the  variation  in  the  efficiency 
of  propellers: 

Knots.       I.H.P. 
12.064  with  1940 


7503 


H.M.S.  "  Amazon,"  with  a  4-bladed  screw,  gave 

H.M.S.  lt  Amazon,"  with  a  2-bladed  screw,  increased  pitch, 

and  less  revolutions  per  minute 12.396 

H.M.S.  "Iris,"  with  a  4-bladed  screw 16.577 

H.M.S.  "Iris,"  with  2-bladed  screw,  increased  pitch,  less 

revolutions  per  knot 18.587     "     7556 

Relative  Horse-power  Required  for  Different  Speeds  of 
Vessels.  (Horse-power  for  10  knots  —  1.) — The  horse-power  is  taken  usually 
to  vary  as  the  cube  of  the  speed,  but  in  different  vessels  and  at  different 
speeds  it  may  vary  from  the  2.8  power  to  the  3.5  power,  depending  upon  the 
lines  of  the  vessel  and  upon  the  efficiency  of  the  engines,  the  propeller,  etc. 


II 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

HP  a 

.0769 

.239 

.535 

1. 

.666 

2.565 

3.729 

5.185 

6.964 

9.095 

11.60 

14.52 

17.87 

21.67 

.<?*•• 

.0701 

.227 

.524 

1  . 

.697 

2.653 

3.908 

5.499 

7.464 

9.841 

12.67 

15.97 

19.80 

24.19 

,S3 

.0640 

.216 

.512 

1. 

.728 

2.744 

4.096 

5.832 

8, 

10  65 

13  82 

17  58 

21  95 

S3-1 

.0584 

.205 

.501 

1. 

.760 

2.838 

4.293 

6.185 

8.574 

11.52 

15.09 

19.34 

24.33 

30  14 

#3-8 

.0533 

.195 

.490 

1. 

.792 

2.935 

4.500 

6.559 

9.189 

12.47 

16.47 

21.28 

26  97 

33  63 

fi3-3 

.0486 

.185 

.479 

1. 

.825 

3.036 

4.716 

6  957 

9.849 

13.49 

17  98 

23  41 

29  90 

37.54 

fl3  -4 

.0444 

.176 

.468 

1. 

.859 

3.139 

4.943 

7.378 

10.56 

14.60 

19.62 

25.76 

33  14 

41  90 

£3-6 

.0405 

.167 

.458 

1.1   .893 

3.247 

5.181 

7.824 

11.31 

15.79 

21.42 

28.34 

36.73 

46.77 

EXAMPLE  IN  USE  OP  THE  TABLE. — A  certain  vessel  makes  14  knots  speed 
with  587  I.H.P.  and  16  knots  with  900  I.H.P.  What  I.H.P.  will  be  required  at 
18  knots,  the  rate  of  increase  of  horse-power  with  increase  of  speed  remain- 
ing constant  ?  The  first  step  is  to  find  the  rate  of  increase,  thus:  14X  :  16^  :: 
587  :  900. 

x  log  16  -  x  log  14  =  log  900  -  log  587; 

#(0.204120  -  0.146128)  =  2.954243  -  2.768638, 

whence  x  (the  exponent  of  S  in  formula  H.P.  ocS^')  =  32. 

From  the  table,  for  S3'2  and  16  knots,  the  I  H.P.  is  4.5  times  the  I.H.P.  at 
10  knots,  .'.  H.P.  at  10  knots  =  900  -j-  4.5  =  200. 

From  the  table,  forS3'2  and  18  knots,  the  I.H.P.  is  6.559  times  the  I.H.P.  at 
10  knots;  /.  H.P.  at  18  knots  =  200  X  6.559  =  1312  H.P. 

Resistance  per  Horse-power  for  Different  Speeds.  (One 
horse-power  --  33,000  Ibs.  resistance  overcome  through  1  ft.  in  1  inin.) — The 
resistances  per  horse-power  for  various  speeds  are  as  follows:  For  a  speed  of 
1  knot,  or  6080  feet  per  hour  -  101^  ft.  per  min.,  33,000  -H  101^  =  325.658  Ibs. 
per  horse-power;  and  for  any  other  speed  325.658  Ibs.  divided  by  the  speed 
in  knots;  or  for 


1  knot  325. 66  Ibs. 

2  knots  162. 83    " 
8     "      108.55    " 
4     *'        81.41     " 
&     "       65.13    " 


6  knots  54. 28  Ibs. 

7  u      46.52    " 

8  "      40.71     " 

9  "      36.18    " 
10     *4      32.57    " 


11  knots  29. 61  Ibs. 

12  "      27.14    " 

13  "      25.05    " 

14  "      23.26    " 

15  "      21.71     " 


16  knots  20. 35  Ibs. 

17  "      19.16    " 

18  "       18.09    " 

19  "       17.14     " 

20  k4       16  28    " 


MARINE   ENGINEERING. 


1007 


ftesults  of  Trials  of  Steam-vessels  of  Various  Sizes. 

(From  Seaton's  Marine  Engineering.) 


S.S. 
"Torpedo." 

P.S. 
"  John  Penn." 

03 

QD| 

«s 

P.S. 
"Mary  Powell" 

rfiS 

w  3 

R.M.P.S. 
"Connaught." 

Length  perpendiculars  

90'  0" 

171'  9" 

130'  0" 

286'  0" 

230'  0" 

3>7/  Q// 

Breadth,  extreme  .  

10'  6" 

18'  9" 

21'  0" 

34'  3" 

29'  0" 

35'  0" 

Mean  draught  water  

2'  6" 

6'  9U" 

8'  10" 

6'  0" 

13'  6" 

13'  0" 

Displacement  (tons)              

29.73 

280 

370 

800 

1500 

1900 

Area  Immersed  mid.  section  — 
w  .  r  Wetted  skin       .         

24? 

903 

99 
3793 

148 
3754 

200 
8222 

340 
10  075 

336 

15  782 

•£j.  a  I 
C  -2  •<  Length  fore-body  

45'  0" 

72'  00" 

42'  6" 

143'  0" 

79'  6" 

1°9'  0" 

t£ 
CQ^  (Angle  of  entrance 

12°  40' 

11°  30' 

23°  50' 

13°  21' 

17°  0" 

11°  26' 

Displacement  X  35 

0  481 

0  576 

0  608 

0  489 

0  671 

0  605 

Length  X  Imm.  mid  area'" 
Speed  (knots)      

22  01 

15.3 

10.74 

17.20 

10  04 

17  8 

Indicated  horse-power  —  
I.H.P.  per  100  ft.  wetted  skin  .... 
I.H.P.  per  100  ft.  wetted  skin,  re- 
duced to  10  knots         

460 
50.9 

4.78 

798 
21.04 

5.87 

371 
9.88 

7.97 

1490 
18.12 

3  56 

503 
5.00 

4.90 

4751 
30.00 

5.32 

D§X<S8 

223 

192 

172  8 

293  7 

266 

182 

I.H.P.  " 

Immersed  mid  area  X  S3 

556  9 

445 

495 

683 

6i)0 

399 

I.H.P.                    •"••• 

H.M.S. 
"  Active." 

ri~tft 

a'3 

Wx 

fi 

«= 

S.S. 
"Garonne." 

oJJ5 

*:l 

w^ 

R.M.S.S. 
"  Britannic." 

270'  0" 

300'  0" 

300'  0" 

370'  0" 

392    0" 

450'  0" 

Breadth  extreme               

42'  0" 

46'  0" 

46'  0" 

41'  0" 

39   0" 

45'  2'' 

18'  10" 

18'  2" 

18'  2" 

18'  11" 

21'  4" 

23'  7" 

Displacement  (tons)               .   .  . 

3057 

3290 

3.190 

4635 

5767 

8500 

632 

700 

700 

656 

738 

926 

*      (  Wetted  skin 

16,008 

18,168 

18,168 

22,633 

26,235 

32,578 

*! 

"3  •»•*  <  Length  fore-body 

101'  0'' 

135'  6" 

135'  6" 

123'  0" 

118'  0" 

129'  0" 

co*      1  Angle  of  entrance             . 

18°  44' 

16°  16' 

16°  16' 

16°  4' 

16°  30' 

17°  16' 

Displacement  X  35 

0  629 

0  548 

0  548 

0  668 

0.698 

0.714 

Length  X  Imm.  mid  area 
Speed  (knots)                       

14.966 

18.573 

15.746 

13.80 

12.054 

15.045 

Indicated  horse-power  
I.H.P.  per  100  ft.  wetted  skin  .... 
I.H.P.  per  100  ft.  wetted  skin,  re- 
duced  to  10  knots 

4015 
25.08 

7  49 

7714 
42.46 

6.634 

3958 
21.78 

5.58 

2500 
11.04 

4.20 

1758 
6.7 

3.83 

4900 
15.04 

4.42 

D§  X  -S» 

175.8 

183.7 

218.2 

292 

320 

289.3 

I.H.P.  " 
Immersed  mid  area  X  S3 

527  5 

581  4 

690  5 

689 

735 

642.5 

I.H.P.                    

1008 


MARINE   EKGIXEERIHG. 


Results  of  Progressive  Speed  Trials  in  Typical  Vessels. 

(Eng'g,  April  15,  1892,  p.  463.) 


^; 

a 

u 

*'».!-' 

t^ 

-    t-° 

6 

liif 

..  .2 

|f 

"    tc 

n 

fl 

«  pi 

O) 

^"SS  OJ 

•n—  J 

O.'4 

T3    . 

c^_. 

B  |  i 

p< 

H  5j*    o 

4)  V 

*-  V 

1  M  u 

T*    V 

J=2d£ 

g 

o 
% 

^g 

£8 

;  3 

-       05 

Length  (in  feet)  .        ... 

135 

230 

265 

300 

360 

375 

525 

Breadth"     "    

14 

27 

41 

43 

60 

65 

63 

Draught  (mean 
Displacement.  ( 

)  on  trial 

5'  1" 
103 

8'  3" 
735 

16'  6/x 

2800 

16'  2" 
3330 

23*  9" 
7390 

25'  9" 
9100 

21'.  3" 
11550 

tons)  

I  H  P 

10  knot 

s. 

110 

450 

700 

800 

1  000 

1500 

2000 

14     ** 

260 

1100 

2100 

2400 

3000 

4000 

4600 

it 

18     " 

870 

2500 

6400 

6000 

7500 

9000 

10000 

a, 

20     " 

1130 

3500 

10000 

9000 

11000 

12500 

14500 

Speed 

Ratio  of 
speed3 

10 

1 

Ratio  of  H.P.  = 

1 

1 

1 

1 

1 

1 

1 

14 

2.744 

*'          *'     = 

2.36 

2.44 

3 

3 

3 

2.67 

2.3 

18 

5.832 

"          "     = 

7.91 

5.56 

9.14 

7.5 

7.5 

6. 

5 

20 

8. 

it          t<     __ 

10.27 

7.78 

14.14 

11.25 

11 

8.42 

7.25 

Admiralty  coeff  .        f  10  knots. 

200 

181 

284 

279 

380 

290 

255 

Z)§  XS3 

1  14      ' 
1  ia      *' 

232 
147 

203 

1Qft 

259 

255 

91  7 

347 

OQK 

298 

OftO 

304 

9Q7 

I.H.P. 

1  20      " 

156 

186 

159 

198 

276 

278 

281 

The  figures  for  I.H.P.  are  "  round."  The  "  Medusa's  "  figures  for  20  knots 
are  from  trial  on  Stokes  Bay,  and  show  the  retarding  effect  of  shallow  water. 
The  figures  for  the  other  ships  for  20  knots  are  estimated  for  deep  water. 

More  accurate  methods  than  those  above  given  for  estimating  the 
horse-power  required  for  any  proposed  ship  are:  1.  Estimations  calculated 
from  the  results  of  trials  of  "  similar"  vessels  driven  at "  corresponding" 
speeds;  "  similar  "  vessels  being  those  that  have  the  same  ratio  of  length  to 
breadth  and  to  draught,  and  the  same  coefficient  of  fineness,  and  "corre- 
sponding" speeds  those  which  are  proportional  to  the  square,  roots  of 
the  lengths  of  the  respective  vessels.  Froude  found  that  the  resistances  of 
such  vessels  varied  almost  exactly  as  wetted  surface  x  (speed)2. 

2.  The  method  employed  by  the  British  Admiralty  and  by  some  Clyde 
shipbuilders,  viz.,  ascertaining  the  resistance  of  a  model  of  the  vessel,  12  to 
20  ft.  long,  in  a  tank,  arid  calculating  the  power  from  the  results  obtained. 

Speed  on  Canals.— A  great  loss  of  speed  occurs  when  a  steam-vessel 
passes  from  open  water  into  a  more  or  less  restricted  channel.  The  average 
speed  of  vessels  in  the  Suez  Canal  in  1882  was  only  514  statute  miles  per  hour. 
(Engig.  Feb.  15,  1884.  p.  139.) 

Estimated  Displacement,  Horse-power,  etc. -The  table  on 
the  next  page,  calculated  by  the  author,  will  be  found  convenient  for  mak- 
ing approximate  estimates. 

The  figures  in  7th  column  are  calculated  by  the  formula  H.P.  =  <S3i)s-f-  r, 
in  which  c  =  200  for  vessels  under  200  ft.  long  when  C  —  .65,  and  210 
when  C  =  .55;  c  =  200  for  vessels  200  to  400  ft.  long  when  C  =  .75,  220  when 
C  =  .65,  240  when  C  =  .55;  c  =  230  for  vessels  over  400  ft.  long  when  C  =  .75, 
250  when  C  =  .65,  260  when  C  =  .55. 

The  figures  in  the  8th  column  are  based  on  5  H.P.  per  100  sq.  ft.  of  wetted 
surface. 

The  diameters  of  screw  in  the  9th  column  are  from  formula  D  — 
3.31  I/LHLP.,  and  in  the  10th  column  from  formula  D  =  2.71  |/lTHTPT 

To  find  the  diameter  of  screw  for  any  other  speed  than  10  knots,  revolu- 
tions being  100  per  minute,  multiply  the  diameter  given  in  the  table  by  the 
5th  root  of  the  cube  of  the  given  speed  -+- 10.  For  any  other  revolutions  per 
minute  than  100,  divide  by  the  revolutions  and  multiply  by  100. 

To  find  the  approximate  horse-power  for  any  other  speed  than  10  knots, 
multiply  the  horse-power  given  in  the  table  by  the  cube  of  the  ratio  of  the 
given  speed  to  10,  or  by  the  relative  figure  from  table  on  p.  1006. 


MARINE   ENGINEERING. 


1009 


Intimated  Displacement,  Horse-power,  etc.,  of  Steam- 
vessels  of  Various  Sizes. 


fivJ 

•jf 

5CQ 

II 

15 
!•» 

|c° 

pi 

I  Displace- 
ment. 
\LBD  X  C 

Wetted  Surface 
L(1.1D  +  BC) 
Sq.  ft. 

Estimated  Horse- 
power at  10  knots. 

Diam.  of  Screw  for  10 
knots  speed  and  100 
revs,  per  minute. 

Calc. 
from  Dis- 
placem't. 

Calc.  Irom 
Wetted 
Surface. 

35 

tons. 

If  Pitch  = 
Diam. 

If  Pitrh  = 
1.4  Diam. 

12 

3 

1.5 

.55 

.85 

48 

4.3 

2.4 

4.4 

3.6 

ifij 

3 

1.5 

i   .55 

1.13 

64 

5.2 

3.2 

4.6 

3  8 

16  1 

4 

2 

.65 

2.38 

96 

8.9 

4.8 

5.1 

4.2 

90  J 

3 

1.5 

.55 

1.41 

80 

6.0 

4.0 

4.7 

3.9 

20  { 

4 

o 

.65 

2.97 

120 

10.3 

6.0 

5.3 

4.3 

OJ  j 

3.5 

1.5 

.55 

1.98 

104 

7.5 

5.2 

5 

4.1 

~4  1 

4.5 

2 

.65 

4.01 

152 

12.6 

7.6 

5.5 

4.5 

4 

'2 

.55 

3.77 

168 

11.5 

8.4 

5.4 

4.4 

30  ] 

5 

2.5 

.65 

6.96 

224 

18.2 

11.2 

5.9 

4.8 

Af\] 

4.5 

2 

.'55 

5.66 

235 

15.1 

11.8 

5.7 

4.7 

4U  -< 

6 

2.5 

.65 

11.1 

326 

24.9 

16.3 

6.3 

5.2 

K0j 

6 

1 

.55 

14.1 

420 

27.8 

21.0 

6.4 

5.4 

50  -j 

8 

3.5 

.65 

-   26 

558 

43.9 

27.9 

7.1 

5.8 

RhJ 

8 

3.5 

.55 

26.4 

621 

42.2 

31.1 

7.0 

5.7 

00  1 

10 

4 

.65 

44.6 

798 

62.9 

39.9 

7.6 

6.2 

WJ 

10 

4 

.55 

44 

861 

59.4 

43.1 

7.5 

6.1 

<0i 

12 

4.5 

.65 

70.2 

1082 

85.1 

54.1 

8.1 

6.6 

on 

12 

4.5 

.55 

67.9 

1140 

79.2 

57.0 

7.9 

6.5 

80  1 

14 

.65 

104.0 

1408 

111 

704 

8.5 

.0 

13 

5 

.55 

91.9 

1408 

97 

70.4 

8.3 

90  1   16 

6 

.65 

160 

1854 

147 

92.7 

9 

.*3 

j 

13 

5 

.55 

102 

1565 

104 

78.3 

8.4 

9 

100^ 

15 

5.5 

.65 

153 

1910 

143 

95.5 

8.9 

.3 

j 

17 

6 

.75 

219 

2295 

202 

115 

9.6 

''.8 

( 

14 

5.5 

.55 

145 

2046 

131 

102 

8.8 

.2 

120^ 

16 

6 

.65 

214 

2472 

179 

124 

9.4 

.6 

|18 

6.5 

.75 

301 

2946 

250 

147 

10 

\\n 

6 

.55 

211 

2660 

169 

133 

9.2 

1  .4 

140^  118 

6.5 

.65 

306 

3185 

227 

159 

9.8 

.0 

1  20 

7 

.75 

420 

3766 

312 

188 

10.5 

.5 

17 

6.5 

.55 

278 

3264 

203 

163 

9.6 

.8 

160^  19 

7 

.65 

395 

3880 

269 

194 

10.1 

8.3 

j 

21 

7.5 

.75 

540 

4560 

368 

228 

10.8 

8.8 

( 

20 

7 

.55 

396 

4122 

257 

206 

10.1 

8.2 

180-^ 

22 

7.5 

.05 

552 

4869 

337 

243 

10.6 

8.7 

j 

24 

8 

.75 

741 

5688 

455 

284 

11.3 

9.2 

( 

22 

7 

.55 

484 

4800 

257 

240 

10.1 

8.2 

200  -< 

25 

8 

.65 

743 

5970 

373 

299 

10.8 

8.8 

( 

28 

9 

.75 

1080 

7260 

526 

363 

11.6 

9.5 

28 

8 

.55 

880 

7250 

383 

363 

10.9 

8.9 

250^ 

32 

10 

.65 

1486 

9450 

592 

473 

11.9 

9.7 

j 

36 

12 

.75 

2314 

11850 

875 

593 

12.8 

10.5 

j 

32 

10 

.55 

1509 

10380 

548 

519 

11.7 

9.6 

300^ 

36 

12 

.65 

2407 

13140 

806 

657 

12.6 

10.4 

1 

40 

14 

.75 

3600 

17140 

1175 

857 

13.6 

11.1 

( 

38 

12 

.55 

2508 

14455 

769 

723 

12.5 

10.2 

850  •< 

42 

14 

.65 

3822 

17885 

1111 

894 

13.5 

11.0 

( 

46 

16 

.75 

5520 

21595 

1562 

1080 

14.4 

11.8 

( 

44 

14 

.55 

3872 

19200 

1028 

960 

13.3 

10.8 

400^ 

48 

16 

.65 

5705 

23360 

1451 

1168 

14.2 

11.6 

] 

52 

18 

75 

8023 

27840 

2006 

1392 

15.2 

12.4 

50 

16 

!55 

5657 

24515 

1221 

1226 

13.7 

11.2 

450-^ 

54 

18 

.65 

8123 

29565 

1616 

1478 

14.5 

11.9 

( 

58 

20 

.75 

11157 

34875 

2171 

1744 

15.4 

12.6 

52 

18 

.55 

7354 

29600 

1454 

1480 

14.2 

11.6 

500-,' 

56 

20 

.65 

10400 

35200 

1966 

1760 

15.1 

12.4 

1 

60 

22 

.75 

14143 

41200 

2543 

2060 

15.9 

13.0 

i 

56 

20 

.55 

9680 

36245 

1747 

1812 

14.7 

12.0 

550-^ 

60 

22 

.65 

13483 

42735 

2266 

2137 

15  5 

12.7 

1 

64 

24 

.75 

18103 

49665 

2998 

2483 

16.4 

13.4 

j 

60 

22 

.55 

12446 

42900 

2065 

2145 

15.2 

12.5 

600  •{  64 

24 

.65 

17115 

50220 

2656 

2511 

15.4 

13.1 

168 

26 

.75 

22731 

58020 

3489 

2901 

16,9           13.8 

1010  MA1UKE   EXGIHEERIKG.  ' 

THE  SCRBW-PROPEL.L.ER. 

The  "  pitch  "  of  a  propeller  is  the  distance  which  any  point  in  a  blade, 
describing  a  helix,  will  travel  in  the  direction  of  the  axis  during  one  revolu- 
tion, the  point  being  assumed  to  move  around  the  axis.  The  pitch  of  a 
propeller  with  a  uniform  pitch  is  equal  to  the  distance  a  propeller  will 
advance  during  one  revolution,  provided  there  is  no  slip.  In  a  case  of  this 
kind,  the  term  "pitch'1  is  analogous  to  the  term  "pitch  of  the  thread"  of 
an  ordinary  single-threaded  screw. 

Let  P  —  pitch  of  screw  in  feet,  R  =  number  of  revolutions  per  second, 
F  =  velocity  of  stream  from  the  propeller  =  P  x  R,  v  =  velocity  of  the  ship 
in  feet  per  second,  V  —  v  =  slip,  A  =  area  in  square  feet  of  section  of  stream 
from  the  screw,  approximately  the  area  of  a  circle  of  the  same  diameter., 
A  X  V  =  volume  of  water  projected  astern  from  the  ship  in  cubic  feet  per 
second.  Taking  the  weight  of  a  cubic  foot  of  sea-water  at  64  Ibs.,  and  the 
force  of  gravity  at  32,  we  have  from  the  common  formula  for  force  of  accel- 

v        W  v  W 

eration,  viz.:  F  =  M-^  =  —  -~,  or  J^=  —vlt  when  t  =  1  second,  v^  being 

t        g   t  g 

the  acceleration. 

64.4  V 
Thrust  of  sere  win  pounds  =  —  — -(F  -  v)  =  2AV(V  —  v). 

Oii 

Rankine  (Rules,  Tables,  and  Data,  p.  275)  gives  the  following:  To  calculate 
the  thrust  of  a  propelling  instrument  (jet,  paddle,  or  screw)  in  pounds, 
multiply  together  the  transverse  sectional  area,  in  square  feet,  of  the  stream 
driven  astern  by  the  propeller;  the  speed  of  the  stream  relatively  to  the  snip 
in  knots;  the  real  slip,  or  part  of  that  speed  which  is  impressed  on  that 
stream  by  the  propeller,  also  in  knots;  and  the  constant  5.66  for  sea- water, 
or  5.5  for  fresh  water.  If  S  =  speed  of  the  screw  in  knots,  s  =  speed  of  ship 
in  knots,  A  =  area  of  the  stream  in  square  feet  (of  sea- water), 

Thrust  in  pounds  =  A  X  8(8  -  s)  X  5.66. 

The  real  slip  is  the  velocity  (relative  to  water  at  rest)  of  the  water  pro- 
jected sternward;  the  apparent  slip  is  the  difference  between  the  speed  of 
the  ship  and  the  speed  of  the  screw;  i.e.,  the  product  of  the  pitch  of  the 
screw  by  the  number  of  revolutions. 

This  apparent  slip  is  sometimes  negative,  due  to  the  working  of  the  screw 
in  disturbed  water  which  has  a  forward  velocity,  following  the  ship.  Nega- 
tive apparent  slip  is  an  indication  that  the  propeller  is  not  suited  to  the 
ship. 

The  apparent  slip  should  generally  be  about  8#  to  10#  at  full  speed  in  well- 
formed  vessels  with  moderately  fine  lines;  in  bluff  cargo  boats  it  rarely 
exceeds  5#. 

The  effective  area  of  a  screw  is  the  sectional  area  of  the  stream  of  water 
laid  hold  of  by  the  propeller,  and  is  generally,  if  not  always,  greater  than 
the  actual  area,  in  a  ratio  which  in  good  ordinary  examples  is  1.2  or  there- 
abouts, and  is  sometimes  as  high  as  1.4;  a  fact  probably  due  to  the  stiffness 
of  the  water,  which  communicates  motion  laterally  amongst  its  particles. 
(Rankiue's  Shipbuilding,  p.  89.) 

Prof.  D.  S.  Jacobus,  Trans.  A.  S.  M.  E.,  xi.  1028,  found  the  ratio  of  the  ef- 
fective to  the  actual  disk  area  of  the  screws  of  different  vessels  to  be  as 
follows : 

Tug-boat,  with  ordinary  true-pitch  screw 1 .42 

"    screw  having  blades  projecting  backward 57 

Ferryboat"   Bergen,"    with    or- j  at  speed  of  12.09  stat.  miles  per  hour.  1.53 

dioary  true-pitch  screw  )     "  "  13.4      "        "        "        "      1.48 

Steamer  "  Homer  Rainsdell,"  with  ordinary  true-pitch  screw 1  20 

Size  of  Screw, — Seaton  says:  The  size  of  a  screw  depends  on  so  many 
things  that  it  is  very  difficult  to  lay  down  any  rule  for  guidance,  and  much 
must  always  be  left  to  the  experience  of  the  designer,  to  allow  for  all  the 
circumstances  of  each  particular  case.  The  following  rules  are  given  for 
ordinary  cases.  (Seaton  and  Rounthwaite's  Pocket-book): 

P  =  pitch  of  propeller  in  feet  =       ^  _  g.y  in  which  S  =  speed  in  knots, 
R  =  revolutions  per  minute,  and  x  =  percentage  of  apparent  slip 

•j  1  p   f.  O 

For  a  slip  of  10*,  pitch  =  ~  r— . 


THE    SCREW   PROPELLER. 


1011 


D  =  diameter  of  propeller  =  . 


I.H.P. 


rg  ,  K  being  a  coefficient  given 


in  the  table  below.     If  K  =  20,  D  =  20000 A/     I'H'P>  y 


Total  developed  area  of  blades  =  C 


•",  in  which  C  is  a  coefficient 


to  be  taken  from  the  table. 
Another  formula  for  pitch,    given  in  Beaton's  Marine    Engineering,  is 

C  3/1  H  P 

P=~R4/     D?    »  in  which  C  =  737  for  ordinary  vessels,  and  660  for  slow- 
speed  cargo  vessels  with  full  lines. 

/d* 

Thickness  of  blade  at  root  =  A/  -^  x  fc,  in  which  d  =  diameter  of  tail- 
shaft  in  inches,  n  =  number  of  blades,  b  =  breadth  of  blade  in  inches  where 
it  joins  the  boss,  measured  parallel  to  the  shaft  axis;  k  =  4  for  cast  iron,  1.5 
for  cast  steel,  2  for  gun-metal,  1.5  for  high-class  bronze. 

Thickness  of  blade  at  tip:  Cast  iron  .04D  4-  .4  in. ;  cast  steel  .03D  -f  .4  in.; 
gun -metal  .03  D  -f-  .2  in. ;  high-class  bronze  .02D  -J-.  3  in.,  where  D  =  diameter 
of  propeller  in  feet. 

Propeller  Coefficients. 


1 

.     & 

<M 
0  K  * 

M 

c 

£ 

.S  g-g 

0>r2    — 

o 

o 

^  O  0) 

Description  of  Vessel. 

pM* 

g| 

S5^ 

02 
2 

1 

g-p 

<      '" 

* 

P 

•3 

05 
P 

Bluff  cargo  boats  

8-10 

One 

4 

17    -17  5 

19    -17.5 

Cast  iron 

Cargo,  moderate  lines.   . 

10-13 

4 

18    -19 

17    -15,5 

Pass,  and  mail,  fine  lines. 

13-17 

•* 

4 

19.5-20.5 

15    -13 

C.  I.  or  S. 

"           it           tt           tt          i 

13-17 

Twin 

4 

20.5-21-5 

14.5-12.5 

"      "  »» 

"       "     very  fi  le. 

17-22 

One 

4 

21    -22 

12.5-11 

G.  M.  or  B 

17-22 

Twin 

3 

22    -23 

10.5-  9 

Naval  vessels,      **         * 

16-22 

" 

4 

21    -22.5 

11.5-10.5 

n      tt  it 

ik           »'           "         ' 

16-22 

M 

3 

22    -23.5 

8.5-  7 

ti      it   it 

Torpedo-boats,    4  '         ' 

20-26 

One 

3 

25 

7-  6 

B.  or  F.  S. 

o/^-;=f^,ifp=, 


C.  I.,  cast  iron;  G.  M.,  gun-metal;  B.,  bronze;  S.,  steel;  F.  S.,  forged  steel. 

HP 

From  the  formulae  D  —  20000 4 /  ;^T/p'.o  • 

.  J^r 

and  R  =  100,  we  obtain  D  =  ^400  X  I-H^pT  =  3311 

If  P  =  IAD  and  #  =  100,  then  D  =  ^145.8  X  I.H.P.  =  2.71  j^I.H. P. 

From  these  two  formulas  the  figures  for  diameter  of  screw  in  the  table  on 
page  1009  have  been  calculated.  They  may  be  used  as  rough  approximations 
to  the  correct  diameter  of  screw  for  any  given  horse-power,  for  a  speed  of 
10  knots  and  100  revolutions  per  minute. 

For  any  other  number  of  revolutions  per  minute  multiply  the  figures  in 
the  table  by  100  and  divide  by  the  given  number  of  revolutions.  For  any 
other  speed  than  10  knots,  since  the  I.H.P.  varies  approximately  as  the  cube 
of  the  speed,  and  the  diameter  of  the  screw  as  the  5th  root  of  the  I.H.P., 
multiply  the  diameter  given  for  10  knots  by  the  5th  root  of  the  cube  of  one 
tenth  of  the  given  speed.  Or,  multiply  by  the  following  factors: 

For  speed  of  knots: 

4  5         6          7         8          9        11        12        13        14        15        16 


.807     .875     .939  1.059  1.116  1.170  1.224  1.275  1.327 


1012 


MARINE    ENGINEERING. 


Speed: 


17        18 


19 


20        21         22      23        24        25        26        27        28 


_ 
/(S  -H  10)3 

=  1.375  1.423  1.470  1.515  1.561  1.605  1.648  1.691  1.733  1.774  1.815  1.855 

For  more  accurate  determinations  of  diameter  and  pitch  of  screw,  the 
formulae  and  coefficients  given  by  Seatou,  quoted  above,  should  be  used. 

Efficiency  of  the  Propeller.—  According  to  Rankine,  if  the  slip  of 
the  water  be  s,  its  weight  W>  the  resistance  R,  and  the  speed  of  the  ship  v, 


Ws 


Rv  = 


Wsv 


This  impelling  action  must,  to  secure  maximum  efficiency  of  propeller,  be 
effected  by  an  instrument  which  takes  hold  of  the  fluid  without  shock  or 
disturbance  of  the  surrounding  mass,  and,  by  a  steady  acceleration,  gives  it 
the  required  final  velocity  of  discharge.  The  velocity  of  the  propeller  over- 
coming the  resistance  R  would  then  be 

v  +  (v  +  s)  _      ,  s. 

2  ~S' 


and  the  work  performed  would  be 
^f     ,  *\ 


Ws* 


the  first  of  the  last  two  terms  being  useful,  the  second  the  minimum  lost 
work;  the  latter  being  the  wasted  energy  of  the  water  thrown  backward. 
The  efficiency  is 

E  —  v  -s-  (  V4~n )  » 

and  this  is  the  limit  attainable  with  a  perfect  propelling  instrument,  which 
iimit  is  approached  the  more  nearly  as  the  conditions  above  prescribed  are 
the  more  nearly  fulfilled.  The  efficiency  of  the  propelling  instrument  is 
probably  rarely" much  above  0.60,  and  never  above  0.80. 

In  designing  the  screw-propeller,  as  was  shown  by  Dr.  Froude,  the  best 
angle  for  the  surface  is  that  of  45°  with  the  plane  of  the  disk;  but  as  all 
parts  of  the  blade  cannot  be  given  the  same  angle,  it  should,  where  practi- 
cable, be  so  proportioned  that  the  "  pitch-angle  at  the  centre  of  effort" 
should  be  made  45°.  The  maximum  possible  efficiency  is  then,  according 
to  Froude,  77#. 

In  order  that  the  water  should  be  taken  on  without  shock  and  discharged 
with  maximum  backward  velocity,  the  screw  must  have  an  axially  increas- 
ing pitch. 

The  true  screw  is  by  far  the  more  usual  form  of  propeller,  in  all  steamers, 
both  merchant  and  naval.  (Thurston,  Manual  of  the  Steam-engine,  part  ii. 
p.  176.) 

The  combined  efficiency  of  screw,  shaft,  engine,  etc.,  is  generelly  taken 
at  50$.  In  some  cases  it  may  reach  60#  or  65$.  Rankine  takes  the  effective 
H.P.  to  equal  the  I.H.P.  -r-  1.63. 

Pitcn-ratio  and  Slip  for  Screws  of  Standard  Form. 


Pitch-ratio. 

Real  Slip  of 
Screw. 

Pitch-  ratio. 

Real  Slip  of 
Screw 

.8 

15.55 

1.7 

21.3 

.9 

16.22 

1.8 

21.8 

.0 

16.88 

1.9 

22.4 

.1 

17.55 

2.0 

22.9 

.2 

18.2 

2.1 

23.5 

.3 

18.8 

2.2 

24.0 

.4 

19.5 

2.3 

24.5 

.5 

20.1 

2.4 

25.0 

.6 

20.7 

2.5 

25.4 

THE    PADDLE-WHEEL.  1013 

Results  of  Recent  Researches  on  the  efficiency  of  screw-propel- 
lers are  summarized  by  S.  W.  Baruaby,  in  a  paper  read  before  section  (i  of 
the  Engineering  Congress,  Chicago,  1893.  He  states  that  the  following  gen- 
eral principles  have  been  established: 

(a)  There  is  a  definite  amount  of  real  slip  at  which,  and  at  which  only, 
maximum  efficiency  can  be  obtained  with  a  screw  of  any  given  type,  and 
this  amount  varies  with  the  pitch-ratio.  The  slip-ratio  proper  to  a  given 
ratio  of  pitch  to  diameter  has  been  discovered  and  tabulated  for  a  screw 
of  a  standard  type,  as  below  (see  table  on  page  1012): 

(6)  Screws  of  large  pitch-ratio,  besides  being  less  efficient  in  themselves, 
add  to  the  resistance  of  the  hull  by  an  amount  bearing  some  proportion  to 
their  distance  from  it,  and  to  the  amount  of  rotation  left  in  the  race. 

(c)  The  best  pitch-ratio  lies  probably  between  1.1  and  1.5. 

(d)  The  fuller  the  lines  of  the  vessel,  the  less  the  pitch-ratio  should  be. 

(e)  Coarse-pitched  screws  should  be  placed  further  from  the  stern  than 
fine-pitched  ones. 

(/)  Apparent  negative  slip  is  a  natural  result  of  abnormal  proportions  of 
propellers. 

(g)  Three  blades  are  to  be  preferred  for  high-speed  vessels,  but  when  the 
diameter  is  unduly  restricted,  four  or  even  more  may  be  advantageously 
employed. 

(7i)  An  efficient  form  of  blade  is  an  ellipse  having  a  minor  axis  equal  to 
four  tenths  the  major  axis. 

(i)  The  pitch  of  wide-bladed  screws  should  increase  from  forward  to  aft, 
but  a  uniform  pitch  gives  satisfactory  results  when  the  blades  are  narrow, 
and  the  amount  of  the  pitch  variation  should  be  a  function  of  the  \vidth  of 
the  blade. 

(j)  A  considerable  inclination  of  screw  shaft  produces  vibration,  and  with 
right-handed  twin-screws  turning  outwards,  if  the  shafts  are  inclined  at 
all.  it  should  be  upwards  and  outwards  from  the  propellers. 

For  results  of  experiments  with  screw-propellers,  see  F.  C.  Marshall,  Proc. 
Inst.  M.  E.  1881;  R.  E.  Fronde,  Trans.  Institution  of  Naval  Architects,  1886; 
G.  A.  Calvert,  Trans.  Institution  of  Naval  Architects  1887;  and  S.  W.  Bar- 
naby,  Proc.  Inst.  Civil  Eng'rs  1890,  vol.  cii. 

One  of  the  most  important  results  deduced  from  experiments  on  model 
screws  is  that  they  appear  to  have  practically  equal  efficiencies  throughout 
a  wide  range  both  in  pitch-ratio  and  in  surface-ratio;  so  that  great  latitude 
is  left  to  the  designer  in  regard  to  the  form  of  the  propeller.  Another  im- 
portant feature  is  that,  although  these  experiments  are  not  a  direct  guide  to 
the  selection  of  the  most  efficient  propeller  for  a  particular  ship,  they  sup- 
ply the  means  of  analyzing  the  performances  of  screws  fitted  to  vessels,  and 
of  thus  indirectly  determining  what  are  likely  to  be  the  best  dimensions  of 
screw  for  a  vessel  of  a  class  whose  results  are  known.  Thus  a  great  ad- 
vance has  been  made  on  the  old  method  of  trial  upon  the  ship  itself,  which 
was  the  origin  of  almost  every  conceivable  erroneous  view  respecting  the 
screw-propeller.  (Proc.  Inst.  M.  E.,  July,  1891.) 

THE   PADITJLE-WHEEI,. 

Paddle-wheels  with  Radial  Floats.  (Seaton's  Marine  En- 
gineering.)— The  effective  diameter  of  a  radial  wheel  is  usually  taken  from 
the  centres  of  opposite  floats;  but  it  is  difficult  to  say  what  is  absolutely 
that  diameter,  as  much  depends  on  the  form  of  float,  the  amount  of  dip, 
and  the  waves  set  in  motion  by  the  wheel.  The  slip  of  a  radial  wheel  is 
from  15  to  30  per  cent,  depending  on  the  size  of  float. 

Area  of  one  float  =        '••'  X  C. 

D  is  the  effective  diameter  in  feet,  and  C  is  a  multiplier,  varying  from 
0  25  in  tugs  to  0.175  in  fast-running  light  steamers. 

The  breadth  of  the  float  is  usually  about  *4  its  length,  and  its  thickness 
about  y%  its  breadth.  The  number  of  floats  varies  directly  with  the  diam- 
eter, and  there  should  be  one  float  for  every  foot  of  diameter. 

(For  a  discussion  of  the  action  of  the  radial  wheel,  see  Thurston,  Manual 
of  the  Steam-engine,  part  ii.,  p,  182.) 

Feathering  Paddle-wheels.  (Seaton.)  —  The  diameter  of  a 
feathering-wheel  is  found  as  follows  :  The  amount  of  slip  varies  from  VI  to 
20  per  cent,  although  when  the  floats  are  small  or  the  resistance  great  it 


1014  MARINE    ENGINEERING. 

is  as  high  as  25  per  cent;  a  well-designed  wheel  on  a  well-formed  ship  should 
not  exceed  15  per  cent  under  ordinary  circumstances. 

If  K  is  t  he  speed  of  the  ship  in  knots,  S  the  percentage  of  slip,  and  R  the 
revolutions  per  minute, 

Diameter  of  wheel  at  centres  = 


—  --  —  . 

The  diameter,  however,  must  be  such  as  will  suit  the  structure  of  the 
ship,  so  that  a  modification  may  be  necessary  on  this  account,  and  the 
revolutions  altered  to  suit  it. 

The  diameter  will  also  depend  on  the  amount  of  "  dip  "  or  immersion  of 
float. 

When  a  ship  is  working  always  in  smooth  water  the  immersion  of  the  top 
edge  should  not  exceed  £g  the  breadth  of  the  float;  and  for  general  service 
at  sea  an  immension  of  y%  the  breadth  of  the  float  is  sufficient.  If  the  ship 
is  intended  to  carry  cargo,  the  immersion  when  light  need  not  be  more  than 
2  or  3  inches,  and  should  not  be  more  than  the  breadth  of  float  when  at  the 
deepest  draught;  indeed,  the  efficiency  of  the  wheel  falls  off  rapidly  with 
the  immersion  of  the  wheel. 

Area  of  one  float  =  —  —  '-  —  -  x  (7. 

C  is  a  multiplier,  varying  from  0.3  to  0.35;  D  is  the  diameter  of  the  wheel 
to  the  float  centres,  in  feet. 

The  number  of  floats        =  ^(D  4-  2). 

The  breadth  of  the  float  =  0.35  x  the  length. 

The  thickness  of  floats     -1/12  the  breadth. 

Diameter  of  gudgeons     =  thickness  of  float. 
Seaton  and  Rounthwaite's  Pocket-book  gives: 

Number  of  floats  =  ------ 

VR 

where  R  is  number  of  revolutions  per  minute. 

Area  of  one  float  (in  square  feet)  =  LI^P-  *^8°°°  *  g, 

where  N  =  number  of  floats  in  one  wheel. 

For  vessels  plying  always  in  smooth  water  K  =  1200.  For  sea-going 
steamers  K  =  1400.  For  tugs  and  such  craft  as  require  to  stop  and  start 
frequently  in  a  tide-way  K  =  1600. 

It  will  be  quite  accurate  enough  if  the  last  four  figures  of  the  cube 
(D  X  -R)3  be  taken  as  ciphers. 

For  illustrated  description  of  the  feathering  paddle-wheel  see  Seaton's 
Marine  Engineering,  or  Seaton  and  Rounthwaite's  Pocket-book.  The  diam- 
eter of  a  feathering  -wheel  is  about  one  half  that  of  a  radial  wheel  for  equal 
efficiency.  (Thurston.) 

Efficiency  of  Paddle-wheels.—  Computations  by  Prof.  Thurston 
of  the  efficiency  of  propulsion  by  paddle-wheels  give  for  light  river  steamers 
with  ratio  of  velocity  of  the  vessel,  v,  to  velocity  of  the  paddle  -float  at 

centre  of  pressure,  F,  or  -=.,  =  -,  with  a  dip  =  3/20  radius  of  the  wheel,  and 
a  slip  of  25  per  cent,  an  efficiency  of  .714  ;  and  for  ocean  steamers  with 
the  same  slip  and  ratio  of  -^,  and  a  dip  =  ^  radius,  an  efficiency  of  .685. 

JET-PROPULSION. 

Numerous  experiments  have  been  made  in  driving  a  vessel  by  the 
•eaction  of  a  jet  of  water  pumped  through  an  orifice  in  the  stern,  but 

>rwi 

gave  an  efficiency  of  apparatus  of  only  18  per  cent.  The  latter  gave  a  speed 
of  J2  knots,  as  against  17  knots  attained  by  a  sister-ship  having  a  screw  and 
equal  steam-power.  The  mathematical  theory  of  the  efficiency  of  the  jet 
was  discussed  by  Rankine  in  The  Engineer,  Jan.  11,  1867.  and  he  showed  thnt 
the  greater  the  quantity  of  water  operated  on  by  a  jet-propeller,  the  greater 


RECENT    PRACTICE    IN    MARINE    ENGINES.        1015 

is  the  efficiency.  In  defiance  both  of  the  theory  and  of  the  results  of  earlier 
experiments,  and  also  of  the  opinions  of  many  naval  engineers,  more  than 
$'.200,000  were  spent  in  1888-90  in  New  York  upon  two  experimental  boats,  the 
'•  Prima  Vista  "  and  the"  Evolution,'1  in  which  the  jet  was  made  of  very  small 
size,  in  the  latter  case  only  %-inch  diameter,  and  with  a  pressure  of  2500 
Ibs.  per  square  inch.  As  had  been  predicted,  the  vessel  was  a  total  failure. 
(See  article  by  the  author  in  Mechanics,  March,  1891.) 

The  theory  of  the  jet-propeller  is  similar  to  that  of  the  screw-propeller. 
If  A  =  the  area  of  the  jet  in  square  feet,  Fits  velocity  with  reference  to  the 
orifice,  in  feet  per  second,  v  —  the  velocity  of  the  ship  in  reference  to  the 
earth,  then  the  thrust  of  the  jet  (see  Screw-propeller,  ante)  if.  '1AV  (V  '  —  v). 
The  work  done  on  the  vessel  is  2  A  V(  V—  v)v,  and  the  work  wasted  on  the 
rearward  projection  of  the  jet  is  ^2  X  2AV(V  -  v)z.  The  efficiency  is 

™S  exPressi°n  e<luals  """y  when 


-  „)»       F 

V  •=.  v,  that  is,  when  the  velocity  of  the  jet  with  reference  to  the  earth,  or 
V  —  v,  =  0;  but  then  the  thrust  of  the  propeller  is  also  0.    The  greater  the 
" 


, 

ue  of  F"as  compared  with  v,  the  less  the  efficiency.  For  V  =  20v,  as  was 
proposed  in  the  tk  Evolution,11  the  efficiency  of  the  jet  would  be  less  than  10 
per  cent,  and  this  would  be  further  reduced  by  the  friction  of  the  pumping 
mechanism  and  of  the  water  in  pipes. 

The  whole  theory  of  propulsion  may  be  summed  up  in  Rankine's  words: 
"That  propeller  is  the  best,  other  things  being  equal,  which  drives  astern 
the  largest  body  of  water  at  the  lowest  velocity.1' 

It  is  practically  impossible  to  devise  any  system  of  hydraulic  or  jet  propul- 
sion which  can  compare  favorably,  under  these  conditions,  with  the  screw 
or  the  paddle-wheel. 

Reaction  of  a  Jet.—  If  a  jet  of  water  issues  horizontally  from  a  ves- 
sel, the  reaction  on  the  side  of  the  vessel  opposite  the  orifice  is  equal  to  the 
weight  of  a  column  of  water  the  section  of  which  is  the  area  of  the  orifice, 
and  the  height  is  twice  the  head. 

The  propelling  force  in  jet-propulsion  is  the  reaction  of  the  stream  issuing 
from  the  orifice,  and  it  is  the  same  whether  the  jet  is  discharged  under 
water,  in  the  open  air,  or  against  a  solid  wall.  For  proof,  see  account  of 
trials  by  C.  J.  Everett,  Jr.,  given  by  Prof.  J.  Burkitt  Webb,  Trans.  A.  S.  M. 
E.,  xii.  904. 

RECENT    PRACTICE    IN    MARINE    ENGINES. 

(From  a  paper  by  A.  Blechyriden  on  Marine  Engineering  during  the  past 
Decade,  Proc.  Inst.  M.  E.,  July,  1891.) 

Since  1881  the  three-stage-expansion  engine  has  become  the  rute,  and  the 
boiler-pressure  has  been  increased  to  160  Ibs.  and  even  as  high  as  200  Ibs.  per 
square  inch.  Four-stage-expansion  engines  of  various  forms  have  also  been 
adopted. 

Forced  Draught  has  become  the  rule  in  alt  vessels  for  naval  service, 
and  is  comparatively  common  in  both  passenger  and  cargo  vessels.  By  this 
means  it  is  possible  considerably  to  augment  the  power  obtained  from  a 
given  boiler:  and  so  long  as  it  is  kept  within  certain  limits  it  need  result  in 
no  injury  to  the  boiler,  but  when  pushed  too  far  the  increase  is  sometimes 
purchased  at  considerable  cost. 

In  regard  to  the  economy  of  forced  draught,  an  examination  of  the  ap- 
pended table  (page  1018)  will  show  that  while  the  mean  consumption  of  coal 
in  those  steamers  working  under  natural  draught  is  1.573  Ibs.  per  indicated 
horse-power  per  hour,  it  is  only  1.336  Ibs.  in  those  fitted  with  forced  draught. 
Tiiis  is  equivalent  to  an  economy  of  15£.  Part  of  this  economy,  however, 
may  be  due  to  the  other  heat-saving  appliances  with  which  the  latter 
steamers  are  fitted. 

Boilers.—  As  a  material  for  boilers,  iron  is  now  a  thing  of  the  past, 
though  it  seems  probable  that  it  will  continue  yet  awhile  to  be  the  material 
for  tubes.  Steel  plates  can  be  procured  at  13'J  square  feet  superficial  area 
and  \y%  inches  thick.  For  purely  boiler  work  a  punching-machine  has  be- 
come obsolete  in  marine-engine  work. 

The  increased  pressures  of  steam  have  also  caused  attention  to  be  directed 
to  the  furnace,  and  have  led  to  the  adoption  of  various  artifices  in  the  shape 
of  corrugated,  ribbed,  and  spiral  flues,  with  the  object  of  giving  increased 
strength  against  collapse  without  abnormally  increasing  the  thickness  ot 
the  plate.  A  thick  furnace-plate  is  viewed  by  many  engineers  with  great 


1016  MARINE   ENGINEERING. 

suspicion ;  and  the  advisers  of  the  Board  of  Trade  have  fixed  the  limit  of 
thickness  for  furnace-plates  at  %  inch;  but  whether  this  limitation  will 
stand  in  the  light  of  prolonged  experience  remains  to  be  seen.  It  is  a  fact 
generally  accepted  that  the  conditions  of  the  surfaces  of  a  plate  are  far 
greater  factors  in  its  resistance  to  the  transmission  of  heat  than  either  the 
material  or  the  thickness.  With  a  plate  free  from  lamination,  thickness 
being  a  mere  secondary  element.it  would  appear  that  a  furnace-plate  might 
be  increased  from  V£  inch  to  %  inch  thickness  without  increasing  its  resist- 
ance more  than  1J4#.  So  convinced  have  some  engineers  become  of  the 
soundness  of  this  view  that  they  have  adopted  flues  %  inch  thick. 

Piston- valves.— Since  higher  steam -pressures  have  become  common, 
piston-valves  have  become  the  rule  for  the  high-pressure  cylinder,  and  are 
not  unusual  for  the  intermediate.  When  well  designed  they  have  the  great 
advantage  of  being  almost  free  from  friction,  so  far  as  the  valve  itself  is 
concerned.  In  the  earlier  piston-valves  it  was  customary  to  fit  spring 
rings,  which  were  a  frequent  source  of  trouble  and  absorbed  a  large  amount 
of  power  in  friction ;  but  in  recent  practice  it  has  become  usual  to  fit  spring- 
less  adjustable  sleeves. 

For  low-pressure  cylinders  piston-valves  are  not  in  favor;  if  fitted  with 
spring  rings  their  friction  is  about  as  great  as  and  occasionally  greater  than 
that  of  a  well-balanced  slide-valve;  while  if  fitted  with  springless  rings  there 
is  always  some  leakage,  which  is  irrecoverable.  But  the  large  port  clear- 
ances inseparable  from  the  use  of  piston- valves  are  most  objectionable; 
and  with  triple  engines  this  is  especially  so,  because  with  the  customary 
late  cut-off  it  becomes  difficult  to  compress  sufficiently  for  insuring  econo- 
my and  smoothness  of  working  when  in  "  full  gear,"  without  some  special 
device. 

Steam-pipes.— The  failures  of  copper  steam-pipes  on  large  vessels 
have  drawn  serious  attention  both  to  the  material  and  the  modes  of  con- 
struction of  the  pipes.  As  the  brazed  joint  is  liable  to  be  imperfect,  it  is 
proposed  to  substitute  solid  drawn  tubes,  but  as  these  are  not  made  of  large 
sizes  two  or  more  tubes  may  be  needed  to  take  the  place  of  one  brazed  tube. 
Reinforcing  the  ordinary  brazed  tubes  by  serving  them  with  steel  or  copper 
wire,  or  by  hooping  them  at  intervals  with  steel  or  iron  bauds,  has  been 
tried  and  found  to  answer  perfectly. 

Auxiliary  Supply  of  Fresh  Water—  Evaporators.—  To  make 
up  the  losses  of  water  due  to  escape  of  steam  from  safety-valves,  leakage  at 
glands,  joints,  etc.,  either  a  reserve  supply  of  fresh  water  is  carried  in  tanks, 
or  the  supplementary  feed  is  distilled  from  sea-water  by  special  apparatus 
provided  for  the  purpose.  In  practice  the  distillation  is  effected  by  passing 
steam,  say  from  the  first  receiver,  through  a  nest  of  tubes  inside  a  still  or 
evaporator,  of  which  the  steam-space  is  connected  either  with  the  second 
receiver  or  vith  the  condenser.  The  temperature  of  the  steam  inside  the 
tubes  being  higher  than  that  of  the  steam  either  in  the  second  receiver  or  in 
the  condenser,  the  result  is  that  the  water  inside  the  still  is  evaporated,  and 
passes  with  the  rest  of  the  steam  into  the  condenser,  where  it  is  condensed 
and  serves  to  make  up  the  loss.  This  plan  localizes  the  trouble  of  the  de- 
posit, and  frees  it  from  its  dangerous  character,  because  an  evaporator  can- 
not become  overheated  like  a  boiler,  even  though  it  be  neglected  until  ir 
salts  up  solid;  and  if  the  same  precautions  are  taken  in  working  the  evapo- 
rator which  used  to  be  adopted  with  low-pressure  boilers  when  they  were 
fe<l  with  salt  water,  no  serious  trouble  should  result. 

Weir's  Feed-water  Heater.— The  principle  of  a  method  of  heating 
feed-water  introduced  by  Mr.  James  Weir  and  widely  adopted  in  the 
marine  service  i«  founded  on  the  fact  that,  if  the  feed -water  as  it  is  drawn 
from  the  hot-well  be  raised  in  temperature  by  the  heat  of  a  portion  of  steam 
introduced  into  it  from  one  of  the  steam-receivers,  the  decrease  of  the  coal 
necessary  to  generate  steam  from  the  water  of  the  higher  temperature  bears 
a  greater  ratio  to  the  coal  required  without  feed-heating  than  the  power 
winch  would  be  developed  in  the  cylinder  by  that  portion  of  steam  would 
bear  to  the  whole  power  developed'when  passing  all  the  steam  through  all 
the  cylinders.  Suppose  a  triple-expansion  engine  were  working  under  the 


heating  the  same  engine  might  work  as  follows:  the  feed  might  be  heated  to 
•J*JO°  F..  and  the  percentage  of  steam  from  the  first  receiver  required  to  beat 
it  would  be  10.9£;  the  I.H.P.  in  the  h.p.  cylinder  would  be  as  before  398.  and 
in  the  three  cylinders  it  would  be  1103,  or  93#  of  the  power  developed  without 


RECENT   PRACTICE   IN    MARINE   ENGINES.        1017 


feed-heating.  Mean  while  the  heat  to  be  added  to  each  pound  of  the  feed-water 
at  220°  F.  for  converting  it  into  steam  would  be  1005  units  against  1125  units 
.vith  feed  at  100°  F.,  equivalent  to  an  expenditure  of  only  89. 4$  of  the  heat 
required  without  feed-beating.  Hence  the  expenditure  of  heat  in  relation 
to  power  would  be  89.4  -:-  93.0  —  96.4$,  equivalent  to  a  heat  economy  of  3.6$. 
If  the  steam  for  heating  can  be  taken  from  the  low-pressure  receiver,  the 
economy  is  about  doubled. 

Passenger  Steamers  fitted  with  Twin  Screws. 


Vessels. 

Length  be- 
tween Per- 
pendiculars. 

Feet 
63M 

58 

57^ 
55^ 

51 

48 
54^ 

Cylinders,  two  sets 
in  all. 

Boiler- 
pressure 
per  sq.  in. 

Indicated 
Horse-power 

Diameters. 

Stro. 

City  of  New  York  } 

Feet 
525 

565 

500 

463^ 

440 

415 
460 

Inches 
45,  71,  113 

43,  68,  110 

40,  67,  106 
41,  66,  101 

32,51,  82 

34,  54,  85 
3414.  57^,  92 

In. 

60 

60 

66 
66 

54 

51 
60 

Lbs. 
150 

180 

160 
160 

160 

100 
170 

I.H.P. 
20,000 

18,000 

11,500 
12,500 

10,125 

10,000 
11,656 

"    "    Paris            f  

Majestic    < 

Teutonic  j  '  ' 
Norrnannia  

(.  Columbia 

Empress  of  India    ) 
"•         "  Japan  >  
"  China  ) 
Orel        

Scot  

Comparative  Results  of  Working  of  JHarme  Engines. 
1872,  1881,  and  1891. 


Boilers,  Engines,  and  Coal. 

1872. 

1881. 

1891. 

]3oiler-pressure   Ibs  per  sq  in 

52.4 

77.4 

158  5 

Heating-surface  per  horse-power,  sq.  ft  
Revolutions  per  minute,  revs  

4.410 
55.67 

3.9J7 
59.76 

3.275 
63.75 

Piston-speed  feet  per  in  in                             . 

376 

467 

529 

Coal  per  horse-power  per  hour,  Ibs  

2.110 

1.828 

1  522 

Weight  of  Three  -  stage  -  expansion  Engines  in  Nine 
Steamers  in  Relation  to  Indicated  Horse-power  and 
to  Cylinder-capacity. 


i 

Weight  of 
Machinery. 

Relative  Weight  of  Machinery. 

3 

Per  Indicated  Horse- 

!«•£ • 

sdbo  . 

Type  of 

OQ 

S  ^ 

i| 

a 

power. 

!?'!'§" 

|j|| 

Machinery. 

6 

|s 

'o  o 

£ 

Engine- 

Boiler- 

Total 

li^t 

'O    ~<M    M 

^ 

room. 

room. 

y     *o 

Mao 

tons. 

tons. 

tons. 

Ibs. 

Ibs. 

Ibs. 

tons. 

tons. 

1 

681 

662 

1313 

226 

220 

446 

1.30 

3.75 

Mercantile 

2 

638 

619 

1257 

259 

251 

510 

1.46 

4.10 

" 

3 

134 

128 

262 

207 

198 

405 

1.23 

3.23 

44 

4 

38.8 

46.2 

85 

170 

203 

373 

1.29 

3.30 

** 

5 

719 

695 

1414 

167 

162 

329 

1.41 

3.44 

*' 

6 

75.2 

107.8 

183 

141 

202 

343 

1.37 

3  37 

*•' 

7 

44 

61 

105 

108 

185 

1.21 

2.72J 

Naval 
liorizontal 

8 

73.5 

109 

182.5 

78 

11C 

194 

1.11 

2.78 

do. 

9     i  202 

429 

691 

62.5 

102 

165 

0.82 

2.70J 

Naval 
vertical 

1018 


MAIUKE    ENGINEERING. 


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^lutiq  i  BOQ 


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nty-eight 
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draught 


CONSTRUCTION   OF    BUILDINGS. 


1019 


DiiBic  ia*ioiis,  Indicated  Horse  -  power,  and  Cylinder  - 
capacity  of  Three  -  stage  •  expansion  Engines  in  Nine 
Steamers. 


°i 

®  £ 

0)  U 

Tico 

Cylinders. 

utions 
linute. 

*.s 
.  g  ¥ 

ij 

u  ?* 

If 

Heating-sur- 
face. 

•°  s 

0  B 

EH 

Diameters. 

Stroke 

D  o> 

tf  a 

PQ 

3  0 

qS 

Total. 

Per 
I.H.P. 

Single 

ins. 
40      66    100 

ins. 

revs. 
64.5 

Ibs. 
160 

I.H.P. 
6751 

cu.ft. 
522 

sq.  ft. 
17.640 

sq.  ft. 
2.62 

2 

39      61      97 

66 

67.8 

160 

5525 

436 

15.107 

2.73 

3 

tk 

23      38      61 

42 

83 

160 

1450 

109 

3,973 

2.73 

4 

41 

17      26^  42 

24 

90 

150 

510 

30 

1,403 

2.75 

5 

Twin 

32      54      82 

54 

88 

160 

9625 

508 

20,193 

2.10 

6 

" 

15      24      38 

27 

113 

150 

1194 

55 

3,200 

2.68 

Single 

20      30      45 

24 

191 

145 

1265 

36.3 

2,227 

1.76 

8 

Twin 

18J4  29      43 

24 

182.5 

140 

2105 

66.2 

3,928 

1.87 

9 

" 

33}^  49      74 

39 

145 

150 

9400 

319 

15,882 

1.62 

CONSTRUCTION    OP  BUILDINGS.* 

(Extract  from  the  Building  Laws  of  the  City  of  New  "York,  1893.) 
Walls*  of  Warehouses,  Stores,  Factories,  and  Stables.— 

25  feet  or  less  in  width  between  walls,  not  Jess  than  12  in.  to  height  of  40  ft.; 
If  40  to  60  ft.  in  height,  not  less  than  16  in.  to  40  ft.,  and  12  in.  thence  to  top; 
60  to  80    "  "          "      "       "     20      "      25        "       16 

75  to  85    "  "          "      "       "    24     "      20  ft.;  20  in.  to  60ft.,  and  16  in. 

to  top; 
85  to  100  ft.  in  height,  not  less  than  28  in.  to  25  ft. ;  24  in.  to  50  ft.;  20  in* 

to  75  ft.,  and  16  in.  to  top; 

Over  100  ft.  in  height,  each  additional  25  ft.  in  height,  or  part  thereof,  next 
above  the  curb,  shall  be  increased  4  inches  in  thickness,  the  upper  100 
feet  remaining  the  same  as  specified  for  a  wall  of  that  weight. 
If  walls  are  over  25  feet  apart,  the  bearing-walls  shall  be  4  inches  thicker 
than  above  specified  for  every  12*4  feet  or  fraction  thereof  that  said  walls 
are  more  than  25  feet  apart. 

Strength  ot  Floors,  Roofs,  and  Supports. 

Floors  calculated  to  bear 
safely  per  sq.  ft.,  in  addition 

to  their  own  weight. 
Floors  of  dwelling,  tenement,  apartment-house  or  hotel,  not 

lessthan 70  Ibs. 

Floors  of  office-building,  not  less  than 

public-assembly  building,  not  less  than 

"        store,  factory,  warehouse,  etc.,  not  less  than 150 

Roofs  of  all  buildings,' not  less  than... 50    " 

Every  floor  shall  be  of  sufficient  strength  to  bear  safely  the  weight  to  be 
imposed  thereon,  in  addition  to  the  weight  of  the  materials  of  which  the 
floor  is  composed. 

Columns  and  Posts.— The  strength  of  all  columns  and  posts  shall 
be  computed  according  to  Gordon's  formulae,  and  the  crushing  weights  in 
pounds,  to  the  square  inch  of  section,  for  tne  following-named  materuim, 
shall  be  taken  as  the  coefficients  in  said  formulae,  namely:  Cast  iron,  80.000; 
*  The  limitations  of  space  forbid  any  extended  treatment  of  this  subject. 
Much  valuable  information  upon  it  will  be  found  in  Trautwinejs  Civil  Engi- 


^uperintendence,"  by 'A.  ±->..  v>ic«  n.  v«-  •"•  >-"•>.-, ~- —  —  — ?  —  -  '>, 
American  House  Carpenter,'1  by  R.  G.  Hatfield;  "  Graphical  Analysis  of 
Roof-trusses,1'  by  Prof.  C.  E.  Greene;  "The  Fire  Protection  of  Mills,"  by  C. 
J  H.  Woodbury;  -'House  Drainage  and  Water  Service,1'  by  James  C. 
Bayles;  "  The  Builder's  Guide  and  Estimator's  Price- book,"  and  kk  Plaster- 
ing Mortars  and  Cements,"  by  Fred.  T.  Hodgson;  -'Foundations  and  Con- 
crete Works  "  and  "Art  of  Bui'lding,"  by  E.  Dobson,  Weale's  Series,  London. 


1020        CONSTRUCTION  OF  BUILDINGS. 

wrought  or  rolled  iron,  40,000;  rolled  steel,  48,000;  white  pine  and  spruce, 
3500;  pitch  or  Georgia  pine,  5000;  American  oak,  GOUO.  The  breaking  strength 
of  wooden  beams  and  girders  shall  be  CDinputed  according  to  the  formulae 
in  which  the  constants  for  transverse  strains  for  central  load  shall  be  as 
follows,  namely:  Hemlock,  400;  white  pine,  450;  spruce,  450;  pitch  or  Georgia 
pine,  550;  American  oak,  550;  and  for  wooden  beams  and  girders  carrying  a 
uniformly  distributed  load  the  constants  will  be  doubled.  The  factors  of 
safety  shall  be  as  one  to  four  for  all  beams,  girders,  and  other  pieces  subject 
to  a  transverse  strain;  as  one  to  four  for  all  posts,  columns,  and  other 
vertical  supports  when  of  wrought  iron  or  rolled  steel;  as  one  to  five  for 
other  materials,  subject  to  a  compressive  strain;  as  one  to  six  for  tie- 
rods,  tie-beams,  and  other  pieces  subject  to  a  tensile  strain.  Good,  solid, 
natural  earth  shall  be  deemed  to  safely  sustain  a  load  of  four  tons  to  the 
superficial  foot,  or  as  otherwise  determined  by  the  superintendent  of  build- 
ings, and  the  width  of  footing-courses  shall  be  at  least  sufficient  to  meet  this 
requirement.  In  computing  the  width  of  walls,  a  cubic  foot  of  brickwork 
shall  be  deemed  to  weigh  115  Ibs.  Sandstone,  white  marble,  granite,  and 
other  kinds  of  building-stone  shall  deemed  to  weigh  i60  Ibs.  per  cubic  foot, 
The  safe-bearing  load  to  apply  to  good  brickwork  shall  be  taken  at  8  tons 
per  superficial  foot  when  good  lime  mortar  is  used,  11 J^  tons  per  superficial 
foot  when  good  lime  and  cement  mortar  mixed  is  used,  and  15  Ions  per  sup 
erficial  fool  when  good  cement  mortar  is  used. 

Fire-proof  Buildings— Iron  and  Steel  Columns.— All  cast 
iron,  wrought-irou,  or  rolleu-steel  columns  shall  be  made  true  and  smooth 
at  both  ends,  and  shall  rest  on  iron  or  steel  bed-plates,  and  have  iron  01 
steel  cap-plates,  which  shall  also  be  made  true.  All  iron  or  steel  trimmei- 
beams,  headers,  and  tail-beams  shall  be  suitably  framed  and  connected  to- 
gether, and  the  iron  girders,  columns,  beams,  trusses,  and  all  other  ironwork 
of  all  floors  and  roofs  shall  be  strapped,  bolted,  ancnored,  and  connected  to 
gether,  and  to  the  walls,  in  a  strong  and  substantial  manner.  Where  beams 
are  framed  into  headers,  the  angle-irons,  which  are  bolted  to  the  tail-beams, 
shall  have  at  least  two  bolts  for  all  beams  over  7  inches  in  depth,  and  three 
bolls  for  all  beams  12  inches  and  over  in  depth,  and  these  bolts  shall  not  b 
less  than  %  inch  in  diameter.  Each  one  of  such  angles  or  knees,  when  bolte< 
to  girders,  shall  have  the  same  number  of  bolts  as  stated  for  the  oilier  leg 
The  angle-iron  in  no  case  shall  be  less  in  thickness  than  the  header  or  trim 
mer  to  which  it  is  bolted,  and  the  width  of  angle  in  no  case  shall  be  less  than 
one  third  the  depth  of  beam,  excepting  that  no  angle-knee  shall  be  less  than 
2)4  inches  wide,  nor  required  to  be  more  than  0  inches  wide.  All  wrought- 
iron  or  rolled-steel  beams'  8  inches  deep  and  under  shall  have  bearings  equal 
to  their  depth,  if  resting  on  a  wall;  9  to  12  inch  beams  shall  have  a  bearing 
of  10  inches,  and  all  beams  more  than  12  inches  in  depth  shall  have  bearings 
of  not  less  than  12  inches  if  resting  on  a  wall.  Where  beams  rest  on  iron 
supports,  and  are  properly  tied  to  the  same,  no  greater  bearings  shall  be  re- 
quired than  one  third  of  the  depth  of  the  beams.  Iron  or  steel  floor-beams 
shall  be  so  arranged  as  to  spacing  and  length  of  beams  that  the  load  to  bt 
supported  by  them,  together  with  the  weights  of  the  materials  used  in  the 
construction  of  the  said  floors,  shall  not  cause  a  deflection  of  the  said  beams 
of  more  than  1/30  of  an  inch  per  linear  foot  of  span;  and  they  shall  be  tied 
together  at  intervals  of  not  more  than  eight  times  the  depth  of  the  beam. 

Under  the  ends  of  all  iron  or  steel  beams,  where  they  rest  on  the  walls,  a 
stone  or  cast  iron  template  shall  be  built  into  the  walls.  Said  template  shall 
be  8  inches  wide  in  12 -inch  walls,  and  in  all  walls  of  greater  thickness  said 
template  shall  be  12  inches  wide;  and  such  templates,  if  of  stone,  shall  not  be 
in  any  case  less  than  2^>  inches  in  thickness,  and  no  template  shall  be  less 
than  12  inches  long. 

No  cast-iron  post  or  column  shall  be  used  in  any  building  of  a  less  average 
thickness  of  shaft  than  three  quarters  of  an  inch,  nor  shall  it  have  an  un- 
supported length  of  more  than  twenty  times  its  least  lateral  dimensions  or 
diameter.  No  wrought-iron  or  rolled-steel  column  shall  have  an  unsupported 
length  of  more  than  thirty  times  its  least  lateral  dimension  or  diameter,  nor 
shall  its  metal  be  less  than  one  fourth  of  an  inch  in  thickness. 

Lintels,  Bearings  and  Supports.— All  iron  or  steel  lintels  shall 
have  bearings  proportionate  to  the  weight  to  be  imposed  thereon,  but  no 
lintel  used  to  span  any  opening  more  than  10  feet  in  width  shall  have  a  bear- 
ing less  than  12  inches  at  each  end,  if  resting  on  a  wall;  but  if  resting  on  an 
iron  post,  such  lintel  shall  have  a  bearing  of  at  least  6  inches  at  each  end, 
by  the  thickness  of  the  wall  to  be  supported 

Strains  on  Girders  and  Rivets,— Rolled  iron  or  steel  beam  gir- 


STRENGTH    OF   FLOORS.  1021 

ders,  or  riveted  iron  or  steel  plate  girders  used  as  lintels  or  as  girders, 
carrying  a  wall  or  floor  or  both,  shall  be  so  proportioned  that  the  loaiis 
which  may  come  upon  them  shall  not  produce  strains  in  tension  or  com- 
pression upon  the  flanges  of  more  than  12,000  Ibs.  for  iron,  nor  more  than 
15,000  Ibs.  for  steel  per  square  inch  of  the  gross  section  of  each  of  such 
flanges,  nor  a  shearing  strain  upon  the  web-plate  of  more  than  6000  Ibs.  per 
square  inch  of  section  of  such  web-plate,  if  of  iron,  nor  more  than  'JOOO 
pounds  if  of  steel;  but  no  web-plate  shall  be  less  than  y±  inch  in 
thickness.  Rivets  in  plate  girders  shall  not  be  less  than  %  inch  in  diameter, 
and  shall  not  be  spaced  more  than  6  inches  apart  in  any  case.  They  shall  be 
so  spaced  that  their  shearing  strains  shall  not  exceed  9000  Ibs.  per  square 
inch,  on  their  diameter,  multiplied  by  the  thickness  of  the  plates  through 
which  they  pass.  The  riveted  plate  girders  shall  be  proportioned  upon  the 
supposition  that  the  bending  or  chord  strains  are  resisted  entirely  by  the 
upper  and  lower  flanges,  and  that  the  shearing  strains  are  resisted  entirely 
by  the  web-plate.  No  part  of  the  web  shall  be  estimated  as  flange  area,  nor 
more  than  one  half  of  that  portion  of  the  angle  iron  which  lies  against  the 
web.  The  distance  between  the  centres  of  gravity  of  the  flange  areas  will 
be  considered  as  the  effective  depth  of  the  girder. 

The  building  laws  of  the  City  of  New  York  contain  a  great  amount  of  de- 
tail in  addition  to  the  extracts  above,  and  penalties  are  provided  for  viola- 
tion. See  An  Act  creating  a  Department  of  Buildings,  etc.,  Chapter  275, 
Laws  of  1892.  Pamphlet  copy  published  by  Baker,  Voorhies  &  Co.,  New 

MAXIMUM  LOAD  ON  FLOORS. 

(Eng'g,  Nov.  18,  189-).  p.  644.)— Maximum  load  per  square  foot  of  floor 
surface  due  to  the  weight  of  a  dense  crowd.  Considerable  variation  is 
apparent  in  the  figures  given  by  many  authorities,  as  the  following  table 
shows: 

Authorities  Weight  of  Crowd, 

Autnt     ties.  lbs<  per  gq   ft< 

French  practice,  quoted  by  Trautwine  and  Stoney  41 

HatfleldC*  Transverse  Strains,"  p.  80)  70 

Mr.  Page.  London,  quoted  by  Trautwine 84 

Maximum  load  on  American  highway  bridges  according  to 

Waddell's  general  specifications 100 

Mr.  Nash,  architect  of  Buckingham  Palace 

Experiments  by  Prof.  W.  N.  Kernot,  at  Melbourne 143  j 

Experiments  by  Mr.  B.  B.  Stoney  ("  On  Stresses,"  p.  617)  . . .  147.4 

The  highest  results  were  obtained  by  crowding  a  number  of  persons  pre- 
viously weighed  into  a  small  room,  the  men  being  tightly  packed  so  as  to 
resemble  such  a  crowd  as  frequently  occurs  on  the  stairways  and  platforms 
of  a  theatre  or  other  public  building. 

STRENGTH  OF  FLOORS. 
(From  circular  of  the  Boston  Manufacturers1  Mutual  Insurance  Co.) 

The  following  tables  were  prepared  by  C.  J.  H.  Woodbuty,  for  determining 
safe  loads  on  floors.  Care  should  be  observed  to  select  the  figure  giving  the 
greatest  possible  amount  and  concentration  of  load  as  the  one  which  may 
be  put  upon  any  beam  or  set  of  floor-beams:  and  in  no  case  should  beams  be 
subjected  to  greater  loads  than  those  specified,  unless  a  lower  factor  of 
safetv  is  warranted  under  the  advice  of  a  competent  engineer. 

Whenever  and  wherever  solid  beams  or  heavy  timbers  are  made  use  of  in 
the  construction  of  a  factory  or  warehouse,  they  should  not  be  painted,  var- 
nished or  oiled,  filled  or  encased  in  impervious  concrete,  air-proof  plastering, 
or  metal  for  at  least  three  years,  lest  fermentation  should  destroy  them  by 
what  is  called  "  dry  rot.^ 

It  is,  on  the  whole,  safer  to  make  floor-beams  in  two  parts,  with  a  small 
open  space  between,  so  that  proper  ventilation  may  be  secured,  even  if  the 
outside  should  be  inadvertently  painted  or  filled. 

These  tables  apply  to  distributed  loads,  but  the  first  can  be  used  in  respect 
to  floors  which  may  carry  concentrated  loads  by  using  half  the  figure  given 
in  the  table,  since  a  beam  will  bear  twice  as  much  load  when  evenly  distrib- 
uted over  its  length  as  it  would  if  the  load  was  concentrated  in  the  centre 

°Theewefglit  of  the  floor  should  be  deducted  from  the  figure  given  in  the 
table,  in  order  to  ascertain  the  net  load  which  may  be  placed  upon  any  floor. 
The  weight  of  spruce,  may  be  taken  at  36  Ibs.  per  cubic  foot,  and  that  of 
(southern  pine  at  48  Ibs.  per  cubic  foot. 


1022  CONSTRUCTION    OF    BUILDINGS. 

Table  I  was  computed  upon  a  working  modulus  of  rupture  of  Southern 
pine  at  2160  Ibs.,  using  a  factor  of  safety  of  six.  It  can  also  be  applied  to 
ascertaining  the  strength  of  spruce  beams  if  the  figures  given  in  the  table 
are  multiplied  by  0.78;  or  in  designing  a  floor  to  be  sustained  by  spruce 
beams,  multiply  the  required  load  by  1.28,  and  use  the  dimensions  as  given 
by  the  table. 

Theses  tables  are  computed  for  beams  one  inch  in  width,  because  the 
strength  of  beams  increases  directly  as  the  width  when  the  beams  are  broad 
enough  not  to  cripple. 

EXAMPLE.— Required  the  safe  load  per  square  foot  of  floor,  which  may  be 
safely  sustained  by  a  floor  on  Southern  pine  10x14  inch  beams,  8  feet  on 
centres,  and  20  feet  span.  In  Table  I  a  1  X  14  inch  beam,  20  feet  span,  will 
sustain  118  Ibs.  per  foot  of  span;  and  for  a  beam  10  inches  wide  the  load 
would  be  1180  Ibs.  per  foot  of  span,  or  147J4  Ibs.  per  square  foot  of  floor  for 
Southern- pine  beams.  From  this  should  be  deducted  ihe  weight  of  the  floor, 
which  would  amount  to  17^  Ibs.  per  square  foot,  leaving  130  Ibs.  per  square 
foot  as  a  safe  load  to  be  carried  upon  such  a  floor.  If  the  beams  are  of 
spruce,  the  result  of  147J^  Ibs.  would  be  multiplied  by  0.78,  reducing  the  load 
to  115  Ibs.  The  weight  of  the  floor,  in  this  instance  amounting  to  16  Ibs., 
would  leave  the  safe  net  load  as  90  Ibs.  per  square  foot  for  spruce  beams. 

Table  II  applies  to  the  design  of  floors  whose  strength  must  be  in  excess 
of  that  necessary  to  sustain  the  weight,  in  order  to  meet  the  conditions  of 
delicate  or  rapidly  moving  machinery,  to  the  end  that  the  vibration  or  dis- 
tortion of  the  floor  may  be  reduced  to  the  least  practicable  limit. 

In  the  table  the  limit  is  that  of  load  which  would  cause  a  bending  of  the 
beams  to  a  curve  of  which  the  average  radius  would  be  1250  feet. 

This  table  is  based  upon  a  modulus  of  elasticity  obtained  from  observa- 
tions upon  the  deflection  of  loaded  storehouse  floors,  and  is  taken  at  2,000.000 
Ibs.  for  Southern  pine;  the  same  table  can  be  applied  to  spruce,  whose 
modulus  of  elasticity  is  taken  as  1.200,000  Ibs.,  if  six  tenths  of  the  load  for 
Southern  pine  is  taken  as  the  proper  load  for  spruce;  or,  in  the  matter  of 
designing,  the  load  should  be  increased  one  and  two  thirds  times,  and  the 
dimension  of  timbers  for  this  increased  load  as  found  in  the  table  should  be 
used  for  spruce. 

It  can  also  be  applied  to  beams  and  floor-timbers  which  are  supported  at 
each  end  and  in  the  middle,  remembering  that  the  deflection  of  a  beam 
supported  in  that  manner  is  only  four  tenths  that  of  a  beam  of  equal  span 
which  rests  at  each  end;  that  is  to  say,  the  floor-planks  are  two  and  one 
half  times  as  st.iff,  cut  two  bays  in  length,  as  they  would  be  if  cut  only  one 
bay  in  length.  When  a  floor-plank  two  bays  in  length  is  evenly  loaded, 
three  sixteenths  of  the  load  on  the  plank  is  su  tained  by  the  beani  at  each 
end  of  the  plank,  and  ten  sixteenths  by  the  beam  under  the  middle  of  the 
plank;  so  that  for  a  completed  floor  three  eighths  of  the  load  would  be  sus- 
tained by  the  beams  under  the  joints  of  the  plank,  and  five  eighths  of  the  load 
by  the  beams  under  the  middle  of  the  plank:  this  is  the  reason  of  the  impor- 
tance of  breaking  joints  in  a  floor-plank  every  three  feet  in  order  that  each 
beam  shall  receive  an  identical  load.  If  it  were  not  so,  three  eighths  of  the 
whole  load  upon  the  floor  would  be  sustained  by  every  other  beam,  and  five 
eighths  of  the  load  by  the  corresponding  alternate  beams. 

Repeating  the  former  example  for  the  load  on  a  mill  floor  on  Southern- 
pine  beams  10  X  14  inches,  and  20  feet  span,  laid  8  feet  on  centres:  In'Table 
II  a  1  X  14  inch  beam  should  receive  61  Ibs.  per  foot  of  span,  or  75  Ibs.  per 
sq.  ft.  of  floor,  for  Southern-pine  beams.  Deducting  the  weight  of  the  floor, 
17}^  Ibs.  per  sq.  ft.,  leaves  57  Ibs.  per  sq.  ft.  as  the  advisable  load. 

If  the  beams  are  of  spruce,  the  result  of  75  Ibs.  should  be  multiplied  by  0.6, 
reducing  the  load  to  45  Ibs.  The  weight  of  the  floor,  in  this  instance  amount- 
ing to  16  Ibs.,  would  leave  the  net  load  as  29  Ibs.  for  spruce  beams. 

If  the  beams  were  two  spans  in  length,  they  could,  under  these  conditions, 
support  two  and  a  half  times  as  much  load  with  an  equal  amount  of  deflec- 
tion, unless  such  load  should  exceed  the  limit  of  safe  load  as  found  by  Table 
I.  as  would  be  the  case  under  the  conditions  of  this  problem. 

]?Iill  Columns. --Timber  posts  offer  more  resistance  to  fire  than  iron 
pillars,  an.i  have  generally  displaced  them  in  millwork.  Experiments 
made  on  the  testing-machine  at  the  U.  S.  Arsenal  at  Watertown,  Mass.. 
show  that  sound  timber  posts  of  the  proportions  customarily  used  in  mill- 
work  yield  by  direct  crushing,  the  strength  being  directly  as  the  area  at  the 
smallest  part.  The  columns  yielded  at  about  4500  Ibs.  per  square  inch,  con- 
firming the  general  practice  of  allowing  GOO  ibs.  per  square  inch,  as  a  safe 
load.  Square  columns  are  one  fourth  stronger  than  round  ones  of  the  same* 
diameter. 


STRENGTH    OF    FLOORS. 


1023 


I.  Safe  Distributed  Loads  upon  Southern-nine  Beams 
One  Inch  in  Width. 

(C.  J.  H.  Woodbury.) 

fit'  the  load  is  concentrated  at  the  centre  of  the  span,  the  beams  will  sus 
tain  half  the  amount  as  given  in  the  table.) 


1 

C 

a 

cc 

Depth  of  Beam  in  inches. 

a  |  3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14  |  15 

16 

Load  in  pounds  per  foot  of  Span. 

5 

6 

8 
9 
10 
11 
12 
13 
14 
15 
16 
\7 
18 
19 
20 
21 
22 
23 
24 
25 

38 
27 
20 
15 

86 
60 
44 
34 
27 
22 

154 
107 
78 
60 
47 
38 
32 
27 

240 
167 
122 
94 
74 
60 
50 
42 
36 
31 
27 

346 
240 
176 
135 
107 
86 
71 
60 
51 
44 
38 
34 
30 

470 
327 
240 
184 
145 
118 
97 
82 
70 
60 
52 
46 
41 
36 

614 
427 
314 
240 
190 
151 
127 
107 
90 
78 
68 
60 
53 
47 
43 
38 

V78 
540 
397 
304 
240 
194 
161 
135 
115 
99 
86 
76 
67 
60 
54 
49 
44 

960 
667 
490 
375 
296 
240 
198 
167 
142 
K>3 
107 
94 
83 
74 
66 
60 
54 
50 
45 

807 
593 
454 
359 
290 
240 
202 
172 
148 
129 
113 
101 
90 
80 
73 
66 
60 
55 
50 
46 

705 
540 
427 
346 
286 
240 
205 
176 
154 
135 
120 
107 
96 
86 
78 
71 
65 
60 
55 

628 
634 
501 
406 
335 
282 
240 
207 
180 
158 
140 
125 
112 
101 
92 
84 
77 
70 
65 

735 
581 
470 
389 
327 
278 
240 
209 
184 
163 
145 
130 
111 
107 
97 
89 
82 
75! 

667 
540 
446 
375 
320 
276 
240 
211 
187 
167 
150 
135 
122 
11* 
102 
94 
86 

759 
614 
508 
474 
364 
314 
273 
240 
217 
190 
170 
154 
139 
127 
116 
107 
98 

II.   Distributed  Loads  upon  Southern-pine  Beams  suffi- 
cient to  produce  Standard  Limit  of  Deflection. 

(C.  J.  H.  Woodbury.) 


1 

I 

5 
6 

8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 

Depth  of  Beam  in  inches. 

Deflection, 
inches. 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14  |  15  |  16 

Load  in  pounds  per  foot  of  Span. 

3 

2 

10 
7 
5 
4 

23 
16 
12 
9 

7 
6 

44 
31 
23 
17 

14 
11 
9 

77 
53 
39 
30 
24 
19 
10 
13 
11 

122 

85 
62 
48 
38 
30 
25 
21 
18 
16 
14 

182 
126 
93 
71 
56 
46 
38 
32 
27 
23 
20 
18 
16 

259 
180 
132 
101 
80 
65 
54 
45 
38 
33 
29 
25 
22 
20 
18 

247 
181 
139 
110 
89 
73 
62 
53 
45 
40 
35 
31 
27 
25 

20 

241 
185 
146 
118 
98 
82 
70 
60 
53 
46 
41 
37 
33 
30 

24 

240 
190 
154 
127 
107 
91 
78 
68 
60 
53 
47 
43 
38 
35 
32 
29 
27 
25 

305 
241 
195 
16! 
136 
116 
100 
87 
76 
68 
60 
54 
49 
44 
40 
37 
34 
31 

301 
244 
20-,' 
169 
144 
124 
108 
95 
84 
75 
68 
61 
55 
50 
46 
42 
39 

300 
248 
208 
178 
153 
133 
117 
104 
93 
83 
75 
68 
62 
57 
52 
48 

301 
253 
215 
186 
162 
147 
126 
112 
101 
91 
83 
75 
69 
63 
58 

.0300 
.0432 
.0588 
.0768 
.0972 
.1200 
.1452 
.1728 
.2028 
.2352 
.2700 
.3072 
.3468 
.3888 
.4332 
.4800 
.5292 
.5808 
.6348 
.6912 
.7500 

1024  ELECTRICAL    ENGINEERING. 


ELECTRICAL    ENGINEERING. 

STANDARDS    OF    MEASUREMENT. 

C.G.S.  (Centimetre,  Gramme,  Second)  or  "  Absolute  *• 
System  of  Physical  Measurements  : 

Unit  of  space  or  distance  =  1  centimetre,  cm.; 

Unit  of  mass  =  1  gramme,  gm. ; 

Unit  of  time  =  1  second,  s.; 

Unit  of  velocity  =  space  -4-  time  —  1  centimetre  in  1  second; 

Unit  of  acceleration  —  change  of  1  unit  of  velocity  in  1  second ; 

Acceleration  due  to  gravity,  at  Paris,   =  981  centimetres  in  1  second; 

1  0022046 

Unit  of  force  =  1  dyne  =  —  gramme  =  — — —  Ib.  =  .000002247  lb. 

A  dyne  is  that  force  which,  acting  on  a  mass  of  one  gramme  during  om 
second,  will  give  it  a  velocity  of  one  centimetre  per  second.  The  weight  oi 
one  gramme  in  latitude  40°  to  45°  is  about  980  dynes,  at,  the  equator  973  dynes 
and  at  the  poles  nearly  984  dynes.  Taking  the  value  of  g,  the  accelerator 
due  to  gravity,  in  British  measures  at  32.185  feet  per  second  at  Paris,  and  the 
metre  =  39.37  inches,  we  have 

1  gramme  =  32.185  x  12  +  .3937  =  981. 00  dynes. 

Unit  of  work    =  1  erg    =  1  dyne-centimetre  =  .00000007373  foot-pound  ; 
Unit  of  power  =  1  watt  =  10  million  ergs  per  second, 
=  .7373  foot-pound  per  second, 

i-  070         -i 

=  ^p  =  ^  of  1  horse-power  =  .00134  H.P. 

C.G.S.  Unit  of  magnetism  =  the  quantity  which  attracts  or  repels  an 
equal  quantity  at  a  centimetre's  distance  with  the  force  of  1  dyne. 

C.G.S.  Unit  of  electrical  current  ==  the  current  which,  flowing  through  a 
length  of  1  centimetre  of  wire,  acts  with  a  force  of  1  dyne  upon  a  unit  o1 
magnetism  distant  1  centimetre  from  every  point  of  the  wire.  The  ampere 
the  commercial  unit  of  current,  is  one  tenth  of  the  C.G.S.  unit. 

The  Practical  Units  used  in  Electrical  Calculations  are: 

Ampere,  the  unit  of  current  strength,  or  rate  of  flow,  represented  by  C. 

Volt,  the  unit  of  electro-motive  force,  electrical  pressure,  or  difference  ol 
potential,  represented  by  E. 

Ohm,  the  unit  of  resistance,  represented  by  R. 

Coulomb  (or  ampere-second),  the  unit  of  quantity,  Q. 

Ampere-hour  =  3600  coulombs,  Q'. 

Watt  (ampere-volt,  or  volt -ampere),  the  unit  of  power,  P. 

Joule  (volt-coulomb),  the  unit  of  energy  or  work,  W. 

Farad,  the  unit  of  capacity,  represented  by  K. 

Henry,  the  unit  of  induction,  represented  by  L. 

Using  letters  to  represent  the  units,  the  relations  between  them  may  be 
expressed  by  the  following  formulae,  in  which  t  represents  one  second 'anc 
Tone  hour: 

C  =  -  ,      Q  =  Ct,     Q'  =  CT,     K  =  %,      W  =  QE,     P  =  CE. 
R  -tii 

As  these  relations  contain  no  coefficient  other  than  unity,  the  letters  may 
represent  any  quantities  given  in  terms  of  those  units.  For  example,  if  f 
represents  the  number  of  volts  electro-motive  force,  and  H  the  number  ol 
ohms  resistance  in  a  circuit,  then  their  ratio  E  -t-  R  will  give  the  number  ol 
amperes  current  strength  in  that  circuit. 

The  above  six  formulas  can  be  combined  by  substitution  or  elimination 
so  as  to  give  the  relations  between  any  of  the  quantities.  The  most  impor- 
tant of  these  are  the  following  : 

0  =  §f,    K=^t,      W=  CEi  =  '^t  =  C*Rt  =  Ptt 


STANDARDS   OF   MEASUREMENT.  1025 

The  definitions  of  these  units  as  adopted  at  the  International  Electrical 
Congress  at  Chicago  in  1893,  and  as  established  by  Act  of  Congress  of  the 
United  States,  July  12,  1894,  are  as  follows: 

The  ohm  is  substantially  equal  to  109  (or  1,000,000,000)  units  or  resistance 
of  the  C.G.S.  system,  and  is  represented  by  the  resistance  offered  to  an  un- 
varying electric  current  by  a  column  of  mercury  at  32°  F.,  14.4521  grammes 
in  mass,  of  a  constant  cross-sectional  area,  and  of  the  length  of  106.3  centi- 
metres. 

The  ampere  is  1/10  of  the  unit  of  current  of  the  C.G.S.  system  and  is  the 
practical  equivalent  of  the  unvarying  current  which  when  passed  through 
a  solution  of  nitrate  of  silver  in  water  in  accordance  with  standard  speci- 
fications deposits  silver  at  the  rate  of  .001118  gramme  per  second. 

The  volt  is  the  electro-motive  force  that,  steadily  applied  to  a  conductor 
whose  resistance  is  one  ohm,  will  produce  a  current  of  one  ampere,  and  is 
practically  equivalent  to  1000/1434  (or  .6974)  of  the  electro-motive  force  be- 
tween the  poles  or  electrodes  of  a  Clark's  cell  at  a  temperature  of  15°  C., 
and  prepared  in  the  manner  described  in  ihe  standard  specifications. 

The  coulomb  is  the  quantity  of  electricity  transferred  by  a  current  of  one 
ampere  in  one  second. 

The  farad  is  the  capacity  of  a  condenser  charged  to  a  potential  of  one 
volt  by  one  coulomb  of  electricity. 

The  joule  is  equal  to  10,000,000  units  of  work  in  the  C.G.S.  system,  and  is 

Eractically  equivalent  to  the  energy  expended  in  one  second  by  an  ampere 
i  an  ohm. 

The  watt  is  equal  to  10,000,000  units  of  power  in  the  C.G.S.  system,  and  is 
practically  equivalent  to  the  work  done  at  the  rate  of  one  joule  per  second. 
The  henry  is  the  induction  in  a  circuit  when  the  electro-motive  force  in- 
duced in  this  circuit  is  one  volt,  while  the  inducing  current  varies  at  the  rate 
of  one  ampere  per  second. 

The  ohm,  volt,  etc.,  as  above  defined,  are  called  the  "international "  ohm, 
volt,  etc.,  to  distinguish  them  from  the  "  legal  "  ohm,  B.A.  unit,  etc. 

The  value  of  the  ohm,  determined  by  a  committee  of  the  British  Associa- 
tion in  1863,  called  the  B.A.  unit,  was  the  resistance  of  a  certain  piece  of 
copper  wire  preserved  in  London.  The  so-called  "  legal  "  ohm,  as  adopted 
at  the  International  Congress  of  Electricians  in  Paris  in  1884,  was  a  correc- 
tion of  the  B.A.  unit,  and  was  defined  as  the  resistance  of  a  column  of 
mercury  1  square  millimetre  in  section  and  106  centimetres  long,  at  a  tem- 
perature of  32°  F. 

1  legal  ohm  =  1.0112  B.A.  units,    1  B.A.  unit  =  0.9889  legal  ohm; 

1  international  ohm  =  1.0136    "       "         1    "       "      =  0.9866  int.  ohm; 
1  "     =  1.0023  legal  ohm,    1  legal  ohm  =  0.9977   "      " 

DERIVED  UNITS. 

1  megohm        =  1  million  ohms; 
1  microhm        =  1  millionth  of  aa  ohm; 
1  milliampere  =  1/1000  of  an  ampere; 
1  micro-farad  =  1  millionth  of  a  farad. 
RELATIONS  OP  VARIOUS  UNITS. 

1  ampere =  1  coulomb  per  second ; 

1  volt-ampere , =1  watt  =  1  volt-coulomb  per  second; 

(    =  .7373  foot-pound  per  second, 

1  watt •<    =  .0009477  heat-units  per  second  (Fahr.), 

f    =  1/746  of  one  horse-power; 
(   =  .7373  foot-pound, 

1  joule •<    =  work  done  by  one  watt  in  one  second, 

(    =  .0009477  heat-unit; 

\  British  thermal  unit =  1055.2  joules; 

{   =  737.3  foot-pound  per  second, 

1  kilowatt,  or  1000  watts <   =  .9477  heat-units  per  second, 

(   =  1000/746  or  1.3405  horse- powers; 

1  Kilowatt-hours,  i   =  1.3405  horse-power  hours, 

:000  volt-ampere  hours,  •<   =  2,654,200  foot-pounds, 

1  British  Board  of  Trade  unit,  (  =  3416  heat-units; 
l  horse  nowpr  J   =  746  wat'"s  =  746  volt -amperes, 

P°wer •  " "I" *.1  =  33,000  foct-pounds  per  minute. 

The  ohm,  ampere,  and  volt  arc-  defined  in  terms  of  one  another  as  follows: 
Ohm,  the  resistancs  of  a  conduct v2  through  which  a  current  of  one  ampere 
ivilJ  pass  when  the  electro-mctive  fcrce  is  one  volt.  Ampere,  the  quantity 


1026 


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FLOW   OF   WATER  AKD   ELECTRICTY.  1027 

of  current  which  will  flow  through  a  resistance  of  one  ohm  when  the  electro- 
motive force  is  one  volt.    Volt,  the  electro-motive  force  required  to  cause  a 
current  of  one  ampere  to  flow  through  a  resistance  of  one  ohm 
S»§^SiR?4*4?l^agffiB5&S^?2=l<??S  Electro-magnet^page  1058.) 


ing 

Tab 

on  Electrical  Engineering. 

Equivalent  Electrical  and  Mechanical  Units.— EJ  Ward 
Leonard  published  in  The  Electrical  Engineer.  Feb.  25,  1895,  a  table  of  use- 
ful equivalents  of  electrical  and  mechanical  units,  from  which  the  table  on 
page  1026  is  taken,  with  some  modifications. 

ANALOGIES  BETWEEN  THE  FLOW  OF  WATER  AND 
ELECTRICITY. 

WATER.  ELECTRICITY. 

Head,  difference  of  level,  in  feet.          (  Volts;  electro-motive  force  ;  differ- 
Difference  of  pressure  per  sq.  in.,  in  <     ence  of  potential  or  of  pressure-  E 

Ibs.  (     or  E.M.F. 

Resistance  of  pipes,  apertures,  etc.,  f  Ohms,  resistance  #.  The  resistance 
increases  with  length  of  pipe,  with  increases  directly  as  the  length  of 
contractions,  roughness,  etc.;  de-  the  conductor  or  wire  and  inversely 


creases  with  increase  of  sectional  •{  Jf   ,lts.    sec.^ "^    area,  R  oc  I  H-  s. 

i.    The  law  of  increase  and  de-  Tf  v"ria"  wlrtl  f>1°  "°f"^ "1"^' 

ise   is   expressed    by  complex 
nulse.    See  Flow  of  Water. 

Rate  of  flow,  as  cubic  ft.  per  second, 
gallons  per  minute,  etc.,  or  volume 


area.    The  law  of  increase  and  de- 
crease    i«     *™ros«Arl     Vnr    ™m^w       _.  Of  the  Conductor. 

fornc 


It  varies  with  the  nature  or  quality 
of  the  conductor. 

Conductivity  is  the  reciprocal  of  spe- 
cific resistance. 

Amperes;  current;  current  strength; 
intensity  of  current;  rate  of  flow;  1 


tianuijs  pei    IIIIIIULC,  ciu.,  ui    vuiuuio  ..  ,         t  ' 

divided  by  the  time.  In  the  mining  J     ampere  =  1  coulomb  per  second. 

regions   sometimes   expressed     in  |  volts  E 

"  miners'  inches."  i  Amperes  =  ofrms  »    G~  »~;  E  =  CR- 

Quantity,  usually  measured  in  cubic  ") 

feet  or  gallons,  but  is  also  equiva-  j  Coulomb,  unit  of  quantity,  Q,  =  rate 
lent   to     rate   of   flow  X  time,  as  V     of  flow  X  time,  as  ampere-seconds, 
cubic  feet  per  second  for  so  many  j      1  ampere-hour  =  3600  coulombs, 
hours.  J 

f  Joule,  volt-coulomb,  W,  the  unit  of 

Work,  or  energy,  measured  in  foot-  work,  =  product  of  quantity  by  the 
pounds;  product  of  weight  of  fall-  electro-motive  force  =  volt-ampere- 
ing  water  into  height  of  fall;  in  |  second.  1  joule=  .7373  foot-pound. 


pumping,  product  of  quantity  in 
cubic  feet  into  the  pressure  in  Ibs. 
per  square  foot  against  which  the 
water  is  pumped. 


If  C  (amperes)  =  rate  of  flow,  and 
E  (volts)  —  difference  of  pressure 
between  two  points  in  a  circuit, 
energy  expended  =  CEt,  =  C'*Rt, 


since  E  =  CR. 
Power,  rate  of  work.  Horse-power,ft.-  ] 

Ibs.  of  work  done  in  1  min.-^- 33,000.  Watt,  unit  of  power,  P,  =  volts  X 
In  falling  water,  pounds  falling  in  |  amperes,  =  current  or  rate  of  flow 

one  second  -f-  550.  In  water  flowing  }-     X  difference  of  potential. 

in  pipes,  rate  of  flow  in  cubic  feet  I  1  watt  =  .7373  foot-pound  per  second 

§er  second  X  pressure  resisting  the  |      =  1/746  of  a  horse-power, 
ow  in  Ibs.  per  sq.  ft.  -5-  550. 

Analogy  between  the  Ampere  and  the  Miner's  Inch. 
(T.  O'Connor  Sloane.) — The  miner's  inch  is  defined  as  the  quantity  of  water 
which  will  flow  through  an  aperture  an  inch  square  in  a  board  two  inches 
thick,  under  a  head  of  water  of  six  inches.  Here,  as  in  the  case  of  the  am- 
pere, we  have  no  reference  to  any  abstract  quantity,  such  as  gallons  or 
pounds.  There  is  no  reference  to  time.  It  is  simply  a  rate  of  flow.  We 
may  consider  the  head  of  water,  six  inches,  as  the  representative  of  electri- 
cal pressure;  i.e.,  one  volt.  The  aperture  restricting  the  flow  of  water  may 
be  assumed  to  represent  the  resistance  of  one  ohm;  the  flow  through  a  re- 
sistance of  one  ohm  under  the  pressure  of  one  volt  is  one  ampere;  the  flow 
through  the  resistance  of  a  one-inch  hole  two  inches  long  under  the  pressure 
of  six  inches  to  the  upper  edge  of  the  opening  is  one  miner's  inch. 

The  miner's  inch-second  is  the  correct  analogue  of  the  ampere-second;  the 
one  denotes  a  specific  quantity  of  water,  0.194  gallon;  the  other  a  specific 
quantity  of  electricity,  a  coulomb. 


1028 


ELECTKICAL    ENGINEERING. 


ELECTRICAL  RESISTANCE. 

Laws  of  Electrical  Resistance.—  The  resistance,  R,  of  any  con- 
ductor varies  directly  as  its  length,  I,  and  inversely  as  its  sectional  area,  s, 

or  R  oc  —  . 

a 

EXAMPLE.—  If  one  foot  of  copper  wire  .01  in.  diameter  has  a  resistance  of 
.10323  ohm,  what  will  be  the  resistance  of  a  mile  of  wire  .3  in.  diam.  at  the 
same  temperature  ?  The  sectional  areas  being  proportional  to  the  squares 
of  the  diameters,  the  ratio  of  the  areas  is  .32  :  .Ol2  =  900  to  1.  The  lengths 
are  as  5280  to  1.  The  resistances  being  directly  as  the  lengths  and  inversely 
as  the  sectional  areas,  the  resistance  of  the  second  wire  is  .10323  X  5280  H- 
900  =  .6056  ohm. 

Conductance,  c,  is  the  inverse  of  resistance.  R  =  —  ,     c  —  -—  -.  If  c  and  Co 

sc  sR 

represent  the  conductances,  and  R  and  jR"2  the  respective  resistance  of  two 
substances  of  the  same  length  and  section,  then  c  :  c2  :  :  R$  :  R. 

Equivalent  Conductors.—  With  two  conductors  of  length  /,  lt,  of 
conductances  c,  clf  and  sectional  areas  $,  s^  we  have  the  same  resistance, 

and  one  may  be  substituted  for  the  other  when  —  =  —  —  . 

CS  CiSj. 

The  specific  resistance,  also  called  resistivity,  a,  of  a  material  of  unit 
length  and  section  is  its  resistance  as  compared  with  the  resistance  of  a 
standard  conductor,  such  as  pure  copper.  Conductivity,  or  specific  con- 
ductance, is  the  reciprocal  of  resistivity. 


If  two  wires  have  lengths  I,  llt  areas  s,  sl5  and  specific  resistances  a,  al5  their 

al    ,         OiZi          ,    R         als, 

actual  resistances  are  R  —  —  ,  J?,  =  -±-t,  and    —  -  =  —  ^. 
s  st  R!       aiM 

Electrical  Conductivity  of  Different  Metals  and  Alloys. 

—  Lazare  Weiler  presented  to  the  Soci6te  Internationale  des  Electriciens  the 
results  of  his  experiments  upon  the  relative  electrical  conductivity  of  certain 
metals  and  alloys,  as  here  appended  : 


2   Pure  copper  .        

100 

18   Alloy  of  gold    and   silver 

3    Refined    and    crystallized 

(50$)                      

16.12 

copper 

99  9 

19    Swedish  iron 

16 

4  Telegraphic  silicious  bronze 

98 

20    Pure  Banca  tin 

15  45 

5   Alloy  of  copper  and  silver 

21    Antiinonial  copper 

12.7 

(50$)           

86.65 

22    Aluminum  bronze  (10$)     . 

12  6 

6    Pure  gold 

78 

23    Siemens  steel 

12 

7.  Silicide  of  copper,  4%  Si.  .  .  . 
8.  Silicide  of  copper,  12$  Si.  .  . 
9.  Pure  aluminum  
10.  Tin  with  12$  of  sodium... 
11.  Telephonic  silicious  bronze 
12.  Copper  with  10$  of  lead    . 

75 
54.7 
54.2 
46.9 
35 
30 

24.  Pure  platinum  
25.  Copper  with  10$  of  nickel.. 
26.  Cadmium  amalgam  (15$). 
27.  Droni<jr  mercurial  bronze.. 
28.  Arsenical  copper  (10$)  ...   . 
29    Pure  lead 

10.6 
10.6 
10.2 
10.14 
9.1 
8.88 

13    Pure  zinc 

29  9 

30    Bronze  with  ~0$  of  tin 

8  4 

14    Telephonic         phosphor  - 

31    Pure  nickel 

7  89 

bronze  
15.  Silicious  brass,  25$  zinc  
16.  Brass  with  35$  of  zinc.  .  . 

29 
26.49 
21.5 

32.  Phosphor-bronze,  10$  tin  .. 
33.  Phosphor-copper,  9$  phos.. 
34.  Antimony... 

6.5 
4.9 

3.88 

The  above  comparative  resistances  may  be  reduced  to  ohms  on  the  basis 
that  a  wire  of  soft  copper  one  milimetre  in  diameter  at  a  temperature  of 
0°,C.  has  a  resistance  of  .02029  international  ohms  per  metre;  or  a  wire  .001 
inch  diam.  has  a  resistance  of  9,59  international  ohms  per  foot. 


ELECTRICAL   RESISTANCE. 


1029 


Relative  Conductivities  of  Different  Metals  at  0    and 
IUU°  C.     (Mattiiiessen.) 


Metals. 

Conductivities. 

Metals. 

Conductivities. 

At    0°  C. 
"  32°  K. 

At  100°  C. 

14  212°  F. 

At   0°  C. 
"   32°  F. 

At  100°  C. 
"  212°  F. 

Silver,  hard  

100 
99.95 
77.96 
29.02 
23.72 
18.00 
16.80 

71.56 
70.27 
55.90 
20.67 
16.77 

Tin  ... 

12.36 
8.32 
4.76 
4.62 
1.60 
1.245 

8.67 
5.86 
3.33 
3.26 

'"61878" 

Copper,  hard  .... 
Gold,  hard  
Zinc,  pressed  
Cadmium 

Lead  
Arsenic  . 

Antimony  
Mercury,  pure.. 
Bismuth 

Platinum,  soft.  .. 
Iron,  soft...,  

Conductors  and  Insulators  in  Order  of  their  Value. 


Conductors. 
All  metals 

Well- burned  charcoal 
Plumbago 
Acid  solutions 
Saline  solutions 
Metallic  ores 
Animal  fluids 

Living  vegetable  substances 
Moist  earth 
Water 


Insulators  (Non-conductors). 
Dry  Air  Ebonite 


Shellac 

Paraffin 

Amber 

Resins 

Sulphur 

Wax 

Jet 

Glass 

Mica 


Gutta-percha 

India-rubber 

Silk 

Dry  Paper 

Parchment 

Dry  Leather 

Porcelain 

Oils 


According  to  Culley,  the  resistance  of  distilled  water  is  6754  million  times 
as  great  as  that  of  copper. 

Resistance  Varies  with  Temperature.— For  every  degree  Cen- 
tigrade the  resistance  of  copper  increases  about  0.4#,  or  for  every  degree  F. 
0.2222#.  Thus  a  piece  of  copper  wire  having  a  resistance  of  10  ohms  at  32° 
would  have  a  resistance  of  11.11  ohms  at  82°  F. 

The  following  table  shows  the  amount  of  resistance  of  a  few  substances 
used  for  various  electrical  purposes  by  which  1  ohm  is  increased  by  a  rise 
of  temperature  1°  F.,  or  1°  C. 

Material.  Rise  °0f  R'  of  1  Ohm  when  Heated— 

Platinoid 00013  .00021 

Platinum-silver 00018  .00031 

German  silver  (see  below)  ...  .00024  .00044 

Gold,  silver... 00036  .00065 

Cast  iron .00044  .00080 

Copper 00222  .00400 

Annealing.— The  degree  of  hardness  or  softness  of  a  metal  or  alloy 
affects  its  resistance.  Resistance  is  lessened  by  annealing.  Matrhiessen 
gives  the  following  relative  conductivities  for  copper  and  silver,  the  com- 
parison being  made  with  pure  silver  at  100°  C. : 

Metals.  Temp.  C.  Hard.         Annealed. 

Copper 11°  95.31  97.83 

Silver  14.6°  95.36  103.33 

Dr.  Siemens  compared  the  conductivities  of  copper,  silver,  and  brass  with 
pure  mercury  at  0°  C.,  with  the  following  results: 

Metal.  Hard.  Annealed. 

Copper 52.207  55.253 

Silver 56.252  64.380 

Brass  11.439  13502 

Edward  Weston  (Proc.  Electrical  Congress  1893,  p.  179)  says  that  the  re- 
sistance of  German  silver  depends  on  its  composition.  Mattliiessen  gives  itas 
nearly  13  times  that  of  copper,  with  a  temperature  coefficient  of  .0004433  per 
degree  C.  Weston,  however,  has  found  copper-nickel-zinc  alloys  (German 


1030  ELECTRICAL  E 


silver)  which  had  a  resistance  of  nearly  28  times  that  of  copper,  and  a  tem- 
perature coefficient  of  about  one  half  that  given  by  Matthiessen.  Kennelly 
and  Fessenden  (Proc.  Elec.  Cong.,  p.  186)  find  that  copper  has  a  uniform 
temperature  coefficient  of  0.406#  per  degree  C.,  between  the  limits  of  20°  and 
250°  C. 

Standard  of  Resistance  of  Copper  Wire.  (Trans.  A.  I.  E.  E., 
Sept.  and  Nov.  1890.)—Matthiessen's  standard  is:  A  hard-drawn  copper  wire 
1  metre  long,  weighing  1  gramme  has  a  resistance  of  0.1469  B.A.  unit  at 
0°  C.  (1  B.A.  unit  =  0.9889  legal  ohm  =  0.9866  international  ohm.)  Resist- 
ance of  hard  copper  =  1.0226  times  that  of  soft  copper.  Relative  conducting 
power  (Matthiessen):  silver,  100;  hard  or  unannealed  copper,  99.95;  soft  or 
annealed  copper,  102.21.  Conductivity  of  copper  at  other  temperatures  than 
0°C., 

Ct  =  C0(l  -  .00387*  -j-  .000009009**). 

The  resistance  is  the  reciprocal  of  the  conductivity,  and  is 

Et  -  R0(l  -f  .00387*  +  .00000597*2). 

A  committee  of  the  Am.  Inst.  Electrical  Engineers  recommend  the  follow- 
ing as  the  most  correct  form  of  the  Matthiessen  standard,  taking  8.89  as  the 
sp.  gr.  of  pure  copper  : 

A  soft  copper  wire  1  metre  long  and  1  mm.  diam.  has  an  electrical  resist- 
ance of  .02057  B.A.  unit  at  0°  C.  From  this  the  resistance  of  a  soft  copper 
wire  1  foot  long  and  .001  in.  diam.  (mil-foot)  is  found  to  be  9.720  B.A.  units 
at  0°  C. 

Standard  Resistance  at  0°  C.          B.A.  Units.     Legal  Ohms,    ^^f  t- 

Metre-millimetre,  soft  copper  ..........  02057  .02034              .02029 

Cubic  centimetre     "         "       ..........  000001616  .000001598        .000001593 

Mil-foot                      "         "       .........  9.720  9.612  9.590 

1  mil-foot,  of  soft  copper  at  10°.22  C.  or  50°.  4  F.  .  .  10  9.  977 

"      "    "          "        "  15°.5        "    59°.9F...     10.20  10.175 

"      "     "          *'        "  23°.9        "    75°      F...     10.53  10.505 

For  tables  of  the  resistance  of  copper  wire,  see  pages  218  to  220,  also 
pp.  1034,  1035. 

Taking  Matthiessen's  standard  of  pure  copper  as  100#,  some  refined  metal 
has  exhibited  an  electrical  conductivity  equivalent  to  103$. 

Matthiessen  found  that  impurities  in  copper  sufficient  to  decrease  its 
density  from  8.94  to  8.90  produced  a  marked  increase  of  electrical  resistance. 

ELECTRIC  CURRENTS. 

Oil  ill's  Jit  air,—  This  law  expresses  the  relation  between  the  three  fun- 
damental units  of  resistance,  electrical  pressure,  and  current.  It  is  : 

electrical  pressure      ._,       E  E 

Curr6Dt  =  -  resistance        ;    C=   B;    WheDCe    E  =  CB>   and   B  =  ff 
In  terms  of  the  units  of  the  three  quantities, 

Amperes  =  ir-  —  ;    volts  =  amperes  X  ohms;     ohms  =  —  V°   S    . 
ohms  amperes 

EXAMPLES:  Simple  Circuits.—  1.  If  the  source  has  an  effective  electrical 
pressure  of  100  volts,  and  the  resistance  is  two  ohms,  what  is  the  current  ? 

C  =  —  =  —  =  50  amperes. 

K          A 

2.  What  pressure  will  give  a  current  of  50  amperes  through  a  resistance  of 

2  ohms  ?    E  =  CR  =  50  X  2  =  100  volts. 

3.  What  resistance  is  required  to  obtain  a  current  of  50  amperes  when  the 

jp       100 

pressure  is  100  volts  ?    R  =  —  =  —  -  =  2  ohms. 
G         50 

The  following  examples  are  from  R.  E.  Day's  "  Electric  Light  Arithmetic:" 
1.  The  internal  resistance  of  a  certain  Brush  dynamo-machine  is  10.9  ohms, 
and  the  external  resistance  is  73  ohms;  the  electro-motive  force  of  the  ma- 
chine being  839  volts.   Find  the  strength  of  the  current  flowing  in  the  circuit. 
E  =  839;    R  =  73  -f-  10.9  =  83.9  ohms; 
C  =  E  -*-  R  =  839  -*-  83.9  =  10  amperes. 


1031 

2.  Three  arc  lamps  in  series  have  a  resistance  of  9.36  ohms,  while  the  re- 
sistance of  the  leading  wires  is  1.1  ohm,  and  that  of  the  dynamo  is  2.8  ohms. 
Find  what  must  be  the  electro-motive  force  of  the  machine  when  the  strength 
of  the  current  produced  is  14.8  amperes. 

E  =  2.8  4-  9.36  -f  1.1  =  13.26  ohms;    C  =  14.8  amperes; 
E  =  C  X  R  =  13.26  X  14.8  =  196.3  volts. 

3.  Calculate  from  the  following  data  the  average  resistance  of  each  of 
three  arc  lamps  arranged  in  series.  The  electro-motive  force  of  the  machine 
is  244  volts  and  its  resistance  is  3.7  ohms,  while  that  of  the  leading  wires  is  2 
ohms,  and  the  strength  of  current  through  each  lamp  is  21  amperes. 

If  x  represent  the  average  resistance  in  ohms  of  each  lamp,  then  the  total 
resistance  of  the  circuit  is  R  -  3x  +  2  -f-  3.7. 

But  by  Ohm's  law  R  =  E  -+-  C,  .'.  Zx  -f  5.7  =  244/21  =  11.61  ohms,  whence 
x  =  1.97  ohms,  nearly. 

4.  Three  Maxim  incandescent  lamps  were  placed  in  series.    The  average 
resistance,  when  hot,  of  each  lamp  was  39.3  ohms,  and  that  of  the  dynamo 
and  leading  wires  11.2  ohms.    What  electro-motive  force  was  required  to 
maintain  a  current  of  1.2  amperes  through  this  circuit  ? 

In  this  case  we  have 

R  =  3  x  39.3  -f  11.2  =  129.1  ohms,  and 
C  =  1.2  ampere; 
and  therefore,  by  Ohm's  law, 

E  -  C  X  R  =  1.2  X  129.1  =  154.9  volts. 

5.  The  resistance  of  the  arc  of  a  certain  Brush  lamp  was  3.8  ohms  when  a 
current  of  10  amperes  was  flowing  through  it.    What  was  the  electro-motive 
force  between  the  two  terminals  ? 

E  =  C  X  R  =  10  X  3.8  =  38  volts. 

6.  Twenty  -five  exactly  similar  galvanic  cells,  each  of  which  had  an  aver- 
age internal  resistance  of  15  ohms,  were  joined  up  in  series  to  one  incandes- 
cent lamp  of  70  ohms  resistance,  and  produced  a  current  of  0.112  amperes. 
What  would  be  the  strength  of  current  produced  by  a  series  of  30  such  cells 
through  2  lamps,  each  of  30  ohms  resistance  ? 

The  data  of  the  first  part  of  the  problem  enable  us  to  determine  the 
average  electro-motive  force  of  each  cell  of  the  battery.  Let  this  be  repre- 
sented by  E]  then  we  have 

25E  =  C  X  R  =  .112  X  (25  X  15  -f  70)  =  .112  X  445; 
.  E=.  112X445  =  2 

Then  from  the  data  in  the  second  part  of  the  problem,  we  have,  by  Ohm's 


Divided  Circuits.—  If  the  circuit  has  two  paths,  the  total  current  in 
both  divides  itself  inversely  as  the  resistances. 
If  R  and  Rl  are  the  resistances  of  the  two  branches,  and  C  and  d  the  cur- 

C1         7? 

rents,  C  X  R  =  Ci  X  #1,  and  —  =  -^,  whence 


In  the  case  of  the  double  circuit,  one  circuit  is  said  to  be  in  shunt  to  the 
other,  or  the  circuits  are  in  multiple  arc  or  in  parallel. 

Conductors  in  Series.— If  conductors  are  arranged  one  after  the 
other  they  are  said  to  be  in  series,  and  the  total  resistance  is  the  sum  of  their 
several  resistances.  R  —  R^  -f-  R9  -{-  R^. 

Internal  Resistance.— In  a  simple  circuit  we  have  two  resistances, 
that  of  the  circuit  R  and  that  of  the  internal  parts  of  the  source,  called  in- 


1032  ELECTRICAL 

ternal  resistance,  r.    The  formula  of  Ohm's  law  when  the  internal  resistance 

is  considered  is  C  =  ^r—.  —  . 
jR-t-r 

Total  or  Joint  Resistance  of  Two  Branch  es.—  Let  C  be  the 
total  current,  and  Oj,  (72  the  currents  in  branches  whose  resistances  respect- 

ively are  Rlt  fla.    Then  C  =  Cl  +  C2;  C  =  §;  C,  =  ™;  C.,  =  —  ;  or,  if  JS7  = 

XV  XVj  /lo 

1  1  1  7?   7? 

1,  <7  =  -5-  =  B-  +  •£->  whence  #  =        *    '   ,  which  is  the  joint  resistance  of 

K       /t[       -n-a  zti-|-/ia 

2?!  and  R^. 
Similarly,  the  joint  resistances  of  three  branches  have  resistances  respect- 

ively  of  Bl,  *,,  *3,  is  B  =  ^  +*£jgWt. 
When  the  branch  resistances  are  equal,  the  formula  becomes 


where  R^  =  the  resistance  of  one  branch,  and  n  =  the  number  of  branches. 

Kircnhoff's  Laws.—!.  The  sum  of  the  currents  in  all  the  wires  which 
meet  in  a  point  is  nothing. 

2.  The  sum  of  all  the  products  of  the  currents  and  resistances  in  all  the 
branches  forming  a  closed  circuit  is  equal  to  the  sum  of  all  the  electrical 
pressures  in  the  same  circuit. 

When  E=  EI  +  EI  +  Et,  etc.,  and  C  =  Ct  +  Ca  +  C3,  etc.,  and  R  is  the 
total  resistance  of  R^R^R^  etc.,  then 

E!  +  E*  +  E3,  etc.  =  dBi  +  <7a#3  +  C3#3,  etc. 

Power  of  the  Circuit.—  The  power,  or  rate  of  work,  in  watts  = 
current  in  amperes  X  electro-motive  force  in  volts  =  C'X  J£.  Since  C  —  E-+-R. 

E% 
watts  =  —  =  electro-motive  force2  -*-  resistance. 

EXAMPLE.—  What  H.P.  is  required  to  supply  100  lamps  of  40  ohms  resist- 
ance each,  requiring  an  electro-motive  force  of  60  volts  ? 

The  number  of  volt-amperes  for  each  lamp  is  —  -  =  --  ,  1  volt-ampere  = 

.00134  H.P.;  therefore  ^X  100  X  .00134  =  12  H.P.  (electrical)  very  nearly. 

If  the  loss  in  the  dynamo  is  20  per  cent,  then  12  H.P.  is  80  per  cent  of  the 
actual  H.P.  required;  which  therefore  is  —  =  15  H.P. 

Heat  Generated  by  a  Current.—  Joule's  law  shows  that  the  heat 
developed  in  a  conductor  is  directly  proportional,  1st,  to  its  resistance;  2d, 
to  the  square  of  the  current  strength;  and  3d,  to  the  time  during  which  the 
current  flows,  or  H  =  C*Rt.  Since  C  -  E  -*-  R, 

C*Rt  =  ^CRt  =  ECt  =  E^t  =  ^. 

K  K  K 

Or,  heat  =  current2  X  resistance  X  time 

=  electro  -motive  force  X  current  X  time 

=  electro-motive  force2  X  time  -f-  resistance. 

•pi 

Q  =  quantity  of  electricity  flowing  =  Ct  -  —  t. 
H  =  EQ;  or  heat  =  electro-motive  force  X  quantity. 

The  electro-motive  force  here  is  that  causing  the  flow,  or  the  difference  in 
potential  between  the  ends  of  the  conductor. 

The  electrical  unit  of  heat,  or  "joule"  =  107  ergs  =  heat  generated  in  one 
second  by  a  current  of  1  ampere  flowing  through  a  resistance  of  one  ohm  — 
.239  gramme  of  water  raised  1°  C.  H  =  C*Rt  X  .239  gramme  calories  = 
C*Rt  X  .0009478  British  thermal  units. 

In  electric  lighting  the  energy  of  the  current  is  converted  into  heat  in  the 
lamps.  The  resistance  of  the  lamp  is  made  great  so  that  the  required 
quantity  of  heat  may  be  developed,  while  in  the  wire  leading  to  and  from 


ELECTRIC   CURRENTS. 


1033 


the  lamp  the  resistance  is  made  as  small  as  is  commercially  practicable,  so 
that  as  little  energy  as  possible  may  be  wasted  in  heating  the  wire.  The 
transformations  of  energy  from  the  fuel  burned  in  the  boiler  to  the  electric 
light  are  the  following: 

Heat  energy  is  transformed  into  mechanical  energy  by  means  of  the  boiler 
and  engine. 

Mechanical  energy  is  transformed  into  electrical  energy  in  the  dynamo. 

Electrical  energy  is  transformed  into  heat  in  the  electric  light. 

The  heat  generated  in  a  conductor  is  the  equivalent  of  the  energy  causing 
the  flow.  Thus,  rate  of  expenditure  of  energy  in  watts  =  electro-motive 
force  in  volts  X  current  in  amperes  =  EC,  and  the  energy  in  -joules  =  watts 
X  time  in  seconds  =  ECt.  Heat  =  C^Rt  =  ECt. 

Heating  of  Conductors.  (From  Kapp's  Electrical  Transmission 
of  Energy.)— It  becomes  a  matter  of  great  importance  to  determine  before- 
hand what  rise  in  temperature  is  to  be  expected  in  each  given  case,  and  if 
that  rise  should  be  found  to  be  greater  than  appears  safe,  provision  must  be 
made  to  increase  the  rate  at  which  h^at  is  carried  off.  This  can  generally 
be  done  by  increasing  the  superficial  area  of  the  conductor.  Say  we  have 
one  circular  conductor  of  1  square  inch  area,  and  find  that  with  1000  amperes 
flowing  it  would  become  too  hot.  Now  by  splitting  up  this  conductor  into 
10  separate  wires  each  one  tenth  of  a  square  inch  cross-sectional  area,  we 
have  not  altered  the  total  amount  of  energy  transformed  into  heat,  but  we 
have  increased  the  surface  exposed  to  the  cooling  action  of  the  surrounding 
air  in  the  ratio  of  1  :  ^lO,  and  therefore  the  ten  thin  wires  can  dissipate  more 
than  three  times  the  heat,  as  compared  with  the  single  thick  wire. 
Heating  of  Wire*  of  Subaqueous  and  Aerial  Cables  (in- 
sulated with  Gutta-percha).  (Prof.  Forbes.) 
Diameter  of  cable  -s-  Diameter  of  conductor  =  4. 

Temperature  of  air  =  20°  C.  =  68°  F. 
t  —  excess  of  temperature  of  conductor  over  air. 


Diameter  in  centi- 
metres and  mils. 

Current  in  amperes. 

Cm. 

Mils. 

t  =  1°  C. 

=  1.8°  F. 

t  =  9°  C. 
=  16.2°  F. 

t  =  25°  C. 
=  45°  F. 

t  =  49°  C. 
=  92.2°  F. 

t  =  81°  C. 
=  145.8°  F. 

.1 

40 

3.7 

11.0 

17.8 

24.0 

29.5 

.2 

80 

9.1 

27.0 

43.8 

59.0 

72.5 

.3 

120 

15.0 

44.4 

72.1 

97.3 

119 

.4 

160 

21.2 

62.5 

102 

137 

168 

.5 

200 

27.4 

81.0 

131 

177 

218 

.6 

240 

33.7 

100 

164 

219 

268 

.7 

280 

40.1 

119 

192 

259 

319 

.8 

310 

46.4 

137 

223 

301 

369 

.9 

350 

52.9 

157 

253 

342 

420 

1.0 

390 

59.3 

175 

285 

384 

472 

2.0 

780 

124 

367 

595 

803 

988 

3.0 

1180 

189 

559 

908 

1225 

1503 

4.0 

1570 

254 

753 

1221 

1646 

2021 

5.0 

1970 

319 

945 

1534 

2068 

2523 

6.0 

2360 

385 

1138 

1846 

2491 

3058 

7.0 

2760 

450 

1330 

2158 

2846 

3575 

8.0 

3150 

514 

1525 

.  2472 

3335 

4094 

9.0 

3540 

580 

1716 

2785 

3755 

4611 

10.0 

3940 

645 

1909 

3097 

4178 

5130 

Prof.  Forbes  states  that  an  insulated  wire  carries  a  greater  current  without 
overheating  than  a  bare  wire  if  the  diameter  be  not  too  great.  Assuming 
the  diameter  of  the  cable  to  be  twice  the  diam.  of  the  conductor,  a  greater 
current  can  be  carried  in  insulated  wires  than  in  bare  wires  up  to  1  9  inch 
diam.  of  conductor.  If  diam.  of  cable  =  4  times  diam.  of  conductor,  this  is 
the  case  up  to  1.1  inch  diam.  of  conductor. 

Copper- wire  Table.— The  table  on  pages  1034  and  1035  is  abridged 
from  one  computed  by  the  Committee  on  Units  and  Standards  of  the  Ameri- 
can Institute  of  Electrical  Engineers  (Trans.  Oct.  1893). 


1034 


ELECTRICAL   ENGINEERING. 


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ELECTRIC   CURRENTS. 


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1036  ELECTRICAL  EKGIKEERISTG. 

The  data  from  which  the  foregoing  table  has  been  computed  are  as  follows: 
Matthiessen's  standard  resistivity,  Matthiessen's  temperature  coefficients, 
specific  gravity  of  copper  =  8.89.  Resistance  iu  terms  of  the  international 
ohm. 

Matthiessen's  standard  1  metre-gramme  of  hard-drawn  copper  =  0.1469 
B.  A.  U.  @  0°  C.  Ratio  of  resistivity  hard  to  soft  copper  1.0226. 

Matthiessen's  standard  1  metre-gramme  of  soft-drawn  copper  =  0.14365 
B.  A.  U.  ©  0°  C.  One  B.  A.  U.  =  0.9866  international  ohm. 

Matthiesse>rs  standard  1  metre-gramme  of  soft-drawn  copper  =  0.141729 
international  ohm  @  0°  C. 

Temperature  coefficients  of  resistance  for  20°  C.,  50°  C.,  and  80°  C.,  1.07968 
1.20625,  and  1.33681  respectively.  1  foot  =  0.3048028  metre,  1  pound  = 
453.59256  grammes, 

Heating  of  Coils.  -To  calculate  the  heating  of  a  coil,  given  the  cool- 
ing surface  and  its  resistance.  (Forbes.) 

Let  p  =  the  resistance  of  a  coil  in  ohms  at  the  permissible  temperature 

(the  resistance  (cold)  m  ust  be  increased  by  1  /5  of  its  value  to  give  p) ; 

S  =  the  surface  exposed  to  the  air  measured  in  square  centimetres 

(1  square  cm.  =  .155  square  inch;  1  sq.  in.  =  6.45  square  cm.); 
t  =  the  rise  in  temperature,  centigrade  scale; 
C  =  the  current  in  amperes. 

.24<72p  —  heat  generated  =  etS. 

where  e  is  McFarlane's  constant,  varying  from  .0002  to  .0003.    The  latter 
value  may  be  taken.     If  50°  C.  be  the  permissible  rise  in  temperature, 


,  /.0003  X  50  X 

C  =  / 


_     OK  A  /S 
~   '~5V    p 


.24  Xp 

EXAMPLE.— The  resistance  of  the  field-magnets  of  a  dynamo  is  1.5  ohms 
cold,  and  the  surface  exposed  to  the  air  is  1  square  metre;  find  the  current 
to  heat  it  not  more  than  50°  C. 

/ 10  000 
Here  S  =  10,000;  p  =  1.8  ohms;  and  C  =  3&A/  ~Tg-  =  33-5  amperes. 

For  the  heating  of  coils  of  field-magnets  Mr.  C.  Hering  gives  1  watt  of 
energy  dissipated  for  every  223  square  inches  of  cooling-surface  for  each 
degree  F.  of  difference  between  the  temperature  of  the  coil  and  the  sur- 
rounding air. 

W  =  CE  -  1/223T.S  =  0.004476TS,  in  which  W  =  watts  lost  in  coil,  T  = 
degrees  Fahr.,  arid  S  =  square  inches. 

C  =  OOQ  j-,  is  the  greatest  current  which  can  be  used  in  the  magnet  coils  of 


a  shunt  machine  having  a  certain  pressure  in  order  that  they  do  not  heat 
above  a  certain  temperature.  Thus  for  a  rise  of  temperature  of  50°  F.  above 
the  surrounding  air, 

0  =  ^^  =  .224  ^.    Substituting  for  E  its  equivalent  OR,  we  get 

Mi 


If  80°  F.  is  the  maximum  difference  of  temperature, 


The  formula  can  be  used  for  series  machines  when  Cis  known,  for  writing 

TS 
C*R  =  1/223TS,    we  get  R  =  ^^. 

With  a  permissible  rise  of  50°  F.  or  80°  F.,  we  have  respectively, 


The  surface  area  of  the  coil  in  square  inches  may  be  found  from 
^  __  223  W  _  223  CE 
T          ~T~ 


ELECTRIC   CURRENTS. 


For  a  rise  of  temperature  of  50°  F.  or  80°  F.,  respectively,  the  surface  will 


be 


Fusion  of  Wires.-W.  H.  Preece  gives  a  formula  for  the  current  re- 
quired  to  fuse  wires  of  different  metals,  viz.:  C=  ad%->  in  which  d  is  the 
diameter  in  inches  and  a  a  coefficient  whose  value  for  different  metals  is  as 
follows:  Copper  10244;  aluminum  7585;  platinum  5172;  German  silver  5230; 
platinoid  4750;  iron  3148;  tin,  1642;  lead,  1379;  alloy  of  2  lead  and  1  tin,  1318. 

Diameters  of  Various  Wires  which  will  be  Fused  by  a 
given  Current. 

(C\% 
-  J3;  a  =  1642  for  tin  =  1379  for  lead  =  10244  for  copper  = 

3148  for  iron. 


Current, 
in 
amperes. 

Tin  Wire. 

Lead  Wire. 

Copper  Wire. 

Iron  Wire. 

Diam. 

inches. 

Approx. 
S.W.  G. 

Diam. 
inches. 

Approx. 
S.W.  G. 

Diam. 
inches. 

Approx. 
S.W.  G. 

Diam. 
inches. 

Approx. 
S.W.  G. 

1 

.0072 

36 

.0081 

35 

.0021 

47 

.0047 

40 

2 

.0113 

31 

.0128 

30 

.0034 

43 

.0074 

36 

3 

.0149 

28 

.0168 

27 

.0044 

41 

.0097 

33 

4 

.0181 

26 

.0203 

25 

.0053 

39 

.0117 

31 

5 

.0210 

25 

.0236 

23 

.0062 

38 

.0136 

29 

10 

.0334 

21 

.0375 

20 

.0098 

33 

.0216 

24 

15 

.0437 

19 

.0491 

18 

.0129 

30 

.0283 

22 

20 

.0529 

17 

.0595 

17 

.0156 

28 

.0343 

20.5 

25 

.0614 

16 

.0690 

15 

.0181 

26 

.0398 

19 

30 

.0694 

15 

.0779 

14 

.0205 

25 

.0450 

18.5 

35 

.0769 

14.5 

.0864 

13.5 

.0227 

24 

.0498 

18 

40 

.0840 

13.5 

.0944 

13 

.0248 

23 

.0545 

17 

45 

•0909 

13 

.1021 

12 

.0268 

22 

.0589 

16.5 

50 

.0975 

12.5 

.1095 

11.5 

.0288 

22 

.0632 

16 

60 

.1101 

11 

.1237 

10 

.0325 

21 

.0714 

15 

70 

.1220 

10 

.1371 

9.5 

.0360 

20 

.0791 

14 

80 

.1334 

9.5 

.1499 

8.5 

.0394 

19 

.0864 

13.5 

90 

.1443 

9 

.1621 

8 

.0426 

18.5 

.0935 

13 

100 

.1548 

8.5 

.1739 

7 

.0457 

18 

.1003 

12 

120 

.1748 

7 

.1964 

6 

.0516 

17.5 

.1133 

11 

140 

.1937 

6 

.2176 

5 

.0572 

17 

.1255 

10 

160 

.2118 

5 

.2379 

4 

.0625 

16 

.1372 

9»5 

180 

.2291 

4 

.2573 

3 

.0676 

16 

.1484 

9 

200 

.2457 

3.5 

.2760 

o 

.0725 

15 

.1592 

8 

250 

.2851 

1.5 

.8203 

0 

.0841 

13.5 

.1848 

6.5 

300 

.3220 

0 

.3617 

00.5 

.0950 

12.5 

.2086 

5 

Current  in  Amperes  Required  to  Fuse  Wires  According 
to  the  Formula  C  =  ad$- 


No. 
S.W.  G. 

Diameter, 
inches. 

di- 

Tin. 
a  =  1642. 

Lead 
a  =  1379. 

Copper 
a  =  10244 

Iron. 
a  =  3148. 

14 

.080 

.022627 

37.15 

31.20 

231.8 

71.22 

16 

.064 

.016191 

26.58 

22.32 

165.8 

50.96 

18 

.048 

.010516 

17.27 

14.50 

107.7 

33.10 

20 

.036 

.006831 

11.22 

9.419 

69.97 

21.50 

22 

.028 

.004685 

7.692 

6.461 

48.00 

14.75 

24 

.022 

.003263 

5.357 

4.499 

33.43 

10.27 

26 

.018 

.002415 

3.965 

3.330 

24.74 

7.602 

28 

.0148 

.001801 

2.956 

2.483 

18.44 

5.667 

30 

.0124 

.001381 

2.267 

1.904 

14.15 

4.347 

32 

.0108 

.001122 

1.843 

1.548 

11.50 

3.533 

1038  ELECTRICAL 

ELECTRIC   TRANSMISSION. 

Cross-section   of  Wire  Required  for  a  Given  Current.— 

Constant  Current  (Series)  System.— The  cross-sectional  area  of  copper 
necessary  in  any  circuit  for  a  given  constant  current  depends  on  the  differ- 
ence between  the  pressure  at  the  generating  station  and  the  maximum 
pressure  required  by  all  the  apparatus  on  the  circuit,  and  on  the  total  length 
of  the  circuit.  The  following  formulae  are  given  in  "  Practical  Electrical 
Engineering:" 

If  F  =  pressure  in  volts  at  generators; 

v  =  sum  of  all  the  pressures  (in  volts)  required  by  apparatus  supplied 

in  the  circuit; 

n  —  total  length  (going  and  return)  of  circuit  in  miles; 
G—  current  in  amperes; 
r  =  resistance  of  1  mile  of  copper-conductor  of  1  square  inch  sectional 

area  in  ohms; 
a  =  required  cross-sectional  area  of  copper  in  square  inches,— 

nrC 


~  V-v' 

If  we  take  the  temperature  of  the  conductor  when  the  current  has  been 
flowing  for  some  time  through  it,  as  80°  F., 

r=-  0.0455  Ohm,    and     a  = 


. 
V  —  v 

It  generally  happens,  however,  that  we  are  not  tied  down  to  a  particular 
value  of  F,  as  the  pressure  at  the  generators  can  be  varied  by  a  few  volts  to 
suit  requirements.  In  this  case  it  is  usual  to  fix  upon  a  current  density  and 
determine  the  cross-sectional  area  of  copper  in  accordance  with  it. 

If  D  =  current  density  in  amperes  per  square  inch  determined  upon, 

•-4 

The  current  density  is  frequently  taken  at  1000  amperes  to  the  square  inch, 
but  should  in  general  be  determined  by  economical  considerations  for 
every  case  in  question. 

Allowable  Current  Density  in  Insulated  Cables.  —  Experiments  on 
insulated  cables  in  casing  gave  the  results  shown  below,  but  they  need  con- 
firmation or  correction  of  the  current  densities  permissible  in  different  sizes. 
of  insulated  cables  run  underground.  C  and  D  are  the  current  in  amperes 
and  the  current  density  in  amperes  per  square  inch,  respectively,  which  will 
raise  the  temperature  of  the  conductor  by  the  number  of  degrees  Fahr. 
indicated  by  the  suffix. 


No.  S.W.G.*of  Qn:  r>                 n  r>  n 

Strands,  each  Wire,  ^tnches.  ^             ^  ^  °" 

7                   20  0.0072  18  2,500  28  3,900 

7                    14  0.0357  59  1,400  95  2,700 

19                    14  0.0975  126  1,300  205  2,100 

37                   14  0.191  210  1,100  339  1,800 

Constant  Pressure  (Parallel  System).—  To  determine  the   loss   in 
pressure  in  a  feeder  of  given  size  in  the  case  of  two-wire  parallel  distribution. 

Let    a  =  cross-sectional  area  of  copper  of  one  conductor  of  the  feeder  in 

square  inches; 

n  =  length  of  feeder  (going  and  return)  in  miles; 
C  =  current  in  amperes  ; 
V  —  v  =  loss  of  pressure  in  feeder  in  volts; 

r  =  resistance  of  1  mile  of  copper  conductor  of  1  square  inch  sec- 
tional area  in  ohms. 


*  Standard  (British)  Wire-gauge. 


ELECTRIC  TRANSMISSION.  1039 

If  the  temperature  of  the  conductor  with  this  current  flowing  in  it  is 
assumed  to  be  80°  F., 

r  =  0.0455  ohm,    and     V  -  v  =  -  0455nC 


ing  station,  an 


a    =  cross-sectional  area  of  each  of  the  outer  conductors  in  square  inches; 

a'  =  cross-sectional  area  of  middle  conductor; 

n   =  length  in  miles  of  each  conductor  of  feeder  ; 

F!  =  pressure  between  p^  and  p'  in  volts  at  generating  station; 

Fj  —  pressure  between  p'  and  p2  |n  volts  at  generating  station; 

Vj.  =  pressure  between  q^  and  q'  in  volts  at  feeding-point; 

vt  =  pressure  between  q'  and  ga  in  volts  at  feeding-point; 

<7i  =  current  inptfi  in  amperes; 


C2  =  current  in  p«aa  in  amperes; 

r    =  resistance  of  1  mile  of  copper  conductor  of  1  square  inch  sectional 

area  in  ohms. 
Then 


It  will  be  noticed  that  if  Vj.  =  v2,  and  if  <7t  is  greater  than  C« ,  Fi  is  greater 
than  F2  by  twice  the  loss  of  pressure  in  the  middle  wire;  this  result  shows 
that  the  regulators  must  be  in  circuit  with  the  two  outer  conductors. 

It  is  usual  to  make  a'  half  a;  then,  if  the  greatest  want  of  balance  between 
the  loads  of  the  two  sections  of  the  three-wire  system  is  m*  per  cent  of  the 
maximum  load  of  the  more  heavily  loaded  section,  and  if  C,  is  the  maximum 
current  in  either  of  the  outer  conductors  of  the  feeder  under  consideration, 

Ca  will  not  be  less  than  d  (l  -  ^  ),  and  consequently  C^  -  Ca  will  not  be 

greater  than  ^p 

We  have  then 

_  nrCi      200  -f-m        _  _1 

Kl      Vl~     a     X      200 

go  that  if  Vi  and  v2  are  each  equal  to  F— the  pressure  required  to  be  main- 
tained constant  at  the  feeding-point — we  can  calculate  Fx  and  Fa  for  given 
values  of  n,  a,  and  Clf  employing  the  value  of  m,  which  we  estimate  should 
be  the  maximum  it  can  have. 

These  last  expressions  show  that  the  difference  in  the  pressures  required 
at  the  station  across  the  two  sections  of  a  three -wire  feeder  increases  with 
the  current  carried  by  the  feeder  ;  hence  the  regulators  on  each  of  the  outer 
conductors  should  be  equivalent  to  a  variable  resistance  having  at  least 
nrm  . 
-—  ohms  as  a  maximum. 

It  is  usual  to  make  the  area  of  the  middle  conductor  one  half  of  that  of 
each  of  the  outer  conductors,  but  this  is  not  invariably  the  case. 

Snort-circuiting.— From  the  law  C=  —  it  is  seen  that  with  any  pres- 

ti 

sure  E  the  current  C  will  become  very  great  if  R  is  made  very  small.  In 
short-circuiting  the  resistance  becomes-small  and  the  current  therefore  great. 
Hence  the  dangers  of  short-circuiting  a  current. 

Economy  of  Electric  Transmission.  (R.  G.  Elaine,  Eng'g,  June 
5, 1891.)— Sir  W.  Thomson's  rule  for  the  most  economical  section  of  conductor 

*  The  value  to  be  assigned  to  m  may  vary  from  10  to  25,  according  to  the 
care  exercised  in  connecting  customers  to  one  section  or  the  other,  or  both, 
and  according  to  the  local  conditions.  At  a  certain  station  supplying  current 
on  the  three- wire  low-pressure  system  to  about  25,000  8-c.p.  lamps,  we  were 
informed  that  m  had  never  exceeded  7  or  8. 


1040 


ELECTRICAL   ENGINEERING. 


is  that  for  which  the  "  annual  interest  on  capital  outlay  is  equal  to  the 
annual  cost  of  energy  wasted,"  and  its  practical  outcome  is  that  the  area  of 

the  copper  conductor  should  be  such   that  its   resistance  per  mile  =  — 

o 

(C  being  the  current  in  amperes). 

Tables  have  been  compiled  by  Professor  Forbes  and  others  in  accordance 
with  modifications  of  Sir  W.  Thomson's  rule.  For  a  given  entering  horse- 
power the  question  is  merely  one  as  to  what  current  density,  or  how  many 
amperes  per  square  inch  of  conductor,  should  be  employed.  Sir  W.  Thom- 
son's rule  gives  about  393  amperes  per  square  inch,  and  Professor  Forbes's 
tables— for  a  medium  cost  of  one  electrical  horse-power  per  hour— give  a 
current  density  of  about  380  amperes  per  square  inch  as  most  economical. 

When  a  given  horse-power  is  to  be  delivered  at  a  given  distance,  the  case 
is  somewhat  different,  and  Prof essors  Ayrton  and  Perry  (Electrician,  March, 
1886)  have  shown  that  in  that  case  both  the  current  and  resistance  are 
variables,  and  that  their  most  economical  values  may  be  found  from  the  fol- 
lowing formulae: 


and    r  =  — 


nw  (1  -f  sin  <f>)9  ' 

in  which  C  =  the  proper  current  in  amperes;  r  =  resistance  in  ohms  per 
mile  which  should  be  given  to  the  conductor;  P=  pressure  at  entrance  in 
volts;  n  =  number  of  miles  of  conductor;  w  =  power  delivered  in  watts; 
<£  =  such  an  angle  that  tan  $  =  nt  -H  P,  t  being  a  constant  depending  on 
the  price  of  copper,  the  cost  of  one  electrical  horse-power,  interest,  etc.:  it 
may  be  taken  as  about  17. 

In  this  case  the  current  density  should  not  remain  constant,  but  should 
diminish  as  the  length  increases,  being  in  all  cases  less  than  that  calculated 
by  Sir  W.  Thomson's  rule. 

'EXAMPLE.— If  the  current  for  an  electric  railway  is  sent  in  at  200  volts,  100 
horse-power  being  delivered,  find  the  waste  of  power  in  heating  the  con- 
ductor, the  distance  being  5  miles  and  there  being  a  return  conductor. 

Here  n  =  10,  t  =  17,  P  =  200;  tan  <f>  =  170  -*-  200  =  .85,  <f>  =  40°  22',  sin  $  = 
.6477. 

Hence  most  economical  resistance 


X 


10  X74600 

or  .1279  ohm  in  its  total  length. 

74600 
The  most  economical  current,  C  =  ~^r  X  1.6477  =  614.68  amperes,  and  W, 


the  power  wasted  in  heat,  = 


(~      614'58       '18'9 


=  64.75  horse-power. 


~  - 
The  following  tables  show  the  power  wasted  as  heat  in  the  conductor. 


HORSE-POWER  WASTED  IN  TRANSMITTING  POWER  ELECTRICALLY  TO  A  GIVEN 
DISTANCE,  THE  ENTERING  POWER  BEING  FIXED.  PRESSURE  AT  ENTRANCE, 
200  VOLTS.  CURRENT  DENSITY,  380  AMPERES  PER  SQUARE  INCH. 


Horse-power 
sent  ijis* 

Horse-power  Wasted,  the 
t      Distance  to  which  the 
^  Power  is  Transmitted  being 
one  Mile  (there  being  a 
Return  Conductor). 

Horse-power  Wasted. 
Distance  Five  Miles. 

10 
20 
40 
50 
80 

ipo 
too 

1.663 
3.327 
6.654 
8.318 
13.308 
16.636 
33.272 

8.818 
16  636 
33.27 
41.59 
66.54 
83.18 
166.36 

"*»,    *  That  is,  horse-power  at  the  generator  terminals. 


ELECTRIC   TRANSMISSION. 


1041 


PRESSURE  AT  ENTRANCE,  2000  VOLTS. 


Horse- 
power 
sent  in. 

Horse-power 
Wasted.   Distance 
One  Mile  (there 
being:  a  Return 
Conductor). 

Horse- 
power 
Wasted.   Dis- 
tance Five 
Miles. 

Horse- 
power 
Wasted. 
Distance  Ten 
Miles. 

Horse-power 
Wasted. 
Distance 
Twenty  Miles. 

100 
200 
400 
500 
800 
1000 
2000 

1.663 
3.327 
6.654 
8.318 
13.308 
16.636 
33.272 

8.318 
16.636 
33.272 
41.59 
66.54 
83.18 
166.36 

16.636 
33.272 
66.54 
83.18 
133.08 
166.36 
332.72 

33.27 
66.54 
133.08 
166.36 
266.17 
332.72 
665.44 

It  will  be  seen  from  these  numbers  that  when  the  current  density  is  fixed 
the  power  wasted  is  proportional  to  the  entering  horse-power  and  the  length 
of  the  conductor,  and  is  inversely  proportional  to  the  potential.  For  a 
copper  conductor  the  rule  may  be  simply  stated  as 

W=  16.6358^X2, 

E  being  the  horse-power  and  P  the  pressure  at  entrance,  and  I  the  length  of 
the  conductor  in  miles. 

HORSE-POWER  WASTED  IN  ELECTRIC  TRANSMISSION  TO  A  GIVEN  DISTANCE, 
THE  POWER  TO  BE  DELIVERED  AT  THE  DISTANT  END  BEING  FIXED.  PRES- 
SURE AT  ENTRANCE,  200  VOLTS.  CURRENT  AND  RESISTANCE  CALCULATED 
BY  AYRTON  AND  PERRY'S  RULES. 


H.orse-power 
Delivered, 

Horse-power  Wasted, 
the  Distance  to  which 
the  Power  is  Transmitted 
being  One  Mile  (there 
being  a  Return 
Conductor). 

Horse-power 
Wasted. 
Distance  Five 
Miles. 

Horse-power 
Wasted. 
Distance  Ten 
Miles. 

10 
20 
40 
50 
80 
100 
200 

1.676 
3.352 
6.704 
8.38 
13.408 
16.76 
33.52 

6.476 
12.952 
25.904 
32.38 
51.808 
64.86 
129.52 

8.620 
17.24 
34.48 
43.10 
68.96 
86.20 
172.4 

PRESSURE  AT  ENTRANCE,  2000  VOLTS. 


•tear  I-SF- 

! 

Horse-power 
Wasted.  Distance 
Five  Miles. 

Horse-power 
Wasted.    Distance 
Ten  Miles. 

100 
200 
400 
500 
800 
1000 
2000 

1.716 
3.432 
6.864 
8.58 
13.728 
17.16 
34.32 

8.484 
16.968 
33.938 
42.42 
67.87 
,     84.84 
••   169.68 

16.763 
33.526 
67.052 
83.815 
134.104 
167  63 
335.26 

If  H  =  horse-power  sent  in,  w  =  power  delivered  in  watts,  C  =  current  in 
amperes,  r  &=  resistance  in  ohms  per  mile,  P  —  pressure  at  entrance  in 
vo^ts,  and  rv=s  number  of  miles  of  conductor, 

(w  +  C2r)  -*-  746  =  H;    w  =  746H  -  C2r; 


1042  ELECTRICAL 

and  the  formulae  for  best  current  and  resistance  become 


~~  n(746fl  -  C2r 
Energy  wasted  as  heat  in  watts  per  mile  =  02r  =  n  i  s|p  A* 

Horse-power  wasted  per  mile  =  W^.  =  n  _|_  sin  ^ 

(<f>  =  angle  whose  tangent  =  nt  -H  P,  and  the  value  of  t  corresponding  to  a 
current  density  of  380  amperes  per  sq.  in.  is  16.636.) 

TABLE    OF   ELECTRICAL    HORSE-POWERS. 

Formula  :  Volts  X7^mperes  =  H.P.,    or    1  volt-ampere  =  .0013405  H.P. 
Read  amperes  at  top  and  volts  at  side,  or  vice  versa. 


Volts  or  Amperes. 


1 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

.00134 

.0134 

.0268 

.0402 

.0536 

.0570 

.0804 

.0938 

.1072 

.1206 

.1341 

.1475 

.1609 

.00268 

.0268 

.0536 

.0804 

.1072 

.1341 

.1609 

.1877 

.2145 

.2413 

.2681 

.2949 

.3217 

.00402 

.0402 

.0804 

.1206 

.1609 

.2011 

.2413 

.2815 

.3217 

.3619 

.4022 

.4424 

.4826 

.00536 

.0536 

.1072 

.1609 

.2145 

.2681 

.3217 

.3753 

.4290 

.4826 

.5362 

.5898 

.6434 

.00670 

.0670 

.1341 

.2011 

.2681 

.3351 

.4022 

.4692 

.5362 

.6032 

.6703 

.7373 

.8043 

.00804 

.0804 

.1609 

.2413 

.3217 

.4022 

.4826 

.5630 

.6434 

.7239 

.8043 

.8847 

.9652 

.00938 

.0938 

.1877 

.2815 

.3753 

.4692 

.5630 

.6568 

.7507 

.8445 

.9384 

1.032 

1.126 

.01072 

.1072 

.2145 

.3217 

.4290 

.5362 

.6434 

.7507 

.8579 

.9652 

1.072 

1  180 

1.287 

.01206 

.1206 

.2413 

.3619 

.4826 

.6032 

.7239 

.8445 

.9652 

1.086 

1.206 

1.327 

1.448 

.01341 

.1341 

.2681 

.4022 

.5362 

.6703 

.8043 

.9383 

1.072 

1.206 

1.341 

1.475 

1.609 

.01475 

.1475 

.2949 

.4424 

.5898 

.7373 

.8847 

1.032 

1.180 

1.327 

1.475 

1.622 

1.769 

.01609 

.1609 

.3217 

.4826 

.6434 

.8043 

.9652 

1.126 

1.287 

1.448 

1.609 

1.769 

1.930 

.01743 

.1743 

.3485 

.5228 

.6970 

.8713 

1.046 

1.220 

1.394 

1.568 

1.743 

1.917 

2.091 

.01877 

.1877 

.3753 

.5630 

.7507 

.9384 

1.126 

1.314 

1.501 

1.689 

1.877 

2.064 

2.252 

.02011 

.2011 

.4022 

.6032 

.8043 

1.005 

1.206 

1.408 

1.609 

1.810 

2.011 

2.212 

2.413 

.02145 

.2145 

.4290 

.6434 

.8579 

1.072 

1.287 

1.501 

1.716 

1.930 

2.145 

2.359 

2.574 

.02279 

.2279 

.4558 

.6837 

.9115 

1.139 

1.367 

1.595 

1.823 

2.051 

2.279 

2.507 

2.735 

.02413 

.2413 

.4826 

.7239 

.9653 

1.206 

1.448 

1.689 

1.930 

2.172 

2.413 

2.654 

2.895 

.02547 

.2547 

.5094 

.7641 

1.019 

1.273 

1.528 

1.783 

2.037 

2.292 

2.547 

2.801 

3.056 

.02681 

.2681 

.5362 

.8043 

1.072 

1.340 

1.609 

1.877 

2.145 

2.413 

2.681 

2.949 

3.217 

.02815 

.2815 

.5630 

.8445 

1.126 

1.408 

1.689 

1.971 

2.252 

2.533 

2.815 

3.097 

3.378 

0294 

.2949 

.5898 

.8847 

1.180 

1.475 

1.769 

2.064 

2.359 

2.654 

2.949 

3.244 

3.539 

.0308: 

.3083 

.6166 

.9249 

1.233 

1.542 

1.850 

2.158 

2.467 

2.775 

3.083 

3.391 

8.700 

.03217 

.3217 

.6434 

.9652 

1.287 

1.609 

1.930 

2.252 

2.574 

2.895 

3.217 

3  539 

3.861 

.03351 

.3351 

.6703 

1.005 

1.341 

1.676 

2.011 

2.346 

2.681 

3.016 

3,351 

3.686 

4.022 

.03485 

.3485 

.6971 

1.046 

1.394 

1.743 

2.091 

2.440 

2.788 

3.137 

3.485 

3.834 

4.182 

.03619 

.3619 

.7239 

1.086 

1.448 

1.810 

2.172 

2.534 

2.895 

3.257 

3.619 

3.981 

4.343 

.0375 

.3753 

.7507 

1.126 

1.501 

1.877 

2.252 

2.627 

3.003 

3.378 

3.753 

4.129 

4.504 

0388 

.3887 

.7775 

1.166 

1.555 

1.944 

2.332 

2.721 

3.110 

3.499 

3.887 

4.276 

4.665 

.0402 

.4022 

.8043 

1.206 

1.609 

2.011 

2.413 

2.815 

3.217 

3.619 

4.022 

4.424 

4.826 

.04156 

.4156 

.8311 

1.247 

1.662 

2.078 

2.493 

2.909 

3.324 

3.740 

4.156 

4.571 

4.987 

.0429 

.4290 

.8579 

1.287 

1.716 

2.145 

2.574 

3.003 

3432 

3.861 

4.290 

4.719 

5.148 

.0442 

.4424 

.8847 

1.327 

1.769 

2.212 

2.654 

3.097 

3.539 

3.986 

4.424 

4.866 

5.308 

.0455 

.4558 

.9115 

1.367 

1.823 

2.279 

2.735 

3.190 

3.646 

4.102 

4.558 

5.013 

5.469 

.0469 

.4692 

.9384 

1.408 

1.877 

2.346 

2.815 

3.284 

3.753 

4.223 

4.692 

5.161 

5.630 

.0482 

.4826 

.9652 

1.448 

1.930 

2.413 

2.895 

3.378 

3.861 

4.343 

4.826 

5.308 

5.791 

.0496 

.4960 

.9920 

1.488 

1.984 

2.480 

2.976 

3.472 

3.968 

4.464 

4.960 

5.456 

5.952 

.0509 

.5094 

1.019 

1.528 

2.038 

2.547 

3.056 

3.566 

4.075 

4.585 

5.094 

5.603 

6.113 

.0522 

.5228 

1.046 

1.568 

2.091 

2.614 

3.137 

3.660 

4.182 

4.705 

5.228 

5.751 

6.274 

.0536 

.5362 

1.072 

1.609 

2.145 

2681 

3.217 

3.753 

4.290 

4.826 

5.362 

5.898 

6.434 

.0549 

.5496 

1.099 

1.649 

2.198 

2.748 

3.298 

3.847 

4.397 

4.946 

5.496 

6.046 

6.595 

.0563 

.5630 

1.126 

1.689 

2.252 

2.815 

3.378 

3.941 

4.504 

5.067 

5.630 

6.193 

6.756 

.0576 

.5764 

1.153 

1.729 

2.306 

2.882 

3.458 

4.035 

4.611 

5.187 

5.764 

6.341 

6.917 

.0589 

.5898 

1.180 

1.769 

2.359 

2.949 

3.539 

4.129 

4.719 

5.308 

5.898 

6.488 

7.078 

.0603 

.6032 

1.206 

1.810 

2.413 

3.016 

3.619 

4.223 

4.826 

5.439 

6.032 

6.635 

7.239 

.0616 

.616C 

1.233 

1.850 

2.467 

3.083 

3.700 

4.316 

4.933 

5.550 

6.166 

6.783 

7.400 

.063(K 

.6300 

1.260 

1.890 

2.520 

3.150 

3.780 

4.410 

5.040 

5.670 

6.300 

6.930 

7.560 

.0643 

.6434 

1.287 

1.930 

2.574 

3.217 

3.861 

4.504 

5.148 

5.791 

6.434 

7.078 

7.721 

19  .0656 

.656 

1.314 

1.970 

2.627 

3.284 

3.941 

4.598 

5.255 

5.912 

6.568 

7.225 

7.882 

)0  .0670 

.670 

1.341 

2.011 

2.681 

3.351 

4.022 

4.692 

5.362 

6.032 

6.703 

7.373 

8.043 

TABLE  OF  ELECTRICAL  HORSE-POWERS.       1043 

TABLE   OF  ELECTRICAL,  HORSE-POWERS- 


gjS 

ij3 

Volts  or  Amperes. 

If 

1 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100 

110 

120 

55 

.0737? 

.7373 

1.475 

2.212 

2.949 

3.686 

4.424 

5.161 

5.898 

6.635 

7.373 

8.110 

8.847 

60 

.08043 

.8043 

1.609 

2.413 

3.217 

4.022 

4.826 

5.630 

6.434 

7.239 

8.043 

8.847 

9.652 

65 

.08713 

.8713 

1.743 

2.614 

3.485 

4.357 

5.228 

6.099 

6.970 

7.842 

8.713 

9.584 

10.46 

70 

.0938* 

.9384 

1.877 

2.815 

3.753 

4.692 

5.630 

6.568i     7.507 

8.445 

9.384 

10.32 

11.26 

75 

.1005* 

1.005 

2.011 

3.016 

4.021 

5.027 

6.032 

7.037 

8.043 

9.048 

10.05 

11.06 

12.06 

801  .10724 

1.072 

2.145 

3.217 

4.290 

5.362 

6.434 

7.507 

8.579 

9.652 

10.72 

11.80 

12.87 

85    .11394 

1.139 

2.279 

3.418 

4.558 

5.697      6.836 

7.976 

9.115 

10.26 

11.39 

12.53 

13.67 

90    .12065 

1.206!  2.413 

3.619 

4.826 

6.032      7.239 

8.445 

9.652 

10.86 

12.06 

13.27 

14.48 

95|  .12735 

1.2731  2.547 

3.820 

5.094 

6.367      7.641 

8.914 

10.18 

11.46 

12.73 

14.01 

15.28 

100|  .13405 

1.341    2.681 

4.022 

5.362 

6.703 

8.043 

9.384 

10.72 

12.06 

13.41 

14.75 

16.09 

200 

.26810 

2.681    5.362     8.043 

10.72 

13.41 

16.09 

18.77 

21.45 

24.13 

26.81 

29.49 

32.17 

300 

.40215 

4.022    8.043    12.06 

16.09 

20.11 

24.13 

28.15 

32.17 

36.19 

40.22 

44.24 

48.26 

400 

.53620J     5.36210.72 

16.09 

21.45 

26.81 

32.17 

37.53|    42.90 

48.26 

53.62     58.98 

64.34 

500 

.67025 

6.70313.41 

20.11 

26.81 

33.51 

40.22 

46.92 

53.62 

60.32 

67.03     73.73 

80.43 

600 

.80430 

8.043 

16.09 

24.13 

32.17 

40.22 

48.26 

56.30 

64.34 

72.39 

80.43 

88.47 

96.52 

700 

.93835 

9.384 

18.77 

28.15 

37.53 

46.92 

56.30 

65.68 

75.07 

84.45 

93.84 

103.2 

112.6 

800 

1.0724 

10.72 

21.45   32.17 

42.90 

53.62 

64.34 

75.07 

85.79 

96.52 

107.2 

118.0 

128.7 

900 

1.2065 

12.06 

24.13    36.19 

48.26 

60.32 

72.39 

84.45 

96.52 

108.6 

120.6 

132.7 

144.8 

1,000 

1.3405 

13.41 

26.811  40.22 

53.62 

67.03 

80.43 

93.84 

107.2 

120.6 

134.1 

147.5 

160.9 

2,000 

2.6810 

26.81 

53.62;  80.43 

107.2 

134.1 

160.9 

187.7 

214.5 

241.3 

268.1 

294.9 

321.7 

3,000 

4.0215 

40.22 

80.43  120.6 

160.9 

201.1 

241.3 

281.5 

321.7 

361.9 

402.2 

442.4 

482.6 

4,000 

5.3620 

53.62 

107.2    160.9 

214.5 

268.1     321.7 

375.3 

429.0 

482.6 

536.2 

589.8 

643.4 

5,000 

6.7025!  67.03 

134.1    201.1 

268.1 

335.1     402.2 

469.2 

536.2 

603.2 

670.3 

737.3 

804.3 

6,000 

8.0430 

80.43 

160.9    241.3 

321.7 

402.2     482.6 

563.0 

643.4 

723.9 

804.3 

884.7 

965.2 

7,000 

9.3835 

93.84 

187.7    281.5 

375.3 

469.2 

563.0 

656.8 

750.7 

844.5 

938.4 

1032 

1126 

8000 

10.724  Jl07.2 

214.5   321.7 

429.0 

536.2 

643.4 

750.7 

857.9 

965.2 

1072 

1180 

1287 

9,000 
10,000 

12.065   120.6 
13.405  !  134.1 

241.3 
268.1 

361.9 
402.2 

482.6 
536.2 

603.2 
670.3 

723.9 
804.3 

844.5 
938.3 

965.2 
1072 

1086 
1206 

1206 
1341 

1327 
1475 

1448 
1609 

"Wire  Table.— The  wire  table  on  the  following  page  (from  a  circular  of 
the  Westinghouse  El.  &  Mfg.  Co.)  shows  at  a  glance  the  size  of  wire  neces- 
sary for  the  transmission  of  any  given  current  over  a  known  distance  with 
a  given  amount  of  drop,  for  100-volt  and  500-volt  circuits,  with  varying 
losses.  The  formula  by  which  this  table  has  been  calculated  is 


DXlOOO 
CX2L 


=  R, 


in  which  D  equals  the  volts  drop  in  electro-motive  force,  Cthe  current,  L  the 
distance  from  the  dynamo  to  the  point  of  distribution,  and  R  the  line  resist- 
ance in  ohms  per  thousand  feet. 

EXAMPLE  1.— Required  the  size  of  wire  necessary  to  carry  a  current  of  60 
amperes  a  distance  of  650  feet  with  a  loss  of  5£  at  100  volts. 

Referring  to  the  table,  under  60  amperes,  we  find  the  given  distance,  650 
feet.  In  the  same  horizontal  line  and  under  5^  drop  at  100  volts,  we  find  No. 
000  wire,  which  is  the  size  required. 

EXAMPLE  2.— What  size  will  be  required  for  10  amperes  2000  feet,  with  a 
drop  of  10%  at  500  volts. 

Under  10  amperes  find  1930— the  nearest  figure  to  2000— and  in  the  same 
horizontal  line  under  \Q%  at  500  volts  find  No.  11,  the  size  required. 

Wiring  Formulae  for  Incandescent  Lighting.  (W.  D. 
Weaver,  Elec.  World,  Oct.  15,  1892.)— A  formula  for  calculating  wiring 
tables  is 

.      2150TFrv  .      2150LC7 

A  =  -^W~L*>    °r'    A=-^E~< 

where  A  =  section  in  circular  mils;  W=  watt  rating  of  lamps;  E  =  volt- 
age; L  =  distance  to  centre  of  distribution,  in  feet;  N  =  number  of  lamps; 
a  -  percentage  of  drop;  C  =  current  in  amperes. 

EXAMPLE.— Volts,  50;  amperes,  100;  feet  to  centre  of  distribution,  100; 
drop,  2%. 

2150  X  100  X  100  =  2)5i000  cjrculal.  milSi 

2  X  50 
or  about  0000  B.  &  S,  gauge. 


1044 


ELECTRICAL 


ISill  SHE"*2 


£sgl8gs§38888£S3--* 


sss 


S838 


i§83i  gSSSl  ----- 


pSsS  1SSS§  g^ss^ 


O5  lO  O*  OS  t- 


W  «      «  : 


OOf-(N*9 


DOO^W 


ELECTRIC  TRANSMISSION. 


1045 


The  horse-power  and  efficiency  of  a  motor  being  given,  the  size  of  the  con- 
ducting wire  in  circular  mils  can  be  found  from  the  following  formula: 

160,400,000  X  H.P.  X  L 
aE*  X  efficiency 

EXAMPLE.—  Horse-power,  10;    volts,  500;    drop, 
point,  600:  efficiency  of  motor,  75$. 


A  = 


feed  to  distributing 


A  = 


r  mils-  or  about  No-  8  B-  &  s- 


Cost  of  Copper  for  Long-distance  Transmission. 

(Westinghouse  El.  &  Mfg.  Co.) 

COST  OP  COPPER  REQUIRED  FOR  THE  DELIVERY  OP  ONE  MECHANICAL  HORSE- 
POWER AT  MOTOR  SHAFT  WITH  1000,  2000,  3000,  4000,  5000,  AND  10,000  VOLTS 
AT  MOTOR  TERMINALS,  OR  AT  TERMINALS  OF  LOWERING  TRANSFORMERS. 

Loss  of  energy  in  conductors  (drop),  equals  20$. 
Distances  equal  one  to  twenty  miles. 
Motor  efficiency  equals  90$. 

Length  of  conductor  per  mile  of  single  distance,  11,000  feet,  to  allow  for 
sag. 
Cost  of  copper  equals  16  cents  per  pound. 


Miles. 

1000  v. 

2000  v. 

3000  v. 

4000  v. 

5000  v. 

10,000  v. 

1 

$2.08 

$0.52 

$0.23 

$0.13 

$0.08 

$0.02 

2 

8.33 

2.08 

0.93 

0.52 

0.33 

0.08 

3 

18.70 

4.68 

2.08 

1.17 

0.75 

0.19 

4 

33.30 

8.32 

3.70 

2.08 

1.33 

0.33 

5 

52.05 

13.00 

5.78 

3.25 

2.08 

0.52 

6 

74.90 

18.70 

8.32 

4.68 

3.00 

0.75 

7 

102.00 

25.50 

11.30 

6.37 

4.08 

1.02 

8 

133.25 

33.30 

14.80 

8.32 

5.33 

1.33 

'9 

168.60 

42.20 

18.70 

10.50 

6.74 

1.69 

10 

208.19 

52.05 

23.14 

13.01 

8.33 

2.08 

11 

251.90 

63.00 

28  00 

15.75 

10.08 

2.52 

12 

299.80 

75.00 

33.30 

18.70 

12.00 

3.00 

18 

352.00 

88.00 

39.00 

22.00 

14.08 

3.52 

14 

408  00 

102.00 

45.30 

25.50 

16.32 

4.08 

15 

468.00 

117.00 

52.00 

29.25 

18.72 

4.68 

16 

533.00 

133.00 

59.00 

33.30 

21.32 

5.33 

17 

600.00 

150.00 

67.00 

37.60 

24.00 

6.00 

18 

675.00 

169.00 

75.00 

42.20 

27.00 

6.75 

19 

750.00 

188.00 

83.50 

47.00 

30.00 

7.50 

20 

833.00 

208.00 

92.60 

52.00 

33.3.2 

8.33 

A  Graphical  Method  of  calculating  leads  for  wiring  for  electric 
lighting  is  described  by  Carl  Hering  in  Trans.  A.  I.  E.  E.,  1891.  He  furnishes 
a  chart  containing  three  sets  of  diagonal  straight-line  diagrams  so  con- 
nected that  the  examples  under  the  general  formula  for  wiring  may  be 
solved  without  calculation  by  simply  locating  three  points  in  succession  on 
the  chart. 

The  general  principle  upon  which  the  chart  is  based  is  that  for  any 
formula  containing  three  variable  quantities,  one  of  which  is  the  product 
or  the  quotient  of  the  other  two,  the  "  curves  "  representing  their  relative 
values  may  always  be  represented  by  a  series  of  straight  diagonal  lines 
drawn  through  the  centre  or  zero-point.  Such  a  set  of  lines  will  therefore 
enable  one  to  make  any  calculations  graphically  for  that  formula.  For 
instance,  horse-power  =  volts  X  amperes;  the  constant  746  does  not  con- 
cern us  at  present.  A  series  of  diagonal  lines  properly  spaced  will  there- 
fore give  directly  either  the  horse-power,  the  volts,  or  the  amperes,  when 
the  other  two  are  given. 

One  scale  is  vertical,  the  other  horizontal,  and  the  diagonal  lines  (or  the 
hyperbolas)  each  represent  one  unit  (or  a  number  of  units)  of  the  third 
scale  To  make  the  "curves"  straight  lines  the  diagonals  must  be  made. 


1046 


ELECTRICAL  ENGINEERING. 


COST  OF  COPPER  REQUIRED  TO  DELIVER  ONE  MECHANICAL  HORSE-POWER  AI 
MOTOR-SHAFT  WITH  VARYING  PERCENTAGES  OF  Loss  IN  CONDUCTORS,  UPOI 
THE  ASSUMPTION  THAT  THE  POTENTIAL  AT  MOTOR  TERMINALS  is  IN  EACI 
CASE  3000  VOLTS. 

Distances  equal  one  to  twenty  miles. 
Motor  efficiency  equals  90$. 

Length  of  conductor  per  mile  of  single  distance,  11,000  feet,  to  allow  foi 
sag. 
Cost  of  copper  equals  16  cents  per  pound. 


Miles. 

i<* 

15* 

20$ 

25$ 

30$ 

1 

$0.52 

SO.  33 

$0.23 

$0.17 

$0.13 

2 

2.08 

1.31 

0.93 

0.69 

0.54 

3 

4.68 

2.95 

2.08 

1.55 

1.21 

4 

8.32 

5.25 

3.70 

2.77 

2.15 

5 

13.00 

8.20 

5.78 

4.33 

3.37 

6 

18.70 

11.75 

8.32 

6.23 

4.85 

7 

25.50 

16.00 

11.30 

8.45 

6.60 

8 

33.30 

21.00 

14.80 

11.00 

8.60 

9 

42.20 

26.60 

18.75 

14.00 

10.90 

10 

52.05 

32.78 

23.14 

17.31 

13.50 

11 

63.00 

39.75 

28.00 

21.00 

16.30 

12 

75.00 

47.20 

33.30 

24.90 

19.40 

13 

88.00 

55.30 

39.00 

29.20 

22.80 

14 

102.00 

64.20 

45.30 

33.90 

26.40 

15 

117.00 

73.75 

52.00 

38.90 

30.30 

16 

133.00 

83.80 

59.00 

44.30 

34.50 

17 

150.00 

94.75 

67.00 

50.00 

39.00 

18 

169.00 

106.00 

75.00 

56.20 

43.80 

19 

188.00 

118.00 

83.50 

62.50 

48.70 

20 

208.00 

131.00 

92.60 

69.25 

54.00 

to  represent  one  of  the  two  quantities  which  is  equal  to  the  quotient  of  th< 
other  two,  and  not  the  one  which  is  equal  to  the  product  of  the  other  two 
because  the  curves  would  then  be  hyperbolas.  In  the  example  given  th< 
diagonals  must  represent  volts  or  amperes,  but  not  horse-powers.  The  con 
stants  in  such  formulae  affect  only  the  positions  of  the  diagonals;  althougl 
they  increase  considerably  the  work  of  arithmetically  calculating  the  results 
they  do  not  affect  in  the  least  the  graphical  calculations  after  tne  diagram! 
are  once  drawn. 
The  general  formula  for  wiring  is  : 


Cross-section  = 


current  for  one  lamp  X  No.  of  lamps  X  distance  X  constant 
loss  in  volts 

containing  six  quantities  only,  one  of  which  is  always  constant,  being  equa 
to  twice  the  mil-foot  resistance  of  copper,  if  the  cross-section  is  in  circula; 
mils.  Calculations  involving  three  of  these  five  quantities  may  readily  b< 
made  graphically  by  means  of  a  single  set  of  diagonal  lines. 

In  Mr.  Bering's  method  the  formula  is  split  up  into  three  smaller  ones 
each  of  which  contains  no  more  than  three  variable  quantities.  Eacl 
formula  can  then  be  calculated  separately  by  a  simple  diagram,  as  de 
scribed,  thus  permitting  the  whole  formula  to  be  calculated  graphically. 

To  do  this,  let  the  first  diagram  perform  the  calculation, 

_  current  for  one  lamp 
loss  in  volts         ' 

in  which  #  is  a  mere  auxiliary  quantity.  Let  a  second  similar  diagran 
perform  the  next  calculation, 

y  =  x  X  number  of  lamps; 
a,nd,  a  third  diagram  the  final  calculation, 

(jross-section  =  y  x  distan.<?Q, 


ELECTRIC   TRANSMISSION. 


1047 


The  constant  may  be  combined  with  any  one  of  these,  it  is  immaterial 
which  one.  This  triple  calculation  may  at  first  seem  to  complicate  matters 
on  account  of  the  new  quantities,  x  and  y.  These,  however  are  easily 
eliminated  by  the  simple  device  of  placing  the  three  diagrams  together  side 
by  side,  in  such  a  position  that  the  two  x  scales  coincide,  and  similarly  the 
two  y  scales.  By  doing  this  one  has  merely  to  pass  directly  from  one  set  of 
diagonals  to  the  next  to  perform  the  successive  steps  of  the  calculation 
without  being  concerned  about  the  intermediate  auxiliary  quantities  These 
intermediate  quantities  correspond,  and  are  equal  to  the  successive  products 
or  quotients  which  are  obtained  in  the  successive  arithmetical  multiplications 
and  divisions  of  these  five  quantities  in  the  formula,  which  cannot  of 
course,  be  eliminated  in  making  the  calculations  arithmetically. 

Weight  of  Copper  required  for  Long-  distance  Trans- 
mission.— W.  F.  C.  Hasson  (Trans.  Tech.  Socy.  of  the  Pacific  Coast,  vol. 
x,  No.  4)  gives  the  following  formula: 


where  Wis  the  weight  of  copper  wire  in  pounds;  D,  the  distance  in  miles; 
E.  the  E.M.F.  at  the  motor  in  hundreds  of  volts;  H.P.,  the  horse-power 
delivered  to  the  motor;  L,  the  per  cent  of  line  loss. 

Thus,  to  transmit  200  horse-power  ten  miles  with  10  per  cent  loss,  and 
have  3000  volts  at  the  motor,  we  have 


"  30  X  30 


x  «0  x 


10 


x  266.5  =  53,300  Ibs. 


Efficiency  of  Long-distance  Transmission.  (F.  R.  Hart, 
Power,  Feb.  1892.)— The  mechanical  efficiency  of  a  system  is  the  ratio  of  the 
power  delivered  to  the  dynamo-electric  machines  at  one  end  of  the  line  to 
the  power  delivered  by  the  electric  motors  at  the  distant  end.  The  com- 
mercial efficiency  of  a  dynamo  or  motor  varies  with  its  load.  The  maximum 
efficiency  of  good  machines  should  not  be  under  90$  and  is  seldom  above 
92$.  Under  the  most  favorable  conditions,  then,  we  must  expect  a  loss  of 
say  9$  in  the  dynamo  and  9$  in  the  motor.  The  loss  in  transmission,  due  to 
fall  in  electrical  pressure  or  "  drop  "  in  the  line,  is  governed  by  the  size  of 
the  wires,  the  other  conditions  remaining  the  same.  For  a  long-distance 
transmission  plant  this  will  vary  from  5$  upwards.  With  a  loss  of  5$  in  the 
line,  the  total  efficiency  of  transmission  will  be  slightly  under  79$.  With  a 
loss  of  10$  in  the  line,  the  efficiency  would  be  slightly  under  75$.  We  may 
call  80$  the  practical  limit  of  the  efficiency  with  the  apparatus  of  to-day. 
The  methods  for  long-distance  power  transmission  by  electricity  may  be 
divided  into  three  general  classes:  (1)  Those  using  continuous  current;  (2) 
those  using  alternating  current;  and  (3)  regenerating  or  "  motor-dynamo  " 
systems.  The  subdivisions  of  each  of  these  general  classes  are  tabulated  as 
follows: 

Low 
voltage 


Continuous 
current 


2-wire 


High 
voltage 


Alternating 
current 


Regenerating 
systems 


One  machine. 
Machines  in  parallel. 
One  machine. 
Machines  in  parallel. 
Machines  in  series. 
2  machines  in  series. 
Machines  in  multiple  series. 
Machines  in  series. 
Without  conversions. 
With  conversions. 
Without  conversions, 
aversions. 


3- wire 

t  Multiple-wire 
[    Alternating  single  phase 

[  Alternating  multiphase 

f  Alternating  continuous. 

|    Alternating  converter;  line  converter;   alternating  con- 
•{        tinuous. 
I    Continuous-continuous. 
{  Partial  reconversion  of  any  system. 

The  relative  advantages  of  these  systems  vary  with  each  particular  trans- 
mission prob.lem,  but  in  a  general  way  may  be  tabulated  as  bejow, 


1048 


ELECTRICAL  ENGINEERING. 


System. 

Advantages. 

Disadvantages. 

(  Low  voltage. 
2-wireK  

Safety,  simplicity. 

Expense  for  copper. 

(  High  voltage. 

Economy,  simplicity. 

Danger,  difficulty  of 
building  machines. 

3-wire. 

Low  voltage  on  machines 
and  saving  in  copper. 

Not  saving  enough  in 
copper  for  long  dis- 
tances. Necessity  for 
"  balanced  "  system. 

Multiple-wire. 

Low  voltage  at  machines 
and  saving  in  copper. 

Single  phase. 

Economy  of  copper. 

Cannot  start  under  load. 
Low  efficiency. 

Multiphase. 

Economy  of  copper,  syn- 
chronous speed  unnec- 
essary; applicable  to 
very  long  distances. 

Complexity.  Lower  ef- 
ficiency of  terminal 
apparatus.  Not  as  yet 
"standard.'1 

Motor-dynamo. 

High-voltage  transmis- 
sion. Low-voltage  de- 
livery. 

Expensive. 
Low  efficiency. 

There  are  many  factors  which  govern  the  selection  of  a  system.  For  each 
problem  considered  there  will  be  found  certain  fixed  and  certain  unfixed 
conditions.  In  general  the  fixed  factors  are:  (1)  capacity  of  source  of 
power;  (2)  cost  of  power  at  source:  (3)  cost  of  power  by  other  means  at  point 
of  delivery;  (4)  danger  considerations  at  motors;  (5)  operation  conditions; 
(6)  construction  conditions  (length  of  line,  character  of  country,  etc.).  The 
partly  fixed  conditions  are:  (7)  power  which  must  be  delivered,  i.e.,  the  effi- 
ciency of  the  system;  (8)  size  and  number  of  delivery  units.  The  variable 
conditions  are:  (9)  initial  voltage;  (10)  pounds  of  copper  on  line;  (11)  origi- 
nal cost  of  all  apparatus  and  construction:  (12)  expenses,  operating  (fixed 
charges,  interest,  depreciation,  taxes,  insurance,  etc.);  (13)  liability  of  trouble 
and  stoppages;  (14)  danger  at  station  and  on  line;  (15)  convenience  in  oper- 
ating, making  changes,  extensions,  etc.  Assuming  that  the  cost  of  dyna- 
mos, motors,  etc.,  will  be  approximately  the  same  whatever  the  initial 
pressure,  the  great  variation  in  the  cost  of  wire  at  different  pressures  is 
shown  by  Mr.  Hart  in  the  following  figures,  giving  the  weights  of  copper 
required  for  transmitting  100  horse-power  5  miles  : 

Voltage.  Drop  10  per  cent.  Drop  20  per  cent. 

2,000  16,800  Ibs.  8,400  Ibs. 

3,000  7,400    "  3,700    " 

10,000  6-20    "  310    " 


p 
d 


Efficiency  of  a  Combined  Engine  and  Dynamo.  —  A  com- 
ound double  -crank  Willans  engine  mounted    on   a   single  base  with    a 
ynamo  of  the  Edison-Hopkinson  type  was  tested  in  1890,  with  results  as 
follows:    The  low-pressure  cylinder  is  14  in.  diarn.,  16  in.  stroke;  steam- 
pressure  120  Ibs.    It  is  coupled  to  a  dynamo  constructed  for  an  output  of  475 
amperes  at  110  volts  when  driven  at  430  revolutions  per  minute.    The  arma- 
ture is  of  the  bar  construction,  is  plain  shunt-wound,  and  is  fitted  with  a 
commutator  of  hard-drawn  copper  with  mica  insulation.     Four  brushes  are 
carried  on  each  rocker-arm. 

Resistance  of  magnets  .....................  ...........  16.         ohms 

Resistance  of  armature  ...................  .............    0.0055 

I.H.P  .................................................  83.3 

E.H.P  .......  .  ..........................................  72.2 

Total  efficiency  ..................................  .  .....  86.7  per  cent 

Consumption  of  water  per  I.H.P.  hour  ...............  .21.6  pounds 

Consumption  of  water  per  E.H.P.  hour  ................  25 

The  engine  and  dynamo  were  worked  above  their  full  normal  output, 
.which  fact  would  tend  to  slightly  increase  the  efficiency. 

The  electrical  losses  were  :  Loss  in  magnet  coils,  756  watts,  equal  to  1.4$; 
loss  in  armature  coil,  1386  watts,  equal  to  2.  6#;  so  that  the  electrical  efficiency 


ELECTRIC   TRANSMISSION. 


1049 


of  the  machine  due  to  ohmic  resistance  alone  was  96$.  The  remainder  of 
the  losses,  a  little  over  8  horse-power,  is  due  to  friction  of  engine  and 
dynamo,  hysteresis,  and  the  like. 

Electrical  Efficiency  of  a  Generator  and  Motor.— A  twelve- 
mile  transmission  of  power  at  Bodie,  Cal.,  is  described  by  T.  H.  Leggett 
(Trans.  A.  I.  M  E.  1894).  A  single-phase  alternating  current  is  used  The 
generator  is  a  Westinghouse  120  K.  W.  constant-potential  12-pole  machine 
speed  860  to  870  revs,  per  min.  The  motor  is  a  synchronous  constant-po- 
tential machine  of  120  horse-power.  It  is  brought  up  to  speed  by  a  10-H.P 
Tesla  starting  motor.  Tests  of  the  electrical  efficiency  of  the  generator  and 
motor  gave  the  following  results  : 

TEST  ON  GENERATOR. 


Amperes 

Volts. 

Watts. 

Self-excited  field  

15  8 

60 

948 

Separately-excited  field        

18  2 

78 

1419  6 

Resistance  of  armature,  1.6618  ohms. 
(72J?,  loss  in  armature  

664  72 

Total  loss  in  machine  

3032  32 

Load  

20 

3414 

68280 

Apparent  electrical  efficiency  of  generator,  95.559$. 
TEST  ON  MOTOR. 


Amperes 

Volts. 

Watts. 

Self-excited  field                      .                    .... 

52 

62  4 

3244  8 

Resistance  of  armature,  1.4  ohms. 
C'^R)  loss  in  armature 

560  0 

Total  loss  in  machine  

3804  08 

Load  

20 

3110 

62200 

Apparent  electrical  efficiency  of  motor,  93.883$. 

Efficiency  of  an  Electrical  Pumping-plant.  (Eng.  &  M. 
Jour.,  Feb.  7,  1891.)— A  pumping-piant  at  a  mine  at  Normanton,  England, 
was  tested,  with  results  given  below: 

Above  ground  there  is  a  pair  of  20^  x  48-in.  engines  running  at  20  revs,  per 
min.,  driving  two  series  dynamos  giving  690  volts  and  59  amperes.  The  cur- 
rent from  each  dynamo  is  carried  into  the  mine  by  an  insulated  cable  about 
3000  feet  long.  There  they  are  connected  to  two  50-h.p.  motors  which  oper- 
ate a  pair  of  differential  ram-pumps,  with  rams  6  in.  and  4}/£  in.  diarn.  and 
24  in.  stroke.  The  total  head  against  which  the  pumps  operate  is  890  feet. 
Connected  to  the  same  dynamos  there  is  also  a  set  of  gearing  for  driving  a 
hauling  plant  on  a  continuous-rope  system,  and  a  set  of  three-throw  ram- 
pumps  with  6-inch  rams  and  12-inch  stroke  can  also  be  thrown  into  gear. 
The  connections  are  so  made  that  either  motor  can  operate  any  or  all  three 
of  the  sets  of  machinery  just  described.  Indicator-diagrams  gave  the  fol- 
lowing results: 

Friction  of  engine 6.9H.P.       9.4$ 

Belt  and  dynamo  friction 4.8  6.5$ 

Leads  and  motor  6.7  9.4$ 

Motor  belt,  gearing  and  pumps  empty 10.2  14.0$ 

Load  of  117  gallons  through  890  feet 31.5  43.1$ 

Water  friction  in  pumps  and  rising  main 12.9  17.6$ 

TEolTp.   100.0$ 

At  the  time  when  these  data  were  obtained  the  total  efficiency  of  the  plant 
was  43.1$,  but  in  a  later  test  it  rose  to  47$. 

References  on  Power  Distribution.— Kapp,  Electric  Transmis- 
sion of  Energy;  Badt,  Electric  Transmission  Handbook;  Martin  and  Wetzler, 
The  Electric  Motor  and  its  Applications;  Hospitalier,  Poly  phased  Electric 
Currents. 


1050  ELECTRICAL 

EL.ECTRIC   RAILWAYS. 

Space  will  not  admit  of  a  proper  treatment  of  this  subject  in  this  work. 
Consult  Crosby  and  Bell,  The  Electric  Railway  in  Theory  and  Practice, 
price  $2.50;  Fairchild,  Street  Railways,  price  $4.00;  Merrill,  Reference 
Book  of  Tables  and  Formulae  for  Street  Railway  Engineers,  price  $1.00. 

Test  of  a  Street  Railway  Plant.— A  test  of  a  small  electric-rail- 
way plant  is  reported  by  Jesse  M.  Smith  in  Trans.  A.  S.  M.  E.,  vol.  xv.  The 
following  are  some  of  the  results  obtained: 

Friction  of  engine,  air-pump,  and  boiler  feed-pump ;  main  belt  off    9.22  I.H.P. 
Friction  of  engine,  air  and  feed  pumps,  and  dynamo,  brushes  off.  11.34  I.H.P. 

Friction  of  dynamo  and  belt 2.12  I.H.P. 

Power  consumed  by  engine,  air  and  feed  pumps  and  dynamo, 

with  brushes  on  and  main  circuit  open 14.34  I.H.P. 

Power  required  to  charge  fields  of  dynamo 3.00  I.H.P. 

Rated  capacity  of  engine  and  dynamo  each      150  I.H.P. 

Power  developed  by  engine min.  21.27;  max.  141.4;  mean,  70.1  I.H.P. 

Volts  developed  by  dynamo range,  480  to  520;  average,  501  volts 

Amperes  developed  by  dynamo max.  200;  min.  4.7;  average.  67  amperes 

Average  watts  delivered  by  dynamo 33,567  Watts 

Average  electrical  horse-power  delivered  by  dynamo 45  E.H.P. 

Average  I.H.P.  del'd  to  pulley  of  dynamo,  estimating  friction  of 

armature  shaft  to  be  the  same  as  friction  of  belt 59.8  I.H.P. 

Average  commercial  efficiency  of  dynamo 45  -f-  59.8  =  75.25# 

Average  number  of  cars  in  use  during  test 2.89  cars. 

Number  of  single  trips  of  cars 64 

Average  number  of  passengers  on  cars  per  single  trip. .   15.2 

Weight  of  cars  14,500  Ibs. 

Est.  total  weight  of  cars  and  persons 15,900  Ibs. 

Average  weight  in  motion 45,950  Ibs. 

Average  electrical  horse -power  per  1000  Ibs.  of  weight  moved. .  0.98  E.H.P. 
Average  horse-power  developed  by  engine  per  1000  Ibs.  of  weight 

moved 1 .52  I.H.P. 

Average  watts  required  per  car. 11,615  watts 

Average  electrical  horse-power  per  car 15.54  E.H.P. 

Average  horse-power  developed  in  engine  per  car  24.25  I.H.P. 

Length  of  road  10. 5  miles. 

Average  speed,  including  all  stops,  21  miles  in  1 .5  hours  =  14  miles  per  hour. 
Average  speed  between  stops,  21  m.  in  1.366  hours  =  15.38  miles  per  hour. 

Proportioning:  Boiler,  Kii«:iiie,  and  Generator  for  Power- 
stations.  —  Wm.  Lee  Church  (Street  Railway  Journal,  1892)  gives  a 
diagram  showing  the  abrupt  variations  in  the  current  required  for  an 
electric  railway  with  variable  grades.  For  this  case,  in  which  the  maximum 
current  for  a  minute  or  two  at  a  time  is  175  amperes,  ranging  from  that  to 
zero,  and  averaging  about  50  amperes,  he  advises  that  the  nominal  capacity 
of  the  generator  be  100  amperes.  The  reason  of  this  is  found  in  the  fact 
that  an  electric  generator  can  stand  an  overload,  or  even  an  excessive  over- 
load, provided  it  does  not  have  to  stand  it  long.  The  question  is  simply  one 
of  heat.  The  overload  here  was  seen  to  continue  for  only  about  one  minute, 
during  which  time  the  generator  could  carry  it  with  ease  with  no  perceptible 
rise  of  temperature  to  injure  the  insulation.  Had  this  load  been  continuous 
for  an  hour  or  so,  as  would  occur  in  an  electric-lighting  station,  a  much 
higher  relative  generating  capacity  would  be  required,  approximating  the 
maximum  load. 

An  engine  has  no  such  capacity  for  excessive  overload  as  a  generator.  In 
other  words,  the  element  of  time  does  not  enter  into  the  engine  problem, 
but  it  becomes  a  question  of  how  much  the  engine  can  actually  lift  by  main 
strength  without  taking  the  governor  to  an  extreme  which  shall  slow  down 
the  speed.  In  general  terms,  the  engine  should  not  be  called  to  perform, 
even  for  a  short  time,  more  than  20$,  or  possibly  25$,  above  its  rating. 

The  engine  capacity,  therefore,  would  have  a  nominal  rating  greater 
than  that  of  the  generator,  say  about  25#  greater. 

The  capacity  of  the  engine  should  be  determined  without  reference  to 
condensation.  This  is  for  the  obvious  reason  that  a  condenser  may  become 
choked,  or  disabled,  or  leaky,  and  the  vacuum  may  be  poor,  or  lost  entirely 
under  sudden  fluctuations. 

The  boiler  has  to  deal  only  with  the  average  of  the  total  load.  In  this 
particular  electric  railways  exactly  resemble  rolling  -  mills,  saw  -  mills, 


ELECTRIC  LIGHTING.  1051 

and  kindred  industries,  where  the  load  is  spasmodic,  with  variations 
lasting  but  a  few  seconds,  or  at  most  but  a  few  minutes.  The  stored  heat 
in  the  water  of  a  boiler  is  enormous  in  quantity,  and  responds  instantly  to  a 
release  of  pressure.  That  is  to  say,  the  boiler  is  an  immense  reservoir  of 
power,  and  provided  the  drain  upon  it  is  not  continued  too  long,  it  will 
stand  exactions  far  beyond  its  nominal  capacity,  and  without  any  effect 
whatever  upon  the  firing. 

The  actual  size  of  the  boiler  will  depend  upon  the  type  of  engine.  With 
the  compound  engine  described  by  Mr.  Church,  running  non-condensing,  an 
allowance  of  30  pounds  of  water  actually  evaporated  per  I.H.P.per  hour  will 
give  a  margin  for  all  contingencies.  The  engine  duty  under  an  average  uni- 
form load  is  a  very  different  thing  from  the  duty  under  a  variable  load  rep- 
resented by  the  average.  Under  the  uniform  load,  23  pounds  of  water 
would  be  the  actual  engine  performance,  arid  the  boiler  could  be  propor- 
tioned with  reference  to  this  figure.  Under  the  violent  fluctuations  of  rail- 
way service,  the  average  duty  of  the  engine  will  rise  to  about  28  pounds, 
and  if  the  maximum  average  load  is  taken,  and  the  boiler  proportioned  for 
30  pounds,  there  will  be  a  sufficient  margin.  Other  compound  engines  not 
possessing  the  feature  which  secures  uniformity  of  duty  will  range  up  to  at 
least  45  pounds  under  light  loads,  and  often  to  60  pounds,  and  represent  an 
average  duty  not  better  than  35  to  40  pounds.  The  same  is  true  of  every 
form  of  non-compounded  engine,  whether  high  speed  or  low  speed,  both  of 
which  show  a  tremendous  falling  back  of  fuel  duty  under  variable  load. 


LIGHTING. 

Quantity  of  Energy  required  to  produce  Light.—  Accord- 
ing to  Mr.  Preece,  the  quantity  of  energy,  measured  in  watts,  required  to  pro- 
duce light  equivalent  to  one  candle-power,  measured  by  the  light  given  out 
by  the  standard  candle,  is  as  follows  for  different  light-giving  substances: 

Tallow  ..............  124  watts  Coal  gas  .............  68  watts. 

Wax  ................     94       "  Cannel  gas  ..........  48      ** 

Spermaceti  ........    86      "  Incandescent  lamp  ..  15      '* 

Mineral  oils  .........     80       "  Arc  lamp  ............    3      " 

Vegetable  oils  ......    57      " 

And  the  relative  costs  of  production  are  about  1  for  the  arc  lamp  ;  6  for  the 
incandescent  lamp;  5  for  the  mineral-oil  lamp;  10  for  the  gas-light;  67  for  the 
spermaceti  candle. 

Life  of  Incandescent  Lamps.  (Enq^q,  Sept.  1,  1893,  p.  282.)—  From 
experiments  made  by  Messrs.  Siemens  and  Halske,  Berlin,  it  appears  that 
the  average  life  of  incandescent  lamps  at  different  expenditure  of  watts  per 
candle-power  is  as  follows: 

Watts  per  candle-power  .......     1.5         2         2.5          3  3.5 

Life  of  lamp,  hours  ............     45        200       450       1000       1000 

Life  and  Efficiency  Tests  of  Lamps.  (P.  G.  Gossler,  Elec. 
World,  Sept.  17,  1892.)—  Lamps  burning  at  a  voltage  above  that  for  which 
they  are  rated  give  a  much  greater  illuminating  power  than  16  candles,  but 
at  the  same  time  their  life  is  very  considerably  shortened.  It  has  been  ob- 
served that  lamps  received  from  the  factory  do  not  average  the  same  candle- 
power  and  efficiency  for  different  invoices;  that  is,  lamps  which  are  received 
in  one  invoice  are  usually  quite  uniform  throughout  that  lot,  but  they  vary 
considerably  from  lamps  made  at  other  times. 

The  following  figures  show  the  different  illuminating-powers  of  a  16.c.p., 
50-volt,  52-watt  lamp,  for  various  voltages  from  25  to  80  volts: 


v  uits; 
25        34.8 

40 

48 

50 

52.5 

55.6 

59.5 

62 

68.2 

72.5 

80 

Amperes 
.561       .774 

'.898 

.968 

1.055 

1.097 

1.161 

1.226 

1.29 

1.419 

1.484 

1.58 

Candles: 

.4       2.47 

5.1 

12.6 

15.8 

20.5 

[28.4 

39.3 

50.7 

74.5 

103.2 

141 

Watts: 

14.03    26.94 

35.92 

46.34 

52.75 

57.57 

64.55 

72.92 

79.98 

96.78 

107.5 

126.4 

Watts  per  c.p.: 
35.1     10.81     7.04 

3.68 

3.34 

2.81 

2.30 

1.96 

1.58 

1.30 

1.04 

.90 

Street-lighting.    (H.  Robinson,  M.I.C.E.,  Eng'g  News,  Sept.  13,  1891.) 
—For  street-lighting  the  arc-lamp  is  the  most  economical.    The  smallest 


1052 


ELECTRICAL   ENGINEERING. 


size  of  arc-lamp  at  present  manufactured  requires  a  current  of  about  5 
amperes;  but  for  steadiness  and  efficiency  it  is  desirable  to  use  not  less  than 
G  amperes.  The  candle-power  of  arc-lamps  varies  considerably,  according 
to  the  angle  at  which  it  is  measured.  The  greatest  intensity  with  continuous- 
current  lamps  is  found  at  an  angle  of  about  40°  below  the  horizontal  line. 
The  following  table  gives  the  approximate  candle-power  at  various  angles. 
The  height  of  the  lamps  should  be  arranged  so  as  to  give  an  angle  of  not 
less  than  7°  to  the  most  distant  point  it  is  intended  to  serve. 


Lighting-power  of  Arc-lamps. 


Current 
in  Amperes. 

6 
8 
10 


Candle-power. 


Horizontal 


At  Angle    Maximum  at 


of  20°.       Angle  of  40° 

92  175  207  322  4GO 

156  300  350  546  780 

220  420  495  770  1100 

The  following  data  enable  the  coefficient  of  minimum  lighting-power  in 
streets  to  be  determined: 
Let  P  —  candle-power  of  lamps; 

L  —  maximum  distance  from  lamp  in  feet; 
H  —  height  of  lamp  in  feet; 
X  —  a  coefficient. 

The  light  falling  on  the  unit  area  of  pavement  varies  inversely  as  the  square 
of  the  distance  from  the  lamp,  and  is  directly  proportional  to  the  angle  at 
which  it  falls.  This  angle  is  nearly  proportional  to  the  height  of  the  lamp 
divided  by  the  distance.  Therefore 

Pff  T>TT 

.rz  _.         JrJrJ. 

JL  —  ™  X  -f    or    X  =  -=-% . 

Li*          Li  Lia 

The  usual  standard  of  gas-lighting  is  represented  by  the  amount  of  light 
falling  on  the  unit  area  of  pavement  50  feet  away  from  a  12-c.p.  gas-lamp  9 
feet  high,  which  gives  a  coefficient  as  follows: 

-2T=^y^  =  0.000864. 


The  minimum  standard  represents  the  amount  of  light,  on  a  unit  area  50 
feet  away  from  a  24-c.p.  lamp,  9  ft.  high,  and  gives  the  coefficient  .001728. 

Adopting  the  first  of  the  above  coefficients.  Mr.  Robinson  calculates  that 
the  before-mentioned  sizes  of  arc-lights  will  give  the  same  standard  of 
light  at  the  heights  and  distances  stated  in  Table  A.  Table  B  gives  the 
corresponding  distances,  assuming  the  minimum  standard  to  be  adopted. 


TABLE  A. 


Hgt.  of  Lamps. 

20  ft. 

25ft. 

30ft. 

35ft. 

Height  

20  ft. 

25ft. 

30ft. 

35ft. 

Current  in 
Amperes. 

Max.  distances  served 
from  lamp,  in  ft. 

Amperes. 

Max.  distances  served 
from  Lamp. 

6 

8 
10 

160 
186 

205 

175 
202 
225 

190 
220 
243 

202 
235 
260 

6 
8 
10 

130 
150 
170 

144 

165 
190 

155 
180 
205 

166 
193 
220 

The  distances  the  lamps  are  apart  would,  of  course,  be  double  the  dis- 
tances mentioned  in  Tables  A  and  B.    One  arc-lamp  will  take  the  place  of 

TABLE  B. 


from  3  to  6  gas-lamps,  according  to  the  locality,  arrangement,  and  standard 
of  light  adopted.  A  scheme  of  arc-lighting,  based  on  the  substitution  of  one 
arc-light  on  the  average  for  3^  to  4  gas -lamps,  would  double  the  minimum 
standard  of  light,  while  the  average  standard  would  be  increased  10  or  12 
times. 

Candle-power  of  the  Arc-liglit.  (Elibu  Thomson,  EL  World, 
Feb.  28,  1891.) — With  the  lon^  an- 1  he  maximum  intensity  of  the  light  is  from 
40°  to  60°  downward  from  the  horizontal.  The  spherical  candle-power  is 
Only  a  fraction  of  the  rated  c.p.,  which  is  generally  taken  at  the  maximum 
obtainable  in  the  best  direction.  For  this  reason  the  term  2000  c.p.  has  little 


ELECTRIC   WELDING.  1053 

significance  as  indicating  the  illuminating-power  of  an  arc.  It  is  now  gener- 
ally taken  to  mean  an  arc  with  10  amperes  and  not  le>s  than  45  volts  between 
the  carbons,  or  a  450-watt  arc.  The  quality  of  the  carbons  will  determine 
whether  the  450  watts  are  expended  in  obtaining  the  most  light  or  not  or 
whether  that  light  will  have  a  maximum  iu  tensity  at  one  angle  or  another 
within  certain  limits.  The  larger  the  current  passing  in  an  arc  the  less  is 
its  resistance.  Well-developed  arcs  with  4  amperes  wil  1  have  about  1  1  ohms 
with  10  amperes  4.5  ohms,  and  with  100  amperes  .45  ohm. 

It  is  not  unusual  to  run  from  50  to  60  lights  in  a  series,  each  demanding 
from  45  to  50  volts,  or  a  total  of,  say,  3000  volts.  In  going  beyond  this  the 
difficulties  of  insulation  are  greatly  increased 

Reference  Books  on  Electric  Lighting.—  Noll,  How  to  Wire 
Buildings,  $1.00;  Hedges,  Continental  Electi  u.--light  Central  Stations,  $6.00; 
Fleming,  Alternating  Current  Transformers  in  Theory  and  Practice,  2  vols 
$8.00;  Atkinson,  Elements  of  Electric  Lighting,  $1.50;  Algave  and  Boulard' 
Electric  Light:  its  History,  Production,  and  Application,  $5.00. 


ELECTRIC    WELDING. 


a  limited 
extent. 

The  conductivity  for  heat  of  the  metal  to  be  welded  has  a  decided  influ- 
ence on  the  heating,  and  in  welding  iron  its  comparatively  low  heat  conduc- 
tion assists  the  work  materially.  (See  papers  by  Sir  F.  Bramwell,  Proc. 
Inst.  C.  E.,  part  iv.,  vol.  cii.  p.  1;  and  Elihu  Thomson,  Trans.  A.  I.  M.E.,  xix. 
877.) 

Fred.  P.  Royce,  Iron  Age,  Nov.  28,  1892,  gives  the  following  figures  show- 
ing the  amount  of  power  required  to  weld  axles  and  tires: 

AXLE-WELDING. 

Seconds. 
1-inch  round  axle  requires  25  H.P.  for  ............................     45 

1-inch  square  axle  requires  30  H.P.  for  ............................    48 

1^4-inch  round  axle  requires  35  H.P.  for  ..........................     60 

1^4-inch  square  axle  requires  40  H.P.  for  ..........................    70 

2-inch  round  axle  requires  75  H.P.  for  ............................     95 

2-inch  square  axle  requires  90  H.P.  for  ............................  100 

The  slightly  increased  time  and  power  required  for  welding  the  square 
axle  is  not  only  due  to  the  extra  metal  in  it,  but  in  part  to  the  care  which  it 
is  best  to  use  to  secure  a  perfect  alignment. 

TIRE  -WELDING. 

Seconds. 
1  X  3/16-inch  tire  requires  11  H.P.  for  ............................     15 

1*4  X  %-inch  tire  requires  23  H.P.  for  .............................    25 

\y%  x  %-inch  tire  requires  20  H.P.  for  ...........................    30 

1  J4  X  i^-inch  tire  requires  23  H.P,  for  .............................    40 

2  X  ^-inch  tire  requires  29  H.P.  for  ..............................    55 

2  X  %-inch  tire  requires  42  H.P.  for  ...............................    62 

The  time  above  given  for  welding  is  of  course  that  required  for  the  actual 
application  of  the  current  only,  and  does  not  include  that  consumed  by 
placing  the  axles  or  tires  in  the  machine,  the  removal  of  the  upset  and 
other  finishing  processes.  From  the  data  thus  submitted,  the  cost  of  welding 
can  be  readily  figured  for  any  locality  where  the  price  of  fuel  and  cost  of 
labor  are  known. 

In  almost  all  cases  the  cost  of  the  fuel  used  under  the  boilers  for  produc- 
ing power  for  electric  welding  is  practically  the  same  as  the  cost  of  fuel 
vised  in  forges  for  the  same  amount  of  work,  taking  into  consideration  the 
difference  in  price  of  fuel  used  in  either  case. 

Prof.  A.  B.  W.  Kennedy  found  that  2^-inch  iron  tubes  *4  inch  thick  were 
welded  in  61  seconds,  the  net  horse-power  required  at  this  speed  being  23.4 
(say  33  indicated  horse-power)  per  square  inch  of  section.  Brass  tubing  re- 


1054  ELECTRICAL  ENGINEERING. 

quired  21 .2  net  horse-power.  About  60  total  indicated  horse-power  would  be 
required  for  the  welding  of  angle  irons  3  X  3  X  Yz  inch  in  from  two  to  three 
minutes.  Copper  requires  about  80  horse-power  per  square  inch  of  section, 
and  an  inch  bar  can  be  welded  in  25  seconds.  It  takes  about  90  seconds  to 
weld  a  steel  bar  2  inches  in  diameter. 

ELECTRIC    HEATERS. 

Wherever  a  comparatively  small  amount  of  heat  is  desired  to  be  auto- 
matically and  uniformly  maintained,  and  started  or  stopped  on  the  instant 
without  waste,  there  is  the  province  of  the  electric  heater. 

The  elementary  form  of  heater  is  some  form  of  resistance,  such  as  coils 
of  thin  wire  introduced  into  an  electric  circuit  and  surrounded  with  a  sub- 
stance, which  will  permit  the  conduction  and  radiation  of  heat,  and  at  the 
same  time  serve  to  electrically  insulate  the  resistance. 

This  resistance  should  be  proportional  to  the  electro-motive  force  of  the 
current  used  and  to  the  equation  of  Joule's  law  : 

H  -  C*Rt  X  0.24, 

where  Ois  the  current  in  amperes;  #,  the  resistance  in  ohms;  t,  the  time  in 
seconds;  and  /i,  the  heat  in  gram -centigrade  units. 

Since  the  resistance  of  metals  increases  as  their  temperature  increases,  a 
thin  wire  heated  by  current  passing  through  it  will  resist  more,  and  grou 
hotter  and  hotter  until  its  rate  of  loss  of  heat  by  conduction  and  radiatior 
equals  the  rate  at  which  heat  is  supplied  by  the  current.  In  a  short  wire 
before  heat  enough  can  be  dispelled  for  commercial  purposes,  fusion  wil 
begin;  and  in  electric  heaters  it  is  necessary  to  use  either  long  lengths  oi 
thin  wire,  or  carbon,  which  alone  of  all  conductors  resists  fusion.  In  tht 
majority  of  heaters,  coils  of  thin  wire  are  used,  separately  embedded  n 
some  substance  of  poor  electrical  but  good  thermal  conductivity. 

The  Consolidated  Car-heating  Co.'s  electric  heater  consists  of  a  galvamzec 
iron  wire  wound  in  a  spiral  groove  upon  a  porcelain  insulator.  Each  heatei 
is  30%  in.  long,  8%  in.  high,  and  6&6  in.  wide.  Upon  it  is  wound  625  ft.  o 
wire.  The  weight  of  the  whole  is  23^  Ibs. 

Each  heater  is  designed  to  absorb  two  amperes  of  a  500-volt  current  fen 
heaters  are  the  complement  for  an  ordinary  electric  car.  For  ordinary 
weather  the  heaters  may  be  combined  by  the  switch  in  different  ways  s< 
that  five  different  intensities  of  heating- surf  ace  are  possible,  besides  th< 
position  in  which  no  heat  is  generated,  the  current  being  turned  entirely  off 

For  heating  an  ordinary  electric  car  the  Consolidated  Co.  states  tha 
from  2  to  12  amperes  on  a  500-volt  circuit  is  sufficient.  With  the  outsid 


cars,  as  follows : 

1  B  T.U.  =  0.29084  watt-hours. 

6  amperes  on  a  500-volt  circuit  =  3000  watts. 

A  current  consumption  of  6  amperes  will  generate  3000  H-  0.290*         10,dl 

In  steam- car  heating,  a  passenger  coach  usually  requires  from  60  Ibs.  c 


the  s 

eq ufvalen?o^he"thermaT  units  delivered" by  the  electrical-heating  system  i 
pounds  of  steam,  is  10,315  -*-  983  =  10^,  nearly. 

Thus  the  Consolidated  Co.'s  estimates  for  electric-heating  provide  th 
equivalent  of  10J4  Ibs.  of  steam  per  car  per  hour  in  freezing  weather  and  4 

Suppose  that  by  the  use  of  good  coal,  careful  firing,  well  designed  boiler 
and  triple-expansion  engines  we  are  able  in  daily  practice  to  general 
1  H.P.  delivered  at  the  fly-wheel  with  an  expenditure  of  2j^  Ibs.  of  coal  p( 

We*  have  then  to  convert  this  energy  into  electricity,  transmit  it  by  wii 
to  the  heater,  and  convert  it  into  heat  by  passing  it  through  a  resistance-coi 
We  may  set  the  combined  efficiency  of  the  dynamo  and  line  circuit  at  85. 
and  will  suppose  that  ail  the  electricity  is  converted  into  heat  in  the  resis 
ance-coils  of  the  radiator.  Then  1  brake  H.P.  at  the  engine  =  0.85  electric 
H.P.  at  the  resistance-coil  =  1,683,000  ft.-lbs.  energy  per  hour  =  2180  hea 
units.  But  since  it  required  2^  Ibs.  of  coal  to  develop  1  brake  H.P.,  it  fo 


ELECTRICAL  ACCUMULATOR  OK  STORAGE-BATTERIES.  1055 

lows  that  the  heat  given  out  at  the  radiator  per  pound  of  coal  burned  in  the 
boiler  furnace  will  be  2180  -t-  2*6  =  872  H.U.  An  ordinary  steam-heating 
system  utilizes  9652  H.U.  per  Ib.  of  coal  for  heating;  hence  the  efficiency 
of  the  electric  system  is  to  the  efficiency  of  the  steam-heating  system  as  872 
to  9652,  or  about  1  to  11.  (Eng'g  News,  Aug.  9,  '90;  Mar.  30,  '92;  May  15,  '93.) 

ELECTRICAL   ACCUMULATORS  OR  STORAGE- 
BATTERIES. 

Storage-batteries  may  be  divided  into  two  classes:  viz.,  those  in  which  the 
active  material  is  formed  from  the  substance  of  the  element  itself,  either 
by  direct  chemical  or  electro -chemical  action,  and  those  in  which  the 
chemical  formation  is  accelerated  by  the  application  of  some  easily  reduci- 
ble salt  of  lead.  Elements  of  the  former  type  are  usually  called  Plant6,  and 
those  of  the  latter  "  Faure,"  or  *'  pasted." 

Faraday  when  electrolyzing  a  solution  of  acetate  of  lead  found  that  per- 
oxide of  lead  was  produced  at  the  positive  and  metallic  lead  at  the  negative 
pole.  The  surfaces  of  the  elements  in  a  newly  and  fully  charged  Plants  cell 
consists  of  nearly  pure  peroxide  of  lead,  PbO2,  and  spongy  metallic  lead, 
Pb,  respectively  on  the  positive  and  negative  plates. 

During  the  discharge,  or  if  the  cell  be  allowed  to  remain  at  rest,  the  sul- 
phuric acid  (H2SO4)  in  the  solution  enters  into  combination  with  the  per- 
oxide and  spongy  lead,  and  partially  converts  it  into  sulphate.  The  acid 
being  continually  abstracted  from  the  electrolyte  as  the  discharge  proceeds, 
the  density  of  the  solution  becomes  less.  In  the  charging  operation  this 
action  is  reversed,  as  the  reducible  sulphates  of  lead  which  have  been 
formed  are  apparently  decomposed,  the  acid  being  reinstated  in  the  liquid 
and  therefore  causing  an  increase  in  its  density. 

The  difference  of  potential  developed  by  lead  and  lead  peroxide  immersed 
in  dilute  H2SO4  is,  as  nearly  as  may  be,  two  volts. 

A  lead-peroxide  plate  gradually  loses  its  electrical  energy  by  local  action, 
the  rate  of  such  loss  varying  according  to  the  circumstances  of  its  prepara- 
tion and  the  condition  of  the  cell.  Various  forms  of  both  Plants  and  Faure 
batteries  are  illustrated  in  "  Practical  Electrical  Engineering." 

In  the  Faure  or  pasted  cells  lead  plates  are  coated  with  minium  or 
litharge  made  into  a  paste  with  acidulated  water.  When  dry  these  plates 
are  placed  in  a  bath  of  dilute  H2SO4  and  subjected  to  the  action  of  the 
current,  by  which  the  oxide  on  the  positive  plate  is  converted  into  peroxide 
of  lead  and  that  on  the  negative  plate  reduced  to  finely  divided  or  porous 
lead. 

Gladstone  and  Tribe  found  that  the  initial  electro-motive  force  of  the 
Faure  cell  averaged  2.25  volts,  but  after  being  allowed  to  rest  some  little 
time  it  was  reduced  to  about  2.0  volts.  The  following  tables  show  the  size 
and  capacity  of  two  types  of  Faure  cells,  known  as  the  E.  P.  S.  cells.  (Eng- 
lish.) 

«*  E.  P.  S.»  Storage-cells,  L  Type. 


Description  of 
Cell. 


No.  of 
Plates. 


Material  of 
Box. 


H 

::i 

*j 
H 


Wood.... 
Glass 
Wood.... 
{Glass..   . 
'Wood.... 
Glass.... 
Wood. . . . 
Glass..  . 
Wood. . . 
Glass 


1 


Ibs. 
18 
25 
25 
35 
86 
47 
53 
67 
70 
88 


Working  Rate. 


Charge 


Amper. 
10  to  13 


Dis- 
charge. 


Amper. 
1  to  13 
"  13 
"  22 
"  22 
"  30 
"  30 
"  46 
"  46 
1  "  60 
1  "  60f 


130 
130 
220 
220 
330 
330 
500 
500 
660 
660 


Approximate  Exter- 
nal Dimensions. 


«M  oca 
°tg'S 


Ibs. 
74 
68 
107 
101 
143 
128 
228 
211 
286 
265 


1056 


ELECTRICAL   ENGINEERING, 


"  E.  P.  S."  Cells,  T  Type. 


Description  of  Cell. 

a- 

Working  Rate 

.•i 

Approx.    External 
Dimensions. 

?£ 

a'o 

5-a 

2^3 

No.  of 
Plates. 

Material  of 
Box. 

&c£ 

|l 
!>H 

Charge 

Dis- 
charge. 

Cap£ 
Ampere 

to 
n 

3 

"3 

| 

W 

•7  > 
o 

V  O 

J 

Wood  (no  lid)  
"     (with  lid).. 

Ibs. 

10 
10 

Amper. 
16  to  20 
16  "   20 

Amper. 
1  to  20 

1  "  20 

66 
66 

in. 

6% 
6% 

in. 

8% 

in. 

11% 
11% 

!    in 

Ibs. 
37 

38 

| 

Ebonite  (no  lid).. 

10 

16  "  20 

1  "  20 

66 

6 

7% 

11 

12^4 

30 

15-S 

Wood  (no  lid).... 
'•     (with  lid).. 

14 
14 

24  "  28 
24    *  28 

1  "  30 
1  "  30 

95 

8% 

tify 

11% 

13% 

52 
53 

„! 

Ebonite  (no  lid.).. 
Wood  (no  lid)  ... 
"     (with  lid)  .  . 
Ebonite  (no  lid).. 

14 

18 
18 
18 

24    '  28 
30    '  35 
30    '  35 
30    '  35 

1  "  30 
1  "  40 
1  "  40 
1  "  40 

95 
120 
120 

120 

8 
11 
11 
10^ 

'i% 

11 

11^ 

11* 

IS*}! 

42 
65 
66 
54 

Wood  (no  lid)  .  .  . 
"     (with  lid). 

22 
28 

38  "  42 
38  "  52 

1  "  50 

1  "  60 

145 
145 

1314 

8% 

11$ 

1  13% 

79 
80 

1 

Ebonite  

22 

38  "  42 

1  "  50 

145 

1214 

v% 

11 

I  12%        66 

For  a  very  full  description  of  various  forms  of  storage-batteries,  see 
"  Practical  Electrical  Engineering,1'  part  xii.  For  theory  of  the  battery  and 
practice  wath  the  Julien  battery,  see  paper  on  Electrical  Accumulators  by 
P.  G.  Salom,  Trans.  A.  I.  M.  E.,  xviii.  348. 

Use  of  Storage-batteries  in  Power  and  Liignt  Stations, 
(Iron  Aye,  Nov.  2,  1893.)— The  storage-batteries  in  the  Edison  station,  in 
Fifty-third  Street,  New  York,  relieve  the  other  stations  at  the  hours  of  heavy 
load,  by  delivering  into  the  mains  a  certain  amount  of  current  that  would 
otherwise  have  to  come,  and  at  greater  loss  or  "  drop,1'  from  one  or  another 
of  the  stations  connecting  with  the  network  of  mains.  Hence  the  load  may 
be  varied  more  or  less  arbitrarily  at  these  stations  according  to  the  propor- 
tion of  load  that  the  larger  stations  are  desired  or  able  to  carry. 

The  battery  consists  of  140  cells  each  of  about  1000  ampere-hour  capacity, 
weighing  some  750  Ibs.,  and  of  about  48  inches  in  length.  21  inches  in  width, 
and  15  inches  in  depth.  The  battery  has  a  normal  discharge  rate  of  about 
200  amperes,  but  can  be  discharged,  if  necessary,  at  500  amperes.  . 

A  test  made  when  the  station  was  running  only  12  hours  per  day,  from 
noon  to  midnight,  showed  that  the  battery  furnished  about  23. 2$  of  the  total 
energy  delivered  to  the  mains.  The  maximum  rate  of  discharge  attained 
bv  the  battery  was  about  2TO  amperes.  Thus,  in  this  case,  we  have  an  ex- 
ample of  a  battery  which  is  used  for  the  purpose:  1.  Of  giving  a  load  to 
station  machinery  that  would  otherwise  be  idle.  2.  Utilizing  the  stored 
energy  to  increase  the  rate  of  output  of  the  station  at  the  tune  of  heavy 
load,  which  would  otherwise  necessitate  greater  dynamo  capacity. 

The  Working  Current,  or  Energy  Efficiency,  of  a  storage- 
cell  is  the  ratio  between  the  value  of  the  current  or  energy  expended  in  the 
charging  operation,  and  that  obtained  when  the  cell  is  discharged  at  any 

SPIn  Vlead  storage  cell,  if  the  surface  and  quantity  of  active  material  be 
accurately  proportioned,  and  if  the  discharge  be  commenced  immediately 
after  the  termination  of  the  charge,  then  a  current  efficiency  of  as  much  as 
98$  may  be  obtained,  provided  the  rate  of  discharge  is  low  and  well  regu- 
lated In  practice  it  is  found  that  low-  rates  of  d  ischarge  are  not  economical, 
and  as  the  current  efficiency  always  decreases  as  The  discharge  rate  in 
creases,  it  is  found  that  the  normal  current  efficiency  seldom  exceeds  90$, 
and  averages  about  85$. 


required  to  charge  it  and  that  given  out  during  its  discharge. 

As  the  normal  discharging  potential  is  continually  being  reduced  as  the 
rate  of  discharge  increases,  it  follows  that  an  energy  efficiency  of  80$  car, 


ELECTROLYSIS. 


105? 


never  be  realized.     As  a  matter  of  fact,  a  maximum  of  75$  and  a  mean  of 
60$  is  the  usual  energy  efficiency  of  lead-sulphuric-acid  storage-cells. 

ELECTRO-CHEMICAL  EQUIVALENTS. 


Elements. 

Valency.* 

Atomic  Weight.t 

Chemical  Equiv- 
alent. 

Electro-chemical 
Equivalent  (mil- 
ligrammes per 
coulomb). 

Coulombs  per 
gramme. 

Grammes  per 
ampere  hour. 

ELECTRO-POSITIVE. 
Hydrogen  

Hi 

1.00 

1.00 

010384 

96293  00 

0  03738 

K! 

39.04 

39.04 

40539 

2467  50 

1  45950 

Sodium          

Na, 

22  99 

22.99 

23873 

4188  90 

0  85942 

\luminum  

AU 

27.3 

9.1 

.09449 

1058  30 

3  40180 

Magnesium            .... 

M^3 

23  94 

11.97 

12430 

804  03 

4  47470 

Gold     

A  113 

196  2 

65.4 

67911 

1473  50 

2  44480 

Silver 

Agj 

107  66 

107  66 

1  11800 

894  41 

4  02500 

Copper  (cupric)  
*  '       (cuprous)  

Cu2 
Cu, 

63.00 
63.00 

31.5 
63.00 

.32709 
65419 

3058.60 
1525  30 

1.17700 
2  35500 

Mercury  (mercuric)..  .  . 
"        (mercurous).. 
Tin  (stannic) 

gKi 

Hg! 

Sn4 

199.8 
199.8 
117  8 

99.9 
199.8 
29  45 

1.03740 
2.07470 
30581 

963.99 
481.99 
3270  00 

3.73450 
7.46900 
1  10090 

Sn2 

117  8 

58.9 

61162 

1635  00 

2  20180 

Iron  (ferric)  .  .  
"    (ferrous) 

£i 

55.9 
55  9 

18.64$ 
27'  95 

.19356 
29035 

5166.4 
3445  50 

0.69681 
1  04480 

Nickel  

Ni2 

58  6 

29.3 

30425 

3286  80 

1.09530 

Zinc  

Zii 

64.9 

32.45 

.33696 

2967.10 

1.21330 

PbJ 

206  4 

103.2 

1  07160 

933  26 

3  85780 

ELECTRO  -  NEGATIVE. 
Oxygen     .     

o« 

15.96 

7.98 

.08286 

Chlorine  

Gli 

35.37 

35.37 

.36728 

Tt 

126.53 

126.53 

1.31390 

Bromine  
Nitrogen  

Br, 
NS 

79.75 
14.01 

79.75 
4.67 

.82812 
.04849 

*  Valency  is  the  atom-fixing  or  atom-replacing  power  of  an  element  com- 
pared with  hydrogen,  whose  valency  is  unity. 

t  Atomic  weight  is  the  weight  of  one  atom  of  each  element  compared  with 
hydrogen,  whose  atomic  weight  is  unity. 

$  Becquerel's  extension  of  Faraday's  law  showed  that  the  electro-chemical 
equivalent  of  an  element  is  proportional  to  its  chemical  equivalent.  The 
latter  is  equal  to  its  combining  weight,  and  not  to  atomic  weight -s- valency, 
as  defined  by  Thompson,  Hospitalier,  and  others  who  have  copied  their 
t  ables.  For  example,  the  ferric  salt  is  an  exception  to  Thompson's  rule,  as 
are  sesqui-salts  in  general. 

ELECTROLYSIS. 

The  separation  of  a  chemical  compound  into  its  constituents  by  means  of 
an  electric  current.  Faraday  gave  the  nomenclature  relating  to  electroly- 
sis. He  called  the  compound  to  be  decomposed  the  Electrolyte,  and  the  pro- 
cess Electrolysis.  The  plates  or  poles  of  the  battery  he  called  Electrodes. 
The  plate  where  the  greatest  pressure  exists  he  called  the  Anode,  and  the 
other  pole  the  Cathode.  The  products  of  decomposition  he  called  Ions. 

Lord  Rayleigh  found  that  a  cm-rent  of  one  ampere  will  deposit  0.017253 
grain,  or  0". 001 118  gramme,  of  silver  per  second  on  one  of  the  plates  of  a  sil- 
ver voltameter,  the  liquid  employed  being  a  solution  of  silver  nitrate  con- 
taining from  15$  to  20$  of  the  salt. 

The  weight  of  hydrogen  similarly  set  free  by  a  current  of  one  ampere  is 
.00001038  gramme  per  second. 


1058  ELECTRICAL    ENGINEERING. 

Knowing  the  amount  of  hydrogen  thus  set  free,  and  the  chemical  equiva- 
lents of  the  constituents  of  other  substances,  we  can  calculate  what  weight 
of  their  elements  will  be  set  free  or  deposited  in  a  given  time  by  a  given 
current. 


Thus  the 
grammes 
being  f 

Ton- 


ic current  that  liberates  1  gramme  of  hydrogen  will  liberate  8 
mimes  of  oxygen,  or  107.7  grammes  of  silver,  the  numbers  8  and  107.7 

ing  the  chemical  equivalents  for  oxygen  and  silver  respectively. 

To  find  the  weight  of  metal  deposited  by  a  given  current  in  a  given  time, 
find  the  weight  of  hydrogen  liberated  by  the  given  current  in  the  given 
time,  and  multiply  by  the  chemical  equivalent  of  the  metal. 

Thus:  Weight  of  silver  deposited  in  10  seconds  by  a  current  of  10  amperes 
=:  weight  of  hydrogen  liberated  per  second  X  number  seconds  X  current 
strength  X  107.7  =  .000010:38  X  10  X  10  X  107.7  =  .11178  gramme. 

Weight  of  copper  deposited  in  1  hour  by  a  current  of  10  amperes  = 

.00001038  X  3600  X  10  X  31.5  =  11.77  grammes. 

Since  1  ampere  per  second  liberates  .00001038  gramme  of  hydrogen, 
strength  of  current  in  amperes 

_  weight  in  grammes  of  H.  liberated  per  second 

.00001038 

weight  of  element  liberated  per  second 
~~  .00001038  X  chemical  equivalent  of  element' 

The  table  on  page  1057  (from  "Practical  Electrical  Engineering")  is  cal- 
^•aiated  upon  Lord  Rayleigh's  determination  of  the  electro-chemical  equiva- 
T»nts  and  Roscoe's  atomic  weights. 

ELECTRO-M  A.GNETS. 
Units   of  Electro-magnetic   Measurements. 

C.G.S.  unit  of  force  =  1  dyne  =  1.01936  milligrammes  in  localities  in  which 
the  acceleration  due  to  gravity  is  981  centimetres,  or  32.185  feet,  per  second. 

C.C.S.  unit  of  energy  =  1  erg  =  energy  required  to  overcome  the  resist- 
ance of  1  dyne  at  a  speed  of  1  centimetre  per  second.  1  watt  =  107  ergs. 

Unit  magnetism  =  that  amount  of  magnetic  matter  which,  if  concentrated 
in  a  point,  will  repel  an  equal  amount  of  magnetic  matter  concentrated  in 
another  point  one  centimetre  distant  with  the  force  of  one  dyne. 

Unit  strength  of  field  =  that  flow  of  magnetic  lines  which  will  exert  unit 
mechanical  force  upon  unit  pole,  or  a  density  of  1  line  per  square  centi- 
metre. 

The  following  definitions  of  practical  units  of  the  magnetic  circuit  are 
given  in  Houston  and  Kennelly's  "Electrical  Engineering  Leaflets." 

Gilbert,  the  unit  of  magneto-motive  force;  such  a  M.M.F.  as  would  be 

produced  by  —  or  0.7958  ampere-turn. 

If  an  air-core  solenoid  or  hollow  anchor-ring  were  wound  with  100  turns 
of  insulated  wire  carrying  a  current  of  5  amperes,  the  M.M.F.  exerted  would 
be  500  ampere-turns  =  628.5  gilberts. 

Weber,  the  unit  of  magnetic  flux;  the  flux  due  to  unit  M.M.F.  when  the 
reluctance  is  one  oersted. 

Gauss,  the  unit  of  magnetic  flux-density,  or  one  weber  per  normal  square 
centimetre. 

The  flux-density  of  the  earth's  magnetic  field  in  the  neighborhood  of 
New  York  is  about  0.6  gauss,  directed  downwrards  at  an  inclination  of  about 
72°. 

Oersted,  the  unit  of  magnetic  reluctance;  the  reluctance  of  a  cubic  centi- 
metre of  an  air-pump  vacuum. 

Reluctance  is  that  quantity  in  a  magnetic  circuit  which  limits  the  flux 
under  a  given  M.M.F.  It  corresponds  to  the  resistance  in  the  electric  cir- 
cuit. 

The  reluctivity  of  any  medium  is  its  specific  reluctance,  and  in  the  C.G.S. 
system  is  the  reluctance  offered  by  a  cubic  centimetre  of  the  body  between 
opposed  parallel  faces.  The  reluctivity  of  nearly  all  substances,  other  than 
the  magnetic  metals,  is  sensibly  that  of  vacuum,  is  equal  to  unity,  and  is 
independent  of  the  flux  density. 

Permeability  is  the  reciprocal  of  magnetic  reluctivity. 


ELECTRO-MAGNETS.  1059 

The  fundamental  equation  of  the  magnetic  circuit  is 

Webers  .--gilbertf; 
oersteds 

or,  magnetic  flux  =  magneto-motive  force  -*-  magnetic  reluctance. 
From  this  equation  we  have 

Gilberts  =  webers  X  oersteds;  oersteds  =  gilberts  -*-  webers. 

There  are  therefore  two  ways  of  increasing  the  magnetic  flux:  1.  by  in- 
creasing the  M.M.F. ;  2.  by  decreasing  the  reluctance. 

Lines  and  Loops  of  Force.— In  discussing  magnetic  and  electrical 
phenomena  it  is  conventionally  assumed  that  the  attractions  and  repulsions 


ng.    As  the  iron 

filings  arrange  themselves  in  concentric  circles,  we  may  assume  that  the 
forces  may  be  represented  by  close  curves  or  "  loops  of  force."  The  follow- 
ing assumptions  are  made  concerning  the  loops  of  force  in  a  conductive 
circuit: 

1.  That  the  lines  or  loops  of  force  in  the  conductor  are  parallel  to  the  axis 
of  the  conductor. 

2.  That  the  loops  of  force  external  to  the  conductor  are  proportional  in 
number  to  the  current  in  the  conductor,  that  is,  a  definite  current  generates 
a  definite  number  of  loops  of  force.    These  may  be  stated  as  the  strength  of 
field  in  proportion  to  the  current. 

3.  That  the  radii  of  the  loops  of  force  are  at  right  angles  to  the  axis  of 
the  conductor. 

The  magnetic  force  proceeding  from  a  point  is  equal  at  all  points  on  the 
surface  of  an  imaginary  sphere  described  by  a  given  radius  about  that 
point.  A  sphere  of  radius  1  cm.  has  a  surface  of  4ir  square  centimetres.  If 
F  —  total  field  strength,  expressed  as  the  number  of  lines  of  force  emanat- 
ing from  a  pole  containing  M  units  of  magnetic  matter, 

F=4irM;     M=F-*-4ir. 

Magnetic  moment  of  a  magnet  =  product  of  strength  of  pole  M  and  its 
length,  or  distance  between  its  poles  L.  Magnetic  moment  =  — . 

If  B  —  number  of  lines  flowing  through  each  square  centimetre  of  cross- 
section  of  a  bar -magnet,  or  the  "  specific  induction,"  and  A  =  cross-section, 

Magnetic  moment  =  — — . 

47T 

If  the  bar-magnet  be  suspended  in  a  magnetic  field  whose  induction  is  H, 
and  so  placed  that  the  lines  of  the  field  are  all  horizontal  and  at  right  angles 
to  the  axis  of  the  bar,  the  north  pole  will  be  pulled  forward,  that  is,  in  the 
direction  in  which  the  lines  flow,  and  the  south  pole  will  be  pulled  in  the 
opposite  direction,  the  two  forces  producing  a  torsional  moment  or  torque, 

Torque  =  MLH  —  LABH  -4-  4ir,  in  dyne-centimetres. 

Magnetic  attraction  or  repulsion  emanating  from  a  point  varies  inversely 
as  the  square  of  the  distance  from  that  point.  The  law  of  inverse  squares, 
however,  is  not  true  when  the  magnetism  proceeds  from  a  surface  of  ap- 
preciable extent,  and  the  distances  are  small,  as  in  dynamo-electric 
machines.  (For  an  analogy  see  "  Radiation  of  Heat,"  page  467.) 

Strength  of  an  Electro-magnet.— In  an  electric  magnet  made  by 
coiling  a  current-carrying  conductor  around  a  core  of  soft  iron,  the  space 
in  which  the  loops  of  force  have  influence  is  called  the  magnetic  field,  and 
it  is  convenient  to  assume  that  the  strength  of  the  field  is  proportional  to 
the  number  of  loops  of  magnetic  force  surrounding  the  magnet.  Under 
this  assumption,  if  we  take  a  given  current  passing  through  a  given  number 
of  conductor-turns,  the  number  of  magnetic  loops  will  depend  upon  the 
resistance  of  the  magnetic  circuit,  just  as  the  current  with  a  given  press- 
ure in  the  conductive  circuit  depends  upon  the  resistance  of  the  circuit. 

The  following  laws  express  the  most  important  principles  concerning 
electro-magnets  : 

(1)  The  magnetic  intensity  (strength)  of  an  electro-magnet  is  nearly  pro- 
portional to  the  strength  of  the  magnetizing  current,  provided  the  core  is 
not  saturated. 


1060  ELECTRICAL   ENGINEERING. 

(2)  The  magnetic  strength  is  proportional  to  the  number  of  turns  of  wire 
in  the  magnetizing  coil;  that  is,  to  the  number  of  ampere  turns. 

(3)  The  magnetic  strength  is  independent  of  the  thickness  or  material  of 
tbe  conducting  wires. 

These  laws  may  be  embraced  in  the  more  general  statement  that  the 
strength  of  an  electro -magnet,  the  size  of  the  magnet  being  the  same,  is 
proportional  to  the  number  of  its  ampere  turns. 

Force  in  the  Gap  between  Two  JPoles  of  a  Magnet.— If 
P  =  force  exerted  by  one  of  the  poles  upon  a  unit  pole  in  the  gap,  and  in  = 
density  of  lines  in  the  field  (that  is,  that  there  are  m  absolute  or  C.G.S.  units 
on  each  square  centimetre  of  the  polar  surface  of  the  magnet),  the  polar 
surface  being  large  relative  to  the  breadth  of  the  gap,  P  =  2irm.  The  total 
force  exerted  upon  the  unit  pole  by  both  north  and  south  poles  of  the 
magnet  is  2P  =  4irm,  in  dynes  =•  B,  or  the  induction  in  lines  of  force  per 
square  centimetre.  If  /S  =  number  of  square  centimetres  in  each  polar 
surface,  SB  =  total  flow  of  force,  or  field  strength  =  F:  Sin  =  total  pole 
strength  =  M,  spread  over  each  of  the  polar  surfaces.  We  then  have  F  — 
4irM,  as  before;  that  is,  the  total  field  is  4n  times  the  total  pole  strength. 

Total  attractive  force  between  the  two  opposing  poles  of  a  magnet,  when 

SB  2 
the  distance  apart  is  small,  ==  — - — ,  in  dynes. 

O7T 

This  formula  may  be  used  to  determine  the  lifting-power  of  an  electro- 
magnet, thus: 

A  bent  magnet  provided  with  a  keeper  is  3  cm.  square  on  each  pole,  and 
the  induction  B  =  20,000  lines  per  square  centimetre.  The  attractive  force 

9  X  200002 
of  each  limb  on  the  keeper  in  dynes  =  -^ 5-77- ,  or   in   kilogrammes  for 

o  X  "•  14 

Q  v  40fl   V    1fl6 

b°th  HmbS'    25.18X981000   *  2  =  292  kilogrammes. 

The  Magnetic  Circuit.— In  the  conductive  circuit  we  have  C  =  — -; 

j\ 
electro-motive  force         volts 

Current  =  —  =  — : . 

resistance  ohms 

In  the  magnetic  circuit  we  have 
Number  of  lines,  or  loops,  of  force,  or  magnetism 

Current  x  conductor  turns  Ampere  turns 

~~  Resistance  of  magnetic  circuit  ~~  Resistance  of  magnetic  circuit' 

Or,  in  the  new  notation,  webers  =  —    — £-. 

oersteds 

Let  N=  No.  of  lines  of  force,  Rm  —  total  magnetic  resistance,  At  ~ 
ampere  turns,  then  N=  — — . 

rCm 

4 

The   magnetic  pressure  due  to    the   ampere    turns—  7^*2X7  =  J.257Tc, 

AirTC       1.257TC 

where  T  =  turns  and   C  —  amperes,   whence  N  =      p       =  — 5 . 

ffm  Km 

If  12m  =  total  magnetic  resistance,  and  7?a,  RA.  RF  the  magnetic  resist- 
ances of  the  air-spaces,  the  armature,  and  the  field-magnets,  respectively, 

4nTCt  * 

Rm  =  Ra  -f  R A  +  RF\    and    N  =  - — '          ,    p  • 

Ka  -r  KA    i    *t  p 

Determining  tlie  Polarity  of  Electro-magnets. -If  a  wire 
is  wound  around  a  magnet  in  a  right-handed  helix,  the  end  at  which  the 
current  flows  into  the  helix  is  the  south  pole.  If  a  wire  is  wound  around  an 
ordinary  wood  screw,  and  the  current  flows  around  the  helix  in  the  direc- 
tion from  the  head  of  the  screw  to  the  point,  the  head  of  the  screw  is  the 
south  pole.  If  a  magnet  is  held  so  that  the  south  pole  is  opposite  the  eye  of 
the  observer,  the  wire  being  wound  as  a  right-handed  helix  around  it,  the 
current  flows  in  a  right-handed  direction,  with  the  hands  of  a  clock. 


DYXAMO-ELECTRIC  MACHINES.  lOGl 

DYNAMO-ELECTRIC  MACHINES. 

There  are  four  classes  of  dynamo-electric  machines  viz  • 

1.  The  dynamo,  in  which  mechanical  energy  of  rotation  is  converted  into 
the  energy  of  a  direct  current. 

2.  The  alternator,  in  which  mechanical  energy  of  rotation  is  converted  into 
the  energy  of  an  alternating  current. 

3.  The  motor,  in  which  the  energy  of  a  direct  current  is  converted  into 
mechanical  energy  of  rotation. 

4.  The  alternate-current  motor,  in  which  the  energy  of  one  or  more  alter- 
nating currents  is  converted  into  mechanical  energy  of  rotation 

For  a  steady  direct  current  the  product  of  the  potential  difference  and  the 
current  strength  is  a  true  measure  of  the  energy  given  off  With  alternat- 
ing currents  the  product  of  voltage  into  current  strength  is  greater  than  the 
true  energy,  since  the  conductor  has  the  property  of  reacting  upon  itself 
called  "self-induction." 

Kinds  of  Dynamo-electric  Machines  as  regards  Man- 
ner  of  Winding.  (Houston's  Electrical  Dictionary.) 

1.  Dynamo- electric  Machine.—  A  machine  for  the  conversion  of  mechan- 
ical energy  into  electrical  energy  by  means  of  magneto-electric  induction 

2.  Compound-wound  Dynamo.— The  field-magnets  are  excited  by  more 
than  one  circuit  of  coils  or  by  more  than  a  single  electric  source. 

3.  Closed-coil  Dynamo.— The  armature-coils  are  grouped  in  sections  com- 
municating with  successive  bars  of  a  collector,  so  as  to  be  connected  con- 
tinuously together  in  a  closed  circuit. 

4.  Open-coil  Dynamo.— The  armature-coils,  though  connected  to  the  suc- 
cessive bars  of  the  commutator,  are  not  connected  continuously  in  a  closed 
circuit. 

5.  Separate-coil  Dynamo.— The  field -magnets  are  excited  by  means  of 
coils  on  the  armature  separate  and  distinct  from  those  which  furnish  cur- 
rent to  the  external  circuit. 

6.  Separately-excited  Dynamo. — The  field-magnet  coils  have  no  connec- 
tion with  the  armature-coils,  but  receive  their  current  from  a  separate 
machine  or  source. 

7.  Series-wound  Dynamo.— The  field-current  and  the  external  circuit  are 
connected  in  series  with  the  armature  circuit,  so  that  the  entire  armature 
current  must  pass  through  the  field-coils. 

Since  in  a  series-wound  dynamo  the  armature-coils,  the  field,  and  the  ex- 
ternal-series circuit  are  in  series,  any  increase  in  the  resistance  of  the  ex- 
ternal circuit  will  decrease  the  electro- motive  force  from  the  decrease  in 
the  magnetizing  currents.  A  decrease  in  the  resistance  of  the  external  cir- 
cuit will,  in  a  like  manner,  increase  the  electro-motive  force  from  the  in- 
crease in  the  magnetizing  current.  The  use  of  a  regulator  avoids  these 
changes  in  the  electro-motive  force. 

8.  Series  and  Separately-excited  Compound-wound  Dynamo. — There  are 
two  separate  circuits  in  the  field-magnet  cores,  one  of  which  is  connected 
in  series  with  the  field-magnets-and  the  external  circuit,  and  the  other  with 
some  source  by  which  it  is  separately  excited. 

9.  Shunt-wound  Dynamo.— The  field- magnet  coils  are  placed  in  a  shunt 
to  the  armature  circuit,  so  that  only  a  portion  of  the  circuit  generated 
passes  through  the  field  magnet  coils,  but  all  the  difference  of  potential  of 
the  armature  acts  at  the  terminals  of  the  field-circuit. 

In  a  shunt-dynamo  machine  an  increase  in  the  resistance  of  the  external 
circuit  increases  the  electro-motive  force,  and  a  decrease  in  the  resistance 
of  the  external  circuit  decreases  the  electro-motive  force.  This  is  just  the 
reverse  of  the  series-wound  dynamo. 

In  a  shunt-wound  dynamo  a  continuous  balancing  of  the  current  occurs. 
The  current  dividing  at  the  brushes  between  the  field  and  the  external  cir- 
cuit in  the  inverse  proportion  to  the  resistance  of  these  circuits,if  the  resist- 
ance of  the  external  circuit  becomes  greater,  a  proportionately  greater 
current  passes  through  the  field-magnets,  and  so  causes  the  electro-motive 
force  to  become  greater.  If,  on  the  contrary,  the  resistance  of  the  external 
circuit  decreases,  less  current  passes  through  the  field,  and  the  electro- 
motive force  is  proportionately  decreased. 

10.  Series-  and  Shunt-wound  Compound-wound  Dynamo.— The  field-mag- 
nets are  wound  with  two  separate  coils,  one  of  which  is  in  series  with  the 
armature  and  the  external  circuit,  and  the  other  in  shunt  with  the  arma- 
ture.   Tin's  is  usually  called  a  compound- wound  machine. 

11.  Shunt  and  Separately-excited  Compound-ivound  Dynamo.~Tb.Q  field 


1062  ELECTRICAL 

is  excited  both  by  means  of  a  shunt  to  the  armature  circuit  and  by  a  cur- 
rent produced  by  a  separate  source. 
Current  Generated  by  a  Dynamo-electric  Machine.  —Unit 

current  in  the  C.U.S  system  is  that  current  which,  flowing  in  a  thin  wire 
forming  a  circle  of  one  centimetre  radius,  acts  upon  a  unit  pole  placed  iii 
the  centre  with  a  force  of  2ir  dynes.  One  tenth  of  this  unit  is  the  unit  of 
current  used  in  practice,  called  the  ampere. 

A  wire  through  which  a  current  passes  has,  when  placed  in  a  magnetic 
field,  a  tendency  to  move  perpendicular  to  itself  and  at  right  angles  to  the 
lines  of  the  field.  The  force  producing  this  tendency  is  P  =  IcB  dynes,  in 
which  /  =  length  of  the  wire,  c  =  the  current  in  C.G.S.  units,  and  B  the  in- 
duction in  the  field  in  lines  per  square  centimetre. 

If  the  current  C  is  taken  in  amperes,  P  =  ICBIQ     . 

If  Pk  is  taken  in  kilogrammes, 

]  (~tp> 

Pk  =  ~        =  10.1937ZOS10-8  kilogrammes. 


EXAMPLE.—  The  mean  strength  of  field,  B,  of  a  dynamo  is  5000  C.G.S.  lines; 
a  current  of  100  amperes  flows  through  a  wire;  the  force  acts  upon  10  centi- 
metres of  the  wire  =  10.1937  X  10  X  100  X  5000  X  10"  8=  .5097  kilogrammes. 

In  the  "English"  or  Kapp's  system  of  measurement  a  total  flow  of  600C 
C.G.S.  lines  is  taken  to  equal  one  English  line.  Calling  BE  the  induction  in 
English,  or  Kapp's,  lines  per  square  inch,  and  B  the  induction  in  C.G.S.  lines 
per  square  centimetre,  BE  =  B  -5-  930.04;  and  taking  I"  in  inches  and  PP  in 

pounds,  Pp  =  531  CV'B^  10"  6  pounds. 

Torque  of  an  Armature,—  Pp  in  the  last  formula,  =  the  force  tending 
to  move  one  wire  of  length  I",  which  carries  a  current  of  C  amperes  through 
the  field  whose  induction  is  BE  English  lines  per  square  inch.  The  current 
through  a  drum-armature  splits  at  the  commutator  into  two  branches, 
each  half  going  through  half  of  the  wires  or  bars.  The  force  exerted 
vipon  one  of  the  wires  under  the  influence  of  a  pole-piece  =  Y%Pp.  If  t  =  the 
number  of  wires  under  the  pole-pieces,  then  the  total  force  —  \^Ppt.  If  r  — 
radius  of  the  armature  to  the  centre  of  the  conductors,  expressed  in  feet, 
then  the  torque  =  Y^Pptr,  =  ^  X  531  X  Cl"BE  X  10~6  X  tr  foot-pounds  of 
moment,  or  pounds  acting  at  a  radius  of  1  foot. 

EXAMPLE.  —  Let  the  length  I  of  an  armature  =  20  in.,  the  radius  =  6  in.  or 
.5  ft.,  number  of  conductors  =  120,  of  which  /  =  80  are  under  the  influence 
of  the  two  pole-  pieces  at  one  time,  the  average  induction  or  magnetic  flux 
through  the  armature  -fie  Id  BE  =  5  English  lines  per  square  inch,  and  the 
current  passing  through  the  armature  =  400  amperes;  then 

Torque  =  ^  X  531  X  400  X  20  X  5  X  80  X  .5  X  10~6  =  424.8. 

The  work  done  in  one  revolution  =  torque  X  circumference  of  a  circle  ot 
1  foot  radius  =  424.8  X  6.28  =  2070  foot-pounds. 
Let  the  revolutions  per  minute  =  500,  then  the  horse-power 


Electro-motive  Force  of  the  Armature  Circuit.—  From  the 

horse-power,  calculated  as  above,  together  with  the  amperes,  we  can  obtain 
the  E.M.F.,  for  CE  =  H.P.  X  746,  whence  E.M.F.  or  E  =  H.P.  X  746  -t-  C. 

40  *>  V  74fi 

If  H.P.,  as  above,  rz  40.5,  and  C  =  400,  E  =         40Q          =  75.5  yolts. 

The  E.M.F.  may  also  be  calculated  more  directly  by  the  following  formulas 
given  by  Gisbert  Kapp: 

C  =  Total  current  through  armature;  c,  current  through  single  armature 

conductor; 

ea=  E.M.F.  in  armature  in  volts; 

T  —  Number  of  active  conductors  counted  all  around  armature; 
p  =  Number  of  pairs  of  poles  (p  =  1  in  a  two-pole  machine); 
n  =  Speed  in  revolutions  per  minute; 
F  —  Total  induction  in  C.G.S.  lines; 
Z  =  Total  induction  in  English  lines. 


DYHAMO-ELECTRIC    MACHINES. 


1063 


Electro- motive 
force 


«  60 

ea  =  pZrnlO 


"  for  two-pole  machines. 


for  multipolar  machines  with 
series-wound  armature. 


j   Kilogramme-metres  =  1. 

Torque  \    Foot-  pounds =  7.05ZrC  10  "  6 

I    Kilogramme-metres  =  3.23£¥cp  10  ~10 


i  for  two-pole  ma- 
chines. 

I   for  multipolar  ma- 
^  Foot-pounds =  14.10ZrcplO~6     »  chines. 

EXAMPLE.— T  =  120,  n  -  500,  length  of  armature  I  -  20  in.,  diameter 
d  =  12  in.,  cross-section  =  20  X  12  =  240  sq.  in.,  induction  per  sq.  in  £*,  = 
5  lines  per  sq.  in.,  total  induction  Z  =  240  X  5  =  1200;  then 

E  =  ZrnlO-*  =  1200  X  120  X  500  X  10-«  =: 
A  formula  for  horse-power  given  by  Kapp  is 


H.P.  =  1/7 

=  1/746  2abmNtnlO-«Ca. 

Ca  =  current  in  amperes,  n  =  revs,  per  min.,  2ab  =  sectional  area  of  arm- 
ature-core, m  =  average  density  of  lines  per  sq.  in.  of  armature-core,  Nt  = 
total  number  of  external  wires  counted  all  around  the  circumference,  t  = 
number  of  wires  corresponding  to  one  plater  in  the  commutator,  N  =  num- 
ber of  plates,  Z  =  2abin  =  total  number  of  English  lines  of  force. 

Kapp  says  that  experience  has  shown  that  the  density  of  lines  m  in  the 
core  cannot  exceed  a  certain  limit,  which  is  reached  when  the  core  is  satu- 
rated with  magnetism.  This  value  is  reached  when  m  =  30.  A  fair  average 
value  in  modern  dynamos  and  motors  is  m  =  20,  and  the  area  ab  must  be 
taken  as  that  actually  filled  by  iron,  and  not  the  gross  area  of  the  core.  2o 
English  lines  per  sq.  in.  =  18,600  C.G.S.  lines  per  square  centimetre.  Sil- 
vanus  P.  Thompson  says  it  is  not  advisable  in  continuous-current  machines 
to  push  the  magnetization  further  than  B  =  17,000  C.G.S.  lines  per  square 
centimetre. 

Thompson  gives  as  a  rough  average  for  the  magnetic  field  in  the  gap-space 
of  a  dynamo  or  motor  6300  lines  per  sq.  cm.,  or  40,000  lines  per  sq.  in.,  and 
the  drag  per  inch  of  conductor  .00354  Ib,  for  each  ampere  of  current  carried. 

H  P    V  33  000 

Pounds  average  drag  per  conductor  =  —  —  —  —  ,  in  which  C  is  the 

it.  per  mm.  x  c/ 
number  of  conductors  around  the  armature. 

Strength  of  the  Magnetic  Field.—  Kapp  gives  for  the  total  num- 
ber of  lines  of  force  (Kapp's  lines  =  C.G.S.  lines  -*-  6000)  in  the 


cuit.    Z  = 


,  in  which  Z 


magnetic  cir- 
number of  magnetic  lines,  X  =  the 


=  —  r—^  —  ,    _   , 
Ka  ~r  KA  -\-  KF 

exciting  pressure  due  to  the  ampere  turns  =  AirTC,  Ra,  RA,  and  RF,  —  re- 
spectively the  resistances  of  the  air-spaces,  the  armature,  and  the  field-mag- 
nets. 

Kapp  gives  the  following  empirical  values  Of  Ra,  RA,  and  RF,  for  dynamos 
and  motors  made  of  well-annealed  wrought  iron,  with  a  permeability  of  /m  = 
940: 

#a=1440^;    RA  =  —  ',    RF  =  2  £;', 
\b  ab  AB 

in  which  5  =  distance  across  the  span  between  armature  -core  and  polar 
surface,  6  =  breadth  of  armature  measured  parallel  to  axis,  A  —  length  of 
arc  embraced  by  polar  surface,  so  that  \b  =  the  polar  area  out  of  which 
magnetic  lines  issue,  a  =  radial  depth  of  armature-core,  so  that  ab  =  sec- 
tion of  armature  core  (space  actually  occupied  by  iron  only  being  reckoned, 
AB  =  area  of  field-magnet  core,  I  =  length  of  magnetic  circuit  within  ar- 
mature, L  =  length  of  magnetic  circuit  in  field  magnet;  all  dimensions  in 
inches  or  square  inches. 


1064  ELECTRICAL  ENGINEERING. 

o  sy 
For  cast-iron  magnets,  Z  —  -  ^  —  '—.  -  ^j=- 

i  «nn  ^°  _i_    '      .     oL," 
8°°X6  +  ab  +  T3 

For  double  horse-shoe  magnets  of  wrought  iron, 


and  of  cast  iron,  - 


These  formulae  apply  only  to  cases  in  which  the  intensity  of  magnetization 
is  not  too  great— say  up  to  10  Kapp's  lines  per  square  inch. 

Silvanus  P.  Thompson  gives  the  following  method  of  calculating  the 
strength  of  the  field,  or  the  magnetic  flux,  MF,  or  the  whole  number  of 
magnetic  lines  flowing  in  the  circuit  in  C.G.S.  lines: 

The  magnetic  resistance  of  any  magnetic  conductor  is  proportional  direct- 
ly to  its  length  and  inversely  to  its  cross-section  and  its  permeability. 

Magnetic  resistance  =  — ,  in  which  L  =  length  of  the  magnetic  circuit 

passing  through  any  piece  of  iron,  S  =  section   of  the  magnetic  circuit 
passing  through  any  piece  of  iron,  /u,  =  permeability  of  that  piece  of  iron. 

In  a  dynamo-machine  in  which  the  resistances  are  three,  viz.:  1.  The  field- 
magnet  cores;  2.  The  armature-core;  3.  The  gaps  or  air-spaces  between, 
them,— 

let  Lm,  Sm,  /MW  refer  to  the  field -magnet  part  of  the  circuit ; 
Las,  Sas,  v-as  refer  to  the  air-space  part  of  the  circuit; 
La,  Sa,  na  refer  to  the  armature  part  of  the  circuit: 

the  lengths  across  each  of  the  air-spaces  being  Las,  and  the  exposed  area  of 
polar  surface  at  either  pole  being  Sas. 

Total  magnetic  resistance  =  ^~  +  0Las     -f 


Magnetic  flux,  or  total  number  of  magnetic  lines?, : 

1.2577W? 


MF  = 


Tw  =  turns  of  wires,  ur  number  of  turns  in  the  spiral; 
C  =  current  in  amperes  passing  through  spiral. 

Application  to  Designing  of  Dynamo*.  (S.  P.  Thompson  I—- 
Suppose in  designing  a  dynamo  it  has  been  decided  what  will  be  a  conven- 
ient speed,  how  many  conductors  shall  be  wound  upon  the  armature,  and 
«vhat  quantity  of  magnetic  lines  there  must  be  in  the  field,  it  then  becomes 
necessary  to  calculate  the  sizes  of  the  iron  parts  and  the  quantity  of  exeita 
tion  to  be  provided  for  by  the  field-magnet  coils.  It  being  known  what  MF 
Is  to  be,  the  problem  is  to  design  the  machine  so  as  to  get  the  required 
value.  Experience  shows  that  in  every  type  of  dynamo  there  is  magnetic 
leakage;  also,  that  it  is  not  wise  to  push  the  saturation  of  the  armature-core 
to  more  than  16,000  lines  to  the  square  centimetre  at  the  most  highly  satu- 
rated part,  and  that  the  induction  in  the  field-magnet  ought  to  be  not 
greater  than  this,  even  allowing  for  leakage.  Leakage  may  amount  to  J4 
of  the  whole:  hence,  if  the  magnet -cores  are  made  of  same  quality  of  iron 
as  the  armature-cores,  their  cross-section  ought  to  be  at  least  5/4  as  great 
as  that  of  the  armature-core  at  its  narrowest  point.  If  the  field-magnets 
are  of  cast  iron,  the  section  ought  to  be  at  least  twice  as  great. 

Now,  Ba  (the  induction  in  the  armature-core)  =  Ma  -*-  Sa  (or  magnetic  flux 
through  armature  -5-  cross-sectional  area  of  the  armature  ;  hence,  if  this 
is  fixed  at  16,000  lines  per  centimetre  of  cross-section,  we  at  once  get  Sa  — 
Ma  -T-  Ba.  This  fixes  the  cross-section  of  the  armature-core.  (Example:  If 
Ma  =  4,000,000  of  lines,  then  there  must  be  a  cross-section  equal  to  ^50 

4,000,000 
square  centimetres  for  '       =  250.) 


DYNAMO-ELECTRIC   MACHINES.  1065 

Magnetic  Length  of  Armature  Circuit.— The  size  of  wires  on  the  arma- 
ture is  fixed  by  the  number  of  amperes  which  it  must  carry  without  risk 
Remembering  that  only  half  the  current  (in  ring  or  drum  armatures)  passes. 
through  any  one  coil,  and  as  the  number  is  supposed  to  have  been  fixed  be- 
forehand, this  practically  settles  the  quantity  of  copper  that  must  be  put  on 
the  armature,  and  experience  dictates  that  the  core  should  be  made  so  large 
that  the  thickness  of  the  external  winding  does  not  exceed  1/6  of  the  radial 
depth  of  the  iron  core.  This  settles  the  size  of  the  armature -core,  from 
which  an  estimate  of  La,  the  average  length  of  path  of  the  magnetic  lines 
in  the  core,  can  be  made. 

Length  and  Section  or  Surface  Area  of  Air  -space.— Experience  further 
dictates  the  requisite  clearance,  and  the  advantage  of  making  the  pole- 
pieces  subtend  an  arc  (in  two-pole  machines)  of  at  least  135°  each,  so  as  to 
gain  a  large  polar  area.  This  settles  Las  and  Sas. 

Length  of  Field -magnet  Iron  Cores,  etc. — As  shown  above,  the  minimum 
value  of  Sm  is  settled  by  leakage  and  materials;  Lm  therefore  remains  to 
be  decided.  It  is  clear  that  the  magnet-cores  must  be  long  enough  to  allow 
of  the  requisite  magnetizing  coils,  but  should  not  be  longer.  As  a  rule, 
they  are  made  so  stout,  especially  in  the  yoke  part,  that  they  do  not  add 
much  to  the  magnetic  resistance  of  the  circuit,  then  a  little  extra  length  as 
sumed  in  the  calculation  does  not  matter  much.  It  now  only  remains  to 
calculate  the  number  of  ampere- turns  of  excitation  for  which  it  will  be 
needful  to  provide. 

It  will  now  be  more  convenient  to  rewrite  the  formula  of  the  magnetic 
circuit  as  follows: 

j  A    Lm    4-2      Las     4-     La     I 
A  X  Tmw  =  Ma- — ' a.    a  ,  . 

where  A  =  amperes  of  current  passing  through  the  field-maguet  coils; 
Tmw  —  total  turns  of  the  magnet  wire; 
\  =  leakage  coefficient  (say  5/4). 

Or, 

^                         A Rm  4-  Ras  -f  .Ra 
4.  X  Tmw  =  Ma 0 .. 

Or,  as  before, 


•MT          1    nurr 
Ma  =  1 .257  r 


i4-#a>" 

where  Rm,  Ras,  Ra  stand  for  the  magnetic  resistance  of  magnets,  air- 
space, and  armature,  respectively. 

But  we  cannot  use  this  formula  yet,  because  the  values  of  ju  in  it  depend  on 
the  degree  of  saturation  of  the  iron  in  the  various  parts.  These  have  to  be 
found  from  the  Hopkinson  tables,  given  below;  and,  indeed,  it  is  preferable 
first  to  rearrange  the  formula  once  more,  by  dividing  it  into  its  separate 
members,  ascertaining  separately  the  ampere-turns  requisite  to  force  the 
required  number  of  magnetic  lines  through  the  separate  parts,  and  then 
add  them  together. 

1.  Ampere-turns  required  for  magnet-cores  =  A  — -  x   -—  -t-  1.257. 

2.  Ampere-turns  required  for  air-spaces         =  -^  X  2—*  H-  1.257. 

oas         fJias 

3.  Ampere- turns  required  for  armature-core  =  ^  X  — -*•  1-257. 

oa         M-a 

Now  A— -  is  the  value  of  B  in  the  magnet-cores,  and  reference  to  the  table 

Sm 
of  permeability  will  show  what  the  corresdonding  value  of  /urn  must  be. 

Similarly, -va  will  afford  a  clue  to  /u,a.  When  the  total  number  of  ampere- 
turns  to  be  allowed  for  is  thus  ascertained,  the  size  and  length  of  wire  will 
be  determined  by  the  permissible  rise  of  temperature,  and  the  mode  of 
exciting  the  field -magnets,  whether  in  series,  or  as  a  shunt  machine,  or 
with  a  compound-winding. 


1066 


ELECTRICAL   ENGINEERING. 


Permeability.-  Materials  differ  in  regard  to  the  resistance  they  offer 
to  the  passage  of  lines  of  force;  thus  iron  is  more  permeable  than  air.  The 
permeability  of  a  substance  is  expressed  by  a  coefficient /A,  which  denotes 
its  relation  to  the  permeability  of  air,  which  is  taken  as  1.  If  H  =  number 
of  magnetic  lines  per  square  centimetre  which  will  pass  through  an  air- 


iori  reaching  a  practical  limit  for  soft  wrought  iron  when  B  =  about  18,000 
nd  for  cast  iron  when  B  =  about  10,000  C.G.S.  lines  per  square  centimetre. 
The  following  values  are  given  by  Thompson  as  calculated  from  Hopkin- 

son's  experiments: 


Annealed  Wrought  Iron. 

Gray  Cast  Iron. 

B 

H 

^ 

B 

H 

/"• 

5,000 
9,000 
10,000 
11,000 
12,000 
13,000 
14,000 
15,000 

2 

4 
5 
6.5 

8.5 
12 
17 

28.5 

2,500 
2,250 
2,000 
1,692 
1,412 

i,oas 

823 
526 

4,000 
5,000 
6,000 
7,000 
8,000 
9,000 
10,000 
11,000 

5 

10 
21.5 
42 

80 
127 
188 
292 

800 
500 
279 
133 
100 
71 
53 
37 

16,000 

52 

308 

17,000 

105 

161 

18,000 

200 

90 

19,000 

350 

54 

Permissible  Amperage  and  Permissible  »eptli  of  Wind- 
ing for  Magnets  with  Cotton-covered  Wire.    (Walter  8.  Dix, 

El  Engineer,  Dec.  21,  1892.)-The  tables  on  pp.  1068,  1069,  abridged  from 
those  of  Mr.  Dix,  are  calculated  from  the  formula 


M 


where  C  =  current; 

W  =  emissivity  in  watts  per  square  men; 
GDmf  =  ohms  per  mil  -foot  ; 
M  =  circular  mils  ; 
T  =  turns  per  linear  inch  ; 
L  =  number  of  layers  in  depth. 

The  emissivity  is  taken  at  .4  watt  per  sq.  in.  for  stationary  magnets  for  £ 
rise  of  temperature  of  35°  C.  (63°  F.).  For  armatures,  according  to  Esson  s 
experiments,  it  is  approximately  correct  to  say  that  .9  watt  per  sq.  in.  wil 
be  dissipated  for  a  rise  of  35°  C.  . 

The  insulation  allowed  is  .007  inch  on  No.  0  to  No.  11  B.  &  S.;  .005  incl 
on  No  12  to  No.  24  ;  and  .0045  inch  on  No.  25  to  No.  31  single  ;  twice  these 
values  'for  insulation  of  double-covered  wires.  Fifteen  per  cent  is  allowec 
for  imbedding  of  the  wires. 

The  standard  of  resistance  employed  is  9.612  ohms  per  mil-foot  at  0°.  Th< 
running  temperature  of  tables  is  taken  at  25°  +  35°  =  60°  C.  The  columi 
giving  the  depth  for  one  layer  is  the  diameter  over  insulation. 

Formulae  of  Efficiency  of  Dynamos. 

(S.  P.  Thompson  in  "  Munro  and  Jamieson's  Pocket-Book.'1) 
Total  Electrical  Energy  (per  second)  of  any  dynamo  (expressed  in  watts 
is  the  product  of  the  whole  E.M.F.  generated  by  armature-coils  into  th 
whole  current  which  passes  through  the  armature. 

Useful  Electrical  Energy  (per  second),  or  useful  output  of  the  machine,  i 
the  product  of  the  useful  part  of  the  E.M.F.  (i.e.,  that  part  which  is  avail 
able  at  the  terminals  of  the  machine)  into  the  useful  part  of  the  curren 
(i.e.,  that  part  of  the  current  which  flows  from  the  terminals  into  the  extei 
n$J  circuit). 


DYNAMO-ELECTRIC   MACHINES. 


1067 


Economic  Coefficient  or  " electrical  efficiency"  of  a  dynamo  is  the  ratio 
of  the  useful  energy  to  the  total  energy. 

Commercial  Efficiency  of  a  dynamo  is  the  ratio  of  the  useful  energy  or 
output  to  the  power  actually  absorbed  by  the  machine  in  being  driven. 

Let  Ea  =  total  E.M.F.  generated  in  armature; 

Ee  =  useful  E.M.F.  available  at  terminals; 

Co,  =  total  current  generated  in  armature; 

Ca  =  current  sent  round  shunt-coils; 

Ce  —  useful  current  supplied  to  external  circuit; 

Ra  =  resistance  of  armature-coils ; 
Rm  =  resistance  of  magnet-coils  in  main  circuit  (series)* 

Its  =  resistance  of  magnet-coils  in  shunt; 

Re  =  resistance  of  external  circuit  (lamps,  mains,  etc.); 
Wa  =  Watts  lost  in  armature; 
Wm=  Watts  lost  in  magnet-coils; 

Vl  =  lost  volts; 

Te  —  total  electrical  energy  (per  second); 

Ue  =  useful  electrical  output; 
c  =  economic  coefficient; 
p  =  commercial  efficiency  (percentage). 

When  only  one  circuit  (series  machine)  Ce  =  Ca. 

In   shunt   machines    Cs  should   not   be   more   than    5#   of    Ce       Also 

Ca  •=  Ce  +  Cs. 
In  all  dynamos,  Ra  ought  to  be  less  than  1/40  as  great  as  the  working 

value  of  Re- 
in series  (and  compound)  machines,  Rm  should  be  not  greater  than  Ra 

and  preferably  only  %  as  great. 
In  shunt  (and  compound)  machines,  Rs  should  be  not  less  than  300  times 

as  great  as  Ra  and  preferably  1000  to  1200  times  as  great. 


Series  Machine. 

Shunt  Machine. 

Compound  Machine 
(Short  Shunt). 

c 

p 

E  Re 

/                7?  7?     \ 

c*(  r  -f          ) 

CaRa+CeRm 

V  "    Rs+Rm+Rj 
C*Re 

"'V^Ri+Rj 

Ea      Ra+Rm+Re 
6  (H.P.X746) 

C  gJBg-j~  C  aRa~\-  C  gRg 
6   6(H.P,X746) 

100X  EeCe-*-(H.P.  X  746) 

N.B.  Horse-power 
is  converted  into 
watts  (so  as  to  com- 
pare with  electric 
output  of  the  ma- 
chine) by  multiply- 
ing by  746. 

*  This    will    be    a 
maximum  when  Re 
is    a    mean    propor- 
tional    between    Rs 
and  Ra. 

In  well-constructed   com- 
pound machines  the  differ- 
ence between  "  short  shunt" 
and   "long  shunt"    is  very 
slight,  as  Rm  is  so  small. 

1068 


ELECTRICAL   ENGINEERING- 


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1070  ELECTRICAL  EHGIKEERIN'G. 

Alternating  Currents,  Multiphase  Currents,  Trans* 
formers,  etc.— The  proper  discussion  of  these  subjects  would  take  more 
space  than  can  be  afforded  in  this  work.  Consult  S.  P.  Thompson's  "  Dy- 
unmo-Electric  Machinery,11  Bedell  and  Crehore  on  "  Alternating  Currents,"' 
Fleming  on  "  Alternating  Currents,"  and  Kapp  on  "Dynamos,  Alternators 
and  Transformers." 

The  "Electric  Motor,— The  electric  motor  is  the  same  machine  as 
the  dynamo,  but  with  the  nature  of  its  operation  reversed.  In  the  dynamo 
mechanical  energy,  such  as  from  a  belt,  is  converted  into  electric  current; 
in  the  motor  the  current  entering  the  machine  is  converted  into  mechanical 
energy,  which  may  be  taken  off  by  a  belt.  The  difference  in  the  action  of 
the  machine  as  a  dynamo  and  as  a  motor  is  thus  explained  by  Prof.  F.  B. 
Crocker,  (Gassier 's  Mag.,  March,  1895): 

In  the  case  of  the  dynamo  there  exists  only  one  E.M.F.,  whereas  in  the 
motor  there  must  always  be  two. 

One  kilowatt  dynamo,  C  =  E  •*-  R;  10  amperes  =  100  volts  -*- 10  ohms. 

E  —  e    „  100  volts  -  90  volts 

One  kilowatt  motor,  C  =  —= — ;  10  amperes  = .    ,  — . 

RI    '  1  ohm 

C  is  the  current;  E,  the  direct  E.M.F.;  e,  the  counter  E.M.F.;  J?,  the  total 
resistance  of  the  circuit;  #,,  the  resistance  of  the  armature.  The  current 
and  direct  E.M.F.  are  the  same  in  the  two  cases,  but  the  resistance  is  only 
one  tenth  as  much  in  the  case  of  the  motor,  the  difference  being  replaced 
by  the  counter  E.M.F. ,  which  acts  like  resistance  to  reduce  the  current.  In 
the  case  of  the  motor  the  counter  E.M.F.  represents  the  amount  of  the 
electrical  energy  converted  into  mechanical  energy.  The  so-called  electri- 
cal efficiency  or  conversion  factor  =  counter  E.M.F.  -s-  direct  E.M.F.  The 
actual  or  commercial  efficiency  is  sonxjwhat  less  than  this,  owing  to  fric- 
tion, Foucault  currents,  and  hysteresis. 

For  full  discussions  of  the  theory  and  practice  of  electric  motors  see  S. 
P.  Thompsons  "Dynamo-Electric  Machinery,1'  Kapp's  "Electric  Trans- 
mission of  Energy,'1  Martin  and  Wetzler's  "The  Electric  Motor  and  its 
Applications,"  Cox's  "  Continuous  Current  Dynamos  and  Motors,"  and 
Crocker  and  Wheeler's  "Practical  Management  of  Dynamos  and  Motors." 


LIST  OF  AUTHORITIES  QUOTED  IN  THIS  BOOK. 


When  a  name  is  quoted  but  once  or  a  few  times  only,  the  page  or  pages 
are  given.  The  names  of  leading  writers  of  text-books,  who  are  quoted  fre- 
quently, have  the  word  "various11  affixed  in  place  of  the  page-number. 
The  list  is  somewhat  incomplete  both  as  to  names  and  page  numbers. 


Abel,  F.  A.,  642 

Abendroth  &  Root  Mfg.  Co.,  197,  198 

American  Screw  Co.,  209 

Achard,  Arthur,  886,  919 

Addy,  George,  957 

Addyston  Pipe  and  Steel  Co.,  187, 188 

Alden,  G.  I.,  979 

Alexander,  J.  S.,  629 

Allen,  Kenneth,  295 

Allen,  Leicester,  582 

Andrews,  Thomas,  384 

Ansonia  Brass  and  Copper  Co.,  327 

Arnold,  Horace  L.,  959 

Ashcroft  Mfg.  Co.,  752,  775 

Atkinson,  J.  J.,  532 

Ayrton  and  Perry,  1040 

Babcock,  G.  H.,  524,  933 

Babcock  &  Wilcox  Co.,  538,  636 

Baeruiann,  P.  H.,  188 

Bagshaw,  Walter,  952 

Bailey,  W.  H.,  943 

Baker,  Sir  Benjamin,  239,  247,  402 

Balch,  S.  W.,  898 

Baldwin,  Win.  J.,  541 

Ball,  Frank  H.,  751 

Barlow,  W.  H.,  384 

Barlow,  Prof.,  288 

Barnaby,  S.  W.,  1013 

Barnes,  D.  L.,  631,  861,  863 

Barrus,  Geo.  H.,  636 

Bauer,  Chas.  A.,  207 

Bauschinger,  Prof.,  239 

Bazin,  M.,  563,  587 

Beardslee,  L.  A..  238,  377 

Beaumont,  W.  W.,  979 

Becuel,  L.  A.,  644 

Begtrup,  J.,  348 

Bennett,  P.  D.,  354 

Bernard,  M.  &  E.,  330 

Birkinbine,  John,  605 

Bjorling,  P.,676 

Blaine,  R.  G.,  616,  1039 

Blauvelt,  W.  H.,  639,  649 

Blechynden,  A.,  1015 

Bodmer,  G.  R.,  753 

Bolland,  Simpson,  946 

Booth,  Wm.  H.,  926 

Box,  Thomas,  475 

Briggs,  Robert,  194,  478,  539,  672 

British  Board  of  Trade,  264,  266,  700 

Brown,  A.  G.,  723,  724 

Brown,  E.  H.,  388 

Brown  &  Sharpe  Mfg.  Co.,  219,  890 

Browne,  Ross  E.,  597 

Brush,  Chas.  B.,  566 

Buckle,  W.,  511 


Duel,  Richard  H.,  606,  834 
Buffalo  Forge  Co.,  519,  529 
Builders'  Iron  Foundry,  374 
Burr.  Wm.  A.,  565 
Burr,  Wm.  H.,  247,  259,  290,  381 

Calvert,  F.  Grace,  386 

Calvert  &  Johnson,  469 

Campbell,  H.  H.,  398.  459,  650 

Campredon,  Louis,  403 

Carnegie  Steel  Co.,  177,  272,  277,  391 

Carpenter,  R.  C.,  454,  615,  718,  etc. 

Chad  wick  Lead  Works,  201,  615 

Chamberlain,  P.  M.,  474 

Chance,  H.  M.,  631 

Chandler,  Chas.  F.,  532 

Chapman  Valve  Mfg.  Co.,  193 

Chauvenet,  S.  H.,  370 

Chase,  Chas.  P.,  312 

Chevandier,  Eugene,  640 

Christie,  James,  394 

Church,  Irving  P.,  415 

Church,  Wm.  Lee.  784,  1050 

Clapp,  Geo.  H.,  397,  403,  551 

Clark,  Daniel  Kiunear,  various 

Clarke,  Edwin,  740 

Claudel,455 

Clay,  F.  W.,  291 

Clerk,  Dugald,  847 

Cloud,  John  W.,  351 

Codman,  J.  E.,  193 

Coffey,B.  H.,  810 

Coffin,  Freeman  C.,  292 

Coggswell,  W.  B.,  554 

Cole,  Romaine  C,,  329 

Coleman,  J.  J.,  470 

Cooper,  John  H.,  876,  900 

Cooper,  Theodore,  262,  263,  359 

Cotterill  and  Slade,  432,  974 

Cowles,  Eugene  H.,  329,  331 

Cox,  A.  J.,  290 

Cox,  E.  T.,  629 

Cox,  William,  575 

Coxe,  Eckley  B.,  632 

Craddock,  Thomas,  473 

Cramp,  E.  S.,405 

Crimp,  Santo,  564 

Crocker,  F.  B.,  1070 

Cummins,  Wm.  Russell,  778 

Daelen,  R.  M.,  617 
Dagger,  John  H.  J.,  329 
Daniel,  Wm.,  492 
D'Arcy,  563 
Davenport,  R.  W.,  620 
Day,  R.  E.,  1030 
Dean,  F.  W.,  605,  689 

1071 


1072 


LIST   OF   AUTHORITIES. 


Decoeur,  P.,  600 

DeMeritens,  A.,  386 

Denton,  James  E  ,  730,  761,  781,  932 

Dinsmore,  E.  E.,  963 

Dix,  Walter  S.,  208,  1066 

Dodge  Manufacturing  Co.,  344 

Donald,  J.  T.,  235 

Donkin,  B.,  Jr.,  491,  783 

Dudley,  Chas.  B.,  327,  333 

Dudley,  P.  H.,  401,  622 

Dudley,  W.  D.,  167 

Dulong,  M.,  458,  476 

Dunbar,  J.  H.,  796 

Durand,  Prof.,  56 

Dwelshauvers-Dery,  662 

Egleston,  Thomas,  235,  641 
Emery,  Chas.  E.,  603,  613,  820 
Engelhardt,  F.  E.,  463 
Ellis  and  Rowland,  577 
English,  Thos.,  753 
Ericsson,  John,  286 
Eytelwein,  564 

Fairbairn,  Sir  Wra.,  240,  264,  308,  354 

Fairley,  W.,  531,  533 

Falkenau,  A.,  509 

Fanning,  J.T..  564,  579 

Favre  and  Silbermann,  621 

Felton,  C.  E.,646 

Fernow,  B.  E.,  640 

Field,  C.  J.,  30,  937 

Fitts,  James  H.,  844 

Flather,  J.  J.,  961,  964 

Flynn,  P.  J.,  463,  559 

Foley,  Nelson,  700 

Forbes,  Prof.,  1033 

Forney,  M.  N.,  855 

Forsyth,  Wm.,  630 

Foster,  R.  J.,  651 

Francis,  J.  B.,  586,  739,  867 

Frazer,  Persifor,  624 

Freeman,  J.  R.,  581,  584 

Frith,  A.  J.,  874 

Fulton,  John,  637 

Ganguillet  &  Kutter,  565 

Gantt,  H.L.,  406 

Garrison,  F.  L.,  326,  331,  409 

Garvin  Machine  Co.,  955 

Gause,  F.  T.,  501 

Gay,  Paulin,  966 

Gill,  J.  P.,  657 

Gilmore,  E.  P.,  241 

Glaisher,  483 

Glasgow,  A.  G.,  654 

Goodman,  John,  934 

Gordon,  F.  W.,  689,  740 

Gordon,  247 

Goss,  W.  F.  M.,  863 

Gossler,  P.  G.,  1051 

Graff,  Frederick,  385 

Graham,  W.,  950 

Grant,  George  B.,  898 

Grant,  J.  J.,  960 

Grashof,  Dr.,  284 

Gray,  J.  McFarlane,  661 

Gray,  J.  M.,  958 

Greene,  D.  M.,  567 


Greig  and  Eyth,  363 
Grosseteste,  W.,  715 
Gruner,  L.,  623 

Hadfield,  R.  A.,  391, 409 

Halpin,  Druitt,  789,  854 

Halsey,  Fred'k  A.,  490,  817 

Harkness,  Wm.,  900 

Harrison,  W.  H.,  939 

Hart,  F.  R.,  1047 

Hartig,  J.,  961 

Hartman,  John  M.,  364 

Hartnell,  Wilson,  348,  818,  838 

Hasson,  W.  F.  C.,  1047 

Hawksley,  T.,  485,  513,  564 

Hazen,  H.  Allen,  494 

Henderson,  G.  R.,  347,  851 

Hen  thorn,  J.  T.,  965 

Hering,  Carl,  1045 

Herschel,  Clemens,  583 

Hewitt,  G.  C.,  630 

Hewitt,  Wm.,  917 

Hildenbrand,  Wm.,  913 

Hill,  John  W.,  17 

Hiscox,  G.  D.,  968 

Hoadley,  John  C.,  451,  688 

Hobart,  J.  J.,  962 

Hodgkinson,  246 

Holley,  Alexander  L.,  377 

Honey,  F.  R.,  47,  52 

Hoopes  &  Townsend,  210 

Houston,  Edwin  J.,  1061 

Houston  &  Kennelly,  1058 

Howard,  James  E.,  242,  382,  385 

Howden,  James,  714 

Howe,  Henry  M.,  402,  407,  451,  5H 

Howe,  Malverd  A.,  170,  312 

Rowland,  A.  H.,  292 

Hudson,  John  G.,  465 

Hughes,  D.  E.,  396 

Hughes,  H.  W.,  909 

Hughes,  Thos.  E.,  917 

Humphreys,  Alex.  C.,  652 

Hunsicker,  Millard,  397 

Hunt,  Alfred  E.,  235,  317,  393,  553 

Hunt,  Chas.  V7.,  340,  922 

Huston,  Charles,  383 

Hutton,  Dr.,  64 

Huyghens,  58 

Ingersoll-Sergeant  Drill  Co.,  503 
Isherwood,  Benj.  F.,  472 

Jacobus,  D.  S.,  511,  689,  726,  780 

Johnson,  J.  B.,  309,  314 

Johnson,  W.  B.,  475 

Johnson,  W.  R.,  290 

Jones,  Horace  K.,  387 

Jones  &  Lamson  Machine  Co.,  £54 

Jones  &  Laughlins,  867,  885 

Kapp,  Gisbert,  1033 
Keep,  W.  J.,  365,  951 
Kennedy,  A.  B.  W.,  355,  525,  764 
Kernot,  Prof.  494 
Kerr,  Walter  C.,  781 
Kiersted,  W.,  292 
Kimball,  J.  P.,  499,  632,  637 
Kinealy,  J.  H.,  537 


LIST   OF   AUTHORITIES. 


1073 


Kirk.  A.  C.,  705 
Kirk,  Dr.,  1004 
Kirkaldy,  David,  296 
Kopp,  H.  G.  C.,  472 
Kuichling,  E.,  578 
Kutter,  559 

Landreth,  O.  H.,  712 

Langley,  J.  W.,  409,  410,  412 

Lanza,  Gaetano,  310,  369,  864,  977 

La  Rue,  Benj.  F.,  248 

Leavitt,  E.  D.,  788 

LeChatelier,  M.,452 

Le  Conte,  J.,  565 

Ledoux,  M.,  981 

Leggett,  T.  H.,  1049 

Leonard,  H.  Ward,  1026 

Leonard,  S.  H.,  686 

Lewis,  Fred.  H.,  186,  189,  397 

Lewis,  I.  N.,  498 

Lewis,  Wilfred,  352,  362,  378,  899 

Linde,  G.,  989 

Linden  thai,  Gustav,  385 

Lloyd's  Register,  264,  266,  700 

Loss,  H.  V.,  306 

Love,  E.  G.,  656 

Lovett,  T.  p.,  256 

Lyne,  Lewis  F.,  718 

McBride,  James,  974 

MacCord,  C.  W.,  898 

Macdonald,  W.  R.,  956 

Macgoveru,  E.  E.,  545 

Mackay,  W.  M.,  542,  544 

Mahler,  M.,  633 

Main,  Chas.  T.,  590,  780,  790 

Mannesmann,  L.,  332 

Maiming,  Chas.  H.,  675,  823 

Marks,  Win.  D.,  793,  811 

Master  Car  Builders'  Assoc.,  376 

Mattes,  W.  F.,  399 

Matthiessen,  1029 

Mayer,  Alfred  M.,  468 

Mehrtens,  G.  G.,  395,  405 

Meier,  E.  D.,  688 

Meissner,  C.  A.,  370 

Melville,  Geo.  W.,  674 

Mendenhall,  T.  C.,23 

Merriman,  Mansfield,  241,  260,  282 

Metcalf,  William,  240,  412 

Meyer,  J.  G.  A.,  795,  856 

Meystre,  F.  J..  472 

Miller,  Metcalf  &  Parkin,  412 

Miller,  T.  Spencer,  344,  927 

Mitchell,  A.  E.,  855,  856 

Molesworth,  Sir  G.  L.,  562,  658 

Molyneux  and  Wood,  736 

Moore,  Gideon  E.,  653 

Morin,  435,  930,  933 

Morison,  Geo.  S.,  381,  393 

Morrell,  T.  T.,  407 

Morris,  Tasker  &  Co.,  195,  196 

Mumford,  E.  R.,  1006 

Murgue,  Daniel,  521 

Nagle,  A.  F.,  292,  606,  878 
Napier,  474,  669 
Nason  Mfg.  Co.,  48,  542 
National  Pipe  Bending  Co.,  198 


Nau,  J.  B.,  367,  409 

Newberry,  J.  S.,  624 

Newcomb,  Simon,  432 

New  Jersey  Steel  &  Iron  Co.,  253,  310 

Newton,  Sir  Isaac,  475 

Nichol,  B  C.,  473 

Nichols.  285 

Norris,  R.  Van  A.,  521 

Nor  walk  Iron  Works  Co.,  488,  504 

Nystrom,  John  W.,  265 

Ordway,  Prof.,  469 

Paret,  T.  Dunkin,  967 

Parker,  W.,  354 

Parsons,  H.  de  B.,  361 

Passburg,  Emil,  466 

Pattinson,  John,  629 

Peclet,  M.,  471,  478,  731 

Pelton  Water  Wheel  Co.,  191,  574,  585 

Pence,  W.  D.,  294 

Pencoyd  Iron  Works,  179,  232,  868 

Pennell,  Arthur,  555 

Pennsylvania  R.  R.  Co.,  307,  375,  899 

Philadelphia  Engineering  Works,  526 

Philbrick,  P.  H.,  446 

Phillips,  W.  B.,  629 

Phoenix  Bridge  Co.,  262 

Phoenix  Iron  Co.,  181,  257 

Pierce,  C.  S.,424 

Pierce,  H.  M  ,  641 

Pittsburg  Testing  Laboratory,  243 

Platt,  John,  617 

Pocock,  F.  A.,  505 

Porter,  Chas.  T.,  662,  787,  820 

Potter,  E.  C.,  646 

Pottsville  Iron  &  Steel  Co.,  250 

Pouillet,  455 

Pourcel,  Alexandre,  404 

Poupardin,  M.,  687 

Powell,  A.  M.,975 

Pratt  &  Whitney  Co.,  892,  972 

Price,  C.  S.,  638 

Prony,  564 

Pryibil,  P.,  977 

Quereau,  C.  H.,  858,  862 

Ramsey,  Erskine,  638 

Rand  Drill  Co.,  490,  505 

Randolph  &  Clowes,  198 

Rankine,  W.  J.  M.,  various 

Ransome,  Ernest  L.,  241 

Raymond,  R.  W.,  631,  650 

Reese,  Jacob,  966 

Regnault,  M.,  various 

Reichhelm,  E.  P.,  651 

Retinie,  John,  928 

Reuleaux,  various 

Richards,  Frank,  488,  491,  500 

Richards,  John,  965,  976 

Richards,  Windsor,  404 

Riedler,  Prof.,  507 

Rites,  F.  M.,  783,  818 

Roberts-Austen,  Prof.,  451 

Robinson,  H.,  1051 

Robinson,  S.  W.,  583 

Rock  wood,  G.  J.,  781 

John  A.  Roebling's  Sons'  Co.,  214,  921 


1'0?4 


LIST   OF  AUTHORITIES. 


Roelker,  C.  R.,  265 
Roney,  W.  R.,  711 
Roots,  R  H.  &  F.  M.,526 
Rose,  Joshua,  414,  869,  970 
Roth  well,  R.  P.,  637 
Rowland,  Prof.,  456 
Royce,  Fred.  P.,  1053 
Rudiger,  E.  A.,  671 
Ruggles,  W.  B.,  Jr.,  361 
Russell,  S.  Bent,  567 
Rust  and  Coolidge,  290 

Sadler,  S.  P.,  639 
Saint  Yenant,  282 
Salom,  P.  G.,  406,  1056 
Sandberg,  C.  P.,  384 
Saunders,  J.  L.,  544 
Saunders,  W.  L.,  505 
Scheffler,  F.  A.,  681 
Schroter,  Prof.,  788 
Schutte,  L.,  &  Co.,  527 
Seaton,  various 
Sellers,  Coleman,  890,  953,  975 
Sellers,  Wm.,  204 
Sharpless,  S.  P.,  311,  639 
Shelton,  F.  H.,  653 
Shock,  W.  H.,  307 
Simpson,  56 
Sinclair,  Angus,  863 
Sloane,  T.  O'Connor,  1027 
Smeaton,  Wm.,  493 
Smith,  Chas.  A.,  537,  874 
Smith,  C.  Shaler,  256,  865 
Smith,  Hamilton,  Jr.,  556 
Smith,  Jesse  M.,  1050 
Smith,  J.  Bucknall,  225,  303 
Smith,  Oberlin,  865,  973 
Smith,  R.  H.,  962 
Smith,  Scott  A.,  874 
Snell,  Henry  L,  514 
Stahl,  Albert  W.,  599 
Stanwood,  J.  B,,  803,  809,  813,  818 
Stead,  J.  E.,  409 
Stearns,  Albert,  465 
Stein  and  Schwarz,  410 
Stephens,  B.  F.,  292 
Stillman,  Thos.  B.,  944 
Stockalper,  E.,  493 
Stromeyer,  C.  E.,  396 
Struthers,  Joseph,  451 
Sturtevant,  B.  F.,  Co.,  487,  578 
Stut,  J.  C.  H.,  844 
Styffe,  Kuut,  383 
Suplee,  H.  H.,  769,  772 
Suter,  Geo.  A.,  524 
Sweet,  John  E.,  826 

Tabor,  Harris,  751 
Tatham  &  Bros.,  201 
Taylor,  Fred.  W.,  880 
Taylor,  W.  J.,  646 
Theiss,  Emil,  818 
Thomas,  J.  W.,  369 
Thompson,  Silvanus  P.,  1064,  1066 
Thomson,  Elihu,  1052 
Thomson,  Sir  Wm.,  461,  1039 
Thurston,  R.  H.,  various 
Tilghman,  B.  F.,  966 
Tompkins,  C.  R.,  336 


Torrance,  H.  C.,  401 
Torrey,  Joseph,  582,  820 
Tower,  Beauchamp,  931,  934 
Towne,  Henry  R.,  876,  907,  911 
Townsend,  David,  973 
Trautwine,  J.  C.,  59,  118,  311,  482 
Trautwine,  J.  C.,  Jr.,  255 
Trenton  Iron  Co.,  216,  223,  230,  915 
Tribe,  James,  765 
Trotz,  E  ,  453 
Trowbridge,  John,  467 
Trowbridge,  W.  P.,  478,  513,  733 
Tuit,  J.  E.,  616 
Tweddell,  R.  H.,  619 
Tyler,  A.  H.,  940 

Uchatius,  Gen'l,  321 

Unwin,  W.  Cawthorne,  various 

Urquhart,  Thos.,  645 

U.  S.  Testing  Board,  308 

Vacuum  Oil  Co.,  943 
Vair,  G.  O.,  950 
Violette,  M.,  640,  642 
Vladomiroff,  L.,  316 

Wade,  Major,  321,  374 

Wailes,  J.  W..  404 

Walker  Mfg.  Co.,  905 

Wallis,  Philip,  858 

Warren  Foundry  &  Mach.  Co.,  189 

Weaver,  W.  D.,  1043 

Webber,  Samuel,  591,  963 

Webber,  W.  O.,  608 

Webster,  W.  R.,  389 

Weidemann  &  Franz,  469 

Weightman,  W.  H.,  762 

Weisbach,  Dr.  Julius,  various 

Wellington,  A.  M.,  290,  928,  93ft 

West,  Chas.  D.,  916 

West,  Thomas  D.,  328 

Westinghouse  &  Galton,  928 

Westinghouse  El.  &  Mfg.  Co.,  1043 

Weston,  Edward,  1029 

Whitham,  Jay  M.,  472,  769,  792,  840 

Whitney,  A.  J.,  389 

Willett,  J.  R.,  538,  540 

Williamson,  Prof.,  58 

Wilson,  Robert,  284 

Wheeler,  H.  A.,  908 

White,  Chas.  F.,  714 

White,  Mannsel,  408 

Wohler,  238,  240 

Wolcott,  F.  P.,  949 

Wolff,  Alfred  R  ,  494,  517,  528,  538 

Wood,  De  Volson,  various. 

Wood,  H.  A.,  9 

Wood,  M.  P.,  386,  389 

Wood  bury,  C.  J.  H.,  537,  931 

Wootten,  J.  E.,  855 

Wright,  C.  R.  Alder,  331 

Wright,  A.  W.,289 

Yarrow,  A.  F.,  710 
Yarrow  &  Co.,  307 
Yates,  J.  A..  287 

Zahner,  Robert,  499 
Zeuner,  827 


INDEX. 


Abbreviations,  1 

Abrasive  processes,  965 

Abscissas,  69 

Absolute  zero,  461 

Absorption    refrigerating     machines, 

984 

Accelerated  motion,  427 
Acceleration,  423 

work  of,  430 

Accumulators,  electric,  1055 
Adiabatic  curve,  742 

expansion,  742 
Air,  481-527 

and  vapor,  weights  of,  484 

compressed,  488,  499 

density  and  pressure,  481 

-pumps,  839 

-thermometer,  454 
Algebra,  33 
Algebraical  signs,  1 
Alligation,  10 
Alloys,  319-338 

aluminum,  328 

aluminum-silicon-iron,  330 

antimony,  336 

bismuth,  382 

caution  as  to  strength,  329 

copper-nickel,  326 

copper-tin,  319 

copper-tin-zinc,  322 

copper-zinc,  321,  325 

copper-zinc-iron,  326 

for  bearings,  333 

fusible,  333 

manganese-copper,  331 

steels,  407 

Alternating  currents,  1070 
Altitude  by  barometer,  483 
Aluminum,  167 

alloys  of,  319,  328 

brass,  329 

bronze,  328 

bronze  wire,  225 

hardened,  330 

properties  and  uses,  317 

steel,  409 

wire,  225 
Ammonia  ice-machines,  983 

vapor,  properties  of,  993 
Amperage    permissible    in     magnets, 
1066,  1068 


Analyses  of  alloys  (see  Alloys) 

of  asbestos,  235 

of  coals  (see  Coal) 

of  fire-clay,  234 

of  magnesite,  235 

of  steel  (see  Steel) 

of  water,  553 
Analytical  geometry,  69 
Anemometer,  491 
Angle-bars,    sizes    and    weights,   179 

weight  and  strength,  279 
Angle,  the  economical,  447 
Angles,  plotting  without  protractor,  52 

problems  in,  37-38 
Angular  velocity,  425 
Animal  power.  433 

Annealing,    effect    on    conductivity, 
1029 

iron,  effect  of  on  magnetic  capacity, 

non-oxidizing  process  of,  387 

of  steel,  394,  413 
Annuities,  15-17 
Annular  gearing,  898 
Anthracite,  analyses  of,  624 

gas,  647 

space  occupied  by,  625 

value  of  sizes  of,  632 
Anti-friction  metals,  932 
Antimony,  167 

alloys,  336 
Apothecaries'    measure   and   weight 

18,  19 

Arc  lamps,  lighting  power  of,  1052 
Arches,  tie- rods  for,  281 
Area  of  circles,  103,  108 

of  irregular  figures,  55,  56 
Arithmetic,  2 

Arithmetical  progression,  11 
Armature  circuit,  E.  M.  F.  of,  1062 
Asbestos,  235 

Asymptotes  of  hyperbola  71 
Atmosphere,  moisture  in,  483 
Atomic  weight  of  elements,  163 
Avoirdupois  weight,  19 
Axles,  steel,  specifications  for,  401 

strength  of,  299 

Babbitt  metals,  336 
liabcock  &  Wilcox  boilers,  tests  with 
different  coals,  030 

107.J 


107G 


Bagasse  as  fuel,  643 
Balance,  to  weigh  on  an  incorrect,  19 
Ball  bearings,  940 
Bands  and  belts,  theory  of,  876 
Bands  for  carrying  grain,  911 
Barometric  readings,  482 
Barrels  (see  Casks),  64 
?  No.  of  in  tanks,  126 
Baume's  hydrometer,  165 
Bazin's  experiments  on  weirs,  58? 

formula,  flow  of  wat  er,  563 
Beams  and  channels,  Trenton,  278 
Beams,  flexure  of,  267 

of  uniform  strength,  271 

safe  load  of  pine,  1023 

safe  loads,  269 

strength  of,  268 
Bearing-metal  alloys,  333 
Bearing-metals,  anti-friction,  932 
Bearings  (see  Journal-bearings) 

ball,  940 

for  high  speeds,  941 

pivot,  939 

Bed-plates  of  engines,  817 
Belt  cement,  887 

conveyors,  911 

dressings,  887 
Belting,  876-887 

strength  of,  302,  886 
Belts,  open  and  crossed,  874,  884 
Bends  and  curves,  effect  of  on  flow  of 

water,  578 
Bends,  valves,  etc.,  resistance  to  flow 

in,  488,  672 
Bessemer  steel,  391 
Bessernerized  cast-iron,  375 
Bevel  wheels,  898 
Binomials,  theorem,  33,  35 
Birmingham  Gauge,  28 
Bismuth,  167 

alloys,  332 

Bituminous  coal  (see  Coal) 
Blast-furnace  boilers,  689 
Blocks  or  pulleys,  438 

strength  of,  906 
Blowers  and  fans,  511-526 

experiments  with,  514 

for  cupolas,  519,  950 

positive  rotary,  526 

steam-jet,  527 
Blowing  engines,  526 
Blue  heat,  effect  on  steel,  395 
Board  measure,  20 
Boiler  compounds,  717 

explosions,  720 

furnaces,  height  of,  711 

1  leads,  706 

heads,  strength  of,  284-286 

scale,  552 

ship,  and  tank  plates,  399 

the  steam,  677-741 

tubes,  196 

tubes,  holding  power  of,  307 
Boilers  (see  steam-boilers) 

for  steam -heating,  538 

locomotive,  855 
Boiling-point  of  water,  550 
Boiling-points,  455 
Bolts  and  nuts  209,  211 


Bolts,  holding  power  of,  290 

strength  of,  29> 
Brass  alloys,  325 

composition  of  rolled,  203 

sheet  and  bar.  203  « 

tubing,  198-200 

wire  and  plates,  202 
Brick,  fire,  sizes  of,  238,  234 

strength  of.  3o2, 312 
Bricks,  absorption  of  water  by,  312 

magnesia,  235 
Brickwork,  weight  of,  169 
Bridge     members,    working     strain, 
262 

proportioning      materials     in,    381 

trusses,  443 

Brine,  specific  gravity,  etc.,  464,  994 
Bronze  (see  Alloys),  319 
Bronzes,  ancient,  323 
Building  construction,  1019 

materials,    sizes  and    weights,  170 

184 

Buoyancy,  550 
Burr  truss,  443 

Cables,  electric,  insulated,  1033 

wire,  222,  223 

Cable-ways,  suspension,  915 
Cadmium,  167 
Calculus,  differential,  72 
Caloric  engines,  851 
Calorimeters,  steam,  728 
Calorimetric  tests  of  coal,  636 
Cam.  the,  438 

Canals,  speed  of  vessels  on,  1008 
Canvas,  strength  of,  302 
Carbon,  burned  out  of  steel,  402 

effect  of  on  strength  of  steel,  389 
Car-heating  by  steam,  538 
Casks.  64 
Castings,  iron,  analyses  of,  373 

shrinkage  of,  951 

steel,  405 

weight  of,  from  pattern,  952 
Cast-iron,  365-375 

and  steel  mixtures,  375 

bad,  375 

i)  alleable.  375 

specific  gravity,  374 

specifications,  374 

strength  of,  369,  374 
Catenary,  construction  of,  51 

the  wire  rope,  919 
Cement,  weight  of,  170 

for  belts,  887 

mortar,  strength  of,  313 
Centigrade  and  Fahrenheit  table,  449 
Centre  of  gravity,  418 

of  gyration.  420 

of  oscillation,  421 

of  percussion,  421 
Centrifugal  fans,  511 

force,  423 

force  in  fly-wheels,  820,  822 

tension  of  belts.  876 
Cera-}  erduta  process,  alloys  for,  323 
Chain-blocks,  907 

cables,  308,  340 
Chains,  crane,  232 


INDEX. 


Chains,  weight  and  strength,  307,  339 
Channel-beams,    sizes     and    weight, 

178,  180 

Channels,  steel,  strength  of,  275 
Charcoal,  640 
making  results,  641 

pig-iron,  365,  374 

weight  of,  170 
Chemical  elements,  163 
Chimneys,  731-741 

brick,  737 

for  ventilation.  533 

stability  of,  738 

size  of,  734 

steel,  740 

sheet-iron,  741 

table  of  sizes  of,  735 
Chords  of  circles,  57 
Chrome  steel,  409 
Circle,  equation  of,  70 

measures  of,  57-58 
Circles,  problems,  39-40 

tables  oi,  103.  108 
Circular  arc,  length  of,  57,  58 

arcs,  tables  of,  114,  115 

functions  in  calculus,  78 

measure,  20 

ring,  59 

Circulating-pump,  839 
Circumference  of  circles,  103,  108,  113 
Cisterns,  cylindrical,  121,  126 
Clearance  in  steam-engines,  751,  792 
Coals,  analyses  of,  624-631 

calorimetric  tests,  636 

evaporative  power  of,  636 

heating  value  of,  634 

relative  value  of,  633 
Coal  gas,  illuminating,  651 

hoisting,  343 

products  of  distillation  of,  639 

washing,  638 

weathering  of,  637 
Coefficient  of  elasticity,  237 
Coefficients  of  friction,  928-932 
Coiled  pipes,  199 
Coils,  heating  of,  1036 
Coke,  637 

manufacture,  by-products,  639 
Coking,  experiments  in,  637 
Cold  drawing  steel,  305 
Cold,  effect  of  on  iron  and  steel,  383 

rolling,  effect  of,  393 
Columns,  built,  256 

cast-iron,  weight  of,  185 

iron,  tests  of.  305 

strength  of,  246-250 
Combined  stresses,  282 
Combination,  10 
Combustion,  heat  of,  456,  621 

gases  of,  622 

theory  of,  620 
Composition  of  forces,  415 
Compound  engines,  761-768 

engines,  diameter  of  cylinder,  768 

engines,  economy  of,  780 

engines,  work  of  steam  in,  767 

interest,  14 

locomotives,  862,  863 

numbers,  5 


Compound  units  of  weight  and  ineas 

ure.  27 
Compressed  air,  488,  499 

cranes,  912 

motors,  507 

transmission,  488 

steel,  410 
Compression  and  expansion  of  air,  502 

in  steam-engines,  751 

unit  strains,  380 
Compressive  strength,  244 

of  iron  bars,  304 
Compressors,  air,  503 
Condenser,  evaporative  surface  844 
Condensers,  839-846 
Condenser-tubes,  transmission  of  hern 

in,  473 
Condensing  water,  continuous  use  of, 

Conduction  of  he*t,  468 
Conductivity,  electrical,  1028 
of  steel,  influence  of  composition  on; 

Conductors,  electrical,  1029 
Cone,  measures  of,  61 

pulleys,  874 
Conic  sections,  71 
Conoid,  parabolic,  63 
Connecting  rods,  799 

rods,  tapered,  801 
Conservation  of  energy,  432 
Construction  of  buildings,  1019 
Convection  of  heat,  471 
Conveyors,  belt,  911 
Cooling  of  air  for  ventilation,  531 
Co-ordinate  axes,  69 
Copper,  167 

at  high  temperatures,  strength  of, 

balls,  hollow,  289 

round  bolt.  203 

strength  of,  300 

tubing,  200 

wire  and  plates,  202 

wire,  tables  of,  218-220 

wire,  resistance   of  hot  and    cold, 
1034,  1035 

wire,  cost  of  for  long-distance  trans 

mission,  1045 
Cordage,  341,  344,  906 
Cork,  properties  of,  316 
Corrosion  of  iron,  385 

of  steam-boilers,  716,  719 
Corrosive  agents  in  atmosphere,  3CL; 
Corrugated  iron,  181 

furnaces,  266,  702,  709 
Cosecant  of  an  angle,  65 
Cosine  of  an  angle,  65 
Cosines,  tables  of,  159 
Cost  of  coal  for  steam-power,  789 

of  steam-power,  790 
Cotangent  of  an  angle,  65 
Counterbalancing  engines,  788 

locomotives,  864 

of  winding:  engines,  909 
Couples,  418 

Coverings  for  steam-pipes,  469 
Cox's  formula  for' loss  of  head,  575 
CfrtneSj  classification  of,  911 


1078 


INDEX. 


Cranes,  compressed-air,  912 

stress  in,  440 
Crank  angles,  830 

arms,  805,  806 

pins,  801-804 

shafts,  813 
Cross-head  guides,  798 

pins,  804 

Crucible  steel,  410 

Crushing  strength  of  masonry  mate- 
rials, 312 

Cubature  of  volumes  of  revolution,  75 
Cube  root,  8 

Cubes  and  cube'roots,  table  of,  86 
Cubic  measure,  18 
Cupolas,  blast-pipes  for,  519 

blowers  for,  519 

practice,  946 
Current  motors,  589 
Currents,  electric,  1030 
Cutting  stone  with  wire,  966 
Cycloid,  construction  of,  49 

'differential  equation  of,  79 

measure  of,  60 
Cycloidal  teeth  of  gears,  892 
Cylinders  and  pipes,  contents  of,  120, 
121 

condensation,  752,  753 

engine,  dimensions  of,  792 

hollow,  resistance  of,  264 

hollow,  strength  of,  287-289 

measures  of,  61 
Cylindrical  ring,  62 

Dangerous  steam-boilers,  720 
Dam,  stability  of  a.  417 
D'Arcy's  formula,  flow  of  water,  563 
Decimal  equivalents  of  fractions,  3,  4 
Decimals,  3 

squares  and  cubes  of,  101 
Deck-beams,  sizes  and  weights,  177 
Delta  metal,  326 

wire,  225 

Denominate  numbers,  5 
Deoxidized  bronze,  327 
Derricks,  stresses  in,  441 
Diametral  pitch,  888 
Differential  calculus,  72 

forms,  integrals  of,  78, 79 

gearing,  898 

pulley,  439 

screw,  439 

screw,  efficiency  of,  974 

windlass,  439 
Discount  and  interest,  13 
Disk  fans,  524 

Displacement  of  vessels,  1001,  1008 
Draught  of  chimneys,  731 
D ipn  wing-presses,  blanks  for,  973 
Drilling  holes,  speed  of,  956 

machines,  electric,  956 
Drop-press,  pressure  of,  973 
Drums  for  hoisting-ropes,  917 
Drying  and  evaporation,  462 
Drying  in  vacuum,  466 
Dry  measure,  18 
Ductility  of  metals,  169 
Dust  explosions,  642 

fuel,  642 


Durability  of  iron,  385 
Durand's  rule,  56 

Duty  trials  of  pumping-engines,  609 
Dynamo    and    engine,    efficiency    of, 
1048 

electric  machines,  1061 
Dynamos,  designing  of,  1064 

efficiency  of,  1066 
Dynamometers,  978-980 

Earths,  weight  of,  170 
Earth-filling,  weight  of,  170 
Eccentric  loading  of  columns.  255 
Eccentrics,  steam-engine,  816 
Economizers,  fuel,  ^15 
Edison    or  circular  mil  wire  gauge, 

29,30 
Efficiency  of  a  machine,  432 

of  boilers,  683,  689 

of  electric  transmission,  1047 

of  pumps,  603,  608 

of  steam-engines,  749,  775 
Effort,  definition  of,  429 
Elastic  limit,  236 

elevation  of,  238 
Elastic  resilience,  270 
Elasticity,  modulus  of,  237,  314 
Electric  accumulators,  1055 

conductivity  of  steel,  403 

generator,  efficiency  of,  1048 

heating,  546,  1054 

lighting,  1051 

motor,  1070 

pumping-plant,  1049 

railways,  1050 

transmission,  1038 

transmission,  economy  of,  1039 

welding,  1053 
Electrical  engineering,  1024 

horse-powers,  table  of,  1042 

resistance,  1028 

standards  of  measurement,  1024 

units,  1024 

Electricity,    analogy    with     flow    of 
water,  1027 

heating  by,  546,  1054 
Electro-chemical  equivalents,  1057 

magnetic  measurements,  1058 

magnets,  1058 

magnets,  polarity  of,  1060 
Electrolysis,  1057 
Elements,  chemical,  163 

of  machines,  435 
Ellipse,  construction  of,  45 

equation  of,  70 

measures  of,  59 
Ellipsoid,  63 

Elongation,  measure  of,  243 
Emery,  grades  of,  968 

wheels,  967-969 
Endless  screw,  440 
Energy,  conservation  of,  432 

of  recoil  of  guns,  431 

or  stored  work,  429 

sources  of,  432 

Engine-frames  or  bed-plates,  817 
Engines  (see  Steam-engines^ 

blowing,  526 

gas,  847 


INDEX. 


1079 


Engines,  gasoline,  850 

hoisting,  908 

hot-air,  851 

marine,  sizes  of  steam-pipes,  674 

naphtha,  851 

petroleum,  850 

steam,  742-847 
Epicycloid,  50 
Equalization  of  pipes,  492 
Equation  of  payments,  14 
Equations,  algebraic,  34 
Equilibrium  of  forces,  418 
Equivalent  orifice,  533 
Erosion  by  flow  of  water,  565 
Evaporating  by  exhaust-steam,  465 
Evaporation  and  drying,  462 

by  the  multiple  system,  465 

from  open  channels,  463 

from  reservoirs,  463 

latent  heat  of,  461 

table  of  factors  of,  695 
Evaporators,  fresh-water,  1016 
Evolution,  7 

Exhaust-steam  for  heating,  780 
Exhausters,  steam-jet,  5^7 
Expansion  by  heat,  459 

of  iron  and  steel,  385 

of  steam,  742 

of  steam,  real  ratios  of,  750 

of  wood,  311 

Explosive  energy  of  steam-boilers,  720 
Exponents,  theory  of,  36 
Exponential  functions,  m  calculus,  78 
Eye-bars,  tests  of,  304,  393 

Factor  of  safety,  314 

in  steam-boilers,  700 
Factors  of  evaporation,  tables,  695 
Fahrenheit  and  Centigrade  table,  450 
Failures  of  steel,  403 
Falling  bodies,  423-426 
Fans  and  blowers,  511-526 
Feed-pumps,  843 

water,  cold,  strains  caused  by,  727 

water,  heater,  Weir's,  1016 

water,  heaters,  727 

Avater,  purifying,  554 
Fibre-graphite,  945 
Fifth  roots  and  fifth  powers,  102 
Fink  roof-truss,  446 
Fire  brick,  sizes  of,  233,  234 

clay,  analysis  of,  234 

engines,  capacities  of,  580 
Fireless  locomotive,  866 
Fireproof  buildings,  1020 
Fire-streams,  579 
Fire,  temperature  of,  6'22 
Flagging,  transverse  strength  of,  313 
Flanges,  pipe,  192,  193,  676 
Flat  plates  in  steam-boilers,  701,  709 

plates,  strength  of,  283 
Flexure  of  beams,  267 
Flooring  material,  weight  of,  281 
Floors,  strength  of,  1019,  1021 
Flowing  water,  horse-power  of,  589 
Flow  of  air  in  pipes,  485 

of  air  through  orifices,  484 

of  compressed  air,  489,  493 

of  gas  in  pipes,  657 


Flow  of  metals,  973 

of  steam  in  pipes,  669 

of  water  from  orifices,  555,  584 

of  water  in  house  service-pipes,  578 

of  water  over  weirs,  586 
Flues,  collapse  of,  265 

corrugated,  British  rules,  266,  702 

corrugated,  U.  S.  rules,  709 

(see  also  Tubes  and  Boilers) 
Fly-wheels,  817-824 

arms  of,  820 

wire-wound,  824 

wooden,  823 

Flynn's  formula,  flow  of  water,  562 
Foot,  decimals  of  in  fractions  of  inch 
112 

pound,  unit  of  work,  428 
Forced  draught  in  marine  practice 

1015 
Force  of  a  blow,  430 

of  acceleration,  427 

unit  of,  415 
Forces,  composition  of,  415 

equilibrium  of,  418 

parallel,  417 

parallelogram  of,  416 

parallelopipedon  of,  416 

polygon  of,  416 

resolution  of,  415 
Forcing  and  shrinking  fits,  973 
Forging,  hydraulic,  618,  620 

tool-steel,  413 
Foundry,  the,  946-956 
Fractions,  2 

Francis's  formula  for  weirs,  586 
Freezing  of  water,  550 
French  measures  and  weights,  21-26 
Friction  and  lubrication,  928-945 

brakes,  980 

of  air  in  passages,  531 

of  steam-engines,  941 

rollers,  940 

work  of,  938 

Fractional  heads,  flow  of  water,  577 
Fuel,  620-651 

economizers,  715 

gas,  646 

pressed,  633 

theory  of  combustion  of,  620 

weight  of,  170 

Fuels,  -classification  of,  623,  624 
Furnace,  downward  draught,  635.  712 

kinds  of  for  different  coals,  635 

formulae,  702 
Furnaces,  corrugated,  266,  702,  709 

for  boilers,  711 

gas-fuel,  651 

use  of  steam  in,  650 
Fusible  alloys,  333 

plugs  for  boilers,  710 
Fusibility  of  metais,  169 
Fusing-disk,  Reese's,  966 
Fusing  of  wires  by  electric  currents, 
1037 

temperatures,  455 

g,  value  of,  424 

Gallons  and  cubic  feet,  table,  122 

Galvanized  wire  rope,  228 


1080 


INDEX. 


Gas,  ammonia,  992,  993 

-engines,  8-17 

-fired  steam-boilers,  714 

flow  of  in  pipes,  657 

fuel,  646 

illuminating,  651 

illuminating,  fuel  value  of,  656 

pipe,  sizes  and  weights,  188,  194 

producers,  649,  650 

sulphur-dioxide,  982 
Gases,  expansion  of  by  heat,  459 

heat  of  combustion  of,  456 

weight  and  specific  gravity  of,  166 

properties  of,  479 

specific  heat  of,  458 

waste,  use  under  boilers,  C89,  690 
Gasoline-engines,  850 
Gauges,  wire  and  sheet-metal,  28-31 
Gearing,  efficiency  of,  899 

frictional,  905 

of  lathes,  955 

speed  of,  905 

toothed-wheel.  439,  887-906 
Gear- teeth,  strength  of,  900-905 

-wheels,  size  and  speed  of,  891 
Geometrical  problems,  37 

progression,  11 

propositions,  53 
German  silver,  326,  332 

silver,  strength  of,  300 
Girders  for  boilers,  703 
Glass,  skylight,  184 

strength  of,  308 
Gold,  167 

Gordon's  formula,  247 
Governors,  8'56 
Grain,  weight  of,  170 
Granite,  strength  of,  312 
Grate  and  heating  surface  of  a  boiler, 

678 
Graphite  as  a  lubricant,  945 

paint,  389 
Gravity,  acceleration  due  to,  424 

centre  of,  418 

specific,  163 

Greatest  common  measure,  2 
Greenhouse  heating  by  hot  water,  542 

by  steam,  541 

Green's  fuel  economizers,  712 
Grindstones,  968,  970 
Gyration,  centre  and   radius  of,    247, 
249,  420,  421 

Haulage,  wire-rope,  912 

Hawley  down-draught  furnace,  712 

Heads  of  boilers,  706 

Heat,  448-478 

boiling-points,  455 

conduction  of,  468 

convection  of,  471 

expansion  by,  459 

generated,  by  electric  currents,  1032 

latent,  461 

latent,  of  evaporation,  462 

latent,  of  fusion,  461 

melting-points,  455 

of  combustion.  456 

radiation  of,  467 

specific,  457 


Heat,  storing  of,  789 

transmitting  powers  of  substances, 
478 

unit,  455,  660 
Heaters,  feed-water,  727 
Heating  a  building  to  70°  F.,  545 

and  ventilation,  528-546 

blower  system  of,  545 

by  electricity,  546,  1054 

by  exhaust-steam,  780 

by  hot  water,  542 

of  electric  conductors,  1033 

of  large  buildings,  534 

surface  of  boilers,  678 
Heine  boiler,  test  with  different  coals, 

688 

Helix,  60 

Hodgkinson's  formula,  246 
Hoisting,  906-916 

coal,  343 

engines,  power  of,  908 

pneumatic,  909 

rope,  340 

Hooks,  hoisting,  907 
Horse-gin,  434 

work  of  a,  434 
Horse-power,  429 

constants,  757.  758 

of  flowing  water,  589 

of  steam-boilers,  677.  679 

of  steam-engines,  755 

power-hours.  429 
Hose,  friction  losses  in,  580 
Hot-air  engines,  851 

water  heating,  542 
Howe  truss,  445 
Humidity  in  atmosphere,  483 
Hydraulic  apparatus,  616 

engine,  619 
Hydraulics,  flow  of  water,  555-588 

forging,  618 

grade-line,  578 

power,  617 

pressure  transmission,  616 

rain.  614 
Hydrometer,  165 

Hygrometer,  dry  and  wet  bulb,  483 
Hyperbola,  equation  of,  71 

construction  of,  49 
Hyperbolic  logarithms,  156 

curve  in  indicator  diagrams.  759 
Hypocycloid,  50 

I-beams,  sizes  and  weights,  177 

properties  of.  274 

spacing  of,  273,  280 
Ice  and  snow,  550 
Ice-making  machines,  981-1001 

manufacture,  999 
Illuminating  gas,  651 
Impact  of  bodies,  431 
Incandescent  lamps,  1051 
Inches  and  fractions,   decimals  of  a 

foot,  112 
Inclined  plane,  437 

planes,  hauling  on,  913,  915 

planes,  motion  on,  428 
Incrustation  and  scale,  561,  716 
India  rubber,  tests  of,  316 


1081 


Indicated  horse-power,  755 
Indicator  diagrams,  754,  759 

rigs,  759 

tests  of  locomotives,  863 
Indirect  heating  surface,  537 
Inertia,  415 

moment  of,  247,  419 

of  railroad  trains,  853 
Injectors,  725 

Inspection  of  steam-boilers,  720 
Insulators,  electrical,  1029 
Integral  calculus,  79 
Integrals,  integration,  73-74- 

of  differential  forms,  78,  79 
Intensifier,  the  Aiken,  619 
Interest  and  discount,  13 

compound,  14 
Involute  gear-teeth,  894 

construction  of,  52 
Involution,  6 
Iridium,  167 
Iron, 167 

bars,  sizes  of,  170 

bars,  weight  of,  171 

corrosion  of,  385 

durability  of,  385 

and  steel,  classification  of.  364 

and  steel,  cold  rolling  of,  393 

and  steel,  expansion  of,  385 

and  steel,  strength  of,  296-300 

and  steel,  strength  at  high  temper- 
ature, 382 

and  steel,  strength  at  low  tempera- 
ture, 383 
Irregular  figure,  area  of,  55-56 

solid,  volume  of,  64 
Isothermal  expansion,  742 

Japanese  alloys,  326 
Jet  propulsion  of  vessels,  1014 
Jets,  vertical  water,  579 
Joints,  riveted,  354-363 
Joule^s  equivalent,  456 
Journal-bearings,  810-815 

bearings,  cast-iron,  933 

friction,  930-939 
Journals,  engine,  810-815 

Kerosene  for  scale  in  boilers,  718 
Keys  and  set-screws,  977 

for  mill-gearing,  975 

holding  power  of,  977 
Kinetic  energy,  429 
King-post  truss,  442 
Kirkaldy's  tests  of  materials,  296 
Knot,  or  nautical  mile,  17 
Knots  in  ropes,  344 
Kutter's  formula,  559 

Lacing  of  belts,  883 

Ladles,  foundry,  sizes  of,  953 

Latent  heat,  461 

heat,  of  evaporation,  461 

heat,  of  fusion,  459-461 
Lathe-gearing,  955 

tools,  speed  of,  953 
Lap  and  lead  of  a  valve,  829-833 
Lead,  167 

pipe,  200-201 


Leakage  of  steam  in  engines,  761 

Least  common  multiple,  2 

Leather,  strength  of,  302 

Le  Chatelier's  pyrometer,  451 

Levelling  by  barometer,  482 

Lever,  the  bent,  436 

Levers,  435 

Lignites,  Western,  631 

Lime,  weight  of,  170 

Limestone,  strength  of,  313 

Limit  gauges  for  screw-threads,  205 

Lines  of  force,  1059 

Links,  engine,  816 

Link-motion,  834 

Liquation  of  alloys,  323 

Liquid  measure,  18 

Liquids,  weight  and  sp.  gr.,  164 

Locomotive,  tireless,  866 

Locomotives,  851-866 

dimensions  of,  860 

tests  of.  863 
Logarithmic  curve,  71 

sines,  etc.,  162 
Lo^anthms,  hyperbolic,  156 

differential  of   77 

of  numbers,  127-155 
Logs,  lumber,  etc.,  weight  of,  232 
Loop,  the  steam,  676 
Loss  of  head  in  pipes,  573 
Lubricants,  942 
Lubrication,  942 
Lumber,  weight  of,  232 

Machines,  elements  of,  435 
Machine-shop,  the,  953-978 

shop  practice,  953 

shops,  power  used  in,  965 

screws,  208,  209 

tools,  power  required  for,  960-965 

tools,  proportioning  sizes  of,  975 
Maclaurin's  theorem,  76 
Magnesia  bricks,  235 
Magnesium,  168 
Magnetic  balance,  396 

capacity  of  iron,  effect  of  annealing 
on,  396 

circuit,  1060 

circuit,  units  of,  1058 

field,  strength  of,  1063 
Magnets,  winding  of,  1068 
Malleability  of  metals,  169 
Malleable  castings,  rules  for,  376 

cast-iron,  375 
Mandrels,  sizes  of,  972 
Manganese,  168 

bronze,  331 

influence  of  on  cast-iron,  368 

influence  of  on  steel,  389 

plating  of  iron,  387 

steel,  407 

Mannesman n  tubes,  296 
Manometer,  air,  481 
Man-power,  433 
Manure  as  fuel,  643 
Man-wheel,  434 
Marble,  strength  of,  302 
Marine  engineering,  1001-1018 

engine,  horse-power  of,  760 

engine  practice,  1015 


1082 


Marine  engine,  ratio  of  cylinders,  766, 

773 

Marriotte's  law.  479,  742 
Masonry  materials,  strength  of,  312 
materials,  weight  and  sp.  gr.,  166 
Materials,  163-235 

strength  of,  236-412 
Maxima  and  minima,  76 
Measures  and  weights,  17 

of  work,  power,  and  duty,  27 
Mechanical  equivalent  of  heat,  456 
powers  (see  Elements  of  Machines), 

435 

stokers,  711 
Mechanics,  415-447 

Mekarski  compressed-air  tramway,  509 
Melting-points  of  substances,  455 
Memphis  bridge,  strains  on  steel,  381 
Mensu ration,  54 
Mercury,  168 

bath  pivot,  940 

Merri man's  formula  for  columns,  260 
Mesurg  and  Nouel's  pyrometer,  453 
Metaline,  945 

Metals,  properties  of  the,  167 
table  for  calculating  weight  of,  169 
weight  and  sp.  gr.  of,  164 
Metric  conversion  tables,  22-26 
measures  and  weights,  21-22 
Meters,  water,  579 
Mil,  circular,  18,  29 
Milling  cutters.  957 
cutters  for  gears,  892 
machines,  results  with,  959 
Mill- power,  589 
Miner's  inch,  18 

inch  measurement,  585 
Mine-ventilating  fans,  521 

ventilation.  531 
Modulus  of  elasticity,  237,  314 
Moisture  in  steam,  728 
Molesvvorth's  formula,  flow  of  water, 

562 

Moment  of  force.  416 
of  inertia,  247,  419 
statical,  417 
Momentum,  428 
Morin's  laws  of  friction,  933 
Mortar,  strength  of,  313 
Morion,  Newton's  laws  of,  415 
Motor,  electric,  1070 
Motors,  compressed-air,  507 
Mould  ing  sand,  952 
Moving  strut,  436 
Mules,  power  of,  435 
Multiphase  currents,  1070 
Mushet  steel,  409 

Nails,  213,  215 

screws,  etc.,  holding  power,  289-291 
Naphtha-engines,  851 
Napier's  rule  for  flow  of  steam,  669 
Natural  gas,  649 
Nautical  measure,  17 
Newton's  laws  of  motion,  415 
Nickel,  168 

alloys,  326,  332 

steel.  406 
Nozzles,  measurement  of  water  by,  584 


Nuts  and  bolts,  209,  211 

Ohm,  definition  of,  1025 
Ohm's  law,  1030 
Oil  needed  for  engines,  943 
Oils  and  coal  as  fuel,  646 

lubricating,  944 
Open-hearth  steel.  391 
Ores,  weight  of,  170 
Oscillation,  centre  of,  421 
Oxen,  power  of,  435 
Ordinates,  69 

TT,  value  of,  57 

Packing-rings,  engines,  796 

Paddle-wheels,  1013 

Paint,  qualities  of.  389 

Painting  wood  and  iron  structures, 

Parabola,  construction  of,  48 

equation  of,  70 
Parabolic  conoid,  63 
Parallel  forces,  417 
Parallelogram,  54 

of  forces,  416 
Parentheses,  33 
Partial  payments,  15 
Peat  or  turf,  643 
Pel  ton-wheel  table,  598 

water  wheel,  597 
Pendulum,  422 

conical.  423 

Percussion,  centre  of,  422 
Perforated  plates,  excess  strength  < 

359 

Permutation,  10 
Perpetual  motion,  432 
Petroleum,  645 

as  fuel,  645,  646 

-burning  locomotive,  865 

distillates  of,  645 

engines,  850 

products,  specifications,  944 
Phosphor-bronze,  327,  334 

wire,  225 

Phosphorus,  influence  of  on  cast-iro 
367 

influence  of  on  steel,  389 
Piezometer,  the,  582 
Pig-iron,  anatysisof,  371 

chemistry  of,  370 

grading  of.  365 

influence  of  silicon,  etc.  on,  365 

tests  of,  369 

Pillars,  strength  of,  246 
Pi  tot  tube  gauge,  583 
Pipe, 

fittings,  cast-iron,  187 

lead,  200,  201 

riveted,  197 

sheet-iron  hydraulic,  191 

spiral  riveted,  197 
Pipes,  air-bound,  579 

and  cylinders,  contents  of,  120,  121 

cast-iron,  thickness  of,  188,  190 

cast-iron,  weight  of,  185,  186 

coiled,  199 

effect  of  bends  in,  488,  578,  672 

flow  of  air  in,  485 

ilow  of  gas  in,  657 


INDEX. 


Pipes,  flow  of  steam  in,  669 

iiow  of  water  in,  557 

loss  of  head  in,  573 

riveted,  safe  pressures  in,  707 

steam,  for  steam -heating,  540 

steam,  sizes  for  engines,  673 

water,  riveted,  295 

water,  wrought-iron  and  steel,  295 

wro  light-iron.  194 
Piston-rods,  796-798 

valves,  834 

Pistons,  steam-engine,  795 
Pitch,  diametral,  888 

of  gears,  887 

of  rivets,  357-359 

of  screw  propellers,  1012 
Pivot-bearings,  939 
Plane  surfaces,  mensuration,  54 
Plane,  inclined  (see  Inclined  Plane) 
Plate-iron,  weight  of,  175 

steel,  classification,  399 
Plates,  brass  and  copper,  202 

square  feet  in,  123 

strength  of  for  boilers,  705 
Platinum,  168 

wire,  225 
Pneumatic  hoisting,  909 

postal  transmission,  509 
Polyedrons,  .62 
Polygon  of  forces,  416 
Polygons,  construction  of,  42 

table  of,  55 

tables  of  angles  of,  44 
Population  of  the  United  States,  12 
Potential  energy,  429 
Powell's  screw-thread,  975 
Power,  animal,  433 

of  a  fall  of  water,  588 

rate  of  work,  429 

of  ocean  waves,  599 
Power  stations,  electric,  1050 
Powers  of  numbers,  7,  33 
Pratt  truss,  443 
Pressed  fuel,  632 
Presses,  punches,  etc.,  972 
Prisrn,  measures  of,  60 
Prismoid,  61 

rectangular,  61 
Prismoidal  formula,  62 
Problems,  geometrical,  37-52 

in  circles,  39,  40 

in  lines  and  angles,  37,  38 
Problems  in  polygons,  42 

in  triangles,  41 
Producer  gas,  649 

Progression,    arithmetical    and    geo- 
metrical, 11 
Prony  brake,  979 
Proportion,  5 
Pulley,  differential,  439 
Pulleys,  873-875 

arms  of,  820 

or  blocks,  438 

size  and  speed  of,  884,  891 
Pulsoineter,  612 
Pumping-engine,  tests  of,  783 
Pumping-engines,  duty  trials,  009 

leakage  test,  611 
Pumps,  601-014 


Pumps,  air,  841 

air-lift,  614 

boiler-feed,  605,  726 

capacity  of,  601 

centrifugal,  606.  609 

circulating,  842 

efficiency  of,  603,608 

horse-power  of,  601 

piston  speed  of,  605 

sizes  of,  603 

speed  of  water  through  602 

steam-cylinders  of,  602 

suction  of,  602 

vacuum,  612 

valves  of,  605,  606 
Punched  plates,  strength  of,  354 
Punches  and  dies,  972 
Punching  and  drilling  steel,  395 

steel,  effect  of,  394 
Purifying  feed- water,  554 
Pyramid,  60 
Pyrometers,  451-453 
Pyrometry,  448-454 

Quadratic  equations,  35 
Quadrature  of  a  plane  figure,  74 

of  surfaces  of  revolution,  75 
Quadruple-expansion  engines,  772 
Quantitative   measurement   of    heat, 

455 

Quarter-twist  belts,  883 
Queen-post  truss,  442 

Radiating  surface,  rules  for,  536 

Radiation  of  heat,  467 

Radiators,   transmission   of   heat  by, 

475-477,  545 

Radius  of  gyration,  247,  420,  421 
Railroad  trains,  resistance  of,  851 
Rail-steel,  specifications,  401 
Rails,  maximum  safe  load  on,  865 

steel,  strength  of,  298 
Railways,  narrow-gauge,  865 
Railway  trains,  speed  of,  859 
Ram,  hydraulic,  614 
Ratio  and  proportion,  5 
Reamers,  taper,  972 
Recalescence  of  steel,  402 
Receiver-space  in  engines,  766 
Reciprocals  of  numbers,  80 

use  of,  85 

Red  lead  as  a  preservative,  389 
Reduction,    descending   and    ascend- 
ing, 5 

Reflection  of  heat,  468 
Refrigerating-machim-s,  981  1001 
Registers  and  air-ducts,  539 
Regnaulfs  experiments  on  steam,  6CI 
Resilience,  238 

elastic,  270 
Resistance,  electrical,  1028 

electric,  of  copper  wire,  1030 

electric,  of  steel,  403 

of  ships,  1002 

of  trains,  851 

to  repeated  stresses,  238 
Resolution  of  forces,  415 
Ri  101  n bus  and  rhomboid,  53 
Riveted  joints,  299,  303,  354-362 


1084 


INDEX. 


Riveting-machines,  hydraulic,  618 

of  steam-boilers,  700 

of  steel  plates,  394 

pressures,  362 
Rivets,  diameter  of.  360 

sizes,  etc.,  211 
Rivet-steel,  401 

Roads,  resistance  of  carriages  on  435 
Rock-drills,  air  required  by,  506 
Roof-coverings,  weight  of,  184 

trusses,  446 

Roofing  materials,  181,  184 
Rope-driving,  922-927 

wire,  226-231 
Slopes,  301,  338,  906 

splicing,  341,  345 
Rotary  blowers,  526 

steam-engines,  791 
Rotation,  accelerated,  430 
Rubber  belting,  887 
Rule  of  three,  6 
Rustless  coatings  for  iron,  386 

Safety,  factors  of,  314 
Safety-valves,  721 

Salinometer,  strength  of  brines,  464 
Salt,  manufacture  of,  463 

solubility  of,  464 

weight  of,  170 
Saad- blast,  966 

moulding,  952 
Sawdust  as  fuel,  643 
Sawing  metal,  966 
Scale  and  incrustation,  551 

in  steam-boilers,  716 
Schiele's  anti-friction  curve,  50 

pivot-bearing,  939 
Screw-bolts,  efficiency  of,  974 

differential,  439 

endless,  440 

the,  437 

thread,  Powell's,  975 

threads,  204,  208 

threads,  metric,  956 

propeller,  1010 
Screws  and  screw-threads,  974 

holding  power  of,  290 

machine,  208,  209 
Secant  of  an  angle,  65 
Sectors  and  segments,  59 
Sediment  in  steam-boilers,  717 
Seeger's  fire-clay  pyrometer,  453 
Segments  of  a  circle,  table,  116 
Segregation  in  steel  ingots,  404 
Separators,  steam,  728 
Set-screws,  holding  power  of,  977 
Sewers,  grade  of,  566 
Shaft- bearings,  810 

governor,  838 
Shafting,  867-872 

table  for  laying  out,  872 
Shafts,  engine,  806-815 

fly-wheel,  809 

propeller,  strength  of,  815 
Shapes  of  test-specimens,  243 
Shearing,  effect  of  on  steel,  394 

strength  of  iron,  306 

strength  of  woods,  312 

resistance  of  rivets,  363 


Shearing,  unit  strains,  380 
Shear-poles,  stresses  in,  442 
Sheet-iron  and  steel,  weight  of,  174 
Shells,  spherical  strength,  of,  286 
Shingles,  sizes  and  weight,  183 
Shipping  measure,  19,  1001 
Ships,  resistance  of,  1002 
Shocks,  resistance  to,  240,  241 
Shot,  lead,  204 
Shrinkage  of  castings,  951 
Shrinking-fits,  973 
Signs  of  trigonometrical  functions, 

arithmetical,  1 
Silicon- bronze  wires,  225,  328 
Silicon,  influence  of  on  cast-iron,  36i 

influence  of  on  steel,  389 
Silver,  168 
Simpson's  rule,  56 
Sine  of  an  angle,  65 
Sines,  cosines,  etc.,  table  of,  159 

etc.,  logarithmic,  162 
Sinking-funds,  17 
Siphon,  the,  581 
Slate,  sizes  and  weights,  183 
Slide-valve,  824-835 
Smoke-prevention,  712 
Snow  and  ice,  550 
Soapstone  as  a  lubricant,  945 
Softeners,  use  of  in  foundry,  950 
Softening  hard  water,  555 
Solders,  338 
Solid  bodies,  mensuration  of,  60 

of  revolution,  62 

measure,  18 
Specific  gravity,  163 

gravity  of  alloys,  320,  323 

gravity  of  cast-iron,  374 

gravity  of  gases,  166 

gravity  of  steel,  403,  411 

gravity  of  stones,  brick,  etc.,  166 

heat,  457 

heat  of  air,  484 
Specifications  for  axles,  steel,  400 

for  car-axles,  401 

for  cast-iron,  374 

for  crank-pin  steel,  400 

for  oils,  944 

for  plate-steel,  399,  400 

for  rail-steel,  401 

for  rivets,  401 

for  spring-steel,  400 

for  steel,  397 

for  steel  castings,  406 

for  steel  rods,  400 

for  wrought  iron,  378 
Speed  of  cutting  tools,  953,  954 

of  vessels,  1006 
Sphere,  measures  of,  61 
Spheres,  table  of,  118 

weights  of,  169 
Spherical  polygon,  area  of,  61  • 

segment,  62 

shells,  strength  of,  286 

steam-engine,  792 

triangle,  area  of,  61 

zone,  62 
Spheroid,  63 

Spikes,  sizes  and  weights,  212,  213 
Spindle,  surface  and  volume,  03,  64 


INDEX. 


10S5 


Spiral,  construction  of,  50 
gears,  897 
measures  of,  60 

Splicing  of  ropes,  341 
wire  ropes,  345 

Spring-steel,  specifications,  400 
strength  of,  299 

Springs  for  governors,  838 
formula  for,  347,  353 
tables  of,  349,  353 

Square  measure,  18 
root,  8 

Squares  and  cubes  of  decimals,  101 
and  square  roots,  table  of,  86 

Stability,  417 

Stand-pipes,  design  of,  292-294 

Statical  moment,  417 

Stay-bolt  iron,  379 

Stay-bolts  for  boilers,  710 

Stayed  surfaces,  strength  of,  286 

Stays  for  boilers,  703,  710 

Steam,  659-676 
boiler,  water-tube,  688,  689 
boilers,  677-740 
boilers,  air-space  in  grate,  681 
boilers,  allowable  pressures,  706 
boilers,  economy  of,  682 
boilers,  efficiency  of,  63),  683 
boilers,  explosive  energy  of,  720 
boilers,  factor  of  safety,  700 
boilers,  forced  draught,  714 
boilers,  flues  and  passages,  680 
boilers,  gas-fired,  714 
boilers,  grate  surface  of,  67'8,  680 
boilers,  heating  air-supply  to,  687 
boilers,  heating  surface  of,  678 
boilers,  horse-power  of,  677 
boilers,  hydraulic  test  of,  700 
boilers,  incrustation  and  scale   716 
boilers,  materials  for,  700 
boilers,  measure;of  duty  of,  678 
boilers,  performance  of,  681 
boilers,  Philadelphia  inspection  rule, 

boilers,  proportions  of,  678 

boilers,  rules  for  construction  of,  700 

boilers,  safe  working  pressure  707 

boilers,  strength  of,  700 

boilers,  tests  of,  685 

boilers,  tests,  rules  for,  690-695 

boilers,  tests  with  different  coals, 
636,  688 

boilers,  tubulous,  686 

boilers,  using  waste  gases,  689 

boilers,  use  of  zinc  in,  720 

domes  on  boilers,  711 

dry,  identification  of,  730 

engine  constants,  756-758 

engine  cylinders,  792-795 

engine,  spherical,  792 

engines,  742-847 

engines  at  Columbian  exhibition,  774 

engines,  calculation  of  mean  effec- 
tive pressure,  744 

engines,  counterbalancing,  788 

engines,  dimensions  of  parts  of,  792- 
817 

engines,  economy  at  various  speeds, 
786 


Steam  engines,  economy  of  various 
sizes,  785,  786 

engines,  economy  with  vary  mo- 
loads,  784 

engines,  efficiency  of,  749 

engines,  efficiency  of  non-condensing 
compound,  7.84 

eng*in~.%  ^e(fcyater>  consumption 
or,  ioo,  7oO,  /75 

engines,  friction  of.  941 
engines  in  electric  stations,  7a5 
engines,  marine,  1015 
engines,  measures  of  duty,  748 
engines,  most  economical   point  o? 

cut-off,  777 

engines,  performance  of,  775-789 
engines,  piston  speeds  of,  787 
engines,  putting  on  centre,  834 
engines,  relative  economy  of  780 
engines,  rotary,  791 
engines,  triple-expansion,  769 
expansive  working  of,  747 
flow  of,  668 
flow  of  in  pipes,  669 
heating,  536-540 
jacket,  influence  of,  787 
jet-blowers,  527 
loop,  676 

loss  of  pressure  in  pipes,  671 
mean  pressures,  743 
moisture  in,  728 
pipe  coverings,  469 
pipes,  copper,  674 
pipes,  loss  from  uncovered,  676 
pipes,  marine,  1016 
pipes,  overhead.  537 
pipes,  size  of  for  engines,  673 
pipes,  valves  in,  675 
pipes,  wire-wound,  675 
superheated,  661 
supply  mains,  539 
table  of  properties  of,  659 
temperature,  pressure,  etc.,  659-662 
turbines,  791 
vessels,    dimensions,    horse-pow-r. 

etc.,  1009 

vessels,  trials  of,  1007 
water  in,   effect  of  on  economy  of 

engines.  781 

work  of  in  a  single  cylinder,  746,  749 
Steel,  389-414 
aluminum,  409 

analyses  and  properties  of,  389 
annealing,  413 
Bessemer,  390-392 
blooms,  weight  of,  176 
castings,  405 
chrome,  409 
compressed,  410 
crucible,  410 

effect  of  hammering,  412 
effect  of  heat  on,  412 
effect  of  nicking,  402 
electric  conductivity  of,  403 
failures  of,  403 
hardening  of  soft,  393 
manganese,  407 
M usher,  409 
ope n -heartli. 391,  392 


1086 


INDEX. 


Steel,  segregation  in,  404 

specific  gravity  of,  403,  411 

specifications  for,  397 

strength  of,  389 

tempering,  412,  414 

treatment  of,  394 

tungsten,  409 

use  in  structures,  405 

.variation  in  strength  of,  398 

working  stresses  for,  264 
Stoker,  under-feed.  712 
Stokers,  mechanical,  711 
Stone,  strength  of,  302,  312 
Stones,  etc.,  weight  and  sp.  gr.,  166 
Storage  batteries,  1055 
Storing  steam-heat,  789 
Strains  allowed  in  bridge  members, 
262-264 

in  structural  iron,  379 
Straw  as  fuel,  643 
Stream,  horse-power  of  a,  589 
Streams,  measurement  of,  584 
Strength  of  boiler-heads,  285 

of  bolts,  292 

of  columns,  246,  250-261 

compressive,  244 

of  flat  plates,  283 

of  glass,  308 

of  masonry  materials,  312 

of  materials,  236 

of  materials,  Kirkaldy's  tests,  296 

of  stayed  surfaces,  286 

of  structural  shapes,  272-280 

of  timber,  309 

of  unstayed  surfaces,  284 

tensile,  242 

torsional,  281 

transverse,  266 
Stress  and  strain,  236 

due  to  temperature.  283 
Stresses,  combined,  282 

effect  of,  236 

in  framed  structures,  440 
Structural  iron,  strains  in,  379 

shapes,  elements  of,  249 

shapes,  properties  of,  272 

shapes,  sizes  and  weights,  177 

steel,  treatment  of,  394 
Structures,  framed,  440 
Struts,  strength  of,  246 
Sugar  manufacture,  643 

solutions,  concentration  of,  465 
Sulphate  of  lime,  solubility,  464 
Sulphur      dioxide     refrigerating-ma- 
chines,  985 

influence  of  on  cast-iron,  367 

influence  of  on  steel,  389 
Surface  condensers,  840-844 
Suspension  cable-ways,  915 

Tail-rope  system  of  haulage,  913 
Tan-bark  as  fuel,  643 
Tangent  of  an  angle,  65 
Tangents,  sines,  etc.,  table  of,  159 
Tanks,  cylindrical,  121,  126 

rectangular,  gallons  in,  125 
Tannate  of  soda  for  boiler-scale,  718 
Tap-drills,  970,  971 
Taper-bolts,  pins,  reamers,  972 


Taper,  in  lathes,  956 
Tapered  wire  ropes,  916 
Taylor's  rules  for  belting,  880 

theorem,  76 
Tee-bars,  280 

Tees,  Pericoyd,  sizes  and  weights,  180 
Teeth  of  gears,  forms  of,  892 

proportions  of,  889 
Telegraph-wire,  217-221,  224 
Temperature,  effect  on  strength,  309 
382 

stresses  in  iron,  etc.,  283 
Temperatures  in  furnaces,  451 

judged  by  color,  454 
Tempering  steel,  414 
Tenacity  of  metals,  169 

of  metals  at  different  temperatures 

309,  382 
Tensile  strength,  242 

strength,  increase  by  twisting,  241 
Terra-cotta,  181 

Test-pieces,  comparison  of  small  am 
large,  393 

standard  shapes,  243 
Testing    materials,    precautions     in 

243 

Thermal  unit,  British,  455,  G60 
Thermodynamics,  478 
Thermometers,  448 
Three-wire  currents,  1039 
Tidal  power,  utilization  of,  600 
Tie-rods  for  brick  arches,  281 
Tiles,  sizes  and  weights,  181 
Timber  measure,  20,  21 

strength  of,  309 
Time,  measure  of,  20 
Tin,  168 

roofing,  181,  182 
Tires,  steel,  strength  of,  298 
Tobiu  bronze,  327,  334 
Toggle-joint,  436 
Tonnage  of  vessels,  19,  1001 
Tool-steel,  heating,  412 
Toothed  wheels,  proportions  of,  889 
Torque  of  an  armature,  1062 
Torsional  strength,  281 
Tower  spherical  engine,  792 
Tractive  power  of  locomotives,  857 
Tractrix,  or  Schiele's  curve,  50 
Trains,  resistance  of,  851,  853 
Tramways,  wire-rope,  914 
Transformers,  1070 
Transmission  by  hydraulic   pressure 
617-620 

by  wire  rope,  917-922 

electric,  1038 

electric,  efficiency  of,  1047 

of  heat,  471-478 

of  power  by  ropes,  922-927 
Transporting  power  of  water,  565 
Transverse  strength,  266 
Trapezium.  54 
Trapezoid,  54 
Trapezoidal  rule,  56 
Treatment  of  steel,  394 
Triangle,  mensuration  of,  54 
Triangles,  problems  in,  41 

solution  of,  68 
Trigonometrical  functions,  65-67 


IKDEX. 


1087 


Trigonometrical  functions,  table,  159 

Trigonometry,  piano,  65 

Triple  effect,  multiple  system,  463 

expansion  engine,  769 
Troy  weight,  19 
Truss,  Howe  and  Warren,  445 

king-post,  442 

queen-post,  442 

Pratt  or  Whipple,  443 
Trusses,  roof,  446 
Tubes  for  steam-boilers,  704,  709 

Mannesmann,  296 

or  flues,  collapse  of,  265 

weights  of,  169 

wrought-iron,  196 
Tubing,  brass,  198 
Tungsten-aluminum  alloys,  331 

steel,  409 

Turbines,  steam,  791 
Turbine-wheels,  591 

wheels,  tests  of,  596 
Turf  or  peat,  643 
Turnbuckles,  sizes,  211 
Twin-screw  vessels,  1017 
Twist-drill  gauge,  29 
Twist-drills,  sizes  and  speeds,  957 
Type-metal,  336 

Unit  of  heat,  455 
United  States,  population  of,  12 
Unstayed  surfaces,  strength  of,  284 
Upsetting  of  steel,  394 

Vacuum  pumps.  612 
Valve-diagrams,  825 

motions,  825 

rods,  815 
Valves,  engine,  setting  of,  834 

in  steam-  pipes,  6?5 

of  pumps,  605,  606 
Vapors,  properties  of,  480 

used  in  refrigerating-machines,  982 
Velocities,  parallelogram  of,  426 
Velocity,  angular,  425 
Ventilating-ducts,  discharge  of,  530 

fans,  517-525 
Ventilation  and  heating,  528-546 

blower  system  of,  545 

by  a  steam-jet,  527 

of  large  buildings,  534 
Ventilators  for  mines,  521 
Venturi  meter,  583 
Versed  sine  of  an  arc,  65 
Vessels  (see  Steam- vessels) 
Vibrations  of  engines,  preventing,  789 
Vis-viva,  458 
Volt,  definition  of,  1025 

Warehouse  floors,  1019 
Wan-en  girder,  445 
Washers,  sizes  of,  212 
Water,  547-554 

analyses  of,  553 

compressibility  of,  551 

erosion  by  flowing,  565 

expansion  of,  547 

flow  in  channels,  564 

flow  of,  555-588 

flow  of,  experiments,  566 


Water,  flow  of  in  pipes,  tables,  558,  559, 
567-570 

gas,  648,  652 

impurities  of,  551 

power,  588 

power,  value  of,  590 

pressure  engine,  619 

pressure  of,  549 

softening  of  hard,  555 

specific  heat  of,  550 

transporting  power  of,  565 

weight  of,  27,  547 

wheel,  the  Pelton,  597 
Waves,  power  of  ocean,  599 
Weathering  of  coal,  637 
Wedge,  the,  437 

volume  of  a,  61 
Weight  of  ba'-s,  rods,  plates,  etc.,  159 

of  brickwork,  169 

of  brass  and  copper,  198-503 

of  bolts  and  nuts,  209-211 

of  cast-iron  pipes  and  columns,  185- 
193 

of  cement,  170 

of  flat  rolled  iron,  172 

of  fuel,  170 

of  iron  bars,  171 

of  iron  and  steel  sheets,  174 

of  ores,  earths,  etc.,  170 

of  plate-iron,  175 

of  roofing  materials,  181-184 

of  steel  blooms,  170 

of  structural  shapes,  177-180 

of  tin  plates,  182 

of  wrought-iron  pipe,  194-197 

of  various  materials,  169 
Weights  and  measures,  17 

of  air  and  vapor,  484 
Weir  table,  587 

Weirs,  flow  of  water  over,  586 
Welding,  electric,  1053 

of  steel,  394,  396 
Welds,  strength  of,  300 
Wheel  and  axle,  439 
Whipple  truss.  443 
White-metal  alloys,  336 
Whitworth  compressed  steel,  410 
Wiborgh  air-pyrometer,  453 
Wind,  493 
Winding  engines,  909 

of  magnets,  1068 
Windlass,  439 

differential,  439 
Wind  mills,  495 
Wind  pressures,  493 
Wire  cables,  222 

copper  and  brass,  202 

copper,  tables  of,  218-220, 1034 

gauges,  28-31 

insulated,  221 

iron  and  steel,  217 

iron,  size,  strength,  etc.,  216 

rope,  226.  231 

rope  haulage,  912 

ropes,  durability  of,  919 

ropes,  splicing,  345 

ropes,  strength  of.  301 

ropes,  tapered,  916 

rope  transmission,  917-922 


1088 


INDEX. 


Wire  rope  tramways,  914 

strength  of,  301,  803 

telegraph,  217,  221,  224 

wound  fly-wheels,  824 
Wiring     formula     for     incandescent 

lighting,  1043 

Wires,  current  required  to  fuse,  1037 
Wire  table  for  100  and  500  volts,  1044 

table,  hot  and  cold  wires,  1034,  1035 
Wohler's  experiments,  238 
Wood  as  fuel,  639 

composition  of,  640 

expansion  of,  311 

heating  value  of,  639 

strength  of,  302,  306,  310,  312 

weight  of,  165,  232 
Wooden  fly-wheels,  823 
Woodstone  or  xylolith,  316 
Woolf  type  of  compound  engine,  762 
Wootten  H  locomotive,  855 
Work,  ei-ergy,  power,  429 


Work  of  acceleration,  430 

of  men  and  animals,  433 

unit  of,  428 
Worm-gear,  440 

gearing,  897 
Wrist-pin,  804. 
Wrought- iron,  377-379 

chemistry  of,  377 

specifications,  378 

Xylolith  or  woodstone,  316 
Yield  point,  237 

Z-bars,  properties  of,  276 
sizes  and  weights,  178 

Zinc,  168 
tubing,  200 
use  of  in  steam-boilers,  730 

Zeuner  valve-diagram,  827 

Zero  absolute,  461 


INDEX  TO  ADVERTISEMENTS. 

PAGE 

ABENDROTH  &  ROOT  MANUFACTURING  COMPANY 4 

BERLIN  IRON  BRIDGE  COMPANY,  THE 17 

BOSTON  BELTING  COMPANY 8 

CHAPMAN  VALVE  MANUFACTURING  COMPANY 7 

DEANE  STEAM  PUMP  COMPANY,  THE 1 1 

FUEL  ECONOMIZER  COMPANY,  THE 8 

GOUBERT  MANUFACTURING  COMPANY,  THE 3 

HANCOCK  INSPIRATOR  COMPANY,  THE 14 

HARTFORD   STEAM   BOILER    INSPECTION  AND   INSUR- 
ANCE COMPANY 9 

HAWLEY  DOWN  DRAFT  FURNACE  COMPANY,  THE —   14 
HOLMES  FIBRE  GRAPHITE  MANUFACTURING  COMPANY.   12 

HUNT  COMPANY,  THE  C.  W i 

INGERSOLL-SERGEANT  DRILL  COMPANY 6 

KEASBEY  &  MATTISON  COMPANY 7 

LUKENS  IRON  AND  STEEL  COMPANY 9 

MORRIS,  TASKER  &  COMPANY 10 

NORWALK  IRON  WORKS  COMPANY,  THE 2 

OLSEN  &  COMPANY,  TINIUS 10 

PELTON  WATER-WHEEL  COMPANY  — 6 

RAND  DRILL  COMPANY 4 

RHODE  ISLAND  TOOL  COMPANY 5 

ROEBLING'S  SONS  COMPANY,  JOHN  A 12 

SIMMONS  COMPANY;  JOHN 16 

TAUNTON  LOCOMOTIVE  MANUFACTURING  COMPANY...   13 

WARREN  FOUNDRY  AND  MACHINE  COMPANY 15 

WATTS-CAMPBELL  COMPANY,  THE , —     2 

WILEY  &  SONS,  JOHN 16 

WOOD  &  COMPANY,  R.  D 1 5 


The  C.  W.  HUNT  COMPANY, 

Business  Established        •          45    BROADWAY, 

in  1872.  NEW   YORK, 

MANUFACTURE 

TRANSMISSION   ROPE.     .     .     . 

This  rope  is  intended  to  be  used 
for  Rope  Driving  and  Hoisting 
only,  and  is  sold  under  the  trade 
name  of  "  Stevedore."  We  guar- 
antee that  more  work  can  be  done 
with  it,  in  proportion  to  its  cost,  than 
with  any  other  rope  in  the  market, 
without  any  exception  whatever, 
and  will  gladly  refund  the  difference 
in  price,  if  it  is  not  all  we  claim. 
You  cannot  lose  by  making  a  trial 
of  this  rope,  and  are  sure  to  reduce 
your  expense  account.  This  guar- 
antee  goes  with  every  rope  we 
make.  We  do  not  manufacture 
transmission  pulleys,  shafting,  or 
hangers,  neither  do  we  make  ordinary  rope. 

INDUSTRIAL    RAILWAYS. 


This  system  of  cars  and 
tracks,  21^  inches  gauge,  is 
especially  de- 
signed for  use 
in  manufac- 
turing cstab- 
lishments. 
Our  narrow 
gauge  railroad 
track  is  made 
up  complete, 
ready  to  lay, 
with  steel 
cross  ties  se- 
curely riveted 
to  the  rails, 
and,  with  swit- 
ches, curves, 
crossings,  and  turntables, 
makes  a  perfect  permanent 


COAL    HANDLING    MACHINERY 


way.  The  cars  run  around  a 
curve  of  12  feet  radius  as  easily 
as  a  wagon 
turns  a  corner. 
The  advant- 
age of  this  will 
be  appreciated 
by  every  one 
who  has  had 
experience 
with  rigid 
wheel-base 
cars. 


A  system  of  can 
and  track  in  a  fac- 
tory is  as  much  a 
"machine"  as  a 
"lathe,"  a  "steam 

hammer,"  or  a  "loom,"  and  should  be 

judged  in  the  same  way. 


i\.ciiiways  lor  nanaimg  ana  aistriDuung  v^oai  as 
in  Coal  Yards,  on  Wharves,  and  at  Manufactur- 
ing Establishments,  Coal  Tubs,  Steam  Shovels, 
Mast  and  Gaff  Fittings,  Wheel  Barrows,  and 
Hoisting  Blocks  for  both  Manila  and  Wire  Rope, 

CONVEYORS.     .     .     . 

<$  Noiseless  Conveyors,  which  carry  the  I 
material  without  shock,  breakage,  or  violence 
in  any  direction,  in  which  every  bearing  can  be 
kept  thoroughly  lubricated,  and  the  whole 
machine  is  as  durable  as  an  ordinary  machine  tool.  We  print  a 
Catalogue  describing  the  application  of  this  machine  fo  large 
Steam  Generating  Plants,  Locomotive  Coaling  Stations,  Gas 

Vorks,  and  Coal  Yards. 


THE  WATTS  CAMPBELL  COMPANY 

NEWARK,   N.  J. 

FOUNDERS,  ENGINEERS,  AND  MACHINISTS, 

MANUFACTURERS    OF   THE 

Improved  Corliss  Steam  Engines 

IN    MODERN    VARIETY. 


Established  1851.  Incorporated  1883, 

THE  NORWALK 

IRON  WORKS  CO, 

OF   SOUTH    NORWALK,   CT. 

MANUFACTURE 

AIR  AND   GAS   COMPRESSORS 

ON  THE 

COMPOUND     COMPRESSION 

PRINCIPLE. 

Professor  UN  WIN  says:  "  There  can  be  no  doubt  that  thif 
arrangement  is  more  efficient  than  a  simple  Compressor,  arid  tht 
Norwalk  Iron  Works  Co.  were  the  first  to  use  that  principle  ir 
America," 

DESCRIPTIVE  CIRCULARS  ON  APPLICATION. 


UiERT 


WATE 
HEAT 


ITO/I 

P3R3TOR 


TO  YOUR 


(iOUBERT 

*.**4tt  MAN'FGGQ, 


CHUR.CH 
STREET  c<>r  ( 


AIR   COMPRESSORS 

FOR  MECHANICAL  PURPOSES  A  SPECIALTY. 


t  COMPRESSOR  WITH   BELT-SHI  FTIxNG 


Our  Rock  Drills  are  the  Standard  throughoul 
the  World. 


CRAND  DRILL  coj 

100    BROADWAY,    NEW    YORK    CITY,   U.   S.   A, 

IMPROVED  ROOT  WATER-TUBE 
BOILER 


HIGHEST  ECONOMY— BEST  ADAPTED  TO  HIGH    PRESSURES 
ABSOLUTELY     DRY     STEAM  —  PERFECT    WORKMANSHIP 

ABENDROTH  &  (WOT  MFC,  CO.,  NEW  YORI 

4 


RHODE  ISLAND  TOOL  GO, 


COLD  PUNCHED 
SQUARE  AND  HEXAGON  NUTS, 

(CHAMFERED  AND  TRIMMED  WITH  DRILLED  HOLES.) 


FINISHED 
CASE-HARDENED  HEXAGON  NUTS. 


ENGINEERS'  STEEL  WRENCHES. 


MACHINE  BOLTS. 


ROUGH  AND  MILLED  STUDS. 


CAP  AND  SET  SCREWS. 


TURN  BUCKLES. 


DROP  FORCINGS  TO  ORDER. 


PROVIDENCE,  RHODE  ISLAND, 


The  Pelton  System  of  Power 

represents  the  highest  develop- 
ment yet  attained  in  water 
wheel  practice,  and  affords  the 
most  simple,  efficient  and  eco- 
nomical means  of  utilizing 
water  for  power  purposes. 

Six  Thousand  Wheels 
Now  Running, 

aggregating  over  400,000  horse 
power.    Adaptation  made  to  all  conditions  and  every  variety  of  service. 

Electric  Power  Transmission 

Pelton  "Wheels  are  the  recognized  standard  for  electrical  work,  and  are 
ninning  a  majority  of  the  stations  of  this  character  in  all  parts  of  the 
world.  Catalogues  furnished  on  application.  Address 

PELTON   WATER   WHEEL  CO. 

SAN   FRANCISCO,  NEW   YORK, 

121-123   MAIN   STREET.     '  143   LIBERTY  STREET. 

"~ FNGERSOLL-SERGEANT  DRILL  co,, 

Havemeyer  Bld'g,  26  Cortlandt  St., 
NEW   YORK. 

ROCK  DRILLS, 
AIR  COMPRESSORS 

Coal  Cutters,  Stone  Channeling  Machines 

AND  SPECIAL  MACHINES  FOR 

MINING,  TUNNELING,  QUARRYING, 

AND  FOR  ALL  KINDS  OF 


Submarine  Drilling  Plants, 
POHL£  AIR   LIFT  PUMP. 

Send  for  full  descriptive  catalogues  ; 
state  nature  of  work. 

6 


ABSOLUTELY    FIREPROOF. 

MAGNESIA 

COVERING    FOR 

Heaters,  Heater  Pipes, 

Flue  Linings, 

Steam  Pipes  and  Boilers. 

Saves  coal;  insures  heat  where  needed;  secures  perfect  venti- 
lation. For  samples,  prices  and  full  particulars,  address  the 
manufacturers, 

KEASBEY  &  MATTISON  COMPANY, 

AMBLER, 
NEW  YORK.  PENNSYLVANIA.  BOSTON. 

CHICAGO.  CINCINNATI. 

Chapman  Valve  Mfg.  Co., 

MANUFACTURERS   OF 

VALVES  AND  GATES 

For  Water,  Stearin  Gas,  Ammonia,  Etc. 
GATE     FIRE     HYDRANTS, 

With  and  without  independent  outlets. 

We  make  a  specialty  of  Valves  with  Bronze  Seats  for 
High-Pressure  Steam. 

WORKS    AND    GENERAL    OFFICE: 

INDIAN   ORCHARD,  MASS. 

Treasurer's  Office:  72  Kilby  &  112  Milk  Sts.,  BOSTON,  MASS. 

CHICAGO  OFFICE:  ?A  West  Lake  Street. 
NEW  YORK  OFFICE  :  28  Platt  Street. 
I*  M.  RUMSEY  MFG.  Co.,  St.  Louis,  Mo.,  Southwestern 


ESTABLISHED  1828. 


BOSTON  BELTING  Co. 

James  Bennett  Forsyth,  Mfg.  Agt.  <£  Gen.  Man. 

Manufacturers  of 

Rubber  Belting, 

Rubber  Hose  for  all  Purposes, 

Cotton  and  Linen  Fire  Hose, 

Packings,  Gaskets,   Valves,  Tubing, 
Rubber  Mats  and  Matting, 

Rubber  Covered  Rollers, 

And  the  Hi^K-st  Grades  of  Rubber  Goods  for  all  Mechanical  and 
Manufacturing  Purposes. 


BOSTON: 
256,  258,  260  Devonshire  St. 


NEW  YORK: 

100  Chambers  St. 


GREEN'S   FUEL   ECONOMIZER 

FOR, 


AD  VANTAGES. -Heats  the  feed  water  to  a  Hfeh  Temperature,  thus 
effecting  a  ORE  AT  SAVING  IN  COAL.  Can  be  applied  to  any  type  of  boiler 
without  stoppage  of  works.  A  large  volume  of  water  always  in  reserve  at  the 
evaporative  point  ready  for  immediate  delivery  to  the  boilers. 

Only  Medal  awarded  for  Flue  Renter  at  the  Columbian  Exposition. 

SOLE    MAKERS    IN    THE    UNITED    STATES. 

THE  FUEL  ECONOMIZER  CO.  of  Matteawan,  N.Y. 


Lukens  Iron  and  Steel  Co. 

INCORPORATED    1890. 

THE  FIRST  TO  MAKE  BOILER-PLATES  IH  AMERICA. 

A.  F    HUSTON,  PRESIDENT. 

CHAS.  L.  HUSTON,  VICE-PRESIDENT. 

JOS.  HUMPTON,  SECRETARY  AND  TREASURER. 

STEEL  PLATES,  ALL  GRADES, 

To  Extreme   Dimensions.  Width   up  to   1  O  feet. 

Thickness,   No.   1O  Gauge  to  2  inches. 

ESTABLISHED    1810. 

•* 

Main  Office  and  Works  i  COATESVILLE,  PA,       New  York  Office  \  No.  29  BROADWAY, 

New  Orleans  Office  and  Warehouse :  535  DELTA  and  536  SOUTH  FRONT  STREETS, 

Philadelphia    Office:    FIDELITY    BUILDING,    Rooms    405-6-7-8,    NORTH    BROAD 

STREET,  above  Arch  Street, 


ORGANIZED,     1866. 


THOROUGH    INSPECTIONS 

AND 

Insurance   ftf/ninst    Loss    or   Damaf/e    to   Property    and    Loss   of 
JAfe.  and  Injury  to  Persons  caused  by 

STEAM  BOILER  EXPLOSIONS 

J.  M.  ALLEN,  President. 

WM.  B.  FRANKLIN,  Vice-President. 

F.  B.  ALLEN,  Second  Vice-President. 

J.  B.  PIERCE,  Secretary  and  Treasurer. 

L.  B.  BRAINERD,  Asst.  Treas. 

9 


1821  1888 

MORRIS, TASKER  &  CO. 

INCORPORATED. 

OFFICES:  222  and  224  South  Third  St.,  Philadelphia. 


MANUFACTURERS    OF 


ELECTRIC  LIGHT  AND  RAILWAY  PIPE  POLES 

Boiler  Tubes,  Wrought  Iron   Pipe  and   Fittings, 

Gas  Works  and  Structural  Work,  Heavy 

Castings,  Tools  and  Machinery. 


PASCAL  IRON  WORKS, 

Philadelphia. 


DELAWARE  IRON  WORKS, 

New  Castle,  Del. 


Olsen's  Testing  Machines 

FOR   TESTING 

Iron  Specimens,  Bridge  Materials, 
Chain,  Cement,  Wire,  Springs,  Oils  or 
Lubricants,  also  Viscosimeters,  etc. 


Hydraulic  Presses, 

Accumulators,  Gauges,  an*> 

Pumps. 

Awarded  the  Elliott  Cresson  Gold  Medal  by  the  Franklin  Institute, 

also  Medal  and  Diploma  by  the  World's 

Columbia?  Exposition. 


TINIUSOLSEK&CO. 

500  North  12th  Street,  Philadelphia,  Pa. 

4A 


The   Deane  of  Holyoke 

PUMPING  MACHINERY. 


VERTICAL  CROSS-COMPOUND   HIGH-DUTY 
PUMPING-ENGINE 

BUILT    BY 

The  Deane  Steam  Pump  Co., 

HOLYOKE,    MASS. 

WAREROOMS: 

:\V   YORK.  BOSTON. 

PHILADELPHIA. 
CHICAGO.  ST.  LOUIS. 


11 


y¥!RE  ROPE 


>T.,  NEW  YORK. 

:.5AN  FRANCISCO. 


Fibre=Graphite  Requires  No  Oil! 

Avoid  all  cost  of  oil  and  attendance,  and  annoyance  from 
dripping  oil,  by  using 

FIBRE-GRAPHITE   BEARINGS. 

We  are  prepared  to  furnish  Boxes  for  any  form  of  Hanger, 
Pillow  Block,  or  other  standard  now  in  use,  or  to  furnish  the 
material  in  the  form  of  Bushings,  or  other  desired  shape,  for 
ready  introduction  into  the  frames  of  special  machines  or  else- 
where. The  anti-frictional  and  self-lubricating  qualities  of 
FIBRE=GRAPHITE,  together  with  ease  of  adaptation,  render 
it  eminently  suitable  for  all  bearings  under  light  or  moderate 
pressures  where  freedom  from  oil  is  desired. 

A  few  of  the  special  uses  of  FIBRE=QRAPH1TE  are  in 
Bearings  for  Water  Meters,  Dye  Tubs,  Bearings  subjected  to 
high  temperatures,  Plungers  for  Arc  Lamp  Dash  Pots,  Com- 
mutator Brushes  for  Dynamos  and  Motors,  etc.,  etc. 

Awarded  the  Elliott  Cresson  Gold  Medal  by  the  Frank- 
lin Institute  of  Pennsylvania. 

HOLMES  FIBRE=QRAPHITE  MFG.  CO., 

Station  Z,  Philadelphia,  U.  S.  A. 
12 


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'THE  HANCOCK  INSPIRATOR.' 

Over  200,000  in  Daily  Use. 


Highest  degree 

of  efficiency,  absolute 

reliability  and  durability 

guaranteed. 

Illustrated  Catalogue  mailed 
free  upon  application. 


THE  HANCOCK  INSPIRATOR  COMPANY, 


MANUFACTURERS    OF 


Injectors,    Ejectors,    General    Jet    Apparatus,   and 
Steam=goods   Specialties, 

BOSTON,    MASS. 


Smoke  Prevention  and  Economy, 

Send  for  our  new  Catalogue. 

THE  HAWLEY  DOWN-DRAFT  FURNACE  CO. 

NEW  YORK,  39  Cortlandt  Street. 

BOSTON,  Tremont  Building. 

CHICAGO,  Monadnock. 

CINCINNATI,  328  West  Pearl  Street 

DETROIT,  4O1   Chamber  of  Commerce. 

ST.  LOUIS,  1  West   Broadway. 

BALTIMORE,  1631    Fulton  Avenue. 

PITTSBURGH,  Tradesmen   Building, 

14 


HYDRAl  IIC  RIVETERS, 

11 1  J/lln  U  Ul  I/Fixed  and  Portable; 

INTENSIFIERS,   PUNCHES, 
SHEARS,  PRESSES,  and  LIFTS. 


Matthews'  Fire  Hydrants,  Eddy  Valves, 
Valve-indicator   Posts. 

CAST-IRON  PIPE. 
R.  D.  WOOD  &  CO., 

Engineers,  Iron  Founders,   Machinests, 

'400  Chestnut  St.,  Philadelphia,  Pa. 


Warren  Foundry  and  Machine  Co, 

WORKS  AT  PH1LLIPSBURGH,  N.  J, 

NEW  YORK  OFFICE,    -     160  BROADWAY. 


CAST-IRON  WATER  AND  GAS  PIPE 

From  three  to  forty-eight  inches  diameter. 
BRANCHES,    BENDS,    RETORTS,    ETC. 


JOHN  SIMMONS  Co. 

WROUGHT,  CAST  IRON  AND  BRASS  PIPE, 

FITTINGS  AND  BRASS  WORK, 


STEAM 

GAS 

WATER 

OIL 

ELECTRICAL 

ENGINEERING 


SUPPLIES 


Offices  and  Salesrooms: 

106,   1O8  and   HO   CENTRE    ST\ 
NEW  YORK. 

Books  for  Mechanical  Engineers. 


THURSTON — Manual  of  Steam  Engine,  2  vols $12  00 

PEABODY — Thermodynamics  of  Steam  Engine 5  00 

WOOD — Thermodynamics,  Heat  Motors  and  Refrigerating 

Machines 4  00 

WHITHAM — Constructive  Steam-Engineering 10  00 

KNEASS — Theory  of  Injector 1  50 

HEMENWAY — Indicator  Practice 2  00 

WILSON — FLATHER — Steam  Boilers 2  50 

SPANGLER — Valve  Gears 2  50 

PEABODY — Valve  Gears 2  50 

THURSTON — Steam  Boilers 5  00 

PEABODY — Steam  Tables 1  00 

SINCLAIR — Locomotive  Running 2  00 

REAGAN— Locomotive  Mechanism  . ,  2  00 


JOHN   WILEY   &   SONS, 

NEW    VORK   CITY. 

•   16 


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